diff options
Diffstat (limited to 'src/secp256k1')
136 files changed, 68461 insertions, 0 deletions
diff --git a/src/secp256k1/.cirrus.yml b/src/secp256k1/.cirrus.yml new file mode 100644 index 0000000000..0b904a4e38 --- /dev/null +++ b/src/secp256k1/.cirrus.yml @@ -0,0 +1,409 @@ +env: + ### cirrus config + CIRRUS_CLONE_DEPTH: 1 + ### compiler options + HOST: + WRAPPER_CMD: + # Specific warnings can be disabled with -Wno-error=foo. + # -pedantic-errors is not equivalent to -Werror=pedantic and thus not implied by -Werror according to the GCC manual. + WERROR_CFLAGS: -Werror -pedantic-errors + MAKEFLAGS: -j4 + BUILD: check + ### secp256k1 config + ECMULTWINDOW: auto + ECMULTGENPRECISION: auto + ASM: no + WIDEMUL: auto + WITH_VALGRIND: yes + EXTRAFLAGS: + ### secp256k1 modules + EXPERIMENTAL: no + ECDH: no + RECOVERY: no + SCHNORRSIG: no + ### test options + SECP256K1_TEST_ITERS: + BENCH: yes + SECP256K1_BENCH_ITERS: 2 + CTIMETESTS: yes + # Compile and run the tests + EXAMPLES: yes + +# https://cirrus-ci.org/pricing/#compute-credits +credits_snippet: &CREDITS + # Don't use any credits for now. + use_compute_credits: false + +cat_logs_snippet: &CAT_LOGS + always: + cat_tests_log_script: + - cat tests.log || true + cat_noverify_tests_log_script: + - cat noverify_tests.log || true + cat_exhaustive_tests_log_script: + - cat exhaustive_tests.log || true + cat_ctime_tests_log_script: + - cat ctime_tests.log || true + cat_bench_log_script: + - cat bench.log || true + cat_config_log_script: + - cat config.log || true + cat_test_env_script: + - cat test_env.log || true + cat_ci_env_script: + - env + +merge_base_script_snippet: &MERGE_BASE + merge_base_script: + - if [ "$CIRRUS_PR" = "" ]; then exit 0; fi + - git fetch --depth=1 $CIRRUS_REPO_CLONE_URL "pull/${CIRRUS_PR}/merge" + - git checkout FETCH_HEAD # Use merged changes to detect silent merge conflicts + +linux_container_snippet: &LINUX_CONTAINER + container: + dockerfile: ci/linux-debian.Dockerfile + # Reduce number of CPUs to be able to do more builds in parallel. + cpu: 1 + # Gives us more CPUs for free if they're available. + greedy: true + # More than enough for our scripts. + memory: 1G + +task: + name: "x86_64: Linux (Debian stable)" + << : *LINUX_CONTAINER + matrix: &ENV_MATRIX + - env: {WIDEMUL: int64, RECOVERY: yes} + - env: {WIDEMUL: int64, ECDH: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128} + - env: {WIDEMUL: int128_struct} + - env: {WIDEMUL: int128, RECOVERY: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128, ECDH: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128, ASM: x86_64} + - env: { RECOVERY: yes, SCHNORRSIG: yes} + - env: {CTIMETESTS: no, RECOVERY: yes, ECDH: yes, SCHNORRSIG: yes, CPPFLAGS: -DVERIFY} + - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETESTS: no, BENCH: no} + - env: {CPPFLAGS: -DDETERMINISTIC} + - env: {CFLAGS: -O0, CTIMETESTS: no} + - env: { ECMULTGENPRECISION: 2, ECMULTWINDOW: 2 } + - env: { ECMULTGENPRECISION: 8, ECMULTWINDOW: 4 } + matrix: + - env: + CC: gcc + - env: + CC: clang + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "i686: Linux (Debian stable)" + << : *LINUX_CONTAINER + env: + HOST: i686-linux-gnu + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + matrix: + - env: + CC: i686-linux-gnu-gcc + - env: + CC: clang --target=i686-pc-linux-gnu -isystem /usr/i686-linux-gnu/include + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "arm64: macOS Ventura" + macos_instance: + image: ghcr.io/cirruslabs/macos-ventura-base:latest + env: + HOMEBREW_NO_AUTO_UPDATE: 1 + HOMEBREW_NO_INSTALL_CLEANUP: 1 + # Cirrus gives us a fixed number of 4 virtual CPUs. Not that we even have that many jobs at the moment... + MAKEFLAGS: -j5 + matrix: + << : *ENV_MATRIX + env: + ASM: no + WITH_VALGRIND: no + CTIMETESTS: no + matrix: + - env: + CC: gcc + - env: + CC: clang + brew_script: + - brew install automake libtool gcc + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + << : *CREDITS + +task: + name: "s390x (big-endian): Linux (Debian stable, QEMU)" + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: qemu-s390x + SECP256K1_TEST_ITERS: 16 + HOST: s390x-linux-gnu + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + << : *MERGE_BASE + test_script: + # https://sourceware.org/bugzilla/show_bug.cgi?id=27008 + - rm /etc/ld.so.cache + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "ARM32: Linux (Debian stable, QEMU)" + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: qemu-arm + SECP256K1_TEST_ITERS: 16 + HOST: arm-linux-gnueabihf + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + matrix: + - env: {} + - env: {EXPERIMENTAL: yes, ASM: arm} + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "ARM64: Linux (Debian stable, QEMU)" + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: qemu-aarch64 + SECP256K1_TEST_ITERS: 16 + HOST: aarch64-linux-gnu + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "ppc64le: Linux (Debian stable, QEMU)" + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: qemu-ppc64le + SECP256K1_TEST_ITERS: 16 + HOST: powerpc64le-linux-gnu + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: wine + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + matrix: + - name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)" + env: + HOST: x86_64-w64-mingw32 + - name: "i686 (mingw32-w64): Windows (Debian stable, Wine)" + env: + HOST: i686-w64-mingw32 + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + << : *LINUX_CONTAINER + env: + WRAPPER_CMD: wine + WERROR_CFLAGS: -WX + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + EXPERIMENTAL: yes + SCHNORRSIG: yes + CTIMETESTS: no + # Use a MinGW-w64 host to tell ./configure we're building for Windows. + # This will detect some MinGW-w64 tools but then make will need only + # the MSVC tools CC, AR and NM as specified below. + HOST: x86_64-w64-mingw32 + CC: /opt/msvc/bin/x64/cl + AR: /opt/msvc/bin/x64/lib + NM: /opt/msvc/bin/x64/dumpbin -symbols -headers + # Set non-essential options that affect the CLI messages here. + # (They depend on the user's taste, so we don't want to set them automatically in configure.ac.) + CFLAGS: -nologo -diagnostics:caret + LDFLAGS: -Xlinker -Xlinker -Xlinker -nologo + matrix: + - name: "x86_64 (MSVC): Windows (Debian stable, Wine)" + - name: "x86_64 (MSVC): Windows (Debian stable, Wine, int128_struct)" + env: + WIDEMUL: int128_struct + - name: "x86_64 (MSVC): Windows (Debian stable, Wine, int128_struct with __(u)mulh)" + env: + WIDEMUL: int128_struct + CPPFLAGS: -DSECP256K1_MSVC_MULH_TEST_OVERRIDE + - name: "i686 (MSVC): Windows (Debian stable, Wine)" + env: + HOST: i686-w64-mingw32 + CC: /opt/msvc/bin/x86/cl + AR: /opt/msvc/bin/x86/lib + NM: /opt/msvc/bin/x86/dumpbin -symbols -headers + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +# Sanitizers +task: + << : *LINUX_CONTAINER + env: + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: no + matrix: + - name: "Valgrind (memcheck)" + container: + cpu: 2 + env: + # The `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (https://www.valgrind.org/docs/manual/manual-core.html) + WRAPPER_CMD: "valgrind --error-exitcode=42" + SECP256K1_TEST_ITERS: 2 + - name: "UBSan, ASan, LSan" + container: + memory: 2G + env: + CFLAGS: "-fsanitize=undefined,address -g" + UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1" + ASAN_OPTIONS: "strict_string_checks=1:detect_stack_use_after_return=1:detect_leaks=1" + LSAN_OPTIONS: "use_unaligned=1" + SECP256K1_TEST_ITERS: 32 + # Try to cover many configurations with just a tiny matrix. + matrix: + - env: + ASM: auto + - env: + ASM: no + ECMULTGENPRECISION: 2 + ECMULTWINDOW: 2 + matrix: + - env: + CC: clang + - env: + HOST: i686-linux-gnu + CC: i686-linux-gnu-gcc + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +# Memory sanitizers +task: + << : *LINUX_CONTAINER + name: "MSan" + env: + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + CTIMETESTS: yes + CC: clang + SECP256K1_TEST_ITERS: 32 + ASM: no + WITH_VALGRIND: no + container: + memory: 2G + matrix: + - env: + CFLAGS: "-fsanitize=memory -g" + - env: + ECMULTGENPRECISION: 2 + ECMULTWINDOW: 2 + CFLAGS: "-fsanitize=memory -g -O3" + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "C++ -fpermissive (entire project)" + << : *LINUX_CONTAINER + env: + CC: g++ + CFLAGS: -fpermissive -g + CPPFLAGS: -DSECP256K1_CPLUSPLUS_TEST_OVERRIDE + WERROR_CFLAGS: + ECDH: yes + RECOVERY: yes + SCHNORRSIG: yes + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "C++ (public headers)" + << : *LINUX_CONTAINER + test_script: + - g++ -Werror include/*.h + - clang -Werror -x c++-header include/*.h + - /opt/msvc/bin/x64/cl.exe -c -WX -TP include/*.h + +task: + name: "sage prover" + << : *LINUX_CONTAINER + test_script: + - cd sage + - sage prove_group_implementations.sage + +task: + name: "x86_64: Windows (VS 2022)" + windows_container: + image: cirrusci/windowsservercore:visualstudio2022 + cpu: 4 + memory: 3840MB + env: + PATH: '%CIRRUS_WORKING_DIR%\build\src\RelWithDebInfo;%PATH%' + x64_NATIVE_TOOLS: '"C:\Program Files (x86)\Microsoft Visual Studio\2022\BuildTools\VC\Auxiliary\Build\vcvars64.bat"' + # Ignore MSBuild warning MSB8029. + # See: https://learn.microsoft.com/en-us/visualstudio/msbuild/errors/msb8029?view=vs-2022 + IgnoreWarnIntDirInTempDetected: 'true' + merge_script: + - PowerShell -NoLogo -Command if ($env:CIRRUS_PR -ne $null) { git fetch $env:CIRRUS_REPO_CLONE_URL pull/$env:CIRRUS_PR/merge; git reset --hard FETCH_HEAD; } + configure_script: + - '%x64_NATIVE_TOOLS%' + - cmake -G "Visual Studio 17 2022" -A x64 -S . -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON + build_script: + - '%x64_NATIVE_TOOLS%' + - cmake --build build --config RelWithDebInfo -- -property:UseMultiToolTask=true;CL_MPcount=5 + check_script: + - '%x64_NATIVE_TOOLS%' + - ctest --test-dir build -j 5 + - build\src\RelWithDebInfo\bench_ecmult.exe + - build\src\RelWithDebInfo\bench_internal.exe + - build\src\RelWithDebInfo\bench.exe diff --git a/src/secp256k1/.gitattributes b/src/secp256k1/.gitattributes new file mode 100644 index 0000000000..30efb2244f --- /dev/null +++ b/src/secp256k1/.gitattributes @@ -0,0 +1,2 @@ +src/precomputed_ecmult.c linguist-generated +src/precomputed_ecmult_gen.c linguist-generated diff --git a/src/secp256k1/.gitignore b/src/secp256k1/.gitignore new file mode 100644 index 0000000000..bc7e499de7 --- /dev/null +++ b/src/secp256k1/.gitignore @@ -0,0 +1,63 @@ +bench +bench_ecmult +bench_internal +noverify_tests +tests +exhaustive_tests +precompute_ecmult_gen +precompute_ecmult +ctime_tests +ecdh_example +ecdsa_example +schnorr_example +*.exe +*.so +*.a +*.csv +*.log +*.trs +*.sage.py + +Makefile +configure +.libs/ +Makefile.in +aclocal.m4 +autom4te.cache/ +config.log +config.status +conftest* +*.tar.gz +*.la +libtool +.deps/ +.dirstamp +*.lo +*.o +*~ + +coverage/ +coverage.html +coverage.*.html +*.gcda +*.gcno +*.gcov + +build-aux/ar-lib +build-aux/config.guess +build-aux/config.sub +build-aux/depcomp +build-aux/install-sh +build-aux/ltmain.sh +build-aux/m4/libtool.m4 +build-aux/m4/lt~obsolete.m4 +build-aux/m4/ltoptions.m4 +build-aux/m4/ltsugar.m4 +build-aux/m4/ltversion.m4 +build-aux/missing +build-aux/compile +build-aux/test-driver +libsecp256k1.pc + +# Default CMake build directory. +/build diff --git a/src/secp256k1/CHANGELOG.md b/src/secp256k1/CHANGELOG.md new file mode 100644 index 0000000000..6d23662a93 --- /dev/null +++ b/src/secp256k1/CHANGELOG.md @@ -0,0 +1,75 @@ +# Changelog + +All notable changes to this project will be documented in this file. + +The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), +and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html). + +## [Unreleased] + +## [0.3.1] - 2023-04-10 +We strongly recommend updating to 0.3.1 if you use or plan to use Clang >=14 to compile libsecp256k1, e.g., Xcode >=14 on macOS has Clang >=14. When in doubt, check the Clang version using `clang -v`. + +#### Security + - Fix "constant-timeness" issue with Clang >=14 that could leave applications using libsecp256k1 vulnerable to a timing side-channel attack. The fix avoids secret-dependent control flow and secret-dependent memory accesses in conditional moves of memory objects when libsecp256k1 is compiled with Clang >=14. + +#### Added + - Added tests against [Project Wycheproof's](https://github.com/google/wycheproof/) set of ECDSA test vectors (Bitcoin "low-S" variant), a fixed set of test cases designed to trigger various edge cases. + +#### Changed + - Increased minimum required CMake version to 3.13. CMake builds remain experimental. + +#### ABI Compatibility +The ABI is compatible with version 0.3.0. + +## [0.3.0] - 2023-03-08 + +#### Added + - Added experimental support for CMake builds. Traditional GNU Autotools builds (`./configure` and `make`) remain fully supported. + - Usage examples: Added a recommended method for securely clearing sensitive data, e.g., secret keys, from memory. + - Tests: Added a new test binary `noverify_tests`. This binary runs the tests without some additional checks present in the ordinary `tests` binary and is thereby closer to production binaries. The `noverify_tests` binary is automatically run as part of the `make check` target. + +#### Fixed + - Fixed declarations of API variables for MSVC (`__declspec(dllimport)`). This fixes MSVC builds of programs which link against a libsecp256k1 DLL dynamically and use API variables (and not only API functions). Unfortunately, the MSVC linker now will emit warning `LNK4217` when trying to link against libsecp256k1 statically. Pass `/ignore:4217` to the linker to suppress this warning. + +#### Changed + - Forbade cloning or destroying `secp256k1_context_static`. Create a new context instead of cloning the static context. (If this change breaks your code, your code is probably wrong.) + - Forbade randomizing (copies of) `secp256k1_context_static`. Randomizing a copy of `secp256k1_context_static` did not have any effect and did not provide defense-in-depth protection against side-channel attacks. Create a new context if you want to benefit from randomization. + +#### Removed + - Removed the configuration header `src/libsecp256k1-config.h`. We recommend passing flags to `./configure` or `cmake` to set configuration options (see `./configure --help` or `cmake -LH`). If you cannot or do not want to use one of the supported build systems, pass configuration flags such as `-DSECP256K1_ENABLE_MODULE_SCHNORRSIG` manually to the compiler (see the file `configure.ac` for supported flags). + +#### ABI Compatibility +Due to changes in the API regarding `secp256k1_context_static` described above, the ABI is *not* compatible with previous versions. + +## [0.2.0] - 2022-12-12 + +#### Added + - Added usage examples for common use cases in a new `examples/` directory. + - Added `secp256k1_selftest`, to be used in conjunction with `secp256k1_context_static`. + - Added support for 128-bit wide multiplication on MSVC for x86_64 and arm64, giving roughly a 20% speedup on those platforms. + +#### Changed + - Enabled modules `schnorrsig`, `extrakeys` and `ecdh` by default in `./configure`. + - The `secp256k1_nonce_function_rfc6979` nonce function, used by default by `secp256k1_ecdsa_sign`, now reduces the message hash modulo the group order to match the specification. This only affects improper use of ECDSA signing API. + +#### Deprecated + - Deprecated context flags `SECP256K1_CONTEXT_VERIFY` and `SECP256K1_CONTEXT_SIGN`. Use `SECP256K1_CONTEXT_NONE` instead. + - Renamed `secp256k1_context_no_precomp` to `secp256k1_context_static`. + - Module `schnorrsig`: renamed `secp256k1_schnorrsig_sign` to `secp256k1_schnorrsig_sign32`. + +#### ABI Compatibility +Since this is the first release, we do not compare application binary interfaces. +However, there are earlier unreleased versions of libsecp256k1 that are *not* ABI compatible with this version. + +## [0.1.0] - 2013-03-05 to 2021-12-25 + +This version was in fact never released. +The number was given by the build system since the introduction of autotools in Jan 2014 (ea0fe5a5bf0c04f9cc955b2966b614f5f378c6f6). +Therefore, this version number does not uniquely identify a set of source files. + +[unreleased]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.1...HEAD +[0.3.1]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.0...v0.3.1 +[0.3.0]: https://github.com/bitcoin-core/secp256k1/compare/v0.2.0...v0.3.0 +[0.2.0]: https://github.com/bitcoin-core/secp256k1/compare/423b6d19d373f1224fd671a982584d7e7900bc93..v0.2.0 +[0.1.0]: https://github.com/bitcoin-core/secp256k1/commit/423b6d19d373f1224fd671a982584d7e7900bc93 diff --git a/src/secp256k1/CMakeLists.txt b/src/secp256k1/CMakeLists.txt new file mode 100644 index 0000000000..a70165e356 --- /dev/null +++ b/src/secp256k1/CMakeLists.txt @@ -0,0 +1,297 @@ +cmake_minimum_required(VERSION 3.13) + +if(CMAKE_VERSION VERSION_GREATER 3.14) + # MSVC runtime library flags are selected by the CMAKE_MSVC_RUNTIME_LIBRARY abstraction. + cmake_policy(SET CMP0091 NEW) + # MSVC warning flags are not in CMAKE_<LANG>_FLAGS by default. + cmake_policy(SET CMP0092 NEW) +endif() + +# The package (a.k.a. release) version is based on semantic versioning 2.0.0 of +# the API. All changes in experimental modules are treated as +# backwards-compatible and therefore at most increase the minor version. +project(libsecp256k1 VERSION 0.3.2 LANGUAGES C) + +# The library version is based on libtool versioning of the ABI. The set of +# rules for updating the version can be found here: +# https://www.gnu.org/software/libtool/manual/html_node/Updating-version-info.html +# All changes in experimental modules are treated as if they don't affect the +# interface and therefore only increase the revision. +set(${PROJECT_NAME}_LIB_VERSION_CURRENT 2) +set(${PROJECT_NAME}_LIB_VERSION_REVISION 2) +set(${PROJECT_NAME}_LIB_VERSION_AGE 0) + +set(CMAKE_C_STANDARD 90) +set(CMAKE_C_EXTENSIONS OFF) + +list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake) + +# We do not use CMake's BUILD_SHARED_LIBS option. +option(SECP256K1_BUILD_SHARED "Build shared library." ON) +option(SECP256K1_BUILD_STATIC "Build static library." ON) +if(NOT SECP256K1_BUILD_SHARED AND NOT SECP256K1_BUILD_STATIC) + message(FATAL_ERROR "At least one of SECP256K1_BUILD_SHARED and SECP256K1_BUILD_STATIC must be enabled.") +endif() + +option(SECP256K1_ENABLE_MODULE_ECDH "Enable ECDH module." ON) +if(SECP256K1_ENABLE_MODULE_ECDH) + add_definitions(-DENABLE_MODULE_ECDH=1) +endif() + +option(SECP256K1_ENABLE_MODULE_RECOVERY "Enable ECDSA pubkey recovery module." OFF) +if(SECP256K1_ENABLE_MODULE_RECOVERY) + add_definitions(-DENABLE_MODULE_RECOVERY=1) +endif() + +option(SECP256K1_ENABLE_MODULE_EXTRAKEYS "Enable extrakeys module." ON) +option(SECP256K1_ENABLE_MODULE_SCHNORRSIG "Enable schnorrsig module." ON) +if(SECP256K1_ENABLE_MODULE_SCHNORRSIG) + set(SECP256K1_ENABLE_MODULE_EXTRAKEYS ON) + add_definitions(-DENABLE_MODULE_SCHNORRSIG=1) +endif() +if(SECP256K1_ENABLE_MODULE_EXTRAKEYS) + add_definitions(-DENABLE_MODULE_EXTRAKEYS=1) +endif() + +option(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS "Enable external default callback functions." OFF) +if(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS) + add_definitions(-DUSE_EXTERNAL_DEFAULT_CALLBACKS=1) +endif() + +set(SECP256K1_ECMULT_WINDOW_SIZE "AUTO" CACHE STRING "Window size for ecmult precomputation for verification, specified as integer in range [2..24]. \"AUTO\" is a reasonable setting for desktop machines (currently 15). [default=AUTO]") +set_property(CACHE SECP256K1_ECMULT_WINDOW_SIZE PROPERTY STRINGS "AUTO" 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24) +include(CheckStringOptionValue) +check_string_option_value(SECP256K1_ECMULT_WINDOW_SIZE) +if(SECP256K1_ECMULT_WINDOW_SIZE STREQUAL "AUTO") + set(SECP256K1_ECMULT_WINDOW_SIZE 15) +endif() +add_definitions(-DECMULT_WINDOW_SIZE=${SECP256K1_ECMULT_WINDOW_SIZE}) + +set(SECP256K1_ECMULT_GEN_PREC_BITS "AUTO" CACHE STRING "Precision bits to tune the precomputed table size for signing, specified as integer 2, 4 or 8. \"AUTO\" is a reasonable setting for desktop machines (currently 4). [default=AUTO]") +set_property(CACHE SECP256K1_ECMULT_GEN_PREC_BITS PROPERTY STRINGS "AUTO" 2 4 8) +check_string_option_value(SECP256K1_ECMULT_GEN_PREC_BITS) +if(SECP256K1_ECMULT_GEN_PREC_BITS STREQUAL "AUTO") + set(SECP256K1_ECMULT_GEN_PREC_BITS 4) +endif() +add_definitions(-DECMULT_GEN_PREC_BITS=${SECP256K1_ECMULT_GEN_PREC_BITS}) + +set(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY "OFF" CACHE STRING "Test-only override of the (autodetected by the C code) \"widemul\" setting. Legal values are: \"OFF\", \"int128_struct\", \"int128\" or \"int64\". [default=OFF]") +set_property(CACHE SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY PROPERTY STRINGS "OFF" "int128_struct" "int128" "int64") +check_string_option_value(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY) +if(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY) + string(TOUPPER "${SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY}" widemul_upper_value) + add_definitions(-DUSE_FORCE_WIDEMUL_${widemul_upper_value}=1) +endif() +mark_as_advanced(FORCE SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY) + +set(SECP256K1_ASM "AUTO" CACHE STRING "Assembly optimizations to use: \"AUTO\", \"OFF\", \"x86_64\" or \"arm\" (experimental). [default=AUTO]") +set_property(CACHE SECP256K1_ASM PROPERTY STRINGS "AUTO" "OFF" "x86_64" "arm") +check_string_option_value(SECP256K1_ASM) +if(SECP256K1_ASM STREQUAL "arm") + enable_language(ASM) + add_definitions(-DUSE_EXTERNAL_ASM=1) +elseif(SECP256K1_ASM) + include(Check64bitAssembly) + check_64bit_assembly() + if(HAS_64BIT_ASM) + set(SECP256K1_ASM "x86_64") + add_definitions(-DUSE_ASM_X86_64=1) + elseif(SECP256K1_ASM STREQUAL "AUTO") + set(SECP256K1_ASM "OFF") + else() + message(FATAL_ERROR "x86_64 assembly optimization requested but not available.") + endif() +endif() + +option(SECP256K1_EXPERIMENTAL "Allow experimental configuration options." OFF) +if(NOT SECP256K1_EXPERIMENTAL) + if(SECP256K1_ASM STREQUAL "arm") + message(FATAL_ERROR "ARM assembly optimization is experimental. Use -DSECP256K1_EXPERIMENTAL=ON to allow.") + endif() +endif() + +set(SECP256K1_VALGRIND "AUTO" CACHE STRING "Build with extra checks for running inside Valgrind. [default=AUTO]") +set_property(CACHE SECP256K1_VALGRIND PROPERTY STRINGS "AUTO" "OFF" "ON") +check_string_option_value(SECP256K1_VALGRIND) +if(SECP256K1_VALGRIND) + find_package(Valgrind MODULE) + if(Valgrind_FOUND) + set(SECP256K1_VALGRIND ON) + include_directories(${Valgrind_INCLUDE_DIR}) + add_definitions(-DVALGRIND) + elseif(SECP256K1_VALGRIND STREQUAL "AUTO") + set(SECP256K1_VALGRIND OFF) + else() + message(FATAL_ERROR "Valgrind support requested but valgrind/memcheck.h header not available.") + endif() +endif() + +option(SECP256K1_BUILD_BENCHMARK "Build benchmarks." ON) +option(SECP256K1_BUILD_TESTS "Build tests." ON) +option(SECP256K1_BUILD_EXHAUSTIVE_TESTS "Build exhaustive tests." ON) +option(SECP256K1_BUILD_CTIME_TESTS "Build constant-time tests." ${SECP256K1_VALGRIND}) +option(SECP256K1_BUILD_EXAMPLES "Build examples." OFF) + +# Redefine configuration flags. +# We leave assertions on, because they are only used in the examples, and we want them always on there. +if(MSVC) + string(REGEX REPLACE "/DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_RELWITHDEBINFO "${CMAKE_C_FLAGS_RELWITHDEBINFO}") + string(REGEX REPLACE "/DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE}") + string(REGEX REPLACE "/DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_MINSIZEREL "${CMAKE_C_FLAGS_MINSIZEREL}") +else() + string(REGEX REPLACE "-DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_RELWITHDEBINFO "${CMAKE_C_FLAGS_RELWITHDEBINFO}") + string(REGEX REPLACE "-DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE}") + string(REGEX REPLACE "-DNDEBUG[ \t\r\n]*" "" CMAKE_C_FLAGS_MINSIZEREL "${CMAKE_C_FLAGS_MINSIZEREL}") + # Prefer -O2 optimization level. (-O3 is CMake's default for Release for many compilers.) + string(REGEX REPLACE "-O3[ \t\r\n]*" "-O2" CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE}") +endif() + +# Define custom "Coverage" build type. +set(CMAKE_C_FLAGS_COVERAGE "${CMAKE_C_FLAGS_RELWITHDEBINFO} -O0 -DCOVERAGE=1 --coverage" CACHE STRING + "Flags used by the C compiler during \"Coverage\" builds." + FORCE +) +set(CMAKE_EXE_LINKER_FLAGS_COVERAGE "${CMAKE_EXE_LINKER_FLAGS_RELWITHDEBINFO} --coverage" CACHE STRING + "Flags used for linking binaries during \"Coverage\" builds." + FORCE +) +set(CMAKE_SHARED_LINKER_FLAGS_COVERAGE "${CMAKE_SHARED_LINKER_FLAGS_RELWITHDEBINFO} --coverage" CACHE STRING + "Flags used by the shared libraries linker during \"Coverage\" builds." + FORCE +) +mark_as_advanced( + CMAKE_C_FLAGS_COVERAGE + CMAKE_EXE_LINKER_FLAGS_COVERAGE + CMAKE_SHARED_LINKER_FLAGS_COVERAGE +) + +if(CMAKE_CONFIGURATION_TYPES) + set(CMAKE_CONFIGURATION_TYPES "RelWithDebInfo" "Release" "Debug" "MinSizeRel" "Coverage") +endif() + +get_property(cached_cmake_build_type CACHE CMAKE_BUILD_TYPE PROPERTY TYPE) +if(cached_cmake_build_type) + set_property(CACHE CMAKE_BUILD_TYPE PROPERTY + STRINGS "RelWithDebInfo" "Release" "Debug" "MinSizeRel" "Coverage" + ) +endif() + +set(default_build_type "RelWithDebInfo") +if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES) + message(STATUS "Setting build type to \"${default_build_type}\" as none was specified") + set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE STRING "Choose the type of build." FORCE) +endif() + +include(TryAddCompileOption) +if(MSVC) + try_add_compile_option(/W2) + try_add_compile_option(/wd4146) +else() + try_add_compile_option(-pedantic) + try_add_compile_option(-Wall) + try_add_compile_option(-Wcast-align) + try_add_compile_option(-Wcast-align=strict) + try_add_compile_option(-Wconditional-uninitialized) + try_add_compile_option(-Wextra) + try_add_compile_option(-Wnested-externs) + try_add_compile_option(-Wno-long-long) + try_add_compile_option(-Wno-overlength-strings) + try_add_compile_option(-Wno-unused-function) + try_add_compile_option(-Wreserved-identifier) + try_add_compile_option(-Wshadow) + try_add_compile_option(-Wstrict-prototypes) + try_add_compile_option(-Wundef) +endif() + +set(CMAKE_C_VISIBILITY_PRESET hidden) + +# Ask CTest to create a "check" target (e.g., make check) as alias for the "test" target. +# CTEST_TEST_TARGET_ALIAS is not documented but supposed to be user-facing. +# See: https://gitlab.kitware.com/cmake/cmake/-/commit/816c9d1aa1f2b42d40c81a991b68c96eb12b6d2 +set(CTEST_TEST_TARGET_ALIAS check) +include(CTest) +# We do not use CTest's BUILD_TESTING because a single toggle for all tests is too coarse for our needs. +mark_as_advanced(BUILD_TESTING) +if(SECP256K1_BUILD_BENCHMARK OR SECP256K1_BUILD_TESTS OR SECP256K1_BUILD_EXHAUSTIVE_TESTS OR SECP256K1_BUILD_CTIME_TESTS OR SECP256K1_BUILD_EXAMPLES) + enable_testing() +endif() + +add_subdirectory(src) +if(SECP256K1_BUILD_EXAMPLES) + add_subdirectory(examples) +endif() + +message("\n") +message("secp256k1 configure summary") +message("===========================") +message("Build artifacts:") +message(" shared library ...................... ${SECP256K1_BUILD_SHARED}") +message(" static library ...................... ${SECP256K1_BUILD_STATIC}") +message("Optional modules:") +message(" ECDH ................................ ${SECP256K1_ENABLE_MODULE_ECDH}") +message(" ECDSA pubkey recovery ............... ${SECP256K1_ENABLE_MODULE_RECOVERY}") +message(" extrakeys ........................... ${SECP256K1_ENABLE_MODULE_EXTRAKEYS}") +message(" schnorrsig .......................... ${SECP256K1_ENABLE_MODULE_SCHNORRSIG}") +message("Parameters:") +message(" ecmult window size .................. ${SECP256K1_ECMULT_WINDOW_SIZE}") +message(" ecmult gen precision bits ........... ${SECP256K1_ECMULT_GEN_PREC_BITS}") +message("Optional features:") +message(" assembly optimization ............... ${SECP256K1_ASM}") +message(" external callbacks .................. ${SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS}") +if(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY) + message(" wide multiplication (test-only) ..... ${SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY}") +endif() +message("Optional binaries:") +message(" benchmark ........................... ${SECP256K1_BUILD_BENCHMARK}") +message(" noverify_tests ...................... ${SECP256K1_BUILD_TESTS}") +set(tests_status "${SECP256K1_BUILD_TESTS}") +if(CMAKE_BUILD_TYPE STREQUAL "Coverage") + set(tests_status OFF) +endif() +message(" tests ............................... ${tests_status}") +message(" exhaustive tests .................... ${SECP256K1_BUILD_EXHAUSTIVE_TESTS}") +message(" ctime_tests ......................... ${SECP256K1_BUILD_CTIME_TESTS}") +message(" examples ............................ ${SECP256K1_BUILD_EXAMPLES}") +message("") +if(CMAKE_CROSSCOMPILING) + set(cross_status "TRUE, for ${CMAKE_SYSTEM_NAME}, ${CMAKE_SYSTEM_PROCESSOR}") +else() + set(cross_status "FALSE") +endif() +message("Cross compiling ....................... ${cross_status}") +message("Valgrind .............................. ${SECP256K1_VALGRIND}") +get_directory_property(definitions COMPILE_DEFINITIONS) +string(REPLACE ";" " " definitions "${definitions}") +message("Preprocessor defined macros ........... ${definitions}") +message("C compiler ............................ ${CMAKE_C_COMPILER}") +message("CFLAGS ................................ ${CMAKE_C_FLAGS}") +get_directory_property(compile_options COMPILE_OPTIONS) +string(REPLACE ";" " " compile_options "${compile_options}") +message("Compile options ....................... " ${compile_options}) +if(DEFINED CMAKE_BUILD_TYPE) + message("Build type:") + message(" - CMAKE_BUILD_TYPE ................... ${CMAKE_BUILD_TYPE}") + string(TOUPPER "${CMAKE_BUILD_TYPE}" build_type) + message(" - CFLAGS ............................. ${CMAKE_C_FLAGS_${build_type}}") + message(" - LDFLAGS for executables ............ ${CMAKE_EXE_LINKER_FLAGS_${build_type}}") + message(" - LDFLAGS for shared libraries ....... ${CMAKE_SHARED_LINKER_FLAGS_${build_type}}") +else() + message("Available configurations .............. ${CMAKE_CONFIGURATION_TYPES}") + message("RelWithDebInfo configuration:") + message(" - CFLAGS ............................. ${CMAKE_C_FLAGS_RELWITHDEBINFO}") + message(" - LDFLAGS for executables ............ ${CMAKE_EXE_LINKER_FLAGS_RELWITHDEBINFO}") + message(" - LDFLAGS for shared libraries ....... ${CMAKE_SHARED_LINKER_FLAGS_RELWITHDEBINFO}") + message("Debug configuration:") + message(" - CFLAGS ............................. ${CMAKE_C_FLAGS_DEBUG}") + message(" - LDFLAGS for executables ............ ${CMAKE_EXE_LINKER_FLAGS_DEBUG}") + message(" - LDFLAGS for shared libraries ....... ${CMAKE_SHARED_LINKER_FLAGS_DEBUG}") +endif() +message("\n") +if(SECP256K1_EXPERIMENTAL) + message( + " ******\n" + " WARNING: experimental build\n" + " Experimental features do not have stable APIs or properties, and may not be safe for production use.\n" + " ******\n" + ) +endif() diff --git a/src/secp256k1/COPYING b/src/secp256k1/COPYING new file mode 100644 index 0000000000..4522a5990e --- /dev/null +++ b/src/secp256k1/COPYING @@ -0,0 +1,19 @@ +Copyright (c) 2013 Pieter Wuille + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am new file mode 100644 index 0000000000..36e26e3e8a --- /dev/null +++ b/src/secp256k1/Makefile.am @@ -0,0 +1,266 @@ +.PHONY: clean-precomp precomp + +ACLOCAL_AMFLAGS = -I build-aux/m4 + +# AM_CFLAGS will be automatically prepended to CFLAGS by Automake when compiling some foo +# which does not have an explicit foo_CFLAGS variable set. +AM_CFLAGS = $(SECP_CFLAGS) + +lib_LTLIBRARIES = libsecp256k1.la +include_HEADERS = include/secp256k1.h +include_HEADERS += include/secp256k1_preallocated.h +noinst_HEADERS = +noinst_HEADERS += src/scalar.h +noinst_HEADERS += src/scalar_4x64.h +noinst_HEADERS += src/scalar_8x32.h +noinst_HEADERS += src/scalar_low.h +noinst_HEADERS += src/scalar_impl.h +noinst_HEADERS += src/scalar_4x64_impl.h +noinst_HEADERS += src/scalar_8x32_impl.h +noinst_HEADERS += src/scalar_low_impl.h +noinst_HEADERS += src/group.h +noinst_HEADERS += src/group_impl.h +noinst_HEADERS += src/ecdsa.h +noinst_HEADERS += src/ecdsa_impl.h +noinst_HEADERS += src/eckey.h +noinst_HEADERS += src/eckey_impl.h +noinst_HEADERS += src/ecmult.h +noinst_HEADERS += src/ecmult_impl.h +noinst_HEADERS += src/ecmult_compute_table.h +noinst_HEADERS += src/ecmult_compute_table_impl.h +noinst_HEADERS += src/ecmult_const.h +noinst_HEADERS += src/ecmult_const_impl.h +noinst_HEADERS += src/ecmult_gen.h +noinst_HEADERS += src/ecmult_gen_impl.h +noinst_HEADERS += src/ecmult_gen_compute_table.h +noinst_HEADERS += src/ecmult_gen_compute_table_impl.h +noinst_HEADERS += src/field_10x26.h +noinst_HEADERS += src/field_10x26_impl.h +noinst_HEADERS += src/field_5x52.h +noinst_HEADERS += src/field_5x52_impl.h +noinst_HEADERS += src/field_5x52_int128_impl.h +noinst_HEADERS += src/field_5x52_asm_impl.h +noinst_HEADERS += src/modinv32.h +noinst_HEADERS += src/modinv32_impl.h +noinst_HEADERS += src/modinv64.h +noinst_HEADERS += src/modinv64_impl.h +noinst_HEADERS += src/precomputed_ecmult.h +noinst_HEADERS += src/precomputed_ecmult_gen.h +noinst_HEADERS += src/assumptions.h +noinst_HEADERS += src/checkmem.h +noinst_HEADERS += src/util.h +noinst_HEADERS += src/int128.h +noinst_HEADERS += src/int128_impl.h +noinst_HEADERS += src/int128_native.h +noinst_HEADERS += src/int128_native_impl.h +noinst_HEADERS += src/int128_struct.h +noinst_HEADERS += src/int128_struct_impl.h +noinst_HEADERS += src/scratch.h +noinst_HEADERS += src/scratch_impl.h +noinst_HEADERS += src/selftest.h +noinst_HEADERS += src/testrand.h +noinst_HEADERS += src/testrand_impl.h +noinst_HEADERS += src/hash.h +noinst_HEADERS += src/hash_impl.h +noinst_HEADERS += src/field.h +noinst_HEADERS += src/field_impl.h +noinst_HEADERS += src/bench.h +noinst_HEADERS += contrib/lax_der_parsing.h +noinst_HEADERS += contrib/lax_der_parsing.c +noinst_HEADERS += contrib/lax_der_privatekey_parsing.h +noinst_HEADERS += contrib/lax_der_privatekey_parsing.c +noinst_HEADERS += examples/examples_util.h + +PRECOMPUTED_LIB = libsecp256k1_precomputed.la +noinst_LTLIBRARIES = $(PRECOMPUTED_LIB) +libsecp256k1_precomputed_la_SOURCES = src/precomputed_ecmult.c src/precomputed_ecmult_gen.c +# We need `-I$(top_srcdir)/src` in VPATH builds if libsecp256k1_precomputed_la_SOURCES have been recreated in the build tree. +# This helps users and packagers who insist on recreating the precomputed files (e.g., Gentoo). +libsecp256k1_precomputed_la_CPPFLAGS = -I$(top_srcdir)/src $(SECP_CONFIG_DEFINES) + +if USE_EXTERNAL_ASM +COMMON_LIB = libsecp256k1_common.la +else +COMMON_LIB = +endif +noinst_LTLIBRARIES += $(COMMON_LIB) + +pkgconfigdir = $(libdir)/pkgconfig +pkgconfig_DATA = libsecp256k1.pc + +if USE_EXTERNAL_ASM +if USE_ASM_ARM +libsecp256k1_common_la_SOURCES = src/asm/field_10x26_arm.s +endif +endif + +libsecp256k1_la_SOURCES = src/secp256k1.c +libsecp256k1_la_CPPFLAGS = $(SECP_CONFIG_DEFINES) +libsecp256k1_la_LIBADD = $(COMMON_LIB) $(PRECOMPUTED_LIB) +libsecp256k1_la_LDFLAGS = -no-undefined -version-info $(LIB_VERSION_CURRENT):$(LIB_VERSION_REVISION):$(LIB_VERSION_AGE) + +noinst_PROGRAMS = +if USE_BENCHMARK +noinst_PROGRAMS += bench bench_internal bench_ecmult +bench_SOURCES = src/bench.c +bench_LDADD = libsecp256k1.la +bench_CPPFLAGS = $(SECP_CONFIG_DEFINES) +bench_internal_SOURCES = src/bench_internal.c +bench_internal_LDADD = $(COMMON_LIB) $(PRECOMPUTED_LIB) +bench_internal_CPPFLAGS = $(SECP_CONFIG_DEFINES) +bench_ecmult_SOURCES = src/bench_ecmult.c +bench_ecmult_LDADD = $(COMMON_LIB) $(PRECOMPUTED_LIB) +bench_ecmult_CPPFLAGS = $(SECP_CONFIG_DEFINES) +endif + +TESTS = +if USE_TESTS +TESTS += noverify_tests +noinst_PROGRAMS += noverify_tests +noverify_tests_SOURCES = src/tests.c +noverify_tests_CPPFLAGS = $(SECP_CONFIG_DEFINES) +noverify_tests_LDADD = $(COMMON_LIB) $(PRECOMPUTED_LIB) +noverify_tests_LDFLAGS = -static +if !ENABLE_COVERAGE +TESTS += tests +noinst_PROGRAMS += tests +tests_SOURCES = $(noverify_tests_SOURCES) +tests_CPPFLAGS = $(noverify_tests_CPPFLAGS) -DVERIFY +tests_LDADD = $(noverify_tests_LDADD) +tests_LDFLAGS = $(noverify_tests_LDFLAGS) +endif +endif + +if USE_CTIME_TESTS +noinst_PROGRAMS += ctime_tests +ctime_tests_SOURCES = src/ctime_tests.c +ctime_tests_LDADD = libsecp256k1.la +ctime_tests_CPPFLAGS = $(SECP_CONFIG_DEFINES) +endif + +if USE_EXHAUSTIVE_TESTS +noinst_PROGRAMS += exhaustive_tests +exhaustive_tests_SOURCES = src/tests_exhaustive.c +exhaustive_tests_CPPFLAGS = $(SECP_CONFIG_DEFINES) +if !ENABLE_COVERAGE +exhaustive_tests_CPPFLAGS += -DVERIFY +endif +# Note: do not include $(PRECOMPUTED_LIB) in exhaustive_tests (it uses runtime-generated tables). +exhaustive_tests_LDADD = $(COMMON_LIB) +exhaustive_tests_LDFLAGS = -static +TESTS += exhaustive_tests +endif + +if USE_EXAMPLES +noinst_PROGRAMS += ecdsa_example +ecdsa_example_SOURCES = examples/ecdsa.c +ecdsa_example_CPPFLAGS = -I$(top_srcdir)/include +ecdsa_example_LDADD = libsecp256k1.la +ecdsa_example_LDFLAGS = -static +if BUILD_WINDOWS +ecdsa_example_LDFLAGS += -lbcrypt +endif +TESTS += ecdsa_example +if ENABLE_MODULE_ECDH +noinst_PROGRAMS += ecdh_example +ecdh_example_SOURCES = examples/ecdh.c +ecdh_example_CPPFLAGS = -I$(top_srcdir)/include +ecdh_example_LDADD = libsecp256k1.la +ecdh_example_LDFLAGS = -static +if BUILD_WINDOWS +ecdh_example_LDFLAGS += -lbcrypt +endif +TESTS += ecdh_example +endif +if ENABLE_MODULE_SCHNORRSIG +noinst_PROGRAMS += schnorr_example +schnorr_example_SOURCES = examples/schnorr.c +schnorr_example_CPPFLAGS = -I$(top_srcdir)/include +schnorr_example_LDADD = libsecp256k1.la +schnorr_example_LDFLAGS = -static +if BUILD_WINDOWS +schnorr_example_LDFLAGS += -lbcrypt +endif +TESTS += schnorr_example +endif +endif + +### Precomputed tables +EXTRA_PROGRAMS = precompute_ecmult precompute_ecmult_gen +CLEANFILES = $(EXTRA_PROGRAMS) + +precompute_ecmult_SOURCES = src/precompute_ecmult.c +precompute_ecmult_CPPFLAGS = $(SECP_CONFIG_DEFINES) +precompute_ecmult_LDADD = $(COMMON_LIB) + +precompute_ecmult_gen_SOURCES = src/precompute_ecmult_gen.c +precompute_ecmult_gen_CPPFLAGS = $(SECP_CONFIG_DEFINES) +precompute_ecmult_gen_LDADD = $(COMMON_LIB) + +# See Automake manual, Section "Errors with distclean". +# We don't list any dependencies for the prebuilt files here because +# otherwise make's decision whether to rebuild them (even in the first +# build by a normal user) depends on mtimes, and thus is very fragile. +# This means that rebuilds of the prebuilt files always need to be +# forced by deleting them, e.g., by invoking `make clean-precomp`. +src/precomputed_ecmult.c: + $(MAKE) $(AM_MAKEFLAGS) precompute_ecmult$(EXEEXT) + ./precompute_ecmult$(EXEEXT) +src/precomputed_ecmult_gen.c: + $(MAKE) $(AM_MAKEFLAGS) precompute_ecmult_gen$(EXEEXT) + ./precompute_ecmult_gen$(EXEEXT) + +PRECOMP = src/precomputed_ecmult_gen.c src/precomputed_ecmult.c +precomp: $(PRECOMP) + +# Ensure the prebuilt files will be build first (only if they don't exist, +# e.g., after `make maintainer-clean`). +BUILT_SOURCES = $(PRECOMP) + +maintainer-clean-local: clean-precomp + +clean-precomp: + rm -f $(PRECOMP) + +EXTRA_DIST = autogen.sh CHANGELOG.md SECURITY.md +EXTRA_DIST += doc/release-process.md doc/safegcd_implementation.md +EXTRA_DIST += examples/EXAMPLES_COPYING +EXTRA_DIST += sage/gen_exhaustive_groups.sage +EXTRA_DIST += sage/gen_split_lambda_constants.sage +EXTRA_DIST += sage/group_prover.sage +EXTRA_DIST += sage/prove_group_implementations.sage +EXTRA_DIST += sage/secp256k1_params.sage +EXTRA_DIST += sage/weierstrass_prover.sage + +if ENABLE_MODULE_ECDH +include src/modules/ecdh/Makefile.am.include +endif + +if ENABLE_MODULE_RECOVERY +include src/modules/recovery/Makefile.am.include +endif + +if ENABLE_MODULE_EXTRAKEYS +include src/modules/extrakeys/Makefile.am.include +endif + +if ENABLE_MODULE_SCHNORRSIG +include src/modules/schnorrsig/Makefile.am.include +endif + +EXTRA_DIST += src/wycheproof/WYCHEPROOF_COPYING +EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h +EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json +EXTRA_DIST += tools/tests_wycheproof_generate.py + +TESTVECTORS = src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h + +src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h: + python3 tools/tests_wycheproof_generate.py src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json > $@ + +testvectors: $(TESTVECTORS) + +maintainer-clean-testvectors: clean-testvectors + +clean-testvectors: + rm -f $(TESTVECTORS) diff --git a/src/secp256k1/README.md b/src/secp256k1/README.md new file mode 100644 index 0000000000..19dabe8505 --- /dev/null +++ b/src/secp256k1/README.md @@ -0,0 +1,157 @@ +libsecp256k1 +============ + +[](https://cirrus-ci.com/github/bitcoin-core/secp256k1) + +[](https://web.libera.chat/#secp256k1) + +Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1. + +This library is intended to be the highest quality publicly available library for cryptography on the secp256k1 curve. However, the primary focus of its development has been for usage in the Bitcoin system and usage unlike Bitcoin's may be less well tested, verified, or suffer from a less well thought out interface. Correct usage requires some care and consideration that the library is fit for your application's purpose. + +Features: +* secp256k1 ECDSA signing/verification and key generation. +* Additive and multiplicative tweaking of secret/public keys. +* Serialization/parsing of secret keys, public keys, signatures. +* Constant time, constant memory access signing and public key generation. +* Derandomized ECDSA (via RFC6979 or with a caller provided function.) +* Very efficient implementation. +* Suitable for embedded systems. +* No runtime dependencies. +* Optional module for public key recovery. +* Optional module for ECDH key exchange. +* Optional module for Schnorr signatures according to [BIP-340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki). + +Implementation details +---------------------- + +* General + * No runtime heap allocation. + * Extensive testing infrastructure. + * Structured to facilitate review and analysis. + * Intended to be portable to any system with a C89 compiler and uint64_t support. + * No use of floating types. + * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.") +* Field operations + * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1). + * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys). + * Using 10 26-bit limbs (including hand-optimized assembly for 32-bit ARM, by Wladimir J. van der Laan). + * This is an experimental feature that has not received enough scrutiny to satisfy the standard of quality of this library but is made available for testing and review by the community. +* Scalar operations + * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order. + * Using 4 64-bit limbs (relying on __int128 support in the compiler). + * Using 8 32-bit limbs. +* Modular inverses (both field elements and scalars) based on [safegcd](https://gcd.cr.yp.to/index.html) with some modifications, and a variable-time variant (by Peter Dettman). +* Group operations + * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7). + * Use addition between points in Jacobian and affine coordinates where possible. + * Use a unified addition/doubling formula where necessary to avoid data-dependent branches. + * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space. +* Point multiplication for verification (a*P + b*G). + * Use wNAF notation for point multiplicands. + * Use a much larger window for multiples of G, using precomputed multiples. + * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously. + * Use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones. +* Point multiplication for signing + * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions. + * Intended to be completely free of timing sidechannels for secret-key operations (on reasonable hardware/toolchains) + * Access the table with branch-free conditional moves so memory access is uniform. + * No data-dependent branches + * Optional runtime blinding which attempts to frustrate differential power analysis. + * The precomputed tables add and eventually subtract points for which no known scalar (secret key) is known, preventing even an attacker with control over the secret key used to control the data internally. + +Building with Autotools +----------------------- + + $ ./autogen.sh + $ ./configure + $ make + $ make check # run the test suite + $ sudo make install # optional + +To compile optional modules (such as Schnorr signatures), you need to run `./configure` with additional flags (such as `--enable-module-schnorrsig`). Run `./configure --help` to see the full list of available flags. + +Building with CMake (experimental) +---------------------------------- + +To maintain a pristine source tree, CMake encourages to perform an out-of-source build by using a separate dedicated build tree. + +### Building on POSIX systems + + $ mkdir build && cd build + $ cmake .. + $ make + $ make check # run the test suite + $ sudo make install # optional + +To compile optional modules (such as Schnorr signatures), you need to run `cmake` with additional flags (such as `-DSECP256K1_ENABLE_MODULE_SCHNORRSIG=ON`). Run `cmake .. -LH` to see the full list of available flags. + +### Cross compiling + +To alleviate issues with cross compiling, preconfigured toolchain files are available in the `cmake` directory. +For example, to cross compile for Windows: + + $ cmake .. -DCMAKE_TOOLCHAIN_FILE=../cmake/x86_64-w64-mingw32.toolchain.cmake + +To cross compile for Android with [NDK](https://developer.android.com/ndk/guides/cmake) (using NDK's toolchain file, and assuming the `ANDROID_NDK_ROOT` environment variable has been set): + + $ cmake .. -DCMAKE_TOOLCHAIN_FILE="${ANDROID_NDK_ROOT}/build/cmake/android.toolchain.cmake" -DANDROID_ABI=arm64-v8a -DANDROID_PLATFORM=28 + +### Building on Windows + +To build on Windows with Visual Studio, a proper [generator](https://cmake.org/cmake/help/latest/manual/cmake-generators.7.html#visual-studio-generators) must be specified for a new build tree. + +The following example assumes using of Visual Studio 2022 and CMake v3.21+. + +In "Developer Command Prompt for VS 2022": + + >cmake -G "Visual Studio 17 2022" -A x64 -S . -B build + >cmake --build build --config RelWithDebInfo + +Usage examples +----------- +Usage examples can be found in the [examples](examples) directory. To compile them you need to configure with `--enable-examples`. + * [ECDSA example](examples/ecdsa.c) + * [Schnorr signatures example](examples/schnorr.c) + * [Deriving a shared secret (ECDH) example](examples/ecdh.c) + +To compile the Schnorr signature and ECDH examples, you also need to configure with `--enable-module-schnorrsig` and `--enable-module-ecdh`. + +Test coverage +----------- + +This library aims to have full coverage of the reachable lines and branches. + +To create a test coverage report, configure with `--enable-coverage` (use of GCC is necessary): + + $ ./configure --enable-coverage + +Run the tests: + + $ make check + +To create a report, `gcovr` is recommended, as it includes branch coverage reporting: + + $ gcovr --exclude 'src/bench*' --print-summary + +To create a HTML report with coloured and annotated source code: + + $ mkdir -p coverage + $ gcovr --exclude 'src/bench*' --html --html-details -o coverage/coverage.html + +Benchmark +------------ +If configured with `--enable-benchmark` (which is the default), binaries for benchmarking the libsecp256k1 functions will be present in the root directory after the build. + +To print the benchmark result to the command line: + + $ ./bench_name + +To create a CSV file for the benchmark result : + + $ ./bench_name | sed '2d;s/ \{1,\}//g' > bench_name.csv + +Reporting a vulnerability +------------ + +See [SECURITY.md](SECURITY.md) diff --git a/src/secp256k1/SECURITY.md b/src/secp256k1/SECURITY.md new file mode 100644 index 0000000000..b515cc1c8e --- /dev/null +++ b/src/secp256k1/SECURITY.md @@ -0,0 +1,15 @@ +# Security Policy + +## Reporting a Vulnerability + +To report security issues send an email to secp256k1-security@bitcoincore.org (not for support). + +The following keys may be used to communicate sensitive information to developers: + +| Name | Fingerprint | +|------|-------------| +| Pieter Wuille | 133E AC17 9436 F14A 5CF1 B794 860F EB80 4E66 9320 | +| Jonas Nick | 36C7 1A37 C9D9 88BD E825 08D9 B1A7 0E4F 8DCD 0366 | +| Tim Ruffing | 09E0 3F87 1092 E40E 106E 902B 33BC 86AB 80FF 5516 | + +You can import a key by running the following command with that individual’s fingerprint: `gpg --keyserver hkps://keys.openpgp.org --recv-keys "<fingerprint>"` Ensure that you put quotes around fingerprints containing spaces. diff --git a/src/secp256k1/autogen.sh b/src/secp256k1/autogen.sh new file mode 100755 index 0000000000..65286b9353 --- /dev/null +++ b/src/secp256k1/autogen.sh @@ -0,0 +1,3 @@ +#!/bin/sh +set -e +autoreconf -if --warnings=all diff --git a/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4 new file mode 100644 index 0000000000..624f5e956e --- /dev/null +++ b/src/secp256k1/build-aux/m4/bitcoin_secp.m4 @@ -0,0 +1,55 @@ +dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell. +AC_DEFUN([SECP_64BIT_ASM_CHECK],[ +AC_MSG_CHECKING(for x86_64 assembly availability) +AC_LINK_IFELSE([AC_LANG_PROGRAM([[ + #include <stdint.h>]],[[ + uint64_t a = 11, tmp; + __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx"); + ]])],[has_64bit_asm=yes],[has_64bit_asm=no]) +AC_MSG_RESULT([$has_64bit_asm]) +]) + +AC_DEFUN([SECP_VALGRIND_CHECK],[ +AC_MSG_CHECKING([for valgrind support]) +if test x"$has_valgrind" != x"yes"; then + CPPFLAGS_TEMP="$CPPFLAGS" + CPPFLAGS="$VALGRIND_CPPFLAGS $CPPFLAGS" + AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[ + #include <valgrind/memcheck.h> + ]], [[ + #if defined(NVALGRIND) + # error "Valgrind does not support this platform." + #endif + ]])], [has_valgrind=yes]) +fi +AC_MSG_RESULT($has_valgrind) +]) + +dnl SECP_TRY_APPEND_CFLAGS(flags, VAR) +dnl Append flags to VAR if CC accepts them. +AC_DEFUN([SECP_TRY_APPEND_CFLAGS], [ + AC_MSG_CHECKING([if ${CC} supports $1]) + SECP_TRY_APPEND_CFLAGS_saved_CFLAGS="$CFLAGS" + CFLAGS="$1 $CFLAGS" + AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], [flag_works=yes], [flag_works=no]) + AC_MSG_RESULT($flag_works) + CFLAGS="$SECP_TRY_APPEND_CFLAGS_saved_CFLAGS" + if test x"$flag_works" = x"yes"; then + $2="$$2 $1" + fi + unset flag_works + AC_SUBST($2) +]) + +dnl SECP_SET_DEFAULT(VAR, default, default-dev-mode) +dnl Set VAR to default or default-dev-mode, depending on whether dev mode is enabled +AC_DEFUN([SECP_SET_DEFAULT], [ + if test "${enable_dev_mode+set}" != set; then + AC_MSG_ERROR([[Set enable_dev_mode before calling SECP_SET_DEFAULT]]) + fi + if test x"$enable_dev_mode" = x"yes"; then + $1="$3" + else + $1="$2" + fi +]) diff --git a/src/secp256k1/ci/cirrus.sh b/src/secp256k1/ci/cirrus.sh new file mode 100755 index 0000000000..b2af03bb5d --- /dev/null +++ b/src/secp256k1/ci/cirrus.sh @@ -0,0 +1,118 @@ +#!/bin/sh + +set -eux + +export LC_ALL=C + +# Print relevant CI environment to allow reproducing the job outside of CI. +print_environment() { + # Turn off -x because it messes up the output + set +x + # There are many ways to print variable names and their content. This one + # does not rely on bash. + for var in WERROR_CFLAGS MAKEFLAGS BUILD \ + ECMULTWINDOW ECMULTGENPRECISION ASM WIDEMUL WITH_VALGRIND EXTRAFLAGS \ + EXPERIMENTAL ECDH RECOVERY SCHNORRSIG \ + SECP256K1_TEST_ITERS BENCH SECP256K1_BENCH_ITERS CTIMETESTS\ + EXAMPLES \ + HOST WRAPPER_CMD \ + CC CFLAGS CPPFLAGS AR NM + do + eval "isset=\${$var+x}" + if [ -n "$isset" ]; then + eval "val=\${$var}" + # shellcheck disable=SC2154 + printf '%s="%s" ' "$var" "$val" + fi + done + echo "$0" + set -x +} +print_environment + +# Start persistent wineserver if necessary. +# This speeds up jobs with many invocations of wine (e.g., ./configure with MSVC) tremendously. +case "$WRAPPER_CMD" in + *wine*) + # Make sure to shutdown wineserver whenever we exit. + trap "wineserver -k || true" EXIT INT HUP + # This is apparently only reliable when we run a dummy command such as "hh.exe" afterwards. + wineserver -p && wine hh.exe + ;; +esac + +env >> test_env.log + +if [ -n "${CC+x}" ]; then + # The MSVC compiler "cl" doesn't understand "-v" + $CC -v || true +fi +if [ "$WITH_VALGRIND" = "yes" ]; then + valgrind --version +fi +if [ -n "$WRAPPER_CMD" ]; then + $WRAPPER_CMD --version +fi + +./autogen.sh + +./configure \ + --enable-experimental="$EXPERIMENTAL" \ + --with-test-override-wide-multiply="$WIDEMUL" --with-asm="$ASM" \ + --with-ecmult-window="$ECMULTWINDOW" \ + --with-ecmult-gen-precision="$ECMULTGENPRECISION" \ + --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \ + --enable-module-schnorrsig="$SCHNORRSIG" \ + --enable-examples="$EXAMPLES" \ + --enable-ctime-tests="$CTIMETESTS" \ + --with-valgrind="$WITH_VALGRIND" \ + --host="$HOST" $EXTRAFLAGS + +# We have set "-j<n>" in MAKEFLAGS. +make + +# Print information about binaries so that we can see that the architecture is correct +file *tests* || true +file bench* || true +file .libs/* || true + +# This tells `make check` to wrap test invocations. +export LOG_COMPILER="$WRAPPER_CMD" + +make "$BUILD" + +# Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool +EXEC='./libtool --mode=execute' +if [ -n "$WRAPPER_CMD" ] +then + EXEC="$EXEC $WRAPPER_CMD" +fi + +if [ "$BENCH" = "yes" ] +then + { + $EXEC ./bench_ecmult + $EXEC ./bench_internal + $EXEC ./bench + } >> bench.log 2>&1 +fi + +if [ "$CTIMETESTS" = "yes" ] +then + if [ "$WITH_VALGRIND" = "yes" ]; then + ./libtool --mode=execute valgrind --error-exitcode=42 ./ctime_tests > ctime_tests.log 2>&1 + else + $EXEC ./ctime_tests > ctime_tests.log 2>&1 + fi +fi + +# Rebuild precomputed files (if not cross-compiling). +if [ -z "$HOST" ] +then + make clean-precomp clean-testvectors + make precomp testvectors +fi + +# Check that no repo files have been modified by the build. +# (This fails for example if the precomp files need to be updated in the repo.) +git diff --exit-code diff --git a/src/secp256k1/ci/linux-debian.Dockerfile b/src/secp256k1/ci/linux-debian.Dockerfile new file mode 100644 index 0000000000..a83a4e36db --- /dev/null +++ b/src/secp256k1/ci/linux-debian.Dockerfile @@ -0,0 +1,37 @@ +FROM debian:stable + +RUN dpkg --add-architecture i386 && \ + dpkg --add-architecture s390x && \ + dpkg --add-architecture armhf && \ + dpkg --add-architecture arm64 && \ + dpkg --add-architecture ppc64el + +# dkpg-dev: to make pkg-config work in cross-builds +# llvm: for llvm-symbolizer, which is used by clang's UBSan for symbolized stack traces +RUN apt-get update && apt-get install --no-install-recommends -y \ + git ca-certificates \ + make automake libtool pkg-config dpkg-dev valgrind qemu-user \ + gcc clang llvm libc6-dbg \ + g++ \ + gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan6:i386 \ + gcc-s390x-linux-gnu libc6-dev-s390x-cross libc6-dbg:s390x \ + gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \ + gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \ + gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross libc6-dbg:ppc64el \ + gcc-mingw-w64-x86-64-win32 wine64 wine \ + gcc-mingw-w64-i686-win32 wine32 \ + sagemath + +WORKDIR /root +# The "wine" package provides a convience wrapper that we need +RUN apt-get update && apt-get install --no-install-recommends -y \ + git ca-certificates wine64 wine python3-simplejson python3-six msitools winbind procps && \ + git clone https://github.com/mstorsjo/msvc-wine && \ + mkdir /opt/msvc && \ + python3 msvc-wine/vsdownload.py --accept-license --dest /opt/msvc Microsoft.VisualStudio.Workload.VCTools && \ + msvc-wine/install.sh /opt/msvc + +# Initialize the wine environment. Wait until the wineserver process has +# exited before closing the session, to avoid corrupting the wine prefix. +RUN wine64 wineboot --init && \ + while (ps -A | grep wineserver) > /dev/null; do sleep 1; done diff --git a/src/secp256k1/cmake/Check64bitAssembly.cmake b/src/secp256k1/cmake/Check64bitAssembly.cmake new file mode 100644 index 0000000000..3f65887765 --- /dev/null +++ b/src/secp256k1/cmake/Check64bitAssembly.cmake @@ -0,0 +1,14 @@ +include(CheckCSourceCompiles) + +function(check_64bit_assembly) + check_c_source_compiles(" + #include <stdint.h> + + int main() + { + uint64_t a = 11, tmp; + __asm__ __volatile__(\"movq $0x100000000,%1; mulq %%rsi\" : \"+a\"(a) : \"S\"(tmp) : \"cc\", \"%rdx\"); + } + " HAS_64BIT_ASM) + set(HAS_64BIT_ASM ${HAS_64BIT_ASM} PARENT_SCOPE) +endfunction() diff --git a/src/secp256k1/cmake/CheckStringOptionValue.cmake b/src/secp256k1/cmake/CheckStringOptionValue.cmake new file mode 100644 index 0000000000..bc4d7b5749 --- /dev/null +++ b/src/secp256k1/cmake/CheckStringOptionValue.cmake @@ -0,0 +1,12 @@ +function(check_string_option_value option) + get_property(expected_values CACHE ${option} PROPERTY STRINGS) + if(expected_values) + foreach(value IN LISTS expected_values) + if(value STREQUAL "${${option}}") + return() + endif() + endforeach() + message(FATAL_ERROR "${option} value is \"${${option}}\", but must be one of ${expected_values}.") + endif() + message(AUTHOR_WARNING "The STRINGS property must be set before invoking `check_string_option_value' function.") +endfunction() diff --git a/src/secp256k1/cmake/FindValgrind.cmake b/src/secp256k1/cmake/FindValgrind.cmake new file mode 100644 index 0000000000..f6c1f58649 --- /dev/null +++ b/src/secp256k1/cmake/FindValgrind.cmake @@ -0,0 +1,41 @@ +if(CMAKE_HOST_SYSTEM_NAME STREQUAL "Darwin") + find_program(BREW_COMMAND brew) + execute_process( + COMMAND ${BREW_COMMAND} --prefix valgrind + OUTPUT_VARIABLE valgrind_brew_prefix + ERROR_QUIET + OUTPUT_STRIP_TRAILING_WHITESPACE + ) +endif() + +set(hints_paths) +if(valgrind_brew_prefix) + set(hints_paths ${valgrind_brew_prefix}/include) +endif() + +find_path(Valgrind_INCLUDE_DIR + NAMES valgrind/memcheck.h + HINTS ${hints_paths} +) + +if(Valgrind_INCLUDE_DIR) + include(CheckCSourceCompiles) + set(CMAKE_REQUIRED_INCLUDES ${Valgrind_INCLUDE_DIR}) + check_c_source_compiles(" + #include <valgrind/memcheck.h> + #if defined(NVALGRIND) + # error \"Valgrind does not support this platform.\" + #endif + + int main() {} + " Valgrind_WORKS) +endif() + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(Valgrind + REQUIRED_VARS Valgrind_INCLUDE_DIR Valgrind_WORKS +) + +mark_as_advanced( + Valgrind_INCLUDE_DIR +) diff --git a/src/secp256k1/cmake/TryAddCompileOption.cmake b/src/secp256k1/cmake/TryAddCompileOption.cmake new file mode 100644 index 0000000000..f53c252c2d --- /dev/null +++ b/src/secp256k1/cmake/TryAddCompileOption.cmake @@ -0,0 +1,23 @@ +include(CheckCCompilerFlag) + +function(try_add_compile_option option) + string(MAKE_C_IDENTIFIER ${option} result) + string(TOUPPER ${result} result) + set(result "C_SUPPORTS${result}") + set(CMAKE_TRY_COMPILE_TARGET_TYPE STATIC_LIBRARY) + if(NOT MSVC) + set(CMAKE_REQUIRED_FLAGS "-Werror") + endif() + check_c_compiler_flag(${option} ${result}) + if(${result}) + get_property(compile_options + DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}" + PROPERTY COMPILE_OPTIONS + ) + list(APPEND compile_options "${option}") + set_property( + DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}" + PROPERTY COMPILE_OPTIONS "${compile_options}" + ) + endif() +endfunction() diff --git a/src/secp256k1/cmake/arm-linux-gnueabihf.toolchain.cmake b/src/secp256k1/cmake/arm-linux-gnueabihf.toolchain.cmake new file mode 100644 index 0000000000..0d91912b6d --- /dev/null +++ b/src/secp256k1/cmake/arm-linux-gnueabihf.toolchain.cmake @@ -0,0 +1,3 @@ +set(CMAKE_SYSTEM_NAME Linux) +set(CMAKE_SYSTEM_PROCESSOR arm) +set(CMAKE_C_COMPILER arm-linux-gnueabihf-gcc) diff --git a/src/secp256k1/cmake/config.cmake.in b/src/secp256k1/cmake/config.cmake.in new file mode 100644 index 0000000000..46b180ab19 --- /dev/null +++ b/src/secp256k1/cmake/config.cmake.in @@ -0,0 +1,5 @@ +@PACKAGE_INIT@ + +include("${CMAKE_CURRENT_LIST_DIR}/@PROJECT_NAME@-targets.cmake") + +check_required_components(@PROJECT_NAME@) diff --git a/src/secp256k1/cmake/x86_64-w64-mingw32.toolchain.cmake b/src/secp256k1/cmake/x86_64-w64-mingw32.toolchain.cmake new file mode 100644 index 0000000000..96119b72d1 --- /dev/null +++ b/src/secp256k1/cmake/x86_64-w64-mingw32.toolchain.cmake @@ -0,0 +1,3 @@ +set(CMAKE_SYSTEM_NAME Windows) +set(CMAKE_SYSTEM_PROCESSOR x86_64) +set(CMAKE_C_COMPILER x86_64-w64-mingw32-gcc) diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac new file mode 100644 index 0000000000..0b555eac67 --- /dev/null +++ b/src/secp256k1/configure.ac @@ -0,0 +1,474 @@ +AC_PREREQ([2.60]) + +# The package (a.k.a. release) version is based on semantic versioning 2.0.0 of +# the API. All changes in experimental modules are treated as +# backwards-compatible and therefore at most increase the minor version. +define(_PKG_VERSION_MAJOR, 0) +define(_PKG_VERSION_MINOR, 3) +define(_PKG_VERSION_PATCH, 2) +define(_PKG_VERSION_IS_RELEASE, false) + +# The library version is based on libtool versioning of the ABI. The set of +# rules for updating the version can be found here: +# https://www.gnu.org/software/libtool/manual/html_node/Updating-version-info.html +# All changes in experimental modules are treated as if they don't affect the +# interface and therefore only increase the revision. +define(_LIB_VERSION_CURRENT, 2) +define(_LIB_VERSION_REVISION, 2) +define(_LIB_VERSION_AGE, 0) + +AC_INIT([libsecp256k1],m4_join([.], _PKG_VERSION_MAJOR, _PKG_VERSION_MINOR, _PKG_VERSION_PATCH)m4_if(_PKG_VERSION_IS_RELEASE, [true], [], [-dev]),[https://github.com/bitcoin-core/secp256k1/issues],[libsecp256k1],[https://github.com/bitcoin-core/secp256k1]) + +AC_CONFIG_AUX_DIR([build-aux]) +AC_CONFIG_MACRO_DIR([build-aux/m4]) +AC_CANONICAL_HOST + +# Require Automake 1.11.2 for AM_PROG_AR +AM_INIT_AUTOMAKE([1.11.2 foreign subdir-objects]) + +# Make the compilation flags quiet unless V=1 is used. +m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])]) + +if test "${CFLAGS+set}" = "set"; then + CFLAGS_overridden=yes +else + CFLAGS_overridden=no +fi +AC_PROG_CC +AM_PROG_AS +AM_PROG_AR + +# Clear some cache variables as a workaround for a bug that appears due to a bad +# interaction between AM_PROG_AR and LT_INIT when combining MSVC's archiver lib.exe. +# https://debbugs.gnu.org/cgi/bugreport.cgi?bug=54421 +AS_UNSET(ac_cv_prog_AR) +AS_UNSET(ac_cv_prog_ac_ct_AR) +LT_INIT([win32-dll]) + +build_windows=no + +case $host_os in + *darwin*) + if test x$cross_compiling != xyes; then + AC_CHECK_PROG([BREW], brew, brew) + if test x$BREW = xbrew; then + # These Homebrew packages may be keg-only, meaning that they won't be found + # in expected paths because they may conflict with system files. Ask + # Homebrew where each one is located, then adjust paths accordingly. + if $BREW list --versions valgrind >/dev/null; then + valgrind_prefix=$($BREW --prefix valgrind 2>/dev/null) + VALGRIND_CPPFLAGS="-I$valgrind_prefix/include" + fi + else + AC_CHECK_PROG([PORT], port, port) + # If homebrew isn't installed and macports is, add the macports default paths + # as a last resort. + if test x$PORT = xport; then + CPPFLAGS="$CPPFLAGS -isystem /opt/local/include" + LDFLAGS="$LDFLAGS -L/opt/local/lib" + fi + fi + fi + ;; + cygwin*|mingw*) + build_windows=yes + ;; +esac + +# Try if some desirable compiler flags are supported and append them to SECP_CFLAGS. +# +# These are our own flags, so we append them to our own SECP_CFLAGS variable (instead of CFLAGS) as +# recommended in the automake manual (Section "Flag Variables Ordering"). CFLAGS belongs to the user +# and we are not supposed to touch it. In the Makefile, we will need to ensure that SECP_CFLAGS +# is prepended to CFLAGS when invoking the compiler so that the user always has the last word (flag). +# +# Another advantage of not touching CFLAGS is that the contents of CFLAGS will be picked up by +# libtool for compiling helper executables. For example, when compiling for Windows, libtool will +# generate entire wrapper executables (instead of simple wrapper scripts as on Unix) to ensure +# proper operation of uninstalled programs linked by libtool against the uninstalled shared library. +# These executables are compiled from C source file for which our flags may not be appropriate, +# e.g., -std=c89 flag has lead to undesirable warnings in the past. +# +# TODO We should analogously not touch CPPFLAGS and LDFLAGS but currently there are no issues. +AC_DEFUN([SECP_TRY_APPEND_DEFAULT_CFLAGS], [ + # GCC and compatible (incl. clang) + if test "x$GCC" = "xyes"; then + # Try to append -Werror to CFLAGS temporarily. Otherwise checks for some unsupported + # flags will succeed. + # Note that failure to append -Werror does not necessarily mean that -Werror is not + # supported. The compiler may already be warning about something unrelated, for example + # about some path issue. If that is the case, -Werror cannot be used because all + # of those warnings would be turned into errors. + SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS="$CFLAGS" + SECP_TRY_APPEND_CFLAGS([-Werror], CFLAGS) + + SECP_TRY_APPEND_CFLAGS([-std=c89 -pedantic -Wno-long-long -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef], $1) # GCC >= 3.0, -Wlong-long is implied by -pedantic. + SECP_TRY_APPEND_CFLAGS([-Wno-overlength-strings], $1) # GCC >= 4.2, -Woverlength-strings is implied by -pedantic. + SECP_TRY_APPEND_CFLAGS([-Wall], $1) # GCC >= 2.95 and probably many other compilers + SECP_TRY_APPEND_CFLAGS([-Wno-unused-function], $1) # GCC >= 3.0, -Wunused-function is implied by -Wall. + SECP_TRY_APPEND_CFLAGS([-Wextra], $1) # GCC >= 3.4, this is the newer name of -W, which we don't use because older GCCs will warn about unused functions. + SECP_TRY_APPEND_CFLAGS([-Wcast-align], $1) # GCC >= 2.95 + SECP_TRY_APPEND_CFLAGS([-Wcast-align=strict], $1) # GCC >= 8.0 + SECP_TRY_APPEND_CFLAGS([-Wconditional-uninitialized], $1) # Clang >= 3.0 only + SECP_TRY_APPEND_CFLAGS([-Wreserved-identifier], $1) # Clang >= 13.0 only + SECP_TRY_APPEND_CFLAGS([-fvisibility=hidden], $1) # GCC >= 4.0 + + CFLAGS="$SECP_TRY_APPEND_DEFAULT_CFLAGS_saved_CFLAGS" + fi + + # MSVC + # Assume MSVC if we're building for Windows but not with GCC or compatible; + # libtool makes the same assumption internally. + # Note that "/opt" and "-opt" are equivalent for MSVC; we use "-opt" because "/opt" looks like a path. + if test x"$GCC" != x"yes" && test x"$build_windows" = x"yes"; then + SECP_TRY_APPEND_CFLAGS([-W2 -wd4146], $1) # Moderate warning level, disable warning C4146 "unary minus operator applied to unsigned type, result still unsigned" + SECP_TRY_APPEND_CFLAGS([-external:anglebrackets -external:W0], $1) # Suppress warnings from #include <...> files + # We pass -ignore:4217 to the MSVC linker to suppress warning 4217 when + # importing variables from a statically linked secp256k1. + # (See the libtool manual, section "Windows DLLs" for background.) + # Unfortunately, libtool tries to be too clever and strips "-Xlinker arg" + # into "arg", so this will be " -Xlinker -ignore:4217" after stripping. + LDFLAGS="-Xlinker -Xlinker -Xlinker -ignore:4217 $LDFLAGS" + fi +]) +SECP_TRY_APPEND_DEFAULT_CFLAGS(SECP_CFLAGS) + +### +### Define config arguments +### + +# In dev mode, we enable all binaries and modules by default but individual options can still be overridden explicitly. +# Check for dev mode first because SECP_SET_DEFAULT needs enable_dev_mode set. +AC_ARG_ENABLE(dev_mode, [], [], + [enable_dev_mode=no]) + +AC_ARG_ENABLE(benchmark, + AS_HELP_STRING([--enable-benchmark],[compile benchmark [default=yes]]), [], + [SECP_SET_DEFAULT([enable_benchmark], [yes], [yes])]) + +AC_ARG_ENABLE(coverage, + AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis [default=no]]), [], + [SECP_SET_DEFAULT([enable_coverage], [no], [no])]) + +AC_ARG_ENABLE(tests, + AS_HELP_STRING([--enable-tests],[compile tests [default=yes]]), [], + [SECP_SET_DEFAULT([enable_tests], [yes], [yes])]) + +AC_ARG_ENABLE(ctime_tests, + AS_HELP_STRING([--enable-ctime-tests],[compile constant-time tests [default=yes if valgrind enabled]]), [], + [SECP_SET_DEFAULT([enable_ctime_tests], [auto], [auto])]) + +AC_ARG_ENABLE(experimental, + AS_HELP_STRING([--enable-experimental],[allow experimental configure options [default=no]]), [], + [SECP_SET_DEFAULT([enable_experimental], [no], [yes])]) + +AC_ARG_ENABLE(exhaustive_tests, + AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests [default=yes]]), [], + [SECP_SET_DEFAULT([enable_exhaustive_tests], [yes], [yes])]) + +AC_ARG_ENABLE(examples, + AS_HELP_STRING([--enable-examples],[compile the examples [default=no]]), [], + [SECP_SET_DEFAULT([enable_examples], [no], [yes])]) + +AC_ARG_ENABLE(module_ecdh, + AS_HELP_STRING([--enable-module-ecdh],[enable ECDH module [default=yes]]), [], + [SECP_SET_DEFAULT([enable_module_ecdh], [yes], [yes])]) + +AC_ARG_ENABLE(module_recovery, + AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module [default=no]]), [], + [SECP_SET_DEFAULT([enable_module_recovery], [no], [yes])]) + +AC_ARG_ENABLE(module_extrakeys, + AS_HELP_STRING([--enable-module-extrakeys],[enable extrakeys module [default=yes]]), [], + [SECP_SET_DEFAULT([enable_module_extrakeys], [yes], [yes])]) + +AC_ARG_ENABLE(module_schnorrsig, + AS_HELP_STRING([--enable-module-schnorrsig],[enable schnorrsig module [default=yes]]), [], + [SECP_SET_DEFAULT([enable_module_schnorrsig], [yes], [yes])]) + +AC_ARG_ENABLE(external_default_callbacks, + AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]), [], + [SECP_SET_DEFAULT([enable_external_default_callbacks], [no], [no])]) + +# Test-only override of the (autodetected by the C code) "widemul" setting. +# Legal values are: +# * int64 (for [u]int64_t), +# * int128 (for [unsigned] __int128), +# * int128_struct (for int128 implemented as a structure), +# * and auto (the default). +AC_ARG_WITH([test-override-wide-multiply], [] ,[set_widemul=$withval], [set_widemul=auto]) + +AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto], +[assembly optimizations to use (experimental: arm) [default=auto]])],[req_asm=$withval], [req_asm=auto]) + +AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto], +[window size for ecmult precomputation for verification, specified as integer in range [2..24].] +[Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.] +[The table will store 2^(SIZE-1) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.] +[A window size larger than 15 will require you delete the prebuilt precomputed_ecmult.c file so that it can be rebuilt.] +[For very large window sizes, use "make -j 1" to reduce memory use during compilation.] +["auto" is a reasonable setting for desktop machines (currently 15). [default=auto]] +)], +[req_ecmult_window=$withval], [req_ecmult_window=auto]) + +AC_ARG_WITH([ecmult-gen-precision], [AS_HELP_STRING([--with-ecmult-gen-precision=2|4|8|auto], +[Precision bits to tune the precomputed table size for signing.] +[The size of the table is 32kB for 2 bits, 64kB for 4 bits, 512kB for 8 bits of precision.] +[A larger table size usually results in possible faster signing.] +["auto" is a reasonable setting for desktop machines (currently 4). [default=auto]] +)], +[req_ecmult_gen_precision=$withval], [req_ecmult_gen_precision=auto]) + +AC_ARG_WITH([valgrind], [AS_HELP_STRING([--with-valgrind=yes|no|auto], +[Build with extra checks for running inside Valgrind [default=auto]] +)], +[req_valgrind=$withval], [req_valgrind=auto]) + +### +### Handle config options (except for modules) +### + +if test x"$req_valgrind" = x"no"; then + enable_valgrind=no +else + SECP_VALGRIND_CHECK + if test x"$has_valgrind" != x"yes"; then + if test x"$req_valgrind" = x"yes"; then + AC_MSG_ERROR([Valgrind support explicitly requested but valgrind/memcheck.h header not available]) + fi + enable_valgrind=no + else + enable_valgrind=yes + fi +fi + +if test x"$enable_ctime_tests" = x"auto"; then + enable_ctime_tests=$enable_valgrind +fi + +if test x"$enable_coverage" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DCOVERAGE=1" + SECP_CFLAGS="-O0 --coverage $SECP_CFLAGS" + # If coverage is enabled, and the user has not overridden CFLAGS, + # override Autoconf's value "-g -O2" with "-g". Otherwise we'd end up + # with "-O0 --coverage -g -O2". + if test "$CFLAGS_overridden" = "no"; then + CFLAGS="-g" + fi + LDFLAGS="--coverage $LDFLAGS" +else + # Most likely the CFLAGS already contain -O2 because that is autoconf's default. + # We still add it here because passing it twice is not an issue, and handling + # this case would just add unnecessary complexity (see #896). + SECP_CFLAGS="-O2 $SECP_CFLAGS" +fi + +if test x"$req_asm" = x"auto"; then + SECP_64BIT_ASM_CHECK + if test x"$has_64bit_asm" = x"yes"; then + set_asm=x86_64 + fi + if test x"$set_asm" = x; then + set_asm=no + fi +else + set_asm=$req_asm + case $set_asm in + x86_64) + SECP_64BIT_ASM_CHECK + if test x"$has_64bit_asm" != x"yes"; then + AC_MSG_ERROR([x86_64 assembly optimization requested but not available]) + fi + ;; + arm) + ;; + no) + ;; + *) + AC_MSG_ERROR([invalid assembly optimization selection]) + ;; + esac +fi + +# Select assembly optimization +enable_external_asm=no + +case $set_asm in +x86_64) + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_ASM_X86_64=1" + ;; +arm) + enable_external_asm=yes + ;; +no) + ;; +*) + AC_MSG_ERROR([invalid assembly optimizations]) + ;; +esac + +if test x"$enable_external_asm" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_EXTERNAL_ASM=1" +fi + + +# Select wide multiplication implementation +case $set_widemul in +int128_struct) + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_FORCE_WIDEMUL_INT128_STRUCT=1" + ;; +int128) + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_FORCE_WIDEMUL_INT128=1" + ;; +int64) + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_FORCE_WIDEMUL_INT64=1" + ;; +auto) + ;; +*) + AC_MSG_ERROR([invalid wide multiplication implementation]) + ;; +esac + +# Set ecmult window size +if test x"$req_ecmult_window" = x"auto"; then + set_ecmult_window=15 +else + set_ecmult_window=$req_ecmult_window +fi + +error_window_size=['window size for ecmult precomputation not an integer in range [2..24] or "auto"'] +case $set_ecmult_window in +''|*[[!0-9]]*) + # no valid integer + AC_MSG_ERROR($error_window_size) + ;; +*) + if test "$set_ecmult_window" -lt 2 -o "$set_ecmult_window" -gt 24 ; then + # not in range + AC_MSG_ERROR($error_window_size) + fi + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DECMULT_WINDOW_SIZE=$set_ecmult_window" + ;; +esac + +# Set ecmult gen precision +if test x"$req_ecmult_gen_precision" = x"auto"; then + set_ecmult_gen_precision=4 +else + set_ecmult_gen_precision=$req_ecmult_gen_precision +fi + +case $set_ecmult_gen_precision in +2|4|8) + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DECMULT_GEN_PREC_BITS=$set_ecmult_gen_precision" + ;; +*) + AC_MSG_ERROR(['ecmult gen precision not 2, 4, 8 or "auto"']) + ;; +esac + +if test x"$enable_valgrind" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES $VALGRIND_CPPFLAGS -DVALGRIND" +fi + +# Add -Werror and similar flags passed from the outside (for testing, e.g., in CI). +# We don't want to set the user variable CFLAGS in CI because this would disable +# autoconf's logic for setting default CFLAGS, which we would like to test in CI. +SECP_CFLAGS="$SECP_CFLAGS $WERROR_CFLAGS" + +### +### Handle module options +### + +if test x"$enable_module_ecdh" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DENABLE_MODULE_ECDH=1" +fi + +if test x"$enable_module_recovery" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DENABLE_MODULE_RECOVERY=1" +fi + +if test x"$enable_module_schnorrsig" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DENABLE_MODULE_SCHNORRSIG=1" + enable_module_extrakeys=yes +fi + +# Test if extrakeys is set after the schnorrsig module to allow the schnorrsig +# module to set enable_module_extrakeys=yes +if test x"$enable_module_extrakeys" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DENABLE_MODULE_EXTRAKEYS=1" +fi + +if test x"$enable_external_default_callbacks" = x"yes"; then + SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_EXTERNAL_DEFAULT_CALLBACKS=1" +fi + +### +### Check for --enable-experimental if necessary +### + +if test x"$enable_experimental" = x"yes"; then + AC_MSG_NOTICE([******]) + AC_MSG_NOTICE([WARNING: experimental build]) + AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.]) + AC_MSG_NOTICE([******]) +else + if test x"$set_asm" = x"arm"; then + AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.]) + fi +fi + +### +### Generate output +### + +AC_CONFIG_FILES([Makefile libsecp256k1.pc]) +AC_SUBST(SECP_CFLAGS) +AC_SUBST(SECP_CONFIG_DEFINES) +AM_CONDITIONAL([ENABLE_COVERAGE], [test x"$enable_coverage" = x"yes"]) +AM_CONDITIONAL([USE_TESTS], [test x"$enable_tests" != x"no"]) +AM_CONDITIONAL([USE_CTIME_TESTS], [test x"$enable_ctime_tests" = x"yes"]) +AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$enable_exhaustive_tests" != x"no"]) +AM_CONDITIONAL([USE_EXAMPLES], [test x"$enable_examples" != x"no"]) +AM_CONDITIONAL([USE_BENCHMARK], [test x"$enable_benchmark" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_EXTRAKEYS], [test x"$enable_module_extrakeys" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = x"yes"]) +AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$enable_external_asm" = x"yes"]) +AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"]) +AM_CONDITIONAL([BUILD_WINDOWS], [test "$build_windows" = "yes"]) +AC_SUBST(LIB_VERSION_CURRENT, _LIB_VERSION_CURRENT) +AC_SUBST(LIB_VERSION_REVISION, _LIB_VERSION_REVISION) +AC_SUBST(LIB_VERSION_AGE, _LIB_VERSION_AGE) + +AC_OUTPUT + +echo +echo "Build Options:" +echo " with external callbacks = $enable_external_default_callbacks" +echo " with benchmarks = $enable_benchmark" +echo " with tests = $enable_tests" +echo " with ctime tests = $enable_ctime_tests" +echo " with coverage = $enable_coverage" +echo " with examples = $enable_examples" +echo " module ecdh = $enable_module_ecdh" +echo " module recovery = $enable_module_recovery" +echo " module extrakeys = $enable_module_extrakeys" +echo " module schnorrsig = $enable_module_schnorrsig" +echo +echo " asm = $set_asm" +echo " ecmult window size = $set_ecmult_window" +echo " ecmult gen prec. bits = $set_ecmult_gen_precision" +# Hide test-only options unless they're used. +if test x"$set_widemul" != xauto; then +echo " wide multiplication = $set_widemul" +fi +echo +echo " valgrind = $enable_valgrind" +echo " CC = $CC" +echo " CPPFLAGS = $CPPFLAGS" +echo " SECP_CFLAGS = $SECP_CFLAGS" +echo " CFLAGS = $CFLAGS" +echo " LDFLAGS = $LDFLAGS" diff --git a/src/secp256k1/contrib/lax_der_parsing.c b/src/secp256k1/contrib/lax_der_parsing.c new file mode 100644 index 0000000000..bf562303ed --- /dev/null +++ b/src/secp256k1/contrib/lax_der_parsing.c @@ -0,0 +1,148 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <string.h> + +#include "lax_der_parsing.h" + +int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + size_t rpos, rlen, spos, slen; + size_t pos = 0; + size_t lenbyte; + unsigned char tmpsig[64] = {0}; + int overflow = 0; + + /* Hack to initialize sig with a correctly-parsed but invalid signature. */ + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + + /* Sequence tag byte */ + if (pos == inputlen || input[pos] != 0x30) { + return 0; + } + pos++; + + /* Sequence length bytes */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + pos += lenbyte; + } + + /* Integer tag byte for R */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for R */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + rlen = 0; + while (lenbyte > 0) { + rlen = (rlen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + rlen = lenbyte; + } + if (rlen > inputlen - pos) { + return 0; + } + rpos = pos; + pos += rlen; + + /* Integer tag byte for S */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for S */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + slen = 0; + while (lenbyte > 0) { + slen = (slen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + slen = lenbyte; + } + if (slen > inputlen - pos) { + return 0; + } + spos = pos; + + /* Ignore leading zeroes in R */ + while (rlen > 0 && input[rpos] == 0) { + rlen--; + rpos++; + } + /* Copy R value */ + if (rlen > 32) { + overflow = 1; + } else if (rlen) { + memcpy(tmpsig + 32 - rlen, input + rpos, rlen); + } + + /* Ignore leading zeroes in S */ + while (slen > 0 && input[spos] == 0) { + slen--; + spos++; + } + /* Copy S value */ + if (slen > 32) { + overflow = 1; + } else if (slen) { + memcpy(tmpsig + 64 - slen, input + spos, slen); + } + + if (!overflow) { + overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + if (overflow) { + memset(tmpsig, 0, 64); + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + return 1; +} + diff --git a/src/secp256k1/contrib/lax_der_parsing.h b/src/secp256k1/contrib/lax_der_parsing.h new file mode 100644 index 0000000000..034a38e6a0 --- /dev/null +++ b/src/secp256k1/contrib/lax_der_parsing.h @@ -0,0 +1,97 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file defines a function that parses DER with various errors and + * violations. This is not a part of the library itself, because the allowed + * violations are chosen arbitrarily and do not follow or establish any + * standard. + * + * In many places it matters that different implementations do not only accept + * the same set of valid signatures, but also reject the same set of signatures. + * The only means to accomplish that is by strictly obeying a standard, and not + * accepting anything else. + * + * Nonetheless, sometimes there is a need for compatibility with systems that + * use signatures which do not strictly obey DER. The snippet below shows how + * certain violations are easily supported. You may need to adapt it. + * + * Do not use this for new systems. Use well-defined DER or compact signatures + * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and + * secp256k1_ecdsa_signature_parse_compact). + * + * The supported violations are: + * - All numbers are parsed as nonnegative integers, even though X.609-0207 + * section 8.3.3 specifies that integers are always encoded as two's + * complement. + * - Integers can have length 0, even though section 8.3.1 says they can't. + * - Integers with overly long padding are accepted, violation section + * 8.3.2. + * - 127-byte long length descriptors are accepted, even though section + * 8.1.3.5.c says that they are not. + * - Trailing garbage data inside or after the signature is ignored. + * - The length descriptor of the sequence is ignored. + * + * Compared to for example OpenSSL, many violations are NOT supported: + * - Using overly long tag descriptors for the sequence or integers inside, + * violating section 8.1.2.2. + * - Encoding primitive integers as constructed values, violating section + * 8.3.1. + */ + +#ifndef SECP256K1_CONTRIB_LAX_DER_PARSING_H +#define SECP256K1_CONTRIB_LAX_DER_PARSING_H + +/* #include secp256k1.h only when it hasn't been included yet. + This enables this file to be #included directly in other project + files (such as tests.c) without the need to set an explicit -I flag, + which would be necessary to locate secp256k1.h. */ +#ifndef SECP256K1_H +#include <secp256k1.h> +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +/** Parse a signature in "lax DER" format + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. In addition, it will accept signatures + * which violate the DER spec in various ways. Its purpose is to allow + * validation of the Bitcoin blockchain, which includes non-DER signatures + * from before the network rules were updated to enforce DER. Note that + * the set of supported violations is a strict subset of what OpenSSL will + * accept. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +int ecdsa_signature_parse_der_lax( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_LAX_DER_PARSING_H */ diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.c b/src/secp256k1/contrib/lax_der_privatekey_parsing.c new file mode 100644 index 0000000000..a1b8200079 --- /dev/null +++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.c @@ -0,0 +1,112 @@ +/*********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <string.h> + +#include "lax_der_privatekey_parsing.h" + +int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) { + const unsigned char *end = privkey + privkeylen; + int lenb = 0; + int len = 0; + memset(out32, 0, 32); + /* sequence header */ + if (end < privkey+1 || *privkey != 0x30) { + return 0; + } + privkey++; + /* sequence length constructor */ + if (end < privkey+1 || !(*privkey & 0x80)) { + return 0; + } + lenb = *privkey & ~0x80; privkey++; + if (lenb < 1 || lenb > 2) { + return 0; + } + if (end < privkey+lenb) { + return 0; + } + /* sequence length */ + len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0); + privkey += lenb; + if (end < privkey+len) { + return 0; + } + /* sequence element 0: version number (=1) */ + if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) { + return 0; + } + privkey += 3; + /* sequence element 1: octet string, up to 32 bytes */ + if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) { + return 0; + } + if (privkey[1]) memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]); + if (!secp256k1_ec_seckey_verify(ctx, out32)) { + memset(out32, 0, 32); + return 0; + } + return 1; +} + +int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) { + secp256k1_pubkey pubkey; + size_t pubkeylen = 0; + if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) { + *privkeylen = 0; + return 0; + } + if (compressed) { + static const unsigned char begin[] = { + 0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 33; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } else { + static const unsigned char begin[] = { + 0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11, + 0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10, + 0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 65; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } + return 1; +} diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.h b/src/secp256k1/contrib/lax_der_privatekey_parsing.h new file mode 100644 index 0000000000..3749e418fe --- /dev/null +++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.h @@ -0,0 +1,95 @@ +/*********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file contains code snippets that parse DER private keys with + * various errors and violations. This is not a part of the library + * itself, because the allowed violations are chosen arbitrarily and + * do not follow or establish any standard. + * + * It also contains code to serialize private keys in a compatible + * manner. + * + * These functions are meant for compatibility with applications + * that require BER encoded keys. When working with secp256k1-specific + * code, the simple 32-byte private keys normally used by the + * library are sufficient. + */ + +#ifndef SECP256K1_CONTRIB_BER_PRIVATEKEY_H +#define SECP256K1_CONTRIB_BER_PRIVATEKEY_H + +/* #include secp256k1.h only when it hasn't been included yet. + This enables this file to be #included directly in other project + files (such as tests.c) without the need to set an explicit -I flag, + which would be necessary to locate secp256k1.h. */ +#ifndef SECP256K1_H +#include <secp256k1.h> +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +/** Export a private key in DER format. + * + * Returns: 1 if the private key was valid. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: privkey: pointer to an array for storing the private key in BER. + * Should have space for 279 bytes, and cannot be NULL. + * privkeylen: Pointer to an int where the length of the private key in + * privkey will be stored. + * In: seckey: pointer to a 32-byte secret key to export. + * compressed: 1 if the key should be exported in + * compressed format, 0 otherwise + * + * This function is purely meant for compatibility with applications that + * require BER encoded keys. When working with secp256k1-specific code, the + * simple 32-byte private keys are sufficient. + * + * Note that this function does not guarantee correct DER output. It is + * guaranteed to be parsable by secp256k1_ec_privkey_import_der + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der( + const secp256k1_context* ctx, + unsigned char *privkey, + size_t *privkeylen, + const unsigned char *seckey, + int compressed +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Import a private key in DER format. + * Returns: 1 if a private key was extracted. + * Args: ctx: pointer to a context object (cannot be NULL). + * Out: seckey: pointer to a 32-byte array for storing the private key. + * (cannot be NULL). + * In: privkey: pointer to a private key in DER format (cannot be NULL). + * privkeylen: length of the DER private key pointed to be privkey. + * + * This function will accept more than just strict DER, and even allow some BER + * violations. The public key stored inside the DER-encoded private key is not + * verified for correctness, nor are the curve parameters. Use this function + * only if you know in advance it is supposed to contain a secp256k1 private + * key. + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *privkey, + size_t privkeylen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_BER_PRIVATEKEY_H */ diff --git a/src/secp256k1/doc/release-process.md b/src/secp256k1/doc/release-process.md new file mode 100644 index 0000000000..70a35f0910 --- /dev/null +++ b/src/secp256k1/doc/release-process.md @@ -0,0 +1,59 @@ +# Release Process + +This document outlines the process for releasing versions of the form `$MAJOR.$MINOR.$PATCH`. + +We distinguish between two types of releases: *regular* and *maintenance* releases. +Regular releases are releases of a new major or minor version as well as patches of the most recent release. +Maintenance releases, on the other hand, are required for patches of older releases. + +You should coordinate with the other maintainers on the release date, if possible. +This date will be part of the release entry in [CHANGELOG.md](../CHANGELOG.md) and it should match the dates of the remaining steps in the release process (including the date of the tag and the GitHub release). +It is best if the maintainers are present during the release, so they can help ensure that the process is followed correctly and, in the case of a regular release, they are aware that they should not modify the master branch between merging the PR in step 1 and the PR in step 3. + +This process also assumes that there will be no minor releases for old major releases. + +## Regular release + +1. Open a PR to the master branch with a commit (using message `"release: prepare for $MAJOR.$MINOR.$PATCH"`, for example) that + * finalizes the release notes in [CHANGELOG.md](../CHANGELOG.md) (make sure to include an entry for `### ABI Compatibility`), + * updates `_PKG_VERSION_*` and `_LIB_VERSION_*` and sets `_PKG_VERSION_IS_RELEASE` to `true` in `configure.ac`, and + * updates `project(libsecp256k1 VERSION ...)` and `${PROJECT_NAME}_LIB_VERSION_*` in `CMakeLists.txt`. +2. After the PR is merged, tag the commit and push it: + ``` + RELEASE_COMMIT=<merge commit of step 1> + git tag -s v$MAJOR.$MINOR.$PATCH -m "libsecp256k1 $MAJOR.$MINOR.$PATCH" $RELEASE_COMMIT + git push git@github.com:bitcoin-core/secp256k1.git v$MAJOR.$MINOR.$PATCH + ``` +3. Open a PR to the master branch with a commit (using message `"release cleanup: bump version after $MAJOR.$MINOR.$PATCH"`, for example) that + * sets `_PKG_VERSION_IS_RELEASE` to `false` and increments `_PKG_VERSION_PATCH` and `_LIB_VERSION_REVISION` in `configure.ac`, and + * increments the `$PATCH` component of `project(libsecp256k1 VERSION ...)` and `${PROJECT_NAME}_LIB_VERSION_REVISION` in `CMakeLists.txt`. + + If other maintainers are not present to approve the PR, it can be merged without ACKs. +4. Create a new GitHub release with a link to the corresponding entry in [CHANGELOG.md](../CHANGELOG.md). + +## Maintenance release + +Note that bugfixes only need to be backported to releases for which no compatible release without the bug exists. + +1. If `$PATCH = 1`, create maintenance branch `$MAJOR.$MINOR`: + ``` + git checkout -b $MAJOR.$MINOR v$MAJOR.$MINOR.0 + git push git@github.com:bitcoin-core/secp256k1.git $MAJOR.$MINOR + ``` +2. Open a pull request to the `$MAJOR.$MINOR` branch that + * includes the bugfixes, + * finalizes the release notes, + * increments `_PKG_VERSION_PATCH` and `_LIB_VERSION_REVISION` in `configure.ac` + and the `$PATCH` component of `project(libsecp256k1 VERSION ...)` and `${PROJECT_NAME}_LIB_VERSION_REVISION` in `CMakeLists.txt` + (with commit message `"release: bump versions for $MAJOR.$MINOR.$PATCH"`, for example). +3. After the PRs are merged, update the release branch and tag the commit: + ``` + git checkout $MAJOR.$MINOR && git pull + git tag -s v$MAJOR.$MINOR.$PATCH -m "libsecp256k1 $MAJOR.$MINOR.$PATCH" + ``` +4. Push tag: + ``` + git push git@github.com:bitcoin-core/secp256k1.git v$MAJOR.$MINOR.$PATCH + ``` +5. Create a new GitHub release with a link to the corresponding entry in [CHANGELOG.md](../CHANGELOG.md). +6. Open PR to the master branch that includes a commit (with commit message `"release notes: add $MAJOR.$MINOR.$PATCH"`, for example) that adds release notes to [CHANGELOG.md](../CHANGELOG.md). diff --git a/src/secp256k1/doc/safegcd_implementation.md b/src/secp256k1/doc/safegcd_implementation.md new file mode 100644 index 0000000000..5dbbb7bbd2 --- /dev/null +++ b/src/secp256k1/doc/safegcd_implementation.md @@ -0,0 +1,819 @@ +# The safegcd implementation in libsecp256k1 explained + +This document explains the modular inverse and Jacobi symbol implementations in the `src/modinv*.h` files. +It is based on the paper +["Fast constant-time gcd computation and modular inversion"](https://gcd.cr.yp.to/papers.html#safegcd) +by Daniel J. Bernstein and Bo-Yin Yang. The references below are for the Date: 2019.04.13 version. + +The actual implementation is in C of course, but for demonstration purposes Python3 is used here. +Most implementation aspects and optimizations are explained, except those that depend on the specific +number representation used in the C code. + +## 1. Computing the Greatest Common Divisor (GCD) using divsteps + +The algorithm from the paper (section 11), at a very high level, is this: + +```python +def gcd(f, g): + """Compute the GCD of an odd integer f and another integer g.""" + assert f & 1 # require f to be odd + delta = 1 # additional state variable + while g != 0: + assert f & 1 # f will be odd in every iteration + if delta > 0 and g & 1: + delta, f, g = 1 - delta, g, (g - f) // 2 + elif g & 1: + delta, f, g = 1 + delta, f, (g + f) // 2 + else: + delta, f, g = 1 + delta, f, (g ) // 2 + return abs(f) +``` + +It computes the greatest common divisor of an odd integer *f* and any integer *g*. Its inner loop +keeps rewriting the variables *f* and *g* alongside a state variable *δ* that starts at *1*, until +*g=0* is reached. At that point, *|f|* gives the GCD. Each of the transitions in the loop is called a +"division step" (referred to as divstep in what follows). + +For example, *gcd(21, 14)* would be computed as: +- Start with *δ=1 f=21 g=14* +- Take the third branch: *δ=2 f=21 g=7* +- Take the first branch: *δ=-1 f=7 g=-7* +- Take the second branch: *δ=0 f=7 g=0* +- The answer *|f| = 7*. + +Why it works: +- Divsteps can be decomposed into two steps (see paragraph 8.2 in the paper): + - (a) If *g* is odd, replace *(f,g)* with *(g,g-f)* or (f,g+f), resulting in an even *g*. + - (b) Replace *(f,g)* with *(f,g/2)* (where *g* is guaranteed to be even). +- Neither of those two operations change the GCD: + - For (a), assume *gcd(f,g)=c*, then it must be the case that *f=a c* and *g=b c* for some integers *a* + and *b*. As *(g,g-f)=(b c,(b-a)c)* and *(f,f+g)=(a c,(a+b)c)*, the result clearly still has + common factor *c*. Reasoning in the other direction shows that no common factor can be added by + doing so either. + - For (b), we know that *f* is odd, so *gcd(f,g)* clearly has no factor *2*, and we can remove + it from *g*. +- The algorithm will eventually converge to *g=0*. This is proven in the paper (see theorem G.3). +- It follows that eventually we find a final value *f'* for which *gcd(f,g) = gcd(f',0)*. As the + gcd of *f'* and *0* is *|f'|* by definition, that is our answer. + +Compared to more [traditional GCD algorithms](https://en.wikipedia.org/wiki/Euclidean_algorithm), this one has the property of only ever looking at +the low-order bits of the variables to decide the next steps, and being easy to make +constant-time (in more low-level languages than Python). The *δ* parameter is necessary to +guide the algorithm towards shrinking the numbers' magnitudes without explicitly needing to look +at high order bits. + +Properties that will become important later: +- Performing more divsteps than needed is not a problem, as *f* does not change anymore after *g=0*. +- Only even numbers are divided by *2*. This means that when reasoning about it algebraically we + do not need to worry about rounding. +- At every point during the algorithm's execution the next *N* steps only depend on the bottom *N* + bits of *f* and *g*, and on *δ*. + + +## 2. From GCDs to modular inverses + +We want an algorithm to compute the inverse *a* of *x* modulo *M*, i.e. the number a such that *a x=1 +mod M*. This inverse only exists if the GCD of *x* and *M* is *1*, but that is always the case if *M* is +prime and *0 < x < M*. In what follows, assume that the modular inverse exists. +It turns out this inverse can be computed as a side effect of computing the GCD by keeping track +of how the internal variables can be written as linear combinations of the inputs at every step +(see the [extended Euclidean algorithm](https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm)). +Since the GCD is *1*, such an algorithm will compute numbers *a* and *b* such that a x + b M = 1*. +Taking that expression *mod M* gives *a x mod M = 1*, and we see that *a* is the modular inverse of *x +mod M*. + +A similar approach can be used to calculate modular inverses using the divsteps-based GCD +algorithm shown above, if the modulus *M* is odd. To do so, compute *gcd(f=M,g=x)*, while keeping +track of extra variables *d* and *e*, for which at every step *d = f/x (mod M)* and *e = g/x (mod M)*. +*f/x* here means the number which multiplied with *x* gives *f mod M*. As *f* and *g* are initialized to *M* +and *x* respectively, *d* and *e* just start off being *0* (*M/x mod M = 0/x mod M = 0*) and *1* (*x/x mod M += 1*). + +```python +def div2(M, x): + """Helper routine to compute x/2 mod M (where M is odd).""" + assert M & 1 + if x & 1: # If x is odd, make it even by adding M. + x += M + # x must be even now, so a clean division by 2 is possible. + return x // 2 + +def modinv(M, x): + """Compute the inverse of x mod M (given that it exists, and M is odd).""" + assert M & 1 + delta, f, g, d, e = 1, M, x, 0, 1 + while g != 0: + # Note that while division by two for f and g is only ever done on even inputs, this is + # not true for d and e, so we need the div2 helper function. + if delta > 0 and g & 1: + delta, f, g, d, e = 1 - delta, g, (g - f) // 2, e, div2(M, e - d) + elif g & 1: + delta, f, g, d, e = 1 + delta, f, (g + f) // 2, d, div2(M, e + d) + else: + delta, f, g, d, e = 1 + delta, f, (g ) // 2, d, div2(M, e ) + # Verify that the invariants d=f/x mod M, e=g/x mod M are maintained. + assert f % M == (d * x) % M + assert g % M == (e * x) % M + assert f == 1 or f == -1 # |f| is the GCD, it must be 1 + # Because of invariant d = f/x (mod M), 1/x = d/f (mod M). As |f|=1, d/f = d*f. + return (d * f) % M +``` + +Also note that this approach to track *d* and *e* throughout the computation to determine the inverse +is different from the paper. There (see paragraph 12.1 in the paper) a transition matrix for the +entire computation is determined (see section 3 below) and the inverse is computed from that. +The approach here avoids the need for 2x2 matrix multiplications of various sizes, and appears to +be faster at the level of optimization we're able to do in C. + + +## 3. Batching multiple divsteps + +Every divstep can be expressed as a matrix multiplication, applying a transition matrix *(1/2 t)* +to both vectors *[f, g]* and *[d, e]* (see paragraph 8.1 in the paper): + +``` + t = [ u, v ] + [ q, r ] + + [ out_f ] = (1/2 * t) * [ in_f ] + [ out_g ] = [ in_g ] + + [ out_d ] = (1/2 * t) * [ in_d ] (mod M) + [ out_e ] [ in_e ] +``` + +where *(u, v, q, r)* is *(0, 2, -1, 1)*, *(2, 0, 1, 1)*, or *(2, 0, 0, 1)*, depending on which branch is +taken. As above, the resulting *f* and *g* are always integers. + +Performing multiple divsteps corresponds to a multiplication with the product of all the +individual divsteps' transition matrices. As each transition matrix consists of integers +divided by *2*, the product of these matrices will consist of integers divided by *2<sup>N</sup>* (see also +theorem 9.2 in the paper). These divisions are expensive when updating *d* and *e*, so we delay +them: we compute the integer coefficients of the combined transition matrix scaled by *2<sup>N</sup>*, and +do one division by *2<sup>N</sup>* as a final step: + +```python +def divsteps_n_matrix(delta, f, g): + """Compute delta and transition matrix t after N divsteps (multiplied by 2^N).""" + u, v, q, r = 1, 0, 0, 1 # start with identity matrix + for _ in range(N): + if delta > 0 and g & 1: + delta, f, g, u, v, q, r = 1 - delta, g, (g - f) // 2, 2*q, 2*r, q-u, r-v + elif g & 1: + delta, f, g, u, v, q, r = 1 + delta, f, (g + f) // 2, 2*u, 2*v, q+u, r+v + else: + delta, f, g, u, v, q, r = 1 + delta, f, (g ) // 2, 2*u, 2*v, q , r + return delta, (u, v, q, r) +``` + +As the branches in the divsteps are completely determined by the bottom *N* bits of *f* and *g*, this +function to compute the transition matrix only needs to see those bottom bits. Furthermore all +intermediate results and outputs fit in *(N+1)*-bit numbers (unsigned for *f* and *g*; signed for *u*, *v*, +*q*, and *r*) (see also paragraph 8.3 in the paper). This means that an implementation using 64-bit +integers could set *N=62* and compute the full transition matrix for 62 steps at once without any +big integer arithmetic at all. This is the reason why this algorithm is efficient: it only needs +to update the full-size *f*, *g*, *d*, and *e* numbers once every *N* steps. + +We still need functions to compute: + +``` + [ out_f ] = (1/2^N * [ u, v ]) * [ in_f ] + [ out_g ] ( [ q, r ]) [ in_g ] + + [ out_d ] = (1/2^N * [ u, v ]) * [ in_d ] (mod M) + [ out_e ] ( [ q, r ]) [ in_e ] +``` + +Because the divsteps transformation only ever divides even numbers by two, the result of *t [f,g]* is always even. When *t* is a composition of *N* divsteps, it follows that the resulting *f* +and *g* will be multiple of *2<sup>N</sup>*, and division by *2<sup>N</sup>* is simply shifting them down: + +```python +def update_fg(f, g, t): + """Multiply matrix t/2^N with [f, g].""" + u, v, q, r = t + cf, cg = u*f + v*g, q*f + r*g + # (t / 2^N) should cleanly apply to [f,g] so the result of t*[f,g] should have N zero + # bottom bits. + assert cf % 2**N == 0 + assert cg % 2**N == 0 + return cf >> N, cg >> N +``` + +The same is not true for *d* and *e*, and we need an equivalent of the `div2` function for division by *2<sup>N</sup> mod M*. +This is easy if we have precomputed *1/M mod 2<sup>N</sup>* (which always exists for odd *M*): + +```python +def div2n(M, Mi, x): + """Compute x/2^N mod M, given Mi = 1/M mod 2^N.""" + assert (M * Mi) % 2**N == 1 + # Find a factor m such that m*M has the same bottom N bits as x. We want: + # (m * M) mod 2^N = x mod 2^N + # <=> m mod 2^N = (x / M) mod 2^N + # <=> m mod 2^N = (x * Mi) mod 2^N + m = (Mi * x) % 2**N + # Subtract that multiple from x, cancelling its bottom N bits. + x -= m * M + # Now a clean division by 2^N is possible. + assert x % 2**N == 0 + return (x >> N) % M + +def update_de(d, e, t, M, Mi): + """Multiply matrix t/2^N with [d, e], modulo M.""" + u, v, q, r = t + cd, ce = u*d + v*e, q*d + r*e + return div2n(M, Mi, cd), div2n(M, Mi, ce) +``` + +With all of those, we can write a version of `modinv` that performs *N* divsteps at once: + +```python3 +def modinv(M, Mi, x): + """Compute the modular inverse of x mod M, given Mi=1/M mod 2^N.""" + assert M & 1 + delta, f, g, d, e = 1, M, x, 0, 1 + while g != 0: + # Compute the delta and transition matrix t for the next N divsteps (this only needs + # (N+1)-bit signed integer arithmetic). + delta, t = divsteps_n_matrix(delta, f % 2**N, g % 2**N) + # Apply the transition matrix t to [f, g]: + f, g = update_fg(f, g, t) + # Apply the transition matrix t to [d, e]: + d, e = update_de(d, e, t, M, Mi) + return (d * f) % M +``` + +This means that in practice we'll always perform a multiple of *N* divsteps. This is not a problem +because once *g=0*, further divsteps do not affect *f*, *g*, *d*, or *e* anymore (only *δ* keeps +increasing). For variable time code such excess iterations will be mostly optimized away in later +sections. + + +## 4. Avoiding modulus operations + +So far, there are two places where we compute a remainder of big numbers modulo *M*: at the end of +`div2n` in every `update_de`, and at the very end of `modinv` after potentially negating *d* due to the +sign of *f*. These are relatively expensive operations when done generically. + +To deal with the modulus operation in `div2n`, we simply stop requiring *d* and *e* to be in range +*[0,M)* all the time. Let's start by inlining `div2n` into `update_de`, and dropping the modulus +operation at the end: + +```python +def update_de(d, e, t, M, Mi): + """Multiply matrix t/2^N with [d, e] mod M, given Mi=1/M mod 2^N.""" + u, v, q, r = t + cd, ce = u*d + v*e, q*d + r*e + # Cancel out bottom N bits of cd and ce. + md = -((Mi * cd) % 2**N) + me = -((Mi * ce) % 2**N) + cd += md * M + ce += me * M + # And cleanly divide by 2**N. + return cd >> N, ce >> N +``` + +Let's look at bounds on the ranges of these numbers. It can be shown that *|u|+|v|* and *|q|+|r|* +never exceed *2<sup>N</sup>* (see paragraph 8.3 in the paper), and thus a multiplication with *t* will have +outputs whose absolute values are at most *2<sup>N</sup>* times the maximum absolute input value. In case the +inputs *d* and *e* are in *(-M,M)*, which is certainly true for the initial values *d=0* and *e=1* assuming +*M > 1*, the multiplication results in numbers in range *(-2<sup>N</sup>M,2<sup>N</sup>M)*. Subtracting less than *2<sup>N</sup>* +times *M* to cancel out *N* bits brings that up to *(-2<sup>N+1</sup>M,2<sup>N</sup>M)*, and +dividing by *2<sup>N</sup>* at the end takes it to *(-2M,M)*. Another application of `update_de` would take that +to *(-3M,2M)*, and so forth. This progressive expansion of the variables' ranges can be +counteracted by incrementing *d* and *e* by *M* whenever they're negative: + +```python + ... + if d < 0: + d += M + if e < 0: + e += M + cd, ce = u*d + v*e, q*d + r*e + # Cancel out bottom N bits of cd and ce. + ... +``` + +With inputs in *(-2M,M)*, they will first be shifted into range *(-M,M)*, which means that the +output will again be in *(-2M,M)*, and this remains the case regardless of how many `update_de` +invocations there are. In what follows, we will try to make this more efficient. + +Note that increasing *d* by *M* is equal to incrementing *cd* by *u M* and *ce* by *q M*. Similarly, +increasing *e* by *M* is equal to incrementing *cd* by *v M* and *ce* by *r M*. So we could instead write: + +```python + ... + cd, ce = u*d + v*e, q*d + r*e + # Perform the equivalent of incrementing d, e by M when they're negative. + if d < 0: + cd += u*M + ce += q*M + if e < 0: + cd += v*M + ce += r*M + # Cancel out bottom N bits of cd and ce. + md = -((Mi * cd) % 2**N) + me = -((Mi * ce) % 2**N) + cd += md * M + ce += me * M + ... +``` + +Now note that we have two steps of corrections to *cd* and *ce* that add multiples of *M*: this +increment, and the decrement that cancels out bottom bits. The second one depends on the first +one, but they can still be efficiently combined by only computing the bottom bits of *cd* and *ce* +at first, and using that to compute the final *md*, *me* values: + +```python +def update_de(d, e, t, M, Mi): + """Multiply matrix t/2^N with [d, e], modulo M.""" + u, v, q, r = t + md, me = 0, 0 + # Compute what multiples of M to add to cd and ce. + if d < 0: + md += u + me += q + if e < 0: + md += v + me += r + # Compute bottom N bits of t*[d,e] + M*[md,me]. + cd, ce = (u*d + v*e + md*M) % 2**N, (q*d + r*e + me*M) % 2**N + # Correct md and me such that the bottom N bits of t*[d,e] + M*[md,me] are zero. + md -= (Mi * cd) % 2**N + me -= (Mi * ce) % 2**N + # Do the full computation. + cd, ce = u*d + v*e + md*M, q*d + r*e + me*M + # And cleanly divide by 2**N. + return cd >> N, ce >> N +``` + +One last optimization: we can avoid the *md M* and *me M* multiplications in the bottom bits of *cd* +and *ce* by moving them to the *md* and *me* correction: + +```python + ... + # Compute bottom N bits of t*[d,e]. + cd, ce = (u*d + v*e) % 2**N, (q*d + r*e) % 2**N + # Correct md and me such that the bottom N bits of t*[d,e]+M*[md,me] are zero. + # Note that this is not the same as {md = (-Mi * cd) % 2**N} etc. That would also result in N + # zero bottom bits, but isn't guaranteed to be a reduction of [0,2^N) compared to the + # previous md and me values, and thus would violate our bounds analysis. + md -= (Mi*cd + md) % 2**N + me -= (Mi*ce + me) % 2**N + ... +``` + +The resulting function takes *d* and *e* in range *(-2M,M)* as inputs, and outputs values in the same +range. That also means that the *d* value at the end of `modinv` will be in that range, while we want +a result in *[0,M)*. To do that, we need a normalization function. It's easy to integrate the +conditional negation of *d* (based on the sign of *f*) into it as well: + +```python +def normalize(sign, v, M): + """Compute sign*v mod M, where v is in range (-2*M,M); output in [0,M).""" + assert sign == 1 or sign == -1 + # v in (-2*M,M) + if v < 0: + v += M + # v in (-M,M). Now multiply v with sign (which can only be 1 or -1). + if sign == -1: + v = -v + # v in (-M,M) + if v < 0: + v += M + # v in [0,M) + return v +``` + +And calling it in `modinv` is simply: + +```python + ... + return normalize(f, d, M) +``` + + +## 5. Constant-time operation + +The primary selling point of the algorithm is fast constant-time operation. What code flow still +depends on the input data so far? + +- the number of iterations of the while *g ≠ 0* loop in `modinv` +- the branches inside `divsteps_n_matrix` +- the sign checks in `update_de` +- the sign checks in `normalize` + +To make the while loop in `modinv` constant time it can be replaced with a constant number of +iterations. The paper proves (Theorem 11.2) that *741* divsteps are sufficient for any *256*-bit +inputs, and [safegcd-bounds](https://github.com/sipa/safegcd-bounds) shows that the slightly better bound *724* is +sufficient even. Given that every loop iteration performs *N* divsteps, it will run a total of +*⌈724/N⌉* times. + +To deal with the branches in `divsteps_n_matrix` we will replace them with constant-time bitwise +operations (and hope the C compiler isn't smart enough to turn them back into branches; see +`ctime_tests.c` for automated tests that this isn't the case). To do so, observe that a +divstep can be written instead as (compare to the inner loop of `gcd` in section 1). + +```python + x = -f if delta > 0 else f # set x equal to (input) -f or f + if g & 1: + g += x # set g to (input) g-f or g+f + if delta > 0: + delta = -delta + f += g # set f to (input) g (note that g was set to g-f before) + delta += 1 + g >>= 1 +``` + +To convert the above to bitwise operations, we rely on a trick to negate conditionally: per the +definition of negative numbers in two's complement, (*-v == ~v + 1*) holds for every number *v*. As +*-1* in two's complement is all *1* bits, bitflipping can be expressed as xor with *-1*. It follows +that *-v == (v ^ -1) - (-1)*. Thus, if we have a variable *c* that takes on values *0* or *-1*, then +*(v ^ c) - c* is *v* if *c=0* and *-v* if *c=-1*. + +Using this we can write: + +```python + x = -f if delta > 0 else f +``` + +in constant-time form as: + +```python + c1 = (-delta) >> 63 + # Conditionally negate f based on c1: + x = (f ^ c1) - c1 +``` + +To use that trick, we need a helper mask variable *c1* that resolves the condition *δ>0* to *-1* +(if true) or *0* (if false). We compute *c1* using right shifting, which is equivalent to dividing by +the specified power of *2* and rounding down (in Python, and also in C under the assumption of a typical two's complement system; see +`assumptions.h` for tests that this is the case). Right shifting by *63* thus maps all +numbers in range *[-2<sup>63</sup>,0)* to *-1*, and numbers in range *[0,2<sup>63</sup>)* to *0*. + +Using the facts that *x&0=0* and *x&(-1)=x* (on two's complement systems again), we can write: + +```python + if g & 1: + g += x +``` + +as: + +```python + # Compute c2=0 if g is even and c2=-1 if g is odd. + c2 = -(g & 1) + # This masks out x if g is even, and leaves x be if g is odd. + g += x & c2 +``` + +Using the conditional negation trick again we can write: + +```python + if g & 1: + if delta > 0: + delta = -delta +``` + +as: + +```python + # Compute c3=-1 if g is odd and delta>0, and 0 otherwise. + c3 = c1 & c2 + # Conditionally negate delta based on c3: + delta = (delta ^ c3) - c3 +``` + +Finally: + +```python + if g & 1: + if delta > 0: + f += g +``` + +becomes: + +```python + f += g & c3 +``` + +It turns out that this can be implemented more efficiently by applying the substitution +*η=-δ*. In this representation, negating *δ* corresponds to negating *η*, and incrementing +*δ* corresponds to decrementing *η*. This allows us to remove the negation in the *c1* +computation: + +```python + # Compute a mask c1 for eta < 0, and compute the conditional negation x of f: + c1 = eta >> 63 + x = (f ^ c1) - c1 + # Compute a mask c2 for odd g, and conditionally add x to g: + c2 = -(g & 1) + g += x & c2 + # Compute a mask c for (eta < 0) and odd (input) g, and use it to conditionally negate eta, + # and add g to f: + c3 = c1 & c2 + eta = (eta ^ c3) - c3 + f += g & c3 + # Incrementing delta corresponds to decrementing eta. + eta -= 1 + g >>= 1 +``` + +A variant of divsteps with better worst-case performance can be used instead: starting *δ* at +*1/2* instead of *1*. This reduces the worst case number of iterations to *590* for *256*-bit inputs +(which can be shown using convex hull analysis). In this case, the substitution *ζ=-(δ+1/2)* +is used instead to keep the variable integral. Incrementing *δ* by *1* still translates to +decrementing *ζ* by *1*, but negating *δ* now corresponds to going from *ζ* to *-(ζ+1)*, or +*~ζ*. Doing that conditionally based on *c3* is simply: + +```python + ... + c3 = c1 & c2 + zeta ^= c3 + ... +``` + +By replacing the loop in `divsteps_n_matrix` with a variant of the divstep code above (extended to +also apply all *f* operations to *u*, *v* and all *g* operations to *q*, *r*), a constant-time version of +`divsteps_n_matrix` is obtained. The full code will be in section 7. + +These bit fiddling tricks can also be used to make the conditional negations and additions in +`update_de` and `normalize` constant-time. + + +## 6. Variable-time optimizations + +In section 5, we modified the `divsteps_n_matrix` function (and a few others) to be constant time. +Constant time operations are only necessary when computing modular inverses of secret data. In +other cases, it slows down calculations unnecessarily. In this section, we will construct a +faster non-constant time `divsteps_n_matrix` function. + +To do so, first consider yet another way of writing the inner loop of divstep operations in +`gcd` from section 1. This decomposition is also explained in the paper in section 8.2. We use +the original version with initial *δ=1* and *η=-δ* here. + +```python +for _ in range(N): + if g & 1 and eta < 0: + eta, f, g = -eta, g, -f + if g & 1: + g += f + eta -= 1 + g >>= 1 +``` + +Whenever *g* is even, the loop only shifts *g* down and decreases *η*. When *g* ends in multiple zero +bits, these iterations can be consolidated into one step. This requires counting the bottom zero +bits efficiently, which is possible on most platforms; it is abstracted here as the function +`count_trailing_zeros`. + +```python +def count_trailing_zeros(v): + """ + When v is zero, consider all N zero bits as "trailing". + For a non-zero value v, find z such that v=(d<<z) for some odd d. + """ + if v == 0: + return N + else: + return (v & -v).bit_length() - 1 + +i = N # divsteps left to do +while True: + # Get rid of all bottom zeros at once. In the first iteration, g may be odd and the following + # lines have no effect (until "if eta < 0"). + zeros = min(i, count_trailing_zeros(g)) + eta -= zeros + g >>= zeros + i -= zeros + if i == 0: + break + # We know g is odd now + if eta < 0: + eta, f, g = -eta, g, -f + g += f + # g is even now, and the eta decrement and g shift will happen in the next loop. +``` + +We can now remove multiple bottom *0* bits from *g* at once, but still need a full iteration whenever +there is a bottom *1* bit. In what follows, we will get rid of multiple *1* bits simultaneously as +well. + +Observe that as long as *η ≥ 0*, the loop does not modify *f*. Instead, it cancels out bottom +bits of *g* and shifts them out, and decreases *η* and *i* accordingly - interrupting only when *η* +becomes negative, or when *i* reaches *0*. Combined, this is equivalent to adding a multiple of *f* to +*g* to cancel out multiple bottom bits, and then shifting them out. + +It is easy to find what that multiple is: we want a number *w* such that *g+w f* has a few bottom +zero bits. If that number of bits is *L*, we want *g+w f mod 2<sup>L</sup> = 0*, or *w = -g/f mod 2<sup>L</sup>*. Since *f* +is odd, such a *w* exists for any *L*. *L* cannot be more than *i* steps (as we'd finish the loop before +doing more) or more than *η+1* steps (as we'd run `eta, f, g = -eta, g, -f` at that point), but +apart from that, we're only limited by the complexity of computing *w*. + +This code demonstrates how to cancel up to 4 bits per step: + +```python +NEGINV16 = [15, 5, 3, 9, 7, 13, 11, 1] # NEGINV16[n//2] = (-n)^-1 mod 16, for odd n +i = N +while True: + zeros = min(i, count_trailing_zeros(g)) + eta -= zeros + g >>= zeros + i -= zeros + if i == 0: + break + # We know g is odd now + if eta < 0: + eta, f, g = -eta, g, -f + # Compute limit on number of bits to cancel + limit = min(min(eta + 1, i), 4) + # Compute w = -g/f mod 2**limit, using the table value for -1/f mod 2**4. Note that f is + # always odd, so its inverse modulo a power of two always exists. + w = (g * NEGINV16[(f & 15) // 2]) % (2**limit) + # As w = -g/f mod (2**limit), g+w*f mod 2**limit = 0 mod 2**limit. + g += w * f + assert g % (2**limit) == 0 + # The next iteration will now shift out at least limit bottom zero bits from g. +``` + +By using a bigger table more bits can be cancelled at once. The table can also be implemented +as a formula. Several formulas are known for computing modular inverses modulo powers of two; +some can be found in Hacker's Delight second edition by Henry S. Warren, Jr. pages 245-247. +Here we need the negated modular inverse, which is a simple transformation of those: + +- Instead of a 3-bit table: + - *-f* or *f ^ 6* +- Instead of a 4-bit table: + - *1 - f(f + 1)* + - *-(f + (((f + 1) & 4) << 1))* +- For larger tables the following technique can be used: if *w=-1/f mod 2<sup>L</sup>*, then *w(w f+2)* is + *-1/f mod 2<sup>2L</sup>*. This allows extending the previous formulas (or tables). In particular we + have this 6-bit function (based on the 3-bit function above): + - *f(f<sup>2</sup> - 2)* + +This loop, again extended to also handle *u*, *v*, *q*, and *r* alongside *f* and *g*, placed in +`divsteps_n_matrix`, gives a significantly faster, but non-constant time version. + + +## 7. Final Python version + +All together we need the following functions: + +- A way to compute the transition matrix in constant time, using the `divsteps_n_matrix` function + from section 2, but with its loop replaced by a variant of the constant-time divstep from + section 5, extended to handle *u*, *v*, *q*, *r*: + +```python +def divsteps_n_matrix(zeta, f, g): + """Compute zeta and transition matrix t after N divsteps (multiplied by 2^N).""" + u, v, q, r = 1, 0, 0, 1 # start with identity matrix + for _ in range(N): + c1 = zeta >> 63 + # Compute x, y, z as conditionally-negated versions of f, u, v. + x, y, z = (f ^ c1) - c1, (u ^ c1) - c1, (v ^ c1) - c1 + c2 = -(g & 1) + # Conditionally add x, y, z to g, q, r. + g, q, r = g + (x & c2), q + (y & c2), r + (z & c2) + c1 &= c2 # reusing c1 here for the earlier c3 variable + zeta = (zeta ^ c1) - 1 # inlining the unconditional zeta decrement here + # Conditionally add g, q, r to f, u, v. + f, u, v = f + (g & c1), u + (q & c1), v + (r & c1) + # When shifting g down, don't shift q, r, as we construct a transition matrix multiplied + # by 2^N. Instead, shift f's coefficients u and v up. + g, u, v = g >> 1, u << 1, v << 1 + return zeta, (u, v, q, r) +``` + +- The functions to update *f* and *g*, and *d* and *e*, from section 2 and section 4, with the constant-time + changes to `update_de` from section 5: + +```python +def update_fg(f, g, t): + """Multiply matrix t/2^N with [f, g].""" + u, v, q, r = t + cf, cg = u*f + v*g, q*f + r*g + return cf >> N, cg >> N + +def update_de(d, e, t, M, Mi): + """Multiply matrix t/2^N with [d, e], modulo M.""" + u, v, q, r = t + d_sign, e_sign = d >> 257, e >> 257 + md, me = (u & d_sign) + (v & e_sign), (q & d_sign) + (r & e_sign) + cd, ce = (u*d + v*e) % 2**N, (q*d + r*e) % 2**N + md -= (Mi*cd + md) % 2**N + me -= (Mi*ce + me) % 2**N + cd, ce = u*d + v*e + M*md, q*d + r*e + M*me + return cd >> N, ce >> N +``` + +- The `normalize` function from section 4, made constant time as well: + +```python +def normalize(sign, v, M): + """Compute sign*v mod M, where v in (-2*M,M); output in [0,M).""" + v_sign = v >> 257 + # Conditionally add M to v. + v += M & v_sign + c = (sign - 1) >> 1 + # Conditionally negate v. + v = (v ^ c) - c + v_sign = v >> 257 + # Conditionally add M to v again. + v += M & v_sign + return v +``` + +- And finally the `modinv` function too, adapted to use *ζ* instead of *δ*, and using the fixed + iteration count from section 5: + +```python +def modinv(M, Mi, x): + """Compute the modular inverse of x mod M, given Mi=1/M mod 2^N.""" + zeta, f, g, d, e = -1, M, x, 0, 1 + for _ in range((590 + N - 1) // N): + zeta, t = divsteps_n_matrix(zeta, f % 2**N, g % 2**N) + f, g = update_fg(f, g, t) + d, e = update_de(d, e, t, M, Mi) + return normalize(f, d, M) +``` + +- To get a variable time version, replace the `divsteps_n_matrix` function with one that uses the + divsteps loop from section 5, and a `modinv` version that calls it without the fixed iteration + count: + +```python +NEGINV16 = [15, 5, 3, 9, 7, 13, 11, 1] # NEGINV16[n//2] = (-n)^-1 mod 16, for odd n +def divsteps_n_matrix_var(eta, f, g): + """Compute eta and transition matrix t after N divsteps (multiplied by 2^N).""" + u, v, q, r = 1, 0, 0, 1 + i = N + while True: + zeros = min(i, count_trailing_zeros(g)) + eta, i = eta - zeros, i - zeros + g, u, v = g >> zeros, u << zeros, v << zeros + if i == 0: + break + if eta < 0: + eta, f, u, v, g, q, r = -eta, g, q, r, -f, -u, -v + limit = min(min(eta + 1, i), 4) + w = (g * NEGINV16[(f & 15) // 2]) % (2**limit) + g, q, r = g + w*f, q + w*u, r + w*v + return eta, (u, v, q, r) + +def modinv_var(M, Mi, x): + """Compute the modular inverse of x mod M, given Mi = 1/M mod 2^N.""" + eta, f, g, d, e = -1, M, x, 0, 1 + while g != 0: + eta, t = divsteps_n_matrix_var(eta, f % 2**N, g % 2**N) + f, g = update_fg(f, g, t) + d, e = update_de(d, e, t, M, Mi) + return normalize(f, d, Mi) +``` + +## 8. From GCDs to Jacobi symbol + +We can also use a similar approach to calculate Jacobi symbol *(x | M)* by keeping track of an +extra variable *j*, for which at every step *(x | M) = j (g | f)*. As we update *f* and *g*, we +make corresponding updates to *j* using +[properties of the Jacobi symbol](https://en.wikipedia.org/wiki/Jacobi_symbol#Properties): +* *((g/2) | f)* is either *(g | f)* or *-(g | f)*, depending on the value of *f mod 8* (negating if it's *3* or *5*). +* *(f | g)* is either *(g | f)* or *-(g | f)*, depending on *f mod 4* and *g mod 4* (negating if both are *3*). + +These updates depend only on the values of *f* and *g* modulo *4* or *8*, and can thus be applied +very quickly, as long as we keep track of a few additional bits of *f* and *g*. Overall, this +calculation is slightly simpler than the one for the modular inverse because we no longer need to +keep track of *d* and *e*. + +However, one difficulty of this approach is that the Jacobi symbol *(a | n)* is only defined for +positive odd integers *n*, whereas in the original safegcd algorithm, *f, g* can take negative +values. We resolve this by using the following modified steps: + +```python + # Before + if delta > 0 and g & 1: + delta, f, g = 1 - delta, g, (g - f) // 2 + + # After + if delta > 0 and g & 1: + delta, f, g = 1 - delta, g, (g + f) // 2 +``` + +The algorithm is still correct, since the changed divstep, called a "posdivstep" (see section 8.4 +and E.5 in the paper) preserves *gcd(f, g)*. However, there's no proof that the modified algorithm +will converge. The justification for posdivsteps is completely empirical: in practice, it appears +that the vast majority of nonzero inputs converge to *f=g=gcd(f<sub>0</sub>, g<sub>0</sub>)* in a +number of steps proportional to their logarithm. + +Note that: +- We require inputs to satisfy *gcd(x, M) = 1*, as otherwise *f=1* is not reached. +- We require inputs *x &neq; 0*, because applying posdivstep with *g=0* has no effect. +- We need to update the termination condition from *g=0* to *f=1*. + +We account for the possibility of nonconvergence by only performing a bounded number of +posdivsteps, and then falling back to square-root based Jacobi calculation if a solution has not +yet been found. + +The optimizations in sections 3-7 above are described in the context of the original divsteps, but +in the C implementation we also adapt most of them (not including "avoiding modulus operations", +since it's not necessary to track *d, e*, and "constant-time operation", since we never calculate +Jacobi symbols for secret data) to the posdivsteps version. diff --git a/src/secp256k1/examples/CMakeLists.txt b/src/secp256k1/examples/CMakeLists.txt new file mode 100644 index 0000000000..0884b645e0 --- /dev/null +++ b/src/secp256k1/examples/CMakeLists.txt @@ -0,0 +1,34 @@ +add_library(example INTERFACE) +target_include_directories(example INTERFACE + ${PROJECT_SOURCE_DIR}/include +) +target_compile_options(example INTERFACE + $<$<C_COMPILER_ID:MSVC>:/wd4005> +) +target_link_libraries(example INTERFACE + $<$<PLATFORM_ID:Windows>:bcrypt> +) +if(SECP256K1_BUILD_SHARED) + target_link_libraries(example INTERFACE secp256k1) +elseif(SECP256K1_BUILD_STATIC) + target_link_libraries(example INTERFACE secp256k1_static) + if(MSVC) + target_link_options(example INTERFACE /IGNORE:4217) + endif() +endif() + +add_executable(ecdsa_example ecdsa.c) +target_link_libraries(ecdsa_example example) +add_test(ecdsa_example ecdsa_example) + +if(SECP256K1_ENABLE_MODULE_ECDH) + add_executable(ecdh_example ecdh.c) + target_link_libraries(ecdh_example example) + add_test(ecdh_example ecdh_example) +endif() + +if(SECP256K1_ENABLE_MODULE_SCHNORRSIG) + add_executable(schnorr_example schnorr.c) + target_link_libraries(schnorr_example example) + add_test(schnorr_example schnorr_example) +endif() diff --git a/src/secp256k1/examples/EXAMPLES_COPYING b/src/secp256k1/examples/EXAMPLES_COPYING new file mode 100644 index 0000000000..0e259d42c9 --- /dev/null +++ b/src/secp256k1/examples/EXAMPLES_COPYING @@ -0,0 +1,121 @@ +Creative Commons Legal Code + +CC0 1.0 Universal + + CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE + LEGAL SERVICES. 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For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include <stdio.h> +#include <assert.h> +#include <string.h> + +#include <secp256k1.h> +#include <secp256k1_ecdh.h> + +#include "examples_util.h" + +int main(void) { + unsigned char seckey1[32]; + unsigned char seckey2[32]; + unsigned char compressed_pubkey1[33]; + unsigned char compressed_pubkey2[33]; + unsigned char shared_secret1[32]; + unsigned char shared_secret2[32]; + unsigned char randomize[32]; + int return_val; + size_t len; + secp256k1_pubkey pubkey1; + secp256k1_pubkey pubkey2; + + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return 1; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + + /* If the secret key is zero or out of range (bigger than secp256k1's + * order), we try to sample a new key. Note that the probability of this + * happening is negligible. */ + while (1) { + if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) { + printf("Failed to generate randomness\n"); + return 1; + } + if (secp256k1_ec_seckey_verify(ctx, seckey1) && secp256k1_ec_seckey_verify(ctx, seckey2)) { + break; + } + } + + /* Public key creation using a valid context with a verified secret key should never fail */ + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey1, seckey1); + assert(return_val); + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey2, seckey2); + assert(return_val); + + /* Serialize pubkey1 in a compressed form (33 bytes), should always return 1 */ + len = sizeof(compressed_pubkey1); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey1, &len, &pubkey1, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey1)); + + /* Serialize pubkey2 in a compressed form (33 bytes) */ + len = sizeof(compressed_pubkey2); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey2, &len, &pubkey2, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey2)); + + /*** Creating the shared secret ***/ + + /* Perform ECDH with seckey1 and pubkey2. Should never fail with a verified + * seckey and valid pubkey */ + return_val = secp256k1_ecdh(ctx, shared_secret1, &pubkey2, seckey1, NULL, NULL); + assert(return_val); + + /* Perform ECDH with seckey2 and pubkey1. Should never fail with a verified + * seckey and valid pubkey */ + return_val = secp256k1_ecdh(ctx, shared_secret2, &pubkey1, seckey2, NULL, NULL); + assert(return_val); + + /* Both parties should end up with the same shared secret */ + return_val = memcmp(shared_secret1, shared_secret2, sizeof(shared_secret1)); + assert(return_val == 0); + + printf("Secret Key1: "); + print_hex(seckey1, sizeof(seckey1)); + printf("Compressed Pubkey1: "); + print_hex(compressed_pubkey1, sizeof(compressed_pubkey1)); + printf("\nSecret Key2: "); + print_hex(seckey2, sizeof(seckey2)); + printf("Compressed Pubkey2: "); + print_hex(compressed_pubkey2, sizeof(compressed_pubkey2)); + printf("\nShared Secret: "); + print_hex(shared_secret1, sizeof(shared_secret1)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), Or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey1, sizeof(seckey1)); + secure_erase(seckey2, sizeof(seckey2)); + secure_erase(shared_secret1, sizeof(shared_secret1)); + secure_erase(shared_secret2, sizeof(shared_secret2)); + + return 0; +} diff --git a/src/secp256k1/examples/ecdsa.c b/src/secp256k1/examples/ecdsa.c new file mode 100644 index 0000000000..d1d2b0e365 --- /dev/null +++ b/src/secp256k1/examples/ecdsa.c @@ -0,0 +1,139 @@ +/************************************************************************* + * Written in 2020-2022 by Elichai Turkel * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include <stdio.h> +#include <assert.h> +#include <string.h> + +#include <secp256k1.h> + +#include "examples_util.h" + +int main(void) { + /* Instead of signing the message directly, we must sign a 32-byte hash. + * Here the message is "Hello, world!" and the hash function was SHA-256. + * An actual implementation should just call SHA-256, but this example + * hardcodes the output to avoid depending on an additional library. + * See https://bitcoin.stackexchange.com/questions/81115/if-someone-wanted-to-pretend-to-be-satoshi-by-posting-a-fake-signature-to-defrau/81116#81116 */ + unsigned char msg_hash[32] = { + 0x31, 0x5F, 0x5B, 0xDB, 0x76, 0xD0, 0x78, 0xC4, + 0x3B, 0x8A, 0xC0, 0x06, 0x4E, 0x4A, 0x01, 0x64, + 0x61, 0x2B, 0x1F, 0xCE, 0x77, 0xC8, 0x69, 0x34, + 0x5B, 0xFC, 0x94, 0xC7, 0x58, 0x94, 0xED, 0xD3, + }; + unsigned char seckey[32]; + unsigned char randomize[32]; + unsigned char compressed_pubkey[33]; + unsigned char serialized_signature[64]; + size_t len; + int is_signature_valid, is_signature_valid2; + int return_val; + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return 1; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + + /* If the secret key is zero or out of range (bigger than secp256k1's + * order), we try to sample a new key. Note that the probability of this + * happening is negligible. */ + while (1) { + if (!fill_random(seckey, sizeof(seckey))) { + printf("Failed to generate randomness\n"); + return 1; + } + if (secp256k1_ec_seckey_verify(ctx, seckey)) { + break; + } + } + + /* Public key creation using a valid context with a verified secret key should never fail */ + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey, seckey); + assert(return_val); + + /* Serialize the pubkey in a compressed form(33 bytes). Should always return 1. */ + len = sizeof(compressed_pubkey); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey, &len, &pubkey, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey)); + + /*** Signing ***/ + + /* Generate an ECDSA signature `noncefp` and `ndata` allows you to pass a + * custom nonce function, passing `NULL` will use the RFC-6979 safe default. + * Signing with a valid context, verified secret key + * and the default nonce function should never fail. */ + return_val = secp256k1_ecdsa_sign(ctx, &sig, msg_hash, seckey, NULL, NULL); + assert(return_val); + + /* Serialize the signature in a compact form. Should always return 1 + * according to the documentation in secp256k1.h. */ + return_val = secp256k1_ecdsa_signature_serialize_compact(ctx, serialized_signature, &sig); + assert(return_val); + + + /*** Verification ***/ + + /* Deserialize the signature. This will return 0 if the signature can't be parsed correctly. */ + if (!secp256k1_ecdsa_signature_parse_compact(ctx, &sig, serialized_signature)) { + printf("Failed parsing the signature\n"); + return 1; + } + + /* Deserialize the public key. This will return 0 if the public key can't be parsed correctly. */ + if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, compressed_pubkey, sizeof(compressed_pubkey))) { + printf("Failed parsing the public key\n"); + return 1; + } + + /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */ + is_signature_valid = secp256k1_ecdsa_verify(ctx, &sig, msg_hash, &pubkey); + + printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false"); + printf("Secret Key: "); + print_hex(seckey, sizeof(seckey)); + printf("Public Key: "); + print_hex(compressed_pubkey, sizeof(compressed_pubkey)); + printf("Signature: "); + print_hex(serialized_signature, sizeof(serialized_signature)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* Bonus example: if all we need is signature verification (and no key + generation or signing), we don't need to use a context created via + secp256k1_context_create(). We can simply use the static (i.e., global) + context secp256k1_context_static. See its description in + include/secp256k1.h for details. */ + is_signature_valid2 = secp256k1_ecdsa_verify(secp256k1_context_static, + &sig, msg_hash, &pubkey); + assert(is_signature_valid2 == is_signature_valid); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), Or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey, sizeof(seckey)); + + return 0; +} diff --git a/src/secp256k1/examples/examples_util.h b/src/secp256k1/examples/examples_util.h new file mode 100644 index 0000000000..a52b1fa115 --- /dev/null +++ b/src/secp256k1/examples/examples_util.h @@ -0,0 +1,102 @@ +/************************************************************************* + * Copyright (c) 2020-2021 Elichai Turkel * + * Distributed under the CC0 software license, see the accompanying file * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +/* + * This file is an attempt at collecting best practice methods for obtaining randomness with different operating systems. + * It may be out-of-date. Consult the documentation of the operating system before considering to use the methods below. + * + * Platform randomness sources: + * Linux -> `getrandom(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. http://man7.org/linux/man-pages/man2/getrandom.2.html, https://linux.die.net/man/4/urandom + * macOS -> `getentropy(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. https://www.unix.com/man-page/mojave/2/getentropy, https://opensource.apple.com/source/xnu/xnu-517.12.7/bsd/man/man4/random.4.auto.html + * FreeBSD -> `getrandom(2)`(`sys/random.h`), if not available `kern.arandom` should be used. https://www.freebsd.org/cgi/man.cgi?query=getrandom, https://www.freebsd.org/cgi/man.cgi?query=random&sektion=4 + * OpenBSD -> `getentropy(2)`(`unistd.h`), if not available `/dev/urandom` should be used. https://man.openbsd.org/getentropy, https://man.openbsd.org/urandom + * Windows -> `BCryptGenRandom`(`bcrypt.h`). https://docs.microsoft.com/en-us/windows/win32/api/bcrypt/nf-bcrypt-bcryptgenrandom + */ + +#if defined(_WIN32) +#include <windows.h> +#include <ntstatus.h> +#include <bcrypt.h> +#elif defined(__linux__) || defined(__APPLE__) || defined(__FreeBSD__) +#include <sys/random.h> +#elif defined(__OpenBSD__) +#include <unistd.h> +#else +#error "Couldn't identify the OS" +#endif + +#include <stddef.h> +#include <limits.h> +#include <stdio.h> + + +/* Returns 1 on success, and 0 on failure. */ +static int fill_random(unsigned char* data, size_t size) { +#if defined(_WIN32) + NTSTATUS res = BCryptGenRandom(NULL, data, size, BCRYPT_USE_SYSTEM_PREFERRED_RNG); + if (res != STATUS_SUCCESS || size > ULONG_MAX) { + return 0; + } else { + return 1; + } +#elif defined(__linux__) || defined(__FreeBSD__) + /* If `getrandom(2)` is not available you should fallback to /dev/urandom */ + ssize_t res = getrandom(data, size, 0); + if (res < 0 || (size_t)res != size ) { + return 0; + } else { + return 1; + } +#elif defined(__APPLE__) || defined(__OpenBSD__) + /* If `getentropy(2)` is not available you should fallback to either + * `SecRandomCopyBytes` or /dev/urandom */ + int res = getentropy(data, size); + if (res == 0) { + return 1; + } else { + return 0; + } +#endif + return 0; +} + +static void print_hex(unsigned char* data, size_t size) { + size_t i; + printf("0x"); + for (i = 0; i < size; i++) { + printf("%02x", data[i]); + } + printf("\n"); +} + +#if defined(_MSC_VER) +// For SecureZeroMemory +#include <Windows.h> +#endif +/* Cleanses memory to prevent leaking sensitive info. Won't be optimized out. */ +static SECP256K1_INLINE void secure_erase(void *ptr, size_t len) { +#if defined(_MSC_VER) + /* SecureZeroMemory is guaranteed not to be optimized out by MSVC. */ + SecureZeroMemory(ptr, len); +#elif defined(__GNUC__) + /* We use a memory barrier that scares the compiler away from optimizing out the memset. + * + * Quoting Adam Langley <agl@google.com> in commit ad1907fe73334d6c696c8539646c21b11178f20f + * in BoringSSL (ISC License): + * As best as we can tell, this is sufficient to break any optimisations that + * might try to eliminate "superfluous" memsets. + * This method used in memzero_explicit() the Linux kernel, too. Its advantage is that it is + * pretty efficient, because the compiler can still implement the memset() efficently, + * just not remove it entirely. See "Dead Store Elimination (Still) Considered Harmful" by + * Yang et al. (USENIX Security 2017) for more background. + */ + memset(ptr, 0, len); + __asm__ __volatile__("" : : "r"(ptr) : "memory"); +#else + void *(*volatile const volatile_memset)(void *, int, size_t) = memset; + volatile_memset(ptr, 0, len); +#endif +} diff --git a/src/secp256k1/examples/schnorr.c b/src/secp256k1/examples/schnorr.c new file mode 100644 index 0000000000..4c0dd1c1a9 --- /dev/null +++ b/src/secp256k1/examples/schnorr.c @@ -0,0 +1,156 @@ +/************************************************************************* + * Written in 2020-2022 by Elichai Turkel * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include <stdio.h> +#include <assert.h> +#include <string.h> + +#include <secp256k1.h> +#include <secp256k1_extrakeys.h> +#include <secp256k1_schnorrsig.h> + +#include "examples_util.h" + +int main(void) { + unsigned char msg[12] = "Hello World!"; + unsigned char msg_hash[32]; + unsigned char tag[17] = "my_fancy_protocol"; + unsigned char seckey[32]; + unsigned char randomize[32]; + unsigned char auxiliary_rand[32]; + unsigned char serialized_pubkey[32]; + unsigned char signature[64]; + int is_signature_valid, is_signature_valid2; + int return_val; + secp256k1_xonly_pubkey pubkey; + secp256k1_keypair keypair; + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return 1; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + + /* If the secret key is zero or out of range (bigger than secp256k1's + * order), we try to sample a new key. Note that the probability of this + * happening is negligible. */ + while (1) { + if (!fill_random(seckey, sizeof(seckey))) { + printf("Failed to generate randomness\n"); + return 1; + } + /* Try to create a keypair with a valid context, it should only fail if + * the secret key is zero or out of range. */ + if (secp256k1_keypair_create(ctx, &keypair, seckey)) { + break; + } + } + + /* Extract the X-only public key from the keypair. We pass NULL for + * `pk_parity` as the parity isn't needed for signing or verification. + * `secp256k1_keypair_xonly_pub` supports returning the parity for + * other use cases such as tests or verifying Taproot tweaks. + * This should never fail with a valid context and public key. */ + return_val = secp256k1_keypair_xonly_pub(ctx, &pubkey, NULL, &keypair); + assert(return_val); + + /* Serialize the public key. Should always return 1 for a valid public key. */ + return_val = secp256k1_xonly_pubkey_serialize(ctx, serialized_pubkey, &pubkey); + assert(return_val); + + /*** Signing ***/ + + /* Instead of signing (possibly very long) messages directly, we sign a + * 32-byte hash of the message in this example. + * + * We use secp256k1_tagged_sha256 to create this hash. This function expects + * a context-specific "tag", which restricts the context in which the signed + * messages should be considered valid. For example, if protocol A mandates + * to use the tag "my_fancy_protocol" and protocol B mandates to use the tag + * "my_boring_protocol", then signed messages from protocol A will never be + * valid in protocol B (and vice versa), even if keys are reused across + * protocols. This implements "domain separation", which is considered good + * practice. It avoids attacks in which users are tricked into signing a + * message that has intended consequences in the intended context (e.g., + * protocol A) but would have unintended consequences if it were valid in + * some other context (e.g., protocol B). */ + return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg)); + assert(return_val); + + /* Generate 32 bytes of randomness to use with BIP-340 schnorr signing. */ + if (!fill_random(auxiliary_rand, sizeof(auxiliary_rand))) { + printf("Failed to generate randomness\n"); + return 1; + } + + /* Generate a Schnorr signature. + * + * We use the secp256k1_schnorrsig_sign32 function that provides a simple + * interface for signing 32-byte messages (which in our case is a hash of + * the actual message). BIP-340 recommends passing 32 bytes of randomness + * to the signing function to improve security against side-channel attacks. + * Signing with a valid context, a 32-byte message, a verified keypair, and + * any 32 bytes of auxiliary random data should never fail. */ + return_val = secp256k1_schnorrsig_sign32(ctx, signature, msg_hash, &keypair, auxiliary_rand); + assert(return_val); + + /*** Verification ***/ + + /* Deserialize the public key. This will return 0 if the public key can't + * be parsed correctly */ + if (!secp256k1_xonly_pubkey_parse(ctx, &pubkey, serialized_pubkey)) { + printf("Failed parsing the public key\n"); + return 1; + } + + /* Compute the tagged hash on the received messages using the same tag as the signer. */ + return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg)); + assert(return_val); + + /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */ + is_signature_valid = secp256k1_schnorrsig_verify(ctx, signature, msg_hash, 32, &pubkey); + + + printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false"); + printf("Secret Key: "); + print_hex(seckey, sizeof(seckey)); + printf("Public Key: "); + print_hex(serialized_pubkey, sizeof(serialized_pubkey)); + printf("Signature: "); + print_hex(signature, sizeof(signature)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* Bonus example: if all we need is signature verification (and no key + generation or signing), we don't need to use a context created via + secp256k1_context_create(). We can simply use the static (i.e., global) + context secp256k1_context_static. See its description in + include/secp256k1.h for details. */ + is_signature_valid2 = secp256k1_schnorrsig_verify(secp256k1_context_static, + signature, msg_hash, 32, &pubkey); + assert(is_signature_valid2 == is_signature_valid); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), Or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey, sizeof(seckey)); + return 0; +} diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h new file mode 100644 index 0000000000..4ce3e500ba --- /dev/null +++ b/src/secp256k1/include/secp256k1.h @@ -0,0 +1,914 @@ +#ifndef SECP256K1_H +#define SECP256K1_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include <stddef.h> + +/** Unless explicitly stated all pointer arguments must not be NULL. + * + * The following rules specify the order of arguments in API calls: + * + * 1. Context pointers go first, followed by output arguments, combined + * output/input arguments, and finally input-only arguments. + * 2. Array lengths always immediately follow the argument whose length + * they describe, even if this violates rule 1. + * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated + * later go first. This means: signatures, public nonces, secret nonces, + * messages, public keys, secret keys, tweaks. + * 4. Arguments that are not data pointers go last, from more complex to less + * complex: function pointers, algorithm names, messages, void pointers, + * counts, flags, booleans. + * 5. Opaque data pointers follow the function pointer they are to be passed to. + */ + +/** Opaque data structure that holds context information + * + * The primary purpose of context objects is to store randomization data for + * enhanced protection against side-channel leakage. This protection is only + * effective if the context is randomized after its creation. See + * secp256k1_context_create for creation of contexts and + * secp256k1_context_randomize for randomization. + * + * A secondary purpose of context objects is to store pointers to callback + * functions that the library will call when certain error states arise. See + * secp256k1_context_set_error_callback as well as + * secp256k1_context_set_illegal_callback for details. Future library versions + * may use context objects for additional purposes. + * + * A constructed context can safely be used from multiple threads + * simultaneously, but API calls that take a non-const pointer to a context + * need exclusive access to it. In particular this is the case for + * secp256k1_context_destroy, secp256k1_context_preallocated_destroy, + * and secp256k1_context_randomize. + * + * Regarding randomization, either do it once at creation time (in which case + * you do not need any locking for the other calls), or use a read-write lock. + */ +typedef struct secp256k1_context_struct secp256k1_context; + +/** Opaque data structure that holds rewritable "scratch space" + * + * The purpose of this structure is to replace dynamic memory allocations, + * because we target architectures where this may not be available. It is + * essentially a resizable (within specified parameters) block of bytes, + * which is initially created either by memory allocation or TODO as a pointer + * into some fixed rewritable space. + * + * Unlike the context object, this cannot safely be shared between threads + * without additional synchronization logic. + */ +typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space; + +/** Opaque data structure that holds a parsed and valid public key. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage or transmission, + * use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. To + * compare keys, use secp256k1_ec_pubkey_cmp. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_pubkey; + +/** Opaque data structured that holds a parsed ECDSA signature. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, or + * comparison, use the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_ecdsa_signature; + +/** A pointer to a function to deterministically generate a nonce. + * + * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail. + * Out: nonce32: pointer to a 32-byte array to be filled by the function. + * In: msg32: the 32-byte message hash being verified (will not be NULL) + * key32: pointer to a 32-byte secret key (will not be NULL) + * algo16: pointer to a 16-byte array describing the signature + * algorithm (will be NULL for ECDSA for compatibility). + * data: Arbitrary data pointer that is passed through. + * attempt: how many iterations we have tried to find a nonce. + * This will almost always be 0, but different attempt values + * are required to result in a different nonce. + * + * Except for test cases, this function should compute some cryptographic hash of + * the message, the algorithm, the key and the attempt. + */ +typedef int (*secp256k1_nonce_function)( + unsigned char *nonce32, + const unsigned char *msg32, + const unsigned char *key32, + const unsigned char *algo16, + void *data, + unsigned int attempt +); + +# if !defined(SECP256K1_GNUC_PREREQ) +# if defined(__GNUC__)&&defined(__GNUC_MINOR__) +# define SECP256K1_GNUC_PREREQ(_maj,_min) \ + ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min)) +# else +# define SECP256K1_GNUC_PREREQ(_maj,_min) 0 +# endif +# endif + +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(2,7) +# define SECP256K1_INLINE __inline__ +# elif (defined(_MSC_VER)) +# define SECP256K1_INLINE __inline +# else +# define SECP256K1_INLINE +# endif +# else +# define SECP256K1_INLINE inline +# endif + +/* When this header is used at build-time the SECP256K1_BUILD define needs to be set + * to correctly setup export attributes and nullness checks. This is normally done + * by secp256k1.c but to guard against this header being included before secp256k1.c + * has had a chance to set the define (e.g. via test harnesses that just includes + * secp256k1.c) we set SECP256K1_NO_BUILD when this header is processed without the + * BUILD define so this condition can be caught. + */ +#ifndef SECP256K1_BUILD +# define SECP256K1_NO_BUILD +#endif + +/* Symbol visibility. See libtool manual, section "Windows DLLs". */ +#if defined(_WIN32) && !defined(__GNUC__) +# ifdef SECP256K1_BUILD +# ifdef DLL_EXPORT +# define SECP256K1_API __declspec (dllexport) +# define SECP256K1_API_VAR extern __declspec (dllexport) +# endif +# elif defined _MSC_VER +# define SECP256K1_API +# define SECP256K1_API_VAR extern __declspec (dllimport) +# elif defined DLL_EXPORT +# define SECP256K1_API __declspec (dllimport) +# define SECP256K1_API_VAR extern __declspec (dllimport) +# endif +#endif +#ifndef SECP256K1_API +# if defined(__GNUC__) && (__GNUC__ >= 4) && defined(SECP256K1_BUILD) +# define SECP256K1_API __attribute__ ((visibility ("default"))) +# define SECP256K1_API_VAR extern __attribute__ ((visibility ("default"))) +# else +# define SECP256K1_API +# define SECP256K1_API_VAR extern +# endif +#endif + +/* Warning attributes + * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out + * some paranoid null checks. */ +# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__)) +# else +# define SECP256K1_WARN_UNUSED_RESULT +# endif +# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_ARG_NONNULL(_x) __attribute__ ((__nonnull__(_x))) +# else +# define SECP256K1_ARG_NONNULL(_x) +# endif + +/* Attribute for marking functions, types, and variables as deprecated */ +#if !defined(SECP256K1_BUILD) && defined(__has_attribute) +# if __has_attribute(__deprecated__) +# define SECP256K1_DEPRECATED(_msg) __attribute__ ((__deprecated__(_msg))) +# else +# define SECP256K1_DEPRECATED(_msg) +# endif +#else +# define SECP256K1_DEPRECATED(_msg) +#endif + +/* All flags' lower 8 bits indicate what they're for. Do not use directly. */ +#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1) +#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0) +#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1) +/* The higher bits contain the actual data. Do not use directly. */ +#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8) +#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9) +#define SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY (1 << 10) +#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8) + +/** Context flags to pass to secp256k1_context_create, secp256k1_context_preallocated_size, and + * secp256k1_context_preallocated_create. */ +#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT) + +/** Deprecated context flags. These flags are treated equivalent to SECP256K1_CONTEXT_NONE. */ +#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) +#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN) + +/* Testing flag. Do not use. */ +#define SECP256K1_CONTEXT_DECLASSIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY) + +/** Flag to pass to secp256k1_ec_pubkey_serialize. */ +#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION) +#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION) + +/** Prefix byte used to tag various encoded curvepoints for specific purposes */ +#define SECP256K1_TAG_PUBKEY_EVEN 0x02 +#define SECP256K1_TAG_PUBKEY_ODD 0x03 +#define SECP256K1_TAG_PUBKEY_UNCOMPRESSED 0x04 +#define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06 +#define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07 + +/** A built-in constant secp256k1 context object with static storage duration, to be + * used in conjunction with secp256k1_selftest. + * + * This context object offers *only limited functionality* , i.e., it cannot be used + * for API functions that perform computations involving secret keys, e.g., signing + * and public key generation. If this restriction applies to a specific API function, + * it is mentioned in its documentation. See secp256k1_context_create if you need a + * full context object that supports all functionality offered by the library. + * + * It is highly recommended to call secp256k1_selftest before using this context. + */ +SECP256K1_API_VAR const secp256k1_context *secp256k1_context_static; + +/** Deprecated alias for secp256k1_context_static. */ +SECP256K1_API_VAR const secp256k1_context *secp256k1_context_no_precomp +SECP256K1_DEPRECATED("Use secp256k1_context_static instead"); + +/** Perform basic self tests (to be used in conjunction with secp256k1_context_static) + * + * This function performs self tests that detect some serious usage errors and + * similar conditions, e.g., when the library is compiled for the wrong endianness. + * This is a last resort measure to be used in production. The performed tests are + * very rudimentary and are not intended as a replacement for running the test + * binaries. + * + * It is highly recommended to call this before using secp256k1_context_static. + * It is not necessary to call this function before using a context created with + * secp256k1_context_create (or secp256k1_context_preallocated_create), which will + * take care of performing the self tests. + * + * If the tests fail, this function will call the default error handler to abort the + * program (see secp256k1_context_set_error_callback). + */ +SECP256K1_API void secp256k1_selftest(void); + + +/** Create a secp256k1 context object (in dynamically allocated memory). + * + * This function uses malloc to allocate memory. It is guaranteed that malloc is + * called at most once for every call of this function. If you need to avoid dynamic + * memory allocation entirely, see secp256k1_context_static and the functions in + * secp256k1_preallocated.h. + * + * Returns: a newly created context object. + * In: flags: Always set to SECP256K1_CONTEXT_NONE (see below). + * + * The only valid non-deprecated flag in recent library versions is + * SECP256K1_CONTEXT_NONE, which will create a context sufficient for all functionality + * offered by the library. All other (deprecated) flags will be treated as equivalent + * to the SECP256K1_CONTEXT_NONE flag. Though the flags parameter primarily exists for + * historical reasons, future versions of the library may introduce new flags. + * + * If the context is intended to be used for API functions that perform computations + * involving secret keys, e.g., signing and public key generation, then it is highly + * recommended to call secp256k1_context_randomize on the context before calling + * those API functions. This will provide enhanced protection against side-channel + * leakage, see secp256k1_context_randomize for details. + * + * Do not create a new context object for each operation, as construction and + * randomization can take non-negligible time. + */ +SECP256K1_API secp256k1_context *secp256k1_context_create( + unsigned int flags +) SECP256K1_WARN_UNUSED_RESULT; + +/** Copy a secp256k1 context object (into dynamically allocated memory). + * + * This function uses malloc to allocate memory. It is guaranteed that malloc is + * called at most once for every call of this function. If you need to avoid dynamic + * memory allocation entirely, see the functions in secp256k1_preallocated.h. + * + * Cloning secp256k1_context_static is not possible, and should not be emulated by + * the caller (e.g., using memcpy). Create a new context instead. + * + * Returns: a newly created context object. + * Args: ctx: an existing context to copy (not secp256k1_context_static) + */ +SECP256K1_API secp256k1_context *secp256k1_context_clone( + const secp256k1_context *ctx +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Destroy a secp256k1 context object (created in dynamically allocated memory). + * + * The context pointer may not be used afterwards. + * + * The context to destroy must have been created using secp256k1_context_create + * or secp256k1_context_clone. If the context has instead been created using + * secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone, the + * behaviour is undefined. In that case, secp256k1_context_preallocated_destroy must + * be used instead. + * + * Args: ctx: an existing context to destroy, constructed using + * secp256k1_context_create or secp256k1_context_clone + * (i.e., not secp256k1_context_static). + */ +SECP256K1_API void secp256k1_context_destroy( + secp256k1_context *ctx +) SECP256K1_ARG_NONNULL(1); + +/** Set a callback function to be called when an illegal argument is passed to + * an API call. It will only trigger for violations that are mentioned + * explicitly in the header. + * + * The philosophy is that these shouldn't be dealt with through a + * specific return value, as calling code should not have branches to deal with + * the case that this code itself is broken. + * + * On the other hand, during debug stage, one would want to be informed about + * such mistakes, and the default (crashing) may be inadvisable. + * When this callback is triggered, the API function called is guaranteed not + * to cause a crash, though its return value and output arguments are + * undefined. + * + * When this function has not been called (or called with fn==NULL), then the + * default handler will be used. The library provides a default handler which + * writes the message to stderr and calls abort. This default handler can be + * replaced at link time if the preprocessor macro + * USE_EXTERNAL_DEFAULT_CALLBACKS is defined, which is the case if the build + * has been configured with --enable-external-default-callbacks. Then the + * following two symbols must be provided to link against: + * - void secp256k1_default_illegal_callback_fn(const char *message, void *data); + * - void secp256k1_default_error_callback_fn(const char *message, void *data); + * The library can call these default handlers even before a proper callback data + * pointer could have been set using secp256k1_context_set_illegal_callback or + * secp256k1_context_set_error_callback, e.g., when the creation of a context + * fails. In this case, the corresponding default handler will be called with + * the data pointer argument set to NULL. + * + * Args: ctx: an existing context object. + * In: fun: a pointer to a function to call when an illegal argument is + * passed to the API, taking a message and an opaque pointer. + * (NULL restores the default handler.) + * data: the opaque pointer to pass to fun above, must be NULL for the default handler. + * + * See also secp256k1_context_set_error_callback. + */ +SECP256K1_API void secp256k1_context_set_illegal_callback( + secp256k1_context *ctx, + void (*fun)(const char *message, void *data), + const void *data +) SECP256K1_ARG_NONNULL(1); + +/** Set a callback function to be called when an internal consistency check + * fails. + * + * The default callback writes an error message to stderr and calls abort + * to abort the program. + * + * This can only trigger in case of a hardware failure, miscompilation, + * memory corruption, serious bug in the library, or other error would can + * otherwise result in undefined behaviour. It will not trigger due to mere + * incorrect usage of the API (see secp256k1_context_set_illegal_callback + * for that). After this callback returns, anything may happen, including + * crashing. + * + * Args: ctx: an existing context object. + * In: fun: a pointer to a function to call when an internal error occurs, + * taking a message and an opaque pointer (NULL restores the + * default handler, see secp256k1_context_set_illegal_callback + * for details). + * data: the opaque pointer to pass to fun above, must be NULL for the default handler. + * + * See also secp256k1_context_set_illegal_callback. + */ +SECP256K1_API void secp256k1_context_set_error_callback( + secp256k1_context *ctx, + void (*fun)(const char *message, void *data), + const void *data +) SECP256K1_ARG_NONNULL(1); + +/** Create a secp256k1 scratch space object. + * + * Returns: a newly created scratch space. + * Args: ctx: an existing context object. + * In: size: amount of memory to be available as scratch space. Some extra + * (<100 bytes) will be allocated for extra accounting. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT secp256k1_scratch_space *secp256k1_scratch_space_create( + const secp256k1_context *ctx, + size_t size +) SECP256K1_ARG_NONNULL(1); + +/** Destroy a secp256k1 scratch space. + * + * The pointer may not be used afterwards. + * Args: ctx: a secp256k1 context object. + * scratch: space to destroy + */ +SECP256K1_API void secp256k1_scratch_space_destroy( + const secp256k1_context *ctx, + secp256k1_scratch_space *scratch +) SECP256K1_ARG_NONNULL(1); + +/** Parse a variable-length public key into the pubkey object. + * + * Returns: 1 if the public key was fully valid. + * 0 if the public key could not be parsed or is invalid. + * Args: ctx: a secp256k1 context object. + * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a + * parsed version of input. If not, its value is undefined. + * In: input: pointer to a serialized public key + * inputlen: length of the array pointed to by input + * + * This function supports parsing compressed (33 bytes, header byte 0x02 or + * 0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header + * byte 0x06 or 0x07) format public keys. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize a pubkey object into a serialized byte sequence. + * + * Returns: 1 always. + * Args: ctx: a secp256k1 context object. + * Out: output: a pointer to a 65-byte (if compressed==0) or 33-byte (if + * compressed==1) byte array to place the serialized key + * in. + * In/Out: outputlen: a pointer to an integer which is initially set to the + * size of output, and is overwritten with the written + * size. + * In: pubkey: a pointer to a secp256k1_pubkey containing an + * initialized public key. + * flags: SECP256K1_EC_COMPRESSED if serialization should be in + * compressed format, otherwise SECP256K1_EC_UNCOMPRESSED. + */ +SECP256K1_API int secp256k1_ec_pubkey_serialize( + const secp256k1_context *ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_pubkey *pubkey, + unsigned int flags +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Compare two public keys using lexicographic (of compressed serialization) order + * + * Returns: <0 if the first public key is less than the second + * >0 if the first public key is greater than the second + * 0 if the two public keys are equal + * Args: ctx: a secp256k1 context object. + * In: pubkey1: first public key to compare + * pubkey2: second public key to compare + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_cmp( + const secp256k1_context *ctx, + const secp256k1_pubkey *pubkey1, + const secp256k1_pubkey *pubkey2 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Parse an ECDSA signature in compact (64 bytes) format. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to the 64-byte array to parse + * + * The signature must consist of a 32-byte big endian R value, followed by a + * 32-byte big endian S value. If R or S fall outside of [0..order-1], the + * encoding is invalid. R and S with value 0 are allowed in the encoding. + * + * After the call, sig will always be initialized. If parsing failed or R or + * S are zero, the resulting sig value is guaranteed to fail verification for + * any message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_compact( + const secp256k1_context *ctx, + secp256k1_ecdsa_signature *sig, + const unsigned char *input64 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Parse a DER ECDSA signature. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature verification with it is + * guaranteed to fail for every message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_der( + const secp256k1_context *ctx, + secp256k1_ecdsa_signature *sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in DER format. + * + * Returns: 1 if enough space was available to serialize, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: output: a pointer to an array to store the DER serialization + * In/Out: outputlen: a pointer to a length integer. Initially, this integer + * should be set to the length of output. After the call + * it will be set to the length of the serialization (even + * if 0 was returned). + * In: sig: a pointer to an initialized signature object + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_der( + const secp256k1_context *ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_ecdsa_signature *sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Serialize an ECDSA signature in compact (64 byte) format. + * + * Returns: 1 + * Args: ctx: a secp256k1 context object + * Out: output64: a pointer to a 64-byte array to store the compact serialization + * In: sig: a pointer to an initialized signature object + * + * See secp256k1_ecdsa_signature_parse_compact for details about the encoding. + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact( + const secp256k1_context *ctx, + unsigned char *output64, + const secp256k1_ecdsa_signature *sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Verify an ECDSA signature. + * + * Returns: 1: correct signature + * 0: incorrect or unparseable signature + * Args: ctx: a secp256k1 context object. + * In: sig: the signature being verified. + * msghash32: the 32-byte message hash being verified. + * The verifier must make sure to apply a cryptographic + * hash function to the message by itself and not accept an + * msghash32 value directly. Otherwise, it would be easy to + * create a "valid" signature without knowledge of the + * secret key. See also + * https://bitcoin.stackexchange.com/a/81116/35586 for more + * background on this topic. + * pubkey: pointer to an initialized public key to verify with. + * + * To avoid accepting malleable signatures, only ECDSA signatures in lower-S + * form are accepted. + * + * If you need to accept ECDSA signatures from sources that do not obey this + * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to + * verification, but be aware that doing so results in malleable signatures. + * + * For details, see the comments for that function. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify( + const secp256k1_context *ctx, + const secp256k1_ecdsa_signature *sig, + const unsigned char *msghash32, + const secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Convert a signature to a normalized lower-S form. + * + * Returns: 1 if sigin was not normalized, 0 if it already was. + * Args: ctx: a secp256k1 context object + * Out: sigout: a pointer to a signature to fill with the normalized form, + * or copy if the input was already normalized. (can be NULL if + * you're only interested in whether the input was already + * normalized). + * In: sigin: a pointer to a signature to check/normalize (can be identical to sigout) + * + * With ECDSA a third-party can forge a second distinct signature of the same + * message, given a single initial signature, but without knowing the key. This + * is done by negating the S value modulo the order of the curve, 'flipping' + * the sign of the random point R which is not included in the signature. + * + * Forgery of the same message isn't universally problematic, but in systems + * where message malleability or uniqueness of signatures is important this can + * cause issues. This forgery can be blocked by all verifiers forcing signers + * to use a normalized form. + * + * The lower-S form reduces the size of signatures slightly on average when + * variable length encodings (such as DER) are used and is cheap to verify, + * making it a good choice. Security of always using lower-S is assured because + * anyone can trivially modify a signature after the fact to enforce this + * property anyway. + * + * The lower S value is always between 0x1 and + * 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, + * inclusive. + * + * No other forms of ECDSA malleability are known and none seem likely, but + * there is no formal proof that ECDSA, even with this additional restriction, + * is free of other malleability. Commonly used serialization schemes will also + * accept various non-unique encodings, so care should be taken when this + * property is required for an application. + * + * The secp256k1_ecdsa_sign function will by default create signatures in the + * lower-S form, and secp256k1_ecdsa_verify will not accept others. In case + * signatures come from a system that cannot enforce this property, + * secp256k1_ecdsa_signature_normalize must be called before verification. + */ +SECP256K1_API int secp256k1_ecdsa_signature_normalize( + const secp256k1_context *ctx, + secp256k1_ecdsa_signature *sigout, + const secp256k1_ecdsa_signature *sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3); + +/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function. + * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of + * extra entropy. + */ +SECP256K1_API_VAR const secp256k1_nonce_function secp256k1_nonce_function_rfc6979; + +/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */ +SECP256K1_API_VAR const secp256k1_nonce_function secp256k1_nonce_function_default; + +/** Create an ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the secret key was invalid. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: sig: pointer to an array where the signature will be placed. + * In: msghash32: the 32-byte message hash being signed. + * seckey: pointer to a 32-byte secret key. + * noncefp: pointer to a nonce generation function. If NULL, + * secp256k1_nonce_function_default is used. + * ndata: pointer to arbitrary data used by the nonce generation function + * (can be NULL). If it is non-NULL and + * secp256k1_nonce_function_default is used, then ndata must be a + * pointer to 32-bytes of additional data. + * + * The created signature is always in lower-S form. See + * secp256k1_ecdsa_signature_normalize for more details. + */ +SECP256K1_API int secp256k1_ecdsa_sign( + const secp256k1_context *ctx, + secp256k1_ecdsa_signature *sig, + const unsigned char *msghash32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Verify an ECDSA secret key. + * + * A secret key is valid if it is not 0 and less than the secp256k1 curve order + * when interpreted as an integer (most significant byte first). The + * probability of choosing a 32-byte string uniformly at random which is an + * invalid secret key is negligible. + * + * Returns: 1: secret key is valid + * 0: secret key is invalid + * Args: ctx: pointer to a context object. + * In: seckey: pointer to a 32-byte secret key. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify( + const secp256k1_context *ctx, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Compute the public key for a secret key. + * + * Returns: 1: secret was valid, public key stores. + * 0: secret was invalid, try again. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: pubkey: pointer to the created public key. + * In: seckey: pointer to a 32-byte secret key. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Negates a secret key in place. + * + * Returns: 0 if the given secret key is invalid according to + * secp256k1_ec_seckey_verify. 1 otherwise + * Args: ctx: pointer to a context object + * In/Out: seckey: pointer to the 32-byte secret key to be negated. If the + * secret key is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0 and + * seckey will be set to some unspecified value. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_negate( + const secp256k1_context *ctx, + unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Same as secp256k1_ec_seckey_negate, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate( + const secp256k1_context *ctx, + unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) + SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_negate instead"); + +/** Negates a public key in place. + * + * Returns: 1 always + * Args: ctx: pointer to a context object + * In/Out: pubkey: pointer to the public key to be negated. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Tweak a secret key by adding tweak to it. + * + * Returns: 0 if the arguments are invalid or the resulting secret key would be + * invalid (only when the tweak is the negation of the secret key). 1 + * otherwise. + * Args: ctx: pointer to a context object. + * In/Out: seckey: pointer to a 32-byte secret key. If the secret key is + * invalid according to secp256k1_ec_seckey_verify, this + * function returns 0. seckey will be set to some unspecified + * value if this function returns 0. + * In: tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add( + const secp256k1_context *ctx, + unsigned char *seckey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Same as secp256k1_ec_seckey_tweak_add, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( + const secp256k1_context *ctx, + unsigned char *seckey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) + SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_tweak_add instead"); + +/** Tweak a public key by adding tweak times the generator to it. + * + * Returns: 0 if the arguments are invalid or the resulting public key would be + * invalid (only when the tweak is the negation of the corresponding + * secret key). 1 otherwise. + * Args: ctx: pointer to a context object. + * In/Out: pubkey: pointer to a public key object. pubkey will be set to an + * invalid value if this function returns 0. + * In: tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a secret key by multiplying it by a tweak. + * + * Returns: 0 if the arguments are invalid. 1 otherwise. + * Args: ctx: pointer to a context object. + * In/Out: seckey: pointer to a 32-byte secret key. If the secret key is + * invalid according to secp256k1_ec_seckey_verify, this + * function returns 0. seckey will be set to some unspecified + * value if this function returns 0. + * In: tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul( + const secp256k1_context *ctx, + unsigned char *seckey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Same as secp256k1_ec_seckey_tweak_mul, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( + const secp256k1_context *ctx, + unsigned char *seckey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) + SECP256K1_DEPRECATED("Use secp256k1_ec_seckey_tweak_mul instead"); + +/** Tweak a public key by multiplying it by a tweak value. + * + * Returns: 0 if the arguments are invalid. 1 otherwise. + * Args: ctx: pointer to a context object. + * In/Out: pubkey: pointer to a public key object. pubkey will be set to an + * invalid value if this function returns 0. + * In: tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Randomizes the context to provide enhanced protection against side-channel leakage. + * + * Returns: 1: randomization successful + * 0: error + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * In: seed32: pointer to a 32-byte random seed (NULL resets to initial state). + * + * While secp256k1 code is written and tested to be constant-time no matter what + * secret values are, it is possible that a compiler may output code which is not, + * and also that the CPU may not emit the same radio frequencies or draw the same + * amount of power for all values. Randomization of the context shields against + * side-channel observations which aim to exploit secret-dependent behaviour in + * certain computations which involve secret keys. + * + * It is highly recommended to call this function on contexts returned from + * secp256k1_context_create or secp256k1_context_clone (or from the corresponding + * functions in secp256k1_preallocated.h) before using these contexts to call API + * functions that perform computations involving secret keys, e.g., signing and + * public key generation. It is possible to call this function more than once on + * the same context, and doing so before every few computations involving secret + * keys is recommended as a defense-in-depth measure. Randomization of the static + * context secp256k1_context_static is not supported. + * + * Currently, the random seed is mainly used for blinding multiplications of a + * secret scalar with the elliptic curve base point. Multiplications of this + * kind are performed by exactly those API functions which are documented to + * require a context that is not secp256k1_context_static. As a rule of thumb, + * these are all functions which take a secret key (or a keypair) as an input. + * A notable exception to that rule is the ECDH module, which relies on a different + * kind of elliptic curve point multiplication and thus does not benefit from + * enhanced protection against side-channel leakage currently. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize( + secp256k1_context *ctx, + const unsigned char *seed32 +) SECP256K1_ARG_NONNULL(1); + +/** Add a number of public keys together. + * + * Returns: 1: the sum of the public keys is valid. + * 0: the sum of the public keys is not valid. + * Args: ctx: pointer to a context object. + * Out: out: pointer to a public key object for placing the resulting public key. + * In: ins: pointer to array of pointers to public keys. + * n: the number of public keys to add together (must be at least 1). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine( + const secp256k1_context *ctx, + secp256k1_pubkey *out, + const secp256k1_pubkey * const *ins, + size_t n +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Compute a tagged hash as defined in BIP-340. + * + * This is useful for creating a message hash and achieving domain separation + * through an application-specific tag. This function returns + * SHA256(SHA256(tag)||SHA256(tag)||msg). Therefore, tagged hash + * implementations optimized for a specific tag can precompute the SHA256 state + * after hashing the tag hashes. + * + * Returns: 1 always. + * Args: ctx: pointer to a context object + * Out: hash32: pointer to a 32-byte array to store the resulting hash + * In: tag: pointer to an array containing the tag + * taglen: length of the tag array + * msg: pointer to an array containing the message + * msglen: length of the message array + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_tagged_sha256( + const secp256k1_context *ctx, + unsigned char *hash32, + const unsigned char *tag, + size_t taglen, + const unsigned char *msg, + size_t msglen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_H */ diff --git a/src/secp256k1/include/secp256k1_ecdh.h b/src/secp256k1/include/secp256k1_ecdh.h new file mode 100644 index 0000000000..837ae2abe5 --- /dev/null +++ b/src/secp256k1/include/secp256k1_ecdh.h @@ -0,0 +1,63 @@ +#ifndef SECP256K1_ECDH_H +#define SECP256K1_ECDH_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** A pointer to a function that hashes an EC point to obtain an ECDH secret + * + * Returns: 1 if the point was successfully hashed. + * 0 will cause secp256k1_ecdh to fail and return 0. + * Other return values are not allowed, and the behaviour of + * secp256k1_ecdh is undefined for other return values. + * Out: output: pointer to an array to be filled by the function + * In: x32: pointer to a 32-byte x coordinate + * y32: pointer to a 32-byte y coordinate + * data: arbitrary data pointer that is passed through + */ +typedef int (*secp256k1_ecdh_hash_function)( + unsigned char *output, + const unsigned char *x32, + const unsigned char *y32, + void *data +); + +/** An implementation of SHA256 hash function that applies to compressed public key. + * Populates the output parameter with 32 bytes. */ +SECP256K1_API_VAR const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256; + +/** A default ECDH hash function (currently equal to secp256k1_ecdh_hash_function_sha256). + * Populates the output parameter with 32 bytes. */ +SECP256K1_API_VAR const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default; + +/** Compute an EC Diffie-Hellman secret in constant time + * + * Returns: 1: exponentiation was successful + * 0: scalar was invalid (zero or overflow) or hashfp returned 0 + * Args: ctx: pointer to a context object. + * Out: output: pointer to an array to be filled by hashfp. + * In: pubkey: a pointer to a secp256k1_pubkey containing an initialized public key. + * seckey: a 32-byte scalar with which to multiply the point. + * hashfp: pointer to a hash function. If NULL, + * secp256k1_ecdh_hash_function_sha256 is used + * (in which case, 32 bytes will be written to output). + * data: arbitrary data pointer that is passed through to hashfp + * (can be NULL for secp256k1_ecdh_hash_function_sha256). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh( + const secp256k1_context *ctx, + unsigned char *output, + const secp256k1_pubkey *pubkey, + const unsigned char *seckey, + secp256k1_ecdh_hash_function hashfp, + void *data +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_ECDH_H */ diff --git a/src/secp256k1/include/secp256k1_extrakeys.h b/src/secp256k1/include/secp256k1_extrakeys.h new file mode 100644 index 0000000000..52bba240b4 --- /dev/null +++ b/src/secp256k1/include/secp256k1_extrakeys.h @@ -0,0 +1,249 @@ +#ifndef SECP256K1_EXTRAKEYS_H +#define SECP256K1_EXTRAKEYS_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** Opaque data structure that holds a parsed and valid "x-only" public key. + * An x-only pubkey encodes a point whose Y coordinate is even. It is + * serialized using only its X coordinate (32 bytes). See BIP-340 for more + * information about x-only pubkeys. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, use + * use secp256k1_xonly_pubkey_serialize and secp256k1_xonly_pubkey_parse. To + * compare keys, use secp256k1_xonly_pubkey_cmp. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_xonly_pubkey; + +/** Opaque data structure that holds a keypair consisting of a secret and a + * public key. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 96 bytes in size, and can be safely copied/moved. + */ +typedef struct { + unsigned char data[96]; +} secp256k1_keypair; + +/** Parse a 32-byte sequence into a xonly_pubkey object. + * + * Returns: 1 if the public key was fully valid. + * 0 if the public key could not be parsed or is invalid. + * + * Args: ctx: a secp256k1 context object. + * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a + * parsed version of input. If not, it's set to an invalid value. + * In: input32: pointer to a serialized xonly_pubkey. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_parse( + const secp256k1_context *ctx, + secp256k1_xonly_pubkey *pubkey, + const unsigned char *input32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an xonly_pubkey object into a 32-byte sequence. + * + * Returns: 1 always. + * + * Args: ctx: a secp256k1 context object. + * Out: output32: a pointer to a 32-byte array to place the serialized key in. + * In: pubkey: a pointer to a secp256k1_xonly_pubkey containing an initialized public key. + */ +SECP256K1_API int secp256k1_xonly_pubkey_serialize( + const secp256k1_context *ctx, + unsigned char *output32, + const secp256k1_xonly_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Compare two x-only public keys using lexicographic order + * + * Returns: <0 if the first public key is less than the second + * >0 if the first public key is greater than the second + * 0 if the two public keys are equal + * Args: ctx: a secp256k1 context object. + * In: pubkey1: first public key to compare + * pubkey2: second public key to compare + */ +SECP256K1_API int secp256k1_xonly_pubkey_cmp( + const secp256k1_context *ctx, + const secp256k1_xonly_pubkey *pk1, + const secp256k1_xonly_pubkey *pk2 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Converts a secp256k1_pubkey into a secp256k1_xonly_pubkey. + * + * Returns: 1 always. + * + * Args: ctx: pointer to a context object. + * Out: xonly_pubkey: pointer to an x-only public key object for placing the converted public key. + * pk_parity: Ignored if NULL. Otherwise, pointer to an integer that + * will be set to 1 if the point encoded by xonly_pubkey is + * the negation of the pubkey and set to 0 otherwise. + * In: pubkey: pointer to a public key that is converted. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_from_pubkey( + const secp256k1_context *ctx, + secp256k1_xonly_pubkey *xonly_pubkey, + int *pk_parity, + const secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4); + +/** Tweak an x-only public key by adding the generator multiplied with tweak32 + * to it. + * + * Note that the resulting point can not in general be represented by an x-only + * pubkey because it may have an odd Y coordinate. Instead, the output_pubkey + * is a normal secp256k1_pubkey. + * + * Returns: 0 if the arguments are invalid or the resulting public key would be + * invalid (only when the tweak is the negation of the corresponding + * secret key). 1 otherwise. + * + * Args: ctx: pointer to a context object. + * Out: output_pubkey: pointer to a public key to store the result. Will be set + * to an invalid value if this function returns 0. + * In: internal_pubkey: pointer to an x-only pubkey to apply the tweak to. + * tweak32: pointer to a 32-byte tweak. If the tweak is invalid + * according to secp256k1_ec_seckey_verify, this function + * returns 0. For uniformly random 32-byte arrays the + * chance of being invalid is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add( + const secp256k1_context *ctx, + secp256k1_pubkey *output_pubkey, + const secp256k1_xonly_pubkey *internal_pubkey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Checks that a tweaked pubkey is the result of calling + * secp256k1_xonly_pubkey_tweak_add with internal_pubkey and tweak32. + * + * The tweaked pubkey is represented by its 32-byte x-only serialization and + * its pk_parity, which can both be obtained by converting the result of + * tweak_add to a secp256k1_xonly_pubkey. + * + * Note that this alone does _not_ verify that the tweaked pubkey is a + * commitment. If the tweak is not chosen in a specific way, the tweaked pubkey + * can easily be the result of a different internal_pubkey and tweak. + * + * Returns: 0 if the arguments are invalid or the tweaked pubkey is not the + * result of tweaking the internal_pubkey with tweak32. 1 otherwise. + * Args: ctx: pointer to a context object. + * In: tweaked_pubkey32: pointer to a serialized xonly_pubkey. + * tweaked_pk_parity: the parity of the tweaked pubkey (whose serialization + * is passed in as tweaked_pubkey32). This must match the + * pk_parity value that is returned when calling + * secp256k1_xonly_pubkey with the tweaked pubkey, or + * this function will fail. + * internal_pubkey: pointer to an x-only public key object to apply the tweak to. + * tweak32: pointer to a 32-byte tweak. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add_check( + const secp256k1_context *ctx, + const unsigned char *tweaked_pubkey32, + int tweaked_pk_parity, + const secp256k1_xonly_pubkey *internal_pubkey, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5); + +/** Compute the keypair for a secret key. + * + * Returns: 1: secret was valid, keypair is ready to use + * 0: secret was invalid, try again with a different secret + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: keypair: pointer to the created keypair. + * In: seckey: pointer to a 32-byte secret key. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_create( + const secp256k1_context *ctx, + secp256k1_keypair *keypair, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Get the secret key from a keypair. + * + * Returns: 1 always. + * Args: ctx: pointer to a context object. + * Out: seckey: pointer to a 32-byte buffer for the secret key. + * In: keypair: pointer to a keypair. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_sec( + const secp256k1_context *ctx, + unsigned char *seckey, + const secp256k1_keypair *keypair +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Get the public key from a keypair. + * + * Returns: 1 always. + * Args: ctx: pointer to a context object. + * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to + * the keypair public key. If not, it's set to an invalid value. + * In: keypair: pointer to a keypair. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_pub( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const secp256k1_keypair *keypair +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Get the x-only public key from a keypair. + * + * This is the same as calling secp256k1_keypair_pub and then + * secp256k1_xonly_pubkey_from_pubkey. + * + * Returns: 1 always. + * Args: ctx: pointer to a context object. + * Out: pubkey: pointer to an xonly_pubkey object. If 1 is returned, it is set + * to the keypair public key after converting it to an + * xonly_pubkey. If not, it's set to an invalid value. + * pk_parity: Ignored if NULL. Otherwise, pointer to an integer that will be set to the + * pk_parity argument of secp256k1_xonly_pubkey_from_pubkey. + * In: keypair: pointer to a keypair. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_pub( + const secp256k1_context *ctx, + secp256k1_xonly_pubkey *pubkey, + int *pk_parity, + const secp256k1_keypair *keypair +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4); + +/** Tweak a keypair by adding tweak32 to the secret key and updating the public + * key accordingly. + * + * Calling this function and then secp256k1_keypair_pub results in the same + * public key as calling secp256k1_keypair_xonly_pub and then + * secp256k1_xonly_pubkey_tweak_add. + * + * Returns: 0 if the arguments are invalid or the resulting keypair would be + * invalid (only when the tweak is the negation of the keypair's + * secret key). 1 otherwise. + * + * Args: ctx: pointer to a context object. + * In/Out: keypair: pointer to a keypair to apply the tweak to. Will be set to + * an invalid value if this function returns 0. + * In: tweak32: pointer to a 32-byte tweak. If the tweak is invalid according + * to secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_tweak_add( + const secp256k1_context *ctx, + secp256k1_keypair *keypair, + const unsigned char *tweak32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_EXTRAKEYS_H */ diff --git a/src/secp256k1/include/secp256k1_preallocated.h b/src/secp256k1/include/secp256k1_preallocated.h new file mode 100644 index 0000000000..f37744777b --- /dev/null +++ b/src/secp256k1/include/secp256k1_preallocated.h @@ -0,0 +1,134 @@ +#ifndef SECP256K1_PREALLOCATED_H +#define SECP256K1_PREALLOCATED_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/* The module provided by this header file is intended for settings in which it + * is not possible or desirable to rely on dynamic memory allocation. It provides + * functions for creating, cloning, and destroying secp256k1 context objects in a + * contiguous fixed-size block of memory provided by the caller. + * + * Context objects created by functions in this module can be used like contexts + * objects created by functions in secp256k1.h, i.e., they can be passed to any + * API function that expects a context object (see secp256k1.h for details). The + * only exception is that context objects created by functions in this module + * must be destroyed using secp256k1_context_preallocated_destroy (in this + * module) instead of secp256k1_context_destroy (in secp256k1.h). + * + * It is guaranteed that functions in this module will not call malloc or its + * friends realloc, calloc, and free. + */ + +/** Determine the memory size of a secp256k1 context object to be created in + * caller-provided memory. + * + * The purpose of this function is to determine how much memory must be provided + * to secp256k1_context_preallocated_create. + * + * Returns: the required size of the caller-provided memory block + * In: flags: which parts of the context to initialize. + */ +SECP256K1_API size_t secp256k1_context_preallocated_size( + unsigned int flags +) SECP256K1_WARN_UNUSED_RESULT; + +/** Create a secp256k1 context object in caller-provided memory. + * + * The caller must provide a pointer to a rewritable contiguous block of memory + * of size at least secp256k1_context_preallocated_size(flags) bytes, suitably + * aligned to hold an object of any type. + * + * The block of memory is exclusively owned by the created context object during + * the lifetime of this context object, which begins with the call to this + * function and ends when a call to secp256k1_context_preallocated_destroy + * (which destroys the context object again) returns. During the lifetime of the + * context object, the caller is obligated not to access this block of memory, + * i.e., the caller may not read or write the memory, e.g., by copying the memory + * contents to a different location or trying to create a second context object + * in the memory. In simpler words, the prealloc pointer (or any pointer derived + * from it) should not be used during the lifetime of the context object. + * + * Returns: a newly created context object. + * In: prealloc: a pointer to a rewritable contiguous block of memory of + * size at least secp256k1_context_preallocated_size(flags) + * bytes, as detailed above. + * flags: which parts of the context to initialize. + * + * See secp256k1_context_create (in secp256k1.h) for further details. + * + * See also secp256k1_context_randomize (in secp256k1.h) + * and secp256k1_context_preallocated_destroy. + */ +SECP256K1_API secp256k1_context *secp256k1_context_preallocated_create( + void *prealloc, + unsigned int flags +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Determine the memory size of a secp256k1 context object to be copied into + * caller-provided memory. + * + * Returns: the required size of the caller-provided memory block. + * In: ctx: an existing context to copy. + */ +SECP256K1_API size_t secp256k1_context_preallocated_clone_size( + const secp256k1_context *ctx +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Copy a secp256k1 context object into caller-provided memory. + * + * The caller must provide a pointer to a rewritable contiguous block of memory + * of size at least secp256k1_context_preallocated_size(flags) bytes, suitably + * aligned to hold an object of any type. + * + * The block of memory is exclusively owned by the created context object during + * the lifetime of this context object, see the description of + * secp256k1_context_preallocated_create for details. + * + * Cloning secp256k1_context_static is not possible, and should not be emulated by + * the caller (e.g., using memcpy). Create a new context instead. + * + * Returns: a newly created context object. + * Args: ctx: an existing context to copy (not secp256k1_context_static). + * In: prealloc: a pointer to a rewritable contiguous block of memory of + * size at least secp256k1_context_preallocated_size(flags) + * bytes, as detailed above. + */ +SECP256K1_API secp256k1_context *secp256k1_context_preallocated_clone( + const secp256k1_context *ctx, + void *prealloc +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_WARN_UNUSED_RESULT; + +/** Destroy a secp256k1 context object that has been created in + * caller-provided memory. + * + * The context pointer may not be used afterwards. + * + * The context to destroy must have been created using + * secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone. + * If the context has instead been created using secp256k1_context_create or + * secp256k1_context_clone, the behaviour is undefined. In that case, + * secp256k1_context_destroy must be used instead. + * + * If required, it is the responsibility of the caller to deallocate the block + * of memory properly after this function returns, e.g., by calling free on the + * preallocated pointer given to secp256k1_context_preallocated_create or + * secp256k1_context_preallocated_clone. + * + * Args: ctx: an existing context to destroy, constructed using + * secp256k1_context_preallocated_create or + * secp256k1_context_preallocated_clone + * (i.e., not secp256k1_context_static). + */ +SECP256K1_API void secp256k1_context_preallocated_destroy( + secp256k1_context *ctx +) SECP256K1_ARG_NONNULL(1); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PREALLOCATED_H */ diff --git a/src/secp256k1/include/secp256k1_recovery.h b/src/secp256k1/include/secp256k1_recovery.h new file mode 100644 index 0000000000..b12ca4d972 --- /dev/null +++ b/src/secp256k1/include/secp256k1_recovery.h @@ -0,0 +1,113 @@ +#ifndef SECP256K1_RECOVERY_H +#define SECP256K1_RECOVERY_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** Opaque data structured that holds a parsed ECDSA signature, + * supporting pubkey recovery. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 65 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage or transmission, use + * the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + * + * Furthermore, it is guaranteed that identical signatures (including their + * recoverability) will have identical representation, so they can be + * memcmp'ed. + */ +typedef struct { + unsigned char data[65]; +} secp256k1_ecdsa_recoverable_signature; + +/** Parse a compact ECDSA signature (64 bytes + recovery id). + * + * Returns: 1 when the signature could be parsed, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to a 64-byte compact signature + * recid: the recovery id (0, 1, 2 or 3) + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact( + const secp256k1_context *ctx, + secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *input64, + int recid +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Convert a recoverable signature into a normal signature. + * + * Returns: 1 + * Args: ctx: a secp256k1 context object. + * Out: sig: a pointer to a normal signature. + * In: sigin: a pointer to a recoverable signature. + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert( + const secp256k1_context *ctx, + secp256k1_ecdsa_signature *sig, + const secp256k1_ecdsa_recoverable_signature *sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in compact format (64 bytes + recovery id). + * + * Returns: 1 + * Args: ctx: a secp256k1 context object. + * Out: output64: a pointer to a 64-byte array of the compact signature. + * recid: a pointer to an integer to hold the recovery id. + * In: sig: a pointer to an initialized signature object. + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact( + const secp256k1_context *ctx, + unsigned char *output64, + int *recid, + const secp256k1_ecdsa_recoverable_signature *sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Create a recoverable ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the secret key was invalid. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: sig: pointer to an array where the signature will be placed. + * In: msghash32: the 32-byte message hash being signed. + * seckey: pointer to a 32-byte secret key. + * noncefp: pointer to a nonce generation function. If NULL, + * secp256k1_nonce_function_default is used. + * ndata: pointer to arbitrary data used by the nonce generation function + * (can be NULL for secp256k1_nonce_function_default). + */ +SECP256K1_API int secp256k1_ecdsa_sign_recoverable( + const secp256k1_context *ctx, + secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msghash32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Recover an ECDSA public key from a signature. + * + * Returns: 1: public key successfully recovered (which guarantees a correct signature). + * 0: otherwise. + * Args: ctx: pointer to a context object. + * Out: pubkey: pointer to the recovered public key. + * In: sig: pointer to initialized signature that supports pubkey recovery. + * msghash32: the 32-byte message hash assumed to be signed. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover( + const secp256k1_context *ctx, + secp256k1_pubkey *pubkey, + const secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msghash32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_RECOVERY_H */ diff --git a/src/secp256k1/include/secp256k1_schnorrsig.h b/src/secp256k1/include/secp256k1_schnorrsig.h new file mode 100644 index 0000000000..733fee5282 --- /dev/null +++ b/src/secp256k1/include/secp256k1_schnorrsig.h @@ -0,0 +1,182 @@ +#ifndef SECP256K1_SCHNORRSIG_H +#define SECP256K1_SCHNORRSIG_H + +#include "secp256k1.h" +#include "secp256k1_extrakeys.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** This module implements a variant of Schnorr signatures compliant with + * Bitcoin Improvement Proposal 340 "Schnorr Signatures for secp256k1" + * (https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki). + */ + +/** A pointer to a function to deterministically generate a nonce. + * + * Same as secp256k1_nonce function with the exception of accepting an + * additional pubkey argument and not requiring an attempt argument. The pubkey + * argument can protect signature schemes with key-prefixed challenge hash + * inputs against reusing the nonce when signing with the wrong precomputed + * pubkey. + * + * Returns: 1 if a nonce was successfully generated. 0 will cause signing to + * return an error. + * Out: nonce32: pointer to a 32-byte array to be filled by the function + * In: msg: the message being verified. Is NULL if and only if msglen + * is 0. + * msglen: the length of the message + * key32: pointer to a 32-byte secret key (will not be NULL) + * xonly_pk32: the 32-byte serialized xonly pubkey corresponding to key32 + * (will not be NULL) + * algo: pointer to an array describing the signature + * algorithm (will not be NULL) + * algolen: the length of the algo array + * data: arbitrary data pointer that is passed through + * + * Except for test cases, this function should compute some cryptographic hash of + * the message, the key, the pubkey, the algorithm description, and data. + */ +typedef int (*secp256k1_nonce_function_hardened)( + unsigned char *nonce32, + const unsigned char *msg, + size_t msglen, + const unsigned char *key32, + const unsigned char *xonly_pk32, + const unsigned char *algo, + size_t algolen, + void *data +); + +/** An implementation of the nonce generation function as defined in Bitcoin + * Improvement Proposal 340 "Schnorr Signatures for secp256k1" + * (https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki). + * + * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of + * auxiliary random data as defined in BIP-340. If the data pointer is NULL, + * the nonce derivation procedure follows BIP-340 by setting the auxiliary + * random data to zero. The algo argument must be non-NULL, otherwise the + * function will fail and return 0. The hash will be tagged with algo. + * Therefore, to create BIP-340 compliant signatures, algo must be set to + * "BIP0340/nonce" and algolen to 13. + */ +SECP256K1_API_VAR const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340; + +/** Data structure that contains additional arguments for schnorrsig_sign_custom. + * + * A schnorrsig_extraparams structure object can be initialized correctly by + * setting it to SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT. + * + * Members: + * magic: set to SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC at initialization + * and has no other function than making sure the object is + * initialized. + * noncefp: pointer to a nonce generation function. If NULL, + * secp256k1_nonce_function_bip340 is used + * ndata: pointer to arbitrary data used by the nonce generation function + * (can be NULL). If it is non-NULL and + * secp256k1_nonce_function_bip340 is used, then ndata must be a + * pointer to 32-byte auxiliary randomness as per BIP-340. + */ +typedef struct { + unsigned char magic[4]; + secp256k1_nonce_function_hardened noncefp; + void *ndata; +} secp256k1_schnorrsig_extraparams; + +#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC { 0xda, 0x6f, 0xb3, 0x8c } +#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT {\ + SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC,\ + NULL,\ + NULL\ +} + +/** Create a Schnorr signature. + * + * Does _not_ strictly follow BIP-340 because it does not verify the resulting + * signature. Instead, you can manually use secp256k1_schnorrsig_verify and + * abort if it fails. + * + * This function only signs 32-byte messages. If you have messages of a + * different size (or the same size but without a context-specific tag + * prefix), it is recommended to create a 32-byte message hash with + * secp256k1_tagged_sha256 and then sign the hash. Tagged hashing allows + * providing an context-specific tag for domain separation. This prevents + * signatures from being valid in multiple contexts by accident. + * + * Returns 1 on success, 0 on failure. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: sig64: pointer to a 64-byte array to store the serialized signature. + * In: msg32: the 32-byte message being signed. + * keypair: pointer to an initialized keypair. + * aux_rand32: 32 bytes of fresh randomness. While recommended to provide + * this, it is only supplemental to security and can be NULL. A + * NULL argument is treated the same as an all-zero one. See + * BIP-340 "Default Signing" for a full explanation of this + * argument and for guidance if randomness is expensive. + */ +SECP256K1_API int secp256k1_schnorrsig_sign32( + const secp256k1_context *ctx, + unsigned char *sig64, + const unsigned char *msg32, + const secp256k1_keypair *keypair, + const unsigned char *aux_rand32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Same as secp256k1_schnorrsig_sign32, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API int secp256k1_schnorrsig_sign( + const secp256k1_context *ctx, + unsigned char *sig64, + const unsigned char *msg32, + const secp256k1_keypair *keypair, + const unsigned char *aux_rand32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) + SECP256K1_DEPRECATED("Use secp256k1_schnorrsig_sign32 instead"); + +/** Create a Schnorr signature with a more flexible API. + * + * Same arguments as secp256k1_schnorrsig_sign except that it allows signing + * variable length messages and accepts a pointer to an extraparams object that + * allows customizing signing by passing additional arguments. + * + * Creates the same signatures as schnorrsig_sign if msglen is 32 and the + * extraparams.ndata is the same as aux_rand32. + * + * In: msg: the message being signed. Can only be NULL if msglen is 0. + * msglen: length of the message + * extraparams: pointer to a extraparams object (can be NULL) + */ +SECP256K1_API int secp256k1_schnorrsig_sign_custom( + const secp256k1_context *ctx, + unsigned char *sig64, + const unsigned char *msg, + size_t msglen, + const secp256k1_keypair *keypair, + secp256k1_schnorrsig_extraparams *extraparams +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5); + +/** Verify a Schnorr signature. + * + * Returns: 1: correct signature + * 0: incorrect signature + * Args: ctx: a secp256k1 context object. + * In: sig64: pointer to the 64-byte signature to verify. + * msg: the message being verified. Can only be NULL if msglen is 0. + * msglen: length of the message + * pubkey: pointer to an x-only public key to verify with (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify( + const secp256k1_context *ctx, + const unsigned char *sig64, + const unsigned char *msg, + size_t msglen, + const secp256k1_xonly_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_SCHNORRSIG_H */ diff --git a/src/secp256k1/libsecp256k1.pc.in b/src/secp256k1/libsecp256k1.pc.in new file mode 100644 index 0000000000..0fb6f48a6c --- /dev/null +++ b/src/secp256k1/libsecp256k1.pc.in @@ -0,0 +1,12 @@ +prefix=@prefix@ +exec_prefix=@exec_prefix@ +libdir=@libdir@ +includedir=@includedir@ + +Name: libsecp256k1 +Description: Optimized C library for EC operations on curve secp256k1 +URL: https://github.com/bitcoin-core/secp256k1 +Version: @PACKAGE_VERSION@ +Cflags: -I${includedir} +Libs: -L${libdir} -lsecp256k1 + diff --git a/src/secp256k1/sage/gen_exhaustive_groups.sage b/src/secp256k1/sage/gen_exhaustive_groups.sage new file mode 100644 index 0000000000..070bc1285f --- /dev/null +++ b/src/secp256k1/sage/gen_exhaustive_groups.sage @@ -0,0 +1,156 @@ +load("secp256k1_params.sage") + +MAX_ORDER = 1000 + +# Set of (curve) orders we have encountered so far. +orders_done = set() + +# Map from (subgroup) orders to [b, int(gen.x), int(gen.y), gen, lambda] for those subgroups. +solutions = {} + +# Iterate over curves of the form y^2 = x^3 + B. +for b in range(1, P): + # There are only 6 curves (up to isomorphism) of the form y^2 = x^3 + B. Stop once we have tried all. + if len(orders_done) == 6: + break + + E = EllipticCurve(F, [0, b]) + print("Analyzing curve y^2 = x^3 + %i" % b) + n = E.order() + + # Skip curves with an order we've already tried + if n in orders_done: + print("- Isomorphic to earlier curve") + print() + continue + orders_done.add(n) + + # Skip curves isomorphic to the real secp256k1 + if n.is_pseudoprime(): + assert E.is_isomorphic(C) + print("- Isomorphic to secp256k1") + print() + continue + + print("- Finding prime subgroups") + + # Map from group_order to a set of independent generators for that order. + curve_gens = {} + + for g in E.gens(): + # Find what prime subgroups of group generated by g exist. + g_order = g.order() + for f, _ in g.order().factor(): + # Skip subgroups that have bad size. + if f < 4: + print(f" - Subgroup of size {f}: too small") + continue + if f > MAX_ORDER: + print(f" - Subgroup of size {f}: too large") + continue + + # Construct a generator for that subgroup. + gen = g * (g_order // f) + assert(gen.order() == f) + + # Add to set the minimal multiple of gen. + curve_gens.setdefault(f, set()).add(min([j*gen for j in range(1, f)])) + print(f" - Subgroup of size {f}: ok") + + for f in sorted(curve_gens.keys()): + print(f"- Constructing group of order {f}") + cbrts = sorted([int(c) for c in Integers(f)(1).nth_root(3, all=true) if c != 1]) + gens = list(curve_gens[f]) + sol_count = 0 + no_endo_count = 0 + + # Consider all non-zero linear combinations of the independent generators. + for j in range(1, f**len(gens)): + gen = sum(gens[k] * ((j // f**k) % f) for k in range(len(gens))) + assert not gen.is_zero() + assert (f*gen).is_zero() + + # Find lambda for endomorphism. Skip if none can be found. + lam = None + for l in cbrts: + if l*gen == E(BETA*gen[0], gen[1]): + lam = l + break + + if lam is None: + no_endo_count += 1 + else: + sol_count += 1 + solutions.setdefault(f, []).append((b, int(gen[0]), int(gen[1]), gen, lam)) + + print(f" - Found {sol_count} generators (plus {no_endo_count} without endomorphism)") + + print() + +def output_generator(g, name): + print(f"#define {name} SECP256K1_GE_CONST(\\") + print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x,\\" % tuple((int(g[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4))) + print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x,\\" % tuple((int(g[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8))) + print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x,\\" % tuple((int(g[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4))) + print(" 0x%08x, 0x%08x, 0x%08x, 0x%08x\\" % tuple((int(g[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8))) + print(")") + +def output_b(b): + print(f"#define SECP256K1_B {int(b)}") + +print() +print("To be put in src/group_impl.h:") +print() +print("/* Begin of section generated by sage/gen_exhaustive_groups.sage. */") +for f in sorted(solutions.keys()): + # Use as generator/2 the one with lowest b, and lowest (x, y) generator (interpreted as non-negative integers). + b, _, _, HALF_G, lam = min(solutions[f]) + output_generator(2 * HALF_G, f"SECP256K1_G_ORDER_{f}") +print("/** Generator for secp256k1, value 'g' defined in") +print(" * \"Standards for Efficient Cryptography\" (SEC2) 2.7.1.") +print(" */") +output_generator(G, "SECP256K1_G") +print("/* These exhaustive group test orders and generators are chosen such that:") +print(" * - The field size is equal to that of secp256k1, so field code is the same.") +print(" * - The curve equation is of the form y^2=x^3+B for some small constant B.") +print(" * - The subgroup has a generator 2*P, where P.x is as small as possible.") +print(f" * - The subgroup has size less than {MAX_ORDER} to permit exhaustive testing.") +print(" * - The subgroup admits an endomorphism of the form lambda*(x,y) == (beta*x,y).") +print(" */") +print("#if defined(EXHAUSTIVE_TEST_ORDER)") +first = True +for f in sorted(solutions.keys()): + b, _, _, _, lam = min(solutions[f]) + print(f"# {'if' if first else 'elif'} EXHAUSTIVE_TEST_ORDER == {f}") + first = False + print() + print(f"static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_{f};") + output_b(b) + print() +print("# else") +print("# error No known generator for the specified exhaustive test group order.") +print("# endif") +print("#else") +print() +print("static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;") +output_b(7) +print() +print("#endif") +print("/* End of section generated by sage/gen_exhaustive_groups.sage. */") + + +print() +print() +print("To be put in src/scalar_impl.h:") +print() +print("/* Begin of section generated by sage/gen_exhaustive_groups.sage. */") +first = True +for f in sorted(solutions.keys()): + _, _, _, _, lam = min(solutions[f]) + print("# %s EXHAUSTIVE_TEST_ORDER == %i" % ("if" if first else "elif", f)) + first = False + print("# define EXHAUSTIVE_TEST_LAMBDA %i" % lam) +print("# else") +print("# error No known lambda for the specified exhaustive test group order.") +print("# endif") +print("/* End of section generated by sage/gen_exhaustive_groups.sage. */") diff --git a/src/secp256k1/sage/gen_split_lambda_constants.sage b/src/secp256k1/sage/gen_split_lambda_constants.sage new file mode 100644 index 0000000000..7d4359e0f6 --- /dev/null +++ b/src/secp256k1/sage/gen_split_lambda_constants.sage @@ -0,0 +1,114 @@ +""" Generates the constants used in secp256k1_scalar_split_lambda. + +See the comments for secp256k1_scalar_split_lambda in src/scalar_impl.h for detailed explanations. +""" + +load("secp256k1_params.sage") + +def inf_norm(v): + """Returns the infinity norm of a vector.""" + return max(map(abs, v)) + +def gauss_reduction(i1, i2): + v1, v2 = i1.copy(), i2.copy() + while True: + if inf_norm(v2) < inf_norm(v1): + v1, v2 = v2, v1 + # This is essentially + # m = round((v1[0]*v2[0] + v1[1]*v2[1]) / (inf_norm(v1)**2)) + # (rounding to the nearest integer) without relying on floating point arithmetic. + m = ((v1[0]*v2[0] + v1[1]*v2[1]) + (inf_norm(v1)**2) // 2) // (inf_norm(v1)**2) + if m == 0: + return v1, v2 + v2[0] -= m*v1[0] + v2[1] -= m*v1[1] + +def find_split_constants_gauss(): + """Find constants for secp256k1_scalar_split_lamdba using gauss reduction.""" + (v11, v12), (v21, v22) = gauss_reduction([0, N], [1, int(LAMBDA)]) + + # We use related vectors in secp256k1_scalar_split_lambda. + A1, B1 = -v21, -v11 + A2, B2 = v22, -v21 + + return A1, B1, A2, B2 + +def find_split_constants_explicit_tof(): + """Find constants for secp256k1_scalar_split_lamdba using the trace of Frobenius. + + See Benjamin Smith: "Easy scalar decompositions for efficient scalar multiplication on + elliptic curves and genus 2 Jacobians" (https://eprint.iacr.org/2013/672), Example 2 + """ + assert P % 3 == 1 # The paper says P % 3 == 2 but that appears to be a mistake, see [10]. + assert C.j_invariant() == 0 + + t = C.trace_of_frobenius() + + c = Integer(sqrt((4*P - t**2)/3)) + A1 = Integer((t - c)/2 - 1) + B1 = c + + A2 = Integer((t + c)/2 - 1) + B2 = Integer(1 - (t - c)/2) + + # We use a negated b values in secp256k1_scalar_split_lambda. + B1, B2 = -B1, -B2 + + return A1, B1, A2, B2 + +A1, B1, A2, B2 = find_split_constants_explicit_tof() + +# For extra fun, use an independent method to recompute the constants. +assert (A1, B1, A2, B2) == find_split_constants_gauss() + +# PHI : Z[l] -> Z_n where phi(a + b*l) == a + b*lambda mod n. +def PHI(a,b): + return Z(a + LAMBDA*b) + +# Check that (A1, B1) and (A2, B2) are in the kernel of PHI. +assert PHI(A1, B1) == Z(0) +assert PHI(A2, B2) == Z(0) + +# Check that the parallelogram generated by (A1, A2) and (B1, B2) +# is a fundamental domain by containing exactly N points. +# Since the LHS is the determinant and N != 0, this also checks that +# (A1, A2) and (B1, B2) are linearly independent. By the previous +# assertions, (A1, A2) and (B1, B2) are a basis of the kernel. +assert A1*B2 - B1*A2 == N + +# Check that their components are short enough. +assert (A1 + A2)/2 < sqrt(N) +assert B1 < sqrt(N) +assert B2 < sqrt(N) + +G1 = round((2**384)*B2/N) +G2 = round((2**384)*(-B1)/N) + +def rnddiv2(v): + if v & 1: + v += 1 + return v >> 1 + +def scalar_lambda_split(k): + """Equivalent to secp256k1_scalar_lambda_split().""" + c1 = rnddiv2((k * G1) >> 383) + c2 = rnddiv2((k * G2) >> 383) + c1 = (c1 * -B1) % N + c2 = (c2 * -B2) % N + r2 = (c1 + c2) % N + r1 = (k + r2 * -LAMBDA) % N + return (r1, r2) + +# The result of scalar_lambda_split can depend on the representation of k (mod n). +SPECIAL = (2**383) // G2 + 1 +assert scalar_lambda_split(SPECIAL) != scalar_lambda_split(SPECIAL + N) + +print(' A1 =', hex(A1)) +print(' -B1 =', hex(-B1)) +print(' A2 =', hex(A2)) +print(' -B2 =', hex(-B2)) +print(' =', hex(Z(-B2))) +print(' -LAMBDA =', hex(-LAMBDA)) + +print(' G1 =', hex(G1)) +print(' G2 =', hex(G2)) diff --git a/src/secp256k1/sage/group_prover.sage b/src/secp256k1/sage/group_prover.sage new file mode 100644 index 0000000000..9305c215d5 --- /dev/null +++ b/src/secp256k1/sage/group_prover.sage @@ -0,0 +1,353 @@ +# This code supports verifying group implementations which have branches +# or conditional statements (like cmovs), by allowing each execution path +# to independently set assumptions on input or intermediary variables. +# +# The general approach is: +# * A constraint is a tuple of two sets of symbolic expressions: +# the first of which are required to evaluate to zero, the second of which +# are required to evaluate to nonzero. +# - A constraint is said to be conflicting if any of its nonzero expressions +# is in the ideal with basis the zero expressions (in other words: when the +# zero expressions imply that one of the nonzero expressions are zero). +# * There is a list of laws that describe the intended behaviour, including +# laws for addition and doubling. Each law is called with the symbolic point +# coordinates as arguments, and returns: +# - A constraint describing the assumptions under which it is applicable, +# called "assumeLaw" +# - A constraint describing the requirements of the law, called "require" +# * Implementations are transliterated into functions that operate as well on +# algebraic input points, and are called once per combination of branches +# executed. Each execution returns: +# - A constraint describing the assumptions this implementation requires +# (such as Z1=1), called "assumeFormula" +# - A constraint describing the assumptions this specific branch requires, +# but which is by construction guaranteed to cover the entire space by +# merging the results from all branches, called "assumeBranch" +# - The result of the computation +# * All combinations of laws with implementation branches are tried, and: +# - If the combination of assumeLaw, assumeFormula, and assumeBranch results +# in a conflict, it means this law does not apply to this branch, and it is +# skipped. +# - For others, we try to prove the require constraints hold, assuming the +# information in assumeLaw + assumeFormula + assumeBranch, and if this does +# not succeed, we fail. +# + To prove an expression is zero, we check whether it belongs to the +# ideal with the assumed zero expressions as basis. This test is exact. +# + To prove an expression is nonzero, we check whether each of its +# factors is contained in the set of nonzero assumptions' factors. +# This test is not exact, so various combinations of original and +# reduced expressions' factors are tried. +# - If we succeed, we print out the assumptions from assumeFormula that +# weren't implied by assumeLaw already. Those from assumeBranch are skipped, +# as we assume that all constraints in it are complementary with each other. +# +# Based on the sage verification scripts used in the Explicit-Formulas Database +# by Tanja Lange and others, see https://hyperelliptic.org/EFD + +class fastfrac: + """Fractions over rings.""" + + def __init__(self,R,top,bot=1): + """Construct a fractional, given a ring, a numerator, and denominator.""" + self.R = R + if parent(top) == ZZ or parent(top) == R: + self.top = R(top) + self.bot = R(bot) + elif top.__class__ == fastfrac: + self.top = top.top + self.bot = top.bot * bot + else: + self.top = R(numerator(top)) + self.bot = R(denominator(top)) * bot + + def iszero(self,I): + """Return whether this fraction is zero given an ideal.""" + return self.top in I and self.bot not in I + + def reduce(self,assumeZero): + zero = self.R.ideal(list(map(numerator, assumeZero))) + return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot)) + + def __add__(self,other): + """Add two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top + self.bot * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot + self.bot * other.top,self.bot * other.bot) + return NotImplemented + + def __sub__(self,other): + """Subtract two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top - self.bot * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot - self.bot * other.top,self.bot * other.bot) + return NotImplemented + + def __neg__(self): + """Return the negation of a fraction.""" + return fastfrac(self.R,-self.top,self.bot) + + def __mul__(self,other): + """Multiply two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.top,self.bot * other.bot) + return NotImplemented + + def __rmul__(self,other): + """Multiply something else with a fraction.""" + return self.__mul__(other) + + def __truediv__(self,other): + """Divide two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top,self.bot * other) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot,self.bot * other.top) + return NotImplemented + + # Compatibility wrapper for Sage versions based on Python 2 + def __div__(self,other): + """Divide two fractions.""" + return self.__truediv__(other) + + def __pow__(self,other): + """Compute a power of a fraction.""" + if parent(other) == ZZ: + if other < 0: + # Negative powers require flipping top and bottom + return fastfrac(self.R,self.bot ^ (-other),self.top ^ (-other)) + else: + return fastfrac(self.R,self.top ^ other,self.bot ^ other) + return NotImplemented + + def __str__(self): + return "fastfrac((" + str(self.top) + ") / (" + str(self.bot) + "))" + def __repr__(self): + return "%s" % self + + def numerator(self): + return self.top + +class constraints: + """A set of constraints, consisting of zero and nonzero expressions. + + Constraints can either be used to express knowledge or a requirement. + + Both the fields zero and nonzero are maps from expressions to description + strings. The expressions that are the keys in zero are required to be zero, + and the expressions that are the keys in nonzero are required to be nonzero. + + Note that (a != 0) and (b != 0) is the same as (a*b != 0), so all keys in + nonzero could be multiplied into a single key. This is often much less + efficient to work with though, so we keep them separate inside the + constraints. This allows higher-level code to do fast checks on the individual + nonzero elements, or combine them if needed for stronger checks. + + We can't multiply the different zero elements, as it would suffice for one of + the factors to be zero, instead of all of them. Instead, the zero elements are + typically combined into an ideal first. + """ + + def __init__(self, **kwargs): + if 'zero' in kwargs: + self.zero = dict(kwargs['zero']) + else: + self.zero = dict() + if 'nonzero' in kwargs: + self.nonzero = dict(kwargs['nonzero']) + else: + self.nonzero = dict() + + def negate(self): + return constraints(zero=self.nonzero, nonzero=self.zero) + + def map(self, fun): + return constraints(zero={fun(k): v for k, v in self.zero.items()}, nonzero={fun(k): v for k, v in self.nonzero.items()}) + + def __add__(self, other): + zero = self.zero.copy() + zero.update(other.zero) + nonzero = self.nonzero.copy() + nonzero.update(other.nonzero) + return constraints(zero=zero, nonzero=nonzero) + + def __str__(self): + return "constraints(zero=%s,nonzero=%s)" % (self.zero, self.nonzero) + + def __repr__(self): + return "%s" % self + +def normalize_factor(p): + """Normalizes the sign of primitive polynomials (as returned by factor()) + + This function ensures that the polynomial has a positive leading coefficient. + + This is necessary because recent sage versions (starting with v9.3 or v9.4, + we don't know) are inconsistent about the placement of the minus sign in + polynomial factorizations: + ``` + sage: R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex') + sage: R((-2 * (bx - ax)) ^ 1).factor() + (-2) * (bx - ax) + sage: R((-2 * (bx - ax)) ^ 2).factor() + (4) * (-bx + ax)^2 + sage: R((-2 * (bx - ax)) ^ 3).factor() + (8) * (-bx + ax)^3 + ``` + """ + # Assert p is not 0 and that its non-zero coeffients are coprime. + # (We could just work with the primitive part p/p.content() but we want to be + # aware if factor() does not return a primitive part in future sage versions.) + assert p.content() == 1 + # Ensure that the first non-zero coefficient is positive. + return p if p.lc() > 0 else -p + +def conflicts(R, con): + """Check whether any of the passed non-zero assumptions is implied by the zero assumptions""" + zero = R.ideal(list(map(numerator, con.zero))) + if 1 in zero: + return True + # First a cheap check whether any of the individual nonzero terms conflict on + # their own. + for nonzero in con.nonzero: + if nonzero.iszero(zero): + return True + # It can be the case that entries in the nonzero set do not individually + # conflict with the zero set, but their combination does. For example, knowing + # that either x or y is zero is equivalent to having x*y in the zero set. + # Having x or y individually in the nonzero set is not a conflict, but both + # simultaneously is, so that is the right thing to check for. + if reduce(lambda a,b: a * b, con.nonzero, fastfrac(R, 1)).iszero(zero): + return True + return False + + +def get_nonzero_set(R, assume): + """Calculate a simple set of nonzero expressions""" + zero = R.ideal(list(map(numerator, assume.zero))) + nonzero = set() + for nz in map(numerator, assume.nonzero): + for (f,n) in nz.factor(): + nonzero.add(normalize_factor(f)) + rnz = zero.reduce(nz) + for (f,n) in rnz.factor(): + nonzero.add(normalize_factor(f)) + return nonzero + + +def prove_nonzero(R, exprs, assume): + """Check whether an expression is provably nonzero, given assumptions""" + zero = R.ideal(list(map(numerator, assume.zero))) + nonzero = get_nonzero_set(R, assume) + expl = set() + ok = True + for expr in exprs: + if numerator(expr) in zero: + return (False, [exprs[expr]]) + allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1) + for (f, n) in allexprs.factor(): + if normalize_factor(f) not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for (f, n) in zero.reduce(allexprs).factor(): + if normalize_factor(f) not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for expr in exprs: + for (f,n) in numerator(expr).factor(): + if normalize_factor(f) not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for expr in exprs: + for (f,n) in zero.reduce(numerator(expr)).factor(): + if normalize_factor(f) not in nonzero: + expl.add(exprs[expr]) + if expl: + return (False, list(expl)) + else: + return (True, None) + + +def prove_zero(R, exprs, assume): + """Check whether all of the passed expressions are provably zero, given assumptions""" + r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume) + if not r: + return (False, list(map(lambda x: "Possibly zero denominator: %s" % x, e))) + zero = R.ideal(list(map(numerator, assume.zero))) + nonzero = prod(x for x in assume.nonzero) + expl = [] + for expr in exprs: + if not expr.iszero(zero): + expl.append(exprs[expr]) + if not expl: + return (True, None) + return (False, expl) + + +def describe_extra(R, assume, assumeExtra): + """Describe what assumptions are added, given existing assumptions""" + zerox = assume.zero.copy() + zerox.update(assumeExtra.zero) + zero = R.ideal(list(map(numerator, assume.zero))) + zeroextra = R.ideal(list(map(numerator, zerox))) + nonzero = get_nonzero_set(R, assume) + ret = set() + # Iterate over the extra zero expressions + for base in assumeExtra.zero: + if base not in zero: + add = [] + for (f, n) in numerator(base).factor(): + if normalize_factor(f) not in nonzero: + add += ["%s" % normalize_factor(f)] + if add: + ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base]) + # Iterate over the extra nonzero expressions + for nz in assumeExtra.nonzero: + nzr = zeroextra.reduce(numerator(nz)) + if nzr not in zeroextra: + for (f,n) in nzr.factor(): + if normalize_factor(zeroextra.reduce(f)) not in nonzero: + ret.add("%s != 0" % normalize_factor(zeroextra.reduce(f))) + return ", ".join(x for x in ret) + + +def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require): + """Check a set of zero and nonzero requirements, given a set of zero and nonzero assumptions""" + assume = assumeLaw + assumeAssert + assumeBranch + + if conflicts(R, assume): + # This formula does not apply + return (True, None) + + describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert) + if describe != "": + describe = " (assuming " + describe + ")" + + ok, msg = prove_zero(R, require.zero, assume) + if not ok: + return (False, "FAIL, %s fails%s" % (str(msg), describe)) + + res, expl = prove_nonzero(R, require.nonzero, assume) + if not res: + return (False, "FAIL, %s fails%s" % (str(expl), describe)) + + return (True, "OK%s" % describe) + + +def concrete_verify(c): + for k in c.zero: + if k != 0: + return (False, c.zero[k]) + for k in c.nonzero: + if k == 0: + return (False, c.nonzero[k]) + return (True, None) diff --git a/src/secp256k1/sage/prove_group_implementations.sage b/src/secp256k1/sage/prove_group_implementations.sage new file mode 100644 index 0000000000..23799be52b --- /dev/null +++ b/src/secp256k1/sage/prove_group_implementations.sage @@ -0,0 +1,285 @@ +# Test libsecp256k1' group operation implementations using prover.sage + +import sys + +load("group_prover.sage") +load("weierstrass_prover.sage") + +def formula_secp256k1_gej_double_var(a): + """libsecp256k1's secp256k1_gej_double_var, used by various addition functions""" + rz = a.Z * a.Y + s = a.Y^2 + l = a.X^2 + l = l * 3 + l = l / 2 + t = -s + t = t * a.X + rx = l^2 + rx = rx + t + rx = rx + t + s = s^2 + t = t + rx + ry = t * l + ry = ry + s + ry = -ry + return jacobianpoint(rx, ry, rz) + +def formula_secp256k1_gej_add_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_var""" + if branch == 0: + return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z22 = b.Z^2 + z12 = a.Z^2 + u1 = a.X * z22 + u2 = b.X * z12 + s1 = a.Y * z22 + s1 = s1 * b.Z + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s2 + i = i + s1 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r) + if branch == 3: + return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity()) + t = h * b.Z + rz = a.Z * t + h2 = h^2 + h2 = -h2 + h3 = h2 * h + t = u1 * h2 + rx = i^2 + rx = rx + h3 + rx = rx + t + rx = rx + t + t = t + rx + ry = t * i + h3 = h3 * s1 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1""" + if branch == 0: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z12 = a.Z^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s2 + i = i + s1 + if (branch == 2): + r = formula_secp256k1_gej_double_var(a) + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if (branch == 3): + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + rz = a.Z * h + h2 = h^2 + h2 = -h2 + h3 = h2 * h + t = u1 * h2 + rx = i^2 + rx = rx + h3 + rx = rx + t + rx = rx + t + t = t + rx + ry = t * i + h3 = h3 * s1 + ry = ry + h3 + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_zinv_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_zinv_var""" + bzinv = b.Z^(-1) + if branch == 0: + rinf = b.Infinity + bzinv2 = bzinv^2 + bzinv3 = bzinv2 * bzinv + rx = b.X * bzinv2 + ry = b.Y * bzinv3 + rz = 1 + return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz, rinf)) + if branch == 1: + return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + azz = a.Z * bzinv + z12 = azz^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * azz + h = -u1 + h = h + u2 + i = -s2 + i = i + s1 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if branch == 3: + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + rz = a.Z * h + h2 = h^2 + h2 = -h2 + h3 = h2 * h + t = u1 * h2 + rx = i^2 + rx = rx + h3 + rx = rx + t + rx = rx + t + t = t + rx + ry = t * i + h3 = h3 * s1 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge""" + zeroes = {} + nonzeroes = {} + a_infinity = False + if (branch & 2) != 0: + nonzeroes.update({a.Infinity : 'a_infinite'}) + a_infinity = True + else: + zeroes.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + rr = t^2 + m_alt = -u2 + tt = u1 * m_alt + rr = rr + tt + degenerate = (branch & 1) != 0 + if degenerate: + zeroes.update({m : 'm_zero'}) + else: + nonzeroes.update({m : 'm_nonzero'}) + rr_alt = s1 + rr_alt = rr_alt * 2 + m_alt = m_alt + u1 + if not degenerate: + rr_alt = rr + m_alt = m + n = m_alt^2 + q = -t + q = q * n + n = n^2 + if degenerate: + n = m + t = rr_alt^2 + rz = a.Z * m_alt + t = t + q + rx = t + t = t * 2 + t = t + q + t = t * rr_alt + t = t + n + ry = -t + ry = ry / 2 + if a_infinity: + rx = b.X + ry = b.Y + rz = 1 + if (branch & 4) != 0: + zeroes.update({rz : 'r.z = 0'}) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity()) + else: + nonzeroes.update({rz : 'r.z != 0'}) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge_old(branch, a, b): + """libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx""" + a_infinity = (branch & 1) != 0 + zero = {} + nonzero = {} + if a_infinity: + nonzero.update({a.Infinity : 'a_infinite'}) + else: + zero.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + z = a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + n = m^2 + q = n * t + n = n^2 + rr = t^2 + t = u1 * u2 + t = -t + rr = rr + t + t = rr^2 + rz = m * z + infinity = False + if (branch & 2) != 0: + if not a_infinity: + infinity = True + else: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity()) + zero.update({rz : 'r.z=0'}) + else: + nonzero.update({rz : 'r.z!=0'}) + rz = rz * (0 if a_infinity else 2) + rx = t + q = -q + rx = rx + q + q = q * 3 + t = t * 2 + t = t + q + t = t * rr + t = t + n + ry = -t + rx = rx * (0 if a_infinity else 4) + ry = ry * (0 if a_infinity else 4) + t = b.X + t = t * (1 if a_infinity else 0) + rx = rx + t + t = b.Y + t = t * (1 if a_infinity else 0) + ry = ry + t + t = (1 if a_infinity else 0) + rz = rz + t + if infinity: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity()) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz)) + +if __name__ == "__main__": + success = True + success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var) + success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var) + success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var) + success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 8, formula_secp256k1_gej_add_ge) + success = success & (not check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)) + + if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive": + success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43) + success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43) + success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43) + success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 8, formula_secp256k1_gej_add_ge, 43) + success = success & (not check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)) + + sys.exit(int(not success)) diff --git a/src/secp256k1/sage/secp256k1_params.sage b/src/secp256k1/sage/secp256k1_params.sage new file mode 100644 index 0000000000..68f95adec4 --- /dev/null +++ b/src/secp256k1/sage/secp256k1_params.sage @@ -0,0 +1,39 @@ +"""Prime order of finite field underlying secp256k1 (2^256 - 2^32 - 977)""" +P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F + +"""Finite field underlying secp256k1""" +F = FiniteField(P) + +"""Elliptic curve secp256k1: y^2 = x^3 + 7""" +C = EllipticCurve([F(0), F(7)]) + +"""Base point of secp256k1""" +G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798) +if int(G[1]) & 1: + # G.y is even + G = -G + +"""Prime order of secp256k1""" +N = C.order() + +"""Finite field of scalars of secp256k1""" +Z = FiniteField(N) + +""" Beta value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)""" +BETA = F(2)^((P-1)/3) + +""" Lambda value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)""" +LAMBDA = Z(3)^((N-1)/3) + +assert is_prime(P) +assert is_prime(N) + +assert BETA != F(1) +assert BETA^3 == F(1) +assert BETA^2 + BETA + 1 == 0 + +assert LAMBDA != Z(1) +assert LAMBDA^3 == Z(1) +assert LAMBDA^2 + LAMBDA + 1 == 0 + +assert Integer(LAMBDA)*G == C(BETA*G[0], G[1]) diff --git a/src/secp256k1/sage/weierstrass_prover.sage b/src/secp256k1/sage/weierstrass_prover.sage new file mode 100644 index 0000000000..be9cfd4c76 --- /dev/null +++ b/src/secp256k1/sage/weierstrass_prover.sage @@ -0,0 +1,275 @@ +# Prover implementation for Weierstrass curves of the form +# y^2 = x^3 + A * x + B, specifically with a = 0 and b = 7, with group laws +# operating on affine and Jacobian coordinates, including the point at infinity +# represented by a 4th variable in coordinates. + +load("group_prover.sage") + + +class affinepoint: + def __init__(self, x, y, infinity=0): + self.x = x + self.y = y + self.infinity = infinity + def __str__(self): + return "affinepoint(x=%s,y=%s,inf=%s)" % (self.x, self.y, self.infinity) + + +class jacobianpoint: + def __init__(self, x, y, z, infinity=0): + self.X = x + self.Y = y + self.Z = z + self.Infinity = infinity + def __str__(self): + return "jacobianpoint(X=%s,Y=%s,Z=%s,inf=%s)" % (self.X, self.Y, self.Z, self.Infinity) + + +def point_at_infinity(): + return jacobianpoint(1, 1, 1, 1) + + +def negate(p): + if p.__class__ == affinepoint: + return affinepoint(p.x, -p.y) + if p.__class__ == jacobianpoint: + return jacobianpoint(p.X, -p.Y, p.Z) + assert(False) + + +def on_weierstrass_curve(A, B, p): + """Return a set of zero-expressions for an affine point to be on the curve""" + return constraints(zero={p.x^3 + A*p.x + B - p.y^2: 'on_curve'}) + + +def tangential_to_weierstrass_curve(A, B, p12, p3): + """Return a set of zero-expressions for ((x12,y12),(x3,y3)) to be a line that is tangential to the curve at (x12,y12)""" + return constraints(zero={ + (p12.y - p3.y) * (p12.y * 2) - (p12.x^2 * 3 + A) * (p12.x - p3.x): 'tangential_to_curve' + }) + + +def colinear(p1, p2, p3): + """Return a set of zero-expressions for ((x1,y1),(x2,y2),(x3,y3)) to be collinear""" + return constraints(zero={ + (p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x): 'colinear_1', + (p2.y - p3.y) * (p2.x - p1.x) - (p2.y - p1.y) * (p2.x - p3.x): 'colinear_2', + (p3.y - p1.y) * (p3.x - p2.x) - (p3.y - p2.y) * (p3.x - p1.x): 'colinear_3' + }) + + +def good_affine_point(p): + return constraints(nonzero={p.x : 'nonzero_x', p.y : 'nonzero_y'}) + + +def good_jacobian_point(p): + return constraints(nonzero={p.X : 'nonzero_X', p.Y : 'nonzero_Y', p.Z^6 : 'nonzero_Z'}) + + +def good_point(p): + return constraints(nonzero={p.Z^6 : 'nonzero_X'}) + + +def finite(p, *affine_fns): + con = good_point(p) + constraints(zero={p.Infinity : 'finite_point'}) + if p.Z != 0: + return con + reduce(lambda a, b: a + b, (f(affinepoint(p.X / p.Z^2, p.Y / p.Z^3)) for f in affine_fns), con) + else: + return con + +def infinite(p): + return constraints(nonzero={p.Infinity : 'infinite_point'}) + + +def law_jacobian_weierstrass_add(A, B, pa, pb, pA, pB, pC): + """Check whether the passed set of coordinates is a valid Jacobian add, given assumptions""" + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(nonzero={pa.x - pb.x : 'different_x'})) + require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) + + colinear(pa, pb, negate(pc)))) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_double(A, B, pa, pb, pA, pB, pC): + """Check whether the passed set of coordinates is a valid Jacobian doubling, given assumptions""" + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(zero={pa.x - pb.x : 'equal_x', pa.y - pb.y : 'equal_y'})) + require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) + + tangential_to_weierstrass_curve(A, B, pa, negate(pc)))) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_opposites(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(zero={pa.x - pb.x : 'equal_x', pa.y + pb.y : 'opposite_y'})) + require = infinite(pC) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_a(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pb) + + infinite(pA) + + finite(pB)) + require = finite(pC, lambda pc: constraints(zero={pc.x - pb.x : 'c.x=b.x', pc.y - pb.y : 'c.y=b.y'})) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_b(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + infinite(pB) + + finite(pA)) + require = finite(pC, lambda pc: constraints(zero={pc.x - pa.x : 'c.x=a.x', pc.y - pa.y : 'c.y=a.y'})) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_ab(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + infinite(pA) + + infinite(pB)) + require = infinite(pC) + return (assumeLaw, require) + + +laws_jacobian_weierstrass = { + 'add': law_jacobian_weierstrass_add, + 'double': law_jacobian_weierstrass_double, + 'add_opposite': law_jacobian_weierstrass_add_opposites, + 'add_infinite_a': law_jacobian_weierstrass_add_infinite_a, + 'add_infinite_b': law_jacobian_weierstrass_add_infinite_b, + 'add_infinite_ab': law_jacobian_weierstrass_add_infinite_ab +} + + +def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p): + """Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field""" + F = Integers(p) + print("Formula %s on Z%i:" % (name, p)) + points = [] + for x in range(0, p): + for y in range(0, p): + point = affinepoint(F(x), F(y)) + r, e = concrete_verify(on_weierstrass_curve(A, B, point)) + if r: + points.append(point) + + ret = True + for za in range(1, p): + for zb in range(1, p): + for pa in points: + for pb in points: + for ia in range(2): + for ib in range(2): + pA = jacobianpoint(pa.x * F(za)^2, pa.y * F(za)^3, F(za), ia) + pB = jacobianpoint(pb.x * F(zb)^2, pb.y * F(zb)^3, F(zb), ib) + for branch in range(0, branches): + assumeAssert, assumeBranch, pC = formula(branch, pA, pB) + pC.X = F(pC.X) + pC.Y = F(pC.Y) + pC.Z = F(pC.Z) + pC.Infinity = F(pC.Infinity) + r, e = concrete_verify(assumeAssert + assumeBranch) + if r: + match = False + for key in laws_jacobian_weierstrass: + assumeLaw, require = laws_jacobian_weierstrass[key](A, B, pa, pb, pA, pB, pC) + r, e = concrete_verify(assumeLaw) + if r: + if match: + print(" multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity)) + else: + match = True + r, e = concrete_verify(require) + if not r: + ret = False + print(" failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e)) + + print() + return ret + + +def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC): + assumeLaw, require = f(A, B, pa, pb, pA, pB, pC) + return check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require) + +def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): + """Verify an implementation of addition of Jacobian points on a Weierstrass curve symbolically""" + R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex') + lift = lambda x: fastfrac(R,x) + ax = lift(ax) + ay = lift(ay) + Az = lift(Az) + bx = lift(bx) + by = lift(by) + Bz = lift(Bz) + Ai = lift(Ai) + Bi = lift(Bi) + + pa = affinepoint(ax, ay, Ai) + pb = affinepoint(bx, by, Bi) + pA = jacobianpoint(ax * Az^2, ay * Az^3, Az, Ai) + pB = jacobianpoint(bx * Bz^2, by * Bz^3, Bz, Bi) + + res = {} + + for key in laws_jacobian_weierstrass: + res[key] = [] + + print("Formula " + name + ":") + count = 0 + ret = True + for branch in range(branches): + assumeFormula, assumeBranch, pC = formula(branch, pA, pB) + assumeBranch = assumeBranch.map(lift) + assumeFormula = assumeFormula.map(lift) + pC.X = lift(pC.X) + pC.Y = lift(pC.Y) + pC.Z = lift(pC.Z) + pC.Infinity = lift(pC.Infinity) + + for key in laws_jacobian_weierstrass: + success, msg = check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC) + if not success: + ret = False + res[key].append((msg, branch)) + + for key in res: + print(" %s:" % key) + val = res[key] + for x in val: + if x[0] is not None: + print(" branch %i: %s" % (x[1], x[0])) + + print() + return ret diff --git a/src/secp256k1/src/CMakeLists.txt b/src/secp256k1/src/CMakeLists.txt new file mode 100644 index 0000000000..26272d0950 --- /dev/null +++ b/src/secp256k1/src/CMakeLists.txt @@ -0,0 +1,151 @@ +# Must be included before CMAKE_INSTALL_INCLUDEDIR is used. +include(GNUInstallDirs) +set(${PROJECT_NAME}_installables "") + +if(SECP256K1_ASM STREQUAL "arm") + add_library(common OBJECT + asm/field_10x26_arm.s + ) + set(common_obj "$<TARGET_OBJECTS:common>") +else() + set(common_obj "") +endif() + +add_library(precomputed OBJECT + precomputed_ecmult.c + precomputed_ecmult_gen.c +) +set(internal_obj "$<TARGET_OBJECTS:precomputed>" "${common_obj}") + +add_library(secp256k1 SHARED EXCLUDE_FROM_ALL + secp256k1.c + ${internal_obj} +) +target_include_directories(secp256k1 INTERFACE + $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}> +) +target_compile_definitions(secp256k1 PRIVATE + $<$<PLATFORM_ID:Windows>:DLL_EXPORT> +) +set_target_properties(secp256k1 PROPERTIES + VERSION "${${PROJECT_NAME}_LIB_VERSION_CURRENT}.${${PROJECT_NAME}_LIB_VERSION_AGE}.${${PROJECT_NAME}_LIB_VERSION_REVISION}" + SOVERSION "${${PROJECT_NAME}_LIB_VERSION_CURRENT}" +) +if(SECP256K1_BUILD_SHARED) + get_target_property(use_pic secp256k1 POSITION_INDEPENDENT_CODE) + set_target_properties(precomputed PROPERTIES POSITION_INDEPENDENT_CODE ${use_pic}) + set_target_properties(secp256k1 PROPERTIES EXCLUDE_FROM_ALL FALSE) + list(APPEND ${PROJECT_NAME}_installables secp256k1) +endif() + +add_library(secp256k1_static STATIC EXCLUDE_FROM_ALL + secp256k1.c + ${internal_obj} +) +target_include_directories(secp256k1_static INTERFACE + $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}> +) +if(NOT MSVC) + set_target_properties(secp256k1_static PROPERTIES + OUTPUT_NAME secp256k1 + ) +endif() +if(SECP256K1_BUILD_STATIC) + set_target_properties(secp256k1_static PROPERTIES EXCLUDE_FROM_ALL FALSE) + list(APPEND ${PROJECT_NAME}_installables secp256k1_static) +endif() + +add_library(binary_interface INTERFACE) +target_compile_definitions(binary_interface INTERFACE + $<$<C_COMPILER_ID:MSVC>:_CRT_SECURE_NO_WARNINGS> +) + +add_library(link_library INTERFACE) +if(SECP256K1_BUILD_SHARED) + target_link_libraries(link_library INTERFACE secp256k1) +elseif(SECP256K1_BUILD_STATIC) + target_link_libraries(link_library INTERFACE secp256k1_static) +endif() + +if(SECP256K1_BUILD_BENCHMARK) + add_executable(bench bench.c) + target_link_libraries(bench binary_interface link_library) + add_executable(bench_internal bench_internal.c ${internal_obj}) + target_link_libraries(bench_internal binary_interface) + add_executable(bench_ecmult bench_ecmult.c ${internal_obj}) + target_link_libraries(bench_ecmult binary_interface) +endif() + +if(SECP256K1_BUILD_TESTS) + add_executable(noverify_tests tests.c ${internal_obj}) + target_link_libraries(noverify_tests binary_interface) + add_test(noverify_tests noverify_tests) + if(NOT CMAKE_BUILD_TYPE STREQUAL "Coverage") + add_executable(tests tests.c ${internal_obj}) + target_compile_definitions(tests PRIVATE VERIFY) + target_link_libraries(tests binary_interface) + add_test(tests tests) + endif() +endif() + +if(SECP256K1_BUILD_EXHAUSTIVE_TESTS) + # Note: do not include $<TARGET_OBJECTS:precomputed> in exhaustive_tests (it uses runtime-generated tables). + add_executable(exhaustive_tests tests_exhaustive.c ${common_obj}) + target_compile_definitions(exhaustive_tests PRIVATE $<$<NOT:$<CONFIG:Coverage>>:VERIFY>) + target_link_libraries(exhaustive_tests binary_interface) + add_test(exhaustive_tests exhaustive_tests) +endif() + +if(SECP256K1_BUILD_CTIME_TESTS) + add_executable(ctime_tests ctime_tests.c) + target_link_libraries(ctime_tests binary_interface link_library) +endif() + +install(TARGETS ${${PROJECT_NAME}_installables} + EXPORT ${PROJECT_NAME}-targets + RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR} + LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR} + ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR} +) +set(${PROJECT_NAME}_headers + "${PROJECT_SOURCE_DIR}/include/secp256k1.h" + "${PROJECT_SOURCE_DIR}/include/secp256k1_preallocated.h" +) +if(SECP256K1_ENABLE_MODULE_ECDH) + list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_ecdh.h") +endif() +if(SECP256K1_ENABLE_MODULE_RECOVERY) + list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_recovery.h") +endif() +if(SECP256K1_ENABLE_MODULE_EXTRAKEYS) + list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_extrakeys.h") +endif() +if(SECP256K1_ENABLE_MODULE_SCHNORRSIG) + list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_schnorrsig.h") +endif() +install(FILES ${${PROJECT_NAME}_headers} + DESTINATION ${CMAKE_INSTALL_INCLUDEDIR} +) + +install(EXPORT ${PROJECT_NAME}-targets + FILE ${PROJECT_NAME}-targets.cmake + NAMESPACE ${PROJECT_NAME}:: + DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME} +) + +include(CMakePackageConfigHelpers) +configure_package_config_file( + ${PROJECT_SOURCE_DIR}/cmake/config.cmake.in + ${PROJECT_NAME}-config.cmake + INSTALL_DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME} + NO_SET_AND_CHECK_MACRO +) +write_basic_package_version_file(${PROJECT_NAME}-config-version.cmake + COMPATIBILITY SameMajorVersion +) +install( + FILES + ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config.cmake + ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config-version.cmake + DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME} +) diff --git a/src/secp256k1/src/asm/field_10x26_arm.s b/src/secp256k1/src/asm/field_10x26_arm.s new file mode 100644 index 0000000000..42cbf879ef --- /dev/null +++ b/src/secp256k1/src/asm/field_10x26_arm.s @@ -0,0 +1,915 @@ +@ vim: set tabstop=8 softtabstop=8 shiftwidth=8 noexpandtab syntax=armasm: +/*********************************************************************** + * Copyright (c) 2014 Wladimir J. van der Laan * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ +/* +ARM implementation of field_10x26 inner loops. + +Note: + +- To avoid unnecessary loads and make use of available registers, two + 'passes' have every time been interleaved, with the odd passes accumulating c' and d' + which will be added to c and d respectively in the even passes + +*/ + + .syntax unified + @ eabi attributes - see readelf -A + .eabi_attribute 24, 1 @ Tag_ABI_align_needed = 8-byte + .eabi_attribute 25, 1 @ Tag_ABI_align_preserved = 8-byte, except leaf SP + .text + + @ Field constants + .set field_R0, 0x3d10 + .set field_R1, 0x400 + .set field_not_M, 0xfc000000 @ ~M = ~0x3ffffff + + .align 2 + .global secp256k1_fe_mul_inner + .type secp256k1_fe_mul_inner, %function + .hidden secp256k1_fe_mul_inner + @ Arguments: + @ r0 r Restrict: can overlap with a, not with b + @ r1 a + @ r2 b + @ Stack (total 4+10*4 = 44) + @ sp + #0 saved 'r' pointer + @ sp + #4 + 4*X t0,t1,t2,t3,t4,t5,t6,t7,u8,t9 +secp256k1_fe_mul_inner: + stmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14} + sub sp, sp, #48 @ frame=44 + alignment + str r0, [sp, #0] @ save result address, we need it only at the end + + /****************************************** + * Main computation code. + ****************************************** + + Allocation: + r0,r14,r7,r8 scratch + r1 a (pointer) + r2 b (pointer) + r3:r4 c + r5:r6 d + r11:r12 c' + r9:r10 d' + + Note: do not write to r[] here, it may overlap with a[] + */ + + /* A - interleaved with B */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #9*4] @ b[9] + ldr r0, [r1, #1*4] @ a[1] + umull r5, r6, r7, r8 @ d = a[0] * b[9] + ldr r14, [r2, #8*4] @ b[8] + umull r9, r10, r0, r8 @ d' = a[1] * b[9] + ldr r7, [r1, #2*4] @ a[2] + umlal r5, r6, r0, r14 @ d += a[1] * b[8] + ldr r8, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r14 @ d' += a[2] * b[8] + ldr r0, [r1, #3*4] @ a[3] + umlal r5, r6, r7, r8 @ d += a[2] * b[7] + ldr r14, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r8 @ d' += a[3] * b[7] + ldr r7, [r1, #4*4] @ a[4] + umlal r5, r6, r0, r14 @ d += a[3] * b[6] + ldr r8, [r2, #5*4] @ b[5] + umlal r9, r10, r7, r14 @ d' += a[4] * b[6] + ldr r0, [r1, #5*4] @ a[5] + umlal r5, r6, r7, r8 @ d += a[4] * b[5] + ldr r14, [r2, #4*4] @ b[4] + umlal r9, r10, r0, r8 @ d' += a[5] * b[5] + ldr r7, [r1, #6*4] @ a[6] + umlal r5, r6, r0, r14 @ d += a[5] * b[4] + ldr r8, [r2, #3*4] @ b[3] + umlal r9, r10, r7, r14 @ d' += a[6] * b[4] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r8 @ d += a[6] * b[3] + ldr r14, [r2, #2*4] @ b[2] + umlal r9, r10, r0, r8 @ d' += a[7] * b[3] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r14 @ d += a[7] * b[2] + ldr r8, [r2, #1*4] @ b[1] + umlal r9, r10, r7, r14 @ d' += a[8] * b[2] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r8 @ d += a[8] * b[1] + ldr r14, [r2, #0*4] @ b[0] + umlal r9, r10, r0, r8 @ d' += a[9] * b[1] + ldr r7, [r1, #0*4] @ a[0] + umlal r5, r6, r0, r14 @ d += a[9] * b[0] + @ r7,r14 used in B + + bic r0, r5, field_not_M @ t9 = d & M + str r0, [sp, #4 + 4*9] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + /* B */ + umull r3, r4, r7, r14 @ c = a[0] * b[0] + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u0 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u0 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t0 = c & M + str r14, [sp, #4 + 0*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u0 * R1 + umlal r3, r4, r0, r14 + + /* C - interleaved with D */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #2*4] @ b[2] + ldr r14, [r2, #1*4] @ b[1] + umull r11, r12, r7, r8 @ c' = a[0] * b[2] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[1] * b[1] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[2] * b[0] + ldr r0, [r1, #3*4] @ a[3] + umlal r5, r6, r7, r14 @ d += a[2] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[3] * b[9] + ldr r7, [r1, #4*4] @ a[4] + umlal r5, r6, r0, r8 @ d += a[3] * b[8] + ldr r14, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r8 @ d' += a[4] * b[8] + ldr r0, [r1, #5*4] @ a[5] + umlal r5, r6, r7, r14 @ d += a[4] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r14 @ d' += a[5] * b[7] + ldr r7, [r1, #6*4] @ a[6] + umlal r5, r6, r0, r8 @ d += a[5] * b[6] + ldr r14, [r2, #5*4] @ b[5] + umlal r9, r10, r7, r8 @ d' += a[6] * b[6] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r14 @ d += a[6] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r9, r10, r0, r14 @ d' += a[7] * b[5] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r8 @ d += a[7] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r9, r10, r7, r8 @ d' += a[8] * b[4] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r9, r10, r0, r14 @ d' += a[9] * b[3] + umlal r5, r6, r0, r8 @ d += a[9] * b[2] + + bic r0, r5, field_not_M @ u1 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u1 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t1 = c & M + str r14, [sp, #4 + 1*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u1 * R1 + umlal r3, r4, r0, r14 + + /* D */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u2 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u2 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t2 = c & M + str r14, [sp, #4 + 2*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u2 * R1 + umlal r3, r4, r0, r14 + + /* E - interleaved with F */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #4*4] @ b[4] + umull r11, r12, r7, r8 @ c' = a[0] * b[4] + ldr r8, [r2, #3*4] @ b[3] + umlal r3, r4, r7, r8 @ c += a[0] * b[3] + ldr r7, [r1, #1*4] @ a[1] + umlal r11, r12, r7, r8 @ c' += a[1] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r3, r4, r7, r8 @ c += a[1] * b[2] + ldr r7, [r1, #2*4] @ a[2] + umlal r11, r12, r7, r8 @ c' += a[2] * b[2] + ldr r8, [r2, #1*4] @ b[1] + umlal r3, r4, r7, r8 @ c += a[2] * b[1] + ldr r7, [r1, #3*4] @ a[3] + umlal r11, r12, r7, r8 @ c' += a[3] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r3, r4, r7, r8 @ c += a[3] * b[0] + ldr r7, [r1, #4*4] @ a[4] + umlal r11, r12, r7, r8 @ c' += a[4] * b[0] + ldr r8, [r2, #9*4] @ b[9] + umlal r5, r6, r7, r8 @ d += a[4] * b[9] + ldr r7, [r1, #5*4] @ a[5] + umull r9, r10, r7, r8 @ d' = a[5] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umlal r5, r6, r7, r8 @ d += a[5] * b[8] + ldr r7, [r1, #6*4] @ a[6] + umlal r9, r10, r7, r8 @ d' += a[6] * b[8] + ldr r8, [r2, #7*4] @ b[7] + umlal r5, r6, r7, r8 @ d += a[6] * b[7] + ldr r7, [r1, #7*4] @ a[7] + umlal r9, r10, r7, r8 @ d' += a[7] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r5, r6, r7, r8 @ d += a[7] * b[6] + ldr r7, [r1, #8*4] @ a[8] + umlal r9, r10, r7, r8 @ d' += a[8] * b[6] + ldr r8, [r2, #5*4] @ b[5] + umlal r5, r6, r7, r8 @ d += a[8] * b[5] + ldr r7, [r1, #9*4] @ a[9] + umlal r9, r10, r7, r8 @ d' += a[9] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r5, r6, r7, r8 @ d += a[9] * b[4] + + bic r0, r5, field_not_M @ u3 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u3 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t3 = c & M + str r14, [sp, #4 + 3*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u3 * R1 + umlal r3, r4, r0, r14 + + /* F */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u4 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u4 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t4 = c & M + str r14, [sp, #4 + 4*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u4 * R1 + umlal r3, r4, r0, r14 + + /* G - interleaved with H */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #6*4] @ b[6] + ldr r14, [r2, #5*4] @ b[5] + umull r11, r12, r7, r8 @ c' = a[0] * b[6] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r11, r12, r0, r14 @ c' += a[1] * b[5] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r11, r12, r7, r8 @ c' += a[2] * b[4] + ldr r0, [r1, #3*4] @ a[3] + umlal r3, r4, r7, r14 @ c += a[2] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r11, r12, r0, r14 @ c' += a[3] * b[3] + ldr r7, [r1, #4*4] @ a[4] + umlal r3, r4, r0, r8 @ c += a[3] * b[2] + ldr r14, [r2, #1*4] @ b[1] + umlal r11, r12, r7, r8 @ c' += a[4] * b[2] + ldr r0, [r1, #5*4] @ a[5] + umlal r3, r4, r7, r14 @ c += a[4] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[5] * b[1] + ldr r7, [r1, #6*4] @ a[6] + umlal r3, r4, r0, r8 @ c += a[5] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[6] * b[0] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r14 @ d += a[6] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[7] * b[9] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r8 @ d += a[7] * b[8] + ldr r14, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r8 @ d' += a[8] * b[8] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r14 @ d' += a[9] * b[7] + umlal r5, r6, r0, r8 @ d += a[9] * b[6] + + bic r0, r5, field_not_M @ u5 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u5 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t5 = c & M + str r14, [sp, #4 + 5*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u5 * R1 + umlal r3, r4, r0, r14 + + /* H */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u6 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u6 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t6 = c & M + str r14, [sp, #4 + 6*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u6 * R1 + umlal r3, r4, r0, r14 + + /* I - interleaved with J */ + ldr r8, [r2, #8*4] @ b[8] + ldr r7, [r1, #0*4] @ a[0] + ldr r14, [r2, #7*4] @ b[7] + umull r11, r12, r7, r8 @ c' = a[0] * b[8] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r11, r12, r0, r14 @ c' += a[1] * b[7] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[6] + ldr r14, [r2, #5*4] @ b[5] + umlal r11, r12, r7, r8 @ c' += a[2] * b[6] + ldr r0, [r1, #3*4] @ a[3] + umlal r3, r4, r7, r14 @ c += a[2] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r11, r12, r0, r14 @ c' += a[3] * b[5] + ldr r7, [r1, #4*4] @ a[4] + umlal r3, r4, r0, r8 @ c += a[3] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r11, r12, r7, r8 @ c' += a[4] * b[4] + ldr r0, [r1, #5*4] @ a[5] + umlal r3, r4, r7, r14 @ c += a[4] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r11, r12, r0, r14 @ c' += a[5] * b[3] + ldr r7, [r1, #6*4] @ a[6] + umlal r3, r4, r0, r8 @ c += a[5] * b[2] + ldr r14, [r2, #1*4] @ b[1] + umlal r11, r12, r7, r8 @ c' += a[6] * b[2] + ldr r0, [r1, #7*4] @ a[7] + umlal r3, r4, r7, r14 @ c += a[6] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[7] * b[1] + ldr r7, [r1, #8*4] @ a[8] + umlal r3, r4, r0, r8 @ c += a[7] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[8] * b[0] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[9] * b[9] + umlal r5, r6, r0, r8 @ d += a[9] * b[8] + + bic r0, r5, field_not_M @ u7 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u7 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t7 = c & M + str r14, [sp, #4 + 7*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u7 * R1 + umlal r3, r4, r0, r14 + + /* J */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u8 = d & M + str r0, [sp, #4 + 8*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u8 * R0 + umlal r3, r4, r0, r14 + + /****************************************** + * compute and write back result + ****************************************** + Allocation: + r0 r + r3:r4 c + r5:r6 d + r7 t0 + r8 t1 + r9 t2 + r11 u8 + r12 t9 + r1,r2,r10,r14 scratch + + Note: do not read from a[] after here, it may overlap with r[] + */ + ldr r0, [sp, #0] + add r1, sp, #4 + 3*4 @ r[3..7] = t3..7, r11=u8, r12=t9 + ldmia r1, {r2,r7,r8,r9,r10,r11,r12} + add r1, r0, #3*4 + stmia r1, {r2,r7,r8,r9,r10} + + bic r2, r3, field_not_M @ r[8] = c & M + str r2, [r0, #8*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u8 * R1 + umlal r3, r4, r11, r14 + movw r14, field_R0 @ c += d * R0 + umlal r3, r4, r5, r14 + adds r3, r3, r12 @ c += t9 + adc r4, r4, #0 + + add r1, sp, #4 + 0*4 @ r7,r8,r9 = t0,t1,t2 + ldmia r1, {r7,r8,r9} + + ubfx r2, r3, #0, #22 @ r[9] = c & (M >> 4) + str r2, [r0, #9*4] + mov r3, r3, lsr #22 @ c >>= 22 + orr r3, r3, r4, asl #10 + mov r4, r4, lsr #22 + movw r14, field_R1 << 4 @ c += d * (R1 << 4) + umlal r3, r4, r5, r14 + + movw r14, field_R0 >> 4 @ d = c * (R0 >> 4) + t0 (64x64 multiply+add) + umull r5, r6, r3, r14 @ d = c.lo * (R0 >> 4) + adds r5, r5, r7 @ d.lo += t0 + mla r6, r14, r4, r6 @ d.hi += c.hi * (R0 >> 4) + adc r6, r6, 0 @ d.hi += carry + + bic r2, r5, field_not_M @ r[0] = d & M + str r2, [r0, #0*4] + + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + movw r14, field_R1 >> 4 @ d += c * (R1 >> 4) + t1 (64x64 multiply+add) + umull r1, r2, r3, r14 @ tmp = c.lo * (R1 >> 4) + adds r5, r5, r8 @ d.lo += t1 + adc r6, r6, #0 @ d.hi += carry + adds r5, r5, r1 @ d.lo += tmp.lo + mla r2, r14, r4, r2 @ tmp.hi += c.hi * (R1 >> 4) + adc r6, r6, r2 @ d.hi += carry + tmp.hi + + bic r2, r5, field_not_M @ r[1] = d & M + str r2, [r0, #1*4] + mov r5, r5, lsr #26 @ d >>= 26 (ignore hi) + orr r5, r5, r6, asl #6 + + add r5, r5, r9 @ d += t2 + str r5, [r0, #2*4] @ r[2] = d + + add sp, sp, #48 + ldmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc} + .size secp256k1_fe_mul_inner, .-secp256k1_fe_mul_inner + + .align 2 + .global secp256k1_fe_sqr_inner + .type secp256k1_fe_sqr_inner, %function + .hidden secp256k1_fe_sqr_inner + @ Arguments: + @ r0 r Can overlap with a + @ r1 a + @ Stack (total 4+10*4 = 44) + @ sp + #0 saved 'r' pointer + @ sp + #4 + 4*X t0,t1,t2,t3,t4,t5,t6,t7,u8,t9 +secp256k1_fe_sqr_inner: + stmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14} + sub sp, sp, #48 @ frame=44 + alignment + str r0, [sp, #0] @ save result address, we need it only at the end + /****************************************** + * Main computation code. + ****************************************** + + Allocation: + r0,r14,r2,r7,r8 scratch + r1 a (pointer) + r3:r4 c + r5:r6 d + r11:r12 c' + r9:r10 d' + + Note: do not write to r[] here, it may overlap with a[] + */ + /* A interleaved with B */ + ldr r0, [r1, #1*4] @ a[1]*2 + ldr r7, [r1, #0*4] @ a[0] + mov r0, r0, asl #1 + ldr r14, [r1, #9*4] @ a[9] + umull r3, r4, r7, r7 @ c = a[0] * a[0] + ldr r8, [r1, #8*4] @ a[8] + mov r7, r7, asl #1 + umull r5, r6, r7, r14 @ d = a[0]*2 * a[9] + ldr r7, [r1, #2*4] @ a[2]*2 + umull r9, r10, r0, r14 @ d' = a[1]*2 * a[9] + ldr r14, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r8 @ d += a[1]*2 * a[8] + mov r7, r7, asl #1 + ldr r0, [r1, #3*4] @ a[3]*2 + umlal r9, r10, r7, r8 @ d' += a[2]*2 * a[8] + ldr r8, [r1, #6*4] @ a[6] + umlal r5, r6, r7, r14 @ d += a[2]*2 * a[7] + mov r0, r0, asl #1 + ldr r7, [r1, #4*4] @ a[4]*2 + umlal r9, r10, r0, r14 @ d' += a[3]*2 * a[7] + ldr r14, [r1, #5*4] @ a[5] + mov r7, r7, asl #1 + umlal r5, r6, r0, r8 @ d += a[3]*2 * a[6] + umlal r9, r10, r7, r8 @ d' += a[4]*2 * a[6] + umlal r5, r6, r7, r14 @ d += a[4]*2 * a[5] + umlal r9, r10, r14, r14 @ d' += a[5] * a[5] + + bic r0, r5, field_not_M @ t9 = d & M + str r0, [sp, #4 + 9*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + /* B */ + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u0 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u0 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t0 = c & M + str r14, [sp, #4 + 0*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u0 * R1 + umlal r3, r4, r0, r14 + + /* C interleaved with D */ + ldr r0, [r1, #0*4] @ a[0]*2 + ldr r14, [r1, #1*4] @ a[1] + mov r0, r0, asl #1 + ldr r8, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r14 @ c += a[0]*2 * a[1] + mov r7, r8, asl #1 @ a[2]*2 + umull r11, r12, r14, r14 @ c' = a[1] * a[1] + ldr r14, [r1, #9*4] @ a[9] + umlal r11, r12, r0, r8 @ c' += a[0]*2 * a[2] + ldr r0, [r1, #3*4] @ a[3]*2 + ldr r8, [r1, #8*4] @ a[8] + umlal r5, r6, r7, r14 @ d += a[2]*2 * a[9] + mov r0, r0, asl #1 + ldr r7, [r1, #4*4] @ a[4]*2 + umull r9, r10, r0, r14 @ d' = a[3]*2 * a[9] + ldr r14, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r8 @ d += a[3]*2 * a[8] + mov r7, r7, asl #1 + ldr r0, [r1, #5*4] @ a[5]*2 + umlal r9, r10, r7, r8 @ d' += a[4]*2 * a[8] + ldr r8, [r1, #6*4] @ a[6] + mov r0, r0, asl #1 + umlal r5, r6, r7, r14 @ d += a[4]*2 * a[7] + umlal r9, r10, r0, r14 @ d' += a[5]*2 * a[7] + umlal r5, r6, r0, r8 @ d += a[5]*2 * a[6] + umlal r9, r10, r8, r8 @ d' += a[6] * a[6] + + bic r0, r5, field_not_M @ u1 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u1 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t1 = c & M + str r14, [sp, #4 + 1*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u1 * R1 + umlal r3, r4, r0, r14 + + /* D */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u2 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u2 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t2 = c & M + str r14, [sp, #4 + 2*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u2 * R1 + umlal r3, r4, r0, r14 + + /* E interleaved with F */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + ldr r14, [r1, #2*4] @ a[2] + mov r7, r7, asl #1 + ldr r8, [r1, #3*4] @ a[3] + ldr r2, [r1, #4*4] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[3] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[4] + mov r2, r2, asl #1 @ a[4]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[3] + ldr r8, [r1, #9*4] @ a[9] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[2] + ldr r0, [r1, #5*4] @ a[5]*2 + umlal r11, r12, r14, r14 @ c' += a[2] * a[2] + ldr r14, [r1, #8*4] @ a[8] + mov r0, r0, asl #1 + umlal r5, r6, r2, r8 @ d += a[4]*2 * a[9] + ldr r7, [r1, #6*4] @ a[6]*2 + umull r9, r10, r0, r8 @ d' = a[5]*2 * a[9] + mov r7, r7, asl #1 + ldr r8, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r14 @ d += a[5]*2 * a[8] + umlal r9, r10, r7, r14 @ d' += a[6]*2 * a[8] + umlal r5, r6, r7, r8 @ d += a[6]*2 * a[7] + umlal r9, r10, r8, r8 @ d' += a[7] * a[7] + + bic r0, r5, field_not_M @ u3 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u3 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t3 = c & M + str r14, [sp, #4 + 3*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u3 * R1 + umlal r3, r4, r0, r14 + + /* F */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u4 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u4 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t4 = c & M + str r14, [sp, #4 + 4*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u4 * R1 + umlal r3, r4, r0, r14 + + /* G interleaved with H */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + mov r7, r7, asl #1 + ldr r8, [r1, #5*4] @ a[5] + ldr r2, [r1, #6*4] @ a[6] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[5] + ldr r14, [r1, #4*4] @ a[4] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[6] + ldr r7, [r1, #2*4] @ a[2]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[5] + mov r7, r7, asl #1 + ldr r8, [r1, #3*4] @ a[3] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[4] + mov r0, r2, asl #1 @ a[6]*2 + umlal r11, r12, r7, r14 @ c' += a[2]*2 * a[4] + ldr r14, [r1, #9*4] @ a[9] + umlal r3, r4, r7, r8 @ c += a[2]*2 * a[3] + ldr r7, [r1, #7*4] @ a[7]*2 + umlal r11, r12, r8, r8 @ c' += a[3] * a[3] + mov r7, r7, asl #1 + ldr r8, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r14 @ d += a[6]*2 * a[9] + umull r9, r10, r7, r14 @ d' = a[7]*2 * a[9] + umlal r5, r6, r7, r8 @ d += a[7]*2 * a[8] + umlal r9, r10, r8, r8 @ d' += a[8] * a[8] + + bic r0, r5, field_not_M @ u5 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u5 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t5 = c & M + str r14, [sp, #4 + 5*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u5 * R1 + umlal r3, r4, r0, r14 + + /* H */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u6 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u6 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t6 = c & M + str r14, [sp, #4 + 6*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u6 * R1 + umlal r3, r4, r0, r14 + + /* I interleaved with J */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + mov r7, r7, asl #1 + ldr r8, [r1, #7*4] @ a[7] + ldr r2, [r1, #8*4] @ a[8] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[7] + ldr r14, [r1, #6*4] @ a[6] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[8] + ldr r7, [r1, #2*4] @ a[2]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[7] + ldr r8, [r1, #5*4] @ a[5] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[6] + ldr r0, [r1, #3*4] @ a[3]*2 + mov r7, r7, asl #1 + umlal r11, r12, r7, r14 @ c' += a[2]*2 * a[6] + ldr r14, [r1, #4*4] @ a[4] + mov r0, r0, asl #1 + umlal r3, r4, r7, r8 @ c += a[2]*2 * a[5] + mov r2, r2, asl #1 @ a[8]*2 + umlal r11, r12, r0, r8 @ c' += a[3]*2 * a[5] + umlal r3, r4, r0, r14 @ c += a[3]*2 * a[4] + umlal r11, r12, r14, r14 @ c' += a[4] * a[4] + ldr r8, [r1, #9*4] @ a[9] + umlal r5, r6, r2, r8 @ d += a[8]*2 * a[9] + @ r8 will be used in J + + bic r0, r5, field_not_M @ u7 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u7 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t7 = c & M + str r14, [sp, #4 + 7*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u7 * R1 + umlal r3, r4, r0, r14 + + /* J */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + umlal r5, r6, r8, r8 @ d += a[9] * a[9] + + bic r0, r5, field_not_M @ u8 = d & M + str r0, [sp, #4 + 8*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u8 * R0 + umlal r3, r4, r0, r14 + + /****************************************** + * compute and write back result + ****************************************** + Allocation: + r0 r + r3:r4 c + r5:r6 d + r7 t0 + r8 t1 + r9 t2 + r11 u8 + r12 t9 + r1,r2,r10,r14 scratch + + Note: do not read from a[] after here, it may overlap with r[] + */ + ldr r0, [sp, #0] + add r1, sp, #4 + 3*4 @ r[3..7] = t3..7, r11=u8, r12=t9 + ldmia r1, {r2,r7,r8,r9,r10,r11,r12} + add r1, r0, #3*4 + stmia r1, {r2,r7,r8,r9,r10} + + bic r2, r3, field_not_M @ r[8] = c & M + str r2, [r0, #8*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u8 * R1 + umlal r3, r4, r11, r14 + movw r14, field_R0 @ c += d * R0 + umlal r3, r4, r5, r14 + adds r3, r3, r12 @ c += t9 + adc r4, r4, #0 + + add r1, sp, #4 + 0*4 @ r7,r8,r9 = t0,t1,t2 + ldmia r1, {r7,r8,r9} + + ubfx r2, r3, #0, #22 @ r[9] = c & (M >> 4) + str r2, [r0, #9*4] + mov r3, r3, lsr #22 @ c >>= 22 + orr r3, r3, r4, asl #10 + mov r4, r4, lsr #22 + movw r14, field_R1 << 4 @ c += d * (R1 << 4) + umlal r3, r4, r5, r14 + + movw r14, field_R0 >> 4 @ d = c * (R0 >> 4) + t0 (64x64 multiply+add) + umull r5, r6, r3, r14 @ d = c.lo * (R0 >> 4) + adds r5, r5, r7 @ d.lo += t0 + mla r6, r14, r4, r6 @ d.hi += c.hi * (R0 >> 4) + adc r6, r6, 0 @ d.hi += carry + + bic r2, r5, field_not_M @ r[0] = d & M + str r2, [r0, #0*4] + + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + movw r14, field_R1 >> 4 @ d += c * (R1 >> 4) + t1 (64x64 multiply+add) + umull r1, r2, r3, r14 @ tmp = c.lo * (R1 >> 4) + adds r5, r5, r8 @ d.lo += t1 + adc r6, r6, #0 @ d.hi += carry + adds r5, r5, r1 @ d.lo += tmp.lo + mla r2, r14, r4, r2 @ tmp.hi += c.hi * (R1 >> 4) + adc r6, r6, r2 @ d.hi += carry + tmp.hi + + bic r2, r5, field_not_M @ r[1] = d & M + str r2, [r0, #1*4] + mov r5, r5, lsr #26 @ d >>= 26 (ignore hi) + orr r5, r5, r6, asl #6 + + add r5, r5, r9 @ d += t2 + str r5, [r0, #2*4] @ r[2] = d + + add sp, sp, #48 + ldmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc} + .size secp256k1_fe_sqr_inner, .-secp256k1_fe_sqr_inner + diff --git a/src/secp256k1/src/assumptions.h b/src/secp256k1/src/assumptions.h new file mode 100644 index 0000000000..8ed04209e9 --- /dev/null +++ b/src/secp256k1/src/assumptions.h @@ -0,0 +1,83 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ASSUMPTIONS_H +#define SECP256K1_ASSUMPTIONS_H + +#include <limits.h> + +#include "util.h" +#if defined(SECP256K1_INT128_NATIVE) +#include "int128_native.h" +#endif + +/* This library, like most software, relies on a number of compiler implementation defined (but not undefined) + behaviours. Although the behaviours we require are essentially universal we test them specifically here to + reduce the odds of experiencing an unwelcome surprise. +*/ + +struct secp256k1_assumption_checker { + /* This uses a trick to implement a static assertion in C89: a type with an array of negative size is not + allowed. */ + int dummy_array[( + /* Bytes are 8 bits. */ + (CHAR_BIT == 8) && + + /* No integer promotion for uint32_t. This ensures that we can multiply uintXX_t values where XX >= 32 + without signed overflow, which would be undefined behaviour. */ + (UINT_MAX <= UINT32_MAX) && + + /* Conversions from unsigned to signed outside of the bounds of the signed type are + implementation-defined. Verify that they function as reinterpreting the lower + bits of the input in two's complement notation. Do this for conversions: + - from uint(N)_t to int(N)_t with negative result + - from uint(2N)_t to int(N)_t with negative result + - from int(2N)_t to int(N)_t with negative result + - from int(2N)_t to int(N)_t with positive result */ + + /* To int8_t. */ + ((int8_t)(uint8_t)0xAB == (int8_t)-(int8_t)0x55) && + ((int8_t)(uint16_t)0xABCD == (int8_t)-(int8_t)0x33) && + ((int8_t)(int16_t)(uint16_t)0xCDEF == (int8_t)(uint8_t)0xEF) && + ((int8_t)(int16_t)(uint16_t)0x9234 == (int8_t)(uint8_t)0x34) && + + /* To int16_t. */ + ((int16_t)(uint16_t)0xBCDE == (int16_t)-(int16_t)0x4322) && + ((int16_t)(uint32_t)0xA1B2C3D4 == (int16_t)-(int16_t)0x3C2C) && + ((int16_t)(int32_t)(uint32_t)0xC1D2E3F4 == (int16_t)(uint16_t)0xE3F4) && + ((int16_t)(int32_t)(uint32_t)0x92345678 == (int16_t)(uint16_t)0x5678) && + + /* To int32_t. */ + ((int32_t)(uint32_t)0xB2C3D4E5 == (int32_t)-(int32_t)0x4D3C2B1B) && + ((int32_t)(uint64_t)0xA123B456C789D012ULL == (int32_t)-(int32_t)0x38762FEE) && + ((int32_t)(int64_t)(uint64_t)0xC1D2E3F4A5B6C7D8ULL == (int32_t)(uint32_t)0xA5B6C7D8) && + ((int32_t)(int64_t)(uint64_t)0xABCDEF0123456789ULL == (int32_t)(uint32_t)0x23456789) && + + /* To int64_t. */ + ((int64_t)(uint64_t)0xB123C456D789E012ULL == (int64_t)-(int64_t)0x4EDC3BA928761FEEULL) && +#if defined(SECP256K1_INT128_NATIVE) + ((int64_t)(((uint128_t)0xA1234567B8901234ULL << 64) + 0xC5678901D2345678ULL) == (int64_t)-(int64_t)0x3A9876FE2DCBA988ULL) && + (((int64_t)(int128_t)(((uint128_t)0xB1C2D3E4F5A6B7C8ULL << 64) + 0xD9E0F1A2B3C4D5E6ULL)) == (int64_t)(uint64_t)0xD9E0F1A2B3C4D5E6ULL) && + (((int64_t)(int128_t)(((uint128_t)0xABCDEF0123456789ULL << 64) + 0x0123456789ABCDEFULL)) == (int64_t)(uint64_t)0x0123456789ABCDEFULL) && + + /* To int128_t. */ + ((int128_t)(((uint128_t)0xB1234567C8901234ULL << 64) + 0xD5678901E2345678ULL) == (int128_t)(-(int128_t)0x8E1648B3F50E80DCULL * 0x8E1648B3F50E80DDULL + 0x5EA688D5482F9464ULL)) && +#endif + + /* Right shift on negative signed values is implementation defined. Verify that it + acts as a right shift in two's complement with sign extension (i.e duplicating + the top bit into newly added bits). */ + ((((int8_t)0xE8) >> 2) == (int8_t)(uint8_t)0xFA) && + ((((int16_t)0xE9AC) >> 4) == (int16_t)(uint16_t)0xFE9A) && + ((((int32_t)0x937C918A) >> 9) == (int32_t)(uint32_t)0xFFC9BE48) && + ((((int64_t)0xA8B72231DF9CF4B9ULL) >> 19) == (int64_t)(uint64_t)0xFFFFF516E4463BF3ULL) && +#if defined(SECP256K1_INT128_NATIVE) + ((((int128_t)(((uint128_t)0xCD833A65684A0DBCULL << 64) + 0xB349312F71EA7637ULL)) >> 39) == (int128_t)(((uint128_t)0xFFFFFFFFFF9B0674ULL << 64) + 0xCAD0941B79669262ULL)) && +#endif + 1) * 2 - 1]; +}; + +#endif /* SECP256K1_ASSUMPTIONS_H */ diff --git a/src/secp256k1/src/bench.c b/src/secp256k1/src/bench.c new file mode 100644 index 0000000000..833f70718b --- /dev/null +++ b/src/secp256k1/src/bench.c @@ -0,0 +1,229 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <stdio.h> +#include <string.h> + +#include "../include/secp256k1.h" +#include "util.h" +#include "bench.h" + +static void help(int default_iters) { + printf("Benchmarks the following algorithms:\n"); + printf(" - ECDSA signing/verification\n"); + +#ifdef ENABLE_MODULE_ECDH + printf(" - ECDH key exchange (optional module)\n"); +#endif + +#ifdef ENABLE_MODULE_RECOVERY + printf(" - Public key recovery (optional module)\n"); +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG + printf(" - Schnorr signatures (optional module)\n"); +#endif + + printf("\n"); + printf("The default number of iterations for each benchmark is %d. This can be\n", default_iters); + printf("customized using the SECP256K1_BENCH_ITERS environment variable.\n"); + printf("\n"); + printf("Usage: ./bench [args]\n"); + printf("By default, all benchmarks will be run.\n"); + printf("args:\n"); + printf(" help : display this help and exit\n"); + printf(" ecdsa : all ECDSA algorithms--sign, verify, recovery (if enabled)\n"); + printf(" ecdsa_sign : ECDSA siging algorithm\n"); + printf(" ecdsa_verify : ECDSA verification algorithm\n"); + +#ifdef ENABLE_MODULE_RECOVERY + printf(" ecdsa_recover : ECDSA public key recovery algorithm\n"); +#endif + +#ifdef ENABLE_MODULE_ECDH + printf(" ecdh : ECDH key exchange algorithm\n"); +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG + printf(" schnorrsig : all Schnorr signature algorithms (sign, verify)\n"); + printf(" schnorrsig_sign : Schnorr sigining algorithm\n"); + printf(" schnorrsig_verify : Schnorr verification algorithm\n"); +#endif + + printf("\n"); +} + +typedef struct { + secp256k1_context *ctx; + unsigned char msg[32]; + unsigned char key[32]; + unsigned char sig[72]; + size_t siglen; + unsigned char pubkey[33]; + size_t pubkeylen; +} bench_verify_data; + +static void bench_verify(void* arg, int iters) { + int i; + bench_verify_data* data = (bench_verify_data*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1); + CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0)); + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + } +} + +typedef struct { + secp256k1_context* ctx; + unsigned char msg[32]; + unsigned char key[32]; +} bench_sign_data; + +static void bench_sign_setup(void* arg) { + int i; + bench_sign_data *data = (bench_sign_data*)arg; + + for (i = 0; i < 32; i++) { + data->msg[i] = i + 1; + } + for (i = 0; i < 32; i++) { + data->key[i] = i + 65; + } +} + +static void bench_sign_run(void* arg, int iters) { + int i; + bench_sign_data *data = (bench_sign_data*)arg; + + unsigned char sig[74]; + for (i = 0; i < iters; i++) { + size_t siglen = 74; + int j; + secp256k1_ecdsa_signature signature; + CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature)); + for (j = 0; j < 32; j++) { + data->msg[j] = sig[j]; + data->key[j] = sig[j + 32]; + } + } +} + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/bench_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/bench_impl.h" +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG +# include "modules/schnorrsig/bench_impl.h" +#endif + +int main(int argc, char** argv) { + int i; + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + bench_verify_data data; + + int d = argc == 1; + int default_iters = 20000; + int iters = get_iters(default_iters); + + /* Check for invalid user arguments */ + char* valid_args[] = {"ecdsa", "verify", "ecdsa_verify", "sign", "ecdsa_sign", "ecdh", "recover", + "ecdsa_recover", "schnorrsig", "schnorrsig_verify", "schnorrsig_sign"}; + size_t valid_args_size = sizeof(valid_args)/sizeof(valid_args[0]); + int invalid_args = have_invalid_args(argc, argv, valid_args, valid_args_size); + + if (argc > 1) { + if (have_flag(argc, argv, "-h") + || have_flag(argc, argv, "--help") + || have_flag(argc, argv, "help")) { + help(default_iters); + return 0; + } else if (invalid_args) { + fprintf(stderr, "./bench: unrecognized argument.\n\n"); + help(default_iters); + return 1; + } + } + +/* Check if the user tries to benchmark optional module without building it */ +#ifndef ENABLE_MODULE_ECDH + if (have_flag(argc, argv, "ecdh")) { + fprintf(stderr, "./bench: ECDH module not enabled.\n"); + fprintf(stderr, "Use ./configure --enable-module-ecdh.\n\n"); + return 1; + } +#endif + +#ifndef ENABLE_MODULE_RECOVERY + if (have_flag(argc, argv, "recover") || have_flag(argc, argv, "ecdsa_recover")) { + fprintf(stderr, "./bench: Public key recovery module not enabled.\n"); + fprintf(stderr, "Use ./configure --enable-module-recovery.\n\n"); + return 1; + } +#endif + +#ifndef ENABLE_MODULE_SCHNORRSIG + if (have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "schnorrsig_sign") || have_flag(argc, argv, "schnorrsig_verify")) { + fprintf(stderr, "./bench: Schnorr signatures module not enabled.\n"); + fprintf(stderr, "Use ./configure --enable-module-schnorrsig.\n\n"); + return 1; + } +#endif + + /* ECDSA benchmark */ + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + + for (i = 0; i < 32; i++) { + data.msg[i] = 1 + i; + } + for (i = 0; i < 32; i++) { + data.key[i] = 33 + i; + } + data.siglen = 72; + CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig)); + CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key)); + data.pubkeylen = 33; + CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + + print_output_table_header_row(); + if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "verify") || have_flag(argc, argv, "ecdsa_verify")) run_benchmark("ecdsa_verify", bench_verify, NULL, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "sign") || have_flag(argc, argv, "ecdsa_sign")) run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); + +#ifdef ENABLE_MODULE_ECDH + /* ECDH benchmarks */ + run_ecdh_bench(iters, argc, argv); +#endif + +#ifdef ENABLE_MODULE_RECOVERY + /* ECDSA recovery benchmarks */ + run_recovery_bench(iters, argc, argv); +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG + /* Schnorr signature benchmarks */ + run_schnorrsig_bench(iters, argc, argv); +#endif + + return 0; +} diff --git a/src/secp256k1/src/bench.h b/src/secp256k1/src/bench.h new file mode 100644 index 0000000000..bf9a932ff4 --- /dev/null +++ b/src/secp256k1/src/bench.h @@ -0,0 +1,188 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_BENCH_H +#define SECP256K1_BENCH_H + +#include <stdlib.h> +#include <stdint.h> +#include <stdio.h> +#include <string.h> + +#if (defined(_MSC_VER) && _MSC_VER >= 1900) +# include <time.h> +#else +# include "sys/time.h" +#endif + +static int64_t gettime_i64(void) { +#if (defined(_MSC_VER) && _MSC_VER >= 1900) + /* C11 way to get wallclock time */ + struct timespec tv; + if (!timespec_get(&tv, TIME_UTC)) { + fputs("timespec_get failed!", stderr); + exit(1); + } + return (int64_t)tv.tv_nsec / 1000 + (int64_t)tv.tv_sec * 1000000LL; +#else + struct timeval tv; + gettimeofday(&tv, NULL); + return (int64_t)tv.tv_usec + (int64_t)tv.tv_sec * 1000000LL; +#endif +} + +#define FP_EXP (6) +#define FP_MULT (1000000LL) + +/* Format fixed point number. */ +static void print_number(const int64_t x) { + int64_t x_abs, y; + int c, i, rounding, g; /* g = integer part size, c = fractional part size */ + size_t ptr; + char buffer[30]; + + if (x == INT64_MIN) { + /* Prevent UB. */ + printf("ERR"); + return; + } + x_abs = x < 0 ? -x : x; + + /* Determine how many decimals we want to show (more than FP_EXP makes no + * sense). */ + y = x_abs; + c = 0; + while (y > 0LL && y < 100LL * FP_MULT && c < FP_EXP) { + y *= 10LL; + c++; + } + + /* Round to 'c' decimals. */ + y = x_abs; + rounding = 0; + for (i = c; i < FP_EXP; ++i) { + rounding = (y % 10) >= 5; + y /= 10; + } + y += rounding; + + /* Format and print the number. */ + ptr = sizeof(buffer) - 1; + buffer[ptr] = 0; + g = 0; + if (c != 0) { /* non zero fractional part */ + for (i = 0; i < c; ++i) { + buffer[--ptr] = '0' + (y % 10); + y /= 10; + } + } else if (c == 0) { /* fractional part is 0 */ + buffer[--ptr] = '0'; + } + buffer[--ptr] = '.'; + do { + buffer[--ptr] = '0' + (y % 10); + y /= 10; + g++; + } while (y != 0); + if (x < 0) { + buffer[--ptr] = '-'; + g++; + } + printf("%5.*s", g, &buffer[ptr]); /* Prints integer part */ + printf("%-*s", FP_EXP, &buffer[ptr + g]); /* Prints fractional part */ +} + +static void run_benchmark(char *name, void (*benchmark)(void*, int), void (*setup)(void*), void (*teardown)(void*, int), void* data, int count, int iter) { + int i; + int64_t min = INT64_MAX; + int64_t sum = 0; + int64_t max = 0; + for (i = 0; i < count; i++) { + int64_t begin, total; + if (setup != NULL) { + setup(data); + } + begin = gettime_i64(); + benchmark(data, iter); + total = gettime_i64() - begin; + if (teardown != NULL) { + teardown(data, iter); + } + if (total < min) { + min = total; + } + if (total > max) { + max = total; + } + sum += total; + } + /* ',' is used as a column delimiter */ + printf("%-30s, ", name); + print_number(min * FP_MULT / iter); + printf(" , "); + print_number(((sum * FP_MULT) / count) / iter); + printf(" , "); + print_number(max * FP_MULT / iter); + printf("\n"); +} + +static int have_flag(int argc, char** argv, char *flag) { + char** argm = argv + argc; + argv++; + while (argv != argm) { + if (strcmp(*argv, flag) == 0) { + return 1; + } + argv++; + } + return 0; +} + +/* takes an array containing the arguments that the user is allowed to enter on the command-line + returns: + - 1 if the user entered an invalid argument + - 0 if all the user entered arguments are valid */ +static int have_invalid_args(int argc, char** argv, char** valid_args, size_t n) { + size_t i; + int found_valid; + char** argm = argv + argc; + argv++; + + while (argv != argm) { + found_valid = 0; + for (i = 0; i < n; i++) { + if (strcmp(*argv, valid_args[i]) == 0) { + found_valid = 1; /* user entered a valid arg from the list */ + break; + } + } + if (found_valid == 0) { + return 1; /* invalid arg found */ + } + argv++; + } + return 0; +} + +static int get_iters(int default_iters) { + char* env = getenv("SECP256K1_BENCH_ITERS"); + if (env) { + return strtol(env, NULL, 0); + } else { + return default_iters; + } +} + +static void print_output_table_header_row(void) { + char* bench_str = "Benchmark"; /* left justified */ + char* min_str = " Min(us) "; /* center alignment */ + char* avg_str = " Avg(us) "; + char* max_str = " Max(us) "; + printf("%-30s,%-15s,%-15s,%-15s\n", bench_str, min_str, avg_str, max_str); + printf("\n"); +} + +#endif /* SECP256K1_BENCH_H */ diff --git a/src/secp256k1/src/bench_ecmult.c b/src/secp256k1/src/bench_ecmult.c new file mode 100644 index 0000000000..98fb798d82 --- /dev/null +++ b/src/secp256k1/src/bench_ecmult.c @@ -0,0 +1,370 @@ +/*********************************************************************** + * Copyright (c) 2017 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ +#include <stdio.h> + +#include "secp256k1.c" +#include "../include/secp256k1.h" + +#include "util.h" +#include "hash_impl.h" +#include "field_impl.h" +#include "group_impl.h" +#include "scalar_impl.h" +#include "ecmult_impl.h" +#include "bench.h" + +#define POINTS 32768 + +static void help(char **argv) { + printf("Benchmark EC multiplication algorithms\n"); + printf("\n"); + printf("Usage: %s <help|pippenger_wnaf|strauss_wnaf|simple>\n", argv[0]); + printf("The output shows the number of multiplied and summed points right after the\n"); + printf("function name. The letter 'g' indicates that one of the points is the generator.\n"); + printf("The benchmarks are divided by the number of points.\n"); + printf("\n"); + printf("default (ecmult_multi): picks pippenger_wnaf or strauss_wnaf depending on the\n"); + printf(" batch size\n"); + printf("pippenger_wnaf: for all batch sizes\n"); + printf("strauss_wnaf: for all batch sizes\n"); + printf("simple: multiply and sum each point individually\n"); +} + +typedef struct { + /* Setup once in advance */ + secp256k1_context* ctx; + secp256k1_scratch_space* scratch; + secp256k1_scalar* scalars; + secp256k1_ge* pubkeys; + secp256k1_gej* pubkeys_gej; + secp256k1_scalar* seckeys; + secp256k1_gej* expected_output; + secp256k1_ecmult_multi_func ecmult_multi; + + /* Changes per benchmark */ + size_t count; + int includes_g; + + /* Changes per benchmark iteration, used to pick different scalars and pubkeys + * in each run. */ + size_t offset1; + size_t offset2; + + /* Benchmark output. */ + secp256k1_gej* output; +} bench_data; + +/* Hashes x into [0, POINTS) twice and store the result in offset1 and offset2. */ +static void hash_into_offset(bench_data* data, size_t x) { + data->offset1 = (x * 0x537b7f6f + 0x8f66a481) % POINTS; + data->offset2 = (x * 0x7f6f537b + 0x6a1a8f49) % POINTS; +} + +/* Check correctness of the benchmark by computing + * sum(outputs) ?= (sum(scalars_gen) + sum(seckeys)*sum(scalars))*G */ +static void bench_ecmult_teardown_helper(bench_data* data, size_t* seckey_offset, size_t* scalar_offset, size_t* scalar_gen_offset, int iters) { + int i; + secp256k1_gej sum_output, tmp; + secp256k1_scalar sum_scalars; + + secp256k1_gej_set_infinity(&sum_output); + secp256k1_scalar_clear(&sum_scalars); + for (i = 0; i < iters; ++i) { + secp256k1_gej_add_var(&sum_output, &sum_output, &data->output[i], NULL); + if (scalar_gen_offset != NULL) { + secp256k1_scalar_add(&sum_scalars, &sum_scalars, &data->scalars[(*scalar_gen_offset+i) % POINTS]); + } + if (seckey_offset != NULL) { + secp256k1_scalar s = data->seckeys[(*seckey_offset+i) % POINTS]; + secp256k1_scalar_mul(&s, &s, &data->scalars[(*scalar_offset+i) % POINTS]); + secp256k1_scalar_add(&sum_scalars, &sum_scalars, &s); + } + } + secp256k1_ecmult_gen(&data->ctx->ecmult_gen_ctx, &tmp, &sum_scalars); + CHECK(secp256k1_gej_eq_var(&tmp, &sum_output)); +} + +static void bench_ecmult_setup(void* arg) { + bench_data* data = (bench_data*)arg; + /* Re-randomize offset to ensure that we're using different scalars and + * group elements in each run. */ + hash_into_offset(data, data->offset1); +} + +static void bench_ecmult_gen(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int i; + + for (i = 0; i < iters; ++i) { + secp256k1_ecmult_gen(&data->ctx->ecmult_gen_ctx, &data->output[i], &data->scalars[(data->offset1+i) % POINTS]); + } +} + +static void bench_ecmult_gen_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + bench_ecmult_teardown_helper(data, NULL, NULL, &data->offset1, iters); +} + +static void bench_ecmult_const(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int i; + + for (i = 0; i < iters; ++i) { + secp256k1_ecmult_const(&data->output[i], &data->pubkeys[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], 256); + } +} + +static void bench_ecmult_const_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, NULL, iters); +} + +static void bench_ecmult_1p(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int i; + + for (i = 0; i < iters; ++i) { + secp256k1_ecmult(&data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], NULL); + } +} + +static void bench_ecmult_1p_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, NULL, iters); +} + +static void bench_ecmult_0p_g(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + secp256k1_scalar zero; + int i; + + secp256k1_scalar_set_int(&zero, 0); + for (i = 0; i < iters; ++i) { + secp256k1_ecmult(&data->output[i], NULL, &zero, &data->scalars[(data->offset1+i) % POINTS]); + } +} + +static void bench_ecmult_0p_g_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + bench_ecmult_teardown_helper(data, NULL, NULL, &data->offset1, iters); +} + +static void bench_ecmult_1p_g(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int i; + + for (i = 0; i < iters/2; ++i) { + secp256k1_ecmult(&data->output[i], &data->pubkeys_gej[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], &data->scalars[(data->offset1+i) % POINTS]); + } +} + +static void bench_ecmult_1p_g_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + bench_ecmult_teardown_helper(data, &data->offset1, &data->offset2, &data->offset1, iters/2); +} + +static void run_ecmult_bench(bench_data* data, int iters) { + char str[32]; + sprintf(str, "ecmult_gen"); + run_benchmark(str, bench_ecmult_gen, bench_ecmult_setup, bench_ecmult_gen_teardown, data, 10, iters); + sprintf(str, "ecmult_const"); + run_benchmark(str, bench_ecmult_const, bench_ecmult_setup, bench_ecmult_const_teardown, data, 10, iters); + /* ecmult with non generator point */ + sprintf(str, "ecmult_1p"); + run_benchmark(str, bench_ecmult_1p, bench_ecmult_setup, bench_ecmult_1p_teardown, data, 10, iters); + /* ecmult with generator point */ + sprintf(str, "ecmult_0p_g"); + run_benchmark(str, bench_ecmult_0p_g, bench_ecmult_setup, bench_ecmult_0p_g_teardown, data, 10, iters); + /* ecmult with generator and non-generator point. The reported time is per point. */ + sprintf(str, "ecmult_1p_g"); + run_benchmark(str, bench_ecmult_1p_g, bench_ecmult_setup, bench_ecmult_1p_g_teardown, data, 10, 2*iters); +} + +static int bench_ecmult_multi_callback(secp256k1_scalar* sc, secp256k1_ge* ge, size_t idx, void* arg) { + bench_data* data = (bench_data*)arg; + if (data->includes_g) ++idx; + if (idx == 0) { + *sc = data->scalars[data->offset1]; + *ge = secp256k1_ge_const_g; + } else { + *sc = data->scalars[(data->offset1 + idx) % POINTS]; + *ge = data->pubkeys[(data->offset2 + idx - 1) % POINTS]; + } + return 1; +} + +static void bench_ecmult_multi(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + + int includes_g = data->includes_g; + int iter; + int count = data->count; + iters = iters / data->count; + + for (iter = 0; iter < iters; ++iter) { + data->ecmult_multi(&data->ctx->error_callback, data->scratch, &data->output[iter], data->includes_g ? &data->scalars[data->offset1] : NULL, bench_ecmult_multi_callback, arg, count - includes_g); + data->offset1 = (data->offset1 + count) % POINTS; + data->offset2 = (data->offset2 + count - 1) % POINTS; + } +} + +static void bench_ecmult_multi_setup(void* arg) { + bench_data* data = (bench_data*)arg; + hash_into_offset(data, data->count); +} + +static void bench_ecmult_multi_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int iter; + iters = iters / data->count; + /* Verify the results in teardown, to avoid doing comparisons while benchmarking. */ + for (iter = 0; iter < iters; ++iter) { + secp256k1_gej tmp; + secp256k1_gej_add_var(&tmp, &data->output[iter], &data->expected_output[iter], NULL); + CHECK(secp256k1_gej_is_infinity(&tmp)); + } +} + +static void generate_scalar(uint32_t num, secp256k1_scalar* scalar) { + secp256k1_sha256 sha256; + unsigned char c[10] = {'e', 'c', 'm', 'u', 'l', 't', 0, 0, 0, 0}; + unsigned char buf[32]; + int overflow = 0; + c[6] = num; + c[7] = num >> 8; + c[8] = num >> 16; + c[9] = num >> 24; + secp256k1_sha256_initialize(&sha256); + secp256k1_sha256_write(&sha256, c, sizeof(c)); + secp256k1_sha256_finalize(&sha256, buf); + secp256k1_scalar_set_b32(scalar, buf, &overflow); + CHECK(!overflow); +} + +static void run_ecmult_multi_bench(bench_data* data, size_t count, int includes_g, int num_iters) { + char str[32]; + static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + size_t iters = 1 + num_iters / count; + size_t iter; + + data->count = count; + data->includes_g = includes_g; + + /* Compute (the negation of) the expected results directly. */ + hash_into_offset(data, data->count); + for (iter = 0; iter < iters; ++iter) { + secp256k1_scalar tmp; + secp256k1_scalar total = data->scalars[(data->offset1++) % POINTS]; + size_t i = 0; + for (i = 0; i + 1 < count; ++i) { + secp256k1_scalar_mul(&tmp, &data->seckeys[(data->offset2++) % POINTS], &data->scalars[(data->offset1++) % POINTS]); + secp256k1_scalar_add(&total, &total, &tmp); + } + secp256k1_scalar_negate(&total, &total); + secp256k1_ecmult(&data->expected_output[iter], NULL, &zero, &total); + } + + /* Run the benchmark. */ + if (includes_g) { + sprintf(str, "ecmult_multi_%ip_g", (int)count - 1); + } else { + sprintf(str, "ecmult_multi_%ip", (int)count); + } + run_benchmark(str, bench_ecmult_multi, bench_ecmult_multi_setup, bench_ecmult_multi_teardown, data, 10, count * iters); +} + +int main(int argc, char **argv) { + bench_data data; + int i, p; + size_t scratch_size; + + int iters = get_iters(10000); + + data.ecmult_multi = secp256k1_ecmult_multi_var; + + if (argc > 1) { + if(have_flag(argc, argv, "-h") + || have_flag(argc, argv, "--help") + || have_flag(argc, argv, "help")) { + help(argv); + return 0; + } else if(have_flag(argc, argv, "pippenger_wnaf")) { + printf("Using pippenger_wnaf:\n"); + data.ecmult_multi = secp256k1_ecmult_pippenger_batch_single; + } else if(have_flag(argc, argv, "strauss_wnaf")) { + printf("Using strauss_wnaf:\n"); + data.ecmult_multi = secp256k1_ecmult_strauss_batch_single; + } else if(have_flag(argc, argv, "simple")) { + printf("Using simple algorithm:\n"); + } else { + fprintf(stderr, "%s: unrecognized argument '%s'.\n\n", argv[0], argv[1]); + help(argv); + return 1; + } + } + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + scratch_size = secp256k1_strauss_scratch_size(POINTS) + STRAUSS_SCRATCH_OBJECTS*16; + if (!have_flag(argc, argv, "simple")) { + data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size); + } else { + data.scratch = NULL; + } + + /* Allocate stuff */ + data.scalars = malloc(sizeof(secp256k1_scalar) * POINTS); + data.seckeys = malloc(sizeof(secp256k1_scalar) * POINTS); + data.pubkeys = malloc(sizeof(secp256k1_ge) * POINTS); + data.pubkeys_gej = malloc(sizeof(secp256k1_gej) * POINTS); + data.expected_output = malloc(sizeof(secp256k1_gej) * (iters + 1)); + data.output = malloc(sizeof(secp256k1_gej) * (iters + 1)); + + /* Generate a set of scalars, and private/public keypairs. */ + secp256k1_gej_set_ge(&data.pubkeys_gej[0], &secp256k1_ge_const_g); + secp256k1_scalar_set_int(&data.seckeys[0], 1); + for (i = 0; i < POINTS; ++i) { + generate_scalar(i, &data.scalars[i]); + if (i) { + secp256k1_gej_double_var(&data.pubkeys_gej[i], &data.pubkeys_gej[i - 1], NULL); + secp256k1_scalar_add(&data.seckeys[i], &data.seckeys[i - 1], &data.seckeys[i - 1]); + } + } + secp256k1_ge_set_all_gej_var(data.pubkeys, data.pubkeys_gej, POINTS); + + + print_output_table_header_row(); + /* Initialize offset1 and offset2 */ + hash_into_offset(&data, 0); + run_ecmult_bench(&data, iters); + + for (i = 1; i <= 8; ++i) { + run_ecmult_multi_bench(&data, i, 1, iters); + } + + /* This is disabled with low count of iterations because the loop runs 77 times even with iters=1 + * and the higher it goes the longer the computation takes(more points) + * So we don't run this benchmark with low iterations to prevent slow down */ + if (iters > 2) { + for (p = 0; p <= 11; ++p) { + for (i = 9; i <= 16; ++i) { + run_ecmult_multi_bench(&data, i << p, 1, iters); + } + } + } + + if (data.scratch != NULL) { + secp256k1_scratch_space_destroy(data.ctx, data.scratch); + } + secp256k1_context_destroy(data.ctx); + free(data.scalars); + free(data.pubkeys); + free(data.pubkeys_gej); + free(data.seckeys); + free(data.output); + free(data.expected_output); + + return(0); +} diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c new file mode 100644 index 0000000000..c248ab8ebc --- /dev/null +++ b/src/secp256k1/src/bench_internal.c @@ -0,0 +1,407 @@ +/*********************************************************************** + * Copyright (c) 2014-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ +#include <stdio.h> + +#include "secp256k1.c" +#include "../include/secp256k1.h" + +#include "assumptions.h" +#include "util.h" +#include "hash_impl.h" +#include "field_impl.h" +#include "group_impl.h" +#include "scalar_impl.h" +#include "ecmult_const_impl.h" +#include "ecmult_impl.h" +#include "bench.h" + +typedef struct { + secp256k1_scalar scalar[2]; + secp256k1_fe fe[4]; + secp256k1_ge ge[2]; + secp256k1_gej gej[2]; + unsigned char data[64]; + int wnaf[256]; +} bench_inv; + +static void bench_setup(void* arg) { + bench_inv *data = (bench_inv*)arg; + + static const unsigned char init[4][32] = { + /* Initializer for scalar[0], fe[0], first half of data, the X coordinate of ge[0], + and the (implied affine) X coordinate of gej[0]. */ + { + 0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13, + 0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35, + 0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59, + 0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83 + }, + /* Initializer for scalar[1], fe[1], first half of data, the X coordinate of ge[1], + and the (implied affine) X coordinate of gej[1]. */ + { + 0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83, + 0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5, + 0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9, + 0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3 + }, + /* Initializer for fe[2] and the Z coordinate of gej[0]. */ + { + 0x3d, 0x2d, 0xef, 0xf4, 0x25, 0x98, 0x4f, 0x5d, + 0xe2, 0xca, 0x5f, 0x41, 0x3f, 0x3f, 0xce, 0x44, + 0xaa, 0x2c, 0x53, 0x8a, 0xc6, 0x59, 0x1f, 0x38, + 0x38, 0x23, 0xe4, 0x11, 0x27, 0xc6, 0xa0, 0xe7 + }, + /* Initializer for fe[3] and the Z coordinate of gej[1]. */ + { + 0xbd, 0x21, 0xa5, 0xe1, 0x13, 0x50, 0x73, 0x2e, + 0x52, 0x98, 0xc8, 0x9e, 0xab, 0x00, 0xa2, 0x68, + 0x43, 0xf5, 0xd7, 0x49, 0x80, 0x72, 0xa7, 0xf3, + 0xd7, 0x60, 0xe6, 0xab, 0x90, 0x92, 0xdf, 0xc5 + } + }; + + secp256k1_scalar_set_b32(&data->scalar[0], init[0], NULL); + secp256k1_scalar_set_b32(&data->scalar[1], init[1], NULL); + secp256k1_fe_set_b32(&data->fe[0], init[0]); + secp256k1_fe_set_b32(&data->fe[1], init[1]); + secp256k1_fe_set_b32(&data->fe[2], init[2]); + secp256k1_fe_set_b32(&data->fe[3], init[3]); + CHECK(secp256k1_ge_set_xo_var(&data->ge[0], &data->fe[0], 0)); + CHECK(secp256k1_ge_set_xo_var(&data->ge[1], &data->fe[1], 1)); + secp256k1_gej_set_ge(&data->gej[0], &data->ge[0]); + secp256k1_gej_rescale(&data->gej[0], &data->fe[2]); + secp256k1_gej_set_ge(&data->gej[1], &data->ge[1]); + secp256k1_gej_rescale(&data->gej[1], &data->fe[3]); + memcpy(data->data, init[0], 32); + memcpy(data->data + 32, init[1], 32); +} + +static void bench_scalar_add(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + j += secp256k1_scalar_add(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } + CHECK(j <= iters); +} + +static void bench_scalar_negate(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_negate(&data->scalar[0], &data->scalar[0]); + } +} + +static void bench_scalar_mul(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_mul(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } +} + +static void bench_scalar_split(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + secp256k1_scalar tmp; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_split_lambda(&tmp, &data->scalar[1], &data->scalar[0]); + j += secp256k1_scalar_add(&data->scalar[0], &tmp, &data->scalar[1]); + } + CHECK(j <= iters); +} + +static void bench_scalar_inverse(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_inverse(&data->scalar[0], &data->scalar[0]); + j += secp256k1_scalar_add(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } + CHECK(j <= iters); +} + +static void bench_scalar_inverse_var(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_inverse_var(&data->scalar[0], &data->scalar[0]); + j += secp256k1_scalar_add(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } + CHECK(j <= iters); +} + +static void bench_field_half(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_half(&data->fe[0]); + } +} + +static void bench_field_normalize(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_normalize(&data->fe[0]); + } +} + +static void bench_field_normalize_weak(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_normalize_weak(&data->fe[0]); + } +} + +static void bench_field_mul(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_mul(&data->fe[0], &data->fe[0], &data->fe[1]); + } +} + +static void bench_field_sqr(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_sqr(&data->fe[0], &data->fe[0]); + } +} + +static void bench_field_inverse(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_inv(&data->fe[0], &data->fe[0]); + secp256k1_fe_add(&data->fe[0], &data->fe[1]); + } +} + +static void bench_field_inverse_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_inv_var(&data->fe[0], &data->fe[0]); + secp256k1_fe_add(&data->fe[0], &data->fe[1]); + } +} + +static void bench_field_sqrt(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + secp256k1_fe t; + + for (i = 0; i < iters; i++) { + t = data->fe[0]; + j += secp256k1_fe_sqrt(&data->fe[0], &t); + secp256k1_fe_add(&data->fe[0], &data->fe[1]); + } + CHECK(j <= iters); +} + +static void bench_field_is_square_var(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + secp256k1_fe t = data->fe[0]; + + for (i = 0; i < iters; i++) { + j += secp256k1_fe_is_square_var(&t); + secp256k1_fe_add(&t, &data->fe[1]); + secp256k1_fe_normalize_var(&t); + } + CHECK(j <= iters); +} + +static void bench_group_double_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_double_var(&data->gej[0], &data->gej[0], NULL); + } +} + +static void bench_group_add_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_var(&data->gej[0], &data->gej[0], &data->gej[1], NULL); + } +} + +static void bench_group_add_affine(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_ge(&data->gej[0], &data->gej[0], &data->ge[1]); + } +} + +static void bench_group_add_affine_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_ge_var(&data->gej[0], &data->gej[0], &data->ge[1], NULL); + } +} + +static void bench_group_add_zinv_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_zinv_var(&data->gej[0], &data->gej[0], &data->ge[1], &data->gej[0].y); + } +} + +static void bench_group_to_affine_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; ++i) { + secp256k1_ge_set_gej_var(&data->ge[1], &data->gej[0]); + /* Use the output affine X/Y coordinates to vary the input X/Y/Z coordinates. + Note that the resulting coordinates will generally not correspond to a point + on the curve, but this is not a problem for the code being benchmarked here. + Adding and normalizing have less overhead than EC operations (which could + guarantee the point remains on the curve). */ + secp256k1_fe_add(&data->gej[0].x, &data->ge[1].y); + secp256k1_fe_add(&data->gej[0].y, &data->fe[2]); + secp256k1_fe_add(&data->gej[0].z, &data->ge[1].x); + secp256k1_fe_normalize_var(&data->gej[0].x); + secp256k1_fe_normalize_var(&data->gej[0].y); + secp256k1_fe_normalize_var(&data->gej[0].z); + } +} + +static void bench_ecmult_wnaf(void* arg, int iters) { + int i, bits = 0, overflow = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + bits += secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar[0], WINDOW_A); + overflow += secp256k1_scalar_add(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } + CHECK(overflow >= 0); + CHECK(bits <= 256*iters); +} + +static void bench_wnaf_const(void* arg, int iters) { + int i, bits = 0, overflow = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + bits += secp256k1_wnaf_const(data->wnaf, &data->scalar[0], WINDOW_A, 256); + overflow += secp256k1_scalar_add(&data->scalar[0], &data->scalar[0], &data->scalar[1]); + } + CHECK(overflow >= 0); + CHECK(bits <= 256*iters); +} + +static void bench_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_sha256 sha; + + for (i = 0; i < iters; i++) { + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, data->data, 32); + secp256k1_sha256_finalize(&sha, data->data); + } +} + +static void bench_hmac_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_hmac_sha256 hmac; + + for (i = 0; i < iters; i++) { + secp256k1_hmac_sha256_initialize(&hmac, data->data, 32); + secp256k1_hmac_sha256_write(&hmac, data->data, 32); + secp256k1_hmac_sha256_finalize(&hmac, data->data); + } +} + +static void bench_rfc6979_hmac_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_rfc6979_hmac_sha256 rng; + + for (i = 0; i < iters; i++) { + secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64); + secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32); + } +} + +static void bench_context(void* arg, int iters) { + int i; + (void)arg; + for (i = 0; i < iters; i++) { + secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_NONE)); + } +} + +int main(int argc, char **argv) { + bench_inv data; + int iters = get_iters(20000); + int d = argc == 1; /* default */ + print_output_table_header_row(); + + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, iters*100); + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, iters*100); + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "half")) run_benchmark("field_half", bench_field_half, bench_setup, NULL, &data, 10, iters*100); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, iters*100); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, iters*100); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "issquare")) run_benchmark("field_is_square_var", bench_field_is_square_var, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_zinv_var", bench_group_add_zinv_var, bench_setup, NULL, &data, 10, iters*10); + if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "to_affine")) run_benchmark("group_to_affine_var", bench_group_to_affine_var, bench_setup, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, iters); + + if (d || have_flag(argc, argv, "context")) run_benchmark("context_create", bench_context, bench_setup, NULL, &data, 10, iters); + + return 0; +} diff --git a/src/secp256k1/src/checkmem.h b/src/secp256k1/src/checkmem.h new file mode 100644 index 0000000000..571e4cc389 --- /dev/null +++ b/src/secp256k1/src/checkmem.h @@ -0,0 +1,88 @@ +/*********************************************************************** + * Copyright (c) 2022 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/* The code here is inspired by Kris Kwiatkowski's approach in + * https://github.com/kriskwiatkowski/pqc/blob/main/src/common/ct_check.h + * to provide a general interface for memory-checking mechanisms, primarily + * for constant-time checking. + */ + +/* These macros are defined by this header file: + * + * - SECP256K1_CHECKMEM_ENABLED: + * - 1 if memory-checking integration is available, 0 otherwise. + * This is just a compile-time macro. Use the next macro to check it is actually + * available at runtime. + * - SECP256K1_CHECKMEM_RUNNING(): + * - Acts like a function call, returning 1 if memory checking is available + * at runtime. + * - SECP256K1_CHECKMEM_CHECK(p, len): + * - Assert or otherwise fail in case the len-byte memory block pointed to by p is + * not considered entirely defined. + * - SECP256K1_CHECKMEM_CHECK_VERIFY(p, len): + * - Like SECP256K1_CHECKMEM_CHECK, but only works in VERIFY mode. + * - SECP256K1_CHECKMEM_UNDEFINE(p, len): + * - marks the len-byte memory block pointed to by p as undefined data (secret data, + * in the context of constant-time checking). + * - SECP256K1_CHECKMEM_DEFINE(p, len): + * - marks the len-byte memory pointed to by p as defined data (public data, in the + * context of constant-time checking). + * + */ + +#ifndef SECP256K1_CHECKMEM_H +#define SECP256K1_CHECKMEM_H + +/* Define a statement-like macro that ignores the arguments. */ +#define SECP256K1_CHECKMEM_NOOP(p, len) do { (void)(p); (void)(len); } while(0) + +/* If compiling under msan, map the SECP256K1_CHECKMEM_* functionality to msan. + * Choose this preferentially, even when VALGRIND is defined, as msan-compiled + * binaries can't be run under valgrind anyway. */ +#if defined(__has_feature) +# if __has_feature(memory_sanitizer) +# include <sanitizer/msan_interface.h> +# define SECP256K1_CHECKMEM_ENABLED 1 +# define SECP256K1_CHECKMEM_UNDEFINE(p, len) __msan_allocated_memory((p), (len)) +# define SECP256K1_CHECKMEM_DEFINE(p, len) __msan_unpoison((p), (len)) +# define SECP256K1_CHECKMEM_CHECK(p, len) __msan_check_mem_is_initialized((p), (len)) +# define SECP256K1_CHECKMEM_RUNNING() (1) +# endif +#endif + +/* If valgrind integration is desired (through the VALGRIND define), implement the + * SECP256K1_CHECKMEM_* macros using valgrind. */ +#if !defined SECP256K1_CHECKMEM_ENABLED +# if defined VALGRIND +# include <stddef.h> +# include <valgrind/memcheck.h> +# define SECP256K1_CHECKMEM_ENABLED 1 +# define SECP256K1_CHECKMEM_UNDEFINE(p, len) VALGRIND_MAKE_MEM_UNDEFINED((p), (len)) +# define SECP256K1_CHECKMEM_DEFINE(p, len) VALGRIND_MAKE_MEM_DEFINED((p), (len)) +# define SECP256K1_CHECKMEM_CHECK(p, len) VALGRIND_CHECK_MEM_IS_DEFINED((p), (len)) + /* VALGRIND_MAKE_MEM_DEFINED returns 0 iff not running on memcheck. + * This is more precise than the RUNNING_ON_VALGRIND macro, which + * checks for valgrind in general instead of memcheck specifically. */ +# define SECP256K1_CHECKMEM_RUNNING() (VALGRIND_MAKE_MEM_DEFINED(NULL, 0) != 0) +# endif +#endif + +/* As a fall-back, map these macros to dummy statements. */ +#if !defined SECP256K1_CHECKMEM_ENABLED +# define SECP256K1_CHECKMEM_ENABLED 0 +# define SECP256K1_CHECKMEM_UNDEFINE(p, len) SECP256K1_CHECKMEM_NOOP((p), (len)) +# define SECP256K1_CHECKMEM_DEFINE(p, len) SECP256K1_CHECKMEM_NOOP((p), (len)) +# define SECP256K1_CHECKMEM_CHECK(p, len) SECP256K1_CHECKMEM_NOOP((p), (len)) +# define SECP256K1_CHECKMEM_RUNNING() (0) +#endif + +#if defined VERIFY +#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len) SECP256K1_CHECKMEM_CHECK((p), (len)) +#else +#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len) SECP256K1_CHECKMEM_NOOP((p), (len)) +#endif + +#endif /* SECP256K1_CHECKMEM_H */ diff --git a/src/secp256k1/src/ctime_tests.c b/src/secp256k1/src/ctime_tests.c new file mode 100644 index 0000000000..713eb427d3 --- /dev/null +++ b/src/secp256k1/src/ctime_tests.c @@ -0,0 +1,174 @@ +/*********************************************************************** + * Copyright (c) 2020 Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <stdio.h> + +#include "../include/secp256k1.h" +#include "assumptions.h" +#include "checkmem.h" + +#if !SECP256K1_CHECKMEM_ENABLED +# error "This tool cannot be compiled without memory-checking interface (valgrind or msan)" +#endif + +#ifdef ENABLE_MODULE_ECDH +# include "../include/secp256k1_ecdh.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "../include/secp256k1_recovery.h" +#endif + +#ifdef ENABLE_MODULE_EXTRAKEYS +# include "../include/secp256k1_extrakeys.h" +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG +#include "../include/secp256k1_schnorrsig.h" +#endif + +static void run_tests(secp256k1_context *ctx, unsigned char *key); + +int main(void) { + secp256k1_context* ctx; + unsigned char key[32]; + int ret, i; + + if (!SECP256K1_CHECKMEM_RUNNING()) { + fprintf(stderr, "This test can only usefully be run inside valgrind because it was not compiled under msan.\n"); + fprintf(stderr, "Usage: libtool --mode=execute valgrind ./ctime_tests\n"); + return 1; + } + ctx = secp256k1_context_create(SECP256K1_CONTEXT_DECLASSIFY); + /** In theory, testing with a single secret input should be sufficient: + * If control flow depended on secrets the tool would generate an error. + */ + for (i = 0; i < 32; i++) { + key[i] = i + 65; + } + + run_tests(ctx, key); + + /* Test context randomisation. Do this last because it leaves the context + * tainted. */ + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_context_randomize(ctx, key); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret); + + secp256k1_context_destroy(ctx); + return 0; +} + +static void run_tests(secp256k1_context *ctx, unsigned char *key) { + secp256k1_ecdsa_signature signature; + secp256k1_pubkey pubkey; + size_t siglen = 74; + size_t outputlen = 33; + int i; + int ret; + unsigned char msg[32]; + unsigned char sig[74]; + unsigned char spubkey[33]; +#ifdef ENABLE_MODULE_RECOVERY + secp256k1_ecdsa_recoverable_signature recoverable_signature; + int recid; +#endif +#ifdef ENABLE_MODULE_EXTRAKEYS + secp256k1_keypair keypair; +#endif + + for (i = 0; i < 32; i++) { + msg[i] = i + 1; + } + + /* Test keygen. */ + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ec_pubkey_create(ctx, &pubkey, key); + SECP256K1_CHECKMEM_DEFINE(&pubkey, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret); + CHECK(secp256k1_ec_pubkey_serialize(ctx, spubkey, &outputlen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + + /* Test signing. */ + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ecdsa_sign(ctx, &signature, msg, key, NULL, NULL); + SECP256K1_CHECKMEM_DEFINE(&signature, sizeof(secp256k1_ecdsa_signature)); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret); + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature)); + +#ifdef ENABLE_MODULE_ECDH + /* Test ECDH. */ + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ecdh(ctx, msg, &pubkey, key, NULL, NULL); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); +#endif + +#ifdef ENABLE_MODULE_RECOVERY + /* Test signing a recoverable signature. */ + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ecdsa_sign_recoverable(ctx, &recoverable_signature, msg, key, NULL, NULL); + SECP256K1_CHECKMEM_DEFINE(&recoverable_signature, sizeof(recoverable_signature)); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &recoverable_signature)); + CHECK(recid >= 0 && recid <= 3); +#endif + + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ec_seckey_verify(ctx, key); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_ec_seckey_negate(ctx, key); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + SECP256K1_CHECKMEM_UNDEFINE(msg, 32); + ret = secp256k1_ec_seckey_tweak_add(ctx, key, msg); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + SECP256K1_CHECKMEM_UNDEFINE(msg, 32); + ret = secp256k1_ec_seckey_tweak_mul(ctx, key, msg); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + /* Test keypair_create and keypair_xonly_tweak_add. */ +#ifdef ENABLE_MODULE_EXTRAKEYS + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_keypair_create(ctx, &keypair, key); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + /* The tweak is not treated as a secret in keypair_tweak_add */ + SECP256K1_CHECKMEM_DEFINE(msg, 32); + ret = secp256k1_keypair_xonly_tweak_add(ctx, &keypair, msg); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + SECP256K1_CHECKMEM_UNDEFINE(&keypair, sizeof(keypair)); + ret = secp256k1_keypair_sec(ctx, key, &keypair); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG + SECP256K1_CHECKMEM_UNDEFINE(key, 32); + ret = secp256k1_keypair_create(ctx, &keypair, key); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); + ret = secp256k1_schnorrsig_sign32(ctx, sig, msg, &keypair, NULL); + SECP256K1_CHECKMEM_DEFINE(&ret, sizeof(ret)); + CHECK(ret == 1); +#endif +} diff --git a/src/secp256k1/src/ecdsa.h b/src/secp256k1/src/ecdsa.h new file mode 100644 index 0000000000..4441b08398 --- /dev/null +++ b/src/secp256k1/src/ecdsa.h @@ -0,0 +1,21 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECDSA_H +#define SECP256K1_ECDSA_H + +#include <stddef.h> + +#include "scalar.h" +#include "group.h" +#include "ecmult.h" + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size); +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s); +static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message); +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid); + +#endif /* SECP256K1_ECDSA_H */ diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h new file mode 100644 index 0000000000..90b4b22b77 --- /dev/null +++ b/src/secp256k1/src/ecdsa_impl.h @@ -0,0 +1,315 @@ +/*********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + + +#ifndef SECP256K1_ECDSA_IMPL_H +#define SECP256K1_ECDSA_IMPL_H + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult.h" +#include "ecmult_gen.h" +#include "ecdsa.h" + +/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1 + * sage: for t in xrange(1023, -1, -1): + * .. p = 2**256 - 2**32 - t + * .. if p.is_prime(): + * .. print '%x'%p + * .. break + * 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f' + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (EllipticCurve ([F (a), F (b)]).order()) + * 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141' + */ +static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL +); + +/** Difference between field and order, values 'p' and 'n' values defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + * sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order()) + * '14551231950b75fc4402da1722fc9baee' + */ +static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST( + 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL +); + +static int secp256k1_der_read_len(size_t *len, const unsigned char **sigp, const unsigned char *sigend) { + size_t lenleft; + unsigned char b1; + VERIFY_CHECK(len != NULL); + *len = 0; + if (*sigp >= sigend) { + return 0; + } + b1 = *((*sigp)++); + if (b1 == 0xFF) { + /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */ + return 0; + } + if ((b1 & 0x80) == 0) { + /* X.690-0207 8.1.3.4 short form length octets */ + *len = b1; + return 1; + } + if (b1 == 0x80) { + /* Indefinite length is not allowed in DER. */ + return 0; + } + /* X.690-207 8.1.3.5 long form length octets */ + lenleft = b1 & 0x7F; /* lenleft is at least 1 */ + if (lenleft > (size_t)(sigend - *sigp)) { + return 0; + } + if (**sigp == 0) { + /* Not the shortest possible length encoding. */ + return 0; + } + if (lenleft > sizeof(size_t)) { + /* The resulting length would exceed the range of a size_t, so + * certainly longer than the passed array size. + */ + return 0; + } + while (lenleft > 0) { + *len = (*len << 8) | **sigp; + (*sigp)++; + lenleft--; + } + if (*len > (size_t)(sigend - *sigp)) { + /* Result exceeds the length of the passed array. */ + return 0; + } + if (*len < 128) { + /* Not the shortest possible length encoding. */ + return 0; + } + return 1; +} + +static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) { + int overflow = 0; + unsigned char ra[32] = {0}; + size_t rlen; + + if (*sig == sigend || **sig != 0x02) { + /* Not a primitive integer (X.690-0207 8.3.1). */ + return 0; + } + (*sig)++; + if (secp256k1_der_read_len(&rlen, sig, sigend) == 0) { + return 0; + } + if (rlen == 0 || rlen > (size_t)(sigend - *sig)) { + /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1). */ + return 0; + } + if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) { + /* Excessive 0x00 padding. */ + return 0; + } + if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) { + /* Excessive 0xFF padding. */ + return 0; + } + if ((**sig & 0x80) == 0x80) { + /* Negative. */ + overflow = 1; + } + /* There is at most one leading zero byte: + * if there were two leading zero bytes, we would have failed and returned 0 + * because of excessive 0x00 padding already. */ + if (rlen > 0 && **sig == 0) { + /* Skip leading zero byte */ + rlen--; + (*sig)++; + } + if (rlen > 32) { + overflow = 1; + } + if (!overflow) { + if (rlen) memcpy(ra + 32 - rlen, *sig, rlen); + secp256k1_scalar_set_b32(r, ra, &overflow); + } + if (overflow) { + secp256k1_scalar_set_int(r, 0); + } + (*sig) += rlen; + return 1; +} + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) { + const unsigned char *sigend = sig + size; + size_t rlen; + if (sig == sigend || *(sig++) != 0x30) { + /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */ + return 0; + } + if (secp256k1_der_read_len(&rlen, &sig, sigend) == 0) { + return 0; + } + if (rlen != (size_t)(sigend - sig)) { + /* Tuple exceeds bounds or garage after tuple. */ + return 0; + } + + if (!secp256k1_der_parse_integer(rr, &sig, sigend)) { + return 0; + } + if (!secp256k1_der_parse_integer(rs, &sig, sigend)) { + return 0; + } + + if (sig != sigend) { + /* Trailing garbage inside tuple. */ + return 0; + } + + return 1; +} + +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) { + unsigned char r[33] = {0}, s[33] = {0}; + unsigned char *rp = r, *sp = s; + size_t lenR = 33, lenS = 33; + secp256k1_scalar_get_b32(&r[1], ar); + secp256k1_scalar_get_b32(&s[1], as); + while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; } + while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; } + if (*size < 6+lenS+lenR) { + *size = 6 + lenS + lenR; + return 0; + } + *size = 6 + lenS + lenR; + sig[0] = 0x30; + sig[1] = 4 + lenS + lenR; + sig[2] = 0x02; + sig[3] = lenR; + memcpy(sig+4, rp, lenR); + sig[4+lenR] = 0x02; + sig[5+lenR] = lenS; + memcpy(sig+lenR+6, sp, lenS); + return 1; +} + +static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) { + unsigned char c[32]; + secp256k1_scalar sn, u1, u2; +#if !defined(EXHAUSTIVE_TEST_ORDER) + secp256k1_fe xr; +#endif + secp256k1_gej pubkeyj; + secp256k1_gej pr; + + if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) { + return 0; + } + + secp256k1_scalar_inverse_var(&sn, sigs); + secp256k1_scalar_mul(&u1, &sn, message); + secp256k1_scalar_mul(&u2, &sn, sigr); + secp256k1_gej_set_ge(&pubkeyj, pubkey); + secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1); + if (secp256k1_gej_is_infinity(&pr)) { + return 0; + } + +#if defined(EXHAUSTIVE_TEST_ORDER) +{ + secp256k1_scalar computed_r; + secp256k1_ge pr_ge; + secp256k1_ge_set_gej(&pr_ge, &pr); + secp256k1_fe_normalize(&pr_ge.x); + + secp256k1_fe_get_b32(c, &pr_ge.x); + secp256k1_scalar_set_b32(&computed_r, c, NULL); + return secp256k1_scalar_eq(sigr, &computed_r); +} +#else + secp256k1_scalar_get_b32(c, sigr); + secp256k1_fe_set_b32(&xr, c); + + /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n) + * in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p), + * compute the remainder modulo n, and compare it to xr. However: + * + * xr == X(pr) mod n + * <=> exists h. (xr + h * n < p && xr + h * n == X(pr)) + * [Since 2 * n > p, h can only be 0 or 1] + * <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr)) + * [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p] + * <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p) + * [Multiplying both sides of the equations by pr.z^2 mod p] + * <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x) + * + * Thus, we can avoid the inversion, but we have to check both cases separately. + * secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test. + */ + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) { + /* xr + n >= p, so we can skip testing the second case. */ + return 0; + } + secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe); + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + return 0; +#endif +} + +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) { + unsigned char b[32]; + secp256k1_gej rp; + secp256k1_ge r; + secp256k1_scalar n; + int overflow = 0; + int high; + + secp256k1_ecmult_gen(ctx, &rp, nonce); + secp256k1_ge_set_gej(&r, &rp); + secp256k1_fe_normalize(&r.x); + secp256k1_fe_normalize(&r.y); + secp256k1_fe_get_b32(b, &r.x); + secp256k1_scalar_set_b32(sigr, b, &overflow); + if (recid) { + /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log + * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria. + */ + *recid = (overflow << 1) | secp256k1_fe_is_odd(&r.y); + } + secp256k1_scalar_mul(&n, sigr, seckey); + secp256k1_scalar_add(&n, &n, message); + secp256k1_scalar_inverse(sigs, nonce); + secp256k1_scalar_mul(sigs, sigs, &n); + secp256k1_scalar_clear(&n); + secp256k1_gej_clear(&rp); + secp256k1_ge_clear(&r); + high = secp256k1_scalar_is_high(sigs); + secp256k1_scalar_cond_negate(sigs, high); + if (recid) { + *recid ^= high; + } + /* P.x = order is on the curve, so technically sig->r could end up being zero, which would be an invalid signature. + * This is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N. + */ + return (int)(!secp256k1_scalar_is_zero(sigr)) & (int)(!secp256k1_scalar_is_zero(sigs)); +} + +#endif /* SECP256K1_ECDSA_IMPL_H */ diff --git a/src/secp256k1/src/eckey.h b/src/secp256k1/src/eckey.h new file mode 100644 index 0000000000..d54d44c997 --- /dev/null +++ b/src/secp256k1/src/eckey.h @@ -0,0 +1,25 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECKEY_H +#define SECP256K1_ECKEY_H + +#include <stddef.h> + +#include "group.h" +#include "scalar.h" +#include "ecmult.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size); +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed); + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak); + +#endif /* SECP256K1_ECKEY_H */ diff --git a/src/secp256k1/src/eckey_impl.h b/src/secp256k1/src/eckey_impl.h new file mode 100644 index 0000000000..e0506d3e2b --- /dev/null +++ b/src/secp256k1/src/eckey_impl.h @@ -0,0 +1,96 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECKEY_IMPL_H +#define SECP256K1_ECKEY_IMPL_H + +#include "eckey.h" + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) { + if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) { + secp256k1_fe x; + return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD); + } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + secp256k1_fe x, y; + if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) { + return 0; + } + secp256k1_ge_set_xy(elem, &x, &y); + if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) && + secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + return 0; + } + return secp256k1_ge_is_valid_var(elem); + } else { + return 0; + } +} + +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) { + if (secp256k1_ge_is_infinity(elem)) { + return 0; + } + secp256k1_fe_normalize_var(&elem->x); + secp256k1_fe_normalize_var(&elem->y); + secp256k1_fe_get_b32(&pub[1], &elem->x); + if (compressed) { + *size = 33; + pub[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN; + } else { + *size = 65; + pub[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED; + secp256k1_fe_get_b32(&pub[33], &elem->y); + } + return 1; +} + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + secp256k1_scalar_add(key, key, tweak); + return !secp256k1_scalar_is_zero(key); +} + +static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_gej pt; + secp256k1_scalar one; + secp256k1_gej_set_ge(&pt, key); + secp256k1_scalar_set_int(&one, 1); + secp256k1_ecmult(&pt, &pt, &one, tweak); + + if (secp256k1_gej_is_infinity(&pt)) { + return 0; + } + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + int ret; + ret = !secp256k1_scalar_is_zero(tweak); + + secp256k1_scalar_mul(key, key, tweak); + return ret; +} + +static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_scalar zero; + secp256k1_gej pt; + if (secp256k1_scalar_is_zero(tweak)) { + return 0; + } + + secp256k1_scalar_set_int(&zero, 0); + secp256k1_gej_set_ge(&pt, key); + secp256k1_ecmult(&pt, &pt, tweak, &zero); + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +#endif /* SECP256K1_ECKEY_IMPL_H */ diff --git a/src/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h new file mode 100644 index 0000000000..e28c602506 --- /dev/null +++ b/src/secp256k1/src/ecmult.h @@ -0,0 +1,61 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_H +#define SECP256K1_ECMULT_H + +#include "group.h" +#include "scalar.h" +#include "scratch.h" + +#ifndef ECMULT_WINDOW_SIZE +# define ECMULT_WINDOW_SIZE 15 +# ifdef DEBUG_CONFIG +# pragma message DEBUG_CONFIG_MSG("ECMULT_WINDOW_SIZE undefined, assuming default value") +# endif +#endif + +#ifdef DEBUG_CONFIG +# pragma message DEBUG_CONFIG_DEF(ECMULT_WINDOW_SIZE) +#endif + +/* Noone will ever need more than a window size of 24. The code might + * be correct for larger values of ECMULT_WINDOW_SIZE but this is not + * tested. + * + * The following limitations are known, and there are probably more: + * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect + * because the size of the memory object that we allocate (in bytes) + * will not fit in a size_t. + * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect + * because certain expressions will overflow. + */ +#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24 +# error Set ECMULT_WINDOW_SIZE to an integer in range [2..24]. +#endif + +/** The number of entries a table with precomputed multiples needs to have. */ +#define ECMULT_TABLE_SIZE(w) (1L << ((w)-2)) + +/** Double multiply: R = na*A + ng*G */ +static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng); + +typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data); + +/** + * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai. + * Chooses the right algorithm for a given number of points and scratch space + * size. Resets and overwrites the given scratch space. If the points do not + * fit in the scratch space the algorithm is repeatedly run with batches of + * points. If no scratch space is given then a simple algorithm is used that + * simply multiplies the points with the corresponding scalars and adds them up. + * Returns: 1 on success (including when inp_g_sc is NULL and n is 0) + * 0 if there is not enough scratch space for a single point or + * callback returns 0 + */ +static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n); + +#endif /* SECP256K1_ECMULT_H */ diff --git a/src/secp256k1/src/ecmult_compute_table.h b/src/secp256k1/src/ecmult_compute_table.h new file mode 100644 index 0000000000..665f87ff3d --- /dev/null +++ b/src/secp256k1/src/ecmult_compute_table.h @@ -0,0 +1,16 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_H +#define SECP256K1_ECMULT_COMPUTE_TABLE_H + +/* Construct table of all odd multiples of gen in range 1..(2**(window_g-1)-1). */ +static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen); + +/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */ +static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen); + +#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_H */ diff --git a/src/secp256k1/src/ecmult_compute_table_impl.h b/src/secp256k1/src/ecmult_compute_table_impl.h new file mode 100644 index 0000000000..69d59ce595 --- /dev/null +++ b/src/secp256k1/src/ecmult_compute_table_impl.h @@ -0,0 +1,49 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H +#define SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H + +#include "ecmult_compute_table.h" +#include "group_impl.h" +#include "field_impl.h" +#include "ecmult.h" +#include "util.h" + +static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen) { + secp256k1_gej gj; + secp256k1_ge ge, dgen; + int j; + + gj = *gen; + secp256k1_ge_set_gej_var(&ge, &gj); + secp256k1_ge_to_storage(&table[0], &ge); + + secp256k1_gej_double_var(&gj, gen, NULL); + secp256k1_ge_set_gej_var(&dgen, &gj); + + for (j = 1; j < ECMULT_TABLE_SIZE(window_g); ++j) { + secp256k1_gej_set_ge(&gj, &ge); + secp256k1_gej_add_ge_var(&gj, &gj, &dgen, NULL); + secp256k1_ge_set_gej_var(&ge, &gj); + secp256k1_ge_to_storage(&table[j], &ge); + } +} + +/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */ +static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen) { + secp256k1_gej gj; + int i; + + secp256k1_gej_set_ge(&gj, gen); + secp256k1_ecmult_compute_table(table, window_g, &gj); + for (i = 0; i < 128; ++i) { + secp256k1_gej_double_var(&gj, &gj, NULL); + } + secp256k1_ecmult_compute_table(table_128, window_g, &gj); +} + +#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H */ diff --git a/src/secp256k1/src/ecmult_const.h b/src/secp256k1/src/ecmult_const.h new file mode 100644 index 0000000000..417f328535 --- /dev/null +++ b/src/secp256k1/src/ecmult_const.h @@ -0,0 +1,42 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_H +#define SECP256K1_ECMULT_CONST_H + +#include "scalar.h" +#include "group.h" + +/** + * Multiply: R = q*A (in constant-time) + * Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus + * one because we internally sometimes add 2 to the number during the WNAF conversion. + * A must not be infinity. + */ +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits); + +/** + * Same as secp256k1_ecmult_const, but takes in an x coordinate of the base point + * only, specified as fraction n/d (numerator/denominator). Only the x coordinate of the result is + * returned. + * + * If known_on_curve is 0, a verification is performed that n/d is a valid X + * coordinate, and 0 is returned if not. Otherwise, 1 is returned. + * + * d being NULL is interpreted as d=1. If non-NULL, d must not be zero. q must not be zero. + * + * Constant time in the value of q, but not any other inputs. + */ +static int secp256k1_ecmult_const_xonly( + secp256k1_fe *r, + const secp256k1_fe *n, + const secp256k1_fe *d, + const secp256k1_scalar *q, + int bits, + int known_on_curve +); + +#endif /* SECP256K1_ECMULT_CONST_H */ diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h new file mode 100644 index 0000000000..f23e0ec89d --- /dev/null +++ b/src/secp256k1/src/ecmult_const_impl.h @@ -0,0 +1,366 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_IMPL_H +#define SECP256K1_ECMULT_CONST_IMPL_H + +#include "scalar.h" +#include "group.h" +#include "ecmult_const.h" +#include "ecmult_impl.h" + +/** Fill a table 'pre' with precomputed odd multiples of a. + * + * The resulting point set is brought to a single constant Z denominator, stores the X and Y + * coordinates as ge_storage points in pre, and stores the global Z in globalz. + * It only operates on tables sized for WINDOW_A wnaf multiples. + */ +static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) { + secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; + + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr, globalz, a); + secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A), pre, zr); +} + +/* This is like `ECMULT_TABLE_GET_GE` but is constant time */ +#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \ + int m = 0; \ + /* Extract the sign-bit for a constant time absolute-value. */ \ + int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \ + int abs_n = ((n) + mask) ^ mask; \ + int idx_n = abs_n >> 1; \ + secp256k1_fe neg_y; \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \ + /* Unconditionally set r->x = (pre)[m].x. r->y = (pre)[m].y. because it's either the correct one \ + * or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \ + (r)->x = (pre)[m].x; \ + (r)->y = (pre)[m].y; \ + for (m = 1; m < ECMULT_TABLE_SIZE(w); m++) { \ + /* This loop is used to avoid secret data in array indices. See + * the comment in ecmult_gen_impl.h for rationale. */ \ + secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \ + secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \ + } \ + (r)->infinity = 0; \ + secp256k1_fe_negate(&neg_y, &(r)->y, 1); \ + secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \ +} while(0) + +/** Convert a number to WNAF notation. + * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. + * It has the following guarantees: + * - each wnaf[i] an odd integer between -(1 << w) and (1 << w) + * - each wnaf[i] is nonzero + * - the number of words set is always WNAF_SIZE(w) + 1 + * + * Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar + * Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.) + * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlag Berlin Heidelberg 2003 + * + * Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335 + */ +static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) { + int global_sign; + int skew; + int word = 0; + + /* 1 2 3 */ + int u_last; + int u; + + int flip; + secp256k1_scalar s = *scalar; + + VERIFY_CHECK(w > 0); + VERIFY_CHECK(size > 0); + + /* Note that we cannot handle even numbers by negating them to be odd, as is + * done in other implementations, since if our scalars were specified to have + * width < 256 for performance reasons, their negations would have width 256 + * and we'd lose any performance benefit. Instead, we use a variation of a + * technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the + * number we are encoding when it is even, returning a skew value indicating + * this, and having the caller compensate after doing the multiplication. + * + * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in + * particular, to ensure that the outputs from the endomorphism-split fit into + * 128 bits). If we negate, the parity of our number flips, affecting whether + * we want to add to the scalar to ensure that it's odd. */ + flip = secp256k1_scalar_is_high(&s); + skew = flip ^ secp256k1_scalar_is_even(&s); + secp256k1_scalar_cadd_bit(&s, 0, skew); + global_sign = secp256k1_scalar_cond_negate(&s, flip); + + /* 4 */ + u_last = secp256k1_scalar_shr_int(&s, w); + do { + int even; + + /* 4.1 4.4 */ + u = secp256k1_scalar_shr_int(&s, w); + /* 4.2 */ + even = ((u & 1) == 0); + /* In contrast to the original algorithm, u_last is always > 0 and + * therefore we do not need to check its sign. In particular, it's easy + * to see that u_last is never < 0 because u is never < 0. Moreover, + * u_last is never = 0 because u is never even after a loop + * iteration. The same holds analogously for the initial value of + * u_last (in the first loop iteration). */ + VERIFY_CHECK(u_last > 0); + VERIFY_CHECK((u_last & 1) == 1); + u += even; + u_last -= even * (1 << w); + + /* 4.3, adapted for global sign change */ + wnaf[word++] = u_last * global_sign; + + u_last = u; + } while (word * w < size); + wnaf[word] = u * global_sign; + + VERIFY_CHECK(secp256k1_scalar_is_zero(&s)); + VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w)); + return skew; +} + +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) { + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge tmpa; + secp256k1_fe Z; + + int skew_1; + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)]; + int skew_lam; + secp256k1_scalar q_1, q_lam; + int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)]; + + int i; + + /* build wnaf representation for q. */ + int rsize = size; + if (size > 128) { + rsize = 128; + /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar); + skew_1 = secp256k1_wnaf_const(wnaf_1, &q_1, WINDOW_A - 1, 128); + skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128); + } else + { + skew_1 = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size); + skew_lam = 0; + } + + /* Calculate odd multiples of a. + * All multiples are brought to the same Z 'denominator', which is stored + * in Z. Due to secp256k1' isomorphism we can do all operations pretending + * that the Z coordinate was 1, use affine addition formulae, and correct + * the Z coordinate of the result once at the end. + */ + VERIFY_CHECK(!a->infinity); + secp256k1_gej_set_ge(r, a); + secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r); + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_fe_normalize_weak(&pre_a[i].y); + } + if (size > 128) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); + } + + } + + /* first loop iteration (separated out so we can directly set r, rather + * than having it start at infinity, get doubled several times, then have + * its new value added to it) */ + i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); + if (size > 128) { + i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A); + secp256k1_gej_add_ge(r, r, &tmpa); + } + /* remaining loop iterations */ + for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) { + int n; + int j; + for (j = 0; j < WINDOW_A - 1; ++j) { + secp256k1_gej_double(r, r); + } + + n = wnaf_1[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); + if (size > 128) { + n = wnaf_lam[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); + } + } + + { + /* Correct for wNAF skew */ + secp256k1_gej tmpj; + + secp256k1_ge_neg(&tmpa, &pre_a[0]); + secp256k1_gej_add_ge(&tmpj, r, &tmpa); + secp256k1_gej_cmov(r, &tmpj, skew_1); + + if (size > 128) { + secp256k1_ge_neg(&tmpa, &pre_a_lam[0]); + secp256k1_gej_add_ge(&tmpj, r, &tmpa); + secp256k1_gej_cmov(r, &tmpj, skew_lam); + } + } + + secp256k1_fe_mul(&r->z, &r->z, &Z); +} + +static int secp256k1_ecmult_const_xonly(secp256k1_fe* r, const secp256k1_fe *n, const secp256k1_fe *d, const secp256k1_scalar *q, int bits, int known_on_curve) { + + /* This algorithm is a generalization of Peter Dettman's technique for + * avoiding the square root in a random-basepoint x-only multiplication + * on a Weierstrass curve: + * https://mailarchive.ietf.org/arch/msg/cfrg/7DyYY6gg32wDgHAhgSb6XxMDlJA/ + * + * + * === Background: the effective affine technique === + * + * Let phi_u be the isomorphism that maps (x, y) on secp256k1 curve y^2 = x^3 + 7 to + * x' = u^2*x, y' = u^3*y on curve y'^2 = x'^3 + u^6*7. This new curve has the same order as + * the original (it is isomorphic), but moreover, has the same addition/doubling formulas, as + * the curve b=7 coefficient does not appear in those formulas (or at least does not appear in + * the formulas implemented in this codebase, both affine and Jacobian). See also Example 9.5.2 + * in https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch9.pdf. + * + * This means any linear combination of secp256k1 points can be computed by applying phi_u + * (with non-zero u) on all input points (including the generator, if used), computing the + * linear combination on the isomorphic curve (using the same group laws), and then applying + * phi_u^{-1} to get back to secp256k1. + * + * Switching to Jacobian coordinates, note that phi_u applied to (X, Y, Z) is simply + * (X, Y, Z/u). Thus, if we want to compute (X1, Y1, Z) + (X2, Y2, Z), with identical Z + * coordinates, we can use phi_Z to transform it to (X1, Y1, 1) + (X2, Y2, 1) on an isomorphic + * curve where the affine addition formula can be used instead. + * If (X3, Y3, Z3) = (X1, Y1) + (X2, Y2) on that curve, then our answer on secp256k1 is + * (X3, Y3, Z3*Z). + * + * This is the effective affine technique: if we have a linear combination of group elements + * to compute, and all those group elements have the same Z coordinate, we can simply pretend + * that all those Z coordinates are 1, perform the computation that way, and then multiply the + * original Z coordinate back in. + * + * The technique works on any a=0 short Weierstrass curve. It is possible to generalize it to + * other curves too, but there the isomorphic curves will have different 'a' coefficients, + * which typically does affect the group laws. + * + * + * === Avoiding the square root for x-only point multiplication === + * + * In this function, we want to compute the X coordinate of q*(n/d, y), for + * y = sqrt((n/d)^3 + 7). Its negation would also be a valid Y coordinate, but by convention + * we pick whatever sqrt returns (which we assume to be a deterministic function). + * + * Let g = y^2*d^3 = n^3 + 7*d^3. This also means y = sqrt(g/d^3). + * Further let v = sqrt(d*g), which must exist as d*g = y^2*d^4 = (y*d^2)^2. + * + * The input point (n/d, y) also has Jacobian coordinates: + * + * (n/d, y, 1) + * = (n/d * v^2, y * v^3, v) + * = (n/d * d*g, y * sqrt(d^3*g^3), v) + * = (n/d * d*g, sqrt(y^2 * d^3*g^3), v) + * = (n*g, sqrt(g/d^3 * d^3*g^3), v) + * = (n*g, sqrt(g^4), v) + * = (n*g, g^2, v) + * + * It is easy to verify that both (n*g, g^2, v) and its negation (n*g, -g^2, v) have affine X + * coordinate n/d, and this holds even when the square root function doesn't have a + * determinstic sign. We choose the (n*g, g^2, v) version. + * + * Now switch to the effective affine curve using phi_v, where the input point has coordinates + * (n*g, g^2). Compute (X, Y, Z) = q * (n*g, g^2) there. + * + * Back on secp256k1, that means q * (n*g, g^2, v) = (X, Y, v*Z). This last point has affine X + * coordinate X / (v^2*Z^2) = X / (d*g*Z^2). Determining the affine Y coordinate would involve + * a square root, but as long as we only care about the resulting X coordinate, no square root + * is needed anywhere in this computation. + */ + + secp256k1_fe g, i; + secp256k1_ge p; + secp256k1_gej rj; + + /* Compute g = (n^3 + B*d^3). */ + secp256k1_fe_sqr(&g, n); + secp256k1_fe_mul(&g, &g, n); + if (d) { + secp256k1_fe b; +#ifdef VERIFY + VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero(d)); +#endif + secp256k1_fe_sqr(&b, d); + VERIFY_CHECK(SECP256K1_B <= 8); /* magnitude of b will be <= 8 after the next call */ + secp256k1_fe_mul_int(&b, SECP256K1_B); + secp256k1_fe_mul(&b, &b, d); + secp256k1_fe_add(&g, &b); + if (!known_on_curve) { + /* We need to determine whether (n/d)^3 + 7 is square. + * + * is_square((n/d)^3 + 7) + * <=> is_square(((n/d)^3 + 7) * d^4) + * <=> is_square((n^3 + 7*d^3) * d) + * <=> is_square(g * d) + */ + secp256k1_fe c; + secp256k1_fe_mul(&c, &g, d); + if (!secp256k1_fe_is_square_var(&c)) return 0; + } + } else { + secp256k1_fe_add_int(&g, SECP256K1_B); + if (!known_on_curve) { + /* g at this point equals x^3 + 7. Test if it is square. */ + if (!secp256k1_fe_is_square_var(&g)) return 0; + } + } + + /* Compute base point P = (n*g, g^2), the effective affine version of (n*g, g^2, v), which has + * corresponding affine X coordinate n/d. */ + secp256k1_fe_mul(&p.x, &g, n); + secp256k1_fe_sqr(&p.y, &g); + p.infinity = 0; + + /* Perform x-only EC multiplication of P with q. */ +#ifdef VERIFY + VERIFY_CHECK(!secp256k1_scalar_is_zero(q)); +#endif + secp256k1_ecmult_const(&rj, &p, q, bits); +#ifdef VERIFY + VERIFY_CHECK(!secp256k1_gej_is_infinity(&rj)); +#endif + + /* The resulting (X, Y, Z) point on the effective-affine isomorphic curve corresponds to + * (X, Y, Z*v) on the secp256k1 curve. The affine version of that has X coordinate + * (X / (Z^2*d*g)). */ + secp256k1_fe_sqr(&i, &rj.z); + secp256k1_fe_mul(&i, &i, &g); + if (d) secp256k1_fe_mul(&i, &i, d); + secp256k1_fe_inv(&i, &i); + secp256k1_fe_mul(r, &rj.x, &i); + + return 1; +} + +#endif /* SECP256K1_ECMULT_CONST_IMPL_H */ diff --git a/src/secp256k1/src/ecmult_gen.h b/src/secp256k1/src/ecmult_gen.h new file mode 100644 index 0000000000..a430e8d5d9 --- /dev/null +++ b/src/secp256k1/src/ecmult_gen.h @@ -0,0 +1,48 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_H +#define SECP256K1_ECMULT_GEN_H + +#include "scalar.h" +#include "group.h" + +#ifndef ECMULT_GEN_PREC_BITS +# define ECMULT_GEN_PREC_BITS 4 +# ifdef DEBUG_CONFIG +# pragma message DEBUG_CONFIG_MSG("ECMULT_GEN_PREC_BITS undefined, assuming default value") +# endif +#endif + +#ifdef DEBUG_CONFIG +# pragma message DEBUG_CONFIG_DEF(ECMULT_GEN_PREC_BITS) +#endif + +#if ECMULT_GEN_PREC_BITS != 2 && ECMULT_GEN_PREC_BITS != 4 && ECMULT_GEN_PREC_BITS != 8 +# error "Set ECMULT_GEN_PREC_BITS to 2, 4 or 8." +#endif + +#define ECMULT_GEN_PREC_G(bits) (1 << bits) +#define ECMULT_GEN_PREC_N(bits) (256 / bits) + +typedef struct { + /* Whether the context has been built. */ + int built; + + /* Blinding values used when computing (n-b)G + bG. */ + secp256k1_scalar blind; /* -b */ + secp256k1_gej initial; /* bG */ +} secp256k1_ecmult_gen_context; + +static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx); +static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx); + +/** Multiply with the generator: R = a*G */ +static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a); + +static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32); + +#endif /* SECP256K1_ECMULT_GEN_H */ diff --git a/src/secp256k1/src/ecmult_gen_compute_table.h b/src/secp256k1/src/ecmult_gen_compute_table.h new file mode 100644 index 0000000000..e577158d92 --- /dev/null +++ b/src/secp256k1/src/ecmult_gen_compute_table.h @@ -0,0 +1,14 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H +#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H + +#include "ecmult_gen.h" + +static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits); + +#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H */ diff --git a/src/secp256k1/src/ecmult_gen_compute_table_impl.h b/src/secp256k1/src/ecmult_gen_compute_table_impl.h new file mode 100644 index 0000000000..ff6a2992dc --- /dev/null +++ b/src/secp256k1/src/ecmult_gen_compute_table_impl.h @@ -0,0 +1,81 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H +#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H + +#include "ecmult_gen_compute_table.h" +#include "group_impl.h" +#include "field_impl.h" +#include "ecmult_gen.h" +#include "util.h" + +static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits) { + int g = ECMULT_GEN_PREC_G(bits); + int n = ECMULT_GEN_PREC_N(bits); + + secp256k1_ge* prec = checked_malloc(&default_error_callback, n * g * sizeof(*prec)); + secp256k1_gej gj; + secp256k1_gej nums_gej; + int i, j; + + /* get the generator */ + secp256k1_gej_set_ge(&gj, gen); + + /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */ + { + static const unsigned char nums_b32[33] = "The scalar for this x is unknown"; + secp256k1_fe nums_x; + secp256k1_ge nums_ge; + int r; + r = secp256k1_fe_set_b32(&nums_x, nums_b32); + (void)r; + VERIFY_CHECK(r); + r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0); + (void)r; + VERIFY_CHECK(r); + secp256k1_gej_set_ge(&nums_gej, &nums_ge); + /* Add G to make the bits in x uniformly distributed. */ + secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, gen, NULL); + } + + /* compute prec. */ + { + secp256k1_gej gbase; + secp256k1_gej numsbase; + secp256k1_gej* precj = checked_malloc(&default_error_callback, n * g * sizeof(*precj)); /* Jacobian versions of prec. */ + gbase = gj; /* PREC_G^j * G */ + numsbase = nums_gej; /* 2^j * nums. */ + for (j = 0; j < n; j++) { + /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */ + precj[j*g] = numsbase; + for (i = 1; i < g; i++) { + secp256k1_gej_add_var(&precj[j*g + i], &precj[j*g + i - 1], &gbase, NULL); + } + /* Multiply gbase by PREC_G. */ + for (i = 0; i < bits; i++) { + secp256k1_gej_double_var(&gbase, &gbase, NULL); + } + /* Multiply numbase by 2. */ + secp256k1_gej_double_var(&numsbase, &numsbase, NULL); + if (j == n - 2) { + /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */ + secp256k1_gej_neg(&numsbase, &numsbase); + secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL); + } + } + secp256k1_ge_set_all_gej_var(prec, precj, n * g); + free(precj); + } + for (j = 0; j < n; j++) { + for (i = 0; i < g; i++) { + secp256k1_ge_to_storage(&table[j*g + i], &prec[j*g + i]); + } + } + free(prec); +} + +#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H */ diff --git a/src/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h new file mode 100644 index 0000000000..4f5ea9f3c0 --- /dev/null +++ b/src/secp256k1/src/ecmult_gen_impl.h @@ -0,0 +1,133 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_IMPL_H +#define SECP256K1_ECMULT_GEN_IMPL_H + +#include "util.h" +#include "scalar.h" +#include "group.h" +#include "ecmult_gen.h" +#include "hash_impl.h" +#include "precomputed_ecmult_gen.h" + +static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx) { + secp256k1_ecmult_gen_blind(ctx, NULL); + ctx->built = 1; +} + +static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) { + return ctx->built; +} + +static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) { + ctx->built = 0; + secp256k1_scalar_clear(&ctx->blind); + secp256k1_gej_clear(&ctx->initial); +} + +/* For accelerating the computation of a*G: + * To harden against timing attacks, use the following mechanism: + * * Break up the multiplicand into groups of PREC_BITS bits, called n_0, n_1, n_2, ..., n_(PREC_N-1). + * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where: + * * U_i = U * 2^i, for i=0 ... PREC_N-2 + * * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1 + * where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0. + * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is + * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1). + * None of the resulting prec group elements have a known scalar, and neither do any of + * the intermediate sums while computing a*G. + * The prec values are stored in secp256k1_ecmult_gen_prec_table[i][n_i] = n_i * (PREC_G)^i * G + U_i. + */ +static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) { + int bits = ECMULT_GEN_PREC_BITS; + int g = ECMULT_GEN_PREC_G(bits); + int n = ECMULT_GEN_PREC_N(bits); + + secp256k1_ge add; + secp256k1_ge_storage adds; + secp256k1_scalar gnb; + int i, j, n_i; + + memset(&adds, 0, sizeof(adds)); + *r = ctx->initial; + /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */ + secp256k1_scalar_add(&gnb, gn, &ctx->blind); + add.infinity = 0; + for (i = 0; i < n; i++) { + n_i = secp256k1_scalar_get_bits(&gnb, i * bits, bits); + for (j = 0; j < g; j++) { + /** This uses a conditional move to avoid any secret data in array indexes. + * _Any_ use of secret indexes has been demonstrated to result in timing + * sidechannels, even when the cache-line access patterns are uniform. + * See also: + * "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe + * (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and + * "Cache Attacks and Countermeasures: the Case of AES", RSA 2006, + * by Dag Arne Osvik, Adi Shamir, and Eran Tromer + * (https://www.tau.ac.il/~tromer/papers/cache.pdf) + */ + secp256k1_ge_storage_cmov(&adds, &secp256k1_ecmult_gen_prec_table[i][j], j == n_i); + } + secp256k1_ge_from_storage(&add, &adds); + secp256k1_gej_add_ge(r, r, &add); + } + n_i = 0; + secp256k1_ge_clear(&add); + secp256k1_scalar_clear(&gnb); +} + +/* Setup blinding values for secp256k1_ecmult_gen. */ +static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) { + secp256k1_scalar b; + secp256k1_gej gb; + secp256k1_fe s; + unsigned char nonce32[32]; + secp256k1_rfc6979_hmac_sha256 rng; + int overflow; + unsigned char keydata[64]; + if (seed32 == NULL) { + /* When seed is NULL, reset the initial point and blinding value. */ + secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g); + secp256k1_gej_neg(&ctx->initial, &ctx->initial); + secp256k1_scalar_set_int(&ctx->blind, 1); + return; + } + /* The prior blinding value (if not reset) is chained forward by including it in the hash. */ + secp256k1_scalar_get_b32(keydata, &ctx->blind); + /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data, + * and guards against weak or adversarial seeds. This is a simpler and safer interface than + * asking the caller for blinding values directly and expecting them to retry on failure. + */ + VERIFY_CHECK(seed32 != NULL); + memcpy(keydata + 32, seed32, 32); + secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, 64); + memset(keydata, 0, sizeof(keydata)); + /* Accept unobservably small non-uniformity. */ + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + overflow = !secp256k1_fe_set_b32(&s, nonce32); + overflow |= secp256k1_fe_is_zero(&s); + secp256k1_fe_cmov(&s, &secp256k1_fe_one, overflow); + /* Randomize the projection to defend against multiplier sidechannels. + Do this before our own call to secp256k1_ecmult_gen below. */ + secp256k1_gej_rescale(&ctx->initial, &s); + secp256k1_fe_clear(&s); + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + secp256k1_scalar_set_b32(&b, nonce32, NULL); + /* A blinding value of 0 works, but would undermine the projection hardening. */ + secp256k1_scalar_cmov(&b, &secp256k1_scalar_one, secp256k1_scalar_is_zero(&b)); + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + memset(nonce32, 0, 32); + /* The random projection in ctx->initial ensures that gb will have a random projection. */ + secp256k1_ecmult_gen(ctx, &gb, &b); + secp256k1_scalar_negate(&b, &b); + ctx->blind = b; + ctx->initial = gb; + secp256k1_scalar_clear(&b); + secp256k1_gej_clear(&gb); +} + +#endif /* SECP256K1_ECMULT_GEN_IMPL_H */ diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h new file mode 100644 index 0000000000..a9a63850ef --- /dev/null +++ b/src/secp256k1/src/ecmult_impl.h @@ -0,0 +1,868 @@ +/****************************************************************************** + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + ******************************************************************************/ + +#ifndef SECP256K1_ECMULT_IMPL_H +#define SECP256K1_ECMULT_IMPL_H + +#include <string.h> +#include <stdint.h> + +#include "util.h" +#include "group.h" +#include "scalar.h" +#include "ecmult.h" +#include "precomputed_ecmult.h" + +#if defined(EXHAUSTIVE_TEST_ORDER) +/* We need to lower these values for exhaustive tests because + * the tables cannot have infinities in them (this breaks the + * affine-isomorphism stuff which tracks z-ratios) */ +# if EXHAUSTIVE_TEST_ORDER > 128 +# define WINDOW_A 5 +# elif EXHAUSTIVE_TEST_ORDER > 8 +# define WINDOW_A 4 +# else +# define WINDOW_A 2 +# endif +#else +/* optimal for 128-bit and 256-bit exponents. */ +# define WINDOW_A 5 +/** Larger values for ECMULT_WINDOW_SIZE result in possibly better + * performance at the cost of an exponentially larger precomputed + * table. The exact table size is + * (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage) bytes, + * where sizeof(secp256k1_ge_storage) is typically 64 bytes but can + * be larger due to platform-specific padding and alignment. + * Two tables of this size are used (due to the endomorphism + * optimization). + */ +#endif + +#define WNAF_BITS 128 +#define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w)) +#define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w) + +/* The number of objects allocated on the scratch space for ecmult_multi algorithms */ +#define PIPPENGER_SCRATCH_OBJECTS 6 +#define STRAUSS_SCRATCH_OBJECTS 5 + +#define PIPPENGER_MAX_BUCKET_WINDOW 12 + +/* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */ +#define ECMULT_PIPPENGER_THRESHOLD 88 + +#define ECMULT_MAX_POINTS_PER_BATCH 5000000 + +/** Fill a table 'pre_a' with precomputed odd multiples of a. + * pre_a will contain [1*a,3*a,...,(2*n-1)*a], so it needs space for n group elements. + * zr needs space for n field elements. + * + * Although pre_a is an array of _ge rather than _gej, it actually represents elements + * in Jacobian coordinates with their z coordinates omitted. The omitted z-coordinates + * can be recovered using z and zr. Using the notation z(b) to represent the omitted + * z coordinate of b: + * - z(pre_a[n-1]) = 'z' + * - z(pre_a[i-1]) = z(pre_a[i]) / zr[i] for n > i > 0 + * + * Lastly the zr[0] value, which isn't used above, is set so that: + * - a.z = z(pre_a[0]) / zr[0] + */ +static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a) { + secp256k1_gej d, ai; + secp256k1_ge d_ge; + int i; + + VERIFY_CHECK(!a->infinity); + + secp256k1_gej_double_var(&d, a, NULL); + + /* + * Perform the additions using an isomorphic curve Y^2 = X^3 + 7*C^6 where C := d.z. + * The isomorphism, phi, maps a secp256k1 point (x, y) to the point (x*C^2, y*C^3) on the other curve. + * In Jacobian coordinates phi maps (x, y, z) to (x*C^2, y*C^3, z) or, equivalently to (x, y, z/C). + * + * phi(x, y, z) = (x*C^2, y*C^3, z) = (x, y, z/C) + * d_ge := phi(d) = (d.x, d.y, 1) + * ai := phi(a) = (a.x*C^2, a.y*C^3, a.z) + * + * The group addition functions work correctly on these isomorphic curves. + * In particular phi(d) is easy to represent in affine coordinates under this isomorphism. + * This lets us use the faster secp256k1_gej_add_ge_var group addition function that we wouldn't be able to use otherwise. + */ + secp256k1_ge_set_xy(&d_ge, &d.x, &d.y); + secp256k1_ge_set_gej_zinv(&pre_a[0], a, &d.z); + secp256k1_gej_set_ge(&ai, &pre_a[0]); + ai.z = a->z; + + /* pre_a[0] is the point (a.x*C^2, a.y*C^3, a.z*C) which is equivalent to a. + * Set zr[0] to C, which is the ratio between the omitted z(pre_a[0]) value and a.z. + */ + zr[0] = d.z; + + for (i = 1; i < n; i++) { + secp256k1_gej_add_ge_var(&ai, &ai, &d_ge, &zr[i]); + secp256k1_ge_set_xy(&pre_a[i], &ai.x, &ai.y); + } + + /* Multiply the last z-coordinate by C to undo the isomorphism. + * Since the z-coordinates of the pre_a values are implied by the zr array of z-coordinate ratios, + * undoing the isomorphism here undoes the isomorphism for all pre_a values. + */ + secp256k1_fe_mul(z, &ai.z, &d.z); +} + +SECP256K1_INLINE static void secp256k1_ecmult_table_verify(int n, int w) { + (void)n; + (void)w; + VERIFY_CHECK(((n) & 1) == 1); + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); +} + +SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge(secp256k1_ge *r, const secp256k1_ge *pre, int n, int w) { + secp256k1_ecmult_table_verify(n,w); + if (n > 0) { + *r = pre[(n-1)/2]; + } else { + *r = pre[(-n-1)/2]; + secp256k1_fe_negate(&(r->y), &(r->y), 1); + } +} + +SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_lambda(secp256k1_ge *r, const secp256k1_ge *pre, const secp256k1_fe *x, int n, int w) { + secp256k1_ecmult_table_verify(n,w); + if (n > 0) { + secp256k1_ge_set_xy(r, &x[(n-1)/2], &pre[(n-1)/2].y); + } else { + secp256k1_ge_set_xy(r, &x[(-n-1)/2], &pre[(-n-1)/2].y); + secp256k1_fe_negate(&(r->y), &(r->y), 1); + } +} + +SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_storage(secp256k1_ge *r, const secp256k1_ge_storage *pre, int n, int w) { + secp256k1_ecmult_table_verify(n,w); + if (n > 0) { + secp256k1_ge_from_storage(r, &pre[(n-1)/2]); + } else { + secp256k1_ge_from_storage(r, &pre[(-n-1)/2]); + secp256k1_fe_negate(&(r->y), &(r->y), 1); + } +} + +/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), + * with the following guarantees: + * - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1) + * - two non-zero entries in wnaf are separated by at least w-1 zeroes. + * - the number of set values in wnaf is returned. This number is at most 256, and at most one more + * than the number of bits in the (absolute value) of the input. + */ +static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) { + secp256k1_scalar s; + int last_set_bit = -1; + int bit = 0; + int sign = 1; + int carry = 0; + + VERIFY_CHECK(wnaf != NULL); + VERIFY_CHECK(0 <= len && len <= 256); + VERIFY_CHECK(a != NULL); + VERIFY_CHECK(2 <= w && w <= 31); + + memset(wnaf, 0, len * sizeof(wnaf[0])); + + s = *a; + if (secp256k1_scalar_get_bits(&s, 255, 1)) { + secp256k1_scalar_negate(&s, &s); + sign = -1; + } + + while (bit < len) { + int now; + int word; + if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) { + bit++; + continue; + } + + now = w; + if (now > len - bit) { + now = len - bit; + } + + word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry; + + carry = (word >> (w-1)) & 1; + word -= carry << w; + + wnaf[bit] = sign * word; + last_set_bit = bit; + + bit += now; + } +#ifdef VERIFY + { + int verify_bit = bit; + + VERIFY_CHECK(carry == 0); + + while (verify_bit < 256) { + VERIFY_CHECK(secp256k1_scalar_get_bits(&s, verify_bit, 1) == 0); + verify_bit++; + } + } +#endif + return last_set_bit + 1; +} + +struct secp256k1_strauss_point_state { + int wnaf_na_1[129]; + int wnaf_na_lam[129]; + int bits_na_1; + int bits_na_lam; +}; + +struct secp256k1_strauss_state { + /* aux is used to hold z-ratios, and then used to hold pre_a[i].x * BETA values. */ + secp256k1_fe* aux; + secp256k1_ge* pre_a; + struct secp256k1_strauss_point_state* ps; +}; + +static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { + secp256k1_ge tmpa; + secp256k1_fe Z; + /* Split G factors. */ + secp256k1_scalar ng_1, ng_128; + int wnaf_ng_1[129]; + int bits_ng_1 = 0; + int wnaf_ng_128[129]; + int bits_ng_128 = 0; + int i; + int bits = 0; + size_t np; + size_t no = 0; + + secp256k1_fe_set_int(&Z, 1); + for (np = 0; np < num; ++np) { + secp256k1_gej tmp; + secp256k1_scalar na_1, na_lam; + if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) { + continue; + } + /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&na_1, &na_lam, &na[np]); + + /* build wnaf representation for na_1 and na_lam. */ + state->ps[no].bits_na_1 = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1, 129, &na_1, WINDOW_A); + state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &na_lam, WINDOW_A); + VERIFY_CHECK(state->ps[no].bits_na_1 <= 129); + VERIFY_CHECK(state->ps[no].bits_na_lam <= 129); + if (state->ps[no].bits_na_1 > bits) { + bits = state->ps[no].bits_na_1; + } + if (state->ps[no].bits_na_lam > bits) { + bits = state->ps[no].bits_na_lam; + } + + /* Calculate odd multiples of a. + * All multiples are brought to the same Z 'denominator', which is stored + * in Z. Due to secp256k1' isomorphism we can do all operations pretending + * that the Z coordinate was 1, use affine addition formulae, and correct + * the Z coordinate of the result once at the end. + * The exception is the precomputed G table points, which are actually + * affine. Compared to the base used for other points, they have a Z ratio + * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same + * isomorphism to efficiently add with a known Z inverse. + */ + tmp = a[np]; + if (no) { +#ifdef VERIFY + secp256k1_fe_normalize_var(&Z); +#endif + secp256k1_gej_rescale(&tmp, &Z); + } + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp); + if (no) secp256k1_fe_mul(state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &(a[np].z)); + + ++no; + } + + /* Bring them to the same Z denominator. */ + secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, state->aux); + + for (np = 0; np < no; ++np) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_fe_mul(&state->aux[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i].x, &secp256k1_const_beta); + } + } + + if (ng) { + /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */ + secp256k1_scalar_split_128(&ng_1, &ng_128, ng); + + /* Build wnaf representation for ng_1 and ng_128 */ + bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G); + bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G); + if (bits_ng_1 > bits) { + bits = bits_ng_1; + } + if (bits_ng_128 > bits) { + bits = bits_ng_128; + } + } + + secp256k1_gej_set_infinity(r); + + for (i = bits - 1; i >= 0; i--) { + int n; + secp256k1_gej_double_var(r, r, NULL); + for (np = 0; np < no; ++np) { + if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) { + secp256k1_ecmult_table_get_ge(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) { + secp256k1_ecmult_table_get_ge_lambda(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + } + if (i < bits_ng_1 && (n = wnaf_ng_1[i])) { + secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g, n, WINDOW_G); + secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); + } + if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { + secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g_128, n, WINDOW_G); + secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); + } + } + + if (!r->infinity) { + secp256k1_fe_mul(&r->z, &r->z, &Z); + } +} + +static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { + secp256k1_fe aux[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + struct secp256k1_strauss_point_state ps[1]; + struct secp256k1_strauss_state state; + + state.aux = aux; + state.pre_a = pre_a; + state.ps = ps; + secp256k1_ecmult_strauss_wnaf(&state, r, 1, a, na, ng); +} + +static size_t secp256k1_strauss_scratch_size(size_t n_points) { + static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); + return n_points*point_size; +} + +static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { + secp256k1_gej* points; + secp256k1_scalar* scalars; + struct secp256k1_strauss_state state; + size_t i; + const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); + + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n_points == 0) { + return 1; + } + + /* We allocate STRAUSS_SCRATCH_OBJECTS objects on the scratch space. If these + * allocations change, make sure to update the STRAUSS_SCRATCH_OBJECTS + * constant and strauss_scratch_size accordingly. */ + points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej)); + scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar)); + state.aux = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe)); + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); + state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state)); + + if (points == NULL || scalars == NULL || state.aux == NULL || state.pre_a == NULL || state.ps == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + + for (i = 0; i < n_points; i++) { + secp256k1_ge point; + if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + secp256k1_gej_set_ge(&points[i], &point); + } + secp256k1_ecmult_strauss_wnaf(&state, r, n_points, points, scalars, inp_g_sc); + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 1; +} + +/* Wrapper for secp256k1_ecmult_multi_func interface */ +static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + return secp256k1_ecmult_strauss_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0); +} + +static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) { + return secp256k1_scratch_max_allocation(error_callback, scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1); +} + +/** Convert a number to WNAF notation. + * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. + * It has the following guarantees: + * - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w) + * - the number of words set is always WNAF_SIZE(w) + * - the returned skew is 0 or 1 + */ +static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) { + int skew = 0; + int pos; + int max_pos; + int last_w; + const secp256k1_scalar *work = s; + + if (secp256k1_scalar_is_zero(s)) { + for (pos = 0; pos < WNAF_SIZE(w); pos++) { + wnaf[pos] = 0; + } + return 0; + } + + if (secp256k1_scalar_is_even(s)) { + skew = 1; + } + + wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew; + /* Compute last window size. Relevant when window size doesn't divide the + * number of bits in the scalar */ + last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w; + + /* Store the position of the first nonzero word in max_pos to allow + * skipping leading zeros when calculating the wnaf. */ + for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) { + int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); + if(val != 0) { + break; + } + wnaf[pos] = 0; + } + max_pos = pos; + pos = 1; + + while (pos <= max_pos) { + int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); + if ((val & 1) == 0) { + wnaf[pos - 1] -= (1 << w); + wnaf[pos] = (val + 1); + } else { + wnaf[pos] = val; + } + /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit + * is strictly negative or strictly positive respectively. Only change + * coefficients at previous positions because above code assumes that + * wnaf[pos - 1] is odd. + */ + if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) { + if (wnaf[pos - 1] == 1) { + wnaf[pos - 2] += 1 << w; + } else { + wnaf[pos - 2] -= 1 << w; + } + wnaf[pos - 1] = 0; + } + ++pos; + } + + return skew; +} + +struct secp256k1_pippenger_point_state { + int skew_na; + size_t input_pos; +}; + +struct secp256k1_pippenger_state { + int *wnaf_na; + struct secp256k1_pippenger_point_state* ps; +}; + +/* + * pippenger_wnaf computes the result of a multi-point multiplication as + * follows: The scalars are brought into wnaf with n_wnaf elements each. Then + * for every i < n_wnaf, first each point is added to a "bucket" corresponding + * to the point's wnaf[i]. Second, the buckets are added together such that + * r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ... + */ +static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) { + size_t n_wnaf = WNAF_SIZE(bucket_window+1); + size_t np; + size_t no = 0; + int i; + int j; + + for (np = 0; np < num; ++np) { + if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) { + continue; + } + state->ps[no].input_pos = np; + state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1); + no++; + } + secp256k1_gej_set_infinity(r); + + if (no == 0) { + return 1; + } + + for (i = n_wnaf - 1; i >= 0; i--) { + secp256k1_gej running_sum; + + for(j = 0; j < ECMULT_TABLE_SIZE(bucket_window+2); j++) { + secp256k1_gej_set_infinity(&buckets[j]); + } + + for (np = 0; np < no; ++np) { + int n = state->wnaf_na[np*n_wnaf + i]; + struct secp256k1_pippenger_point_state point_state = state->ps[np]; + secp256k1_ge tmp; + int idx; + + if (i == 0) { + /* correct for wnaf skew */ + int skew = point_state.skew_na; + if (skew) { + secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); + secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL); + } + } + if (n > 0) { + idx = (n - 1)/2; + secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL); + } else if (n < 0) { + idx = -(n + 1)/2; + secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); + secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &tmp, NULL); + } + } + + for(j = 0; j < bucket_window; j++) { + secp256k1_gej_double_var(r, r, NULL); + } + + secp256k1_gej_set_infinity(&running_sum); + /* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ... + * = bucket[0] + bucket[1] + bucket[2] + bucket[3] + ... + * + 2 * (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...) + * using an intermediate running sum: + * running_sum = bucket[0] + bucket[1] + bucket[2] + ... + * + * The doubling is done implicitly by deferring the final window doubling (of 'r'). + */ + for(j = ECMULT_TABLE_SIZE(bucket_window+2) - 1; j > 0; j--) { + secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[j], NULL); + secp256k1_gej_add_var(r, r, &running_sum, NULL); + } + + secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL); + secp256k1_gej_double_var(r, r, NULL); + secp256k1_gej_add_var(r, r, &running_sum, NULL); + } + return 1; +} + +/** + * Returns optimal bucket_window (number of bits of a scalar represented by a + * set of buckets) for a given number of points. + */ +static int secp256k1_pippenger_bucket_window(size_t n) { + if (n <= 1) { + return 1; + } else if (n <= 4) { + return 2; + } else if (n <= 20) { + return 3; + } else if (n <= 57) { + return 4; + } else if (n <= 136) { + return 5; + } else if (n <= 235) { + return 6; + } else if (n <= 1260) { + return 7; + } else if (n <= 4420) { + return 9; + } else if (n <= 7880) { + return 10; + } else if (n <= 16050) { + return 11; + } else { + return PIPPENGER_MAX_BUCKET_WINDOW; + } +} + +/** + * Returns the maximum optimal number of points for a bucket_window. + */ +static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) { + switch(bucket_window) { + case 1: return 1; + case 2: return 4; + case 3: return 20; + case 4: return 57; + case 5: return 136; + case 6: return 235; + case 7: return 1260; + case 8: return 1260; + case 9: return 4420; + case 10: return 7880; + case 11: return 16050; + case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX; + } + return 0; +} + + +SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) { + secp256k1_scalar tmp = *s1; + secp256k1_scalar_split_lambda(s1, s2, &tmp); + secp256k1_ge_mul_lambda(p2, p1); + + if (secp256k1_scalar_is_high(s1)) { + secp256k1_scalar_negate(s1, s1); + secp256k1_ge_neg(p1, p1); + } + if (secp256k1_scalar_is_high(s2)) { + secp256k1_scalar_negate(s2, s2); + secp256k1_ge_neg(p2, p2); + } +} + +/** + * Returns the scratch size required for a given number of points (excluding + * base point G) without considering alignment. + */ +static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) { + size_t entries = 2*n_points + 2; + size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int); + return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size; +} + +static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { + const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); + /* Use 2(n+1) with the endomorphism, when calculating batch + * sizes. The reason for +1 is that we add the G scalar to the list of + * other scalars. */ + size_t entries = 2*n_points + 2; + secp256k1_ge *points; + secp256k1_scalar *scalars; + secp256k1_gej *buckets; + struct secp256k1_pippenger_state *state_space; + size_t idx = 0; + size_t point_idx = 0; + int i, j; + int bucket_window; + + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n_points == 0) { + return 1; + } + bucket_window = secp256k1_pippenger_bucket_window(n_points); + + /* We allocate PIPPENGER_SCRATCH_OBJECTS objects on the scratch space. If + * these allocations change, make sure to update the + * PIPPENGER_SCRATCH_OBJECTS constant and pippenger_scratch_size + * accordingly. */ + points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points)); + scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars)); + state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space)); + if (points == NULL || scalars == NULL || state_space == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps)); + state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int)); + buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<<bucket_window) * sizeof(*buckets)); + if (state_space->ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + + if (inp_g_sc != NULL) { + scalars[0] = *inp_g_sc; + points[0] = secp256k1_ge_const_g; + idx++; + secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]); + idx++; + } + + while (point_idx < n_points) { + if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + idx++; + secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]); + idx++; + point_idx++; + } + + secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx); + + /* Clear data */ + for(i = 0; (size_t)i < idx; i++) { + secp256k1_scalar_clear(&scalars[i]); + state_space->ps[i].skew_na = 0; + for(j = 0; j < WNAF_SIZE(bucket_window+1); j++) { + state_space->wnaf_na[i * WNAF_SIZE(bucket_window+1) + j] = 0; + } + } + for(i = 0; i < 1<<bucket_window; i++) { + secp256k1_gej_clear(&buckets[i]); + } + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 1; +} + +/* Wrapper for secp256k1_ecmult_multi_func interface */ +static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + return secp256k1_ecmult_pippenger_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0); +} + +/** + * Returns the maximum number of points in addition to G that can be used with + * a given scratch space. The function ensures that fewer points may also be + * used. + */ +static size_t secp256k1_pippenger_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) { + size_t max_alloc = secp256k1_scratch_max_allocation(error_callback, scratch, PIPPENGER_SCRATCH_OBJECTS); + int bucket_window; + size_t res = 0; + + for (bucket_window = 1; bucket_window <= PIPPENGER_MAX_BUCKET_WINDOW; bucket_window++) { + size_t n_points; + size_t max_points = secp256k1_pippenger_bucket_window_inv(bucket_window); + size_t space_for_points; + size_t space_overhead; + size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int); + + entry_size = 2*entry_size; + space_overhead = (sizeof(secp256k1_gej) << bucket_window) + entry_size + sizeof(struct secp256k1_pippenger_state); + if (space_overhead > max_alloc) { + break; + } + space_for_points = max_alloc - space_overhead; + + n_points = space_for_points/entry_size; + n_points = n_points > max_points ? max_points : n_points; + if (n_points > res) { + res = n_points; + } + if (n_points < max_points) { + /* A larger bucket_window may support even more points. But if we + * would choose that then the caller couldn't safely use any number + * smaller than what this function returns */ + break; + } + } + return res; +} + +/* Computes ecmult_multi by simply multiplying and adding each point. Does not + * require a scratch space */ +static int secp256k1_ecmult_multi_simple_var(secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) { + size_t point_idx; + secp256k1_scalar szero; + secp256k1_gej tmpj; + + secp256k1_scalar_set_int(&szero, 0); + secp256k1_gej_set_infinity(r); + secp256k1_gej_set_infinity(&tmpj); + /* r = inp_g_sc*G */ + secp256k1_ecmult(r, &tmpj, &szero, inp_g_sc); + for (point_idx = 0; point_idx < n_points; point_idx++) { + secp256k1_ge point; + secp256k1_gej pointj; + secp256k1_scalar scalar; + if (!cb(&scalar, &point, point_idx, cbdata)) { + return 0; + } + /* r += scalar*point */ + secp256k1_gej_set_ge(&pointj, &point); + secp256k1_ecmult(&tmpj, &pointj, &scalar, NULL); + secp256k1_gej_add_var(r, r, &tmpj, NULL); + } + return 1; +} + +/* Compute the number of batches and the batch size given the maximum batch size and the + * total number of points */ +static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) { + if (max_n_batch_points == 0) { + return 0; + } + if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) { + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + } + if (n == 0) { + *n_batches = 0; + *n_batch_points = 0; + return 1; + } + /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */ + *n_batches = 1 + (n - 1) / max_n_batch_points; + *n_batch_points = 1 + (n - 1) / *n_batches; + return 1; +} + +typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t); +static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + size_t i; + + int (*f)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t); + size_t n_batches; + size_t n_batch_points; + + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n == 0) { + return 1; + } else if (n == 0) { + secp256k1_scalar szero; + secp256k1_scalar_set_int(&szero, 0); + secp256k1_ecmult(r, r, &szero, inp_g_sc); + return 1; + } + if (scratch == NULL) { + return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); + } + + /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than + * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm. + * As a first step check if there's enough space for Pippenger's algo (which requires less space + * than Strauss' algo) and if not, use the simple algorithm. */ + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(error_callback, scratch), n)) { + return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); + } + if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) { + f = secp256k1_ecmult_pippenger_batch; + } else { + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(error_callback, scratch), n)) { + return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); + } + f = secp256k1_ecmult_strauss_batch; + } + for(i = 0; i < n_batches; i++) { + size_t nbp = n < n_batch_points ? n : n_batch_points; + size_t offset = n_batch_points*i; + secp256k1_gej tmp; + if (!f(error_callback, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) { + return 0; + } + secp256k1_gej_add_var(r, r, &tmp, NULL); + n -= nbp; + } + return 1; +} + +#endif /* SECP256K1_ECMULT_IMPL_H */ diff --git a/src/secp256k1/src/field.h b/src/secp256k1/src/field.h new file mode 100644 index 0000000000..64ceead4d2 --- /dev/null +++ b/src/secp256k1/src/field.h @@ -0,0 +1,144 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_H +#define SECP256K1_FIELD_H + +/** Field element module. + * + * Field elements can be represented in several ways, but code accessing + * it (and implementations) need to take certain properties into account: + * - Each field element can be normalized or not. + * - Each field element has a magnitude, which represents how far away + * its representation is away from normalization. Normalized elements + * always have a magnitude of 0 or 1, but a magnitude of 1 doesn't + * imply normality. + */ + +#include "util.h" + +#if defined(SECP256K1_WIDEMUL_INT128) +#include "field_5x52.h" +#elif defined(SECP256K1_WIDEMUL_INT64) +#include "field_10x26.h" +#else +#error "Please select wide multiplication implementation" +#endif + +static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); +static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST( + 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul, + 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul +); + +/** Normalize a field element. This brings the field element to a canonical representation, reduces + * its magnitude to 1, and reduces it modulo field size `p`. + */ +static void secp256k1_fe_normalize(secp256k1_fe *r); + +/** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */ +static void secp256k1_fe_normalize_weak(secp256k1_fe *r); + +/** Normalize a field element, without constant-time guarantee. */ +static void secp256k1_fe_normalize_var(secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value. */ +static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value, + * without constant-time guarantee. */ +static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r); + +/** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer. + * Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise. + */ +static void secp256k1_fe_set_int(secp256k1_fe *r, int a); + +/** Sets a field element equal to zero, initializing all fields. */ +static void secp256k1_fe_clear(secp256k1_fe *a); + +/** Verify whether a field element is zero. Requires the input to be normalized. */ +static int secp256k1_fe_is_zero(const secp256k1_fe *a); + +/** Check the "oddness" of a field element. Requires the input to be normalized. */ +static int secp256k1_fe_is_odd(const secp256k1_fe *a); + +/** Compare two field elements. Requires magnitude-1 inputs. */ +static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Same as secp256k1_fe_equal, but may be variable time. */ +static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Compare two field elements. Requires both inputs to be normalized */ +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */ +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a); + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a); + +/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input + * as an argument. The magnitude of the output is one higher. */ +static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m); + +/** Adds a small integer (up to 0x7FFF) to r. The resulting magnitude increases by one. */ +static void secp256k1_fe_add_int(secp256k1_fe *r, int a); + +/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that + * small integer. */ +static void secp256k1_fe_mul_int(secp256k1_fe *r, int a); + +/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */ +static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a); + +/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b); + +/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a); + +/** If a has a square root, it is computed in r and 1 is returned. If a does not + * have a square root, the root of its negation is computed and 0 is returned. + * The input's magnitude can be at most 8. The output magnitude is 1 (but not + * guaranteed to be normalized). The result in r will always be a square + * itself. */ +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a); + +/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be + * at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a); + +/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */ +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a); + +/** Convert a field element to the storage type. */ +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a); + +/** Convert a field element back from the storage type. */ +static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag); + +/** Halves the value of a field element modulo the field prime. Constant-time. + * For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'. + * The output is not guaranteed to be normalized, regardless of the input. */ +static void secp256k1_fe_half(secp256k1_fe *r); + +/** Sets each limb of 'r' to its upper bound at magnitude 'm'. The output will also have its + * magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */ +static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m); + +/** Determine whether a is a square (modulo p). */ +static int secp256k1_fe_is_square_var(const secp256k1_fe *a); + +#endif /* SECP256K1_FIELD_H */ diff --git a/src/secp256k1/src/field_10x26.h b/src/secp256k1/src/field_10x26.h new file mode 100644 index 0000000000..9eb65607f1 --- /dev/null +++ b/src/secp256k1/src/field_10x26.h @@ -0,0 +1,50 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_H +#define SECP256K1_FIELD_REPR_H + +#include <stdint.h> + +typedef struct { + /* X = sum(i=0..9, n[i]*2^(i*26)) mod p + * where p = 2^256 - 0x1000003D1 + */ + uint32_t n[10]; +#ifdef VERIFY + int magnitude; + int normalized; +#endif +} secp256k1_fe; + +/* Unpacks a constant into a overlapping multi-limbed FE element. */ +#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ + (d0) & 0x3FFFFFFUL, \ + (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \ + (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \ + (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \ + (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \ + (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \ + (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \ + (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \ + (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \ + (((uint32_t)d7) >> 10) \ +} + +#ifdef VERIFY +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} +#else +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} +#endif + +typedef struct { + uint32_t n[8]; +} secp256k1_fe_storage; + +#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }} +#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0] + +#endif /* SECP256K1_FIELD_REPR_H */ diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h new file mode 100644 index 0000000000..3b7f4d2480 --- /dev/null +++ b/src/secp256k1/src/field_10x26_impl.h @@ -0,0 +1,1415 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_IMPL_H +#define SECP256K1_FIELD_REPR_IMPL_H + +#include "checkmem.h" +#include "util.h" +#include "field.h" +#include "modinv32_impl.h" + +/** See the comment at the top of field_5x52_impl.h for more details. + * + * Here, we represent field elements as 10 uint32_t's in base 2^26, least significant first, + * where limbs can contain >26 bits. + * A magnitude M means: + * - 2*M*(2^22-1) is the max (inclusive) of the most significant limb + * - 2*M*(2^26-1) is the max (inclusive) of the remaining limbs + */ + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe *a) { + const uint32_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + r &= (d[0] <= 0x3FFFFFFUL * m); + r &= (d[1] <= 0x3FFFFFFUL * m); + r &= (d[2] <= 0x3FFFFFFUL * m); + r &= (d[3] <= 0x3FFFFFFUL * m); + r &= (d[4] <= 0x3FFFFFFUL * m); + r &= (d[5] <= 0x3FFFFFFUL * m); + r &= (d[6] <= 0x3FFFFFFUL * m); + r &= (d[7] <= 0x3FFFFFFUL * m); + r &= (d[8] <= 0x3FFFFFFUL * m); + r &= (d[9] <= 0x03FFFFFUL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 32); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[9] == 0x03FFFFFUL)) { + uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2]; + if (mid == 0x3FFFFFFUL) { + r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL); + } + } + } + VERIFY_CHECK(r == 1); +} +#endif + +static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) { + VERIFY_CHECK(m >= 0); + VERIFY_CHECK(m <= 2048); + r->n[0] = 0x3FFFFFFUL * 2 * m; + r->n[1] = 0x3FFFFFFUL * 2 * m; + r->n[2] = 0x3FFFFFFUL * 2 * m; + r->n[3] = 0x3FFFFFFUL * 2 * m; + r->n[4] = 0x3FFFFFFUL * 2 * m; + r->n[5] = 0x3FFFFFFUL * 2 * m; + r->n[6] = 0x3FFFFFFUL * 2 * m; + r->n[7] = 0x3FFFFFFUL * 2 * m; + r->n[8] = 0x3FFFFFFUL * 2 * m; + r->n[9] = 0x03FFFFFUL * 2 * m; +#ifdef VERIFY + r->magnitude = m; + r->normalized = (m == 0); + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + if (x) { + t0 += 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint32_t z0, z1; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) { + uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9; + uint32_t z0, z1; + uint32_t x; + + t0 = r->n[0]; + t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + x = t9 >> 22; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0x3FFFFFFUL; + z1 = z0 ^ 0x3D0UL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) { + return 0; + } + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + t4 = r->n[4]; + t5 = r->n[5]; + t6 = r->n[6]; + t7 = r->n[7]; + t8 = r->n[8]; + + t9 &= 0x03FFFFFUL; + t1 += (x << 6); + + t1 += (t0 >> 26); + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { + VERIFY_CHECK(0 <= a && a <= 0x7FFF); + r->n[0] = a; + r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0; +#ifdef VERIFY + r->magnitude = (a != 0); + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { + const uint32_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return a->n[0] & 1; +} + +SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { + int i; +#ifdef VERIFY + a->magnitude = 0; + a->normalized = 1; +#endif + for (i=0; i<10; i++) { + a->n[i] = 0; + } +} + +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { + int i; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + VERIFY_CHECK(b->normalized); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); +#endif + for (i = 9; i >= 0; i--) { + if (a->n[i] > b->n[i]) { + return 1; + } + if (a->n[i] < b->n[i]) { + return -1; + } + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { + int ret; + r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24); + r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22); + r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20); + r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18); + r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24); + r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22); + r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20); + r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18); + r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24); + r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14); + + ret = !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); +#ifdef VERIFY + r->magnitude = 1; + if (ret) { + r->normalized = 1; + secp256k1_fe_verify(r); + } else { + r->normalized = 0; + } +#endif + return ret; +} + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + r[0] = (a->n[9] >> 14) & 0xff; + r[1] = (a->n[9] >> 6) & 0xff; + r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3); + r[3] = (a->n[8] >> 16) & 0xff; + r[4] = (a->n[8] >> 8) & 0xff; + r[5] = a->n[8] & 0xff; + r[6] = (a->n[7] >> 18) & 0xff; + r[7] = (a->n[7] >> 10) & 0xff; + r[8] = (a->n[7] >> 2) & 0xff; + r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f); + r[10] = (a->n[6] >> 12) & 0xff; + r[11] = (a->n[6] >> 4) & 0xff; + r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf); + r[13] = (a->n[5] >> 14) & 0xff; + r[14] = (a->n[5] >> 6) & 0xff; + r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3); + r[16] = (a->n[4] >> 16) & 0xff; + r[17] = (a->n[4] >> 8) & 0xff; + r[18] = a->n[4] & 0xff; + r[19] = (a->n[3] >> 18) & 0xff; + r[20] = (a->n[3] >> 10) & 0xff; + r[21] = (a->n[3] >> 2) & 0xff; + r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f); + r[23] = (a->n[2] >> 12) & 0xff; + r[24] = (a->n[2] >> 4) & 0xff; + r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf); + r[26] = (a->n[1] >> 14) & 0xff; + r[27] = (a->n[1] >> 6) & 0xff; + r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3); + r[29] = (a->n[0] >> 16) & 0xff; + r[30] = (a->n[0] >> 8) & 0xff; + r[31] = a->n[0] & 0xff; +} + +SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= m); + secp256k1_fe_verify(a); + VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m); +#endif + r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4]; + r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5]; + r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6]; + r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7]; + r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8]; + r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; + r->n[5] *= a; + r->n[6] *= a; + r->n[7] *= a; + r->n[8] *= a; + r->n[9] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + secp256k1_fe_verify(a); +#endif + r->n[0] += a->n[0]; + r->n[1] += a->n[1]; + r->n[2] += a->n[2]; + r->n[3] += a->n[3]; + r->n[4] += a->n[4]; + r->n[5] += a->n[5]; + r->n[6] += a->n[6]; + r->n[7] += a->n[7]; + r->n[8] += a->n[8]; + r->n[9] += a->n[9]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) { +#ifdef VERIFY + secp256k1_fe_verify(r); + VERIFY_CHECK(a >= 0); + VERIFY_CHECK(a <= 0x7FFF); +#endif + r->n[0] += a; +#ifdef VERIFY + r->magnitude += 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +#if defined(USE_EXTERNAL_ASM) + +/* External assembler implementation */ +void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b); +void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a); + +#else + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + VERIFY_BITS(b[0], 30); + VERIFY_BITS(b[1], 30); + VERIFY_BITS(b[2], 30); + VERIFY_BITS(b[3], 30); + VERIFY_BITS(b[4], 30); + VERIFY_BITS(b[5], 30); + VERIFY_BITS(b[6], 30); + VERIFY_BITS(b[7], 30); + VERIFY_BITS(b[8], 30); + VERIFY_BITS(b[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * for 0 <= x <= 9, px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * for 9 <= x <= 18, px is a shorthand for sum(a[i]*b[x-i], i=(x-9)..9) + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)a[0] * b[9] + + (uint64_t)a[1] * b[8] + + (uint64_t)a[2] * b[7] + + (uint64_t)a[3] * b[6] + + (uint64_t)a[4] * b[5] + + (uint64_t)a[5] * b[4] + + (uint64_t)a[6] * b[3] + + (uint64_t)a[7] * b[2] + + (uint64_t)a[8] * b[1] + + (uint64_t)a[9] * b[0]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * b[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)a[1] * b[9] + + (uint64_t)a[2] * b[8] + + (uint64_t)a[3] * b[7] + + (uint64_t)a[4] * b[6] + + (uint64_t)a[5] * b[5] + + (uint64_t)a[6] * b[4] + + (uint64_t)a[7] * b[3] + + (uint64_t)a[8] * b[2] + + (uint64_t)a[9] * b[1]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)a[0] * b[1] + + (uint64_t)a[1] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)a[2] * b[9] + + (uint64_t)a[3] * b[8] + + (uint64_t)a[4] * b[7] + + (uint64_t)a[5] * b[6] + + (uint64_t)a[6] * b[5] + + (uint64_t)a[7] * b[4] + + (uint64_t)a[8] * b[3] + + (uint64_t)a[9] * b[2]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)a[0] * b[2] + + (uint64_t)a[1] * b[1] + + (uint64_t)a[2] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)a[3] * b[9] + + (uint64_t)a[4] * b[8] + + (uint64_t)a[5] * b[7] + + (uint64_t)a[6] * b[6] + + (uint64_t)a[7] * b[5] + + (uint64_t)a[8] * b[4] + + (uint64_t)a[9] * b[3]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[3] + + (uint64_t)a[1] * b[2] + + (uint64_t)a[2] * b[1] + + (uint64_t)a[3] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)a[4] * b[9] + + (uint64_t)a[5] * b[8] + + (uint64_t)a[6] * b[7] + + (uint64_t)a[7] * b[6] + + (uint64_t)a[8] * b[5] + + (uint64_t)a[9] * b[4]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[4] + + (uint64_t)a[1] * b[3] + + (uint64_t)a[2] * b[2] + + (uint64_t)a[3] * b[1] + + (uint64_t)a[4] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[5] * b[9] + + (uint64_t)a[6] * b[8] + + (uint64_t)a[7] * b[7] + + (uint64_t)a[8] * b[6] + + (uint64_t)a[9] * b[5]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[5] + + (uint64_t)a[1] * b[4] + + (uint64_t)a[2] * b[3] + + (uint64_t)a[3] * b[2] + + (uint64_t)a[4] * b[1] + + (uint64_t)a[5] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[6] * b[9] + + (uint64_t)a[7] * b[8] + + (uint64_t)a[8] * b[7] + + (uint64_t)a[9] * b[6]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[6] + + (uint64_t)a[1] * b[5] + + (uint64_t)a[2] * b[4] + + (uint64_t)a[3] * b[3] + + (uint64_t)a[4] * b[2] + + (uint64_t)a[5] * b[1] + + (uint64_t)a[6] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[7] * b[9] + + (uint64_t)a[8] * b[8] + + (uint64_t)a[9] * b[7]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[7] + + (uint64_t)a[1] * b[6] + + (uint64_t)a[2] * b[5] + + (uint64_t)a[3] * b[4] + + (uint64_t)a[4] * b[3] + + (uint64_t)a[5] * b[2] + + (uint64_t)a[6] * b[1] + + (uint64_t)a[7] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[8] * b[9] + + (uint64_t)a[9] * b[8]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[8] + + (uint64_t)a[1] * b[7] + + (uint64_t)a[2] * b[6] + + (uint64_t)a[3] * b[5] + + (uint64_t)a[4] * b[4] + + (uint64_t)a[5] * b[3] + + (uint64_t)a[6] * b[2] + + (uint64_t)a[7] * b[1] + + (uint64_t)a[8] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * b[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)(a[0]*2) * a[9] + + (uint64_t)(a[1]*2) * a[8] + + (uint64_t)(a[2]*2) * a[7] + + (uint64_t)(a[3]*2) * a[6] + + (uint64_t)(a[4]*2) * a[5]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * a[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)(a[1]*2) * a[9] + + (uint64_t)(a[2]*2) * a[8] + + (uint64_t)(a[3]*2) * a[7] + + (uint64_t)(a[4]*2) * a[6] + + (uint64_t)a[5] * a[5]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)(a[0]*2) * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)(a[2]*2) * a[9] + + (uint64_t)(a[3]*2) * a[8] + + (uint64_t)(a[4]*2) * a[7] + + (uint64_t)(a[5]*2) * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[2] + + (uint64_t)a[1] * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)(a[3]*2) * a[9] + + (uint64_t)(a[4]*2) * a[8] + + (uint64_t)(a[5]*2) * a[7] + + (uint64_t)a[6] * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[3] + + (uint64_t)(a[1]*2) * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)(a[4]*2) * a[9] + + (uint64_t)(a[5]*2) * a[8] + + (uint64_t)(a[6]*2) * a[7]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[4] + + (uint64_t)(a[1]*2) * a[3] + + (uint64_t)a[2] * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[5]*2) * a[9] + + (uint64_t)(a[6]*2) * a[8] + + (uint64_t)a[7] * a[7]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[5] + + (uint64_t)(a[1]*2) * a[4] + + (uint64_t)(a[2]*2) * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[6]*2) * a[9] + + (uint64_t)(a[7]*2) * a[8]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[6] + + (uint64_t)(a[1]*2) * a[5] + + (uint64_t)(a[2]*2) * a[4] + + (uint64_t)a[3] * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[7]*2) * a[9] + + (uint64_t)a[8] * a[8]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[7] + + (uint64_t)(a[1]*2) * a[6] + + (uint64_t)(a[2]*2) * a[5] + + (uint64_t)(a[3]*2) * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[8]*2) * a[9]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[8] + + (uint64_t)(a[1]*2) * a[7] + + (uint64_t)(a[2]*2) * a[6] + + (uint64_t)(a[3]*2) * a[5] + + (uint64_t)a[4] * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * a[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} +#endif + +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + VERIFY_CHECK(b->magnitude <= 8); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); +#endif + secp256k1_fe_mul_inner(r->n, a->n, b->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + secp256k1_fe_verify(a); +#endif + secp256k1_fe_sqr_inner(r->n, a->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { + uint32_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); + mask0 = vflag + ~((uint32_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); + r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1); + r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1); + r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1); + r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1); + r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1); +#ifdef VERIFY + if (flag) { + r->magnitude = a->magnitude; + r->normalized = a->normalized; + } +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + uint32_t one = (uint32_t)1; + uint32_t mask = -(t0 & one) >> 6; + +#ifdef VERIFY + secp256k1_fe_verify(r); + VERIFY_CHECK(r->magnitude < 32); +#endif + + /* Bounds analysis (over the rationals). + * + * Let m = r->magnitude + * C = 0x3FFFFFFUL * 2 + * D = 0x03FFFFFUL * 2 + * + * Initial bounds: t0..t8 <= C * m + * t9 <= D * m + */ + + t0 += 0x3FFFC2FUL & mask; + t1 += 0x3FFFFBFUL & mask; + t2 += mask; + t3 += mask; + t4 += mask; + t5 += mask; + t6 += mask; + t7 += mask; + t8 += mask; + t9 += mask >> 4; + + VERIFY_CHECK((t0 & one) == 0); + + /* t0..t8: added <= C/2 + * t9: added <= D/2 + * + * Current bounds: t0..t8 <= C * (m + 1/2) + * t9 <= D * (m + 1/2) + */ + + r->n[0] = (t0 >> 1) + ((t1 & one) << 25); + r->n[1] = (t1 >> 1) + ((t2 & one) << 25); + r->n[2] = (t2 >> 1) + ((t3 & one) << 25); + r->n[3] = (t3 >> 1) + ((t4 & one) << 25); + r->n[4] = (t4 >> 1) + ((t5 & one) << 25); + r->n[5] = (t5 >> 1) + ((t6 & one) << 25); + r->n[6] = (t6 >> 1) + ((t7 & one) << 25); + r->n[7] = (t7 >> 1) + ((t8 & one) << 25); + r->n[8] = (t8 >> 1) + ((t9 & one) << 25); + r->n[9] = (t9 >> 1); + + /* t0..t8: shifted right and added <= C/4 + 1/2 + * t9: shifted right + * + * Current bounds: t0..t8 <= C * (m/2 + 1/2) + * t9 <= D * (m/2 + 1/4) + */ + +#ifdef VERIFY + /* Therefore the output magnitude (M) has to be set such that: + * t0..t8: C * M >= C * (m/2 + 1/2) + * t9: D * M >= D * (m/2 + 1/4) + * + * It suffices for all limbs that, for any input magnitude m: + * M >= m/2 + 1/2 + * + * and since we want the smallest such integer value for M: + * M == floor(m/2) + 1 + */ + r->magnitude = (r->magnitude >> 1) + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { + uint32_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); + mask0 = vflag + ~((uint32_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); + r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1); + r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1); + r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 26; + r->n[1] = a->n[1] >> 6 | a->n[2] << 20; + r->n[2] = a->n[2] >> 12 | a->n[3] << 14; + r->n[3] = a->n[3] >> 18 | a->n[4] << 8; + r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28; + r->n[5] = a->n[6] >> 4 | a->n[7] << 22; + r->n[6] = a->n[7] >> 10 | a->n[8] << 16; + r->n[7] = a->n[8] >> 16 | a->n[9] << 10; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { + r->n[0] = a->n[0] & 0x3FFFFFFUL; + r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL); + r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL); + r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL); + r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL); + r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL; + r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL); + r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL); + r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL); + r->n[9] = a->n[7] >> 10; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) { + const uint32_t M26 = UINT32_MAX >> 6; + const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4], + a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8]; + + /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and + * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8). + */ + VERIFY_CHECK(a0 >> 30 == 0); + VERIFY_CHECK(a1 >> 30 == 0); + VERIFY_CHECK(a2 >> 30 == 0); + VERIFY_CHECK(a3 >> 30 == 0); + VERIFY_CHECK(a4 >> 30 == 0); + VERIFY_CHECK(a5 >> 30 == 0); + VERIFY_CHECK(a6 >> 30 == 0); + VERIFY_CHECK(a7 >> 30 == 0); + VERIFY_CHECK(a8 >> 16 == 0); + + r->n[0] = a0 & M26; + r->n[1] = (a0 >> 26 | a1 << 4) & M26; + r->n[2] = (a1 >> 22 | a2 << 8) & M26; + r->n[3] = (a2 >> 18 | a3 << 12) & M26; + r->n[4] = (a3 >> 14 | a4 << 16) & M26; + r->n[5] = (a4 >> 10 | a5 << 20) & M26; + r->n[6] = (a5 >> 6 | a6 << 24) & M26; + r->n[7] = (a6 >> 2 ) & M26; + r->n[8] = (a6 >> 28 | a7 << 2) & M26; + r->n[9] = (a7 >> 24 | a8 << 6); + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) { + const uint32_t M30 = UINT32_MAX >> 2; + const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4], + a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9]; + +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + + r->v[0] = (a0 | a1 << 26) & M30; + r->v[1] = (a1 >> 4 | a2 << 22) & M30; + r->v[2] = (a2 >> 8 | a3 << 18) & M30; + r->v[3] = (a3 >> 12 | a4 << 14) & M30; + r->v[4] = (a4 >> 16 | a5 << 10) & M30; + r->v[5] = (a5 >> 20 | a6 << 6) & M30; + r->v[6] = (a6 >> 24 | a7 << 2 + | a8 << 28) & M30; + r->v[7] = (a8 >> 2 | a9 << 24) & M30; + r->v[8] = a9 >> 6; +} + +static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = { + {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}}, + 0x2DDACACFL +}; + +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv32_signed30 s; + + tmp = *x; + secp256k1_fe_normalize(&tmp); + secp256k1_fe_to_signed30(&s, &tmp); + secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe); + secp256k1_fe_from_signed30(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +#endif +} + +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv32_signed30 s; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + secp256k1_fe_to_signed30(&s, &tmp); + secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe); + secp256k1_fe_from_signed30(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +#endif +} + +static int secp256k1_fe_is_square_var(const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv32_signed30 s; + int jac, ret; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + /* secp256k1_jacobi32_maybe_var cannot deal with input 0. */ + if (secp256k1_fe_is_zero(&tmp)) return 1; + secp256k1_fe_to_signed30(&s, &tmp); + jac = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe); + if (jac == 0) { + /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back + * to computing a square root. This should be extremely rare with random + * input (except in VERIFY mode, where a lower iteration count is used). */ + secp256k1_fe dummy; + ret = secp256k1_fe_sqrt(&dummy, &tmp); + } else { +#ifdef VERIFY + secp256k1_fe dummy; + VERIFY_CHECK(jac == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1); +#endif + ret = jac >= 0; + } + return ret; +} + +#endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/secp256k1/src/field_5x52.h b/src/secp256k1/src/field_5x52.h new file mode 100644 index 0000000000..50ee3f9ec9 --- /dev/null +++ b/src/secp256k1/src/field_5x52.h @@ -0,0 +1,55 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_H +#define SECP256K1_FIELD_REPR_H + +#include <stdint.h> + +typedef struct { + /* X = sum(i=0..4, n[i]*2^(i*52)) mod p + * where p = 2^256 - 0x1000003D1 + */ + uint64_t n[5]; +#ifdef VERIFY + int magnitude; + int normalized; +#endif +} secp256k1_fe; + +/* Unpacks a constant into a overlapping multi-limbed FE element. */ +#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ + (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \ + ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \ + ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \ + ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \ + ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \ +} + +#ifdef VERIFY +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} +#else +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} +#endif + +typedef struct { + uint64_t n[4]; +} secp256k1_fe_storage; + +#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \ + (d0) | (((uint64_t)(d1)) << 32), \ + (d2) | (((uint64_t)(d3)) << 32), \ + (d4) | (((uint64_t)(d5)) << 32), \ + (d6) | (((uint64_t)(d7)) << 32) \ +}} + +#define SECP256K1_FE_STORAGE_CONST_GET(d) \ + (uint32_t)(d.n[3] >> 32), (uint32_t)d.n[3], \ + (uint32_t)(d.n[2] >> 32), (uint32_t)d.n[2], \ + (uint32_t)(d.n[1] >> 32), (uint32_t)d.n[1], \ + (uint32_t)(d.n[0] >> 32), (uint32_t)d.n[0] + +#endif /* SECP256K1_FIELD_REPR_H */ diff --git a/src/secp256k1/src/field_5x52_asm_impl.h b/src/secp256k1/src/field_5x52_asm_impl.h new file mode 100644 index 0000000000..a2118044ab --- /dev/null +++ b/src/secp256k1/src/field_5x52_asm_impl.h @@ -0,0 +1,502 @@ +/*********************************************************************** + * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/** + * Changelog: + * - March 2013, Diederik Huys: original version + * - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm + * - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly + */ + +#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H +#define SECP256K1_FIELD_INNER5X52_IMPL_H + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { +/** + * Registers: rdx:rax = multiplication accumulator + * r9:r8 = c + * r15:rcx = d + * r10-r14 = a0-a4 + * rbx = b + * rdi = r + * rsi = a / t? + */ + uint64_t tmp1, tmp2, tmp3; +__asm__ __volatile__( + "movq 0(%%rsi),%%r10\n" + "movq 8(%%rsi),%%r11\n" + "movq 16(%%rsi),%%r12\n" + "movq 24(%%rsi),%%r13\n" + "movq 32(%%rsi),%%r14\n" + + /* d += a3 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r13\n" + "movq %%rax,%%rcx\n" + "movq %%rdx,%%r15\n" + /* d += a2 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d = a0 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c = a4 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r14\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += (c & M) * R */ + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* t3 (tmp1) = d & M */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + "movq %%rsi,%q1\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* d += a4 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a0 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += c * R */ + "movq %%r8,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* t4 = d & M (%%rsi) */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* tx = t4 >> 48 (tmp3) */ + "movq %%rsi,%%rax\n" + "shrq $48,%%rax\n" + "movq %%rax,%q3\n" + /* t4 &= (M >> 4) (tmp2) */ + "movq $0xffffffffffff,%%rax\n" + "andq %%rax,%%rsi\n" + "movq %%rsi,%q2\n" + /* c = a0 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r10\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += a4 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* u0 = d & M (%%rsi) */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* u0 = (u0 << 4) | tx (%%rsi) */ + "shlq $4,%%rsi\n" + "movq %q3,%%rax\n" + "orq %%rax,%%rsi\n" + /* c += u0 * (R >> 4) */ + "movq $0x1000003d1,%%rax\n" + "mulq %%rsi\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[0] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,0(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a1 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a0 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a4 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c += (d & M) * R */ + "movq %%rcx,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* r[1] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,8(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a2 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a1 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a0 * b2 (last use of %%r10 = a0) */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */ + "movq %q2,%%rsi\n" + "movq %q1,%%r10\n" + /* d += a4 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c += (d & M) * R */ + "movq %%rcx,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 (%%rcx only) */ + "shrdq $52,%%r15,%%rcx\n" + /* r[2] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,16(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += t3 */ + "addq %%r10,%%r8\n" + /* c += d * R */ + "movq %%rcx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[3] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,24(%%rdi)\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* c += t4 (%%r8 only) */ + "addq %%rsi,%%r8\n" + /* r[4] = c */ + "movq %%r8,32(%%rdi)\n" +: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) +: "b"(b), "D"(r) +: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" +); +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { +/** + * Registers: rdx:rax = multiplication accumulator + * r9:r8 = c + * rcx:rbx = d + * r10-r14 = a0-a4 + * r15 = M (0xfffffffffffff) + * rdi = r + * rsi = a / t? + */ + uint64_t tmp1, tmp2, tmp3; +__asm__ __volatile__( + "movq 0(%%rsi),%%r10\n" + "movq 8(%%rsi),%%r11\n" + "movq 16(%%rsi),%%r12\n" + "movq 24(%%rsi),%%r13\n" + "movq 32(%%rsi),%%r14\n" + "movq $0xfffffffffffff,%%r15\n" + + /* d = (a0*2) * a3 */ + "leaq (%%r10,%%r10,1),%%rax\n" + "mulq %%r13\n" + "movq %%rax,%%rbx\n" + "movq %%rdx,%%rcx\n" + /* d += (a1*2) * a2 */ + "leaq (%%r11,%%r11,1),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c = a4 * a4 */ + "movq %%r14,%%rax\n" + "mulq %%r14\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += (c & M) * R */ + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* t3 (tmp1) = d & M */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + "movq %%rsi,%q1\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* a4 *= 2 */ + "addq %%r14,%%r14\n" + /* d += a0 * a4 */ + "movq %%r10,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d+= (a1*2) * a3 */ + "leaq (%%r11,%%r11,1),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += a2 * a2 */ + "movq %%r12,%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += c * R */ + "movq %%r8,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* t4 = d & M (%%rsi) */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* tx = t4 >> 48 (tmp3) */ + "movq %%rsi,%%rax\n" + "shrq $48,%%rax\n" + "movq %%rax,%q3\n" + /* t4 &= (M >> 4) (tmp2) */ + "movq $0xffffffffffff,%%rax\n" + "andq %%rax,%%rsi\n" + "movq %%rsi,%q2\n" + /* c = a0 * a0 */ + "movq %%r10,%%rax\n" + "mulq %%r10\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += a1 * a4 */ + "movq %%r11,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += (a2*2) * a3 */ + "leaq (%%r12,%%r12,1),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* u0 = d & M (%%rsi) */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* u0 = (u0 << 4) | tx (%%rsi) */ + "shlq $4,%%rsi\n" + "movq %q3,%%rax\n" + "orq %%rax,%%rsi\n" + /* c += u0 * (R >> 4) */ + "movq $0x1000003d1,%%rax\n" + "mulq %%rsi\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[0] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,0(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* a0 *= 2 */ + "addq %%r10,%%r10\n" + /* c += a0 * a1 */ + "movq %%r10,%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a2 * a4 */ + "movq %%r12,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += a3 * a3 */ + "movq %%r13,%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c += (d & M) * R */ + "movq %%rbx,%%rax\n" + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* r[1] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,8(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a0 * a2 (last use of %%r10) */ + "movq %%r10,%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */ + "movq %q2,%%rsi\n" + "movq %q1,%%r10\n" + /* c += a1 * a1 */ + "movq %%r11,%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a3 * a4 */ + "movq %%r13,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c += (d & M) * R */ + "movq %%rbx,%%rax\n" + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 (%%rbx only) */ + "shrdq $52,%%rcx,%%rbx\n" + /* r[2] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,16(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += t3 */ + "addq %%r10,%%r8\n" + /* c += d * R */ + "movq %%rbx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[3] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,24(%%rdi)\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* c += t4 (%%r8 only) */ + "addq %%rsi,%%r8\n" + /* r[4] = c */ + "movq %%r8,32(%%rdi)\n" +: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) +: "D"(r) +: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" +); +} + +#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h new file mode 100644 index 0000000000..6b97157d0f --- /dev/null +++ b/src/secp256k1/src/field_5x52_impl.h @@ -0,0 +1,710 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_IMPL_H +#define SECP256K1_FIELD_REPR_IMPL_H + +#include "checkmem.h" +#include "util.h" +#include "field.h" +#include "modinv64_impl.h" + +#if defined(USE_ASM_X86_64) +#include "field_5x52_asm_impl.h" +#else +#include "field_5x52_int128_impl.h" +#endif + +/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, + * represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to + * contain >52 bits each. + * + * Each field element has a 'magnitude' associated with it. Internally, a magnitude M means: + * - 2*M*(2^48-1) is the max (inclusive) of the most significant limb + * - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs + * + * Operations have different rules for propagating magnitude to their outputs. If an operation takes a + * magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive). + * + * Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either + * 0 or 1, and its value is already reduced modulo the order of the field. + */ + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe *a) { + const uint64_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 2048); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) { + r &= (d[0] < 0xFFFFEFFFFFC2FULL); + } + } + VERIFY_CHECK(r == 1); +} +#endif + +static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) { + VERIFY_CHECK(m >= 0); + VERIFY_CHECK(m <= 2048); + r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m; + r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m; + r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m; + r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m; + r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m; +#ifdef VERIFY + r->magnitude = m; + r->normalized = (m == 0); + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + if (x) { + t0 += 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint64_t z0, z1; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) { + uint64_t t0, t1, t2, t3, t4; + uint64_t z0, z1; + uint64_t x; + + t0 = r->n[0]; + t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + x = t4 >> 48; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0xFFFFFFFFFFFFFULL; + z1 = z0 ^ 0x1000003D0ULL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) { + return 0; + } + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + + t4 &= 0x0FFFFFFFFFFFFULL; + + t1 += (t0 >> 52); + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { + VERIFY_CHECK(0 <= a && a <= 0x7FFF); + r->n[0] = a; + r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; +#ifdef VERIFY + r->magnitude = (a != 0); + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { + const uint64_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return a->n[0] & 1; +} + +SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { + int i; +#ifdef VERIFY + a->magnitude = 0; + a->normalized = 1; +#endif + for (i=0; i<5; i++) { + a->n[i] = 0; + } +} + +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { + int i; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + VERIFY_CHECK(b->normalized); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); +#endif + for (i = 4; i >= 0; i--) { + if (a->n[i] > b->n[i]) { + return 1; + } + if (a->n[i] < b->n[i]) { + return -1; + } + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { + int ret; + r->n[0] = (uint64_t)a[31] + | ((uint64_t)a[30] << 8) + | ((uint64_t)a[29] << 16) + | ((uint64_t)a[28] << 24) + | ((uint64_t)a[27] << 32) + | ((uint64_t)a[26] << 40) + | ((uint64_t)(a[25] & 0xF) << 48); + r->n[1] = (uint64_t)((a[25] >> 4) & 0xF) + | ((uint64_t)a[24] << 4) + | ((uint64_t)a[23] << 12) + | ((uint64_t)a[22] << 20) + | ((uint64_t)a[21] << 28) + | ((uint64_t)a[20] << 36) + | ((uint64_t)a[19] << 44); + r->n[2] = (uint64_t)a[18] + | ((uint64_t)a[17] << 8) + | ((uint64_t)a[16] << 16) + | ((uint64_t)a[15] << 24) + | ((uint64_t)a[14] << 32) + | ((uint64_t)a[13] << 40) + | ((uint64_t)(a[12] & 0xF) << 48); + r->n[3] = (uint64_t)((a[12] >> 4) & 0xF) + | ((uint64_t)a[11] << 4) + | ((uint64_t)a[10] << 12) + | ((uint64_t)a[9] << 20) + | ((uint64_t)a[8] << 28) + | ((uint64_t)a[7] << 36) + | ((uint64_t)a[6] << 44); + r->n[4] = (uint64_t)a[5] + | ((uint64_t)a[4] << 8) + | ((uint64_t)a[3] << 16) + | ((uint64_t)a[2] << 24) + | ((uint64_t)a[1] << 32) + | ((uint64_t)a[0] << 40); + ret = !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL)); +#ifdef VERIFY + r->magnitude = 1; + if (ret) { + r->normalized = 1; + secp256k1_fe_verify(r); + } else { + r->normalized = 0; + } +#endif + return ret; +} + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + r[0] = (a->n[4] >> 40) & 0xFF; + r[1] = (a->n[4] >> 32) & 0xFF; + r[2] = (a->n[4] >> 24) & 0xFF; + r[3] = (a->n[4] >> 16) & 0xFF; + r[4] = (a->n[4] >> 8) & 0xFF; + r[5] = a->n[4] & 0xFF; + r[6] = (a->n[3] >> 44) & 0xFF; + r[7] = (a->n[3] >> 36) & 0xFF; + r[8] = (a->n[3] >> 28) & 0xFF; + r[9] = (a->n[3] >> 20) & 0xFF; + r[10] = (a->n[3] >> 12) & 0xFF; + r[11] = (a->n[3] >> 4) & 0xFF; + r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4); + r[13] = (a->n[2] >> 40) & 0xFF; + r[14] = (a->n[2] >> 32) & 0xFF; + r[15] = (a->n[2] >> 24) & 0xFF; + r[16] = (a->n[2] >> 16) & 0xFF; + r[17] = (a->n[2] >> 8) & 0xFF; + r[18] = a->n[2] & 0xFF; + r[19] = (a->n[1] >> 44) & 0xFF; + r[20] = (a->n[1] >> 36) & 0xFF; + r[21] = (a->n[1] >> 28) & 0xFF; + r[22] = (a->n[1] >> 20) & 0xFF; + r[23] = (a->n[1] >> 12) & 0xFF; + r[24] = (a->n[1] >> 4) & 0xFF; + r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4); + r[26] = (a->n[0] >> 40) & 0xFF; + r[27] = (a->n[0] >> 32) & 0xFF; + r[28] = (a->n[0] >> 24) & 0xFF; + r[29] = (a->n[0] >> 16) & 0xFF; + r[30] = (a->n[0] >> 8) & 0xFF; + r[31] = a->n[0] & 0xFF; +} + +SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= m); + secp256k1_fe_verify(a); + VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); + VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); + VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m); +#endif + r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) { +#ifdef VERIFY + secp256k1_fe_verify(r); + VERIFY_CHECK(a >= 0); + VERIFY_CHECK(a <= 0x7FFF); +#endif + r->n[0] += a; +#ifdef VERIFY + r->magnitude += 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + secp256k1_fe_verify(a); +#endif + r->n[0] += a->n[0]; + r->n[1] += a->n[1]; + r->n[2] += a->n[2]; + r->n[3] += a->n[3]; + r->n[4] += a->n[4]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + VERIFY_CHECK(b->magnitude <= 8); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); +#endif + secp256k1_fe_mul_inner(r->n, a->n, b->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + secp256k1_fe_verify(a); +#endif + secp256k1_fe_sqr_inner(r->n, a->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { + uint64_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); + mask0 = vflag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); +#ifdef VERIFY + if (flag) { + r->magnitude = a->magnitude; + r->normalized = a->normalized; + } +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + uint64_t one = (uint64_t)1; + uint64_t mask = -(t0 & one) >> 12; + +#ifdef VERIFY + secp256k1_fe_verify(r); + VERIFY_CHECK(r->magnitude < 32); +#endif + + /* Bounds analysis (over the rationals). + * + * Let m = r->magnitude + * C = 0xFFFFFFFFFFFFFULL * 2 + * D = 0x0FFFFFFFFFFFFULL * 2 + * + * Initial bounds: t0..t3 <= C * m + * t4 <= D * m + */ + + t0 += 0xFFFFEFFFFFC2FULL & mask; + t1 += mask; + t2 += mask; + t3 += mask; + t4 += mask >> 4; + + VERIFY_CHECK((t0 & one) == 0); + + /* t0..t3: added <= C/2 + * t4: added <= D/2 + * + * Current bounds: t0..t3 <= C * (m + 1/2) + * t4 <= D * (m + 1/2) + */ + + r->n[0] = (t0 >> 1) + ((t1 & one) << 51); + r->n[1] = (t1 >> 1) + ((t2 & one) << 51); + r->n[2] = (t2 >> 1) + ((t3 & one) << 51); + r->n[3] = (t3 >> 1) + ((t4 & one) << 51); + r->n[4] = (t4 >> 1); + + /* t0..t3: shifted right and added <= C/4 + 1/2 + * t4: shifted right + * + * Current bounds: t0..t3 <= C * (m/2 + 1/2) + * t4 <= D * (m/2 + 1/4) + */ + +#ifdef VERIFY + /* Therefore the output magnitude (M) has to be set such that: + * t0..t3: C * M >= C * (m/2 + 1/2) + * t4: D * M >= D * (m/2 + 1/4) + * + * It suffices for all limbs that, for any input magnitude m: + * M >= m/2 + 1/2 + * + * and since we want the smallest such integer value for M: + * M == floor(m/2) + 1 + */ + r->magnitude = (r->magnitude >> 1) + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { + uint64_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); + mask0 = vflag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 52; + r->n[1] = a->n[1] >> 12 | a->n[2] << 40; + r->n[2] = a->n[2] >> 24 | a->n[3] << 28; + r->n[3] = a->n[3] >> 36 | a->n[4] << 16; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { + r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL; + r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL); + r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL); + r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); + r->n[4] = a->n[3] >> 16; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) { + const uint64_t M52 = UINT64_MAX >> 12; + const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4]; + + /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and + * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4). + */ + VERIFY_CHECK(a0 >> 62 == 0); + VERIFY_CHECK(a1 >> 62 == 0); + VERIFY_CHECK(a2 >> 62 == 0); + VERIFY_CHECK(a3 >> 62 == 0); + VERIFY_CHECK(a4 >> 8 == 0); + + r->n[0] = a0 & M52; + r->n[1] = (a0 >> 52 | a1 << 10) & M52; + r->n[2] = (a1 >> 42 | a2 << 20) & M52; + r->n[3] = (a2 >> 32 | a3 << 30) & M52; + r->n[4] = (a3 >> 22 | a4 << 40); + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) { + const uint64_t M62 = UINT64_MAX >> 2; + const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4]; + +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + + r->v[0] = (a0 | a1 << 52) & M62; + r->v[1] = (a1 >> 10 | a2 << 42) & M62; + r->v[2] = (a2 >> 20 | a3 << 32) & M62; + r->v[3] = (a3 >> 30 | a4 << 22) & M62; + r->v[4] = a4 >> 40; +} + +static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = { + {{-0x1000003D1LL, 0, 0, 0, 256}}, + 0x27C7F6E22DDACACFLL +}; + +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv64_signed62 s; + + tmp = *x; + secp256k1_fe_normalize(&tmp); + secp256k1_fe_to_signed62(&s, &tmp); + secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe); + secp256k1_fe_from_signed62(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +#endif +} + +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv64_signed62 s; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + secp256k1_fe_to_signed62(&s, &tmp); + secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe); + secp256k1_fe_from_signed62(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +#endif +} + +static int secp256k1_fe_is_square_var(const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv64_signed62 s; + int jac, ret; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + /* secp256k1_jacobi64_maybe_var cannot deal with input 0. */ + if (secp256k1_fe_is_zero(&tmp)) return 1; + secp256k1_fe_to_signed62(&s, &tmp); + jac = secp256k1_jacobi64_maybe_var(&s, &secp256k1_const_modinfo_fe); + if (jac == 0) { + /* secp256k1_jacobi64_maybe_var failed to compute the Jacobi symbol. Fall back + * to computing a square root. This should be extremely rare with random + * input (except in VERIFY mode, where a lower iteration count is used). */ + secp256k1_fe dummy; + ret = secp256k1_fe_sqrt(&dummy, &tmp); + } else { +#ifdef VERIFY + secp256k1_fe dummy; + VERIFY_CHECK(jac == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1); +#endif + ret = jac >= 0; + } + return ret; +} + +#endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/secp256k1/src/field_5x52_int128_impl.h b/src/secp256k1/src/field_5x52_int128_impl.h new file mode 100644 index 0000000000..18567b95f3 --- /dev/null +++ b/src/secp256k1/src/field_5x52_int128_impl.h @@ -0,0 +1,278 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H +#define SECP256K1_FIELD_INNER5X52_IMPL_H + +#include <stdint.h> + +#include "int128.h" + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#define VERIFY_BITS_128(x, n) VERIFY_CHECK(secp256k1_u128_check_bits((x), (n))) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#define VERIFY_BITS_128(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { + secp256k1_uint128 c, d; + uint64_t t3, t4, tx, u0; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + VERIFY_BITS(b[0], 56); + VERIFY_BITS(b[1], 56); + VERIFY_BITS(b[2], 56); + VERIFY_BITS(b[3], 56); + VERIFY_BITS(b[4], 52); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); + + /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4) + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + secp256k1_u128_mul(&d, a0, b[3]); + secp256k1_u128_accum_mul(&d, a1, b[2]); + secp256k1_u128_accum_mul(&d, a2, b[1]); + secp256k1_u128_accum_mul(&d, a3, b[0]); + VERIFY_BITS_128(&d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + secp256k1_u128_mul(&c, a4, b[4]); + VERIFY_BITS_128(&c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64); + VERIFY_BITS_128(&d, 115); + VERIFY_BITS_128(&c, 48); + /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(t3, 52); + VERIFY_BITS_128(&d, 63); + /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + secp256k1_u128_accum_mul(&d, a0, b[4]); + secp256k1_u128_accum_mul(&d, a1, b[3]); + secp256k1_u128_accum_mul(&d, a2, b[2]); + secp256k1_u128_accum_mul(&d, a3, b[1]); + secp256k1_u128_accum_mul(&d, a4, b[0]); + VERIFY_BITS_128(&d, 115); + /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c)); + VERIFY_BITS_128(&d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(t4, 52); + VERIFY_BITS_128(&d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + secp256k1_u128_mul(&c, a0, b[0]); + VERIFY_BITS_128(&c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + secp256k1_u128_accum_mul(&d, a1, b[4]); + secp256k1_u128_accum_mul(&d, a2, b[3]); + secp256k1_u128_accum_mul(&d, a3, b[2]); + secp256k1_u128_accum_mul(&d, a4, b[1]); + VERIFY_BITS_128(&d, 115); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(u0, 52); + VERIFY_BITS_128(&d, 63); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + secp256k1_u128_accum_mul(&c, u0, R >> 4); + VERIFY_BITS_128(&c, 115); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[0], 52); + VERIFY_BITS_128(&c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + secp256k1_u128_accum_mul(&c, a0, b[1]); + secp256k1_u128_accum_mul(&c, a1, b[0]); + VERIFY_BITS_128(&c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + secp256k1_u128_accum_mul(&d, a2, b[4]); + secp256k1_u128_accum_mul(&d, a3, b[3]); + secp256k1_u128_accum_mul(&d, a4, b[2]); + VERIFY_BITS_128(&d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52); + VERIFY_BITS_128(&c, 115); + VERIFY_BITS_128(&d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[1], 52); + VERIFY_BITS_128(&c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + secp256k1_u128_accum_mul(&c, a0, b[2]); + secp256k1_u128_accum_mul(&c, a1, b[1]); + secp256k1_u128_accum_mul(&c, a2, b[0]); + VERIFY_BITS_128(&c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + secp256k1_u128_accum_mul(&d, a3, b[4]); + secp256k1_u128_accum_mul(&d, a4, b[3]); + VERIFY_BITS_128(&d, 114); + /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64); + VERIFY_BITS_128(&c, 115); + VERIFY_BITS_128(&d, 50); + /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[2], 52); + VERIFY_BITS_128(&c, 63); + /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d)); + secp256k1_u128_accum_u64(&c, t3); + VERIFY_BITS_128(&c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[3], 52); + VERIFY_BITS_128(&c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = secp256k1_u128_to_u64(&c) + t4; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { + secp256k1_uint128 c, d; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + int64_t t3, t4, tx, u0; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + + /** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + secp256k1_u128_mul(&d, a0*2, a3); + secp256k1_u128_accum_mul(&d, a1*2, a2); + VERIFY_BITS_128(&d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + secp256k1_u128_mul(&c, a4, a4); + VERIFY_BITS_128(&c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64); + VERIFY_BITS_128(&d, 115); + VERIFY_BITS_128(&c, 48); + /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(t3, 52); + VERIFY_BITS_128(&d, 63); + /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + a4 *= 2; + secp256k1_u128_accum_mul(&d, a0, a4); + secp256k1_u128_accum_mul(&d, a1*2, a3); + secp256k1_u128_accum_mul(&d, a2, a2); + VERIFY_BITS_128(&d, 115); + /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c)); + VERIFY_BITS_128(&d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(t4, 52); + VERIFY_BITS_128(&d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + secp256k1_u128_mul(&c, a0, a0); + VERIFY_BITS_128(&c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + secp256k1_u128_accum_mul(&d, a1, a4); + secp256k1_u128_accum_mul(&d, a2*2, a3); + VERIFY_BITS_128(&d, 114); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); + VERIFY_BITS(u0, 52); + VERIFY_BITS_128(&d, 62); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + secp256k1_u128_accum_mul(&c, u0, R >> 4); + VERIFY_BITS_128(&c, 113); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[0], 52); + VERIFY_BITS_128(&c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + a0 *= 2; + secp256k1_u128_accum_mul(&c, a0, a1); + VERIFY_BITS_128(&c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + secp256k1_u128_accum_mul(&d, a2, a4); + secp256k1_u128_accum_mul(&d, a3, a3); + VERIFY_BITS_128(&d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52); + VERIFY_BITS_128(&c, 115); + VERIFY_BITS_128(&d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[1], 52); + VERIFY_BITS_128(&c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + secp256k1_u128_accum_mul(&c, a0, a2); + secp256k1_u128_accum_mul(&c, a1, a1); + VERIFY_BITS_128(&c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + secp256k1_u128_accum_mul(&d, a3, a4); + VERIFY_BITS_128(&d, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64); + VERIFY_BITS_128(&c, 115); + VERIFY_BITS_128(&d, 50); + /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[2], 52); + VERIFY_BITS_128(&c, 63); + /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d)); + secp256k1_u128_accum_u64(&c, t3); + VERIFY_BITS_128(&c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); + VERIFY_BITS(r[3], 52); + VERIFY_BITS_128(&c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = secp256k1_u128_to_u64(&c) + t4; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ diff --git a/src/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h new file mode 100644 index 0000000000..0a03076bbc --- /dev/null +++ b/src/secp256k1/src/field_impl.h @@ -0,0 +1,134 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_FIELD_IMPL_H +#define SECP256K1_FIELD_IMPL_H + +#include "util.h" + +#if defined(SECP256K1_WIDEMUL_INT128) +#include "field_5x52_impl.h" +#elif defined(SECP256K1_WIDEMUL_INT64) +#include "field_10x26_impl.h" +#else +#error "Please select wide multiplication implementation" +#endif + +SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero(&na); +} + +SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero_var(&na); +} + +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) { + /** Given that p is congruent to 3 mod 4, we can compute the square root of + * a mod p as the (p+1)/4'th power of a. + * + * As (p+1)/4 is an even number, it will have the same result for a and for + * (-a). Only one of these two numbers actually has a square root however, + * so we test at the end by squaring and comparing to the input. + * Also because (p+1)/4 is an even number, the computed square root is + * itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)). + */ + secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; + int j; + + VERIFY_CHECK(r != a); + + /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in + * { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: + * 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + secp256k1_fe_sqr(&x2, a); + secp256k1_fe_mul(&x2, &x2, a); + + secp256k1_fe_sqr(&x3, &x2); + secp256k1_fe_mul(&x3, &x3, a); + + x6 = x3; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x6, &x6); + } + secp256k1_fe_mul(&x6, &x6, &x3); + + x9 = x6; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x9, &x9); + } + secp256k1_fe_mul(&x9, &x9, &x3); + + x11 = x9; + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&x11, &x11); + } + secp256k1_fe_mul(&x11, &x11, &x2); + + x22 = x11; + for (j=0; j<11; j++) { + secp256k1_fe_sqr(&x22, &x22); + } + secp256k1_fe_mul(&x22, &x22, &x11); + + x44 = x22; + for (j=0; j<22; j++) { + secp256k1_fe_sqr(&x44, &x44); + } + secp256k1_fe_mul(&x44, &x44, &x22); + + x88 = x44; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x88, &x88); + } + secp256k1_fe_mul(&x88, &x88, &x44); + + x176 = x88; + for (j=0; j<88; j++) { + secp256k1_fe_sqr(&x176, &x176); + } + secp256k1_fe_mul(&x176, &x176, &x88); + + x220 = x176; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x220, &x220); + } + secp256k1_fe_mul(&x220, &x220, &x44); + + x223 = x220; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x223, &x223); + } + secp256k1_fe_mul(&x223, &x223, &x3); + + /* The final result is then assembled using a sliding window over the blocks. */ + + t1 = x223; + for (j=0; j<23; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x22); + for (j=0; j<6; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x2); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_sqr(r, &t1); + + /* Check that a square root was actually calculated */ + + secp256k1_fe_sqr(&t1, r); + return secp256k1_fe_equal(&t1, a); +} + +#endif /* SECP256K1_FIELD_IMPL_H */ diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h new file mode 100644 index 0000000000..b79ba597db --- /dev/null +++ b/src/secp256k1/src/group.h @@ -0,0 +1,167 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_GROUP_H +#define SECP256K1_GROUP_H + +#include "field.h" + +/** A group element in affine coordinates on the secp256k1 curve, + * or occasionally on an isomorphic curve of the form y^2 = x^3 + 7*t^6. + * Note: For exhaustive test mode, secp256k1 is replaced by a small subgroup of a different curve. + */ +typedef struct { + secp256k1_fe x; + secp256k1_fe y; + int infinity; /* whether this represents the point at infinity */ +} secp256k1_ge; + +#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0} +#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} + +/** A group element of the secp256k1 curve, in jacobian coordinates. + * Note: For exhastive test mode, secp256k1 is replaced by a small subgroup of a different curve. + */ +typedef struct { + secp256k1_fe x; /* actual X: x/z^2 */ + secp256k1_fe y; /* actual Y: y/z^3 */ + secp256k1_fe z; + int infinity; /* whether this represents the point at infinity */ +} secp256k1_gej; + +#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0} +#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} + +typedef struct { + secp256k1_fe_storage x; + secp256k1_fe_storage y; +} secp256k1_ge_storage; + +#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))} + +#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y) + +/** Set a group element equal to the point with given X and Y coordinates */ +static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y); + +/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness + * for Y. Return value indicates whether the result is valid. */ +static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_ge_is_infinity(const secp256k1_ge *a); + +/** Check whether a group element is valid (i.e., on the curve). */ +static int secp256k1_ge_is_valid_var(const secp256k1_ge *a); + +/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */ +static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a); + +/** Set a group element equal to another which is given in jacobian coordinates. Constant time. */ +static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a); + +/** Set a group element equal to another which is given in jacobian coordinates. */ +static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a); + +/** Set a batch of group elements equal to the inputs given in jacobian coordinates */ +static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len); + +/** Bring a batch of inputs to the same global z "denominator", based on ratios between + * (omitted) z coordinates of adjacent elements. + * + * Although the elements a[i] are _ge rather than _gej, they actually represent elements + * in Jacobian coordinates with their z coordinates omitted. + * + * Using the notation z(b) to represent the omitted z coordinate of b, the array zr of + * z coordinate ratios must satisfy zr[i] == z(a[i]) / z(a[i-1]) for 0 < 'i' < len. + * The zr[0] value is unused. + * + * This function adjusts the coordinates of 'a' in place so that for all 'i', z(a[i]) == z(a[len-1]). + * In other words, the initial value of z(a[len-1]) becomes the global z "denominator". Only the + * a[i].x and a[i].y coordinates are explicitly modified; the adjustment of the omitted z coordinate is + * implicit. + * + * The coordinates of the final element a[len-1] are not changed. + */ +static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr); + +/** Set a group element (affine) equal to the point at infinity. */ +static void secp256k1_ge_set_infinity(secp256k1_ge *r); + +/** Set a group element (jacobian) equal to the point at infinity. */ +static void secp256k1_gej_set_infinity(secp256k1_gej *r); + +/** Set a group element (jacobian) equal to another which is given in affine coordinates. */ +static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a); + +/** Check two group elements (jacobian) for equality in variable time. */ +static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b); + +/** Compare the X coordinate of a group element (jacobian). */ +static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a); + +/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */ +static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_gej_is_infinity(const secp256k1_gej *a); + +/** Set r equal to the double of a. Constant time. */ +static void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a); + +/** Set r equal to the double of a. If rzr is not-NULL this sets *rzr such that r->z == a->z * *rzr (where infinity means an implicit z = 0). */ +static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ +static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */ +static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b); + +/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient + than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time + guarantee, and b is allowed to be infinity. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ +static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */ +static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv); + +/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */ +static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a); + +/** Clear a secp256k1_gej to prevent leaking sensitive information. */ +static void secp256k1_gej_clear(secp256k1_gej *r); + +/** Clear a secp256k1_ge to prevent leaking sensitive information. */ +static void secp256k1_ge_clear(secp256k1_ge *r); + +/** Convert a group element to the storage type. */ +static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a); + +/** Convert a group element back from the storage type. */ +static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag); + +/** Rescale a jacobian point by b which must be non-zero. Constant-time. */ +static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b); + +/** Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve. + * + * In normal mode, the used group is secp256k1, which has cofactor=1 meaning that every point on the curve is in the + * group, and this function returns always true. + * + * When compiling in exhaustive test mode, a slightly different curve equation is used, leading to a group with a + * (very) small subgroup, and that subgroup is what is used for all cryptographic operations. In that mode, this + * function checks whether a point that is on the curve is in fact also in that subgroup. + */ +static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge); + +#endif /* SECP256K1_GROUP_H */ diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h new file mode 100644 index 0000000000..82ce3f8d8b --- /dev/null +++ b/src/secp256k1/src/group_impl.h @@ -0,0 +1,730 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_GROUP_IMPL_H +#define SECP256K1_GROUP_IMPL_H + +#include "field.h" +#include "group.h" + +/* Begin of section generated by sage/gen_exhaustive_groups.sage. */ +#define SECP256K1_G_ORDER_7 SECP256K1_GE_CONST(\ + 0x66625d13, 0x317ffe44, 0x63d32cff, 0x1ca02b9b,\ + 0xe5c6d070, 0x50b4b05e, 0x81cc30db, 0xf5166f0a,\ + 0x1e60e897, 0xa7c00c7c, 0x2df53eb6, 0x98274ff4,\ + 0x64252f42, 0x8ca44e17, 0x3b25418c, 0xff4ab0cf\ +) +#define SECP256K1_G_ORDER_13 SECP256K1_GE_CONST(\ + 0xa2482ff8, 0x4bf34edf, 0xa51262fd, 0xe57921db,\ + 0xe0dd2cb7, 0xa5914790, 0xbc71631f, 0xc09704fb,\ + 0x942536cb, 0xa3e49492, 0x3a701cc3, 0xee3e443f,\ + 0xdf182aa9, 0x15b8aa6a, 0x166d3b19, 0xba84b045\ +) +#define SECP256K1_G_ORDER_199 SECP256K1_GE_CONST(\ + 0x7fb07b5c, 0xd07c3bda, 0x553902e2, 0x7a87ea2c,\ + 0x35108a7f, 0x051f41e5, 0xb76abad5, 0x1f2703ad,\ + 0x0a251539, 0x5b4c4438, 0x952a634f, 0xac10dd4d,\ + 0x6d6f4745, 0x98990c27, 0x3a4f3116, 0xd32ff969\ +) +/** Generator for secp256k1, value 'g' defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + */ +#define SECP256K1_G SECP256K1_GE_CONST(\ + 0x79be667e, 0xf9dcbbac, 0x55a06295, 0xce870b07,\ + 0x029bfcdb, 0x2dce28d9, 0x59f2815b, 0x16f81798,\ + 0x483ada77, 0x26a3c465, 0x5da4fbfc, 0x0e1108a8,\ + 0xfd17b448, 0xa6855419, 0x9c47d08f, 0xfb10d4b8\ +) +/* These exhaustive group test orders and generators are chosen such that: + * - The field size is equal to that of secp256k1, so field code is the same. + * - The curve equation is of the form y^2=x^3+B for some small constant B. + * - The subgroup has a generator 2*P, where P.x is as small as possible. + * - The subgroup has size less than 1000 to permit exhaustive testing. + * - The subgroup admits an endomorphism of the form lambda*(x,y) == (beta*x,y). + */ +#if defined(EXHAUSTIVE_TEST_ORDER) +# if EXHAUSTIVE_TEST_ORDER == 7 + +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_7; +#define SECP256K1_B 6 + +# elif EXHAUSTIVE_TEST_ORDER == 13 + +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_13; +#define SECP256K1_B 2 + +# elif EXHAUSTIVE_TEST_ORDER == 199 + +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_199; +#define SECP256K1_B 4 + +# else +# error No known generator for the specified exhaustive test group order. +# endif +#else + +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G; +#define SECP256K1_B 7 + +#endif +/* End of section generated by sage/gen_exhaustive_groups.sage. */ + +static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, SECP256K1_B); + +static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) { + secp256k1_fe zi2; + secp256k1_fe zi3; + VERIFY_CHECK(!a->infinity); + secp256k1_fe_sqr(&zi2, zi); + secp256k1_fe_mul(&zi3, &zi2, zi); + secp256k1_fe_mul(&r->x, &a->x, &zi2); + secp256k1_fe_mul(&r->y, &a->y, &zi3); + r->infinity = a->infinity; +} + +static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) { + r->infinity = 0; + r->x = *x; + r->y = *y; +} + +static int secp256k1_ge_is_infinity(const secp256k1_ge *a) { + return a->infinity; +} + +static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) { + *r = *a; + secp256k1_fe_normalize_weak(&r->y); + secp256k1_fe_negate(&r->y, &r->y, 1); +} + +static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) { + secp256k1_fe z2, z3; + r->infinity = a->infinity; + secp256k1_fe_inv(&a->z, &a->z); + secp256k1_fe_sqr(&z2, &a->z); + secp256k1_fe_mul(&z3, &a->z, &z2); + secp256k1_fe_mul(&a->x, &a->x, &z2); + secp256k1_fe_mul(&a->y, &a->y, &z3); + secp256k1_fe_set_int(&a->z, 1); + r->x = a->x; + r->y = a->y; +} + +static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) { + secp256k1_fe z2, z3; + if (a->infinity) { + secp256k1_ge_set_infinity(r); + return; + } + secp256k1_fe_inv_var(&a->z, &a->z); + secp256k1_fe_sqr(&z2, &a->z); + secp256k1_fe_mul(&z3, &a->z, &z2); + secp256k1_fe_mul(&a->x, &a->x, &z2); + secp256k1_fe_mul(&a->y, &a->y, &z3); + secp256k1_fe_set_int(&a->z, 1); + secp256k1_ge_set_xy(r, &a->x, &a->y); +} + +static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) { + secp256k1_fe u; + size_t i; + size_t last_i = SIZE_MAX; + + for (i = 0; i < len; i++) { + if (a[i].infinity) { + secp256k1_ge_set_infinity(&r[i]); + } else { + /* Use destination's x coordinates as scratch space */ + if (last_i == SIZE_MAX) { + r[i].x = a[i].z; + } else { + secp256k1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z); + } + last_i = i; + } + } + if (last_i == SIZE_MAX) { + return; + } + secp256k1_fe_inv_var(&u, &r[last_i].x); + + i = last_i; + while (i > 0) { + i--; + if (!a[i].infinity) { + secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u); + secp256k1_fe_mul(&u, &u, &a[last_i].z); + last_i = i; + } + } + VERIFY_CHECK(!a[last_i].infinity); + r[last_i].x = u; + + for (i = 0; i < len; i++) { + if (!a[i].infinity) { + secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x); + } + } +} + +static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr) { + size_t i = len - 1; + secp256k1_fe zs; + + if (len > 0) { + /* Ensure all y values are in weak normal form for fast negation of points */ + secp256k1_fe_normalize_weak(&a[i].y); + zs = zr[i]; + + /* Work our way backwards, using the z-ratios to scale the x/y values. */ + while (i > 0) { + secp256k1_gej tmpa; + if (i != len - 1) { + secp256k1_fe_mul(&zs, &zs, &zr[i]); + } + i--; + tmpa.x = a[i].x; + tmpa.y = a[i].y; + tmpa.infinity = 0; + secp256k1_ge_set_gej_zinv(&a[i], &tmpa, &zs); + } + } +} + +static void secp256k1_gej_set_infinity(secp256k1_gej *r) { + r->infinity = 1; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); + secp256k1_fe_clear(&r->z); +} + +static void secp256k1_ge_set_infinity(secp256k1_ge *r) { + r->infinity = 1; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); +} + +static void secp256k1_gej_clear(secp256k1_gej *r) { + r->infinity = 0; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); + secp256k1_fe_clear(&r->z); +} + +static void secp256k1_ge_clear(secp256k1_ge *r) { + r->infinity = 0; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); +} + +static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) { + secp256k1_fe x2, x3; + r->x = *x; + secp256k1_fe_sqr(&x2, x); + secp256k1_fe_mul(&x3, x, &x2); + r->infinity = 0; + secp256k1_fe_add_int(&x3, SECP256K1_B); + if (!secp256k1_fe_sqrt(&r->y, &x3)) { + return 0; + } + secp256k1_fe_normalize_var(&r->y); + if (secp256k1_fe_is_odd(&r->y) != odd) { + secp256k1_fe_negate(&r->y, &r->y, 1); + } + return 1; + +} + +static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) { + r->infinity = a->infinity; + r->x = a->x; + r->y = a->y; + secp256k1_fe_set_int(&r->z, 1); +} + +static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b) { + secp256k1_gej tmp; + secp256k1_gej_neg(&tmp, a); + secp256k1_gej_add_var(&tmp, &tmp, b, NULL); + return secp256k1_gej_is_infinity(&tmp); +} + +static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) { + secp256k1_fe r, r2; + VERIFY_CHECK(!a->infinity); + secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x); + r2 = a->x; secp256k1_fe_normalize_weak(&r2); + return secp256k1_fe_equal_var(&r, &r2); +} + +static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) { + r->infinity = a->infinity; + r->x = a->x; + r->y = a->y; + r->z = a->z; + secp256k1_fe_normalize_weak(&r->y); + secp256k1_fe_negate(&r->y, &r->y, 1); +} + +static int secp256k1_gej_is_infinity(const secp256k1_gej *a) { + return a->infinity; +} + +static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) { + secp256k1_fe y2, x3; + if (a->infinity) { + return 0; + } + /* y^2 = x^3 + 7 */ + secp256k1_fe_sqr(&y2, &a->y); + secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x); + secp256k1_fe_add_int(&x3, SECP256K1_B); + secp256k1_fe_normalize_weak(&x3); + return secp256k1_fe_equal_var(&y2, &x3); +} + +static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a) { + /* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */ + secp256k1_fe l, s, t; + + r->infinity = a->infinity; + + /* Formula used: + * L = (3/2) * X1^2 + * S = Y1^2 + * T = -X1*S + * X3 = L^2 + 2*T + * Y3 = -(L*(X3 + T) + S^2) + * Z3 = Y1*Z1 + */ + + secp256k1_fe_mul(&r->z, &a->z, &a->y); /* Z3 = Y1*Z1 (1) */ + secp256k1_fe_sqr(&s, &a->y); /* S = Y1^2 (1) */ + secp256k1_fe_sqr(&l, &a->x); /* L = X1^2 (1) */ + secp256k1_fe_mul_int(&l, 3); /* L = 3*X1^2 (3) */ + secp256k1_fe_half(&l); /* L = 3/2*X1^2 (2) */ + secp256k1_fe_negate(&t, &s, 1); /* T = -S (2) */ + secp256k1_fe_mul(&t, &t, &a->x); /* T = -X1*S (1) */ + secp256k1_fe_sqr(&r->x, &l); /* X3 = L^2 (1) */ + secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + T (2) */ + secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + 2*T (3) */ + secp256k1_fe_sqr(&s, &s); /* S' = S^2 (1) */ + secp256k1_fe_add(&t, &r->x); /* T' = X3 + T (4) */ + secp256k1_fe_mul(&r->y, &t, &l); /* Y3 = L*(X3 + T) (1) */ + secp256k1_fe_add(&r->y, &s); /* Y3 = L*(X3 + T) + S^2 (2) */ + secp256k1_fe_negate(&r->y, &r->y, 2); /* Y3 = -(L*(X3 + T) + S^2) (3) */ +} + +static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) { + /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity, + * Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have + * y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p. + * + * Having said this, if this function receives a point on a sextic twist, e.g. by + * a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6, + * since -6 does have a cube root mod p. For this point, this function will not set + * the infinity flag even though the point doubles to infinity, and the result + * point will be gibberish (z = 0 but infinity = 0). + */ + if (a->infinity) { + secp256k1_gej_set_infinity(r); + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + return; + } + + if (rzr != NULL) { + *rzr = a->y; + secp256k1_fe_normalize_weak(rzr); + } + + secp256k1_gej_double(r, a); +} + +static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) { + /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */ + secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t; + + if (a->infinity) { + VERIFY_CHECK(rzr == NULL); + *r = *b; + return; + } + if (b->infinity) { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + *r = *a; + return; + } + + secp256k1_fe_sqr(&z22, &b->z); + secp256k1_fe_sqr(&z12, &a->z); + secp256k1_fe_mul(&u1, &a->x, &z22); + secp256k1_fe_mul(&u2, &b->x, &z12); + secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, rzr); + } else { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 0); + } + secp256k1_gej_set_infinity(r); + } + return; + } + + r->infinity = 0; + secp256k1_fe_mul(&t, &h, &b->z); + if (rzr != NULL) { + *rzr = t; + } + secp256k1_fe_mul(&r->z, &a->z, &t); + + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_negate(&h2, &h2, 1); + secp256k1_fe_mul(&h3, &h2, &h); + secp256k1_fe_mul(&t, &u1, &h2); + + secp256k1_fe_sqr(&r->x, &i); + secp256k1_fe_add(&r->x, &h3); + secp256k1_fe_add(&r->x, &t); + secp256k1_fe_add(&r->x, &t); + + secp256k1_fe_add(&t, &r->x); + secp256k1_fe_mul(&r->y, &t, &i); + secp256k1_fe_mul(&h3, &h3, &s1); + secp256k1_fe_add(&r->y, &h3); +} + +static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) { + /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */ + secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t; + if (a->infinity) { + VERIFY_CHECK(rzr == NULL); + secp256k1_gej_set_ge(r, b); + return; + } + if (b->infinity) { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + *r = *a; + return; + } + + secp256k1_fe_sqr(&z12, &a->z); + u1 = a->x; secp256k1_fe_normalize_weak(&u1); + secp256k1_fe_mul(&u2, &b->x, &z12); + s1 = a->y; secp256k1_fe_normalize_weak(&s1); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, rzr); + } else { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 0); + } + secp256k1_gej_set_infinity(r); + } + return; + } + + r->infinity = 0; + if (rzr != NULL) { + *rzr = h; + } + secp256k1_fe_mul(&r->z, &a->z, &h); + + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_negate(&h2, &h2, 1); + secp256k1_fe_mul(&h3, &h2, &h); + secp256k1_fe_mul(&t, &u1, &h2); + + secp256k1_fe_sqr(&r->x, &i); + secp256k1_fe_add(&r->x, &h3); + secp256k1_fe_add(&r->x, &t); + secp256k1_fe_add(&r->x, &t); + + secp256k1_fe_add(&t, &r->x); + secp256k1_fe_mul(&r->y, &t, &i); + secp256k1_fe_mul(&h3, &h3, &s1); + secp256k1_fe_add(&r->y, &h3); +} + +static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) { + /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */ + secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t; + + if (a->infinity) { + secp256k1_fe bzinv2, bzinv3; + r->infinity = b->infinity; + secp256k1_fe_sqr(&bzinv2, bzinv); + secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv); + secp256k1_fe_mul(&r->x, &b->x, &bzinv2); + secp256k1_fe_mul(&r->y, &b->y, &bzinv3); + secp256k1_fe_set_int(&r->z, 1); + return; + } + if (b->infinity) { + *r = *a; + return; + } + + /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to + * secp256k1's isomorphism we can multiply the Z coordinates on both sides + * by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1). + * This means that (rx,ry,rz) can be calculated as + * (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz. + * The variable az below holds the modified Z coordinate for a, which is used + * for the computation of rx and ry, but not for rz. + */ + secp256k1_fe_mul(&az, &a->z, bzinv); + + secp256k1_fe_sqr(&z12, &az); + u1 = a->x; secp256k1_fe_normalize_weak(&u1); + secp256k1_fe_mul(&u2, &b->x, &z12); + s1 = a->y; secp256k1_fe_normalize_weak(&s1); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, NULL); + } else { + secp256k1_gej_set_infinity(r); + } + return; + } + + r->infinity = 0; + secp256k1_fe_mul(&r->z, &a->z, &h); + + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_negate(&h2, &h2, 1); + secp256k1_fe_mul(&h3, &h2, &h); + secp256k1_fe_mul(&t, &u1, &h2); + + secp256k1_fe_sqr(&r->x, &i); + secp256k1_fe_add(&r->x, &h3); + secp256k1_fe_add(&r->x, &t); + secp256k1_fe_add(&r->x, &t); + + secp256k1_fe_add(&t, &r->x); + secp256k1_fe_mul(&r->y, &t, &i); + secp256k1_fe_mul(&h3, &h3, &s1); + secp256k1_fe_add(&r->y, &h3); +} + + +static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) { + /* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */ + secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr; + secp256k1_fe m_alt, rr_alt; + int degenerate; + VERIFY_CHECK(!b->infinity); + VERIFY_CHECK(a->infinity == 0 || a->infinity == 1); + + /* In: + * Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks. + * In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002. + * we find as solution for a unified addition/doubling formula: + * lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation. + * x3 = lambda^2 - (x1 + x2) + * 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2). + * + * Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives: + * U1 = X1*Z2^2, U2 = X2*Z1^2 + * S1 = Y1*Z2^3, S2 = Y2*Z1^3 + * Z = Z1*Z2 + * T = U1+U2 + * M = S1+S2 + * Q = -T*M^2 + * R = T^2-U1*U2 + * X3 = R^2+Q + * Y3 = -(R*(2*X3+Q)+M^4)/2 + * Z3 = M*Z + * (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.) + * + * This formula has the benefit of being the same for both addition + * of distinct points and doubling. However, it breaks down in the + * case that either point is infinity, or that y1 = -y2. We handle + * these cases in the following ways: + * + * - If b is infinity we simply bail by means of a VERIFY_CHECK. + * + * - If a is infinity, we detect this, and at the end of the + * computation replace the result (which will be meaningless, + * but we compute to be constant-time) with b.x : b.y : 1. + * + * - If a = -b, we have y1 = -y2, which is a degenerate case. + * But here the answer is infinity, so we simply set the + * infinity flag of the result, overriding the computed values + * without even needing to cmov. + * + * - If y1 = -y2 but x1 != x2, which does occur thanks to certain + * properties of our curve (specifically, 1 has nontrivial cube + * roots in our field, and the curve equation has no x coefficient) + * then the answer is not infinity but also not given by the above + * equation. In this case, we cmov in place an alternate expression + * for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these + * expressions for lambda are defined, they are equal, and can be + * obtained from each other by multiplication by (y1 + y2)/(y1 + y2) + * then substitution of x^3 + 7 for y^2 (using the curve equation). + * For all pairs of nonzero points (a, b) at least one is defined, + * so this covers everything. + */ + + secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */ + u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */ + secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */ + s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */ + secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */ + secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */ + t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */ + m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */ + secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */ + secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */ + secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */ + secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */ + /* If lambda = R/M = R/0 we have a problem (except in the "trivial" + * case that Z = z1z2 = 0, and this is special-cased later on). */ + degenerate = secp256k1_fe_normalizes_to_zero(&m); + /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2. + * This means either x1 == beta*x2 or beta*x1 == x2, where beta is + * a nontrivial cube root of one. In either case, an alternate + * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2), + * so we set R/M equal to this. */ + rr_alt = s1; + secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */ + secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */ + + secp256k1_fe_cmov(&rr_alt, &rr, !degenerate); + secp256k1_fe_cmov(&m_alt, &m, !degenerate); + /* Now Ralt / Malt = lambda and is guaranteed not to be Ralt / 0. + * From here on out Ralt and Malt represent the numerator + * and denominator of lambda; R and M represent the explicit + * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */ + secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */ + secp256k1_fe_negate(&q, &t, 2); /* q = -T (3) */ + secp256k1_fe_mul(&q, &q, &n); /* q = Q = -T*Malt^2 (1) */ + /* These two lines use the observation that either M == Malt or M == 0, + * so M^3 * Malt is either Malt^4 (which is computed by squaring), or + * zero (which is "computed" by cmov). So the cost is one squaring + * versus two multiplications. */ + secp256k1_fe_sqr(&n, &n); + secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */ + secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */ + secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Z3 = Malt*Z (1) */ + secp256k1_fe_add(&t, &q); /* t = Ralt^2 + Q (2) */ + r->x = t; /* r->x = X3 = Ralt^2 + Q (2) */ + secp256k1_fe_mul_int(&t, 2); /* t = 2*X3 (4) */ + secp256k1_fe_add(&t, &q); /* t = 2*X3 + Q (5) */ + secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*X3 + Q) (1) */ + secp256k1_fe_add(&t, &n); /* t = Ralt*(2*X3 + Q) + M^3*Malt (3) */ + secp256k1_fe_negate(&r->y, &t, 3); /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */ + secp256k1_fe_half(&r->y); /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */ + + /* In case a->infinity == 1, replace r with (b->x, b->y, 1). */ + secp256k1_fe_cmov(&r->x, &b->x, a->infinity); + secp256k1_fe_cmov(&r->y, &b->y, a->infinity); + secp256k1_fe_cmov(&r->z, &secp256k1_fe_one, a->infinity); + + /* Set r->infinity if r->z is 0. + * + * If a->infinity is set, then r->infinity = (r->z == 0) = (1 == 0) = false, + * which is correct because the function assumes that b is not infinity. + * + * Now assume !a->infinity. This implies Z = Z1 != 0. + * + * Case y1 = -y2: + * In this case we could have a = -b, namely if x1 = x2. + * We have degenerate = true, r->z = (x1 - x2) * Z. + * Then r->infinity = ((x1 - x2)Z == 0) = (x1 == x2) = (a == -b). + * + * Case y1 != -y2: + * In this case, we can't have a = -b. + * We have degenerate = false, r->z = (y1 + y2) * Z. + * Then r->infinity = ((y1 + y2)Z == 0) = (y1 == -y2) = false. */ + r->infinity = secp256k1_fe_normalizes_to_zero(&r->z); +} + +static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) { + /* Operations: 4 mul, 1 sqr */ + secp256k1_fe zz; + VERIFY_CHECK(!secp256k1_fe_is_zero(s)); + secp256k1_fe_sqr(&zz, s); + secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */ + secp256k1_fe_mul(&r->y, &r->y, &zz); + secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */ + secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */ +} + +static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) { + secp256k1_fe x, y; + VERIFY_CHECK(!a->infinity); + x = a->x; + secp256k1_fe_normalize(&x); + y = a->y; + secp256k1_fe_normalize(&y); + secp256k1_fe_to_storage(&r->x, &x); + secp256k1_fe_to_storage(&r->y, &y); +} + +static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) { + secp256k1_fe_from_storage(&r->x, &a->x); + secp256k1_fe_from_storage(&r->y, &a->y); + r->infinity = 0; +} + +static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) { + secp256k1_fe_cmov(&r->x, &a->x, flag); + secp256k1_fe_cmov(&r->y, &a->y, flag); + secp256k1_fe_cmov(&r->z, &a->z, flag); + + r->infinity ^= (r->infinity ^ a->infinity) & flag; +} + +static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) { + secp256k1_fe_storage_cmov(&r->x, &a->x, flag); + secp256k1_fe_storage_cmov(&r->y, &a->y, flag); +} + +static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) { + *r = *a; + secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta); +} + +static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) { +#ifdef EXHAUSTIVE_TEST_ORDER + secp256k1_gej out; + int i; + + /* A very simple EC multiplication ladder that avoids a dependency on ecmult. */ + secp256k1_gej_set_infinity(&out); + for (i = 0; i < 32; ++i) { + secp256k1_gej_double_var(&out, &out, NULL); + if ((((uint32_t)EXHAUSTIVE_TEST_ORDER) >> (31 - i)) & 1) { + secp256k1_gej_add_ge_var(&out, &out, ge, NULL); + } + } + return secp256k1_gej_is_infinity(&out); +#else + (void)ge; + /* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */ + return 1; +#endif +} + +#endif /* SECP256K1_GROUP_IMPL_H */ diff --git a/src/secp256k1/src/hash.h b/src/secp256k1/src/hash.h new file mode 100644 index 0000000000..4e0384cfbf --- /dev/null +++ b/src/secp256k1/src/hash.h @@ -0,0 +1,41 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_HASH_H +#define SECP256K1_HASH_H + +#include <stdlib.h> +#include <stdint.h> + +typedef struct { + uint32_t s[8]; + unsigned char buf[64]; + uint64_t bytes; +} secp256k1_sha256; + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash); +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32); + +typedef struct { + secp256k1_sha256 inner, outer; +} secp256k1_hmac_sha256; + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size); +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32); + +typedef struct { + unsigned char v[32]; + unsigned char k[32]; + int retry; +} secp256k1_rfc6979_hmac_sha256; + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen); +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen); +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng); + +#endif /* SECP256K1_HASH_H */ diff --git a/src/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h new file mode 100644 index 0000000000..0991fe7838 --- /dev/null +++ b/src/secp256k1/src/hash_impl.h @@ -0,0 +1,290 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_HASH_IMPL_H +#define SECP256K1_HASH_IMPL_H + +#include "hash.h" +#include "util.h" + +#include <stdlib.h> +#include <stdint.h> +#include <string.h> + +#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z)))) +#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y)))) +#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10)) +#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7)) +#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3)) +#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10)) + +#define Round(a,b,c,d,e,f,g,h,k,w) do { \ + uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \ + uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \ + (d) += t1; \ + (h) = t1 + t2; \ +} while(0) + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) { + hash->s[0] = 0x6a09e667ul; + hash->s[1] = 0xbb67ae85ul; + hash->s[2] = 0x3c6ef372ul; + hash->s[3] = 0xa54ff53aul; + hash->s[4] = 0x510e527ful; + hash->s[5] = 0x9b05688cul; + hash->s[6] = 0x1f83d9abul; + hash->s[7] = 0x5be0cd19ul; + hash->bytes = 0; +} + +/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */ +static void secp256k1_sha256_transform(uint32_t* s, const unsigned char* buf) { + uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7]; + uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15; + + Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = secp256k1_read_be32(&buf[0])); + Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = secp256k1_read_be32(&buf[4])); + Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = secp256k1_read_be32(&buf[8])); + Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = secp256k1_read_be32(&buf[12])); + Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = secp256k1_read_be32(&buf[16])); + Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = secp256k1_read_be32(&buf[20])); + Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = secp256k1_read_be32(&buf[24])); + Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = secp256k1_read_be32(&buf[28])); + Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = secp256k1_read_be32(&buf[32])); + Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = secp256k1_read_be32(&buf[36])); + Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = secp256k1_read_be32(&buf[40])); + Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = secp256k1_read_be32(&buf[44])); + Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = secp256k1_read_be32(&buf[48])); + Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = secp256k1_read_be32(&buf[52])); + Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = secp256k1_read_be32(&buf[56])); + Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = secp256k1_read_be32(&buf[60])); + + Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0)); + + s[0] += a; + s[1] += b; + s[2] += c; + s[3] += d; + s[4] += e; + s[5] += f; + s[6] += g; + s[7] += h; +} + +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t len) { + size_t bufsize = hash->bytes & 0x3F; + hash->bytes += len; + VERIFY_CHECK(hash->bytes >= len); + while (len >= 64 - bufsize) { + /* Fill the buffer, and process it. */ + size_t chunk_len = 64 - bufsize; + memcpy(hash->buf + bufsize, data, chunk_len); + data += chunk_len; + len -= chunk_len; + secp256k1_sha256_transform(hash->s, hash->buf); + bufsize = 0; + } + if (len) { + /* Fill the buffer with what remains. */ + memcpy(((unsigned char*)hash->buf) + bufsize, data, len); + } +} + +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) { + static const unsigned char pad[64] = {0x80}; + unsigned char sizedesc[8]; + int i; + /* The maximum message size of SHA256 is 2^64-1 bits. */ + VERIFY_CHECK(hash->bytes < ((uint64_t)1 << 61)); + secp256k1_write_be32(&sizedesc[0], hash->bytes >> 29); + secp256k1_write_be32(&sizedesc[4], hash->bytes << 3); + secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64)); + secp256k1_sha256_write(hash, sizedesc, 8); + for (i = 0; i < 8; i++) { + secp256k1_write_be32(&out32[4*i], hash->s[i]); + hash->s[i] = 0; + } +} + +/* Initializes a sha256 struct and writes the 64 byte string + * SHA256(tag)||SHA256(tag) into it. */ +static void secp256k1_sha256_initialize_tagged(secp256k1_sha256 *hash, const unsigned char *tag, size_t taglen) { + unsigned char buf[32]; + secp256k1_sha256_initialize(hash); + secp256k1_sha256_write(hash, tag, taglen); + secp256k1_sha256_finalize(hash, buf); + + secp256k1_sha256_initialize(hash); + secp256k1_sha256_write(hash, buf, 32); + secp256k1_sha256_write(hash, buf, 32); +} + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) { + size_t n; + unsigned char rkey[64]; + if (keylen <= sizeof(rkey)) { + memcpy(rkey, key, keylen); + memset(rkey + keylen, 0, sizeof(rkey) - keylen); + } else { + secp256k1_sha256 sha256; + secp256k1_sha256_initialize(&sha256); + secp256k1_sha256_write(&sha256, key, keylen); + secp256k1_sha256_finalize(&sha256, rkey); + memset(rkey + 32, 0, 32); + } + + secp256k1_sha256_initialize(&hash->outer); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c; + } + secp256k1_sha256_write(&hash->outer, rkey, sizeof(rkey)); + + secp256k1_sha256_initialize(&hash->inner); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c ^ 0x36; + } + secp256k1_sha256_write(&hash->inner, rkey, sizeof(rkey)); + memset(rkey, 0, sizeof(rkey)); +} + +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) { + secp256k1_sha256_write(&hash->inner, data, size); +} + +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32) { + unsigned char temp[32]; + secp256k1_sha256_finalize(&hash->inner, temp); + secp256k1_sha256_write(&hash->outer, temp, 32); + memset(temp, 0, 32); + secp256k1_sha256_finalize(&hash->outer, out32); +} + + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) { + secp256k1_hmac_sha256 hmac; + static const unsigned char zero[1] = {0x00}; + static const unsigned char one[1] = {0x01}; + + memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */ + memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */ + + /* RFC6979 3.2.d. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + + /* RFC6979 3.2.f. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, one, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + rng->retry = 0; +} + +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) { + /* RFC6979 3.2.h. */ + static const unsigned char zero[1] = {0x00}; + if (rng->retry) { + secp256k1_hmac_sha256 hmac; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + } + + while (outlen > 0) { + secp256k1_hmac_sha256 hmac; + int now = outlen; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + if (now > 32) { + now = 32; + } + memcpy(out, rng->v, now); + out += now; + outlen -= now; + } + + rng->retry = 1; +} + +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng) { + memset(rng->k, 0, 32); + memset(rng->v, 0, 32); + rng->retry = 0; +} + +#undef Round +#undef sigma1 +#undef sigma0 +#undef Sigma1 +#undef Sigma0 +#undef Maj +#undef Ch + +#endif /* SECP256K1_HASH_IMPL_H */ diff --git a/src/secp256k1/src/int128.h b/src/secp256k1/src/int128.h new file mode 100644 index 0000000000..5355fbfae0 --- /dev/null +++ b/src/secp256k1/src/int128.h @@ -0,0 +1,90 @@ +#ifndef SECP256K1_INT128_H +#define SECP256K1_INT128_H + +#include "util.h" + +#if defined(SECP256K1_WIDEMUL_INT128) +# if defined(SECP256K1_INT128_NATIVE) +# include "int128_native.h" +# elif defined(SECP256K1_INT128_STRUCT) +# include "int128_struct.h" +# else +# error "Please select int128 implementation" +# endif + +/* Construct an unsigned 128-bit value from a high and a low 64-bit value. */ +static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo); + +/* Multiply two unsigned 64-bit values a and b and write the result to r. */ +static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b); + +/* Multiply two unsigned 64-bit values a and b and add the result to r. + * The final result is taken modulo 2^128. + */ +static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b); + +/* Add an unsigned 64-bit value a to r. + * The final result is taken modulo 2^128. + */ +static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a); + +/* Unsigned (logical) right shift. + * Non-constant time in n. + */ +static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n); + +/* Return the low 64-bits of a 128-bit value as an unsigned 64-bit value. */ +static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a); + +/* Return the high 64-bits of a 128-bit value as an unsigned 64-bit value. */ +static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a); + +/* Write an unsigned 64-bit value to r. */ +static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a); + +/* Tests if r is strictly less than to 2^n. + * n must be strictly less than 128. + */ +static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n); + +/* Construct an signed 128-bit value from a high and a low 64-bit value. */ +static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo); + +/* Multiply two signed 64-bit values a and b and write the result to r. */ +static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b); + +/* Multiply two signed 64-bit values a and b and add the result to r. + * Overflow or underflow from the addition is undefined behaviour. + */ +static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b); + +/* Compute a*d - b*c from signed 64-bit values and write the result to r. */ +static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d); + +/* Signed (arithmetic) right shift. + * Non-constant time in b. + */ +static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int b); + +/* Return the input value modulo 2^64. */ +static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a); + +/* Return the value as a signed 64-bit value. + * Requires the input to be between INT64_MIN and INT64_MAX. + */ +static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a); + +/* Write a signed 64-bit value to r. */ +static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a); + +/* Compare two 128-bit values for equality. */ +static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b); + +/* Tests if r is equal to sign*2^n (sign must be 1 or -1). + * n must be strictly less than 127. + */ +static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign); + +#endif + +#endif diff --git a/src/secp256k1/src/int128_impl.h b/src/secp256k1/src/int128_impl.h new file mode 100644 index 0000000000..cfc573408a --- /dev/null +++ b/src/secp256k1/src/int128_impl.h @@ -0,0 +1,18 @@ +#ifndef SECP256K1_INT128_IMPL_H +#define SECP256K1_INT128_IMPL_H + +#include "util.h" + +#include "int128.h" + +#if defined(SECP256K1_WIDEMUL_INT128) +# if defined(SECP256K1_INT128_NATIVE) +# include "int128_native_impl.h" +# elif defined(SECP256K1_INT128_STRUCT) +# include "int128_struct_impl.h" +# else +# error "Please select int128 implementation" +# endif +#endif + +#endif diff --git a/src/secp256k1/src/int128_native.h b/src/secp256k1/src/int128_native.h new file mode 100644 index 0000000000..7c97aafc74 --- /dev/null +++ b/src/secp256k1/src/int128_native.h @@ -0,0 +1,19 @@ +#ifndef SECP256K1_INT128_NATIVE_H +#define SECP256K1_INT128_NATIVE_H + +#include <stdint.h> +#include "util.h" + +#if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__) +SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; +SECP256K1_GNUC_EXT typedef __int128 int128_t; +# define UINT128_MAX ((uint128_t)(-1)) +# define INT128_MAX ((int128_t)(UINT128_MAX >> 1)) +# define INT128_MIN (-INT128_MAX - 1) +/* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals. */ +#endif + +typedef uint128_t secp256k1_uint128; +typedef int128_t secp256k1_int128; + +#endif diff --git a/src/secp256k1/src/int128_native_impl.h b/src/secp256k1/src/int128_native_impl.h new file mode 100644 index 0000000000..996e542cf9 --- /dev/null +++ b/src/secp256k1/src/int128_native_impl.h @@ -0,0 +1,93 @@ +#ifndef SECP256K1_INT128_NATIVE_IMPL_H +#define SECP256K1_INT128_NATIVE_IMPL_H + +#include "int128.h" + +static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) { + *r = (((uint128_t)hi) << 64) + lo; +} + +static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { + *r = (uint128_t)a * b; +} + +static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { + *r += (uint128_t)a * b; +} + +static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) { + *r += a; +} + +static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + *r >>= n; +} + +static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) { + return (uint64_t)(*a); +} + +static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) { + return (uint64_t)(*a >> 64); +} + +static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) { + *r = a; +} + +static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + return (*r >> n == 0); +} + +static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) { + *r = (((uint128_t)(uint64_t)hi) << 64) + lo; +} + +static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) { + *r = (int128_t)a * b; +} + +static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) { + int128_t ab = (int128_t)a * b; + VERIFY_CHECK(0 <= ab ? *r <= INT128_MAX - ab : INT128_MIN - ab <= *r); + *r += ab; +} + +static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) { + int128_t ad = (int128_t)a * d; + int128_t bc = (int128_t)b * c; + VERIFY_CHECK(0 <= bc ? INT128_MIN + bc <= ad : ad <= INT128_MAX + bc); + *r = ad - bc; +} + +static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + *r >>= n; +} + +static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) { + return (uint64_t)*a; +} + +static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) { + VERIFY_CHECK(INT64_MIN <= *a && *a <= INT64_MAX); + return *a; +} + +static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) { + *r = a; +} + +static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) { + return *a == *b; +} + +static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) { + VERIFY_CHECK(n < 127); + VERIFY_CHECK(sign == 1 || sign == -1); + return (*r == (int128_t)((uint128_t)sign << n)); +} + +#endif diff --git a/src/secp256k1/src/int128_struct.h b/src/secp256k1/src/int128_struct.h new file mode 100644 index 0000000000..6156f82cc2 --- /dev/null +++ b/src/secp256k1/src/int128_struct.h @@ -0,0 +1,14 @@ +#ifndef SECP256K1_INT128_STRUCT_H +#define SECP256K1_INT128_STRUCT_H + +#include <stdint.h> +#include "util.h" + +typedef struct { + uint64_t lo; + uint64_t hi; +} secp256k1_uint128; + +typedef secp256k1_uint128 secp256k1_int128; + +#endif diff --git a/src/secp256k1/src/int128_struct_impl.h b/src/secp256k1/src/int128_struct_impl.h new file mode 100644 index 0000000000..cc17bad167 --- /dev/null +++ b/src/secp256k1/src/int128_struct_impl.h @@ -0,0 +1,199 @@ +#ifndef SECP256K1_INT128_STRUCT_IMPL_H +#define SECP256K1_INT128_STRUCT_IMPL_H + +#include "int128.h" + +#if defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* MSVC */ +# include <intrin.h> +# if defined(_M_ARM64) || defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE) +/* On ARM64 MSVC, use __(u)mulh for the upper half of 64x64 multiplications. + (Define SECP256K1_MSVC_MULH_TEST_OVERRIDE to test this code path on X64, + which supports both __(u)mulh and _umul128.) */ +# if defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE) +# pragma message(__FILE__ ": SECP256K1_MSVC_MULH_TEST_OVERRIDE is defined, forcing use of __(u)mulh.") +# endif +static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) { + *hi = __umulh(a, b); + return a * b; +} + +static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) { + *hi = __mulh(a, b); + return (uint64_t)a * (uint64_t)b; +} +# else +/* On x84_64 MSVC, use native _(u)mul128 for 64x64->128 multiplications. */ +# define secp256k1_umul128 _umul128 +# define secp256k1_mul128 _mul128 +# endif +#else +/* On other systems, emulate 64x64->128 multiplications using 32x32->64 multiplications. */ +static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) { + uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b; + uint64_t lh = (uint32_t)a * (b >> 32); + uint64_t hl = (a >> 32) * (uint32_t)b; + uint64_t hh = (a >> 32) * (b >> 32); + uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl; + *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32); + return (mid34 << 32) + (uint32_t)ll; +} + +static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) { + uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b; + int64_t lh = (uint32_t)a * (b >> 32); + int64_t hl = (a >> 32) * (uint32_t)b; + int64_t hh = (a >> 32) * (b >> 32); + uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl; + *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32); + return (mid34 << 32) + (uint32_t)ll; +} +#endif + +static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) { + r->hi = hi; + r->lo = lo; +} + +static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { + r->lo = secp256k1_umul128(a, b, &r->hi); +} + +static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { + uint64_t lo, hi; + lo = secp256k1_umul128(a, b, &hi); + r->lo += lo; + r->hi += hi + (r->lo < lo); +} + +static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) { + r->lo += a; + r->hi += r->lo < a; +} + +/* Unsigned (logical) right shift. + * Non-constant time in n. + */ +static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + if (n >= 64) { + r->lo = r->hi >> (n-64); + r->hi = 0; + } else if (n > 0) { + r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n; + r->hi >>= n; + } +} + +static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) { + return a->lo; +} + +static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) { + return a->hi; +} + +static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) { + r->hi = 0; + r->lo = a; +} + +static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + return n >= 64 ? r->hi >> (n - 64) == 0 + : r->hi == 0 && r->lo >> n == 0; +} + +static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) { + r->hi = hi; + r->lo = lo; +} + +static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) { + int64_t hi; + r->lo = (uint64_t)secp256k1_mul128(a, b, &hi); + r->hi = (uint64_t)hi; +} + +static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) { + int64_t hi; + uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi); + r->lo += lo; + hi += r->lo < lo; + /* Verify no overflow. + * If r represents a positive value (the sign bit is not set) and the value we are adding is a positive value (the sign bit is not set), + * then we require that the resulting value also be positive (the sign bit is not set). + * Note that (X <= Y) means (X implies Y) when X and Y are boolean values (i.e. 0 or 1). + */ + VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi <= 0x7fffffffffffffffu)); + /* Verify no underflow. + * If r represents a negative value (the sign bit is set) and the value we are adding is a negative value (the sign bit is set), + * then we require that the resulting value also be negative (the sign bit is set). + */ + VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi > 0x7fffffffffffffffu)); + r->hi += hi; +} + +static SECP256K1_INLINE void secp256k1_i128_dissip_mul(secp256k1_int128 *r, int64_t a, int64_t b) { + int64_t hi; + uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi); + hi += r->lo < lo; + /* Verify no overflow. + * If r represents a positive value (the sign bit is not set) and the value we are subtracting is a negative value (the sign bit is set), + * then we require that the resulting value also be positive (the sign bit is not set). + */ + VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi <= 0x7fffffffffffffffu)); + /* Verify no underflow. + * If r represents a negative value (the sign bit is set) and the value we are subtracting is a positive value (the sign sign bit is not set), + * then we require that the resulting value also be negative (the sign bit is set). + */ + VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi > 0x7fffffffffffffffu)); + r->hi -= hi; + r->lo -= lo; +} + +static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) { + secp256k1_i128_mul(r, a, d); + secp256k1_i128_dissip_mul(r, b, c); +} + +/* Signed (arithmetic) right shift. + * Non-constant time in n. + */ +static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) { + VERIFY_CHECK(n < 128); + if (n >= 64) { + r->lo = (uint64_t)((int64_t)(r->hi) >> (n-64)); + r->hi = (uint64_t)((int64_t)(r->hi) >> 63); + } else if (n > 0) { + r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n; + r->hi = (uint64_t)((int64_t)(r->hi) >> n); + } +} + +static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) { + return a->lo; +} + +static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) { + /* Verify that a represents a 64 bit signed value by checking that the high bits are a sign extension of the low bits. */ + VERIFY_CHECK(a->hi == -(a->lo >> 63)); + return (int64_t)secp256k1_i128_to_u64(a); +} + +static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) { + r->hi = (uint64_t)(a >> 63); + r->lo = (uint64_t)a; +} + +static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) { + return a->hi == b->hi && a->lo == b->lo; +} + +static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) { + VERIFY_CHECK(n < 127); + VERIFY_CHECK(sign == 1 || sign == -1); + return n >= 64 ? r->hi == (uint64_t)sign << (n - 64) && r->lo == 0 + : r->hi == (uint64_t)(sign >> 1) && r->lo == (uint64_t)sign << n; +} + +#endif diff --git a/src/secp256k1/src/modinv32.h b/src/secp256k1/src/modinv32.h new file mode 100644 index 0000000000..846c642f8c --- /dev/null +++ b/src/secp256k1/src/modinv32.h @@ -0,0 +1,43 @@ +/*********************************************************************** + * Copyright (c) 2020 Peter Dettman * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODINV32_H +#define SECP256K1_MODINV32_H + +#include "util.h" + +/* A signed 30-bit limb representation of integers. + * + * Its value is sum(v[i] * 2^(30*i), i=0..8). */ +typedef struct { + int32_t v[9]; +} secp256k1_modinv32_signed30; + +typedef struct { + /* The modulus in signed30 notation, must be odd and in [3, 2^256]. */ + secp256k1_modinv32_signed30 modulus; + + /* modulus^{-1} mod 2^30 */ + uint32_t modulus_inv30; +} secp256k1_modinv32_modinfo; + +/* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus). + * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of + * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime. + * + * On output, all of x's limbs will be in [0, 2^30). + */ +static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo); + +/* Same as secp256k1_modinv32_var, but constant time in x (not in the modulus). */ +static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo); + +/* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus + * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result + * cannot be computed. */ +static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo); + +#endif /* SECP256K1_MODINV32_H */ diff --git a/src/secp256k1/src/modinv32_impl.h b/src/secp256k1/src/modinv32_impl.h new file mode 100644 index 0000000000..8e400b697b --- /dev/null +++ b/src/secp256k1/src/modinv32_impl.h @@ -0,0 +1,735 @@ +/*********************************************************************** + * Copyright (c) 2020 Peter Dettman * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODINV32_IMPL_H +#define SECP256K1_MODINV32_IMPL_H + +#include "modinv32.h" + +#include "util.h" + +#include <stdlib.h> + +/* This file implements modular inversion based on the paper "Fast constant-time gcd computation and + * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang. + * + * For an explanation of the algorithm, see doc/safegcd_implementation.md. This file contains an + * implementation for N=30, using 30-bit signed limbs represented as int32_t. + */ + +#ifdef VERIFY +static const secp256k1_modinv32_signed30 SECP256K1_SIGNED30_ONE = {{1}}; + +/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^30). */ +static void secp256k1_modinv32_mul_30(secp256k1_modinv32_signed30 *r, const secp256k1_modinv32_signed30 *a, int alen, int32_t factor) { + const int32_t M30 = (int32_t)(UINT32_MAX >> 2); + int64_t c = 0; + int i; + for (i = 0; i < 8; ++i) { + if (i < alen) c += (int64_t)a->v[i] * factor; + r->v[i] = (int32_t)c & M30; c >>= 30; + } + if (8 < alen) c += (int64_t)a->v[8] * factor; + VERIFY_CHECK(c == (int32_t)c); + r->v[8] = (int32_t)c; +} + +/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. A consists of alen limbs; b has 9. */ +static int secp256k1_modinv32_mul_cmp_30(const secp256k1_modinv32_signed30 *a, int alen, const secp256k1_modinv32_signed30 *b, int32_t factor) { + int i; + secp256k1_modinv32_signed30 am, bm; + secp256k1_modinv32_mul_30(&am, a, alen, 1); /* Normalize all but the top limb of a. */ + secp256k1_modinv32_mul_30(&bm, b, 9, factor); + for (i = 0; i < 8; ++i) { + /* Verify that all but the top limb of a and b are normalized. */ + VERIFY_CHECK(am.v[i] >> 30 == 0); + VERIFY_CHECK(bm.v[i] >> 30 == 0); + } + for (i = 8; i >= 0; --i) { + if (am.v[i] < bm.v[i]) return -1; + if (am.v[i] > bm.v[i]) return 1; + } + return 0; +} +#endif + +/* Take as input a signed30 number in range (-2*modulus,modulus), and add a multiple of the modulus + * to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the + * process. The input must have limbs in range (-2^30,2^30). The output will have limbs in range + * [0,2^30). */ +static void secp256k1_modinv32_normalize_30(secp256k1_modinv32_signed30 *r, int32_t sign, const secp256k1_modinv32_modinfo *modinfo) { + const int32_t M30 = (int32_t)(UINT32_MAX >> 2); + int32_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4], + r5 = r->v[5], r6 = r->v[6], r7 = r->v[7], r8 = r->v[8]; + int32_t cond_add, cond_negate; + +#ifdef VERIFY + /* Verify that all limbs are in range (-2^30,2^30). */ + int i; + for (i = 0; i < 9; ++i) { + VERIFY_CHECK(r->v[i] >= -M30); + VERIFY_CHECK(r->v[i] <= M30); + } + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, -2) > 0); /* r > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 1) < 0); /* r < modulus */ +#endif + + /* In a first step, add the modulus if the input is negative, and then negate if requested. + * This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input + * limbs are in range (-2^30,2^30), this cannot overflow an int32_t. Note that the right + * shifts below are signed sign-extending shifts (see assumptions.h for tests that that is + * indeed the behavior of the right shift operator). */ + cond_add = r8 >> 31; + r0 += modinfo->modulus.v[0] & cond_add; + r1 += modinfo->modulus.v[1] & cond_add; + r2 += modinfo->modulus.v[2] & cond_add; + r3 += modinfo->modulus.v[3] & cond_add; + r4 += modinfo->modulus.v[4] & cond_add; + r5 += modinfo->modulus.v[5] & cond_add; + r6 += modinfo->modulus.v[6] & cond_add; + r7 += modinfo->modulus.v[7] & cond_add; + r8 += modinfo->modulus.v[8] & cond_add; + cond_negate = sign >> 31; + r0 = (r0 ^ cond_negate) - cond_negate; + r1 = (r1 ^ cond_negate) - cond_negate; + r2 = (r2 ^ cond_negate) - cond_negate; + r3 = (r3 ^ cond_negate) - cond_negate; + r4 = (r4 ^ cond_negate) - cond_negate; + r5 = (r5 ^ cond_negate) - cond_negate; + r6 = (r6 ^ cond_negate) - cond_negate; + r7 = (r7 ^ cond_negate) - cond_negate; + r8 = (r8 ^ cond_negate) - cond_negate; + /* Propagate the top bits, to bring limbs back to range (-2^30,2^30). */ + r1 += r0 >> 30; r0 &= M30; + r2 += r1 >> 30; r1 &= M30; + r3 += r2 >> 30; r2 &= M30; + r4 += r3 >> 30; r3 &= M30; + r5 += r4 >> 30; r4 &= M30; + r6 += r5 >> 30; r5 &= M30; + r7 += r6 >> 30; r6 &= M30; + r8 += r7 >> 30; r7 &= M30; + + /* In a second step add the modulus again if the result is still negative, bringing r to range + * [0,modulus). */ + cond_add = r8 >> 31; + r0 += modinfo->modulus.v[0] & cond_add; + r1 += modinfo->modulus.v[1] & cond_add; + r2 += modinfo->modulus.v[2] & cond_add; + r3 += modinfo->modulus.v[3] & cond_add; + r4 += modinfo->modulus.v[4] & cond_add; + r5 += modinfo->modulus.v[5] & cond_add; + r6 += modinfo->modulus.v[6] & cond_add; + r7 += modinfo->modulus.v[7] & cond_add; + r8 += modinfo->modulus.v[8] & cond_add; + /* And propagate again. */ + r1 += r0 >> 30; r0 &= M30; + r2 += r1 >> 30; r1 &= M30; + r3 += r2 >> 30; r2 &= M30; + r4 += r3 >> 30; r3 &= M30; + r5 += r4 >> 30; r4 &= M30; + r6 += r5 >> 30; r5 &= M30; + r7 += r6 >> 30; r6 &= M30; + r8 += r7 >> 30; r7 &= M30; + + r->v[0] = r0; + r->v[1] = r1; + r->v[2] = r2; + r->v[3] = r3; + r->v[4] = r4; + r->v[5] = r5; + r->v[6] = r6; + r->v[7] = r7; + r->v[8] = r8; + +#ifdef VERIFY + VERIFY_CHECK(r0 >> 30 == 0); + VERIFY_CHECK(r1 >> 30 == 0); + VERIFY_CHECK(r2 >> 30 == 0); + VERIFY_CHECK(r3 >> 30 == 0); + VERIFY_CHECK(r4 >> 30 == 0); + VERIFY_CHECK(r5 >> 30 == 0); + VERIFY_CHECK(r6 >> 30 == 0); + VERIFY_CHECK(r7 >> 30 == 0); + VERIFY_CHECK(r8 >> 30 == 0); + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 0) >= 0); /* r >= 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 1) < 0); /* r < modulus */ +#endif +} + +/* Data type for transition matrices (see section 3 of explanation). + * + * t = [ u v ] + * [ q r ] + */ +typedef struct { + int32_t u, v, q, r; +} secp256k1_modinv32_trans2x2; + +/* Compute the transition matrix and zeta for 30 divsteps. + * + * Input: zeta: initial zeta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final zeta + * + * Implements the divsteps_n_matrix function from the explanation. + */ +static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t) { + /* u,v,q,r are the elements of the transformation matrix being built up, + * starting with the identity matrix. Semantically they are signed integers + * in range [-2^30,2^30], but here represented as unsigned mod 2^32. This + * permits left shifting (which is UB for negative numbers). The range + * being inside [-2^31,2^31) means that casting to signed works correctly. + */ + uint32_t u = 1, v = 0, q = 0, r = 1; + uint32_t c1, c2, f = f0, g = g0, x, y, z; + int i; + + for (i = 0; i < 30; ++i) { + VERIFY_CHECK((f & 1) == 1); /* f must always be odd */ + VERIFY_CHECK((u * f0 + v * g0) == f << i); + VERIFY_CHECK((q * f0 + r * g0) == g << i); + /* Compute conditional masks for (zeta < 0) and for (g & 1). */ + c1 = zeta >> 31; + c2 = -(g & 1); + /* Compute x,y,z, conditionally negated versions of f,u,v. */ + x = (f ^ c1) - c1; + y = (u ^ c1) - c1; + z = (v ^ c1) - c1; + /* Conditionally add x,y,z to g,q,r. */ + g += x & c2; + q += y & c2; + r += z & c2; + /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */ + c1 &= c2; + /* Conditionally change zeta into -zeta-2 or zeta-1. */ + zeta = (zeta ^ c1) - 1; + /* Conditionally add g,q,r to f,u,v. */ + f += g & c1; + u += q & c1; + v += r & c1; + /* Shifts */ + g >>= 1; + u <<= 1; + v <<= 1; + /* Bounds on zeta that follow from the bounds on iteration count (max 20*30 divsteps). */ + VERIFY_CHECK(zeta >= -601 && zeta <= 601); + } + /* Return data in t and return value. */ + t->u = (int32_t)u; + t->v = (int32_t)v; + t->q = (int32_t)q; + t->r = (int32_t)r; + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2, the + * aggregate of 30 of them will have determinant 2^30. */ + VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30); + return zeta; +} + +/* secp256k1_modinv32_inv256[i] = -(2*i+1)^-1 (mod 256) */ +static const uint8_t secp256k1_modinv32_inv256[128] = { + 0xFF, 0x55, 0x33, 0x49, 0xC7, 0x5D, 0x3B, 0x11, 0x0F, 0xE5, 0xC3, 0x59, + 0xD7, 0xED, 0xCB, 0x21, 0x1F, 0x75, 0x53, 0x69, 0xE7, 0x7D, 0x5B, 0x31, + 0x2F, 0x05, 0xE3, 0x79, 0xF7, 0x0D, 0xEB, 0x41, 0x3F, 0x95, 0x73, 0x89, + 0x07, 0x9D, 0x7B, 0x51, 0x4F, 0x25, 0x03, 0x99, 0x17, 0x2D, 0x0B, 0x61, + 0x5F, 0xB5, 0x93, 0xA9, 0x27, 0xBD, 0x9B, 0x71, 0x6F, 0x45, 0x23, 0xB9, + 0x37, 0x4D, 0x2B, 0x81, 0x7F, 0xD5, 0xB3, 0xC9, 0x47, 0xDD, 0xBB, 0x91, + 0x8F, 0x65, 0x43, 0xD9, 0x57, 0x6D, 0x4B, 0xA1, 0x9F, 0xF5, 0xD3, 0xE9, + 0x67, 0xFD, 0xDB, 0xB1, 0xAF, 0x85, 0x63, 0xF9, 0x77, 0x8D, 0x6B, 0xC1, + 0xBF, 0x15, 0xF3, 0x09, 0x87, 0x1D, 0xFB, 0xD1, 0xCF, 0xA5, 0x83, 0x19, + 0x97, 0xAD, 0x8B, 0xE1, 0xDF, 0x35, 0x13, 0x29, 0xA7, 0x3D, 0x1B, 0xF1, + 0xEF, 0xC5, 0xA3, 0x39, 0xB7, 0xCD, 0xAB, 0x01 +}; + +/* Compute the transition matrix and eta for 30 divsteps (variable time). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final eta + * + * Implements the divsteps_n_matrix_var function from the explanation. + */ +static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t) { + /* Transformation matrix; see comments in secp256k1_modinv32_divsteps_30. */ + uint32_t u = 1, v = 0, q = 0, r = 1; + uint32_t f = f0, g = g0, m; + uint16_t w; + int i = 30, limit, zeros; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz32_var(g | (UINT32_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* We're done once we've done 30 divsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i)); + /* Bounds on eta that follow from the bounds on iteration count (max 25*30 divsteps). */ + VERIFY_CHECK(eta >= -751 && eta <= 751); + /* If eta is negative, negate it and replace f,g with g,-f. */ + if (eta < 0) { + uint32_t tmp; + eta = -eta; + tmp = f; f = g; g = -tmp; + tmp = u; u = q; q = -tmp; + tmp = v; v = r; r = -tmp; + } + /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more + * than i can be cancelled out (as we'd be done before that point), and no more than eta+1 + * can be done as its sign will flip once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */ + VERIFY_CHECK(limit > 0 && limit <= 30); + m = (UINT32_MAX >> (32 - limit)) & 255U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */ + w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m; + /* Do so. */ + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int32_t)u; + t->v = (int32_t)v; + t->q = (int32_t)q; + t->r = (int32_t)r; + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2, the + * aggregate of 30 of them will have determinant 2^30. */ + VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30); + return eta; +} + +/* Compute the transition matrix and eta for 30 posdivsteps (variable time, eta=-delta), and keeps track + * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^32 rather than 2^30, because + * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Input/Output: (*jacp & 1) is bitflipped if and only if the Jacobi symbol of (f | g) changes sign + * by applying the returned transformation matrix to it. The other bits of *jacp may + * change, but are meaningless. + * Return: final eta + */ +static int32_t secp256k1_modinv32_posdivsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t, int *jacp) { + /* Transformation matrix. */ + uint32_t u = 1, v = 0, q = 0, r = 1; + uint32_t f = f0, g = g0, m; + uint16_t w; + int i = 30, limit, zeros; + int jac = *jacp; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz32_var(g | (UINT32_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* Update the bottom bit of jac: when dividing g by an odd power of 2, + * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */ + jac ^= (zeros & ((f >> 1) ^ (f >> 2))); + /* We're done once we've done 30 posdivsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i)); + /* If eta is negative, negate it and replace f,g with g,f. */ + if (eta < 0) { + uint32_t tmp; + eta = -eta; + /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign + * if both f and g are 3 mod 4. */ + jac ^= ((f & g) >> 1); + tmp = f; f = g; g = tmp; + tmp = u; u = q; q = tmp; + tmp = v; v = r; r = tmp; + } + /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more + * than i can be cancelled out (as we'd be done before that point), and no more than eta+1 + * can be done as its sign will flip once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */ + VERIFY_CHECK(limit > 0 && limit <= 30); + m = (UINT32_MAX >> (32 - limit)) & 255U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */ + w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m; + /* Do so. */ + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int32_t)u; + t->v = (int32_t)v; + t->q = (int32_t)q; + t->r = (int32_t)r; + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2 or -2, + * the aggregate of 30 of them will have determinant 2^30 or -2^30. */ + VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30 || + (int64_t)t->u * t->r - (int64_t)t->v * t->q == -(((int64_t)1) << 30)); + *jacp = jac; + return eta; +} + +/* Compute (t/2^30) * [d, e] mod modulus, where t is a transition matrix for 30 divsteps. + * + * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range + * (-2^30,2^30). + * + * This implements the update_de function from the explanation. + */ +static void secp256k1_modinv32_update_de_30(secp256k1_modinv32_signed30 *d, secp256k1_modinv32_signed30 *e, const secp256k1_modinv32_trans2x2 *t, const secp256k1_modinv32_modinfo* modinfo) { + const int32_t M30 = (int32_t)(UINT32_MAX >> 2); + const int32_t u = t->u, v = t->v, q = t->q, r = t->r; + int32_t di, ei, md, me, sd, se; + int64_t cd, ce; + int i; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, 1) < 0); /* d < modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, 1) < 0); /* e < modulus */ + VERIFY_CHECK(labs(u) <= (M30 + 1 - labs(v))); /* |u|+|v| <= 2^30 */ + VERIFY_CHECK(labs(q) <= (M30 + 1 - labs(r))); /* |q|+|r| <= 2^30 */ +#endif + /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */ + sd = d->v[8] >> 31; + se = e->v[8] >> 31; + md = (u & sd) + (v & se); + me = (q & sd) + (r & se); + /* Begin computing t*[d,e]. */ + di = d->v[0]; + ei = e->v[0]; + cd = (int64_t)u * di + (int64_t)v * ei; + ce = (int64_t)q * di + (int64_t)r * ei; + /* Correct md,me so that t*[d,e]+modulus*[md,me] has 30 zero bottom bits. */ + md -= (modinfo->modulus_inv30 * (uint32_t)cd + md) & M30; + me -= (modinfo->modulus_inv30 * (uint32_t)ce + me) & M30; + /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */ + cd += (int64_t)modinfo->modulus.v[0] * md; + ce += (int64_t)modinfo->modulus.v[0] * me; + /* Verify that the low 30 bits of the computation are indeed zero, and then throw them away. */ + VERIFY_CHECK(((int32_t)cd & M30) == 0); cd >>= 30; + VERIFY_CHECK(((int32_t)ce & M30) == 0); ce >>= 30; + /* Now iteratively compute limb i=1..8 of t*[d,e]+modulus*[md,me], and store them in output + * limb i-1 (shifting down by 30 bits). */ + for (i = 1; i < 9; ++i) { + di = d->v[i]; + ei = e->v[i]; + cd += (int64_t)u * di + (int64_t)v * ei; + ce += (int64_t)q * di + (int64_t)r * ei; + cd += (int64_t)modinfo->modulus.v[i] * md; + ce += (int64_t)modinfo->modulus.v[i] * me; + d->v[i - 1] = (int32_t)cd & M30; cd >>= 30; + e->v[i - 1] = (int32_t)ce & M30; ce >>= 30; + } + /* What remains is limb 9 of t*[d,e]+modulus*[md,me]; store it as output limb 8. */ + d->v[8] = (int32_t)cd; + e->v[8] = (int32_t)ce; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, 1) < 0); /* d < modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, 1) < 0); /* e < modulus */ +#endif +} + +/* Compute (t/2^30) * [f, g], where t is a transition matrix for 30 divsteps. + * + * This implements the update_fg function from the explanation. + */ +static void secp256k1_modinv32_update_fg_30(secp256k1_modinv32_signed30 *f, secp256k1_modinv32_signed30 *g, const secp256k1_modinv32_trans2x2 *t) { + const int32_t M30 = (int32_t)(UINT32_MAX >> 2); + const int32_t u = t->u, v = t->v, q = t->q, r = t->r; + int32_t fi, gi; + int64_t cf, cg; + int i; + /* Start computing t*[f,g]. */ + fi = f->v[0]; + gi = g->v[0]; + cf = (int64_t)u * fi + (int64_t)v * gi; + cg = (int64_t)q * fi + (int64_t)r * gi; + /* Verify that the bottom 30 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK(((int32_t)cf & M30) == 0); cf >>= 30; + VERIFY_CHECK(((int32_t)cg & M30) == 0); cg >>= 30; + /* Now iteratively compute limb i=1..8 of t*[f,g], and store them in output limb i-1 (shifting + * down by 30 bits). */ + for (i = 1; i < 9; ++i) { + fi = f->v[i]; + gi = g->v[i]; + cf += (int64_t)u * fi + (int64_t)v * gi; + cg += (int64_t)q * fi + (int64_t)r * gi; + f->v[i - 1] = (int32_t)cf & M30; cf >>= 30; + g->v[i - 1] = (int32_t)cg & M30; cg >>= 30; + } + /* What remains is limb 9 of t*[f,g]; store it as output limb 8. */ + f->v[8] = (int32_t)cf; + g->v[8] = (int32_t)cg; +} + +/* Compute (t/2^30) * [f, g], where t is a transition matrix for 30 divsteps. + * + * Version that operates on a variable number of limbs in f and g. + * + * This implements the update_fg function from the explanation in modinv64_impl.h. + */ +static void secp256k1_modinv32_update_fg_30_var(int len, secp256k1_modinv32_signed30 *f, secp256k1_modinv32_signed30 *g, const secp256k1_modinv32_trans2x2 *t) { + const int32_t M30 = (int32_t)(UINT32_MAX >> 2); + const int32_t u = t->u, v = t->v, q = t->q, r = t->r; + int32_t fi, gi; + int64_t cf, cg; + int i; + VERIFY_CHECK(len > 0); + /* Start computing t*[f,g]. */ + fi = f->v[0]; + gi = g->v[0]; + cf = (int64_t)u * fi + (int64_t)v * gi; + cg = (int64_t)q * fi + (int64_t)r * gi; + /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK(((int32_t)cf & M30) == 0); cf >>= 30; + VERIFY_CHECK(((int32_t)cg & M30) == 0); cg >>= 30; + /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting + * down by 30 bits). */ + for (i = 1; i < len; ++i) { + fi = f->v[i]; + gi = g->v[i]; + cf += (int64_t)u * fi + (int64_t)v * gi; + cg += (int64_t)q * fi + (int64_t)r * gi; + f->v[i - 1] = (int32_t)cf & M30; cf >>= 30; + g->v[i - 1] = (int32_t)cg & M30; cg >>= 30; + } + /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */ + f->v[len - 1] = (int32_t)cf; + g->v[len - 1] = (int32_t)cg; +} + +/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */ +static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) { + /* Start with d=0, e=1, f=modulus, g=x, zeta=-1. */ + secp256k1_modinv32_signed30 d = {{0}}; + secp256k1_modinv32_signed30 e = {{1}}; + secp256k1_modinv32_signed30 f = modinfo->modulus; + secp256k1_modinv32_signed30 g = *x; + int i; + int32_t zeta = -1; /* zeta = -(delta+1/2); delta is initially 1/2. */ + + /* Do 20 iterations of 30 divsteps each = 600 divsteps. 590 suffices for 256-bit inputs. */ + for (i = 0; i < 20; ++i) { + /* Compute transition matrix and new zeta after 30 divsteps. */ + secp256k1_modinv32_trans2x2 t; + zeta = secp256k1_modinv32_divsteps_30(zeta, f.v[0], g.v[0], &t); + /* Update d,e using that transition matrix. */ + secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv32_update_fg_30(&f, &g, &t); +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* At this point sufficient iterations have been performed that g must have reached 0 + * and (if g was not originally 0) f must now equal +/- GCD of the initial f, g + * values i.e. +/- 1, and d now contains +/- the modular inverse. */ +#ifdef VERIFY + /* g == 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &SECP256K1_SIGNED30_ONE, 0) == 0); + /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &SECP256K1_SIGNED30_ONE, -1) == 0 || + secp256k1_modinv32_mul_cmp_30(&f, 9, &SECP256K1_SIGNED30_ONE, 1) == 0 || + (secp256k1_modinv32_mul_cmp_30(x, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 && + secp256k1_modinv32_mul_cmp_30(&d, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 && + (secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) == 0 || + secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, -1) == 0))); +#endif + + /* Optionally negate d, normalize to [0,modulus), and return it. */ + secp256k1_modinv32_normalize_30(&d, f.v[8], modinfo); + *x = d; +} + +/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (variable time). */ +static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) { + /* Start with d=0, e=1, f=modulus, g=x, eta=-1. */ + secp256k1_modinv32_signed30 d = {{0, 0, 0, 0, 0, 0, 0, 0, 0}}; + secp256k1_modinv32_signed30 e = {{1, 0, 0, 0, 0, 0, 0, 0, 0}}; + secp256k1_modinv32_signed30 f = modinfo->modulus; + secp256k1_modinv32_signed30 g = *x; +#ifdef VERIFY + int i = 0; +#endif + int j, len = 9; + int32_t eta = -1; /* eta = -delta; delta is initially 1 (faster for the variable-time code) */ + int32_t cond, fn, gn; + + /* Do iterations of 30 divsteps each until g=0. */ + while (1) { + /* Compute transition matrix and new eta after 30 divsteps. */ + secp256k1_modinv32_trans2x2 t; + eta = secp256k1_modinv32_divsteps_30_var(eta, f.v[0], g.v[0], &t); + /* Update d,e using that transition matrix. */ + secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv32_update_fg_30_var(len, &f, &g, &t); + /* If the bottom limb of g is 0, there is a chance g=0. */ + if (g.v[0] == 0) { + cond = 0; + /* Check if all other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= g.v[j]; + } + /* If so, we're done. */ + if (cond == 0) break; + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0 or -1. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int32_t)len - 2) >> 31; + cond |= fn ^ (fn >> 31); + cond |= gn ^ (gn >> 31); + /* If so, reduce length, propagating the sign of f and g's top limb into the one below. */ + if (cond == 0) { + f.v[len - 2] |= (uint32_t)fn << 30; + g.v[len - 2] |= (uint32_t)gn << 30; + --len; + } +#ifdef VERIFY + VERIFY_CHECK(++i < 25); /* We should never need more than 25*30 = 750 divsteps */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of + * the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */ +#ifdef VERIFY + /* g == 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &SECP256K1_SIGNED30_ONE, 0) == 0); + /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &SECP256K1_SIGNED30_ONE, -1) == 0 || + secp256k1_modinv32_mul_cmp_30(&f, len, &SECP256K1_SIGNED30_ONE, 1) == 0 || + (secp256k1_modinv32_mul_cmp_30(x, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 && + secp256k1_modinv32_mul_cmp_30(&d, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 && + (secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) == 0 || + secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, -1) == 0))); +#endif + + /* Optionally negate d, normalize to [0,modulus), and return it. */ + secp256k1_modinv32_normalize_30(&d, f.v[len - 1], modinfo); + *x = d; +} + +/* Do up to 50 iterations of 30 posdivsteps (up to 1500 steps; more is extremely rare) each until f=1. + * In VERIFY mode use a lower number of iterations (750, close to the median 756), so failure actually occurs. */ +#ifdef VERIFY +#define JACOBI32_ITERATIONS 25 +#else +#define JACOBI32_ITERATIONS 50 +#endif + +/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1. */ +static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) { + /* Start with f=modulus, g=x, eta=-1. */ + secp256k1_modinv32_signed30 f = modinfo->modulus; + secp256k1_modinv32_signed30 g = *x; + int j, len = 9; + int32_t eta = -1; /* eta = -delta; delta is initially 1 */ + int32_t cond, fn, gn; + int jac = 0; + int count; + + /* The input limbs must all be non-negative. */ + VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0 && g.v[5] >= 0 && g.v[6] >= 0 && g.v[7] >= 0 && g.v[8] >= 0); + + /* If x > 0, then if the loop below converges, it converges to f=g=gcd(x,modulus). Since we + * require that gcd(x,modulus)=1 and modulus>=3, x cannot be 0. Thus, we must reach f=1 (or + * time out). */ + VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4] | g.v[5] | g.v[6] | g.v[7] | g.v[8]) != 0); + + for (count = 0; count < JACOBI32_ITERATIONS; ++count) { + /* Compute transition matrix and new eta after 30 posdivsteps. */ + secp256k1_modinv32_trans2x2 t; + eta = secp256k1_modinv32_posdivsteps_30_var(eta, f.v[0] | ((uint32_t)f.v[1] << 30), g.v[0] | ((uint32_t)g.v[1] << 30), &t, &jac); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv32_update_fg_30_var(len, &f, &g, &t); + /* If the bottom limb of f is 1, there is a chance that f=1. */ + if (f.v[0] == 1) { + cond = 0; + /* Check if the other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= f.v[j]; + } + /* If so, we're done. If f=1, the Jacobi symbol (g | f)=1. */ + if (cond == 0) return 1 - 2*(jac & 1); + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int32_t)len - 2) >> 31; + cond |= fn; + cond |= gn; + /* If so, reduce length. */ + if (cond == 0) --len; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* The loop failed to converge to f=g after 1500 iterations. Return 0, indicating unknown result. */ + return 0; +} + +#endif /* SECP256K1_MODINV32_IMPL_H */ diff --git a/src/secp256k1/src/modinv64.h b/src/secp256k1/src/modinv64.h new file mode 100644 index 0000000000..f4208e6c23 --- /dev/null +++ b/src/secp256k1/src/modinv64.h @@ -0,0 +1,47 @@ +/*********************************************************************** + * Copyright (c) 2020 Peter Dettman * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODINV64_H +#define SECP256K1_MODINV64_H + +#include "util.h" + +#ifndef SECP256K1_WIDEMUL_INT128 +#error "modinv64 requires 128-bit wide multiplication support" +#endif + +/* A signed 62-bit limb representation of integers. + * + * Its value is sum(v[i] * 2^(62*i), i=0..4). */ +typedef struct { + int64_t v[5]; +} secp256k1_modinv64_signed62; + +typedef struct { + /* The modulus in signed62 notation, must be odd and in [3, 2^256]. */ + secp256k1_modinv64_signed62 modulus; + + /* modulus^{-1} mod 2^62 */ + uint64_t modulus_inv62; +} secp256k1_modinv64_modinfo; + +/* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus). + * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of + * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime. + * + * On output, all of x's limbs will be in [0, 2^62). + */ +static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); + +/* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */ +static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); + +/* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus + * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result + * cannot be computed. */ +static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); + +#endif /* SECP256K1_MODINV64_H */ diff --git a/src/secp256k1/src/modinv64_impl.h b/src/secp256k1/src/modinv64_impl.h new file mode 100644 index 0000000000..e33727d385 --- /dev/null +++ b/src/secp256k1/src/modinv64_impl.h @@ -0,0 +1,791 @@ +/*********************************************************************** + * Copyright (c) 2020 Peter Dettman * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODINV64_IMPL_H +#define SECP256K1_MODINV64_IMPL_H + +#include "int128.h" +#include "modinv64.h" + +/* This file implements modular inversion based on the paper "Fast constant-time gcd computation and + * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang. + * + * For an explanation of the algorithm, see doc/safegcd_implementation.md. This file contains an + * implementation for N=62, using 62-bit signed limbs represented as int64_t. + */ + +/* Data type for transition matrices (see section 3 of explanation). + * + * t = [ u v ] + * [ q r ] + */ +typedef struct { + int64_t u, v, q, r; +} secp256k1_modinv64_trans2x2; + +#ifdef VERIFY +/* Helper function to compute the absolute value of an int64_t. + * (we don't use abs/labs/llabs as it depends on the int sizes). */ +static int64_t secp256k1_modinv64_abs(int64_t v) { + VERIFY_CHECK(v > INT64_MIN); + if (v < 0) return -v; + return v; +} + +static const secp256k1_modinv64_signed62 SECP256K1_SIGNED62_ONE = {{1}}; + +/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^62). */ +static void secp256k1_modinv64_mul_62(secp256k1_modinv64_signed62 *r, const secp256k1_modinv64_signed62 *a, int alen, int64_t factor) { + const uint64_t M62 = UINT64_MAX >> 2; + secp256k1_int128 c, d; + int i; + secp256k1_i128_from_i64(&c, 0); + for (i = 0; i < 4; ++i) { + if (i < alen) secp256k1_i128_accum_mul(&c, a->v[i], factor); + r->v[i] = secp256k1_i128_to_u64(&c) & M62; secp256k1_i128_rshift(&c, 62); + } + if (4 < alen) secp256k1_i128_accum_mul(&c, a->v[4], factor); + secp256k1_i128_from_i64(&d, secp256k1_i128_to_i64(&c)); + VERIFY_CHECK(secp256k1_i128_eq_var(&c, &d)); + r->v[4] = secp256k1_i128_to_i64(&c); +} + +/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. A has alen limbs; b has 5. */ +static int secp256k1_modinv64_mul_cmp_62(const secp256k1_modinv64_signed62 *a, int alen, const secp256k1_modinv64_signed62 *b, int64_t factor) { + int i; + secp256k1_modinv64_signed62 am, bm; + secp256k1_modinv64_mul_62(&am, a, alen, 1); /* Normalize all but the top limb of a. */ + secp256k1_modinv64_mul_62(&bm, b, 5, factor); + for (i = 0; i < 4; ++i) { + /* Verify that all but the top limb of a and b are normalized. */ + VERIFY_CHECK(am.v[i] >> 62 == 0); + VERIFY_CHECK(bm.v[i] >> 62 == 0); + } + for (i = 4; i >= 0; --i) { + if (am.v[i] < bm.v[i]) return -1; + if (am.v[i] > bm.v[i]) return 1; + } + return 0; +} + +/* Check if the determinant of t is equal to 1 << n. If abs, check if |det t| == 1 << n. */ +static int secp256k1_modinv64_det_check_pow2(const secp256k1_modinv64_trans2x2 *t, unsigned int n, int abs) { + secp256k1_int128 a; + secp256k1_i128_det(&a, t->u, t->v, t->q, t->r); + if (secp256k1_i128_check_pow2(&a, n, 1)) return 1; + if (abs && secp256k1_i128_check_pow2(&a, n, -1)) return 1; + return 0; +} +#endif + +/* Take as input a signed62 number in range (-2*modulus,modulus), and add a multiple of the modulus + * to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the + * process. The input must have limbs in range (-2^62,2^62). The output will have limbs in range + * [0,2^62). */ +static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int64_t sign, const secp256k1_modinv64_modinfo *modinfo) { + const int64_t M62 = (int64_t)(UINT64_MAX >> 2); + int64_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4]; + int64_t cond_add, cond_negate; + +#ifdef VERIFY + /* Verify that all limbs are in range (-2^62,2^62). */ + int i; + for (i = 0; i < 5; ++i) { + VERIFY_CHECK(r->v[i] >= -M62); + VERIFY_CHECK(r->v[i] <= M62); + } + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, -2) > 0); /* r > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */ +#endif + + /* In a first step, add the modulus if the input is negative, and then negate if requested. + * This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input + * limbs are in range (-2^62,2^62), this cannot overflow an int64_t. Note that the right + * shifts below are signed sign-extending shifts (see assumptions.h for tests that that is + * indeed the behavior of the right shift operator). */ + cond_add = r4 >> 63; + r0 += modinfo->modulus.v[0] & cond_add; + r1 += modinfo->modulus.v[1] & cond_add; + r2 += modinfo->modulus.v[2] & cond_add; + r3 += modinfo->modulus.v[3] & cond_add; + r4 += modinfo->modulus.v[4] & cond_add; + cond_negate = sign >> 63; + r0 = (r0 ^ cond_negate) - cond_negate; + r1 = (r1 ^ cond_negate) - cond_negate; + r2 = (r2 ^ cond_negate) - cond_negate; + r3 = (r3 ^ cond_negate) - cond_negate; + r4 = (r4 ^ cond_negate) - cond_negate; + /* Propagate the top bits, to bring limbs back to range (-2^62,2^62). */ + r1 += r0 >> 62; r0 &= M62; + r2 += r1 >> 62; r1 &= M62; + r3 += r2 >> 62; r2 &= M62; + r4 += r3 >> 62; r3 &= M62; + + /* In a second step add the modulus again if the result is still negative, bringing + * r to range [0,modulus). */ + cond_add = r4 >> 63; + r0 += modinfo->modulus.v[0] & cond_add; + r1 += modinfo->modulus.v[1] & cond_add; + r2 += modinfo->modulus.v[2] & cond_add; + r3 += modinfo->modulus.v[3] & cond_add; + r4 += modinfo->modulus.v[4] & cond_add; + /* And propagate again. */ + r1 += r0 >> 62; r0 &= M62; + r2 += r1 >> 62; r1 &= M62; + r3 += r2 >> 62; r2 &= M62; + r4 += r3 >> 62; r3 &= M62; + + r->v[0] = r0; + r->v[1] = r1; + r->v[2] = r2; + r->v[3] = r3; + r->v[4] = r4; + +#ifdef VERIFY + VERIFY_CHECK(r0 >> 62 == 0); + VERIFY_CHECK(r1 >> 62 == 0); + VERIFY_CHECK(r2 >> 62 == 0); + VERIFY_CHECK(r3 >> 62 == 0); + VERIFY_CHECK(r4 >> 62 == 0); + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 0) >= 0); /* r >= 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */ +#endif +} + +/* Compute the transition matrix and eta for 59 divsteps (where zeta=-(delta+1/2)). + * Note that the transformation matrix is scaled by 2^62 and not 2^59. + * + * Input: zeta: initial zeta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final zeta + * + * Implements the divsteps_n_matrix function from the explanation. + */ +static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) { + /* u,v,q,r are the elements of the transformation matrix being built up, + * starting with the identity matrix times 8 (because the caller expects + * a result scaled by 2^62). Semantically they are signed integers + * in range [-2^62,2^62], but here represented as unsigned mod 2^64. This + * permits left shifting (which is UB for negative numbers). The range + * being inside [-2^63,2^63) means that casting to signed works correctly. + */ + uint64_t u = 8, v = 0, q = 0, r = 8; + uint64_t c1, c2, f = f0, g = g0, x, y, z; + int i; + + for (i = 3; i < 62; ++i) { + VERIFY_CHECK((f & 1) == 1); /* f must always be odd */ + VERIFY_CHECK((u * f0 + v * g0) == f << i); + VERIFY_CHECK((q * f0 + r * g0) == g << i); + /* Compute conditional masks for (zeta < 0) and for (g & 1). */ + c1 = zeta >> 63; + c2 = -(g & 1); + /* Compute x,y,z, conditionally negated versions of f,u,v. */ + x = (f ^ c1) - c1; + y = (u ^ c1) - c1; + z = (v ^ c1) - c1; + /* Conditionally add x,y,z to g,q,r. */ + g += x & c2; + q += y & c2; + r += z & c2; + /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */ + c1 &= c2; + /* Conditionally change zeta into -zeta-2 or zeta-1. */ + zeta = (zeta ^ c1) - 1; + /* Conditionally add g,q,r to f,u,v. */ + f += g & c1; + u += q & c1; + v += r & c1; + /* Shifts */ + g >>= 1; + u <<= 1; + v <<= 1; + /* Bounds on zeta that follow from the bounds on iteration count (max 10*59 divsteps). */ + VERIFY_CHECK(zeta >= -591 && zeta <= 591); + } + /* Return data in t and return value. */ + t->u = (int64_t)u; + t->v = (int64_t)v; + t->q = (int64_t)q; + t->r = (int64_t)r; +#ifdef VERIFY + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2, the + * aggregate of 59 of them will have determinant 2^59. Multiplying with the initial + * 8*identity (which has determinant 2^6) means the overall outputs has determinant + * 2^65. */ + VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 65, 0)); +#endif + return zeta; +} + +/* Compute the transition matrix and eta for 62 divsteps (variable time, eta=-delta). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final eta + * + * Implements the divsteps_n_matrix_var function from the explanation. + */ +static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) { + /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */ + uint64_t u = 1, v = 0, q = 0, r = 1; + uint64_t f = f0, g = g0, m; + uint32_t w; + int i = 62, limit, zeros; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* We're done once we've done 62 divsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i)); + /* Bounds on eta that follow from the bounds on iteration count (max 12*62 divsteps). */ + VERIFY_CHECK(eta >= -745 && eta <= 745); + /* If eta is negative, negate it and replace f,g with g,-f. */ + if (eta < 0) { + uint64_t tmp; + eta = -eta; + tmp = f; f = g; g = -tmp; + tmp = u; u = q; q = -tmp; + tmp = v; v = r; r = -tmp; + /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled + * out (as we'd be done before that point), and no more than eta+1 can be done as its + * sign will flip again once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 6) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 63U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6) + * bits. */ + w = (f * g * (f * f - 2)) & m; + } else { + /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as + * eta tends to be smaller here. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 4) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 15U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4) + * bits. */ + w = f + (((f + 1) & 4) << 1); + w = (-w * g) & m; + } + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int64_t)u; + t->v = (int64_t)v; + t->q = (int64_t)q; + t->r = (int64_t)r; +#ifdef VERIFY + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2, the + * aggregate of 62 of them will have determinant 2^62. */ + VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 0)); +#endif + return eta; +} + +/* Compute the transition matrix and eta for 62 posdivsteps (variable time, eta=-delta), and keeps track + * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^64 rather than 2^62, because + * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Input/Output: (*jacp & 1) is bitflipped if and only if the Jacobi symbol of (f | g) changes sign + * by applying the returned transformation matrix to it. The other bits of *jacp may + * change, but are meaningless. + * Return: final eta + */ +static int64_t secp256k1_modinv64_posdivsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t, int *jacp) { + /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */ + uint64_t u = 1, v = 0, q = 0, r = 1; + uint64_t f = f0, g = g0, m; + uint32_t w; + int i = 62, limit, zeros; + int jac = *jacp; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* Update the bottom bit of jac: when dividing g by an odd power of 2, + * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */ + jac ^= (zeros & ((f >> 1) ^ (f >> 2))); + /* We're done once we've done 62 posdivsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i)); + /* If eta is negative, negate it and replace f,g with g,f. */ + if (eta < 0) { + uint64_t tmp; + eta = -eta; + tmp = f; f = g; g = tmp; + tmp = u; u = q; q = tmp; + tmp = v; v = r; r = tmp; + /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign + * if both f and g are 3 mod 4. */ + jac ^= ((f & g) >> 1); + /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled + * out (as we'd be done before that point), and no more than eta+1 can be done as its + * sign will flip again once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 6) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 63U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6) + * bits. */ + w = (f * g * (f * f - 2)) & m; + } else { + /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as + * eta tends to be smaller here. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 4) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 15U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4) + * bits. */ + w = f + (((f + 1) & 4) << 1); + w = (-w * g) & m; + } + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int64_t)u; + t->v = (int64_t)v; + t->q = (int64_t)q; + t->r = (int64_t)r; +#ifdef VERIFY + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2 or -2, + * the aggregate of 62 of them will have determinant 2^62 or -2^62. */ + VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 1)); +#endif + *jacp = jac; + return eta; +} + +/* Compute (t/2^62) * [d, e] mod modulus, where t is a transition matrix scaled by 2^62. + * + * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range + * (-2^62,2^62). + * + * This implements the update_de function from the explanation. + */ +static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp256k1_modinv64_signed62 *e, const secp256k1_modinv64_trans2x2 *t, const secp256k1_modinv64_modinfo* modinfo) { + const uint64_t M62 = UINT64_MAX >> 2; + const int64_t d0 = d->v[0], d1 = d->v[1], d2 = d->v[2], d3 = d->v[3], d4 = d->v[4]; + const int64_t e0 = e->v[0], e1 = e->v[1], e2 = e->v[2], e3 = e->v[3], e4 = e->v[4]; + const int64_t u = t->u, v = t->v, q = t->q, r = t->r; + int64_t md, me, sd, se; + secp256k1_int128 cd, ce; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0); /* d < modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0); /* e < modulus */ + VERIFY_CHECK(secp256k1_modinv64_abs(u) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(v))); /* |u|+|v| <= 2^62 */ + VERIFY_CHECK(secp256k1_modinv64_abs(q) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(r))); /* |q|+|r| <= 2^62 */ +#endif + /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */ + sd = d4 >> 63; + se = e4 >> 63; + md = (u & sd) + (v & se); + me = (q & sd) + (r & se); + /* Begin computing t*[d,e]. */ + secp256k1_i128_mul(&cd, u, d0); + secp256k1_i128_accum_mul(&cd, v, e0); + secp256k1_i128_mul(&ce, q, d0); + secp256k1_i128_accum_mul(&ce, r, e0); + /* Correct md,me so that t*[d,e]+modulus*[md,me] has 62 zero bottom bits. */ + md -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&cd) + md) & M62; + me -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&ce) + me) & M62; + /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */ + secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[0], md); + secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[0], me); + /* Verify that the low 62 bits of the computation are indeed zero, and then throw them away. */ + VERIFY_CHECK((secp256k1_i128_to_u64(&cd) & M62) == 0); secp256k1_i128_rshift(&cd, 62); + VERIFY_CHECK((secp256k1_i128_to_u64(&ce) & M62) == 0); secp256k1_i128_rshift(&ce, 62); + /* Compute limb 1 of t*[d,e]+modulus*[md,me], and store it as output limb 0 (= down shift). */ + secp256k1_i128_accum_mul(&cd, u, d1); + secp256k1_i128_accum_mul(&cd, v, e1); + secp256k1_i128_accum_mul(&ce, q, d1); + secp256k1_i128_accum_mul(&ce, r, e1); + if (modinfo->modulus.v[1]) { /* Optimize for the case where limb of modulus is zero. */ + secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[1], md); + secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[1], me); + } + d->v[0] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); + e->v[0] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); + /* Compute limb 2 of t*[d,e]+modulus*[md,me], and store it as output limb 1. */ + secp256k1_i128_accum_mul(&cd, u, d2); + secp256k1_i128_accum_mul(&cd, v, e2); + secp256k1_i128_accum_mul(&ce, q, d2); + secp256k1_i128_accum_mul(&ce, r, e2); + if (modinfo->modulus.v[2]) { /* Optimize for the case where limb of modulus is zero. */ + secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[2], md); + secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[2], me); + } + d->v[1] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); + e->v[1] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); + /* Compute limb 3 of t*[d,e]+modulus*[md,me], and store it as output limb 2. */ + secp256k1_i128_accum_mul(&cd, u, d3); + secp256k1_i128_accum_mul(&cd, v, e3); + secp256k1_i128_accum_mul(&ce, q, d3); + secp256k1_i128_accum_mul(&ce, r, e3); + if (modinfo->modulus.v[3]) { /* Optimize for the case where limb of modulus is zero. */ + secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[3], md); + secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[3], me); + } + d->v[2] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); + e->v[2] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); + /* Compute limb 4 of t*[d,e]+modulus*[md,me], and store it as output limb 3. */ + secp256k1_i128_accum_mul(&cd, u, d4); + secp256k1_i128_accum_mul(&cd, v, e4); + secp256k1_i128_accum_mul(&ce, q, d4); + secp256k1_i128_accum_mul(&ce, r, e4); + secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[4], md); + secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[4], me); + d->v[3] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); + e->v[3] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); + /* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */ + d->v[4] = secp256k1_i128_to_i64(&cd); + e->v[4] = secp256k1_i128_to_i64(&ce); +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0); /* d < modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0); /* e < modulus */ +#endif +} + +/* Compute (t/2^62) * [f, g], where t is a transition matrix scaled by 2^62. + * + * This implements the update_fg function from the explanation. + */ +static void secp256k1_modinv64_update_fg_62(secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) { + const uint64_t M62 = UINT64_MAX >> 2; + const int64_t f0 = f->v[0], f1 = f->v[1], f2 = f->v[2], f3 = f->v[3], f4 = f->v[4]; + const int64_t g0 = g->v[0], g1 = g->v[1], g2 = g->v[2], g3 = g->v[3], g4 = g->v[4]; + const int64_t u = t->u, v = t->v, q = t->q, r = t->r; + secp256k1_int128 cf, cg; + /* Start computing t*[f,g]. */ + secp256k1_i128_mul(&cf, u, f0); + secp256k1_i128_accum_mul(&cf, v, g0); + secp256k1_i128_mul(&cg, q, f0); + secp256k1_i128_accum_mul(&cg, r, g0); + /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62); + VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62); + /* Compute limb 1 of t*[f,g], and store it as output limb 0 (= down shift). */ + secp256k1_i128_accum_mul(&cf, u, f1); + secp256k1_i128_accum_mul(&cf, v, g1); + secp256k1_i128_accum_mul(&cg, q, f1); + secp256k1_i128_accum_mul(&cg, r, g1); + f->v[0] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); + g->v[0] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); + /* Compute limb 2 of t*[f,g], and store it as output limb 1. */ + secp256k1_i128_accum_mul(&cf, u, f2); + secp256k1_i128_accum_mul(&cf, v, g2); + secp256k1_i128_accum_mul(&cg, q, f2); + secp256k1_i128_accum_mul(&cg, r, g2); + f->v[1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); + g->v[1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); + /* Compute limb 3 of t*[f,g], and store it as output limb 2. */ + secp256k1_i128_accum_mul(&cf, u, f3); + secp256k1_i128_accum_mul(&cf, v, g3); + secp256k1_i128_accum_mul(&cg, q, f3); + secp256k1_i128_accum_mul(&cg, r, g3); + f->v[2] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); + g->v[2] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); + /* Compute limb 4 of t*[f,g], and store it as output limb 3. */ + secp256k1_i128_accum_mul(&cf, u, f4); + secp256k1_i128_accum_mul(&cf, v, g4); + secp256k1_i128_accum_mul(&cg, q, f4); + secp256k1_i128_accum_mul(&cg, r, g4); + f->v[3] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); + g->v[3] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); + /* What remains is limb 5 of t*[f,g]; store it as output limb 4. */ + f->v[4] = secp256k1_i128_to_i64(&cf); + g->v[4] = secp256k1_i128_to_i64(&cg); +} + +/* Compute (t/2^62) * [f, g], where t is a transition matrix for 62 divsteps. + * + * Version that operates on a variable number of limbs in f and g. + * + * This implements the update_fg function from the explanation. + */ +static void secp256k1_modinv64_update_fg_62_var(int len, secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) { + const uint64_t M62 = UINT64_MAX >> 2; + const int64_t u = t->u, v = t->v, q = t->q, r = t->r; + int64_t fi, gi; + secp256k1_int128 cf, cg; + int i; + VERIFY_CHECK(len > 0); + /* Start computing t*[f,g]. */ + fi = f->v[0]; + gi = g->v[0]; + secp256k1_i128_mul(&cf, u, fi); + secp256k1_i128_accum_mul(&cf, v, gi); + secp256k1_i128_mul(&cg, q, fi); + secp256k1_i128_accum_mul(&cg, r, gi); + /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62); + VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62); + /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting + * down by 62 bits). */ + for (i = 1; i < len; ++i) { + fi = f->v[i]; + gi = g->v[i]; + secp256k1_i128_accum_mul(&cf, u, fi); + secp256k1_i128_accum_mul(&cf, v, gi); + secp256k1_i128_accum_mul(&cg, q, fi); + secp256k1_i128_accum_mul(&cg, r, gi); + f->v[i - 1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); + g->v[i - 1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); + } + /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */ + f->v[len - 1] = secp256k1_i128_to_i64(&cf); + g->v[len - 1] = secp256k1_i128_to_i64(&cg); +} + +/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */ +static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { + /* Start with d=0, e=1, f=modulus, g=x, zeta=-1. */ + secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}}; + secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}}; + secp256k1_modinv64_signed62 f = modinfo->modulus; + secp256k1_modinv64_signed62 g = *x; + int i; + int64_t zeta = -1; /* zeta = -(delta+1/2); delta starts at 1/2. */ + + /* Do 10 iterations of 59 divsteps each = 590 divsteps. This suffices for 256-bit inputs. */ + for (i = 0; i < 10; ++i) { + /* Compute transition matrix and new zeta after 59 divsteps. */ + secp256k1_modinv64_trans2x2 t; + zeta = secp256k1_modinv64_divsteps_59(zeta, f.v[0], g.v[0], &t); + /* Update d,e using that transition matrix. */ + secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv64_update_fg_62(&f, &g, &t); +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* At this point sufficient iterations have been performed that g must have reached 0 + * and (if g was not originally 0) f must now equal +/- GCD of the initial f, g + * values i.e. +/- 1, and d now contains +/- the modular inverse. */ +#ifdef VERIFY + /* g == 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &SECP256K1_SIGNED62_ONE, 0) == 0); + /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, -1) == 0 || + secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, 1) == 0 || + (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && + secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && + (secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) == 0 || + secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) == 0))); +#endif + + /* Optionally negate d, normalize to [0,modulus), and return it. */ + secp256k1_modinv64_normalize_62(&d, f.v[4], modinfo); + *x = d; +} + +/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (variable time). */ +static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { + /* Start with d=0, e=1, f=modulus, g=x, eta=-1. */ + secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}}; + secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}}; + secp256k1_modinv64_signed62 f = modinfo->modulus; + secp256k1_modinv64_signed62 g = *x; +#ifdef VERIFY + int i = 0; +#endif + int j, len = 5; + int64_t eta = -1; /* eta = -delta; delta is initially 1 */ + int64_t cond, fn, gn; + + /* Do iterations of 62 divsteps each until g=0. */ + while (1) { + /* Compute transition matrix and new eta after 62 divsteps. */ + secp256k1_modinv64_trans2x2 t; + eta = secp256k1_modinv64_divsteps_62_var(eta, f.v[0], g.v[0], &t); + /* Update d,e using that transition matrix. */ + secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t); + /* If the bottom limb of g is zero, there is a chance that g=0. */ + if (g.v[0] == 0) { + cond = 0; + /* Check if the other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= g.v[j]; + } + /* If so, we're done. */ + if (cond == 0) break; + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0 or -1. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int64_t)len - 2) >> 63; + cond |= fn ^ (fn >> 63); + cond |= gn ^ (gn >> 63); + /* If so, reduce length, propagating the sign of f and g's top limb into the one below. */ + if (cond == 0) { + f.v[len - 2] |= (uint64_t)fn << 62; + g.v[len - 2] |= (uint64_t)gn << 62; + --len; + } +#ifdef VERIFY + VERIFY_CHECK(++i < 12); /* We should never need more than 12*62 = 744 divsteps */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of + * the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */ +#ifdef VERIFY + /* g == 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &SECP256K1_SIGNED62_ONE, 0) == 0); + /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, -1) == 0 || + secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, 1) == 0 || + (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && + secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && + (secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) == 0 || + secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) == 0))); +#endif + + /* Optionally negate d, normalize to [0,modulus), and return it. */ + secp256k1_modinv64_normalize_62(&d, f.v[len - 1], modinfo); + *x = d; +} + +/* Do up to 25 iterations of 62 posdivsteps (up to 1550 steps; more is extremely rare) each until f=1. + * In VERIFY mode use a lower number of iterations (744, close to the median 756), so failure actually occurs. */ +#ifdef VERIFY +#define JACOBI64_ITERATIONS 12 +#else +#define JACOBI64_ITERATIONS 25 +#endif + +/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1. */ +static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { + /* Start with f=modulus, g=x, eta=-1. */ + secp256k1_modinv64_signed62 f = modinfo->modulus; + secp256k1_modinv64_signed62 g = *x; + int j, len = 5; + int64_t eta = -1; /* eta = -delta; delta is initially 1 */ + int64_t cond, fn, gn; + int jac = 0; + int count; + + /* The input limbs must all be non-negative. */ + VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0); + + /* If x > 0, then if the loop below converges, it converges to f=g=gcd(x,modulus). Since we + * require that gcd(x,modulus)=1 and modulus>=3, x cannot be 0. Thus, we must reach f=1 (or + * time out). */ + VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4]) != 0); + + for (count = 0; count < JACOBI64_ITERATIONS; ++count) { + /* Compute transition matrix and new eta after 62 posdivsteps. */ + secp256k1_modinv64_trans2x2 t; + eta = secp256k1_modinv64_posdivsteps_62_var(eta, f.v[0] | ((uint64_t)f.v[1] << 62), g.v[0] | ((uint64_t)g.v[1] << 62), &t, &jac); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t); + /* If the bottom limb of f is 1, there is a chance that f=1. */ + if (f.v[0] == 1) { + cond = 0; + /* Check if the other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= f.v[j]; + } + /* If so, we're done. When f=1, the Jacobi symbol (g | f)=1. */ + if (cond == 0) return 1 - 2*(jac & 1); + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int64_t)len - 2) >> 63; + cond |= fn; + cond |= gn; + /* If so, reduce length. */ + if (cond == 0) --len; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* The loop failed to converge to f=g after 1550 iterations. Return 0, indicating unknown result. */ + return 0; +} + +#endif /* SECP256K1_MODINV64_IMPL_H */ diff --git a/src/secp256k1/src/modules/ecdh/Makefile.am.include b/src/secp256k1/src/modules/ecdh/Makefile.am.include new file mode 100644 index 0000000000..7f7f95f1fd --- /dev/null +++ b/src/secp256k1/src/modules/ecdh/Makefile.am.include @@ -0,0 +1,4 @@ +include_HEADERS += include/secp256k1_ecdh.h +noinst_HEADERS += src/modules/ecdh/main_impl.h +noinst_HEADERS += src/modules/ecdh/tests_impl.h +noinst_HEADERS += src/modules/ecdh/bench_impl.h diff --git a/src/secp256k1/src/modules/ecdh/bench_impl.h b/src/secp256k1/src/modules/ecdh/bench_impl.h new file mode 100644 index 0000000000..c23aaa94d1 --- /dev/null +++ b/src/secp256k1/src/modules/ecdh/bench_impl.h @@ -0,0 +1,57 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_BENCH_H +#define SECP256K1_MODULE_ECDH_BENCH_H + +#include "../../../include/secp256k1_ecdh.h" + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point; + unsigned char scalar[32]; +} bench_ecdh_data; + +static void bench_ecdh_setup(void* arg) { + int i; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + const unsigned char point[] = { + 0x03, + 0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06, + 0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd, + 0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb, + 0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f + }; + + for (i = 0; i < 32; i++) { + data->scalar[i] = i + 1; + } + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1); +} + +static void bench_ecdh(void* arg, int iters) { + int i; + unsigned char res[32]; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + + for (i = 0; i < iters; i++) { + CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar, NULL, NULL) == 1); + } +} + +static void run_ecdh_bench(int iters, int argc, char** argv) { + bench_ecdh_data data; + int d = argc == 1; + + /* create a context with no capabilities */ + data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT); + + if (d || have_flag(argc, argv, "ecdh")) run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); +} + +#endif /* SECP256K1_MODULE_ECDH_BENCH_H */ diff --git a/src/secp256k1/src/modules/ecdh/main_impl.h b/src/secp256k1/src/modules/ecdh/main_impl.h new file mode 100644 index 0000000000..5408c9de70 --- /dev/null +++ b/src/secp256k1/src/modules/ecdh/main_impl.h @@ -0,0 +1,71 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_MAIN_H +#define SECP256K1_MODULE_ECDH_MAIN_H + +#include "../../../include/secp256k1_ecdh.h" +#include "../../ecmult_const_impl.h" + +static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) { + unsigned char version = (y32[31] & 0x01) | 0x02; + secp256k1_sha256 sha; + (void)data; + + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, &version, 1); + secp256k1_sha256_write(&sha, x32, 32); + secp256k1_sha256_finalize(&sha, output); + + return 1; +} + +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256 = ecdh_hash_function_sha256; +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default = ecdh_hash_function_sha256; + +int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const secp256k1_pubkey *point, const unsigned char *scalar, secp256k1_ecdh_hash_function hashfp, void *data) { + int ret = 0; + int overflow = 0; + secp256k1_gej res; + secp256k1_ge pt; + secp256k1_scalar s; + unsigned char x[32]; + unsigned char y[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(point != NULL); + ARG_CHECK(scalar != NULL); + + if (hashfp == NULL) { + hashfp = secp256k1_ecdh_hash_function_default; + } + + secp256k1_pubkey_load(ctx, &pt, point); + secp256k1_scalar_set_b32(&s, scalar, &overflow); + + overflow |= secp256k1_scalar_is_zero(&s); + secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow); + + secp256k1_ecmult_const(&res, &pt, &s, 256); + secp256k1_ge_set_gej(&pt, &res); + + /* Compute a hash of the point */ + secp256k1_fe_normalize(&pt.x); + secp256k1_fe_normalize(&pt.y); + secp256k1_fe_get_b32(x, &pt.x); + secp256k1_fe_get_b32(y, &pt.y); + + ret = hashfp(output, x, y, data); + + memset(x, 0, 32); + memset(y, 0, 32); + secp256k1_scalar_clear(&s); + + return !!ret & !overflow; +} + +#endif /* SECP256K1_MODULE_ECDH_MAIN_H */ diff --git a/src/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h new file mode 100644 index 0000000000..fa6f232227 --- /dev/null +++ b/src/secp256k1/src/modules/ecdh/tests_impl.h @@ -0,0 +1,165 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_TESTS_H +#define SECP256K1_MODULE_ECDH_TESTS_H + +static int ecdh_hash_function_test_fail(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)output; + (void)x; + (void)y; + (void)data; + return 0; +} + +static int ecdh_hash_function_custom(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)data; + /* Save x and y as uncompressed public key */ + output[0] = 0x04; + memcpy(output + 1, x, 32); + memcpy(output + 33, y, 32); + return 1; +} + +static void test_ecdh_api(void) { + /* Setup context that just counts errors */ + secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + secp256k1_pubkey point; + unsigned char res[32]; + unsigned char s_one[32] = { 0 }; + int32_t ecount = 0; + s_one[31] = 1; + + secp256k1_context_set_error_callback(tctx, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(tctx, counting_illegal_callback_fn, &ecount); + CHECK(secp256k1_ec_pubkey_create(tctx, &point, s_one) == 1); + + /* Check all NULLs are detected */ + CHECK(secp256k1_ecdh(tctx, res, &point, s_one, NULL, NULL) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdh(tctx, NULL, &point, s_one, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdh(tctx, res, NULL, s_one, NULL, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdh(tctx, res, &point, NULL, NULL, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdh(tctx, res, &point, s_one, NULL, NULL) == 1); + CHECK(ecount == 3); + + /* Cleanup */ + secp256k1_context_destroy(tctx); +} + +static void test_ecdh_generator_basepoint(void) { + unsigned char s_one[32] = { 0 }; + secp256k1_pubkey point[2]; + int i; + + s_one[31] = 1; + /* Check against pubkey creation when the basepoint is the generator */ + for (i = 0; i < 2 * COUNT; ++i) { + secp256k1_sha256 sha; + unsigned char s_b32[32]; + unsigned char output_ecdh[65]; + unsigned char output_ser[32]; + unsigned char point_ser[65]; + size_t point_ser_len = sizeof(point_ser); + secp256k1_scalar s; + + random_scalar_order(&s); + secp256k1_scalar_get_b32(s_b32, &s); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point[0], s_one) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &point[1], s_b32) == 1); + + /* compute using ECDH function with custom hash function */ + CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, ecdh_hash_function_custom, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_UNCOMPRESSED) == 1); + /* compare */ + CHECK(secp256k1_memcmp_var(output_ecdh, point_ser, 65) == 0); + + /* compute using ECDH function with default hash function */ + CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, NULL, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1); + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, point_ser, point_ser_len); + secp256k1_sha256_finalize(&sha, output_ser); + /* compare */ + CHECK(secp256k1_memcmp_var(output_ecdh, output_ser, 32) == 0); + } +} + +static void test_bad_scalar(void) { + unsigned char s_zero[32] = { 0 }; + unsigned char s_overflow[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 + }; + unsigned char s_rand[32] = { 0 }; + unsigned char output[32]; + secp256k1_scalar rand; + secp256k1_pubkey point; + + /* Create random point */ + random_scalar_order(&rand); + secp256k1_scalar_get_b32(s_rand, &rand); + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_rand) == 1); + + /* Try to multiply it by bad values */ + CHECK(secp256k1_ecdh(CTX, output, &point, s_zero, NULL, NULL) == 0); + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 0); + /* ...and a good one */ + s_overflow[31] -= 1; + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 1); + + /* Hash function failure results in ecdh failure */ + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, ecdh_hash_function_test_fail, NULL) == 0); +} + +/** Test that ECDH(sG, 1/s) == ECDH((1/s)G, s) == ECDH(G, 1) for a few random s. */ +static void test_result_basepoint(void) { + secp256k1_pubkey point; + secp256k1_scalar rand; + unsigned char s[32]; + unsigned char s_inv[32]; + unsigned char out[32]; + unsigned char out_inv[32]; + unsigned char out_base[32]; + int i; + + unsigned char s_one[32] = { 0 }; + s_one[31] = 1; + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_one) == 1); + CHECK(secp256k1_ecdh(CTX, out_base, &point, s_one, NULL, NULL) == 1); + + for (i = 0; i < 2 * COUNT; i++) { + random_scalar_order(&rand); + secp256k1_scalar_get_b32(s, &rand); + secp256k1_scalar_inverse(&rand, &rand); + secp256k1_scalar_get_b32(s_inv, &rand); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s) == 1); + CHECK(secp256k1_ecdh(CTX, out, &point, s_inv, NULL, NULL) == 1); + CHECK(secp256k1_memcmp_var(out, out_base, 32) == 0); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_inv) == 1); + CHECK(secp256k1_ecdh(CTX, out_inv, &point, s, NULL, NULL) == 1); + CHECK(secp256k1_memcmp_var(out_inv, out_base, 32) == 0); + } +} + +static void run_ecdh_tests(void) { + test_ecdh_api(); + test_ecdh_generator_basepoint(); + test_bad_scalar(); + test_result_basepoint(); +} + +#endif /* SECP256K1_MODULE_ECDH_TESTS_H */ diff --git a/src/secp256k1/src/modules/extrakeys/Makefile.am.include b/src/secp256k1/src/modules/extrakeys/Makefile.am.include new file mode 100644 index 0000000000..0d901ec1f4 --- /dev/null +++ b/src/secp256k1/src/modules/extrakeys/Makefile.am.include @@ -0,0 +1,4 @@ +include_HEADERS += include/secp256k1_extrakeys.h +noinst_HEADERS += src/modules/extrakeys/tests_impl.h +noinst_HEADERS += src/modules/extrakeys/tests_exhaustive_impl.h +noinst_HEADERS += src/modules/extrakeys/main_impl.h diff --git a/src/secp256k1/src/modules/extrakeys/main_impl.h b/src/secp256k1/src/modules/extrakeys/main_impl.h new file mode 100644 index 0000000000..e1003052f4 --- /dev/null +++ b/src/secp256k1/src/modules/extrakeys/main_impl.h @@ -0,0 +1,284 @@ +/*********************************************************************** + * Copyright (c) 2020 Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_MAIN_H +#define SECP256K1_MODULE_EXTRAKEYS_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_extrakeys.h" + +static SECP256K1_INLINE int secp256k1_xonly_pubkey_load(const secp256k1_context* ctx, secp256k1_ge *ge, const secp256k1_xonly_pubkey *pubkey) { + return secp256k1_pubkey_load(ctx, ge, (const secp256k1_pubkey *) pubkey); +} + +static SECP256K1_INLINE void secp256k1_xonly_pubkey_save(secp256k1_xonly_pubkey *pubkey, secp256k1_ge *ge) { + secp256k1_pubkey_save((secp256k1_pubkey *) pubkey, ge); +} + +int secp256k1_xonly_pubkey_parse(const secp256k1_context* ctx, secp256k1_xonly_pubkey *pubkey, const unsigned char *input32) { + secp256k1_ge pk; + secp256k1_fe x; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(input32 != NULL); + + if (!secp256k1_fe_set_b32(&x, input32)) { + return 0; + } + if (!secp256k1_ge_set_xo_var(&pk, &x, 0)) { + return 0; + } + if (!secp256k1_ge_is_in_correct_subgroup(&pk)) { + return 0; + } + secp256k1_xonly_pubkey_save(pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output32, const secp256k1_xonly_pubkey *pubkey) { + secp256k1_ge pk; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output32 != NULL); + memset(output32, 0, 32); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + secp256k1_fe_get_b32(output32, &pk.x); + return 1; +} + +int secp256k1_xonly_pubkey_cmp(const secp256k1_context* ctx, const secp256k1_xonly_pubkey* pk0, const secp256k1_xonly_pubkey* pk1) { + unsigned char out[2][32]; + const secp256k1_xonly_pubkey* pk[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + pk[0] = pk0; pk[1] = pk1; + for (i = 0; i < 2; i++) { + /* If the public key is NULL or invalid, xonly_pubkey_serialize will + * call the illegal_callback and return 0. In that case we will + * serialize the key as all zeros which is less than any valid public + * key. This results in consistent comparisons even if NULL or invalid + * pubkeys are involved and prevents edge cases such as sorting + * algorithms that use this function and do not terminate as a + * result. */ + if (!secp256k1_xonly_pubkey_serialize(ctx, out[i], pk[i])) { + /* Note that xonly_pubkey_serialize should already set the output to + * zero in that case, but it's not guaranteed by the API, we can't + * test it and writing a VERIFY_CHECK is more complex than + * explicitly memsetting (again). */ + memset(out[i], 0, sizeof(out[i])); + } + } + return secp256k1_memcmp_var(out[0], out[1], sizeof(out[1])); +} + +/** Keeps a group element as is if it has an even Y and otherwise negates it. + * y_parity is set to 0 in the former case and to 1 in the latter case. + * Requires that the coordinates of r are normalized. */ +static int secp256k1_extrakeys_ge_even_y(secp256k1_ge *r) { + int y_parity = 0; + VERIFY_CHECK(!secp256k1_ge_is_infinity(r)); + + if (secp256k1_fe_is_odd(&r->y)) { + secp256k1_fe_negate(&r->y, &r->y, 1); + y_parity = 1; + } + return y_parity; +} + +int secp256k1_xonly_pubkey_from_pubkey(const secp256k1_context* ctx, secp256k1_xonly_pubkey *xonly_pubkey, int *pk_parity, const secp256k1_pubkey *pubkey) { + secp256k1_ge pk; + int tmp; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(xonly_pubkey != NULL); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + tmp = secp256k1_extrakeys_ge_even_y(&pk); + if (pk_parity != NULL) { + *pk_parity = tmp; + } + secp256k1_xonly_pubkey_save(xonly_pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32) { + secp256k1_ge pk; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output_pubkey != NULL); + memset(output_pubkey, 0, sizeof(*output_pubkey)); + ARG_CHECK(internal_pubkey != NULL); + ARG_CHECK(tweak32 != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey) + || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) { + return 0; + } + secp256k1_pubkey_save(output_pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_tweak_add_check(const secp256k1_context* ctx, const unsigned char *tweaked_pubkey32, int tweaked_pk_parity, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32) { + secp256k1_ge pk; + unsigned char pk_expected32[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(internal_pubkey != NULL); + ARG_CHECK(tweaked_pubkey32 != NULL); + ARG_CHECK(tweak32 != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey) + || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) { + return 0; + } + secp256k1_fe_normalize_var(&pk.x); + secp256k1_fe_normalize_var(&pk.y); + secp256k1_fe_get_b32(pk_expected32, &pk.x); + + return secp256k1_memcmp_var(&pk_expected32, tweaked_pubkey32, 32) == 0 + && secp256k1_fe_is_odd(&pk.y) == tweaked_pk_parity; +} + +static void secp256k1_keypair_save(secp256k1_keypair *keypair, const secp256k1_scalar *sk, secp256k1_ge *pk) { + secp256k1_scalar_get_b32(&keypair->data[0], sk); + secp256k1_pubkey_save((secp256k1_pubkey *)&keypair->data[32], pk); +} + + +static int secp256k1_keypair_seckey_load(const secp256k1_context* ctx, secp256k1_scalar *sk, const secp256k1_keypair *keypair) { + int ret; + + ret = secp256k1_scalar_set_b32_seckey(sk, &keypair->data[0]); + /* We can declassify ret here because sk is only zero if a keypair function + * failed (which zeroes the keypair) and its return value is ignored. */ + secp256k1_declassify(ctx, &ret, sizeof(ret)); + ARG_CHECK(ret); + return ret; +} + +/* Load a keypair into pk and sk (if non-NULL). This function declassifies pk + * and ARG_CHECKs that the keypair is not invalid. It always initializes sk and + * pk with dummy values. */ +static int secp256k1_keypair_load(const secp256k1_context* ctx, secp256k1_scalar *sk, secp256k1_ge *pk, const secp256k1_keypair *keypair) { + int ret; + const secp256k1_pubkey *pubkey = (const secp256k1_pubkey *)&keypair->data[32]; + + /* Need to declassify the pubkey because pubkey_load ARG_CHECKs if it's + * invalid. */ + secp256k1_declassify(ctx, pubkey, sizeof(*pubkey)); + ret = secp256k1_pubkey_load(ctx, pk, pubkey); + if (sk != NULL) { + ret = ret && secp256k1_keypair_seckey_load(ctx, sk, keypair); + } + if (!ret) { + *pk = secp256k1_ge_const_g; + if (sk != NULL) { + *sk = secp256k1_scalar_one; + } + } + return ret; +} + +int secp256k1_keypair_create(const secp256k1_context* ctx, secp256k1_keypair *keypair, const unsigned char *seckey32) { + secp256k1_scalar sk; + secp256k1_ge pk; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(keypair != NULL); + memset(keypair, 0, sizeof(*keypair)); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey32 != NULL); + + ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &sk, &pk, seckey32); + secp256k1_keypair_save(keypair, &sk, &pk); + secp256k1_memczero(keypair, sizeof(*keypair), !ret); + + secp256k1_scalar_clear(&sk); + return ret; +} + +int secp256k1_keypair_sec(const secp256k1_context* ctx, unsigned char *seckey, const secp256k1_keypair *keypair) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + memset(seckey, 0, 32); + ARG_CHECK(keypair != NULL); + + memcpy(seckey, &keypair->data[0], 32); + return 1; +} + +int secp256k1_keypair_pub(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_keypair *keypair) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(keypair != NULL); + + memcpy(pubkey->data, &keypair->data[32], sizeof(*pubkey)); + return 1; +} + +int secp256k1_keypair_xonly_pub(const secp256k1_context* ctx, secp256k1_xonly_pubkey *pubkey, int *pk_parity, const secp256k1_keypair *keypair) { + secp256k1_ge pk; + int tmp; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(keypair != NULL); + + if (!secp256k1_keypair_load(ctx, NULL, &pk, keypair)) { + return 0; + } + tmp = secp256k1_extrakeys_ge_even_y(&pk); + if (pk_parity != NULL) { + *pk_parity = tmp; + } + secp256k1_xonly_pubkey_save(pubkey, &pk); + + return 1; +} + +int secp256k1_keypair_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_keypair *keypair, const unsigned char *tweak32) { + secp256k1_ge pk; + secp256k1_scalar sk; + int y_parity; + int ret; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(keypair != NULL); + ARG_CHECK(tweak32 != NULL); + + ret = secp256k1_keypair_load(ctx, &sk, &pk, keypair); + memset(keypair, 0, sizeof(*keypair)); + + y_parity = secp256k1_extrakeys_ge_even_y(&pk); + if (y_parity == 1) { + secp256k1_scalar_negate(&sk, &sk); + } + + ret &= secp256k1_ec_seckey_tweak_add_helper(&sk, tweak32); + ret &= secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32); + + secp256k1_declassify(ctx, &ret, sizeof(ret)); + if (ret) { + secp256k1_keypair_save(keypair, &sk, &pk); + } + + secp256k1_scalar_clear(&sk); + return ret; +} + +#endif diff --git a/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h new file mode 100644 index 0000000000..5ecc90d50f --- /dev/null +++ b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h @@ -0,0 +1,68 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H + +#include "../../../include/secp256k1_extrakeys.h" +#include "main_impl.h" + +static void test_exhaustive_extrakeys(const secp256k1_context *ctx, const secp256k1_ge* group) { + secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_pubkey pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + int parities[EXHAUSTIVE_TEST_ORDER - 1]; + unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32]; + int i; + + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_fe fe; + secp256k1_scalar scalar_i; + unsigned char buf[33]; + int parity; + + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_scalar_get_b32(buf, &scalar_i); + + /* Construct pubkey and keypair. */ + CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey[i - 1], buf)); + + /* Construct serialized xonly_pubkey from keypair. */ + CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parities[i - 1], &keypair[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1])); + + /* Parse the xonly_pubkey back and verify it matches the previously serialized value. */ + CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pubkey[i - 1], xonly_pubkey_bytes[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1])); + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0); + + /* Construct the xonly_pubkey from the pubkey, and verify it matches the same. */ + CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pubkey[i - 1], &parity, &pubkey[i - 1])); + CHECK(parity == parities[i - 1]); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1])); + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0); + + /* Compare the xonly_pubkey bytes against the precomputed group. */ + secp256k1_fe_set_b32(&fe, xonly_pubkey_bytes[i - 1]); + CHECK(secp256k1_fe_equal_var(&fe, &group[i].x)); + + /* Check the parity against the precomputed group. */ + fe = group[i].y; + secp256k1_fe_normalize_var(&fe); + CHECK(secp256k1_fe_is_odd(&fe) == parities[i - 1]); + + /* Verify that the higher half is identical to the lower half mirrored. */ + if (i > EXHAUSTIVE_TEST_ORDER / 2) { + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - i - 1], 32) == 0); + CHECK(parities[i - 1] == 1 - parities[EXHAUSTIVE_TEST_ORDER - i - 1]); + } + } + + /* TODO: keypair/xonly_pubkey tweak tests */ +} + +#endif diff --git a/src/secp256k1/src/modules/extrakeys/tests_impl.h b/src/secp256k1/src/modules/extrakeys/tests_impl.h new file mode 100644 index 0000000000..ae1655923b --- /dev/null +++ b/src/secp256k1/src/modules/extrakeys/tests_impl.h @@ -0,0 +1,566 @@ +/*********************************************************************** + * Copyright (c) 2020 Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_H + +#include "../../../include/secp256k1_extrakeys.h" + +static void set_counting_callbacks(secp256k1_context *ctx0, int *ecount) { + secp256k1_context_set_error_callback(ctx0, counting_illegal_callback_fn, ecount); + secp256k1_context_set_illegal_callback(ctx0, counting_illegal_callback_fn, ecount); +} + +static void test_xonly_pubkey(void) { + secp256k1_pubkey pk; + secp256k1_xonly_pubkey xonly_pk, xonly_pk_tmp; + secp256k1_ge pk1; + secp256k1_ge pk2; + secp256k1_fe y; + unsigned char sk[32]; + unsigned char xy_sk[32]; + unsigned char buf32[32]; + unsigned char ones32[32]; + unsigned char zeros64[64] = { 0 }; + int pk_parity; + int i; + + int ecount; + + set_counting_callbacks(CTX, &ecount); + + secp256k1_testrand256(sk); + memset(ones32, 0xFF, 32); + secp256k1_testrand256(xy_sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + + /* Test xonly_pubkey_from_pubkey */ + ecount = 0; + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, NULL, &pk_parity, &pk) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, NULL) == 0); + CHECK(ecount == 2); + memset(&pk, 0, sizeof(pk)); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 0); + CHECK(ecount == 3); + + /* Choose a secret key such that the resulting pubkey and xonly_pubkey match. */ + memset(sk, 0, sizeof(sk)); + sk[0] = 1; + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_memcmp_var(&pk, &xonly_pk, sizeof(pk)) == 0); + CHECK(pk_parity == 0); + + /* Choose a secret key such that pubkey and xonly_pubkey are each others + * negation. */ + sk[0] = 2; + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &pk, sizeof(xonly_pk)) != 0); + CHECK(pk_parity == 1); + secp256k1_pubkey_load(CTX, &pk1, &pk); + secp256k1_pubkey_load(CTX, &pk2, (secp256k1_pubkey *) &xonly_pk); + CHECK(secp256k1_fe_equal(&pk1.x, &pk2.x) == 1); + secp256k1_fe_negate(&y, &pk2.y, 1); + CHECK(secp256k1_fe_equal(&pk1.y, &y) == 1); + + /* Test xonly_pubkey_serialize and xonly_pubkey_parse */ + ecount = 0; + CHECK(secp256k1_xonly_pubkey_serialize(CTX, NULL, &xonly_pk) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, NULL) == 0); + CHECK(secp256k1_memcmp_var(buf32, zeros64, 32) == 0); + CHECK(ecount == 2); + { + /* A pubkey filled with 0s will fail to serialize due to pubkey_load + * special casing. */ + secp256k1_xonly_pubkey pk_tmp; + memset(&pk_tmp, 0, sizeof(pk_tmp)); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &pk_tmp) == 0); + } + /* pubkey_load called illegal callback */ + CHECK(ecount == 3); + + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &xonly_pk) == 1); + ecount = 0; + CHECK(secp256k1_xonly_pubkey_parse(CTX, NULL, buf32) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, NULL) == 0); + CHECK(ecount == 2); + + /* Serialization and parse roundtrip */ + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk_tmp, buf32) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(xonly_pk)) == 0); + + /* Test parsing invalid field elements */ + memset(&xonly_pk, 1, sizeof(xonly_pk)); + /* Overflowing field element */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, ones32) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + memset(&xonly_pk, 1, sizeof(xonly_pk)); + /* There's no point with x-coordinate 0 on secp256k1 */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, zeros64) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + /* If a random 32-byte string can not be parsed with ec_pubkey_parse + * (because interpreted as X coordinate it does not correspond to a point on + * the curve) then xonly_pubkey_parse should fail as well. */ + for (i = 0; i < COUNT; i++) { + unsigned char rand33[33]; + secp256k1_testrand256(&rand33[1]); + rand33[0] = SECP256K1_TAG_PUBKEY_EVEN; + if (!secp256k1_ec_pubkey_parse(CTX, &pk, rand33, 33)) { + memset(&xonly_pk, 1, sizeof(xonly_pk)); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, &rand33[1]) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + } else { + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, &rand33[1]) == 1); + } + } + CHECK(ecount == 2); +} + +static void test_xonly_pubkey_comparison(void) { + unsigned char pk1_ser[32] = { + 0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11, + 0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23 + }; + const unsigned char pk2_ser[32] = { + 0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d, + 0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c + }; + secp256k1_xonly_pubkey pk1; + secp256k1_xonly_pubkey pk2; + int ecount = 0; + + set_counting_callbacks(CTX, &ecount); + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk1, pk1_ser) == 1); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk2, pk2_ser) == 1); + + CHECK(secp256k1_xonly_pubkey_cmp(CTX, NULL, &pk2) < 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, NULL) > 0); + CHECK(ecount == 2); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk2) < 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk1) > 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk1) == 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk2) == 0); + CHECK(ecount == 2); + memset(&pk1, 0, sizeof(pk1)); /* illegal pubkey */ + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk2) < 0); + CHECK(ecount == 3); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk1) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk1) > 0); + CHECK(ecount == 6); +} + +static void test_xonly_pubkey_tweak(void) { + unsigned char zeros64[64] = { 0 }; + unsigned char overflows[32]; + unsigned char sk[32]; + secp256k1_pubkey internal_pk; + secp256k1_xonly_pubkey internal_xonly_pk; + secp256k1_pubkey output_pk; + int pk_parity; + unsigned char tweak[32]; + int i; + + int ecount; + + set_counting_callbacks(CTX, &ecount); + + memset(overflows, 0xff, sizeof(overflows)); + secp256k1_testrand256(tweak); + secp256k1_testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &internal_pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, &pk_parity, &internal_pk) == 1); + + ecount = 0; + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, NULL, &internal_xonly_pk, tweak) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, NULL, tweak) == 0); + CHECK(ecount == 2); + /* NULL internal_xonly_pk zeroes the output_pk */ + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, NULL) == 0); + CHECK(ecount == 3); + /* NULL tweak zeroes the output_pk */ + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + + /* Invalid tweak zeroes the output_pk */ + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + + /* A zero tweak is fine */ + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, zeros64) == 1); + + /* Fails if the resulting key was infinity */ + for (i = 0; i < COUNT; i++) { + secp256k1_scalar scalar_tweak; + /* Because sk may be negated before adding, we need to try with tweak = + * sk as well as tweak = -sk. */ + secp256k1_scalar_set_b32(&scalar_tweak, sk, NULL); + secp256k1_scalar_negate(&scalar_tweak, &scalar_tweak); + secp256k1_scalar_get_b32(tweak, &scalar_tweak); + CHECK((secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, sk) == 0) + || (secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 0)); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + } + + /* Invalid pk with a valid tweak */ + memset(&internal_xonly_pk, 0, sizeof(internal_xonly_pk)); + secp256k1_testrand256(tweak); + ecount = 0; + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); +} + +static void test_xonly_pubkey_tweak_check(void) { + unsigned char zeros64[64] = { 0 }; + unsigned char overflows[32]; + unsigned char sk[32]; + secp256k1_pubkey internal_pk; + secp256k1_xonly_pubkey internal_xonly_pk; + secp256k1_pubkey output_pk; + secp256k1_xonly_pubkey output_xonly_pk; + unsigned char output_pk32[32]; + unsigned char buf32[32]; + int pk_parity; + unsigned char tweak[32]; + + int ecount; + + set_counting_callbacks(CTX, &ecount); + + memset(overflows, 0xff, sizeof(overflows)); + secp256k1_testrand256(tweak); + secp256k1_testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &internal_pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, &pk_parity, &internal_pk) == 1); + + ecount = 0; + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &output_xonly_pk, &pk_parity, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &output_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, NULL, pk_parity, &internal_xonly_pk, tweak) == 0); + CHECK(ecount == 1); + /* invalid pk_parity value */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, 2, &internal_xonly_pk, tweak) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, NULL, tweak) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, NULL) == 0); + CHECK(ecount == 3); + + memset(tweak, 1, sizeof(tweak)); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, NULL, &internal_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &output_xonly_pk, &pk_parity, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, output_pk32, &output_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, pk_parity, &internal_xonly_pk, tweak) == 1); + + /* Wrong pk_parity */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, !pk_parity, &internal_xonly_pk, tweak) == 0); + /* Wrong public key */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &internal_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 0); + + /* Overflowing tweak not allowed */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, pk_parity, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + CHECK(ecount == 3); +} + +/* Starts with an initial pubkey and recursively creates N_PUBKEYS - 1 + * additional pubkeys by calling tweak_add. Then verifies every tweak starting + * from the last pubkey. */ +#define N_PUBKEYS 32 +static void test_xonly_pubkey_tweak_recursive(void) { + unsigned char sk[32]; + secp256k1_pubkey pk[N_PUBKEYS]; + unsigned char pk_serialized[32]; + unsigned char tweak[N_PUBKEYS - 1][32]; + int i; + + secp256k1_testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &pk[0], sk) == 1); + /* Add tweaks */ + for (i = 0; i < N_PUBKEYS - 1; i++) { + secp256k1_xonly_pubkey xonly_pk; + memset(tweak[i], i + 1, sizeof(tweak[i])); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk[i]) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &pk[i + 1], &xonly_pk, tweak[i]) == 1); + } + + /* Verify tweaks */ + for (i = N_PUBKEYS - 1; i > 0; i--) { + secp256k1_xonly_pubkey xonly_pk; + int pk_parity; + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk[i]) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, pk_serialized, &xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk[i - 1]) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, pk_serialized, pk_parity, &xonly_pk, tweak[i - 1]) == 1); + } +} +#undef N_PUBKEYS + +static void test_keypair(void) { + unsigned char sk[32]; + unsigned char sk_tmp[32]; + unsigned char zeros96[96] = { 0 }; + unsigned char overflows[32]; + secp256k1_keypair keypair; + secp256k1_pubkey pk, pk_tmp; + secp256k1_xonly_pubkey xonly_pk, xonly_pk_tmp; + int pk_parity, pk_parity_tmp; + int ecount; + + set_counting_callbacks(CTX, &ecount); + set_counting_callbacks(STATIC_CTX, &ecount); + + CHECK(sizeof(zeros96) == sizeof(keypair)); + memset(overflows, 0xFF, sizeof(overflows)); + + /* Test keypair_create */ + ecount = 0; + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0); + CHECK(ecount == 0); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0); + CHECK(ecount == 0); + CHECK(secp256k1_keypair_create(CTX, NULL, sk) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_create(CTX, &keypair, NULL) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_keypair_create(STATIC_CTX, &keypair, sk) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + CHECK(ecount == 3); + + /* Invalid secret key */ + CHECK(secp256k1_keypair_create(CTX, &keypair, zeros96) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + CHECK(secp256k1_keypair_create(CTX, &keypair, overflows) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + + /* Test keypair_pub */ + ecount = 0; + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_pub(CTX, &pk, &keypair) == 1); + CHECK(secp256k1_keypair_pub(CTX, NULL, &keypair) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_pub(CTX, &pk, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0); + + /* Using an invalid keypair is fine for keypair_pub */ + memset(&keypair, 0, sizeof(keypair)); + CHECK(secp256k1_keypair_pub(CTX, &pk, &keypair) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0); + + /* keypair holds the same pubkey as pubkey_create */ + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_pub(CTX, &pk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(&pk, &pk_tmp, sizeof(pk)) == 0); + + /** Test keypair_xonly_pub **/ + ecount = 0; + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, NULL, &pk_parity, &keypair) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, NULL, &keypair) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0); + /* Using an invalid keypair will set the xonly_pk to 0 (first reset + * xonly_pk). */ + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair) == 1); + memset(&keypair, 0, sizeof(keypair)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0); + CHECK(ecount == 3); + + /** keypair holds the same xonly pubkey as pubkey_create **/ + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk_tmp, &pk_parity_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(pk)) == 0); + CHECK(pk_parity == pk_parity_tmp); + + /* Test keypair_seckey */ + ecount = 0; + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK(secp256k1_keypair_sec(CTX, NULL, &keypair) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0); + + /* keypair returns the same seckey it got */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(sk, sk_tmp, sizeof(sk_tmp)) == 0); + + + /* Using an invalid keypair is fine for keypair_seckey */ + memset(&keypair, 0, sizeof(keypair)); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0); + + secp256k1_context_set_error_callback(STATIC_CTX, NULL, NULL); + secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL); +} + +static void test_keypair_add(void) { + unsigned char sk[32]; + secp256k1_keypair keypair; + unsigned char overflows[32]; + unsigned char zeros96[96] = { 0 }; + unsigned char tweak[32]; + int i; + int ecount = 0; + + set_counting_callbacks(CTX, &ecount); + + CHECK(sizeof(zeros96) == sizeof(keypair)); + secp256k1_testrand256(sk); + secp256k1_testrand256(tweak); + memset(overflows, 0xFF, 32); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, NULL, tweak) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, NULL) == 0); + CHECK(ecount == 2); + /* This does not set the keypair to zeroes */ + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) != 0); + + /* Invalid tweak zeroes the keypair */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, overflows) == 0); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0); + + /* A zero tweak is fine */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, zeros96) == 1); + + /* Fails if the resulting keypair was (sk=0, pk=infinity) */ + for (i = 0; i < COUNT; i++) { + secp256k1_scalar scalar_tweak; + secp256k1_keypair keypair_tmp; + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memcpy(&keypair_tmp, &keypair, sizeof(keypair)); + /* Because sk may be negated before adding, we need to try with tweak = + * sk as well as tweak = -sk. */ + secp256k1_scalar_set_b32(&scalar_tweak, sk, NULL); + secp256k1_scalar_negate(&scalar_tweak, &scalar_tweak); + secp256k1_scalar_get_b32(tweak, &scalar_tweak); + CHECK((secp256k1_keypair_xonly_tweak_add(CTX, &keypair, sk) == 0) + || (secp256k1_keypair_xonly_tweak_add(CTX, &keypair_tmp, tweak) == 0)); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0 + || secp256k1_memcmp_var(&keypair_tmp, zeros96, sizeof(keypair_tmp)) == 0); + } + + /* Invalid keypair with a valid tweak */ + memset(&keypair, 0, sizeof(keypair)); + secp256k1_testrand256(tweak); + ecount = 0; + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0); + /* Only seckey part of keypair invalid */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memset(&keypair, 0, 32); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 0); + CHECK(ecount == 2); + /* Only pubkey part of keypair invalid */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memset(&keypair.data[32], 0, 64); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 0); + CHECK(ecount == 3); + + /* Check that the keypair_tweak_add implementation is correct */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + for (i = 0; i < COUNT; i++) { + secp256k1_xonly_pubkey internal_pk; + secp256k1_xonly_pubkey output_pk; + secp256k1_pubkey output_pk_xy; + secp256k1_pubkey output_pk_expected; + unsigned char pk32[32]; + unsigned char sk32[32]; + int pk_parity; + + secp256k1_testrand256(tweak); + CHECK(secp256k1_keypair_xonly_pub(CTX, &internal_pk, NULL, &keypair) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &output_pk, &pk_parity, &keypair) == 1); + + /* Check that it passes xonly_pubkey_tweak_add_check */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, pk32, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, pk32, pk_parity, &internal_pk, tweak) == 1); + + /* Check that the resulting pubkey matches xonly_pubkey_tweak_add */ + CHECK(secp256k1_keypair_pub(CTX, &output_pk_xy, &keypair) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk_expected, &internal_pk, tweak) == 1); + CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0); + + /* Check that the secret key in the keypair is tweaked correctly */ + CHECK(secp256k1_keypair_sec(CTX, sk32, &keypair) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &output_pk_expected, sk32) == 1); + CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0); + } +} + +static void run_extrakeys_tests(void) { + /* xonly key test cases */ + test_xonly_pubkey(); + test_xonly_pubkey_tweak(); + test_xonly_pubkey_tweak_check(); + test_xonly_pubkey_tweak_recursive(); + test_xonly_pubkey_comparison(); + + /* keypair tests */ + test_keypair(); + test_keypair_add(); +} + +#endif diff --git a/src/secp256k1/src/modules/recovery/Makefile.am.include b/src/secp256k1/src/modules/recovery/Makefile.am.include new file mode 100644 index 0000000000..156ea690fa --- /dev/null +++ b/src/secp256k1/src/modules/recovery/Makefile.am.include @@ -0,0 +1,5 @@ +include_HEADERS += include/secp256k1_recovery.h +noinst_HEADERS += src/modules/recovery/main_impl.h +noinst_HEADERS += src/modules/recovery/tests_impl.h +noinst_HEADERS += src/modules/recovery/tests_exhaustive_impl.h +noinst_HEADERS += src/modules/recovery/bench_impl.h diff --git a/src/secp256k1/src/modules/recovery/bench_impl.h b/src/secp256k1/src/modules/recovery/bench_impl.h new file mode 100644 index 0000000000..57108d4524 --- /dev/null +++ b/src/secp256k1/src/modules/recovery/bench_impl.h @@ -0,0 +1,62 @@ +/*********************************************************************** + * Copyright (c) 2014-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_BENCH_H +#define SECP256K1_MODULE_RECOVERY_BENCH_H + +#include "../../../include/secp256k1_recovery.h" + +typedef struct { + secp256k1_context *ctx; + unsigned char msg[32]; + unsigned char sig[64]; +} bench_recover_data; + +static void bench_recover(void* arg, int iters) { + int i; + bench_recover_data *data = (bench_recover_data*)arg; + secp256k1_pubkey pubkey; + unsigned char pubkeyc[33]; + + for (i = 0; i < iters; i++) { + int j; + size_t pubkeylen = 33; + secp256k1_ecdsa_recoverable_signature sig; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2)); + CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg)); + CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED)); + for (j = 0; j < 32; j++) { + data->sig[j + 32] = data->msg[j]; /* Move former message to S. */ + data->msg[j] = data->sig[j]; /* Move former R to message. */ + data->sig[j] = pubkeyc[j + 1]; /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */ + } + } +} + +static void bench_recover_setup(void* arg) { + int i; + bench_recover_data *data = (bench_recover_data*)arg; + + for (i = 0; i < 32; i++) { + data->msg[i] = 1 + i; + } + for (i = 0; i < 64; i++) { + data->sig[i] = 65 + i; + } +} + +static void run_recovery_bench(int iters, int argc, char** argv) { + bench_recover_data data; + int d = argc == 1; + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + + if (d || have_flag(argc, argv, "ecdsa") || have_flag(argc, argv, "recover") || have_flag(argc, argv, "ecdsa_recover")) run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); +} + +#endif /* SECP256K1_MODULE_RECOVERY_BENCH_H */ diff --git a/src/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h new file mode 100644 index 0000000000..e7906eb62e --- /dev/null +++ b/src/secp256k1/src/modules/recovery/main_impl.h @@ -0,0 +1,159 @@ +/*********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_MAIN_H +#define SECP256K1_MODULE_RECOVERY_MAIN_H + +#include "../../../include/secp256k1_recovery.h" + +static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) { + (void)ctx; + if (sizeof(secp256k1_scalar) == 32) { + /* When the secp256k1_scalar type is exactly 32 byte, use its + * representation inside secp256k1_ecdsa_signature, as conversion is very fast. + * Note that secp256k1_ecdsa_signature_save must use the same representation. */ + memcpy(r, &sig->data[0], 32); + memcpy(s, &sig->data[32], 32); + } else { + secp256k1_scalar_set_b32(r, &sig->data[0], NULL); + secp256k1_scalar_set_b32(s, &sig->data[32], NULL); + } + *recid = sig->data[64]; +} + +static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) { + if (sizeof(secp256k1_scalar) == 32) { + memcpy(&sig->data[0], r, 32); + memcpy(&sig->data[32], s, 32); + } else { + secp256k1_scalar_get_b32(&sig->data[0], r); + secp256k1_scalar_get_b32(&sig->data[32], s); + } + sig->data[64] = recid; +} + +int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) { + secp256k1_scalar r, s; + int ret = 1; + int overflow = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input64 != NULL); + ARG_CHECK(recid >= 0 && recid <= 3); + + secp256k1_scalar_set_b32(&r, &input64[0], &overflow); + ret &= !overflow; + secp256k1_scalar_set_b32(&s, &input64[32], &overflow); + ret &= !overflow; + if (ret) { + secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid); + } else { + memset(sig, 0, sizeof(*sig)); + } + return ret; +} + +int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output64 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(recid != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig); + secp256k1_scalar_get_b32(&output64[0], &r); + secp256k1_scalar_get_b32(&output64[32], &s); + return 1; +} + +int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) { + secp256k1_scalar r, s; + int recid; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(sigin != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin); + secp256k1_ecdsa_signature_save(sig, &r, &s); + return 1; +} + +static int secp256k1_ecdsa_sig_recover(const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) { + unsigned char brx[32]; + secp256k1_fe fx; + secp256k1_ge x; + secp256k1_gej xj; + secp256k1_scalar rn, u1, u2; + secp256k1_gej qj; + int r; + + if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) { + return 0; + } + + secp256k1_scalar_get_b32(brx, sigr); + r = secp256k1_fe_set_b32(&fx, brx); + (void)r; + VERIFY_CHECK(r); /* brx comes from a scalar, so is less than the order; certainly less than p */ + if (recid & 2) { + if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) { + return 0; + } + secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe); + } + if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) { + return 0; + } + secp256k1_gej_set_ge(&xj, &x); + secp256k1_scalar_inverse_var(&rn, sigr); + secp256k1_scalar_mul(&u1, &rn, message); + secp256k1_scalar_negate(&u1, &u1); + secp256k1_scalar_mul(&u2, &rn, sigs); + secp256k1_ecmult(&qj, &xj, &u2, &u1); + secp256k1_ge_set_gej_var(pubkey, &qj); + return !secp256k1_gej_is_infinity(&qj); +} + +int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msghash32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar r, s; + int ret, recid; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(msghash32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_ecdsa_sign_inner(ctx, &r, &s, &recid, msghash32, seckey, noncefp, noncedata); + secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid); + return ret; +} + +int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msghash32) { + secp256k1_ge q; + secp256k1_scalar r, s; + secp256k1_scalar m; + int recid; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(msghash32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(pubkey != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature); + VERIFY_CHECK(recid >= 0 && recid < 4); /* should have been caught in parse_compact */ + secp256k1_scalar_set_b32(&m, msghash32, NULL); + if (secp256k1_ecdsa_sig_recover(&r, &s, &q, &m, recid)) { + secp256k1_pubkey_save(pubkey, &q); + return 1; + } else { + memset(pubkey, 0, sizeof(*pubkey)); + return 0; + } +} + +#endif /* SECP256K1_MODULE_RECOVERY_MAIN_H */ diff --git a/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h new file mode 100644 index 0000000000..6bbc02b9a8 --- /dev/null +++ b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h @@ -0,0 +1,148 @@ +/*********************************************************************** + * Copyright (c) 2016 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H +#define SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H + +#include "main_impl.h" +#include "../../../include/secp256k1_recovery.h" + +static void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group) { + int i, j, k; + uint64_t iter = 0; + + /* Loop */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { /* message */ + for (j = 1; j < EXHAUSTIVE_TEST_ORDER; j++) { /* key */ + if (skip_section(&iter)) continue; + for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) { /* nonce */ + const int starting_k = k; + secp256k1_fe r_dot_y_normalized; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + secp256k1_scalar sk, msg, r, s, expected_r; + unsigned char sk32[32], msg32[32]; + int expected_recid; + int recid; + int overflow; + secp256k1_scalar_set_int(&msg, i); + secp256k1_scalar_set_int(&sk, j); + secp256k1_scalar_get_b32(sk32, &sk); + secp256k1_scalar_get_b32(msg32, &msg); + + secp256k1_ecdsa_sign_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k); + + /* Check directly */ + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig); + r_from_k(&expected_r, group, k, &overflow); + CHECK(r == expected_r); + CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER); + /* The recid's second bit is for conveying overflow (R.x value >= group order). + * In the actual secp256k1 this is an astronomically unlikely event, but in the + * small group used here, it will almost certainly be the case for all points. + * Note that this isn't actually useful; full recovery would need to convey + * floor(R.x / group_order), but only one bit is used as that is sufficient + * in the real group. */ + expected_recid = overflow ? 2 : 0; + r_dot_y_normalized = group[k].y; + secp256k1_fe_normalize(&r_dot_y_normalized); + /* Also the recovery id is flipped depending if we hit the low-s branch */ + if ((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER) { + expected_recid |= secp256k1_fe_is_odd(&r_dot_y_normalized); + } else { + expected_recid |= !secp256k1_fe_is_odd(&r_dot_y_normalized); + } + CHECK(recid == expected_recid); + + /* Convert to a standard sig then check */ + secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig); + secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig); + /* Note that we compute expected_r *after* signing -- this is important + * because our nonce-computing function function might change k during + * signing. */ + r_from_k(&expected_r, group, k, NULL); + CHECK(r == expected_r); + CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER); + + /* Overflow means we've tried every possible nonce */ + if (k < starting_k) { + break; + } + } + } + } +} + +static void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group) { + /* This is essentially a copy of test_exhaustive_verify, with recovery added */ + int s, r, msg, key; + uint64_t iter = 0; + for (s = 1; s < EXHAUSTIVE_TEST_ORDER; s++) { + for (r = 1; r < EXHAUSTIVE_TEST_ORDER; r++) { + for (msg = 1; msg < EXHAUSTIVE_TEST_ORDER; msg++) { + for (key = 1; key < EXHAUSTIVE_TEST_ORDER; key++) { + secp256k1_ge nonconst_ge; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + secp256k1_pubkey pk; + secp256k1_scalar sk_s, msg_s, r_s, s_s; + secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s; + int recid = 0; + int k, should_verify; + unsigned char msg32[32]; + + if (skip_section(&iter)) continue; + + secp256k1_scalar_set_int(&s_s, s); + secp256k1_scalar_set_int(&r_s, r); + secp256k1_scalar_set_int(&msg_s, msg); + secp256k1_scalar_set_int(&sk_s, key); + secp256k1_scalar_get_b32(msg32, &msg_s); + + /* Verify by hand */ + /* Run through every k value that gives us this r and check that *one* works. + * Note there could be none, there could be multiple, ECDSA is weird. */ + should_verify = 0; + for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) { + secp256k1_scalar check_x_s; + r_from_k(&check_x_s, group, k, NULL); + if (r_s == check_x_s) { + secp256k1_scalar_set_int(&s_times_k_s, k); + secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s); + secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s); + secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s); + should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s); + } + } + /* nb we have a "high s" rule */ + should_verify &= !secp256k1_scalar_is_high(&s_s); + + /* We would like to try recovering the pubkey and checking that it matches, + * but pubkey recovery is impossible in the exhaustive tests (the reason + * being that there are 12 nonzero r values, 12 nonzero points, and no + * overlap between the sets, so there are no valid signatures). */ + + /* Verify by converting to a standard signature and calling verify */ + secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid); + secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig); + memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge)); + secp256k1_pubkey_save(&pk, &nonconst_ge); + CHECK(should_verify == + secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk)); + } + } + } + } +} + +static void test_exhaustive_recovery(const secp256k1_context *ctx, const secp256k1_ge *group) { + test_exhaustive_recovery_sign(ctx, group); + test_exhaustive_recovery_verify(ctx, group); +} + +#endif /* SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H */ diff --git a/src/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h new file mode 100644 index 0000000000..3502c71ffe --- /dev/null +++ b/src/secp256k1/src/modules/recovery/tests_impl.h @@ -0,0 +1,373 @@ +/*********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_TESTS_H +#define SECP256K1_MODULE_RECOVERY_TESTS_H + +static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + (void) msg32; + (void) key32; + (void) algo16; + (void) data; + + /* On the first run, return 0 to force a second run */ + if (counter == 0) { + memset(nonce32, 0, 32); + return 1; + } + /* On the second run, return an overflow to force a third run */ + if (counter == 1) { + memset(nonce32, 0xff, 32); + return 1; + } + /* On the next run, return a valid nonce, but flip a coin as to whether or not to fail signing. */ + memset(nonce32, 1, 32); + return secp256k1_testrand_bits(1); +} + +static void test_ecdsa_recovery_api(void) { + /* Setup contexts that just count errors */ + secp256k1_pubkey pubkey; + secp256k1_pubkey recpubkey; + secp256k1_ecdsa_signature normal_sig; + secp256k1_ecdsa_recoverable_signature recsig; + unsigned char privkey[32] = { 1 }; + unsigned char message[32] = { 2 }; + int32_t ecount = 0; + int recid = 0; + unsigned char sig[74]; + unsigned char zero_privkey[32] = { 0 }; + unsigned char over_privkey[32] = { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff }; + + secp256k1_context_set_error_callback(CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(STATIC_CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(STATIC_CTX, counting_illegal_callback_fn, &ecount); + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(CTX, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, privkey) == 1); + + /* Check bad contexts and NULLs for signing */ + ecount = 0; + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, privkey, NULL, NULL) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, NULL, message, privkey, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, NULL, privkey, NULL, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, NULL, NULL, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_sign_recoverable(STATIC_CTX, &recsig, message, privkey, NULL, NULL) == 0); + CHECK(ecount == 4); + /* This will fail or succeed randomly, and in either case will not ARG_CHECK failure */ + secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, privkey, recovery_test_nonce_function, NULL); + CHECK(ecount == 4); + /* These will all fail, but not in ARG_CHECK way */ + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, zero_privkey, NULL, NULL) == 0); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, over_privkey, NULL, NULL) == 0); + /* This one will succeed. */ + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, privkey, NULL, NULL) == 1); + CHECK(ecount == 4); + + /* Check signing with a goofy nonce function */ + + /* Check bad contexts and NULLs for recovery */ + ecount = 0; + CHECK(secp256k1_ecdsa_recover(CTX, &recpubkey, &recsig, message) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdsa_recover(CTX, NULL, &recsig, message) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &recpubkey, NULL, message) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recover(CTX, &recpubkey, &recsig, NULL) == 0); + CHECK(ecount == 3); + + /* Check NULLs for conversion */ + CHECK(secp256k1_ecdsa_sign(CTX, &normal_sig, message, privkey, NULL, NULL) == 1); + ecount = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, NULL, &recsig) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, &normal_sig, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, &normal_sig, &recsig) == 1); + + /* Check NULLs for de/serialization */ + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &recsig, message, privkey, NULL, NULL) == 1); + ecount = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, NULL, &recid, &recsig) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, sig, NULL, &recsig) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, sig, &recid, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, sig, &recid, &recsig) == 1); + + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, NULL, sig, recid) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &recsig, NULL, recid) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &recsig, sig, -1) == 0); + CHECK(ecount == 6); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &recsig, sig, 5) == 0); + CHECK(ecount == 7); + /* overflow in signature will fail but not affect ecount */ + memcpy(sig, over_privkey, 32); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &recsig, sig, recid) == 0); + CHECK(ecount == 7); + + /* cleanup */ + secp256k1_context_set_error_callback(STATIC_CTX, NULL, NULL); + secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL); +} + +static void test_ecdsa_recovery_end_to_end(void) { + unsigned char extra[32] = {0x00}; + unsigned char privkey[32]; + unsigned char message[32]; + secp256k1_ecdsa_signature signature[5]; + secp256k1_ecdsa_recoverable_signature rsignature[5]; + unsigned char sig[74]; + secp256k1_pubkey pubkey; + secp256k1_pubkey recpubkey; + int recid = 0; + + /* Generate a random key and message. */ + { + secp256k1_scalar msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(privkey, &key); + secp256k1_scalar_get_b32(message, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(CTX, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, privkey) == 1); + + /* Serialize/parse compact and verify/recover. */ + extra[0] = 0; + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &rsignature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(CTX, &signature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &rsignature[4], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &rsignature[1], message, privkey, NULL, extra) == 1); + extra[31] = 1; + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &rsignature[2], message, privkey, NULL, extra) == 1); + extra[31] = 0; + extra[0] = 1; + CHECK(secp256k1_ecdsa_sign_recoverable(CTX, &rsignature[3], message, privkey, NULL, extra) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, sig, &recid, &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, &signature[4], &rsignature[4]) == 1); + CHECK(secp256k1_memcmp_var(&signature[4], &signature[0], 64) == 0); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[4], message, &pubkey) == 1); + memset(&rsignature[4], 0, sizeof(rsignature[4])); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, &signature[4], &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[4], message, &pubkey) == 1); + /* Parse compact (with recovery id) and recover. */ + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &recpubkey, &rsignature[4], message) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &recpubkey, sizeof(pubkey)) == 0); + /* Serialize/destroy/parse signature and verify again. */ + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(CTX, sig, &recid, &rsignature[4]) == 1); + sig[secp256k1_testrand_bits(6)] += 1 + secp256k1_testrand_int(255); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(CTX, &signature[4], &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[4], message, &pubkey) == 0); + /* Recover again */ + CHECK(secp256k1_ecdsa_recover(CTX, &recpubkey, &rsignature[4], message) == 0 || + secp256k1_memcmp_var(&pubkey, &recpubkey, sizeof(pubkey)) != 0); +} + +/* Tests several edge cases. */ +static void test_ecdsa_recovery_edge_cases(void) { + const unsigned char msg32[32] = { + 'T', 'h', 'i', 's', ' ', 'i', 's', ' ', + 'a', ' ', 'v', 'e', 'r', 'y', ' ', 's', + 'e', 'c', 'r', 'e', 't', ' ', 'm', 'e', + 's', 's', 'a', 'g', 'e', '.', '.', '.' + }; + const unsigned char sig64[64] = { + /* Generated by signing the above message with nonce 'This is the nonce we will use...' + * and secret key 0 (which is not valid), resulting in recid 1. */ + 0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8, + 0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96, + 0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63, + 0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32, + 0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E, + 0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD, + 0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86, + 0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57 + }; + secp256k1_pubkey pubkey; + /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */ + const unsigned char sigb64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + secp256k1_pubkey pubkeyb; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + int recid; + + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sig64, 0)); + CHECK(!secp256k1_ecdsa_recover(CTX, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sig64, 1)); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sig64, 2)); + CHECK(!secp256k1_ecdsa_recover(CTX, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sig64, 3)); + CHECK(!secp256k1_ecdsa_recover(CTX, &pubkey, &rsig, msg32)); + + for (recid = 0; recid < 4; recid++) { + int i; + int recid2; + /* (4,4) encoded in DER. */ + unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04}; + unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01}; + unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00}; + unsigned char sigbderalt1[39] = { + 0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt2[39] = { + 0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + unsigned char sigbderalt3[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt4[40] = { + 0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + /* (order + r,4) encoded in DER. */ + unsigned char sigbderlong[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, + 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, + 0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04 + }; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sigb64, recid) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkeyb, &rsig, msg32) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbder, sizeof(sigbder)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 1); + for (recid2 = 0; recid2 < 4; recid2++) { + secp256k1_pubkey pubkey2b; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sigb64, recid2) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkey2b, &rsig, msg32) == 1); + /* Verifying with (order + r,4) should always fail. */ + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderlong, sizeof(sigbderlong)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 0); + } + /* DER parsing tests. */ + /* Zero length r/s. */ + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0); + /* Leading zeros. */ + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt1, sizeof(sigbderalt1)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt2, sizeof(sigbderalt2)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0); + sigbderalt3[4] = 1; + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 0); + sigbderalt4[7] = 1; + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 0); + /* Damage signature. */ + sigbder[7]++; + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbder, sizeof(sigbder)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 0); + sigbder[7]--; + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbder, 6) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbder, sizeof(sigbder) - 1) == 0); + for(i = 0; i < 8; i++) { + int c; + unsigned char orig = sigbder[i]; + /*Try every single-byte change.*/ + for (c = 0; c < 256; c++) { + if (c == orig ) { + continue; + } + sigbder[i] = c; + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyb) == 0); + } + sigbder[i] = orig; + } + } + + /* Test r/s equal to zero */ + { + /* (1,1) encoded in DER. */ + unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01}; + unsigned char sigc64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + secp256k1_pubkey pubkeyc; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkeyc, &rsig, msg32) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyc) == 1); + sigcder[4] = 0; + sigc64[31] = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkeyb, &rsig, msg32) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyc) == 0); + sigcder[4] = 1; + sigcder[7] = 0; + sigc64[31] = 1; + sigc64[63] = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(CTX, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(CTX, &pubkeyb, &rsig, msg32) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg32, &pubkeyc) == 0); + } +} + +static void run_recovery_tests(void) { + int i; + for (i = 0; i < COUNT; i++) { + test_ecdsa_recovery_api(); + } + for (i = 0; i < 64*COUNT; i++) { + test_ecdsa_recovery_end_to_end(); + } + test_ecdsa_recovery_edge_cases(); +} + +#endif /* SECP256K1_MODULE_RECOVERY_TESTS_H */ diff --git a/src/secp256k1/src/modules/schnorrsig/Makefile.am.include b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include new file mode 100644 index 0000000000..654fa2e5ae --- /dev/null +++ b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include @@ -0,0 +1,5 @@ +include_HEADERS += include/secp256k1_schnorrsig.h +noinst_HEADERS += src/modules/schnorrsig/main_impl.h +noinst_HEADERS += src/modules/schnorrsig/tests_impl.h +noinst_HEADERS += src/modules/schnorrsig/tests_exhaustive_impl.h +noinst_HEADERS += src/modules/schnorrsig/bench_impl.h diff --git a/src/secp256k1/src/modules/schnorrsig/bench_impl.h b/src/secp256k1/src/modules/schnorrsig/bench_impl.h new file mode 100644 index 0000000000..93a878ede3 --- /dev/null +++ b/src/secp256k1/src/modules/schnorrsig/bench_impl.h @@ -0,0 +1,104 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_BENCH_H +#define SECP256K1_MODULE_SCHNORRSIG_BENCH_H + +#include "../../../include/secp256k1_schnorrsig.h" + +#define MSGLEN 32 + +typedef struct { + secp256k1_context *ctx; + int n; + + const secp256k1_keypair **keypairs; + const unsigned char **pk; + const unsigned char **sigs; + const unsigned char **msgs; +} bench_schnorrsig_data; + +static void bench_schnorrsig_sign(void* arg, int iters) { + bench_schnorrsig_data *data = (bench_schnorrsig_data *)arg; + int i; + unsigned char msg[MSGLEN] = {0}; + unsigned char sig[64]; + + for (i = 0; i < iters; i++) { + msg[0] = i; + msg[1] = i >> 8; + CHECK(secp256k1_schnorrsig_sign_custom(data->ctx, sig, msg, MSGLEN, data->keypairs[i], NULL)); + } +} + +static void bench_schnorrsig_verify(void* arg, int iters) { + bench_schnorrsig_data *data = (bench_schnorrsig_data *)arg; + int i; + + for (i = 0; i < iters; i++) { + secp256k1_xonly_pubkey pk; + CHECK(secp256k1_xonly_pubkey_parse(data->ctx, &pk, data->pk[i]) == 1); + CHECK(secp256k1_schnorrsig_verify(data->ctx, data->sigs[i], data->msgs[i], MSGLEN, &pk)); + } +} + +static void run_schnorrsig_bench(int iters, int argc, char** argv) { + int i; + bench_schnorrsig_data data; + int d = argc == 1; + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + data.keypairs = (const secp256k1_keypair **)malloc(iters * sizeof(secp256k1_keypair *)); + data.pk = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + data.msgs = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + data.sigs = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + + CHECK(MSGLEN >= 4); + for (i = 0; i < iters; i++) { + unsigned char sk[32]; + unsigned char *msg = (unsigned char *)malloc(MSGLEN); + unsigned char *sig = (unsigned char *)malloc(64); + secp256k1_keypair *keypair = (secp256k1_keypair *)malloc(sizeof(*keypair)); + unsigned char *pk_char = (unsigned char *)malloc(32); + secp256k1_xonly_pubkey pk; + msg[0] = sk[0] = i; + msg[1] = sk[1] = i >> 8; + msg[2] = sk[2] = i >> 16; + msg[3] = sk[3] = i >> 24; + memset(&msg[4], 'm', MSGLEN - 4); + memset(&sk[4], 's', 28); + + data.keypairs[i] = keypair; + data.pk[i] = pk_char; + data.msgs[i] = msg; + data.sigs[i] = sig; + + CHECK(secp256k1_keypair_create(data.ctx, keypair, sk)); + CHECK(secp256k1_schnorrsig_sign_custom(data.ctx, sig, msg, MSGLEN, keypair, NULL)); + CHECK(secp256k1_keypair_xonly_pub(data.ctx, &pk, NULL, keypair)); + CHECK(secp256k1_xonly_pubkey_serialize(data.ctx, pk_char, &pk) == 1); + } + + if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "sign") || have_flag(argc, argv, "schnorrsig_sign")) run_benchmark("schnorrsig_sign", bench_schnorrsig_sign, NULL, NULL, (void *) &data, 10, iters); + if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "verify") || have_flag(argc, argv, "schnorrsig_verify")) run_benchmark("schnorrsig_verify", bench_schnorrsig_verify, NULL, NULL, (void *) &data, 10, iters); + + for (i = 0; i < iters; i++) { + free((void *)data.keypairs[i]); + free((void *)data.pk[i]); + free((void *)data.msgs[i]); + free((void *)data.sigs[i]); + } + + /* Casting to (void *) avoids a stupid warning in MSVC. */ + free((void *)data.keypairs); + free((void *)data.pk); + free((void *)data.msgs); + free((void *)data.sigs); + + secp256k1_context_destroy(data.ctx); +} + +#endif diff --git a/src/secp256k1/src/modules/schnorrsig/main_impl.h b/src/secp256k1/src/modules/schnorrsig/main_impl.h new file mode 100644 index 0000000000..cd651591c4 --- /dev/null +++ b/src/secp256k1/src/modules/schnorrsig/main_impl.h @@ -0,0 +1,267 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_MAIN_H +#define SECP256K1_MODULE_SCHNORRSIG_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_schnorrsig.h" +#include "../../hash.h" + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/nonce")||SHA256("BIP0340/nonce"). */ +static void secp256k1_nonce_function_bip340_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x46615b35ul; + sha->s[1] = 0xf4bfbff7ul; + sha->s[2] = 0x9f8dc671ul; + sha->s[3] = 0x83627ab3ul; + sha->s[4] = 0x60217180ul; + sha->s[5] = 0x57358661ul; + sha->s[6] = 0x21a29e54ul; + sha->s[7] = 0x68b07b4cul; + + sha->bytes = 64; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/aux")||SHA256("BIP0340/aux"). */ +static void secp256k1_nonce_function_bip340_sha256_tagged_aux(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x24dd3219ul; + sha->s[1] = 0x4eba7e70ul; + sha->s[2] = 0xca0fabb9ul; + sha->s[3] = 0x0fa3166dul; + sha->s[4] = 0x3afbe4b1ul; + sha->s[5] = 0x4c44df97ul; + sha->s[6] = 0x4aac2739ul; + sha->s[7] = 0x249e850aul; + + sha->bytes = 64; +} + +/* algo argument for nonce_function_bip340 to derive the nonce exactly as stated in BIP-340 + * by using the correct tagged hash function. */ +static const unsigned char bip340_algo[13] = "BIP0340/nonce"; + +static const unsigned char schnorrsig_extraparams_magic[4] = SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC; + +static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + secp256k1_sha256 sha; + unsigned char masked_key[32]; + int i; + + if (algo == NULL) { + return 0; + } + + if (data != NULL) { + secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha); + secp256k1_sha256_write(&sha, data, 32); + secp256k1_sha256_finalize(&sha, masked_key); + for (i = 0; i < 32; i++) { + masked_key[i] ^= key32[i]; + } + } else { + /* Precomputed TaggedHash("BIP0340/aux", 0x0000...00); */ + static const unsigned char ZERO_MASK[32] = { + 84, 241, 105, 207, 201, 226, 229, 114, + 116, 128, 68, 31, 144, 186, 37, 196, + 136, 244, 97, 199, 11, 94, 165, 220, + 170, 247, 175, 105, 39, 10, 165, 20 + }; + for (i = 0; i < 32; i++) { + masked_key[i] = key32[i] ^ ZERO_MASK[i]; + } + } + + /* Tag the hash with algo which is important to avoid nonce reuse across + * algorithms. If this nonce function is used in BIP-340 signing as defined + * in the spec, an optimized tagging implementation is used. */ + if (algolen == sizeof(bip340_algo) + && secp256k1_memcmp_var(algo, bip340_algo, algolen) == 0) { + secp256k1_nonce_function_bip340_sha256_tagged(&sha); + } else { + secp256k1_sha256_initialize_tagged(&sha, algo, algolen); + } + + /* Hash masked-key||pk||msg using the tagged hash as per the spec */ + secp256k1_sha256_write(&sha, masked_key, 32); + secp256k1_sha256_write(&sha, xonly_pk32, 32); + secp256k1_sha256_write(&sha, msg, msglen); + secp256k1_sha256_finalize(&sha, nonce32); + return 1; +} + +const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340 = nonce_function_bip340; + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/challenge")||SHA256("BIP0340/challenge"). */ +static void secp256k1_schnorrsig_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x9cecba11ul; + sha->s[1] = 0x23925381ul; + sha->s[2] = 0x11679112ul; + sha->s[3] = 0xd1627e0ful; + sha->s[4] = 0x97c87550ul; + sha->s[5] = 0x003cc765ul; + sha->s[6] = 0x90f61164ul; + sha->s[7] = 0x33e9b66aul; + sha->bytes = 64; +} + +static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32) +{ + unsigned char buf[32]; + secp256k1_sha256 sha; + + /* tagged hash(r.x, pk.x, msg) */ + secp256k1_schnorrsig_sha256_tagged(&sha); + secp256k1_sha256_write(&sha, r32, 32); + secp256k1_sha256_write(&sha, pubkey32, 32); + secp256k1_sha256_write(&sha, msg, msglen); + secp256k1_sha256_finalize(&sha, buf); + /* Set scalar e to the challenge hash modulo the curve order as per + * BIP340. */ + secp256k1_scalar_set_b32(e, buf, NULL); +} + +static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_nonce_function_hardened noncefp, void *ndata) { + secp256k1_scalar sk; + secp256k1_scalar e; + secp256k1_scalar k; + secp256k1_gej rj; + secp256k1_ge pk; + secp256k1_ge r; + unsigned char buf[32] = { 0 }; + unsigned char pk_buf[32]; + unsigned char seckey[32]; + int ret = 1; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(sig64 != NULL); + ARG_CHECK(msg != NULL || msglen == 0); + ARG_CHECK(keypair != NULL); + + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_bip340; + } + + ret &= secp256k1_keypair_load(ctx, &sk, &pk, keypair); + /* Because we are signing for a x-only pubkey, the secret key is negated + * before signing if the point corresponding to the secret key does not + * have an even Y. */ + if (secp256k1_fe_is_odd(&pk.y)) { + secp256k1_scalar_negate(&sk, &sk); + } + + secp256k1_scalar_get_b32(seckey, &sk); + secp256k1_fe_get_b32(pk_buf, &pk.x); + ret &= !!noncefp(buf, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata); + secp256k1_scalar_set_b32(&k, buf, NULL); + ret &= !secp256k1_scalar_is_zero(&k); + secp256k1_scalar_cmov(&k, &secp256k1_scalar_one, !ret); + + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rj, &k); + secp256k1_ge_set_gej(&r, &rj); + + /* We declassify r to allow using it as a branch point. This is fine + * because r is not a secret. */ + secp256k1_declassify(ctx, &r, sizeof(r)); + secp256k1_fe_normalize_var(&r.y); + if (secp256k1_fe_is_odd(&r.y)) { + secp256k1_scalar_negate(&k, &k); + } + secp256k1_fe_normalize_var(&r.x); + secp256k1_fe_get_b32(&sig64[0], &r.x); + + secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, pk_buf); + secp256k1_scalar_mul(&e, &e, &sk); + secp256k1_scalar_add(&e, &e, &k); + secp256k1_scalar_get_b32(&sig64[32], &e); + + secp256k1_memczero(sig64, 64, !ret); + secp256k1_scalar_clear(&k); + secp256k1_scalar_clear(&sk); + memset(seckey, 0, sizeof(seckey)); + + return ret; +} + +int secp256k1_schnorrsig_sign32(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) { + /* We cast away const from the passed aux_rand32 argument since we know the default nonce function does not modify it. */ + return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg32, 32, keypair, secp256k1_nonce_function_bip340, (unsigned char*)aux_rand32); +} + +int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) { + return secp256k1_schnorrsig_sign32(ctx, sig64, msg32, keypair, aux_rand32); +} + +int secp256k1_schnorrsig_sign_custom(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_schnorrsig_extraparams *extraparams) { + secp256k1_nonce_function_hardened noncefp = NULL; + void *ndata = NULL; + VERIFY_CHECK(ctx != NULL); + + if (extraparams != NULL) { + ARG_CHECK(secp256k1_memcmp_var(extraparams->magic, + schnorrsig_extraparams_magic, + sizeof(extraparams->magic)) == 0); + noncefp = extraparams->noncefp; + ndata = extraparams->ndata; + } + return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg, msglen, keypair, noncefp, ndata); +} + +int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_xonly_pubkey *pubkey) { + secp256k1_scalar s; + secp256k1_scalar e; + secp256k1_gej rj; + secp256k1_ge pk; + secp256k1_gej pkj; + secp256k1_fe rx; + secp256k1_ge r; + unsigned char buf[32]; + int overflow; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig64 != NULL); + ARG_CHECK(msg != NULL || msglen == 0); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_fe_set_b32(&rx, &sig64[0])) { + return 0; + } + + secp256k1_scalar_set_b32(&s, &sig64[32], &overflow); + if (overflow) { + return 0; + } + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + + /* Compute e. */ + secp256k1_fe_get_b32(buf, &pk.x); + secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, buf); + + /* Compute rj = s*G + (-e)*pkj */ + secp256k1_scalar_negate(&e, &e); + secp256k1_gej_set_ge(&pkj, &pk); + secp256k1_ecmult(&rj, &pkj, &e, &s); + + secp256k1_ge_set_gej_var(&r, &rj); + if (secp256k1_ge_is_infinity(&r)) { + return 0; + } + + secp256k1_fe_normalize_var(&r.y); + return !secp256k1_fe_is_odd(&r.y) && + secp256k1_fe_equal_var(&rx, &r.x); +} + +#endif diff --git a/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h new file mode 100644 index 0000000000..55f9028a63 --- /dev/null +++ b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h @@ -0,0 +1,214 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H + +#include "../../../include/secp256k1_schnorrsig.h" +#include "main_impl.h" + +static const unsigned char invalid_pubkey_bytes[][32] = { + /* 0 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 + }, + /* 2 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 + }, + /* order */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 24) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 16) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 8) & 0xFF, + (EXHAUSTIVE_TEST_ORDER + 0UL) & 0xFF + }, + /* order + 1 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 24) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 16) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 8) & 0xFF, + (EXHAUSTIVE_TEST_ORDER + 1UL) & 0xFF + }, + /* field size */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F + }, + /* field size + 1 (note that 1 is legal) */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 + }, + /* 2^256 - 1 */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + } +}; + +#define NUM_INVALID_KEYS (sizeof(invalid_pubkey_bytes) / sizeof(invalid_pubkey_bytes[0])) + +static int secp256k1_hardened_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg, + size_t msglen, + const unsigned char *key32, const unsigned char *xonly_pk32, + const unsigned char *algo, size_t algolen, + void* data) { + secp256k1_scalar s; + int *idata = data; + (void)msg; + (void)msglen; + (void)key32; + (void)xonly_pk32; + (void)algo; + (void)algolen; + secp256k1_scalar_set_int(&s, *idata); + secp256k1_scalar_get_b32(nonce32, &s); + return 1; +} + +static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, const secp256k1_xonly_pubkey* pubkeys, unsigned char (*xonly_pubkey_bytes)[32], const int* parities) { + int d; + uint64_t iter = 0; + /* Iterate over the possible public keys to verify against (through their corresponding DL d). */ + for (d = 1; d <= EXHAUSTIVE_TEST_ORDER / 2; ++d) { + int actual_d; + unsigned k; + unsigned char pk32[32]; + memcpy(pk32, xonly_pubkey_bytes[d - 1], 32); + actual_d = parities[d - 1] ? EXHAUSTIVE_TEST_ORDER - d : d; + /* Iterate over the possible valid first 32 bytes in the signature, through their corresponding DL k. + Values above EXHAUSTIVE_TEST_ORDER/2 refer to the entries in invalid_pubkey_bytes. */ + for (k = 1; k <= EXHAUSTIVE_TEST_ORDER / 2 + NUM_INVALID_KEYS; ++k) { + unsigned char sig64[64]; + int actual_k = -1; + int e_done[EXHAUSTIVE_TEST_ORDER] = {0}; + int e_count_done = 0; + if (skip_section(&iter)) continue; + if (k <= EXHAUSTIVE_TEST_ORDER / 2) { + memcpy(sig64, xonly_pubkey_bytes[k - 1], 32); + actual_k = parities[k - 1] ? EXHAUSTIVE_TEST_ORDER - k : k; + } else { + memcpy(sig64, invalid_pubkey_bytes[k - 1 - EXHAUSTIVE_TEST_ORDER / 2], 32); + } + /* Randomly generate messages until all challenges have been hit. */ + while (e_count_done < EXHAUSTIVE_TEST_ORDER) { + secp256k1_scalar e; + unsigned char msg32[32]; + secp256k1_testrand256(msg32); + secp256k1_schnorrsig_challenge(&e, sig64, msg32, sizeof(msg32), pk32); + /* Only do work if we hit a challenge we haven't tried before. */ + if (!e_done[e]) { + /* Iterate over the possible valid last 32 bytes in the signature. + 0..order=that s value; order+1=random bytes */ + int count_valid = 0, s; + for (s = 0; s <= EXHAUSTIVE_TEST_ORDER + 1; ++s) { + int expect_valid, valid; + if (s <= EXHAUSTIVE_TEST_ORDER) { + secp256k1_scalar s_s; + secp256k1_scalar_set_int(&s_s, s); + secp256k1_scalar_get_b32(sig64 + 32, &s_s); + expect_valid = actual_k != -1 && s != EXHAUSTIVE_TEST_ORDER && + (s_s == (actual_k + actual_d * e) % EXHAUSTIVE_TEST_ORDER); + } else { + secp256k1_testrand256(sig64 + 32); + expect_valid = 0; + } + valid = secp256k1_schnorrsig_verify(ctx, sig64, msg32, sizeof(msg32), &pubkeys[d - 1]); + CHECK(valid == expect_valid); + count_valid += valid; + } + /* Exactly one s value must verify, unless R is illegal. */ + CHECK(count_valid == (actual_k != -1)); + /* Don't retry other messages that result in the same challenge. */ + e_done[e] = 1; + ++e_count_done; + } + } + } + } +} + +static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsigned char (*xonly_pubkey_bytes)[32], const secp256k1_keypair* keypairs, const int* parities) { + int d, k; + uint64_t iter = 0; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + + /* Loop over keys. */ + for (d = 1; d < EXHAUSTIVE_TEST_ORDER; ++d) { + int actual_d = d; + if (parities[d - 1]) actual_d = EXHAUSTIVE_TEST_ORDER - d; + /* Loop over nonces. */ + for (k = 1; k < EXHAUSTIVE_TEST_ORDER; ++k) { + int e_done[EXHAUSTIVE_TEST_ORDER] = {0}; + int e_count_done = 0; + unsigned char msg32[32]; + unsigned char sig64[64]; + int actual_k = k; + if (skip_section(&iter)) continue; + extraparams.noncefp = secp256k1_hardened_nonce_function_smallint; + extraparams.ndata = &k; + if (parities[k - 1]) actual_k = EXHAUSTIVE_TEST_ORDER - k; + /* Generate random messages until all challenges have been tried. */ + while (e_count_done < EXHAUSTIVE_TEST_ORDER) { + secp256k1_scalar e; + secp256k1_testrand256(msg32); + secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, sizeof(msg32), xonly_pubkey_bytes[d - 1]); + /* Only do work if we hit a challenge we haven't tried before. */ + if (!e_done[e]) { + secp256k1_scalar expected_s = (actual_k + e * actual_d) % EXHAUSTIVE_TEST_ORDER; + unsigned char expected_s_bytes[32]; + secp256k1_scalar_get_b32(expected_s_bytes, &expected_s); + /* Invoke the real function to construct a signature. */ + CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig64, msg32, sizeof(msg32), &keypairs[d - 1], &extraparams)); + /* The first 32 bytes must match the xonly pubkey for the specified k. */ + CHECK(secp256k1_memcmp_var(sig64, xonly_pubkey_bytes[k - 1], 32) == 0); + /* The last 32 bytes must match the expected s value. */ + CHECK(secp256k1_memcmp_var(sig64 + 32, expected_s_bytes, 32) == 0); + /* Don't retry other messages that result in the same challenge. */ + e_done[e] = 1; + ++e_count_done; + } + } + } + } +} + +static void test_exhaustive_schnorrsig(const secp256k1_context *ctx) { + secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + int parity[EXHAUSTIVE_TEST_ORDER - 1]; + unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32]; + unsigned i; + + /* Verify that all invalid_pubkey_bytes are actually invalid. */ + for (i = 0; i < NUM_INVALID_KEYS; ++i) { + secp256k1_xonly_pubkey pk; + CHECK(!secp256k1_xonly_pubkey_parse(ctx, &pk, invalid_pubkey_bytes[i])); + } + + /* Construct keypairs and xonly-pubkeys for the entire group. */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; ++i) { + secp256k1_scalar scalar_i; + unsigned char buf[32]; + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_scalar_get_b32(buf, &scalar_i); + CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf)); + CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parity[i - 1], &keypair[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1])); + } + + test_exhaustive_schnorrsig_sign(ctx, xonly_pubkey_bytes, keypair, parity); + test_exhaustive_schnorrsig_verify(ctx, xonly_pubkey, xonly_pubkey_bytes, parity); +} + +#endif diff --git a/src/secp256k1/src/modules/schnorrsig/tests_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_impl.h new file mode 100644 index 0000000000..062005ee63 --- /dev/null +++ b/src/secp256k1/src/modules/schnorrsig/tests_impl.h @@ -0,0 +1,879 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_TESTS_H +#define SECP256K1_MODULE_SCHNORRSIG_TESTS_H + +#include "../../../include/secp256k1_schnorrsig.h" + +/* Checks that a bit flip in the n_flip-th argument (that has n_bytes many + * bytes) changes the hash function + */ +static void nonce_function_bip340_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes, size_t msglen, size_t algolen) { + unsigned char nonces[2][32]; + CHECK(nonce_function_bip340(nonces[0], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1); + secp256k1_testrand_flip(args[n_flip], n_bytes); + CHECK(nonce_function_bip340(nonces[1], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1); + CHECK(secp256k1_memcmp_var(nonces[0], nonces[1], 32) != 0); +} + +/* Tests for the equality of two sha256 structs. This function only produces a + * correct result if an integer multiple of 64 many bytes have been written + * into the hash functions. */ +static void test_sha256_eq(const secp256k1_sha256 *sha1, const secp256k1_sha256 *sha2) { + /* Is buffer fully consumed? */ + CHECK((sha1->bytes & 0x3F) == 0); + + CHECK(sha1->bytes == sha2->bytes); + CHECK(secp256k1_memcmp_var(sha1->s, sha2->s, sizeof(sha1->s)) == 0); +} + +static void run_nonce_function_bip340_tests(void) { + unsigned char tag[13] = "BIP0340/nonce"; + unsigned char aux_tag[11] = "BIP0340/aux"; + unsigned char algo[13] = "BIP0340/nonce"; + size_t algolen = sizeof(algo); + secp256k1_sha256 sha; + secp256k1_sha256 sha_optimized; + unsigned char nonce[32], nonce_z[32]; + unsigned char msg[32]; + size_t msglen = sizeof(msg); + unsigned char key[32]; + unsigned char pk[32]; + unsigned char aux_rand[32]; + unsigned char *args[5]; + int i; + + /* Check that hash initialized by + * secp256k1_nonce_function_bip340_sha256_tagged has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, tag, sizeof(tag)); + secp256k1_nonce_function_bip340_sha256_tagged(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + /* Check that hash initialized by + * secp256k1_nonce_function_bip340_sha256_tagged_aux has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, aux_tag, sizeof(aux_tag)); + secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + secp256k1_testrand256(msg); + secp256k1_testrand256(key); + secp256k1_testrand256(pk); + secp256k1_testrand256(aux_rand); + + /* Check that a bitflip in an argument results in different nonces. */ + args[0] = msg; + args[1] = key; + args[2] = pk; + args[3] = algo; + args[4] = aux_rand; + for (i = 0; i < COUNT; i++) { + nonce_function_bip340_bitflip(args, 0, 32, msglen, algolen); + nonce_function_bip340_bitflip(args, 1, 32, msglen, algolen); + nonce_function_bip340_bitflip(args, 2, 32, msglen, algolen); + /* Flip algo special case "BIP0340/nonce" */ + nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen); + /* Flip algo again */ + nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen); + nonce_function_bip340_bitflip(args, 4, 32, msglen, algolen); + } + + /* NULL algo is disallowed */ + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, NULL, 0, NULL) == 0); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + /* Other algo is fine */ + secp256k1_testrand_bytes_test(algo, algolen); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + + for (i = 0; i < COUNT; i++) { + unsigned char nonce2[32]; + uint32_t offset = secp256k1_testrand_int(msglen - 1); + size_t msglen_tmp = (msglen + offset) % msglen; + size_t algolen_tmp; + + /* Different msglen gives different nonce */ + CHECK(nonce_function_bip340(nonce2, msg, msglen_tmp, key, pk, algo, algolen, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); + + /* Different algolen gives different nonce */ + offset = secp256k1_testrand_int(algolen - 1); + algolen_tmp = (algolen + offset) % algolen; + CHECK(nonce_function_bip340(nonce2, msg, msglen, key, pk, algo, algolen_tmp, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); + } + + /* NULL aux_rand argument is allowed, and identical to passing all zero aux_rand. */ + memset(aux_rand, 0, 32); + CHECK(nonce_function_bip340(nonce_z, msg, msglen, key, pk, algo, algolen, &aux_rand) == 1); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce_z, nonce, 32) == 0); +} + +static void test_schnorrsig_api(void) { + unsigned char sk1[32]; + unsigned char sk2[32]; + unsigned char sk3[32]; + unsigned char msg[32]; + secp256k1_keypair keypairs[3]; + secp256k1_keypair invalid_keypair = {{ 0 }}; + secp256k1_xonly_pubkey pk[3]; + secp256k1_xonly_pubkey zero_pk; + unsigned char sig[64]; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + secp256k1_schnorrsig_extraparams invalid_extraparams = {{ 0 }, NULL, NULL}; + + /** setup **/ + int ecount = 0; + + secp256k1_context_set_error_callback(CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(STATIC_CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(STATIC_CTX, counting_illegal_callback_fn, &ecount); + + secp256k1_testrand256(sk1); + secp256k1_testrand256(sk2); + secp256k1_testrand256(sk3); + secp256k1_testrand256(msg); + CHECK(secp256k1_keypair_create(CTX, &keypairs[0], sk1) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypairs[1], sk2) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypairs[2], sk3) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[0], NULL, &keypairs[0]) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[1], NULL, &keypairs[1]) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[2], NULL, &keypairs[2]) == 1); + memset(&zero_pk, 0, sizeof(zero_pk)); + + /** main test body **/ + ecount = 0; + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypairs[0], NULL) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_schnorrsig_sign32(CTX, NULL, msg, &keypairs[0], NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, NULL, &keypairs[0], NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, NULL, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &invalid_keypair, NULL) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_schnorrsig_sign32(STATIC_CTX, sig, msg, &keypairs[0], NULL) == 0); + CHECK(ecount == 5); + + ecount = 0; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], &extraparams) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, NULL, msg, sizeof(msg), &keypairs[0], &extraparams) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, NULL, sizeof(msg), &keypairs[0], &extraparams) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, NULL, 0, &keypairs[0], &extraparams) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), NULL, &extraparams) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &invalid_keypair, &extraparams) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], NULL) == 1); + CHECK(ecount == 4); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], &invalid_extraparams) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_schnorrsig_sign_custom(STATIC_CTX, sig, msg, sizeof(msg), &keypairs[0], &extraparams) == 0); + CHECK(ecount == 6); + + ecount = 0; + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypairs[0], NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk[0]) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_schnorrsig_verify(CTX, NULL, msg, sizeof(msg), &pk[0]) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, NULL, sizeof(msg), &pk[0]) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, NULL, 0, &pk[0]) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &zero_pk) == 0); + CHECK(ecount == 4); + + secp256k1_context_set_error_callback(STATIC_CTX, NULL, NULL); + secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL); +} + +/* Checks that hash initialized by secp256k1_schnorrsig_sha256_tagged has the + * expected state. */ +static void test_schnorrsig_sha256_tagged(void) { + unsigned char tag[17] = "BIP0340/challenge"; + secp256k1_sha256 sha; + secp256k1_sha256 sha_optimized; + + secp256k1_sha256_initialize_tagged(&sha, (unsigned char *) tag, sizeof(tag)); + secp256k1_schnorrsig_sha256_tagged(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); +} + +/* Helper function for schnorrsig_bip_vectors + * Signs the message and checks that it's the same as expected_sig. */ +static void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *aux_rand, const unsigned char *msg32, const unsigned char *expected_sig) { + unsigned char sig[64]; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey pk, pk_expected; + + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg32, &keypair, aux_rand)); + CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0); + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk_expected, pk_serialized)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + CHECK(secp256k1_memcmp_var(&pk, &pk_expected, sizeof(pk)) == 0); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg32, 32, &pk)); +} + +/* Helper function for schnorrsig_bip_vectors + * Checks that both verify and verify_batch (TODO) return the same value as expected. */ +static void test_schnorrsig_bip_vectors_check_verify(const unsigned char *pk_serialized, const unsigned char *msg32, const unsigned char *sig, int expected) { + secp256k1_xonly_pubkey pk; + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk, pk_serialized)); + CHECK(expected == secp256k1_schnorrsig_verify(CTX, sig, msg32, 32, &pk)); +} + +/* Test vectors according to BIP-340 ("Schnorr Signatures for secp256k1"). See + * https://github.com/bitcoin/bips/blob/master/bip-0340/test-vectors.csv. */ +static void test_schnorrsig_bip_vectors(void) { + { + /* Test vector 0 */ + const unsigned char sk[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03 + }; + const unsigned char pk[32] = { + 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, + 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, + 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, + 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 + }; + unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 + }; + const unsigned char msg[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 + }; + const unsigned char sig[64] = { + 0xE9, 0x07, 0x83, 0x1F, 0x80, 0x84, 0x8D, 0x10, + 0x69, 0xA5, 0x37, 0x1B, 0x40, 0x24, 0x10, 0x36, + 0x4B, 0xDF, 0x1C, 0x5F, 0x83, 0x07, 0xB0, 0x08, + 0x4C, 0x55, 0xF1, 0xCE, 0x2D, 0xCA, 0x82, 0x15, + 0x25, 0xF6, 0x6A, 0x4A, 0x85, 0xEA, 0x8B, 0x71, + 0xE4, 0x82, 0xA7, 0x4F, 0x38, 0x2D, 0x2C, 0xE5, + 0xEB, 0xEE, 0xE8, 0xFD, 0xB2, 0x17, 0x2F, 0x47, + 0x7D, 0xF4, 0x90, 0x0D, 0x31, 0x05, 0x36, 0xC0 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1); + } + { + /* Test vector 1 */ + const unsigned char sk[32] = { + 0xB7, 0xE1, 0x51, 0x62, 0x8A, 0xED, 0x2A, 0x6A, + 0xBF, 0x71, 0x58, 0x80, 0x9C, 0xF4, 0xF3, 0xC7, + 0x62, 0xE7, 0x16, 0x0F, 0x38, 0xB4, 0xDA, 0x56, + 0xA7, 0x84, 0xD9, 0x04, 0x51, 0x90, 0xCF, 0xEF + }; + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x68, 0x96, 0xBD, 0x60, 0xEE, 0xAE, 0x29, 0x6D, + 0xB4, 0x8A, 0x22, 0x9F, 0xF7, 0x1D, 0xFE, 0x07, + 0x1B, 0xDE, 0x41, 0x3E, 0x6D, 0x43, 0xF9, 0x17, + 0xDC, 0x8D, 0xCF, 0x8C, 0x78, 0xDE, 0x33, 0x41, + 0x89, 0x06, 0xD1, 0x1A, 0xC9, 0x76, 0xAB, 0xCC, + 0xB2, 0x0B, 0x09, 0x12, 0x92, 0xBF, 0xF4, 0xEA, + 0x89, 0x7E, 0xFC, 0xB6, 0x39, 0xEA, 0x87, 0x1C, + 0xFA, 0x95, 0xF6, 0xDE, 0x33, 0x9E, 0x4B, 0x0A + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1); + } + { + /* Test vector 2 */ + const unsigned char sk[32] = { + 0xC9, 0x0F, 0xDA, 0xA2, 0x21, 0x68, 0xC2, 0x34, + 0xC4, 0xC6, 0x62, 0x8B, 0x80, 0xDC, 0x1C, 0xD1, + 0x29, 0x02, 0x4E, 0x08, 0x8A, 0x67, 0xCC, 0x74, + 0x02, 0x0B, 0xBE, 0xA6, 0x3B, 0x14, 0xE5, 0xC9 + }; + const unsigned char pk[32] = { + 0xDD, 0x30, 0x8A, 0xFE, 0xC5, 0x77, 0x7E, 0x13, + 0x12, 0x1F, 0xA7, 0x2B, 0x9C, 0xC1, 0xB7, 0xCC, + 0x01, 0x39, 0x71, 0x53, 0x09, 0xB0, 0x86, 0xC9, + 0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xB8 + }; + unsigned char aux_rand[32] = { + 0xC8, 0x7A, 0xA5, 0x38, 0x24, 0xB4, 0xD7, 0xAE, + 0x2E, 0xB0, 0x35, 0xA2, 0xB5, 0xBB, 0xBC, 0xCC, + 0x08, 0x0E, 0x76, 0xCD, 0xC6, 0xD1, 0x69, 0x2C, + 0x4B, 0x0B, 0x62, 0xD7, 0x98, 0xE6, 0xD9, 0x06 + }; + const unsigned char msg[32] = { + 0x7E, 0x2D, 0x58, 0xD8, 0xB3, 0xBC, 0xDF, 0x1A, + 0xBA, 0xDE, 0xC7, 0x82, 0x90, 0x54, 0xF9, 0x0D, + 0xDA, 0x98, 0x05, 0xAA, 0xB5, 0x6C, 0x77, 0x33, + 0x30, 0x24, 0xB9, 0xD0, 0xA5, 0x08, 0xB7, 0x5C + }; + const unsigned char sig[64] = { + 0x58, 0x31, 0xAA, 0xEE, 0xD7, 0xB4, 0x4B, 0xB7, + 0x4E, 0x5E, 0xAB, 0x94, 0xBA, 0x9D, 0x42, 0x94, + 0xC4, 0x9B, 0xCF, 0x2A, 0x60, 0x72, 0x8D, 0x8B, + 0x4C, 0x20, 0x0F, 0x50, 0xDD, 0x31, 0x3C, 0x1B, + 0xAB, 0x74, 0x58, 0x79, 0xA5, 0xAD, 0x95, 0x4A, + 0x72, 0xC4, 0x5A, 0x91, 0xC3, 0xA5, 0x1D, 0x3C, + 0x7A, 0xDE, 0xA9, 0x8D, 0x82, 0xF8, 0x48, 0x1E, + 0x0E, 0x1E, 0x03, 0x67, 0x4A, 0x6F, 0x3F, 0xB7 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1); + } + { + /* Test vector 3 */ + const unsigned char sk[32] = { + 0x0B, 0x43, 0x2B, 0x26, 0x77, 0x93, 0x73, 0x81, + 0xAE, 0xF0, 0x5B, 0xB0, 0x2A, 0x66, 0xEC, 0xD0, + 0x12, 0x77, 0x30, 0x62, 0xCF, 0x3F, 0xA2, 0x54, + 0x9E, 0x44, 0xF5, 0x8E, 0xD2, 0x40, 0x17, 0x10 + }; + const unsigned char pk[32] = { + 0x25, 0xD1, 0xDF, 0xF9, 0x51, 0x05, 0xF5, 0x25, + 0x3C, 0x40, 0x22, 0xF6, 0x28, 0xA9, 0x96, 0xAD, + 0x3A, 0x0D, 0x95, 0xFB, 0xF2, 0x1D, 0x46, 0x8A, + 0x1B, 0x33, 0xF8, 0xC1, 0x60, 0xD8, 0xF5, 0x17 + }; + unsigned char aux_rand[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + }; + const unsigned char msg[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + }; + const unsigned char sig[64] = { + 0x7E, 0xB0, 0x50, 0x97, 0x57, 0xE2, 0x46, 0xF1, + 0x94, 0x49, 0x88, 0x56, 0x51, 0x61, 0x1C, 0xB9, + 0x65, 0xEC, 0xC1, 0xA1, 0x87, 0xDD, 0x51, 0xB6, + 0x4F, 0xDA, 0x1E, 0xDC, 0x96, 0x37, 0xD5, 0xEC, + 0x97, 0x58, 0x2B, 0x9C, 0xB1, 0x3D, 0xB3, 0x93, + 0x37, 0x05, 0xB3, 0x2B, 0xA9, 0x82, 0xAF, 0x5A, + 0xF2, 0x5F, 0xD7, 0x88, 0x81, 0xEB, 0xB3, 0x27, + 0x71, 0xFC, 0x59, 0x22, 0xEF, 0xC6, 0x6E, 0xA3 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1); + } + { + /* Test vector 4 */ + const unsigned char pk[32] = { + 0xD6, 0x9C, 0x35, 0x09, 0xBB, 0x99, 0xE4, 0x12, + 0xE6, 0x8B, 0x0F, 0xE8, 0x54, 0x4E, 0x72, 0x83, + 0x7D, 0xFA, 0x30, 0x74, 0x6D, 0x8B, 0xE2, 0xAA, + 0x65, 0x97, 0x5F, 0x29, 0xD2, 0x2D, 0xC7, 0xB9 + }; + const unsigned char msg[32] = { + 0x4D, 0xF3, 0xC3, 0xF6, 0x8F, 0xCC, 0x83, 0xB2, + 0x7E, 0x9D, 0x42, 0xC9, 0x04, 0x31, 0xA7, 0x24, + 0x99, 0xF1, 0x78, 0x75, 0xC8, 0x1A, 0x59, 0x9B, + 0x56, 0x6C, 0x98, 0x89, 0xB9, 0x69, 0x67, 0x03 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x3B, 0x78, 0xCE, 0x56, 0x3F, + 0x89, 0xA0, 0xED, 0x94, 0x14, 0xF5, 0xAA, 0x28, + 0xAD, 0x0D, 0x96, 0xD6, 0x79, 0x5F, 0x9C, 0x63, + 0x76, 0xAF, 0xB1, 0x54, 0x8A, 0xF6, 0x03, 0xB3, + 0xEB, 0x45, 0xC9, 0xF8, 0x20, 0x7D, 0xEE, 0x10, + 0x60, 0xCB, 0x71, 0xC0, 0x4E, 0x80, 0xF5, 0x93, + 0x06, 0x0B, 0x07, 0xD2, 0x83, 0x08, 0xD7, 0xF4 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1); + } + { + /* Test vector 5 */ + const unsigned char pk[32] = { + 0xEE, 0xFD, 0xEA, 0x4C, 0xDB, 0x67, 0x77, 0x50, + 0xA4, 0x20, 0xFE, 0xE8, 0x07, 0xEA, 0xCF, 0x21, + 0xEB, 0x98, 0x98, 0xAE, 0x79, 0xB9, 0x76, 0x87, + 0x66, 0xE4, 0xFA, 0xA0, 0x4A, 0x2D, 0x4A, 0x34 + }; + secp256k1_xonly_pubkey pk_parsed; + /* No need to check the signature of the test vector as parsing the pubkey already fails */ + CHECK(!secp256k1_xonly_pubkey_parse(CTX, &pk_parsed, pk)); + } + { + /* Test vector 6 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0xFF, 0xF9, 0x7B, 0xD5, 0x75, 0x5E, 0xEE, 0xA4, + 0x20, 0x45, 0x3A, 0x14, 0x35, 0x52, 0x35, 0xD3, + 0x82, 0xF6, 0x47, 0x2F, 0x85, 0x68, 0xA1, 0x8B, + 0x2F, 0x05, 0x7A, 0x14, 0x60, 0x29, 0x75, 0x56, + 0x3C, 0xC2, 0x79, 0x44, 0x64, 0x0A, 0xC6, 0x07, + 0xCD, 0x10, 0x7A, 0xE1, 0x09, 0x23, 0xD9, 0xEF, + 0x7A, 0x73, 0xC6, 0x43, 0xE1, 0x66, 0xBE, 0x5E, + 0xBE, 0xAF, 0xA3, 0x4B, 0x1A, 0xC5, 0x53, 0xE2 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 7 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x1F, 0xA6, 0x2E, 0x33, 0x1E, 0xDB, 0xC2, 0x1C, + 0x39, 0x47, 0x92, 0xD2, 0xAB, 0x11, 0x00, 0xA7, + 0xB4, 0x32, 0xB0, 0x13, 0xDF, 0x3F, 0x6F, 0xF4, + 0xF9, 0x9F, 0xCB, 0x33, 0xE0, 0xE1, 0x51, 0x5F, + 0x28, 0x89, 0x0B, 0x3E, 0xDB, 0x6E, 0x71, 0x89, + 0xB6, 0x30, 0x44, 0x8B, 0x51, 0x5C, 0xE4, 0xF8, + 0x62, 0x2A, 0x95, 0x4C, 0xFE, 0x54, 0x57, 0x35, + 0xAA, 0xEA, 0x51, 0x34, 0xFC, 0xCD, 0xB2, 0xBD + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 8 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x6C, 0xFF, 0x5C, 0x3B, 0xA8, 0x6C, 0x69, 0xEA, + 0x4B, 0x73, 0x76, 0xF3, 0x1A, 0x9B, 0xCB, 0x4F, + 0x74, 0xC1, 0x97, 0x60, 0x89, 0xB2, 0xD9, 0x96, + 0x3D, 0xA2, 0xE5, 0x54, 0x3E, 0x17, 0x77, 0x69, + 0x96, 0x17, 0x64, 0xB3, 0xAA, 0x9B, 0x2F, 0xFC, + 0xB6, 0xEF, 0x94, 0x7B, 0x68, 0x87, 0xA2, 0x26, + 0xE8, 0xD7, 0xC9, 0x3E, 0x00, 0xC5, 0xED, 0x0C, + 0x18, 0x34, 0xFF, 0x0D, 0x0C, 0x2E, 0x6D, 0xA6 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 9 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x12, 0x3D, 0xDA, 0x83, 0x28, 0xAF, 0x9C, 0x23, + 0xA9, 0x4C, 0x1F, 0xEE, 0xCF, 0xD1, 0x23, 0xBA, + 0x4F, 0xB7, 0x34, 0x76, 0xF0, 0xD5, 0x94, 0xDC, + 0xB6, 0x5C, 0x64, 0x25, 0xBD, 0x18, 0x60, 0x51 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 10 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x76, 0x15, 0xFB, 0xAF, 0x5A, 0xE2, 0x88, 0x64, + 0x01, 0x3C, 0x09, 0x97, 0x42, 0xDE, 0xAD, 0xB4, + 0xDB, 0xA8, 0x7F, 0x11, 0xAC, 0x67, 0x54, 0xF9, + 0x37, 0x80, 0xD5, 0xA1, 0x83, 0x7C, 0xF1, 0x97 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 11 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x4A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A, + 0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB, + 0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7, + 0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D, + 0x69, 0xE8, 0x9B, 0x4C, 0x55, 0x64, 0xD0, 0x03, + 0x49, 0x10, 0x6B, 0x84, 0x97, 0x78, 0x5D, 0xD7, + 0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F, + 0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 12 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F, + 0x69, 0xE8, 0x9B, 0x4C, 0x55, 0x64, 0xD0, 0x03, + 0x49, 0x10, 0x6B, 0x84, 0x97, 0x78, 0x5D, 0xD7, + 0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F, + 0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 13 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x6C, 0xFF, 0x5C, 0x3B, 0xA8, 0x6C, 0x69, 0xEA, + 0x4B, 0x73, 0x76, 0xF3, 0x1A, 0x9B, 0xCB, 0x4F, + 0x74, 0xC1, 0x97, 0x60, 0x89, 0xB2, 0xD9, 0x96, + 0x3D, 0xA2, 0xE5, 0x54, 0x3E, 0x17, 0x77, 0x69, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, + 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0); + } + { + /* Test vector 14 */ + const unsigned char pk[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 + }; + secp256k1_xonly_pubkey pk_parsed; + /* No need to check the signature of the test vector as parsing the pubkey already fails */ + CHECK(!secp256k1_xonly_pubkey_parse(CTX, &pk_parsed, pk)); + } +} + +/* Nonce function that returns constant 0 */ +static int nonce_function_failing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + (void) nonce32; + return 0; +} + +/* Nonce function that sets nonce to 0 */ +static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + + memset(nonce32, 0, 32); + return 1; +} + +/* Nonce function that sets nonce to 0xFF...0xFF */ +static int nonce_function_overflowing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + + memset(nonce32, 0xFF, 32); + return 1; +} + +static void test_schnorrsig_sign(void) { + unsigned char sk[32]; + secp256k1_xonly_pubkey pk; + secp256k1_keypair keypair; + const unsigned char msg[32] = "this is a msg for a schnorrsig.."; + unsigned char sig[64]; + unsigned char sig2[64]; + unsigned char zeros64[64] = { 0 }; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + unsigned char aux_rand[32]; + + secp256k1_testrand256(sk); + secp256k1_testrand256(aux_rand); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + /* Check that deprecated alias gives the same result */ + CHECK(secp256k1_schnorrsig_sign(CTX, sig2, msg, &keypair, NULL) == 1); + CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0); + + /* Test different nonce functions */ + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + memset(sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_failing; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 0); + CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0); + memset(&sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_0; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 0); + CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0); + memset(&sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_overflowing; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + + /* When using the default nonce function, schnorrsig_sign_custom produces + * the same result as schnorrsig_sign with aux_rand = extraparams.ndata */ + extraparams.noncefp = NULL; + extraparams.ndata = aux_rand; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig2, msg, &keypair, extraparams.ndata) == 1); + CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0); +} + +#define N_SIGS 3 +/* Creates N_SIGS valid signatures and verifies them with verify and + * verify_batch (TODO). Then flips some bits and checks that verification now + * fails. */ +static void test_schnorrsig_sign_verify(void) { + unsigned char sk[32]; + unsigned char msg[N_SIGS][32]; + unsigned char sig[N_SIGS][64]; + size_t i; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey pk; + secp256k1_scalar s; + + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + + for (i = 0; i < N_SIGS; i++) { + secp256k1_testrand256(msg[i]); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[i], msg[i], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[i], msg[i], sizeof(msg[i]), &pk)); + } + + { + /* Flip a few bits in the signature and in the message and check that + * verify and verify_batch (TODO) fail */ + size_t sig_idx = secp256k1_testrand_int(N_SIGS); + size_t byte_idx = secp256k1_testrand_bits(5); + unsigned char xorbyte = secp256k1_testrand_int(254)+1; + sig[sig_idx][byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + sig[sig_idx][byte_idx] ^= xorbyte; + + byte_idx = secp256k1_testrand_bits(5); + sig[sig_idx][32+byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + sig[sig_idx][32+byte_idx] ^= xorbyte; + + byte_idx = secp256k1_testrand_bits(5); + msg[sig_idx][byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + msg[sig_idx][byte_idx] ^= xorbyte; + + /* Check that above bitflips have been reversed correctly */ + CHECK(secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + } + + /* Test overflowing s */ + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[0], msg[0], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + memset(&sig[0][32], 0xFF, 32); + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + + /* Test negative s */ + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[0], msg[0], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + secp256k1_scalar_set_b32(&s, &sig[0][32], NULL); + secp256k1_scalar_negate(&s, &s); + secp256k1_scalar_get_b32(&sig[0][32], &s); + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + + /* The empty message can be signed & verified */ + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig[0], NULL, 0, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], NULL, 0, &pk) == 1); + + { + /* Test varying message lengths */ + unsigned char msg_large[32 * 8]; + uint32_t msglen = secp256k1_testrand_int(sizeof(msg_large)); + for (i = 0; i < sizeof(msg_large); i += 32) { + secp256k1_testrand256(&msg_large[i]); + } + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig[0], msg_large, msglen, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg_large, msglen, &pk) == 1); + /* Verification for a random wrong message length fails */ + msglen = (msglen + (sizeof(msg_large) - 1)) % sizeof(msg_large); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg_large, msglen, &pk) == 0); + } +} +#undef N_SIGS + +static void test_schnorrsig_taproot(void) { + unsigned char sk[32]; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey internal_pk; + unsigned char internal_pk_bytes[32]; + secp256k1_xonly_pubkey output_pk; + unsigned char output_pk_bytes[32]; + unsigned char tweak[32]; + int pk_parity; + unsigned char msg[32]; + unsigned char sig[64]; + + /* Create output key */ + secp256k1_testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &internal_pk, NULL, &keypair) == 1); + /* In actual taproot the tweak would be hash of internal_pk */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, tweak, &internal_pk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &output_pk, &pk_parity, &keypair) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, output_pk_bytes, &output_pk) == 1); + + /* Key spend */ + secp256k1_testrand256(msg); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, NULL) == 1); + /* Verify key spend */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &output_pk, output_pk_bytes) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &output_pk) == 1); + + /* Script spend */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, internal_pk_bytes, &internal_pk) == 1); + /* Verify script spend */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &internal_pk, internal_pk_bytes) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk_bytes, pk_parity, &internal_pk, tweak) == 1); +} + +static void run_schnorrsig_tests(void) { + int i; + run_nonce_function_bip340_tests(); + + test_schnorrsig_api(); + test_schnorrsig_sha256_tagged(); + test_schnorrsig_bip_vectors(); + for (i = 0; i < COUNT; i++) { + test_schnorrsig_sign(); + test_schnorrsig_sign_verify(); + } + test_schnorrsig_taproot(); +} + +#endif diff --git a/src/secp256k1/src/precompute_ecmult.c b/src/secp256k1/src/precompute_ecmult.c new file mode 100644 index 0000000000..10aba5b97d --- /dev/null +++ b/src/secp256k1/src/precompute_ecmult.c @@ -0,0 +1,90 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#include <inttypes.h> +#include <stdio.h> + +#include "../include/secp256k1.h" + +#include "assumptions.h" +#include "util.h" + +#include "field_impl.h" +#include "group_impl.h" +#include "int128_impl.h" +#include "ecmult.h" +#include "ecmult_compute_table_impl.h" + +static void print_table(FILE *fp, const char *name, int window_g, const secp256k1_ge_storage* table) { + int j; + int i; + + fprintf(fp, "const secp256k1_ge_storage %s[ECMULT_TABLE_SIZE(WINDOW_G)] = {\n", name); + fprintf(fp, " S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 + ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", + SECP256K1_GE_STORAGE_CONST_GET(table[0])); + + j = 1; + for(i = 3; i <= window_g; ++i) { + fprintf(fp, "#if WINDOW_G > %d\n", i-1); + for(;j < ECMULT_TABLE_SIZE(i); ++j) { + fprintf(fp, ",S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 + ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", + SECP256K1_GE_STORAGE_CONST_GET(table[j])); + } + fprintf(fp, "#endif\n"); + } + fprintf(fp, "};\n"); +} + +static void print_two_tables(FILE *fp, int window_g) { + secp256k1_ge_storage* table = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage)); + secp256k1_ge_storage* table_128 = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage)); + + secp256k1_ecmult_compute_two_tables(table, table_128, window_g, &secp256k1_ge_const_g); + + print_table(fp, "secp256k1_pre_g", window_g, table); + print_table(fp, "secp256k1_pre_g_128", window_g, table_128); + + free(table); + free(table_128); +} + +int main(void) { + /* Always compute all tables for window sizes up to 15. */ + int window_g = (ECMULT_WINDOW_SIZE < 15) ? 15 : ECMULT_WINDOW_SIZE; + FILE* fp; + + fp = fopen("src/precomputed_ecmult.c","w"); + if (fp == NULL) { + fprintf(stderr, "Could not open src/precomputed_ecmult.h for writing!\n"); + return -1; + } + + fprintf(fp, "/* This file was automatically generated by precompute_ecmult. */\n"); + fprintf(fp, "/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and\n"); + fprintf(fp, " * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G.\n"); + fprintf(fp, " */\n"); + fprintf(fp, "#include \"../include/secp256k1.h\"\n"); + fprintf(fp, "#include \"group.h\"\n"); + fprintf(fp, "#include \"ecmult.h\"\n"); + fprintf(fp, "#include \"precomputed_ecmult.h\"\n"); + fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); + fprintf(fp, "#if ECMULT_WINDOW_SIZE > %d\n", window_g); + fprintf(fp, " #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n"); + fprintf(fp, "# error Cannot compile precomputed_ecmult.c in exhaustive test mode\n"); + fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n"); + fprintf(fp, "#define WINDOW_G ECMULT_WINDOW_SIZE\n"); + + print_two_tables(fp, window_g); + + fprintf(fp, "#undef S\n"); + fclose(fp); + + return 0; +} diff --git a/src/secp256k1/src/precompute_ecmult_gen.c b/src/secp256k1/src/precompute_ecmult_gen.c new file mode 100644 index 0000000000..bfe212fdd2 --- /dev/null +++ b/src/secp256k1/src/precompute_ecmult_gen.c @@ -0,0 +1,80 @@ +/********************************************************************************* + * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *********************************************************************************/ + +#include <inttypes.h> +#include <stdio.h> + +#include "../include/secp256k1.h" + +#include "assumptions.h" +#include "util.h" + +#include "group.h" +#include "int128_impl.h" +#include "ecmult_gen.h" +#include "ecmult_gen_compute_table_impl.h" + +int main(int argc, char **argv) { + const char outfile[] = "src/precomputed_ecmult_gen.c"; + FILE* fp; + int bits; + + (void)argc; + (void)argv; + + fp = fopen(outfile, "w"); + if (fp == NULL) { + fprintf(stderr, "Could not open %s for writing!\n", outfile); + return -1; + } + + fprintf(fp, "/* This file was automatically generated by precompute_ecmult_gen. */\n"); + fprintf(fp, "/* See ecmult_gen_impl.h for details about the contents of this file. */\n"); + fprintf(fp, "#include \"../include/secp256k1.h\"\n"); + fprintf(fp, "#include \"group.h\"\n"); + fprintf(fp, "#include \"ecmult_gen.h\"\n"); + fprintf(fp, "#include \"precomputed_ecmult_gen.h\"\n"); + fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n"); + fprintf(fp, "# error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode\n"); + fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n"); + fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); + fprintf(fp, "const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = {\n"); + + for (bits = 2; bits <= 8; bits *= 2) { + int g = ECMULT_GEN_PREC_G(bits); + int n = ECMULT_GEN_PREC_N(bits); + int inner, outer; + + secp256k1_ge_storage* table = checked_malloc(&default_error_callback, n * g * sizeof(secp256k1_ge_storage)); + secp256k1_ecmult_gen_compute_table(table, &secp256k1_ge_const_g, bits); + + fprintf(fp, "#if ECMULT_GEN_PREC_BITS == %d\n", bits); + for(outer = 0; outer != n; outer++) { + fprintf(fp,"{"); + for(inner = 0; inner != g; inner++) { + fprintf(fp, "S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 + ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")", + SECP256K1_GE_STORAGE_CONST_GET(table[outer * g + inner])); + if (inner != g - 1) { + fprintf(fp,",\n"); + } + } + if (outer != n - 1) { + fprintf(fp,"},\n"); + } else { + fprintf(fp,"}\n"); + } + } + fprintf(fp, "#endif\n"); + free(table); + } + + fprintf(fp, "};\n"); + fprintf(fp, "#undef S\n"); + fclose(fp); + + return 0; +} diff --git a/src/secp256k1/src/precomputed_ecmult.c b/src/secp256k1/src/precomputed_ecmult.c new file mode 100644 index 0000000000..fbc634ef1b --- /dev/null +++ b/src/secp256k1/src/precomputed_ecmult.c @@ -0,0 +1,16457 @@ +/* This file was automatically generated by precompute_ecmult. */ +/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and + * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G. + */ +#include "../include/secp256k1.h" +#include "group.h" +#include "ecmult.h" +#include "precomputed_ecmult.h" +#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) +#if ECMULT_WINDOW_SIZE > 15 + #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build. +#endif +#ifdef EXHAUSTIVE_TEST_ORDER +# error Cannot compile precomputed_ecmult.c in exhaustive test mode +#endif /* EXHAUSTIVE_TEST_ORDER */ +#define WINDOW_G ECMULT_WINDOW_SIZE +const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(79be667e,f9dcbbac,55a06295,ce870b07,29bfcdb,2dce28d9,59f2815b,16f81798,483ada77,26a3c465,5da4fbfc,e1108a8,fd17b448,a6855419,9c47d08f,fb10d4b8) +#if WINDOW_G > 2 +,S(f9308a01,9258c310,49344f85,f89d5229,b531c845,836f99b0,8601f113,bce036f9,388f7b0f,632de814,fe337e6,2a37f356,6500a999,34c2231b,6cb9fd75,84b8e672) +#endif +#if WINDOW_G > 3 +,S(2f8bde4d,1a072093,55b4a725,a5c5128,e88b84bd,dc619ab7,cba8d569,b240efe4,d8ac2226,36e5e3d6,d4dba9dd,a6c9c426,f788271b,ab0d6840,dca87d3a,a6ac62d6) +,S(5cbdf064,6e5db4ea,a398f365,f2ea7a0e,3d419b7e,330e39c,e92bdded,cac4f9bc,6aebca40,ba255960,a3178d6d,861a54db,a813d0b8,13fde7b5,a5082628,87264da) +#endif +#if WINDOW_G > 4 +,S(acd484e2,f0c7f653,9ad178a,9f559abd,e0979697,4c57e714,c35f110d,fc27ccbe,cc338921,b0a7d9fd,64380971,763b61e9,add888a4,375f8e0f,5cc262a,c64f9c37) +,S(774ae7f8,58a9411e,5ef4246b,70c65aac,5649980b,e5c17891,bbec1789,5da008cb,d984a032,eb6b5e19,243dd56,d7b7b365,372db1e2,dff9d6a8,301d74c9,c953c61b) +,S(f28773c2,d975288b,c7d1d205,c3748651,b075fbc6,610e58cd,deeddf8f,19405aa8,ab0902e,8d880a89,758212eb,65cdaf47,3a1a06da,521fa91f,29b5cb52,db03ed81) +,S(d7924d4f,7d43ea96,5a465ae3,95ff411,31e5946f,3c85f79e,44adbcf8,e27e080e,581e2872,a86c72a6,83842ec2,28cc6def,ea40af2b,d896d3a5,c504dc9f,f6a26b58) +#endif +#if WINDOW_G > 5 +,S(defdea4c,db677750,a420fee8,7eacf21,eb9898ae,79b97687,66e4faa0,4a2d4a34,4211ab06,94635168,e997b0ea,d2a93dae,ced1f4a0,4a95c0f6,cfb199f6,9e56eb77) +,S(2b4ea0a7,97a443d2,93ef5cff,444f4979,f06acfeb,d7e86d27,74756561,38385b6c,85e89bc0,37945d93,b343083b,5a1c8613,1a01f60c,50269763,b570c854,e5c09b7a) +,S(352bbf4a,4cdd1256,4f93fa33,2ce33330,1d9ad402,71f81071,81340aef,25be59d5,321eb407,5348f534,d59c1825,9dda3e1f,4a1b3b2e,71b1039c,67bd3d8b,cf81998c) +,S(2fa2104d,6b38d11b,2300105,59879124,e42ab8df,eff5ff29,dc9cdadd,4ecacc3f,2de1068,295dd865,b6456933,5bd5dd80,181d70ec,fc882648,423ba76b,532b7d67) +,S(9248279b,9b4d68d,ab21a9b0,66edda83,263c3d84,e09572e2,69ca0cd7,f5453714,73016f7b,f234aade,5d1aa71b,dea2b1ff,3fc0de2a,887912ff,e54a32ce,97cb3402) +,S(daed4f2b,e3a8bf27,8e70132f,b0beb752,2f570e14,4bf615c0,7e996d44,3dee8729,a69dce4a,7d6c98e8,d4a1aca8,7ef8d700,3f83c230,f3afa726,ab40e522,90be1c55) +,S(c44d12c7,65d812e,8acf28d7,cbb19f90,11ecd9e9,fdf281b0,e6a3b5e8,7d22e7db,2119a460,ce326cdc,76c45926,c982fdac,e106e86,1edf61c5,a039063f,e0e6482) +,S(6a245bf6,dc698504,c89a20cf,ded60853,152b6953,36c28063,b61c65cb,d269e6b4,e022cf42,c2bd4a70,8b3f5126,f16a24ad,8b33ba48,d0423b6e,fd5e6348,100d8a82) +#endif +#if WINDOW_G > 6 +,S(1697ffa6,fd9de627,c077e3d2,fe541084,ce13300b,bec1146,f95ae57f,d0bd6a5,b9c398f1,86806f5d,27561506,e4557433,a2cf1500,9e498ae7,adee9d63,d01b2396) +,S(605bdb01,9981718b,986d0f07,e834cb0d,9deb8360,ffb7f61d,f982345e,f27a7479,2972d2d,e4f8d206,81a78d93,ec96fe23,c26bfae8,4fb14db4,3b01e1e9,56b8c49) +,S(62d14dab,4150bf49,7402fdc4,5a215e10,dcb01c35,4959b10c,fe31c7e9,d87ff33d,80fc06bd,8cc5b010,98088a19,50eed0db,1aa1329,67ab4722,35f56424,83b25eaf) +,S(80c60ad0,40f27da,de5b4b06,c408e56b,2c50e9f5,6b9b8b42,5e555c2f,86308b6f,1c38303f,1cc5c30f,26e66bad,7fe72f70,a65eed4c,be7024eb,1aa01f56,430bd57a) +,S(7a9375ad,6167ad54,aa74c634,8cc54d34,4cc5dc94,87d84704,9d5eabb0,fa03c8fb,d0e3fa9,eca87269,9559e0d,79269046,bdc59ea1,c70ce2b,2d499ec,224dc7f7) +,S(d528ecd9,b696b54c,907a9ed0,45447a79,bb408ec3,9b68df50,4bb51f45,9bc3ffc9,eecf4125,3136e5f9,9966f218,81fd656e,bc434540,5c520dbc,63465b5,21409933) +,S(49370a4,b5f43412,ea25f514,e8ecdad0,5266115e,4a7ecb13,87231808,f8b45963,758f3f41,afd6ed42,8b3081b0,512fd62a,54c3f3af,bb5b6764,b653052a,12949c9a) +,S(77f23093,6ee88cbb,d73df930,d64702ef,881d811e,e1498e2,f1c13eb1,fc345d74,958ef42a,7886b640,a08266e,9ba1b378,96c95330,d97077cb,be8eb3c7,671c60d6) +,S(f2dac991,cc4ce4b9,ea44887e,5c7c0bce,58c80074,ab9d4dba,eb28531b,7739f530,e0dedc9b,3b2f8dad,4da1f32d,ec2531df,9eb5fbeb,598e4fd,1a117dba,703a3c37) +,S(463b3d9f,662621fb,1b4be8fb,be252012,5a216cdf,c9dae3de,bcba4850,c690d45b,5ed430d7,8c296c35,43114306,dd8622d7,c622e27c,970a1de3,1cb377b0,1af7307e) +,S(f16f8042,44e46e2a,9232d4a,ff3b5997,6b98fac1,4328a2d1,a32496b4,9998f247,cedabd9b,82203f7e,13d206fc,df4e33d9,2a6c53c2,6e5cce26,d6579962,c4e31df6) +,S(caf75427,2dc84563,b0352b7a,14311af5,5d245315,ace27c65,369e15f7,151d41d1,cb474660,ef35f5f2,a41b643f,a5e46057,5f4fa9b7,962232a5,c32f9083,18a04476) +,S(2600ca4b,282cb986,f85d0f17,9979d8b,44a09c07,cb86d7c1,24497bc8,6f082120,4119b887,53c15bd6,a693b03f,cddbb45d,5ac6be74,ab5f0ef4,4b0be947,5a7e4b40) +,S(7635ca72,d7e8432c,338ec53c,d12220bc,1c48685,e24f7dc8,c602a774,6998e435,91b6496,9489d61,3d1d5e59,f78e6d7,4ecfc061,d57048ba,d9e76f30,2c5b9c61) +,S(754e3239,f325570c,dbbf4a87,deee8a66,b7f2b334,79d468fb,c1a50743,bf56cc18,673fb86,e5bda30f,b3cd0ed3,4ea49a0,23ee33d0,197a695d,c5d9809,3c536683) +,S(e3e6bd10,71a1e96a,ff57859c,82d570f0,33080066,1d1c952f,9fe26946,91d9b9e8,59c9e0bb,a394e76f,40c0aa58,379a3cb6,a5a22839,93e90c41,67002af4,920e37f5) +#endif +#if WINDOW_G > 7 +,S(186b483d,56a0338,26ae73d8,8f732985,c4ccb1f3,2ba35f4b,4cc47fdc,f04aa6eb,3b952d32,c67cf77e,2e17446e,204180ab,21fb8090,895138b4,a4a797f8,6e80888b) +,S(df9d70a6,b9876ce5,44c98561,f4be4f72,5442e6d2,b737d9c9,1a832172,4ce0963f,55eb2daf,d84d6ccd,5f862b78,5dc39d4a,b1572227,20ef9da2,17b8c45c,f2ba2417) +,S(5edd5cc2,3c51e87a,497ca815,d5dce0f8,ab52554f,849ed899,5de64c5f,34ce7143,efae9c8d,bc141306,61e8cec0,30c89ad0,c13c66c0,d17a2905,cdc706ab,7399a868) +,S(290798c2,b6476830,da12fe02,287e9e77,7aa3fba1,c355b17a,722d362f,84614fba,e38da76d,cd440621,988d00bc,f79af25d,5b29c094,db2a2314,6d003afd,41943e7a) +,S(af3c423a,95d9f5b3,54754ef,a150ac39,cd29552f,e3602573,62dfdece,f4053b45,f98a3fd8,31eb2b74,9a93b0e6,f35cfb40,c8cd5aa6,67a15581,bc2feded,498fd9c6) +,S(766dbb24,d134e745,cccaa28c,99bf2749,6bb66b2,6dcf98df,8d2fed50,d884249a,744b1152,eacbe5e3,8dcc8879,80da38b8,97584a65,fa06cedd,2c924f97,cbac5996) +,S(59dbf46f,8c94759b,a21277c3,3784f416,45f7b44f,6c596a58,ce92e666,191abe3e,c534ad44,175fbc30,f4ea6ce,648309a0,42ce739a,7919798c,d85e216c,4a307f6e) +,S(f13ada95,103c4537,305e691e,74e9a4a8,dd647e71,1a95e73c,b62dc601,8cfd87b8,e13817b4,4ee14de6,63bf4bc8,8341f32,6949e21a,6a75c257,778419b,daf5733d) +,S(7754b4fa,e8aced0,6d4167a2,c59cca4c,da1869c0,6ebadfb6,48855001,5a88522c,30e93e86,4e669d82,224b967c,3020b8fa,8d1e4e35,b6cbcc5,37a48b57,841163a2) +,S(948dcadf,5990e048,aa3874d4,6abef9d7,1858f95,de8041d2,a6828c99,e2262519,e491a425,37f6e597,d5d28a32,24b1bc25,df9154ef,bd2ef1d2,cbba2cae,5347d57e) +,S(79624144,50c76c16,89c7b48f,8202ec37,fb224cf5,ac0bfa15,70328a8a,3d7c77ab,100b610e,c4ffb476,d5c1fc1,33ef6f6b,12507a05,1f04ac57,60afa5b2,9db83437) +,S(35140878,34964b54,b15b1606,44d91548,5a169772,25b8847b,b0dd0851,37ec47ca,ef0afbb2,5620544,8e1652c4,8e8127fc,6039e77c,15c2378b,7e7d15a0,de293311) +,S(d3cc30ad,6b483e4b,c79ce2c9,dd8bc549,93e947eb,8df787b4,42943d3f,7b527eaf,8b378a22,d827278d,89c5e9be,8f9508ae,3c2ad462,90358630,afb34db0,4eede0a4) +,S(1624d847,80732860,ce1c78fc,bfefe08b,2b29823d,b913f649,3975ba0f,f4847610,68651cf9,b6da903e,914448c,6cd9d4ca,896878f5,282be4c8,cc06e2a4,4078575) +,S(733ce80d,a955a8a2,6902c956,33e62a98,5192474b,5af207da,6df7b4fd,5fc61cd4,f5435a2b,d2badf7d,485a4d8b,8db9fcce,3e1ef8e0,201e4578,c54673bc,1dc5ea1d) +,S(15d94412,54945064,cf1a1c33,bbd3b49f,8966c509,2171e699,ef258dfa,b81c045c,d56eb30b,69463e72,34f5137b,73b84177,434800ba,cebfc685,fc37bbe9,efe4070d) +,S(a1d0fcf2,ec9de675,b612136e,5ce70d27,1c21417c,9d2b8aaa,ac138599,d0717940,edd77f50,bcb5a3ca,b2e90737,309667f2,641462a5,4070f3d5,19212d39,c197a629) +,S(e22fbe15,c0af8ccc,5780c073,5f84dbe9,a790bade,e8245c06,c7ca3733,1cb36980,a855bab,ad5cd60c,88b430a6,9f53a1a7,a3828915,4964799b,e43d06d7,7d31da06) +,S(311091dd,9860e8e2,ee13473,c1155f5f,69635e39,4704eaa7,40094522,46cfa9b3,66db656f,87d1f04f,ffd1f047,88c06830,871ec5a6,4feee685,bd80f0b1,286d8374) +,S(34c1fd04,d301be89,b31c0442,d3e6ac24,883928b4,5a934078,1867d423,2ec2dbdf,9414685,e97b1b59,54bd46f7,30174136,d57f1cee,b487443d,c5321857,ba73abee) +,S(f219ea5d,6b54701c,1c14de5b,557eb42a,8d13f3ab,bcd08aff,cc2a5e6b,49b8d63,4cb95957,e83d40b0,f73af454,4cccf6b1,f4b08d3c,7b27fb8,d8c2962a,400766d1) +,S(d7b8740f,74a8fbaa,b1f683db,8f45de26,543a5490,bca62708,72369124,69a0b448,fa779681,28d9c92e,e1010f33,7ad4717e,ff15db5e,d3c049b3,411e0315,eaa4593b) +,S(32d31c22,2f8f6f0e,f86f7c98,d3a3335e,ad5bcd32,abdd9428,9fe4d309,1aa824bf,5f3032f5,892156e3,9ccd3d79,15b9e1da,2e6dac9e,6f26e961,118d14b8,462e1661) +,S(7461f371,914ab326,71045a15,5d9831ea,8793d77c,d59592c4,340f86cb,c18347b5,8ec0ba23,8b96bec0,cbdddcae,aa44254,2eee1ff5,c986ea6,b39847b3,cc092ff6) +,S(ee079adb,1df18600,74356a25,aa38206a,6d716b2c,3e67453d,287698ba,d7b2b2d6,8dc2412a,afe3be5c,4c5f37e0,ecc5f9f6,a446989a,f04c4e25,ebaac479,ec1c8c1e) +,S(16ec93e4,47ec83f0,467b1830,2ee620f7,e65de331,874c9dc7,2bfd8616,ba9da6b5,5e463115,e62fb40,d0e8c2a7,ca5804a3,9d58186a,50e49713,9626778e,25b0674d) +,S(eaa5f980,c245f6f0,38978290,afa70b6b,d8855897,f98b6aa4,85b96065,d537bd99,f65f5d3e,292c2e08,19a52839,1c994624,d784869d,7e6ea67f,b1804102,4edc07dc) +,S(78c9407,544ac132,692ee191,a024399,58ae0487,7151342e,a96c4b6b,35a49f51,f3e03191,69eb9b85,d5404795,539a5e68,fa1fbd58,3c064d24,62b675f1,94a3ddb4) +,S(494f4be2,19a1a770,16dcd838,431aea00,1cdc8ae,7a6fc688,726578d9,702857a5,42242a96,9283a5f3,39ba7f07,5e36ba2a,f925ce30,d767ed6e,55f4b031,880d562c) +,S(a598a803,da6d86c,6bc7f2f5,144ea549,d28211ea,58faa70e,bf4c1e66,5c1fe9b5,204b5d6f,84822c30,7e4b4a71,40737aec,23fc63b6,5b35f86a,10026dbd,2d864e6b) +,S(c4191636,5abb2b5d,9192f5f,2dbeafec,208f020f,12570a18,4dbadc3e,58595997,4f14351,d0087efa,49d245b3,28984989,d5caf945,f34bfc0,ed16e96b,58fa9913) +,S(841d6063,a586fa47,5a724604,da03bc5b,92a2e0d2,e0a36acf,e4c73a55,14742881,73867f5,9c0659e8,1904f9a1,c7543698,e62562d6,744c169c,e7a36de0,1a8d6154) +#endif +#if WINDOW_G > 8 +,S(5e95bb39,9a6971d3,76026947,f89bde2f,282b3381,928be4d,ed112ac4,d70e20d5,39f23f36,6809085b,eebfc711,81313775,a99c9aed,7d8ba38b,161384c7,46012865) +,S(36e4641a,53948fd4,76c39f8a,99fd974e,5ec07564,b5315d8b,f99471bc,a0ef2f66,d2424b1b,1abe4eb8,164227b0,85c9aa94,56ea1349,3fd563e0,6fd51cf5,694c78fc) +,S(336581e,a7bfbbb2,90c191a2,f507a41c,f5643842,170e914f,aeab27c2,c579f726,ead12168,595fe1be,99252129,b6e56b33,91f7ab14,10cd1e0e,f3dcdcab,d2fda224) +,S(8ab89816,dadfd6b6,a1f2634f,cf00ec84,3781025,ed6890c4,84974270,6bd43ede,6fdcef09,f2f6d0a0,44e654ae,f624136f,503d459c,3e898458,58a47a91,29cdd24e) +,S(1e33f1a7,46c9c577,8133344d,9299fcaa,20b0938e,8acff254,4bb40284,b8c5fb94,6066025,7dd11b3a,a9c8ed61,8d24edff,2306d320,f1d03010,e33a7d20,57f3b3b6) +,S(85b7c1dc,b3cec1b7,ee7f30de,d79dd20a,ed1f4cc,18cbcfcf,a410361f,d8f08f31,3d98a9cd,d026dd43,f39048f2,5a8847f4,fcafad18,95d7a633,c6fed3c3,5e999511) 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+,S(a6597869,4d168b00,d9df41de,fcd48ae9,68313394,db683407,330ffae9,f2559a11,6bf65c42,13317a5d,fb561e8c,872c8b1b,90bdabc8,8a8d2e1e,39919f8e,5043ced3) +,S(9e62e468,1e22abde,4d7a2fa1,2f7867f6,ecbfc15b,54990e26,821a8cde,fed76985,4877297b,a64fa8ed,c039ab1a,e62ac72d,8d7bbf05,7513d1,4237b8dd,9f1acd37) +,S(d24333b4,de55b0f5,d47c72e4,88cee8ee,8c960903,260a64d2,c89bca45,db7352c5,688b20b0,617ac12d,5be38fa2,ab52e785,69766a83,2d8b44d5,cfd6ee88,b19b9f1d) +,S(d203301a,13d1c8ae,a8c79007,1ef8116c,3916bb3e,dd5110a7,304b9145,465be838,a606dcea,398dc313,e61c8fbb,dbbc3874,3c103297,164e66a1,4412a21a,5319e55c) +,S(d1aa98ab,7010146f,16a9d6b,cd911535,2595bfa5,1bccb3d5,5e3a4a87,62666610,3abafa4,999294e8,80e3fae9,edb4206b,9b9786d,bddcaec,e2d01cf1,ab715690) +,S(1e20823e,81051b2,65535085,9aefed6,3631dbe,23b4e79,abd3c17c,21f053f4,e238adb6,86592008,f7fe34b9,9b934060,15c323ec,55981b27,85feae6e,5fde7186) +,S(d878afb8,8527a861,4b4276d8,fba39300,72196017,6f437014,980b7bbf,d4320ffc,7403107b,fca8ac64,baa94a4b,128e72ee,4a015675,845519ba,d5609331,1680e7) +,S(53f86d45,61deef96,ca88a685,38fd35ec,a95740a4,3a52c601,faaad0c2,aa3ab72f,667a6ece,bfb97682,c5e9e5df,b6d29156,9604f63,d9ab00ab,8cb10000,e6b01514) +,S(20990660,f1055420,b885fb0a,38824740,3b141c37,5aa20dce,8a29191a,e77bbb16,7d434476,9e302e38,9e14c02e,f5fd8a5c,64cfcf3d,e9813f1c,f53bc6d3,4da93559) +,S(1e70619c,381a6adc,e5d925e0,c9c74f97,3c02ff64,ff2662d7,34efc485,d2bce895,c923f771,f543ffed,42935c28,8474aaaf,80a46ad4,3c579ce0,bb5e663d,668b24b3) +#endif +}; +const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(8f68b9d2,f63b5f33,9239c1ad,981f162e,e88c5678,723ea335,1b7b444c,9ec4c0da,662a9f2d,ba063986,de1d90c2,b6be215d,bbea2cfe,95510bfd,f23cbf79,501fff82) +#if WINDOW_G > 2 +,S(38381dbe,2e509f22,8ba93363,f2451f08,fd845cb3,51d954be,18e2b8ed,d23809fa,e4a32d0a,fb917dc,b09405a5,520eb1cc,3681fccb,32d8f24d,bd707518,331fed52) +#endif +#if WINDOW_G > 3 +,S(49262724,e4372ae6,f6921b82,aa4699a1,f186aea5,40122630,3ea42648,97c2a310,1337e773,bca7abf9,5a2cfa56,9714303b,6d163612,a75ff8ce,c41b681,5e27ded0) +,S(e306568c,1a240c90,d5e253b3,e477e2f8,4dcc1a56,ff06db8d,1384b079,cebd2d31,eac6fe3,78934260,888f2b10,7f7d0db6,ffbc8042,be373826,692b4083,92546e44) +#endif +#if WINDOW_G > 4 +,S(3b9e100e,2428cefc,271b0e76,23fbd633,74ebf8d9,aab41dd9,c530c39e,363136b0,fafb9815,2d16bb71,df1533eb,8f475b26,a2ae28a3,3ad31f81,953ec16f,6cdbbc8a) +,S(bb0aad49,712ac9a9,2b76ca80,f5dedef7,17ca0768,8107beee,9608f047,2f485d3f,ea699c53,c5835479,8ecd201f,7297da34,895a5afa,31670bff,e7939250,3ca2f975) +,S(79090ac8,e4eefcc0,d4e8eb19,7afe0113,e1e58b4d,b01123de,4aeed33a,36718dc9,eaab722b,91905b8f,13d816cb,cd9aaa56,dd36afb7,ba9008b,963322b1,1cfae7c5) +,S(e77c81ad,e9f97b55,1c03dbbc,e549ba66,8dd71de7,cd775ad2,a269694c,7f60c7d1,3acf1478,eef81321,c5fc3b32,3ea81543,631470f7,1c2986d3,4ec581f2,82d72449) +#endif +#if WINDOW_G > 5 +,S(de2b5ce9,dbce511c,f2d8878e,3ded87cc,3d633dae,a2d45341,501fb3a4,55ccf6b0,f10576f3,d3c3e0e1,bbf717e9,8b1a3744,65b8c45a,c66318bb,34829eb7,11100666) +,S(d07bddff,d491a2fe,1ea59fbd,7c121217,29659ca5,de46658b,26b1460b,13c03c56,b2ad4708,cd3c97dd,f9c40e2,a1de04d5,61d963ff,8cc2eea7,6be3f60c,2b405ce7) +,S(82403e7c,5d3016af,3765ec4c,396ce8e1,f8da45c,434b8257,10edab41,bb6a4d51,d09661b,e27cb767,4456badd,b3e84051,99ab6ccc,4ec67c1b,11e92ead,7b463b19) +,S(eadc3131,fbd626f5,263faa58,c4caf4d9,930f933d,9541c23f,438cb486,750680cf,d3c977b1,c9b4a897,5c64b36c,972d5d01,a388fb9d,c3791a74,36094ff1,2c87a914) +,S(3903ee5f,6758ff24,c518a4b3,86748f4f,36bdd65c,b77e78ac,609f2909,fc7987d9,e92194e,a15241d6,40915934,bd234749,8d222a18,4927a8da,b0cfe2ae,182be83b) +,S(d0803b78,39ab48a3,8475bdcc,f9a9f219,5759c343,dbbf8e93,23e1f882,5be6a5d9,2cc3b180,ff29c97e,a12ec15f,b38bafa4,4ecf06c,e51d1d24,2894a926,64582f0b) +,S(1f56f096,b18a7499,a153a5ae,acf8be05,8496dd23,da8e6c19,215628fb,c0567ed0,fef22b8a,3b52f490,83004436,b65cd69,c94189f4,1a93c0d5,1fc13cb4,379dff58) +,S(1d9f69b1,a4a47432,e386f525,234aa30,79e947cf,cf203297,4e0fc05b,638e213b,d898ec17,949c0761,b38500c3,a2b1da24,5438d5b3,d3f6f720,41f15d6e,e4d4ccbb) +#endif +#if WINDOW_G > 6 +,S(128c913,4d9dcb78,12fc4361,5c67ad0,55213354,dc8008b1,aeb5a9dc,fb629efd,fee3e54a,dd152610,d9725936,99d662,c160c8e4,ec6f76e4,5ff41818,be67c96) +,S(21ec012f,5a95b94d,244b8d51,9756075c,301f2854,8e2c51fc,49c0e3d9,d1a9685,2def2105,77af497f,4c7fef71,6949f28e,7418eda6,fd5fc162,d128de19,3cde08ae) +,S(688f5202,fb9d8bc0,9e480e89,4c7cfc74,761c3be7,7dafb11c,58422836,3e331cc5,96ba7d59,63b541a7,2ec7cabd,92403434,1a393eaf,89eebd94,62d9c218,c7302cd3) +,S(fb5c9eea,1cb9a8f5,b3314c30,a50d35,744d0ef,e8bbf68,2e4d3ab4,f7f02baf,29fb8844,e18fc551,fb28bd26,95c5e95c,6868e0cc,7e526af0,91157e9d,fb630418) +,S(f1479fe2,2eedae3f,2f5f6a5d,84a9de1d,593168ec,7b52380d,e0b3625c,cac03421,1a642d5d,2fd88b82,13b50d1a,3fbd3419,c0b4630c,48352131,cb856b2e,22764606) +,S(2273edc5,e8199774,93c5b0e0,9fe0effa,f60f7b,2898565a,69f5c7b2,bf1a7950,b3aea238,8fd978d9,29f1a1df,98495358,b64691fc,4f50b530,906ae39e,fe7bda12) +,S(99f8480c,30504378,b47d10b3,2b39da2f,496d59f4,b1462856,56f05ad7,9bef5214,e001d55d,8e224286,8d8bd397,cb5aa99e,d930e437,e4e62151,71da7ae6,6264b2cd) +,S(382257f,e4751280,d74fdfc6,993c8642,9c000d5,87f57635,bc9656ba,996a6f1f,c2dc733d,fe52cb06,265a4f1d,a6b5f1f9,30dbfa39,e3659973,1c672aad,8b51d474) +,S(23a13632,9125386b,e45f4e1b,2acc847a,62e5eaf9,f6d5f452,6e145e7f,ecefb24b,9129777e,643ba22,2bf817a1,af7155f1,413cc370,3734ba6f,49f15f55,996854c0) +,S(6659ea60,58a664de,a35791a1,8c5cded4,8cf5593d,c440b9d4,8a30ac35,79149f0b,2adcc705,a85d836f,b347b69e,742fc6c3,5300d1d8,e534f1ff,c820c6d6,b2f2199d) +,S(52dc3bc6,e1acd3b4,7ece6f6c,89fd2a3e,2899b487,41421033,37a67dd,1ba939fc,5daeb346,32ad107f,bd83d9da,15a3c4ff,1e8f6ba3,ee5193e2,709e89c3,43d05746) +,S(524b2a97,93cd5745,bd9189ba,9c947bc1,693fbceb,75f074f6,17376b10,d5573551,9e8099d6,cb23fb1a,9deb92cc,3e8a2fb5,a6865ac6,3dececa0,2d146e1b,bcc80b71) +,S(732181a8,e2bc5953,923e6c3d,d960e9b7,525b7b95,e5906997,6fe79156,1782756e,2516c6b3,5592eb0a,42ba193c,bae98ab,e3c42d96,148f1d84,edac621a,722e4823) +,S(b8e8942d,926e38fd,f338496a,c2ef6fca,49a7ae3d,f76eb15d,8d570111,e502664b,7990d56e,7dea588e,4d670ba2,2031e6c7,97248641,69e51d77,f792f5ed,befaf8eb) +,S(144e88f6,3e73abff,72cac11e,7ddccf79,19e744e6,278941ae,18d1b797,e098e4e5,63cdbf3,5df3c655,c58197f,ea54633d,158705cf,7dc2eb3b,4e09f83c,3021837c) +,S(9436e3dc,489ecd8e,2d16a739,c9c73e3d,60e5bc93,68157039,75b8efbd,5c3a9081,1460531f,50cb6ebf,d1aa7806,ea84e7f7,8e8d76b2,b3a66d5e,3a0bf60,39a7e59c) +#endif +#if WINDOW_G > 7 +,S(9d3c2561,7a56d10b,46d9b01a,1710d193,e840e005,df669e76,1936c275,20890db9,6bbdc0bc,4c4ae9bc,c2dfee9b,82da9b94,1f89ffcd,e8af2aca,4467ce3,78521ea3) +,S(29f98e50,f51b7f8b,e18c6ae0,b453c4f2,d0aca5a8,b0e61d2d,dda8506,3fdb76c8,daf3bcdc,ae8e031c,73eb8b21,14058063,58a6ec30,ad379186,df80e3c7,f0e5d28f) +,S(d67d30c2,c71daa36,1805e31,1dd6046e,17a89752,94d76e1a,538af074,4dc22c94,48b9b0e7,12c807b0,b92e690a,a2e068cc,e87ebbbe,aaf4bd96,9c1114bb,a54f670c) +,S(f22c2ba8,8ce9c2e4,b772c9b7,6d03a017,59aa7b9,97a78334,83566027,2fc81649,6aa9e710,f190be16,243a4e0f,1570270a,2d92dca9,8cf99a3,cbc06fdd,f9b7028f) +,S(c5e718d,6b94c83,e52533c9,ef3234f,36b722ed,cfc074a5,eff30969,9ac5f894,24961051,ccfc6619,dd64e810,fa9c504b,f7f8ce9e,cc445d7e,642b3166,eeef436) +,S(26a8bcaa,c836eb7d,57618999,ef87ee4e,c291dc8b,333554a2,c1f66f73,7944d611,c20051ba,7236663,ace2da29,c1e0763c,e57192d0,e199e7a6,c69cc65d,bbbcecc9) +,S(388e3570,fb7b1545,9bf01ba1,7a6496d5,6bcf65e1,764e7aa,2c083346,2dfa098c,2d4e0d22,a2eb0ff0,545561e5,ae344be6,99120d12,45db6bde,a9500f5f,a07be798) +,S(68189bab,b5a0783e,23227efa,4eab2c6e,da2d1c,2ea57fca,7a7f8f72,15250709,bd30bd83,3694d3fa,a14954f6,251445f8,3e42d517,30d30855,a0eb834d,3c7ae856) +,S(642e0823,bb347795,967b7aa9,418a25,ea6ff683,fd7b3d42,b88d90d1,292190ab,db73dea7,86ec052f,e3674892,639daf39,286b4690,63b68903,210639c7,f3b4000f) +,S(9ab6ea81,e5bf5505,751addea,5896afab,7f4eff2f,d3986027,f916835c,64924afa,38c06aa7,4870a5e7,2ff29efc,bce4b3e7,dd951c9b,29966f2b,47d007ac,7629bb6c) +,S(b09805ae,e567f69c,71a98248,e89e64f9,e059e015,bde01a62,dd18158e,e94a8ee7,62aea16a,7ec912ef,cc5382eb,6d220ac3,dea885a8,e3da12c,8147b28e,1983d221) +,S(3d632a5b,636ed5a3,4a58bfbc,9831691a,91d6b5f0,975bfb5a,82b4c1bc,107e6e5,577a449e,75bf16d9,2eb6ba0f,9cb4d496,7a7ee09c,f1605aef,682cfa31,cf395a1c) +,S(6b821bf0,f70d5ff2,ceedb69d,d96ac8bb,b51e3635,3a36d50a,b1c1a697,40cef707,5212ce11,993fc120,88028674,5cddea94,6371b4,dfa2f47a,6d83b789,c6d12e5d) +,S(bf294951,4496fe0b,8527740b,5cd9394e,dc33b330,c91d996c,789db854,45728b23,790aede5,da35ce7a,343f745c,410de38f,4c53bc2a,bb41bbae,c13272b1,e912782c) +,S(a55354c3,82bf968a,16668267,c4498946,4906f69b,114f6f06,742b6035,1d75ec80,2809bddc,45661a5f,28b31967,6cdfb5b1,9dd6d296,d1828c88,179a630c,ca5962e8) +,S(fc015036,abcd8311,bbfa1574,ffb4980f,b893f8af,84f519f4,5a6fa344,2649a693,d0f6a278,1946e04b,385cd004,29acd3f6,f5542aca,3e7c789,657f676b,f19db819) +,S(6164410d,9f81f352,272a799f,b4afbe24,59caea6c,511fa4ea,b7578980,d9a7aae,92bc1480,ba19fcd,3cbee69c,95b9396f,4982fff5,d4e7dac0,abec7153,ee5a7966) +,S(ef816535,8de9d737,728f9a9b,3182b4f5,6e25917d,1ec05fc6,faa0fc85,170b5f2d,dc372426,403ca9c4,50649df8,8b6fd32d,f1721dc,cb1c7d7e,155c83ea,747ec595) +,S(428c34b9,89a436dd,dc704e68,170d2c40,178c5646,841eb2e2,642c0a48,8987a8ed,b1f24158,251c4646,ca04dc3e,64369634,3836f97e,71945f4f,51237abd,3aeebe06) +,S(6eb61782,f909157b,415e6243,7bebbd6a,5f19da73,7eda64a5,5acfe206,65417a9e,4fe7c546,baedf2b1,6c92f168,f99c42f6,af03edee,290ecc39,4c4efff,e8577b72) +,S(992e0af1,466d4fec,5ef83009,98ce31df,cb6f9573,d14c1646,e4371c62,a376fa4b,d0e3da69,1e4396b2,eb01e3a9,964365,50d000e6,31d79ae3,871690d5,29f9e825) +,S(fedb564b,adc70078,f20f31d1,12496934,513e9903,8cf5b9c3,1084383,5721d11,1a8e2a49,57e8420c,f2d5d97d,657f1602,ba26ae87,d5408b2f,a9448def,38157a39) +,S(f3f2068a,4dd89d18,1247088d,3c424916,3e683226,6274b575,e54430d0,73b24bd,f2aabd19,a7f462,1426ab1e,e0aa7e33,12381c5f,e1f1cf0e,75c1a7f7,7ba2bfa8) +,S(32b9225e,4217a359,8de4e7c1,476a8581,5b6aa458,d93dae02,b3d30772,3ca13680,7466e804,26856340,12985683,dd071e97,53246214,733808a3,96f35d0e,5a133802) +,S(85008a87,385ed6b0,4ff89979,2eb592f9,ee6c6b93,fa24dc7f,c6299b9f,dae64a8a,1f279e2b,8a5b0576,fb9569f6,c0825876,84b5b38f,a250e362,2ae6e284,a504a2df) +,S(4dac7833,ebbeab0b,ec8edac7,cfc49bfd,b835362,f0130e9,e44452f6,a82effd4,fc9d1970,f230aa68,6114ada5,7b4237dd,133dc3b5,db8ec1f0,ccd09aa,23c740a) +,S(9b755881,45a65d54,19b40226,e535df5b,4b44de41,1b93d71,31f3102,d56dbeeb,d0324171,d6937b7,c9b38290,7dbba3b5,c1516061,59e7ce1f,a1ed9d11,e089a02d) +,S(1bd6ceb9,2592a7d7,a66e6e8b,1b645db5,98b525ca,461dc4bd,b583ed9a,cbbc8bdd,9a59de87,84a98bea,48b7abb1,a5b7055,5a1c4ce5,551cde4e,7b790ac4,9a29944c) +,S(25a8b2b9,3b360941,6525b08a,7fe786e9,6b3a3c7d,8b444637,268f5355,bd5b56ee,3c58ccf7,5734687f,dbd027e6,3ec6c550,45f131ae,df71a40a,c45e4e8b,965f22ec) +,S(244b2833,27c33efb,221a5767,15225d6a,bf5a1caa,8da543c0,d88b21e5,17ed9f5f,220036ac,e48d8953,5aecec92,a29f5012,37f83ce6,44380db,c229f0bf,c1f53d7d) +,S(6f97ac0f,27b87905,6b442d13,e566978e,91f0cc1d,d6ac1e64,e9764a35,325dd1b7,83c6e70c,fac6c707,226ce1cc,691b38a0,7e937f5a,5f2d9c81,4dd0d3ff,9f433d32) +,S(72c5d60f,eb014e2d,ba8265ca,d454f261,2d6abcd4,b2236bad,c94c4801,561dce1f,e3119a19,7ef91963,b3b28216,3c5d3acb,97b281b6,d246cbf0,690b40da,63978fe2) +#endif +#if WINDOW_G > 8 +,S(a96d2da0,1b10186,6998659d,f441a1b0,2af32b94,aae8c6ea,707d9ed0,d5f33825,660d7d83,5da5235,9f7cfd41,28c370aa,5659ea71,16a91690,6c0e8108,a513f9f) +,S(2cce6f63,4d815ecc,1981d200,87616677,d906aa27,990c4875,17314dc5,5be3c4fa,615210dd,bd599e91,1b6f997a,fd05475,b33cb274,c9ecb6e5,d3c23323,beba4b50) +,S(992b0084,525dd399,d98602d9,8b8d53b2,4558fafc,758a2f46,60e89bd6,a645f0c4,83ca98d2,26545a29,8c45f40b,11420602,f5a5c70e,595eea57,2da64d61,a4e2f98d) +,S(434efb45,3089619f,cc761ee4,3fd4b77d,c6b0c69e,b45eb88e,44ef766e,9beb7357,3dbb0d6d,1c0b92e,5965586d,236c0be9,26967ac8,830b9bd0,1e9efc2,2a9291ea) +,S(a2179ad,2c683306,a2e4735,93efe304,f0dbf589,c4dc2b88,4bddc5c7,e3fbc156,ee4539f8,ab980176,a18e6dfa,bdb609d2,88a2d223,86dcb20,19207afa,f6033c1f) +,S(3934081e,d3e1e147,aa52bb40,9221ef6,a445f22a,66718f14,6d63907a,ef05a2e1,bc370656,31391b7a,209e79d4,9f1e959b,d3a9fefe,752c6062,14fab290,a7b5b3c7) +,S(35bc24e1,59a2b939,438354,6cc4255f,f1f3f7e2,105293db,39688e07,df95d8ef,dee1fc70,a9698da,f7abeb5c,56724f8,e87e0cd3,8849edfa,246ed0a8,9223ae15) +,S(f5d1e75c,251fb473,8552a0ee,f05d8e65,63aa14e1,bcae5b48,bc7e5258,b948127d,e260c1bc,7044f058,8f409134,d298528b,e7d586f4,bf7b6fe,92d212a8,6f7170fe) +,S(ee0a76d3,6fed282f,a1170dd,6acb7743,f9617bb3,60350f54,d12da1cc,7eb121c,f8cfc2db,eba6960f,e6135ef,ff9e10ca,4e56c458,4b42b516,6dbf7af1,420ba5b1) +,S(9e3b87cf,78927664,15cab377,f1774d14,4d1879f6,16da5676,f94790d1,9ca689d8,f8f34522,da3ca2ac,b273b0c2,b1b1f26a,7a9c2d96,b4547482,266a8e6d,bab3b577) 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+,S(d404209e,8530d674,9bb88a5,525211a1,19fb2523,63e2698,6bd03080,4c49c123,3763fd68,fdb85d19,e8506275,3b5a327c,46ef87be,8a3432c5,62bcc622,40a7a128) +,S(f3abf8cf,c232849,58e330c2,fc327ac4,d40b4497,f422aa4e,d42e9381,9bffdd96,50861f05,d831327c,3e907643,2d7a7621,d1dfe9ec,7ccf2061,cc720e9a,7d5b0d5d) +,S(78a32893,2ee9dbfb,3f84755a,651b9d23,5cf92b46,c3e4bb4e,57b7ff6f,7c874dea,925b783a,966721f4,6eaccd87,495eab7d,b3c36eb2,92c1a473,b4617f6b,9ac85895) +,S(8165210f,5d146f8a,1ac1ed91,a7bb678d,1b7d15e4,3ed55e8d,f6503209,a750cd4a,fe390d3a,19e22bdc,cbd45875,e396c713,85954166,a1edb63a,384b8587,915d260d) +,S(75269de8,6c2f3d34,cdf17dd6,f3efa198,ba73431f,cf0072f3,633ca57f,7dfe3f09,b162a65f,d19927ec,4446e3db,d5ee8850,f463f39f,1df1a0b1,f5ed153e,704805bd) +,S(5e36ce8f,b393949e,5b9c4e10,44fb2ff7,c520a7b7,a9016b38,9544e512,427145b0,7c40e718,292f96a4,1d9822ce,d54aea90,22074c5c,c82ba4e,7d39a4e0,7811614c) +,S(c8cc7129,fdebbfc6,c0576edc,6ac983e5,c249d360,76da7d25,b05c0b6b,16632746,48a8cce3,a77e4498,76d1a332,c539feba,2653fbaf,d4f75e68,e4674d78,4c716fb1) +,S(9fe1db36,f1ee3e6d,3924d2a9,ae3ddcaf,fa85798b,7383a1dd,2d6c0c14,ea46973f,1d35b6a8,607045c0,95ed9658,80212b63,43dc55ec,beb3223e,7c2e76ce,2c74f6d2) +,S(4ca8ab8a,3d45748e,6e19e02d,dc351279,e23648db,d26d2465,7c9713f5,bc8ecda2,8a5866ad,9bb7db92,273c9f23,c0876c95,13b8a68d,bb20c5cf,164a9a39,4e3e73da) +,S(c8d0150,e4a989ec,5cdbc724,21b1e29f,f1f30818,1d8117b1,3d376f58,b72060c0,5c5880a4,c5a73a4a,1ae42a9d,f0b20032,7ac4a732,cb26e717,49e63365,5082ebd1) +,S(3d61557b,b4b9fde6,49fe1b7c,981c9883,9e368444,f130bfea,fc1e1a0c,12f2aa31,933167ff,62cd840b,3a960c90,e6b1c37e,1e233695,318ea286,71c87992,de5b56f9) +,S(67569f9f,fd44ca09,5b478dbb,85c3ed1f,feaadaed,cb624552,ccfaf169,24e69e2a,62bb2948,230fbd2c,aa941288,7adfb24b,d16619de,af0fc102,feb1b26d,67eb7fcc) +,S(6313d13e,debf1401,eb7d279,2c66daa8,6e3075d0,3cf0daf7,f3b753e,7372fbc2,44621230,50eb1245,86975455,63e06e2f,2839f874,beaff9c2,f65e26ad,d3573ef3) +,S(6f8ec9e7,fbbe6e8c,d0e3085b,47c6cb2b,88529f2,15f13195,5e2fde24,4dd23968,1fb61e14,523b3fae,b543b215,dc46eeeb,23e1950a,8301c78d,c510c76f,ed36cd79) +,S(56613dac,3c5aa1ac,bd9a0ec2,f839b4c3,36f0ae58,e0e02244,7bec0546,710b7f6c,247263ab,86c398f9,3b23319,4434af8b,530908bd,dd7f716c,f7b73aa9,8eca79e8) +,S(c9de15e7,b4147219,137e6e57,c5a7ddd6,17e91ab0,6859dda0,41eb3c21,87aee08c,c7178ea5,cfa056d0,dfd11c87,715591cc,40cc5db1,f5e4b70f,d8ffbfc4,3f8b0009) +,S(7590a4a,627d5e90,e42a4b0f,6be6497a,f906182d,d2dddc48,a8b6bbfd,f56c0504,d611e21a,b5498760,5c97e878,baa464bc,cc5bd875,353b69f8,1f93ce2a,a6c38587) +,S(94b1da0f,b310e056,db0dff72,81db3362,1fcc555d,bf3c973b,76097908,7fe19d6a,8318893d,d5b41a56,33a2ab4,ae4b953c,45c42e9c,8f2fd159,85286de3,fd4fc217) +#endif +#if WINDOW_G > 9 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+,S(c117681e,b55bff67,feda80a1,ae88b4be,c806860d,91916619,288a7ce0,b31aef86,d94ae124,dca678bc,b69c9421,f295405f,d6dc1fac,de96a2b4,58ba5fd2,72faa032) +,S(5ccc0619,92744a57,683de5e3,7b956fa1,fd7287d,b4516fc9,f8635be3,a0db42a9,af1f73ea,4d2168e1,7550ffc,dcbba288,8397931b,e457ce6f,3f8082f8,cfc5f03) +,S(858b019c,8a93524f,6c86738d,cb10b534,d8caaf86,5c0ce75c,fc9b83b0,7c661a0a,7c59d30,1ffc8ce1,b0767ed7,91f84bc5,60bb8ca,ed3464ba,698a53c,160ec570) +,S(e1e217b8,69da0c77,599dcc38,40fa1d8c,a8d08b1a,4ac9a882,da1476cc,cc76fa56,83f0ef77,905f0801,4bd86e17,63b8c2cf,ab2018a8,9586620a,b49a15,9fc314ca) +,S(15a1ae40,b4fc51dc,554b75d4,db0c2bfd,62dfbbfc,dede18e1,4edbb689,91525cff,4f0453b7,e4e0e99d,9663e5c6,bb018007,b52c8e14,d78a28d,c4a888e4,8c4326c2) +,S(1b9a142f,fc4d03ea,4b079f2d,b05fad98,8ddb2d32,b359967f,c173801f,63320825,59bda7ed,5b691c20,4fc8f8ac,f53be298,ae628954,a8134d0f,dd097e67,be9ff9b6) +#endif +}; +#undef S diff --git a/src/secp256k1/src/precomputed_ecmult.h b/src/secp256k1/src/precomputed_ecmult.h new file mode 100644 index 0000000000..a4aa83e4ca --- /dev/null +++ b/src/secp256k1/src/precomputed_ecmult.h @@ -0,0 +1,37 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_PRECOMPUTED_ECMULT_H +#define SECP256K1_PRECOMPUTED_ECMULT_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include "group.h" +#if defined(EXHAUSTIVE_TEST_ORDER) +# if EXHAUSTIVE_TEST_ORDER == 7 +# define WINDOW_G 3 +# elif EXHAUSTIVE_TEST_ORDER == 13 +# define WINDOW_G 4 +# elif EXHAUSTIVE_TEST_ORDER == 199 +# define WINDOW_G 8 +# else +# error No known generator for the specified exhaustive test group order. +# endif +static secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; +static secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; +#else /* !defined(EXHAUSTIVE_TEST_ORDER) */ +# define WINDOW_G ECMULT_WINDOW_SIZE +extern const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; +extern const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; +#endif /* defined(EXHAUSTIVE_TEST_ORDER) */ + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PRECOMPUTED_ECMULT_H */ diff --git a/src/secp256k1/src/precomputed_ecmult_gen.c b/src/secp256k1/src/precomputed_ecmult_gen.c new file mode 100644 index 0000000000..e9d62a1c1b --- /dev/null +++ b/src/secp256k1/src/precomputed_ecmult_gen.c @@ -0,0 +1,9747 @@ +/* This file was automatically generated by precompute_ecmult_gen. */ +/* See ecmult_gen_impl.h for details about the contents of this file. */ +#include "../include/secp256k1.h" +#include "group.h" +#include "ecmult_gen.h" +#include "precomputed_ecmult_gen.h" +#ifdef EXHAUSTIVE_TEST_ORDER +# error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode +#endif /* EXHAUSTIVE_TEST_ORDER */ +#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) +const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = { +#if ECMULT_GEN_PREC_BITS == 2 +{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), +S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), +S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb), +S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823)}, +{S(1b8462eb,1ccdf7b2,b8372f2f,cec1f479,ab07c09f,cb26d6c3,965ec73,4d654f81,62f6755,b4a7891d,55de6427,fbc37d33,e4eea418,a2c04392,a3d11807,ccc9025), +S(c3b55f99,9cd9113c,fcb4f29,be00c785,cc70d1c1,f1cfd0ed,593abe8d,260bd2bb,8945790b,5696225a,1c6a1f45,1d6b085e,cde2f332,df068271,f6279877,6d1015aa), +S(a4b41b41,1a255142,ee62144d,96ccfdc,a3cdf5a6,af32bdd8,d1c3d26b,d6aab0b9,3ade7f6a,299ee56c,299fcaad,72a146d2,62db1dcd,2ea1a355,d6e00294,ee34c3), +S(d4af67c6,75f97f30,4a621fe5,343dfa5b,e432d9f1,43758d4d,62df1e09,b79abfe8,d0fea700,2a851a85,33929e5f,1f41d4a9,68b9e520,6c19f3b0,35ce96a5,12b61921)}, +{S(6ae991de,18418b49,160194f,a735eb72,c299b987,1981a4f9,aa717ad2,bcdcf13,7ee8011a,40f384f2,e50add2d,97005173,2787cc7c,89dafb66,301bc94d,24b913f), +S(c28203a6,e0f93259,778bddca,10f994be,67cec8a3,109d0001,d830a8e7,b452794b,18df3a42,ec24b713,2ac4b6ec,dd7605e4,169aa07a,41d7559e,bde808d9,bbfbcb14), +S(4848adb6,b0350cd7,b745b603,cff69deb,8be10519,cc02881c,4b980157,5635aa37,7a814076,187ed7b9,84d0be65,b2f83b90,325441cf,54325183,beb01136,d626ca5c), +S(515d497f,f274da3d,9bb9e4f7,e1b77e8a,af859d52,be7c7e93,f197267,d73ce5ae,da648754,a5ed476,3fad55e1,e93f9687,2d1fe961,b448b9bf,2c42c885,b44678f0)}, +{S(64850a04,76870a44,2cfa57e0,4e4707f7,eccc5e99,12dbcb07,3b457317,717f5686,7c5facd2,91a6defb,a1837cb9,3bcbd0f5,bc37572e,68ccb2a0,c062a155,46656fcc), +S(c3ae412c,a3e5f22b,44863ab1,b5e64719,99078ac0,d5844d9,6a37899f,3e064475,e491d89e,b38b0443,50d96e01,7baceb35,fa0e247,8c982d25,5a2a332c,239e0a54), +S(e72c3804,a774f3db,42348883,297b5035,c9dd3970,7e3bc60d,1e51e41,d7d8e395,e3cb5abb,c3c259ab,2c9e5,fa059c10,fe6f633b,4f99da29,61b9117e,61fbb457), +S(6a7b9de1,8d16a0e2,1b30cb61,3586ebc6,78b60618,e2b45e2d,8c94ad09,36227f74,ac1fb735,266d34,eb995f8f,91cbc339,f63b6e6,bd4c89f0,d7607908,75a4918f)}, +{S(92133195,a4fd0c59,7e0cf65e,8ce1d939,e333f7a8,441523aa,31e339e1,2ae51e8d,556a388,7a7d579e,87de7f49,8c54bf24,2ca4b8a2,8b959e21,ceec4555,b8fabccf), +S(1b3ee78b,df5cbab,a7649125,40852351,602bb558,e4bea533,dbb08eb0,299ae994,9a0c2165,5512777f,fac5ed54,b8e5b4ce,d7a6b17d,643f8c3d,d0173a96,3a4c7aa), +S(6be3de2d,1ceb66ac,1ecd3435,3f241a89,cdaf48f4,a8d5522a,1d6f0083,3c4b2a39,88e10da0,e53b8f5a,ada0db7e,e1ce75c2,8898d5e,156e777f,7acc3ba0,9fee727f), +S(b38c82e4,3e0559db,6732e87a,7cb1e6e6,6164f6f2,258ce060,6d239836,5af9ec0d,9e0f87f4,9d240b33,dc325bd0,49e9fac5,6b7a64e8,57f27ab9,ad765604,2fe47653)}, +{S(ae5fb021,e9256cc0,6236d667,b76b9bdf,304a4683,d2916ffe,489cf019,6b4c5683,e768366b,5c8d36b6,18e45550,d57493e2,41fed17d,12627e37,b29b4b74,d3603696), +S(e4f916f1,a96dc6dd,8867a619,fef6cf67,14ec2642,12d7ba2b,14b5fbda,b584f339,b44855e3,3ddf19b4,31f109b1,daeea11c,340a9ad8,c17b78ea,c9979ecb,791c31fd), +S(4baca037,647377c6,f3146dcc,d732b21d,32449773,f55766d4,de5b239b,2ef89e6a,50b4b046,b9e3cab5,dffdefa,fa305051,7bdb2deb,9bd9fb,9d3cfca0,34a72228), +S(867d7d44,734389e9,71363522,9d4f2c3b,bfc66e57,44a5f01d,1c93c201,9dd3f363,e9b94307,b39ceb65,653f2206,ffc8c858,37654fb5,90eb8d1f,24a9c82e,d8b4d210)}, +{S(782d5c9a,d970322e,deff2e7b,57844184,c589a4da,c042fcf3,86c1a9f8,26c1babb,27bba565,405cb392,64762d97,cbaff552,1bc38b20,56afe313,556542d3,f200eb06), +S(d07eb76,bb6694dd,4d6160e7,4d4a397d,963ea132,f74d0b9,e9f35c06,830940,2b7f902,62c67203,d6f3fc8c,2d435309,7f8e80fa,c2a732a5,dfdf6dee,ab47f017), +S(36afeed4,b7507388,285fc481,beb1de1,bc8e143c,ce7b8e46,7c1e22c0,395fef48,5318e7c9,686171a8,ceefff55,3fc98e41,d9e0d789,a2e880fd,6487c2f5,54816a97), +S(cfc25614,fc96d911,24b3b74,7aed144d,8656693b,a2844934,d2ee61ab,ab794160,fa9e529b,be133fe2,835ec397,b130ff27,187aefdd,df524ed0,9fdd0486,5cf6c014)}, +{S(ebc119d3,8e794efa,85fcbd,5affac35,f73c7428,590ede0f,6365f1ea,87c65b4b,183a9992,3911b1b1,cd9b0fea,3667b6e1,52af7499,8d32beb3,d2ecb91d,af6e8a06), +S(456dfac3,c239290c,336d1b46,e9638bd2,592484bc,f76d011d,104cea57,dd0e5167,62264555,8de68f49,170a8aa4,121aa307,378984a1,76b8affc,241419e6,95500049), +S(71108a04,a50b30f8,29f1420f,b9994ba,384c2ff0,8a581672,e3464bb2,93f0f756,ff6a402c,eb50bb4f,7ae17680,458f53fe,d627b0b,dca24cb1,b033feda,f27cbff4), +S(f8261d8e,ea970b26,fb13ed01,cec553b0,a374b03e,c14763ec,13e68ff9,b219f39,3cee77fb,6e684798,68499e40,fd33fd61,e43ab21d,96a6bf78,35dad6c8,2fea2407)}, +{S(bc4bb9a6,292aa09f,5c66dc9b,667c4642,6b08211f,a9a80f5e,f3f17b,21f275de,5d0e0492,39a862ec,b9649572,6f11bc09,cebd9f29,d9407ab3,1603054d,d9b76b07), +S(ccf3d9af,434d96b9,fd9e12ee,45ea3858,5060b000,896f1de7,a73a12a1,3f635c73,7efe7415,8a3893af,d408b0c,fcd992d9,cff412f0,f77d6a9c,5d5a9235,d14f5e21), +S(18ade473,1ee3019f,ad5621f0,cfc0d6ee,ba69ab38,fdca04ae,fedddf1d,f9cad1ab,1ea6e4d3,63f1cbfb,e9d11c54,c2ab43a4,49e9610f,24b6adf4,446454c9,c3bdccf0), +S(8bc05563,1b13b451,5a99eebd,837e67e9,e80ab8d3,58ee840e,3140ac8e,131cc214,cede3aba,b11b6a91,4ef1ef36,30c12127,bb818ec9,b4d3ad38,a9e68641,a7b799a)}, +{S(c8e595d2,666f4913,1f375b67,81b9113a,d0760e5,9477ca17,8863828b,307488f0,a82cf2a9,d823af13,5c23a04b,bc12dd81,2c352a48,27e19030,8e089d9d,9c316596), +S(d194c03b,ff719a14,6bba239,fc3e1255,7637c9b1,30609ff9,1501942d,348930ee,5e9387d6,4bbc72de,39ca8141,c6c6d526,530e82,47b43161,72717b68,28d1c1c1), +S(cfe58760,54b85d2b,e1220cbc,28ba55f4,51cb3c4b,1ef1d39e,b82e8c25,7538b631,a7616b4a,f3564048,b5cdc6bd,b0250abb,ab1bdd33,a7a15857,31119d26,94ff4bea), +S(190a763e,58315639,578def37,53f4610e,5a802af9,e4873d3e,8c3186c0,e424ac42,b156da85,b8462fa6,83f85c7e,5f718ed7,34a159c2,5b18d092,185ff467,8b8840ed)}, +{S(49e7429b,e0d97bf9,3f17e9a8,53fedb6a,a9bc6edd,8e85f44b,9d2f1469,b2d3b178,ff9e5dfc,2746679e,9826039d,578bac31,c08fbaac,a075214c,73c50f,74568fff), +S(2beda894,682676e6,11bf6a,78cae329,c26b47c6,237d0e52,61a70b9c,36796207,103a18d9,a6785ad0,2129ca1b,96834d9f,f185d49c,edd1c053,96a8c9f4,dd16be16), +S(9602058a,fce0160a,70bd2a32,6cd3eb1b,e5ffbaa8,e05bc2db,fbb9c303,7b449ceb,1fa171c,682393c8,2b237910,2ba5ca8,7efa0543,b8cd65af,de324f14,cc53945b), +S(118d0b52,f418dcd2,b6864967,a49f9d88,809f2468,8bbb6c47,c68f2eb7,bbe7ab31,30ebfb30,ba0bac02,57bf568d,479b7bed,2b1512f9,33aaa040,4966b6fd,5e1678)}, +{S(9a1db7bf,53241ed1,df8d3ea0,f70c0b26,76b43ebc,bcb4622a,9704b0a,3067400a,e3638ad2,95740505,455b2e1e,d495c57a,54ed8e8f,c647a6b9,c69b7dd0,715cef52), +S(b5c353a5,c86b2d4a,9b00804e,f0439259,335d0bde,91dd2bac,a567cd5e,284be39a,5bba9f1e,877d5e0d,21e384d,52de73eb,9aefcaa5,132117d1,2dd984c9,4a0562e1), +S(337a0242,62b9fd60,28f5fcdb,c2305543,385010d6,98fb258a,d5c25b1c,4a765fed,e179c1fb,d671e158,36050d89,48fac97c,57abcae6,79e3be7f,16ed8b98,84dcb013), +S(ecc024ca,640ec936,f7e2320b,58147466,686528ed,579865d0,f61672e8,3e6b0f18,a1335b77,ddb11959,24d40e4c,81270679,270f87e4,158a745c,8d2d810c,ee7024eb)}, +{S(50cd2e16,997d7d45,98bb2d9b,61aceaff,5ad5f38c,8286a0e1,d08055ad,726c7800,dd19c3b,c08b8d97,88f9de1,5941f5fa,6402bbbb,5fdc708b,cfc08844,eb23733b), +S(34d6a7b6,733bf5e9,ae6aad06,5ee0793b,4f5e1ba9,97de99f9,8771ca57,81fb2382,22f8c6f6,dc7203a8,53e64cf1,dbf26d6d,e255f0bf,bddd9508,a759db8f,2c55cbd9), 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+{S(35e48872,5074158a,8d2ed392,d178f6e2,e4c43fc9,689b32d,5f374c05,d637a53b,95143742,7bb0105b,5e7f60f2,d95ff164,ff808b7b,c2ad592d,68988e5e,bb5d5679), +S(8619863a,d49d8ab5,6c999e77,4653e1a7,4acb7a63,edb65840,76f3b3ae,903f3579,451500a1,3dac87a8,ace7fe4e,64dc6174,896b5002,67163bea,1d3db275,b8274cc5), +S(afeffbdc,dede5aaf,dc91475c,100918d2,f59039df,b5754f58,a330a469,1855e858,e05eacad,fe537099,35be0173,3d4b4dc6,7674d1a3,7d911d02,ea4f74f,6b63da04), +S(2b697c1a,2d2de701,16536722,945e46c9,21f02fd7,d8e9fd46,8fa9f159,1dec4273,6dd6ad5b,44541355,83b4833f,10de56a1,ed16c5a8,77d593ed,2538b95c,ce8785ef)}, +{S(cce6ccb3,fc1cbcc1,1f40457f,25157d24,6d3fefa2,24c340f1,ebdb3b02,3f02e3cf,9797a15e,ace0c660,eb93b185,7f6de7de,2d1d0f36,8c9a2eeb,a53b2860,b392bf2f), +S(71e75cd4,592214c9,556dc1b7,a7c8c5cf,77ab0249,a6a7ad9a,378e3e5d,d150939d,4e0c9607,c1b2866e,214f38e0,d4759bf3,b38f1f7a,35490b6d,70cf2e65,fde90bc4), 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+{S(463080f9,19ecd42f,593dc20a,2d3160cc,74d9592e,446f299d,be5446f4,236a5b17,2a65200d,e1b16975,9d5c75d6,fa6c666,ba45728d,343d6339,48233391,60c14a16), +S(547eef23,516851a2,2f160ec0,781a49f1,1480d07d,2607ab5a,89656c94,2f774b5a,eb6f249d,ee624cae,cbc59f02,63da0fcc,e33a515c,843c3632,661f13e4,39c4f0e4), +S(77f0c9a2,51d48b39,62f92e2a,679fd9cc,f458f17a,edf588be,d4bd6448,47f9306f,355f4827,b10e614b,4590242b,da546e53,dbd419de,1d1a7fa3,208d9350,3496db0c), +S(81e606c1,19b6ef80,418aa008,7ebaf9d3,7adff1ff,a81f739a,172a580b,27c7545c,ddb0404c,e56113c5,93920382,6d2adab2,6590b509,45865406,ce1fd256,6565209a)}, +{S(92d469ed,e0969dd6,7e9d7b31,f0f703e3,97cad53b,e6101b2e,eeb8714d,645eaa9c,24a0a786,916297f4,6a53c7c2,29a3c95,80eec521,355b823,f0488460,39595dd2), +S(e5035341,5c49c24d,f672a74e,4eb2d108,57fa987a,afc50178,ffba8797,5503006f,38522661,fe682984,7b6dda61,9dbbe47b,35c0c9eb,b79b5d2f,2c6ba882,26cb95d4), +S(d0777020,cf6dc469,cf020ce5,e64bc2e4,1e2bf116,4f4e814f,18bbbc4f,f468b0b8,997b2163,c4670401,281ad84b,a914cbe4,e76a5cb1,cb90c1bd,ecdac585,621cb0a6), +S(881abd9c,717f0a2,360de50d,66a9b655,b9459e62,80a985da,e811f2b2,154e307a,beec571,1375031f,354dda5c,b9d8377d,1cb49816,1f4c738d,f6b9d323,f9acacd)}, +{S(ab7d18ba,955fdaaa,b1a0bb25,25844e2a,9d2e204d,ff224588,ae96c41,e690e010,4e0090b1,dcd619c3,10ff5027,9c534612,84ec2467,77b63179,c80724c4,42d00204), +S(1a5982e3,37e3eb50,e679f24e,c3473b4d,1af3dcbe,ac3c7a96,a95f51f9,a9875266,dca6c614,85d55985,1fdc229,56ee59cd,fac74069,6276299b,a199f39c,869e5c9c), +S(bcdf870f,8d5394b4,f1f3446c,a25ec6d,5b4c939,b598e596,814a6dda,a054bb2f,71cfbdd,d1aa7722,892f83e4,ea2dec50,81c4d14e,548a16c4,2818b76d,5721fb7c), +S(cb28eeda,338a5088,db505da,949cddf2,741e071e,378f92f1,dbba270e,9c322c57,d98cba61,cceca53f,7d84d71f,f892b962,6f26e156,841d2dfb,7aaab839,3f515903)} +#endif +#if ECMULT_GEN_PREC_BITS == 4 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+S(f9fb85f3,fc4e45a1,6b6eef55,cd8656db,de777390,f20b576,a28110da,e8ce5713,51de9f5a,7b2f0101,cd02e6c7,c98cdf93,a430d62a,1fec4f3e,95bdc3bf,a2212e13), +S(d5fa0933,f13c1f4e,89caeba4,101f44c0,420da5c6,7bfe1ea9,66cf01a5,ef48b1d8,5efc8918,8b9eb65d,faa6e0e9,812407ef,35d8db,76f9e722,ff63bc3c,3afc3b1a), +S(93899e6f,fc291a4b,e986f938,b8b378be,bf4c3d35,f9a1bdd3,ecea5f04,d8f4bada,a19a2983,55cb62fc,43334649,1c89f26d,fbb67bc3,872f7512,9229cb73,d126293e), +S(8fe07488,b5b173c,d530d796,a18eac08,80164c2a,ed787b05,90ac8dce,3bb120d8,829abce1,43ea8009,e4f5f481,125ca6d4,ecff3f32,577cdbf1,c054a23e,67f18b0b), +S(10c3b093,5461407c,369494a7,631eb4a2,365b122e,ce0a6b95,7c1bdbee,387394a4,f09d69ec,925c9a43,57648509,f7db85a9,22f609cd,32b400ce,3a80567,88a74627), +S(cfe48dfc,f5566fbd,7562ed68,576a7911,baef64f0,dc63e158,1a29bf23,3e1a058e,440c6051,19f2a948,b4b6c3a2,7e711cea,c7983d7,f4a2db9,537536db,fdebab76)}, +{S(53d772b6,b18211f7,1478e9d3,3a0c061e,2d232358,44177867,af91508d,e014f22d,b2e85a07,8160d31c,3ca32d9c,ba025904,1bea0368,d9eb13de,8af8f505,73142ed8), +S(b9d6067c,fc26ba4a,1f5bab8e,d5f28ffc,bb6bd6,b61990c4,1b091ec8,2cba973f,532d0ab,7731c02d,91cc7e51,71b625b3,af5a605,d92d02a5,fc4cee4f,afa09ebb), +S(e8a93ceb,3db0a4a3,9a3b768c,700fb504,652161e0,4a1d4d92,df52cd4b,83e65e38,791b967f,22543fea,9ec38e5e,a14a94cc,9d11ea8a,73ca0c13,e022d53b,f8bf1148), +S(ac6130f7,41e1601f,5a92bb75,90a799a8,3e8ad9c,c911ed7b,7dee1bcf,da14f332,97ea5d16,d5c7e368,c7b97c2d,7283cb03,f215f79c,d1d80276,6f9923e0,ce80ce44), +S(ac34d4c1,1d2d4ade,2f044e88,6b57cd45,c1b23550,538059c4,e9855077,4132643c,7191e155,aeb3b578,6b55db41,652e8af2,bac1f933,d6f62723,808c6172,bf0eb0aa), +S(a7c4bafb,f1988992,1ce15754,187d41b9,eb653dd,bc97cf05,ddf449d8,c9ff734c,ccf20733,da4aab6d,81db8d5a,d3f12d1d,9cbc943,8b92165c,e83c5afa,5ee108e3), +S(c04ba857,e758fdb0,29c02712,1671fe33,9b7184b3,50ad952e,9d234681,43f7568d,9ce5d9ca,65f96b76,b4b06f57,f34de7e3,c64a1d21,f07fd6fd,eb7d47e7,bbf4e6c8), +S(8230e7e7,81259e58,e9b74a49,340733dc,252bef7b,5b7dc82,a4e99f0b,2998ba67,9c71921,3b3254d1,f53b4f30,d0a8e665,186e272c,d0e5d316,a7451eb3,2ac8bb3f), +S(720c2f5f,6465d38d,3916939f,8d095657,e547cc5f,849f4a41,30485b1,2d94b5c7,8635961f,5f74d176,e4ae0ec6,e4b3b394,6d5b1766,fcb902fd,9f9bd982,2ad4e4c4), +S(263b45ca,b3547cf1,5eca4381,3d1c402e,5c209d3e,34a288cf,182aa4a3,f04304f,3516b1f3,524bbdcc,fddd94bc,fb86a43a,27a7a78a,fcbbefdd,6692fc21,87364438), +S(4edb7d61,a45ebb51,1fb0c220,6f16fe60,5a202976,9007c3e7,11b94889,a983d0c8,b482fee3,fe824b1a,3251cd2c,3f38ab4f,adad1fee,d398be92,58d2c81d,79b0eb36), +S(f44c286a,b8196e25,87c225f7,2091db05,e47f18b,5b9a0b9,79d2cd3b,15441767,b7aa2018,5925845e,661ad980,a6c215d5,fd7072cb,46010930,ae64089,4c8a0af8), +S(593f9bdd,b246bd1e,19eeaafa,17e348e,5199decc,8e63ef68,ed8bff89,bdffad48,5201d11f,a4ac67db,dd66fbaf,5c2ba20f,8bb1a6b3,18cdfbac,6b257aa8,d30dd316), +S(823b4c96,8be9e125,262d52d9,4aaff240,55def10d,6353a347,e4248de0,7889ecb2,adfafa7a,fb1c60e,e7fb3e2e,73c66063,5a9e97e0,4a38a120,b7a81f17,7d1a6c41), +S(8daef78b,c46e0f5f,858fd74c,68be31bd,3b474d9,6bd74deb,eeba69af,5ef3056a,15db0684,bb6d4e7f,b135a4ab,f4b81d4a,a9fc7e93,c26e3616,b7b938da,25d44a06), +S(2b7616ca,eb608427,5a14eb53,b67a2ee3,b831fb55,6f63e0b2,e01650f6,e6900a0d,915e7dbc,62f8e349,8ffdf22d,d3604d77,bb701137,b6c36543,84cce993,c4613ca4)} +#endif +#if ECMULT_GEN_PREC_BITS == 8 +{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), +S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), +S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb), +S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823), +S(b692c750,d23d3674,c351e3b7,e1a8a87b,14a5df81,852eaf35,209d0ec5,6e22a2cf,b18c4f17,252db89f,838de32f,b3340ea2,bb961a39,54b38c47,f9a8219c,4820a0cb), +S(691fc741,80e75b55,47b375f1,1bf60abe,451d27de,1743a436,5f8e4bac,ad421c09,8eb5fd9d,f3c03240,6cebf370,8125955f,bf2ef703,475d3fd6,1a0291b6,69b52d9d), +S(703b5f14,a7d82473,1196b52f,ae9ca8cb,b245b004,7a9928d7,d0c42f33,391411dc,5ed74eaa,49f276c0,4d61f31b,6da4137c,bde5673d,8e3f815d,efea7951,f88585c), +S(29b8ec47,d241eda1,e51bbb1e,3928444c,3747b4fe,7cecb365,2bbc4587,2f504875,88693238,8562f8bf,f7d72324,62ebc54,6b93a95f,77936b02,eb1cd6a7,d4199bcb), +S(444a07ad,e81916c9,32bdeec2,21c556c4,6b7f6491,e99b479,2cfec82f,4ec17910,2e084c2f,eead5200,77c151b6,eff9375a,713b9d15,5306708d,b3f538e1,8eb18cf), +S(e0dd618b,226ceddc,f560527e,20b4fe58,e5fcf28,39911ea6,c3e8a4a7,e15f9121,a063a157,3377bbbf,1b9a5ebe,afbe11aa,660c1e65,df1392b8,97205858,3c86a3fc), +S(9b99461a,2e8360f2,f2ba0bb8,bcaeb699,159e0652,69d9042a,fa0c4e30,a7b6f30d,3fe7fe04,3cb45303,3d4f5560,7d41cd76,9036a49b,82912350,6d8b9995,254154fd), +S(504da3a9,d9d9c81b,c2065398,4ed28cb1,b5beec9b,6ce5dfb6,cea94e54,fdff044b,cbd40d1e,858133c9,cd20b9e4,ff9fe94,f7cc9579,39e6df49,7a6bd702,797f96cf), +S(ddec0aac,1ebce6aa,ad6300d5,60f0e503,829f0bc6,479641f9,b19d9f6,484376fb,332ff5b1,fc83085e,736736bf,3c265e4c,8f80925e,6f38479d,6563bc34,e5faea1), +S(dc530ceb,b82c246e,41c522f1,d2571d31,4b14edf3,91577a2b,64e42172,b23562c1,563ddd93,857d6529,8b81de24,19e5cede,7a4c5b7,a2fe98f6,9efb8906,6f32a98a), +S(7604d60f,418dd132,78058942,fb2d2153,c0a2bfeb,e83c5011,a451bcb1,58db0773,38be14ae,d9e1c404,63ef92bd,d62c599a,b37625a8,182a3763,4fa2de90,535d50a9), +S(cb896744,77b20829,f5e2bd42,8852c70b,91cbd0af,cadf219,a69727b4,cbec8d7a,5710d17a,20ea0dff,980d3f06,38d8b910,b8940d00,dd4a323f,d777d942,213e1093), +S(501915b1,391e083d,e88c795f,8464c846,f699a79e,edb1b963,3e29f71a,9ce4d022,9e1dcc94,17ceb0e,15762f8f,7d0db85f,3bce3ad6,fecbe2c3,567853ef,ccd6d0f9), +S(a63c0b8a,4eb2cb10,1e556904,a7246356,9909055,f45aa4c0,e89c2237,cbffafca,9650b428,12374811,738f4ac3,a2ac0505,396339be,4eeeda8b,c35e6fdd,c51a1e56), +S(a16760e5,c3643d19,da15c034,5feced27,488ccafa,ad5298fa,6ee1070d,a258a761,736a7c7e,69db053,6f541079,158d671d,598efb1c,d75ec804,c7b2b49b,1ad7638a), +S(840693fe,73b96819,bb1b24a9,35d5dc83,f361273c,d0989e76,1edc35ef,50faf90b,4294e19b,49558667,bc6237c6,86c30aba,a2660580,563d465a,fde9875d,74c9a57f), +S(97273c3e,26e12369,1d0ade3,3aa261cd,a45b2d2c,d749af71,a60c0d15,85e18e03,2700c565,dbb08439,fb74317e,60776fca,d0efc1a5,5d0ad87c,18f82f2d,a97caf19), +S(978d68a0,5ce30528,e4db2dae,99f6a245,f69cbd04,3c7171ce,ce2bee57,60e68b9,ffef379c,1515b068,df562f3f,bdadacfb,8aabe5aa,466105d1,97a8febc,1596915b), +S(dfaea7bc,c78d275d,9f6a74fd,21fdec14,bcabfa45,e44070c1,9c44d449,c5d52231,927b810b,c2994b8d,2ed5124d,98e2f5cc,58410607,82b1ed80,d0fae288,8c42d538), +S(ca0b766b,8b8d76fd,ce471a88,18e043d2,604d1ad2,b689cbce,70ceae78,fddf5a27,ddf9e3bc,935ea0bc,22f977ab,98a92414,643140ae,be0448a3,35d6d44a,1bedfc48), +S(11dcc001,3be8d4b7,85e87153,e060d13,57cabb5,34a2c1de,2a4a70cb,9803a031,5b5d46b0,6a96c30c,b1901c12,eaa1c656,3a2f35b1,e9026954,36e087aa,3deb777e), +S(a828121a,18d23262,bce26648,ab44c45d,c5027ae3,f74786b9,598f22b3,c408bf08,37893209,80d7d2de,6074778b,2e8916f0,4043a616,982a9b61,d4089623,31375cab), +S(291ec5eb,e010daff,3ac00825,3452b065,d9f7fcb3,66e125af,22f11358,6263fbaf,4647cba2,45d190d8,2337f217,c278c98c,370120b3,d4e04110,e6df2c54,92d63bb7), +S(44735d48,4c584d70,6afc573e,8ece7670,c79c7b99,99eb0141,4a73905d,34a1cf01,30a27c9f,67b47348,583f1e84,5e7af221,438d4c9f,a1e0cc19,7312ec6b,908d613b), +S(fce8958f,507d5d59,bf0fb944,7be40c23,db2741e6,f89351a7,f29fc642,a60c7d4a,69de744b,9d2ef778,a7280325,bc699cb8,29874d33,bacc1fe7,6264eff,600c815b), +S(171a3251,bc6e72cd,630f8130,d4695e48,e0e649c6,82bdd5b1,b87c7b7c,968cf664,3492ac7,faf2ab56,cfdd5278,9831ea1d,e90ddaa6,b4d6e6e6,fa960bab,2b55a55c), +S(adc566cc,6c9afbe1,41a011fe,e121f0b9,a5dded68,fa9cdf63,45a00fdd,d38d69b3,38db9e85,26ab355b,5ed12b5e,84e795e7,7e2d2c57,24cec516,9cca1946,1d8d9c04), +S(9694e1df,8067defc,de9dd34b,4a4bc91b,653ede57,3139b9f9,4df55858,74f04,f002d8b4,3940cd6b,7cba586e,18f1616e,db907010,230445d1,a96b9eee,b43778fa), 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+S(1d45c89f,fddd05a5,5043c44d,b8d0211a,f49f3aba,31e3ac62,5687413,4ecaa89,ab2abf54,db899f51,6c19848d,f0fb6e8e,9b43de72,3c74c33,9ac74611,7a64592c), +S(61531e01,5b2f0ca3,e36a20e6,b6d7f2ba,e2a1e245,340afb7,f134c3c8,799374ae,fae6274c,1e646987,2aa0b680,8a7fda0b,f3d495a1,24e859c0,2ac50be2,72dd4596), +S(a1b129b7,c1803643,6136bc8e,f7b99895,c5551ae4,71b2c0cc,ee48c266,bcdf2808,b9f97676,9623c4b0,bf10a738,6081cb23,f68693cd,626abaa6,b3874be2,5af886c8), +S(27e38dcd,d63bab65,c77eedfa,7e1f4b46,203ff350,20c86fb0,4ce2ffb8,af8d7056,81f30a56,7340be31,52ce5c6b,877f2c67,a7db7acc,7f24e13b,bf836660,9d61f04e), +S(64919bfc,50072a00,8769f559,3ad0e5b7,72ed6575,81ecf37c,8c759a3d,51149fc4,5759727c,20ae86e,b38aa3f,5e53b848,8ecd2b,477dca0a,ffb83903,65e70900), +S(d392e5cf,3c2d4a0a,20779b28,f4957800,ec7148aa,63b2bcb2,348afe9b,d28ad57d,54062719,a0ee0869,b1a99d9a,e4716487,70386747,9ead4774,66df29e1,78c87c6b), +S(6b9fe223,333b0802,34fb49d4,85218d11,9123c430,94e4ffba,38f33bb2,dbe7d9e2,5ea16bea,b5101109,4d34ec62,e6a63a71,c78de1f1,fcb7ce23,4ba2f51e,e4eb2ef1), +S(b1a505c,eb85f130,ef6e4a49,e429b0c5,51a87831,f850ed83,6bc8649d,6097ce12,a887e16a,805c0708,45589bff,2b22fc6f,4187cc06,cecef137,9130becb,5d5d149f), +S(8bd25993,c653b1e3,6f477988,61743aba,a5ffdaf,fd0890c3,caeb2963,736cbb44,341aef51,13b0d08d,90e90ffa,56570d57,5777260f,e85a15c2,2b5b3139,4f0a8c20), +S(2da121de,147507bd,b8836321,40394006,afc65465,7c6d4399,97cf6c88,ce0c4016,3ec87a24,eb19c502,848ff433,7ac3f48b,9a56ca56,3d0bffe8,eaa98e97,49f04aaa), +S(147541,9e9e9ff8,5b93f56,2832e74f,6c8c311a,676a759e,7dc62c63,5faa0b07,40fb95e4,810607ce,7ed10d9d,61404078,10ddbc55,261badc0,5e07bd1a,579ca271), +S(7c48371b,7eb5655f,b9d95bc3,5660d783,b1884573,d2934346,c5a5342b,a0949cb0,8b8cfb2,4cab96fa,1ee1e5d7,7dade5bd,23fa7868,445d9ad4,723529db,38110dae), +S(6ac2912f,d959d41c,19ff8ac4,bc136e85,91944b79,470d633f,b9fe65f0,f72541f4,63351f35,d4a7787a,31ef0bd6,f28aedd7,864ec5ab,7d841f11,9163e351,e070fcba), +S(db08e4fd,63e16bf6,abc05d78,be6bccc7,c9b8e15e,334ad697,9205a2e9,c2100e15,eeb0ba62,e1a5ee98,c2e2cc5a,8d9cbf11,d265019c,9eea8f50,4aa1e50,a422d4e), +S(4160dad,5255da89,12f69754,77b445a7,26fb7b8f,6ae8e2bb,d6276ae7,2a31afb8,ab0817bc,7a9b6907,9f6db9f3,c9a77718,23a1d79d,9f2739b2,cbeca18f,e5b8fbf8), +S(3794fc72,f432c983,2f9ba8dd,b46b1c64,d979e899,78b3c14f,2f903ec4,75af091e,a898cdf,7cdaf6c0,3715e38a,4bea1081,fda150b3,7faa4a11,ddbdc350,c7e0bb05), +S(244b87a4,fcecef37,76c16c5c,24c7785,be3b3c13,46595363,b8c066ec,45bfe561,9642f5fd,e0ec25ed,bd2129ca,6c023ec1,a2eadac7,f6ec5b7d,2b7fe894,41e5aa11), +S(9de52b81,157165cc,aef44485,4c2b3535,a599a79,80d024de,5334b385,ecbb2e91,74fca165,26fe2f87,a41ce510,4dd5634,5cf98c11,803c0392,3eb4b8b7,60240c02)} +#endif +}; +#undef S diff --git a/src/secp256k1/src/precomputed_ecmult_gen.h b/src/secp256k1/src/precomputed_ecmult_gen.h new file mode 100644 index 0000000000..7256ad2e30 --- /dev/null +++ b/src/secp256k1/src/precomputed_ecmult_gen.h @@ -0,0 +1,26 @@ +/********************************************************************************* + * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *********************************************************************************/ + +#ifndef SECP256K1_PRECOMPUTED_ECMULT_GEN_H +#define SECP256K1_PRECOMPUTED_ECMULT_GEN_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include "group.h" +#include "ecmult_gen.h" +#ifdef EXHAUSTIVE_TEST_ORDER +static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; +#else +extern const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; +#endif /* defined(EXHAUSTIVE_TEST_ORDER) */ + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PRECOMPUTED_ECMULT_GEN_H */ diff --git a/src/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h new file mode 100644 index 0000000000..63c0d646a3 --- /dev/null +++ b/src/secp256k1/src/scalar.h @@ -0,0 +1,102 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_H +#define SECP256K1_SCALAR_H + +#include "util.h" + +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low.h" +#elif defined(SECP256K1_WIDEMUL_INT128) +#include "scalar_4x64.h" +#elif defined(SECP256K1_WIDEMUL_INT64) +#include "scalar_8x32.h" +#else +#error "Please select wide multiplication implementation" +#endif + +/** Clear a scalar to prevent the leak of sensitive data. */ +static void secp256k1_scalar_clear(secp256k1_scalar *r); + +/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */ +static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Access bits from a scalar. Not constant time. */ +static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Set a scalar from a big endian byte array. The scalar will be reduced modulo group order `n`. + * In: bin: pointer to a 32-byte array. + * Out: r: scalar to be set. + * overflow: non-zero if the scalar was bigger or equal to `n` before reduction, zero otherwise (can be NULL). + */ +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow); + +/** Set a scalar from a big endian byte array and returns 1 if it is a valid + * seckey and 0 otherwise. */ +static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin); + +/** Set a scalar to an unsigned integer. */ +static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v); + +/** Convert a scalar to a byte array. */ +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a); + +/** Add two scalars together (modulo the group order). Returns whether it overflowed. */ +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */ +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag); + +/** Multiply two scalars (modulo the group order). */ +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Shift a scalar right by some amount strictly between 0 and 16, returning + * the low bits that were shifted off */ +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); + +/** Compute the inverse of a scalar (modulo the group order). */ +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */ +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the complement of a scalar (modulo the group order). */ +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Check whether a scalar equals zero. */ +static int secp256k1_scalar_is_zero(const secp256k1_scalar *a); + +/** Check whether a scalar equals one. */ +static int secp256k1_scalar_is_one(const secp256k1_scalar *a); + +/** Check whether a scalar, considered as an nonnegative integer, is even. */ +static int secp256k1_scalar_is_even(const secp256k1_scalar *a); + +/** Check whether a scalar is higher than the group order divided by 2. */ +static int secp256k1_scalar_is_high(const secp256k1_scalar *a); + +/** Conditionally negate a number, in constant time. + * Returns -1 if the number was negated, 1 otherwise */ +static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); + +/** Compare two scalars. */ +static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Find r1 and r2 such that r1+r2*2^128 = k. */ +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k); +/** Find r1 and r2 such that r1+r2*lambda = k, where r1 and r2 or their + * negations are maximum 128 bits long (see secp256k1_ge_mul_lambda). It is + * required that r1, r2, and k all point to different objects. */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar * SECP256K1_RESTRICT r1, secp256k1_scalar * SECP256K1_RESTRICT r2, const secp256k1_scalar * SECP256K1_RESTRICT k); + +/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */ +static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag); + +#endif /* SECP256K1_SCALAR_H */ diff --git a/src/secp256k1/src/scalar_4x64.h b/src/secp256k1/src/scalar_4x64.h new file mode 100644 index 0000000000..700964291e --- /dev/null +++ b/src/secp256k1/src/scalar_4x64.h @@ -0,0 +1,19 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include <stdint.h> + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef struct { + uint64_t d[4]; +} secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}} + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h new file mode 100644 index 0000000000..1959dae986 --- /dev/null +++ b/src/secp256k1/src/scalar_4x64_impl.h @@ -0,0 +1,898 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +#include "checkmem.h" +#include "int128.h" +#include "modinv64_impl.h" + +/* Limbs of the secp256k1 order. */ +#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL) +#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL) +#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL) +#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) + +/* Limbs of 2^256 minus the secp256k1 order. */ +#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) +#define SECP256K1_N_C_1 (~SECP256K1_N_1) +#define SECP256K1_N_C_2 (1) + +/* Limbs of half the secp256k1 order. */ +#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL) +#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL) +#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) +#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL) + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { + r->d[0] = 0; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { + r->d[0] = v; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6); + return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1); +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK(count < 32); + VERIFY_CHECK(offset + count <= 256); + if ((offset + count - 1) >> 6 == offset >> 6) { + return secp256k1_scalar_get_bits(a, offset, count); + } else { + VERIFY_CHECK((offset >> 6) + 1 < 4); + return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1); + } +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */ + no |= (a->d[2] < SECP256K1_N_2); + yes |= (a->d[2] > SECP256K1_N_2) & ~no; + no |= (a->d[1] < SECP256K1_N_1); + yes |= (a->d[1] > SECP256K1_N_1) & ~no; + yes |= (a->d[0] >= SECP256K1_N_0) & ~no; + return yes; +} + +SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) { + secp256k1_uint128 t; + VERIFY_CHECK(overflow <= 1); + secp256k1_u128_from_u64(&t, r->d[0]); + secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_0); + r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[1]); + secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_1); + r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[2]); + secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_2); + r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[3]); + r->d[3] = secp256k1_u128_to_u64(&t); + return overflow; +} + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + int overflow; + secp256k1_uint128 t; + secp256k1_u128_from_u64(&t, a->d[0]); + secp256k1_u128_accum_u64(&t, b->d[0]); + r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, a->d[1]); + secp256k1_u128_accum_u64(&t, b->d[1]); + r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, a->d[2]); + secp256k1_u128_accum_u64(&t, b->d[2]); + r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, a->d[3]); + secp256k1_u128_accum_u64(&t, b->d[3]); + r->d[3] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + overflow = secp256k1_u128_to_u64(&t) + secp256k1_scalar_check_overflow(r); + VERIFY_CHECK(overflow == 0 || overflow == 1); + secp256k1_scalar_reduce(r, overflow); + return overflow; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + secp256k1_uint128 t; + VERIFY_CHECK(bit < 256); + bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */ + secp256k1_u128_from_u64(&t, r->d[0]); + secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F)); + r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[1]); + secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F)); + r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[2]); + secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F)); + r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[3]); + secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F)); + r->d[3] = secp256k1_u128_to_u64(&t); +#ifdef VERIFY + VERIFY_CHECK(secp256k1_u128_hi_u64(&t) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int over; + r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56; + r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56; + r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56; + r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56; + over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); + if (overflow) { + *overflow = over; + } +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3]; + bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2]; + bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1]; + bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0); + secp256k1_uint128 t; + secp256k1_u128_from_u64(&t, ~a->d[0]); + secp256k1_u128_accum_u64(&t, SECP256K1_N_0 + 1); + r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, ~a->d[1]); + secp256k1_u128_accum_u64(&t, SECP256K1_N_1); + r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, ~a->d[2]); + secp256k1_u128_accum_u64(&t, SECP256K1_N_2); + r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, ~a->d[3]); + secp256k1_u128_accum_u64(&t, SECP256K1_N_3); + r->d[3] = secp256k1_u128_to_u64(&t) & nonzero; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_H_3); + yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; + no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */ + no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; + yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; + return yes; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + /* If we are flag = 0, mask = 00...00 and this is a no-op; + * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ + uint64_t mask = !flag - 1; + uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1; + secp256k1_uint128 t; + secp256k1_u128_from_u64(&t, r->d[0] ^ mask); + secp256k1_u128_accum_u64(&t, (SECP256K1_N_0 + 1) & mask); + r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[1] ^ mask); + secp256k1_u128_accum_u64(&t, SECP256K1_N_1 & mask); + r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[2] ^ mask); + secp256k1_u128_accum_u64(&t, SECP256K1_N_2 & mask); + r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); + secp256k1_u128_accum_u64(&t, r->d[3] ^ mask); + secp256k1_u128_accum_u64(&t, SECP256K1_N_3 & mask); + r->d[3] = secp256k1_u128_to_u64(&t) & nonzero; + return 2 * (mask == 0) - 1; +} + +/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ + +/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd(a,b) { \ + uint64_t tl, th; \ + { \ + secp256k1_uint128 t; \ + secp256k1_u128_mul(&t, a, b); \ + th = secp256k1_u128_hi_u64(&t); /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = secp256k1_u128_to_u64(&t); \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl); /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* overflow is handled on the next line */ \ + c2 += (c1 < th); /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ +} + +/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ +#define muladd_fast(a,b) { \ + uint64_t tl, th; \ + { \ + secp256k1_uint128 t; \ + secp256k1_u128_mul(&t, a, b); \ + th = secp256k1_u128_hi_u64(&t); /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = secp256k1_u128_to_u64(&t); \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl); /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK(c1 >= th); \ +} + +/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define sumadd(a) { \ + unsigned int over; \ + c0 += (a); /* overflow is handled on the next line */ \ + over = (c0 < (a)); \ + c1 += over; /* overflow is handled on the next line */ \ + c2 += (c1 < over); /* never overflows by contract */ \ +} + +/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ +#define sumadd_fast(a) { \ + c0 += (a); /* overflow is handled on the next line */ \ + c1 += (c0 < (a)); /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ + VERIFY_CHECK(c2 == 0); \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */ +#define extract(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = c2; \ + c2 = 0; \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */ +#define extract_fast(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = 0; \ + VERIFY_CHECK(c2 == 0); \ +} + +static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) { +#ifdef USE_ASM_X86_64 + /* Reduce 512 bits into 385. */ + uint64_t m0, m1, m2, m3, m4, m5, m6; + uint64_t p0, p1, p2, p3, p4; + uint64_t c; + + __asm__ __volatile__( + /* Preload. */ + "movq 32(%%rsi), %%r11\n" + "movq 40(%%rsi), %%r12\n" + "movq 48(%%rsi), %%r13\n" + "movq 56(%%rsi), %%r14\n" + /* Initialize r8,r9,r10 */ + "movq 0(%%rsi), %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += n0 * c0 */ + "movq %8, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract m0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += l1 */ + "addq 8(%%rsi), %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += n1 * c0 */ + "movq %8, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n0 * c1 */ + "movq %9, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract m1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += l2 */ + "addq 16(%%rsi), %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n2 * c0 */ + "movq %8, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n1 * c1 */ + "movq %9, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n0 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract m2 */ + "movq %%r10, %q2\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += l3 */ + "addq 24(%%rsi), %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n3 * c0 */ + "movq %8, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n2 * c1 */ + "movq %9, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n1 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* extract m3 */ + "movq %%r8, %q3\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += n3 * c1 */ + "movq %9, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n2 */ + "addq %%r13, %%r9\n" + "adcq $0, %%r10\n" + "adcq $0, %%r8\n" + /* extract m4 */ + "movq %%r9, %q4\n" + /* (r10,r8) += n3 */ + "addq %%r14, %%r10\n" + "adcq $0, %%r8\n" + /* extract m5 */ + "movq %%r10, %q5\n" + /* extract m6 */ + "movq %%r8, %q6\n" + : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6) + : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc"); + + /* Reduce 385 bits into 258. */ + __asm__ __volatile__( + /* Preload */ + "movq %q9, %%r11\n" + "movq %q10, %%r12\n" + "movq %q11, %%r13\n" + /* Initialize (r8,r9,r10) */ + "movq %q5, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += m4 * c0 */ + "movq %12, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract p0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += m1 */ + "addq %q6, %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += m5 * c0 */ + "movq %12, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += m4 * c1 */ + "movq %13, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract p1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += m2 */ + "addq %q7, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m6 * c0 */ + "movq %12, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m5 * c1 */ + "movq %13, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m4 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract p2 */ + "movq %%r10, %q2\n" + /* (r8,r9) += m3 */ + "addq %q8, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += m6 * c1 */ + "movq %13, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* (r8,r9) += m5 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + /* extract p3 */ + "movq %%r8, %q3\n" + /* (r9) += m6 */ + "addq %%r13, %%r9\n" + /* extract p4 */ + "movq %%r9, %q4\n" + : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4) + : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc"); + + /* Reduce 258 bits into 256. */ + __asm__ __volatile__( + /* Preload */ + "movq %q5, %%r10\n" + /* (rax,rdx) = p4 * c0 */ + "movq %7, %%rax\n" + "mulq %%r10\n" + /* (rax,rdx) += p0 */ + "addq %q1, %%rax\n" + "adcq $0, %%rdx\n" + /* extract r0 */ + "movq %%rax, 0(%q6)\n" + /* Move to (r8,r9) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p1 */ + "addq %q2, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += p4 * c1 */ + "movq %8, %%rax\n" + "mulq %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* Extract r1 */ + "movq %%r8, 8(%q6)\n" + "xorq %%r8, %%r8\n" + /* (r9,r8) += p4 */ + "addq %%r10, %%r9\n" + "adcq $0, %%r8\n" + /* (r9,r8) += p2 */ + "addq %q3, %%r9\n" + "adcq $0, %%r8\n" + /* Extract r2 */ + "movq %%r9, 16(%q6)\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p3 */ + "addq %q4, %%r8\n" + "adcq $0, %%r9\n" + /* Extract r3 */ + "movq %%r8, 24(%q6)\n" + /* Extract c */ + "movq %%r9, %q0\n" + : "=g"(c) + : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "cc", "memory"); +#else + secp256k1_uint128 c128; + uint64_t c, c0, c1, c2; + uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7]; + uint64_t m0, m1, m2, m3, m4, m5; + uint32_t m6; + uint64_t p0, p1, p2, p3; + uint32_t p4; + + /* Reduce 512 bits into 385. */ + /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */ + c0 = l[0]; c1 = 0; c2 = 0; + muladd_fast(n0, SECP256K1_N_C_0); + extract_fast(m0); + sumadd_fast(l[1]); + muladd(n1, SECP256K1_N_C_0); + muladd(n0, SECP256K1_N_C_1); + extract(m1); + sumadd(l[2]); + muladd(n2, SECP256K1_N_C_0); + muladd(n1, SECP256K1_N_C_1); + sumadd(n0); + extract(m2); + sumadd(l[3]); + muladd(n3, SECP256K1_N_C_0); + muladd(n2, SECP256K1_N_C_1); + sumadd(n1); + extract(m3); + muladd(n3, SECP256K1_N_C_1); + sumadd(n2); + extract(m4); + sumadd_fast(n3); + extract_fast(m5); + VERIFY_CHECK(c0 <= 1); + m6 = c0; + + /* Reduce 385 bits into 258. */ + /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */ + c0 = m0; c1 = 0; c2 = 0; + muladd_fast(m4, SECP256K1_N_C_0); + extract_fast(p0); + sumadd_fast(m1); + muladd(m5, SECP256K1_N_C_0); + muladd(m4, SECP256K1_N_C_1); + extract(p1); + sumadd(m2); + muladd(m6, SECP256K1_N_C_0); + muladd(m5, SECP256K1_N_C_1); + sumadd(m4); + extract(p2); + sumadd_fast(m3); + muladd_fast(m6, SECP256K1_N_C_1); + sumadd_fast(m5); + extract_fast(p3); + p4 = c0 + m6; + VERIFY_CHECK(p4 <= 2); + + /* Reduce 258 bits into 256. */ + /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */ + secp256k1_u128_from_u64(&c128, p0); + secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_0, p4); + r->d[0] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); + secp256k1_u128_accum_u64(&c128, p1); + secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_1, p4); + r->d[1] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); + secp256k1_u128_accum_u64(&c128, p2); + secp256k1_u128_accum_u64(&c128, p4); + r->d[2] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); + secp256k1_u128_accum_u64(&c128, p3); + r->d[3] = secp256k1_u128_to_u64(&c128); + c = secp256k1_u128_hi_u64(&c128); +#endif + + /* Final reduction of r. */ + secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); +} + +static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) { +#ifdef USE_ASM_X86_64 + const uint64_t *pb = b->d; + __asm__ __volatile__( + /* Preload */ + "movq 0(%%rdi), %%r15\n" + "movq 8(%%rdi), %%rbx\n" + "movq 16(%%rdi), %%rcx\n" + "movq 0(%%rdx), %%r11\n" + "movq 8(%%rdx), %%r12\n" + "movq 16(%%rdx), %%r13\n" + "movq 24(%%rdx), %%r14\n" + /* (rax,rdx) = a0 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + /* Extract l0 */ + "movq %%rax, 0(%%rsi)\n" + /* (r8,r9,r10) = (rdx) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a0 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a1 * b0 */ + "movq %%rbx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l1 */ + "movq %%r8, 8(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a0 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a1 * b1 */ + "movq %%rbx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a2 * b0 */ + "movq %%rcx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l2 */ + "movq %%r9, 16(%%rsi)\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += a0 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Preload a3 */ + "movq 24(%%rdi), %%r15\n" + /* (r10,r8,r9) += a1 * b2 */ + "movq %%rbx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a2 * b1 */ + "movq %%rcx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a3 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Extract l3 */ + "movq %%r10, 24(%%rsi)\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a1 * b3 */ + "movq %%rbx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a2 * b2 */ + "movq %%rcx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a3 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l4 */ + "movq %%r8, 32(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a2 * b3 */ + "movq %%rcx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a3 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l5 */ + "movq %%r9, 40(%%rsi)\n" + /* (r10,r8) += a3 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + /* Extract l6 */ + "movq %%r10, 48(%%rsi)\n" + /* Extract l7 */ + "movq %%r8, 56(%%rsi)\n" + : "+d"(pb) + : "S"(l), "D"(a->d) + : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory"); +#else + /* 160 bit accumulator. */ + uint64_t c0 = 0, c1 = 0; + uint32_t c2 = 0; + + /* l[0..7] = a[0..3] * b[0..3]. */ + muladd_fast(a->d[0], b->d[0]); + extract_fast(l[0]); + muladd(a->d[0], b->d[1]); + muladd(a->d[1], b->d[0]); + extract(l[1]); + muladd(a->d[0], b->d[2]); + muladd(a->d[1], b->d[1]); + muladd(a->d[2], b->d[0]); + extract(l[2]); + muladd(a->d[0], b->d[3]); + muladd(a->d[1], b->d[2]); + muladd(a->d[2], b->d[1]); + muladd(a->d[3], b->d[0]); + extract(l[3]); + muladd(a->d[1], b->d[3]); + muladd(a->d[2], b->d[2]); + muladd(a->d[3], b->d[1]); + extract(l[4]); + muladd(a->d[2], b->d[3]); + muladd(a->d[3], b->d[2]); + extract(l[5]); + muladd_fast(a->d[3], b->d[3]); + extract_fast(l[6]); + VERIFY_CHECK(c1 == 0); + l[7] = c0; +#endif +} + +#undef sumadd +#undef sumadd_fast +#undef muladd +#undef muladd_fast +#undef extract +#undef extract_fast + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + uint64_t l[8]; + secp256k1_scalar_mul_512(l, a, b); + secp256k1_scalar_reduce_512(r, l); +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = r->d[0] & ((1 << n) - 1); + r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n)); + r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n)); + r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n)); + r->d[3] = (r->d[3] >> n); + return ret; +} + +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) { + r1->d[0] = k->d[0]; + r1->d[1] = k->d[1]; + r1->d[2] = 0; + r1->d[3] = 0; + r2->d[0] = k->d[2]; + r2->d[1] = k->d[3]; + r2->d[2] = 0; + r2->d[3] = 0; +} + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { + uint64_t l[8]; + unsigned int shiftlimbs; + unsigned int shiftlow; + unsigned int shifthigh; + VERIFY_CHECK(shift >= 256); + secp256k1_scalar_mul_512(l, a, b); + shiftlimbs = shift >> 6; + shiftlow = shift & 0x3F; + shifthigh = 64 - shiftlow; + r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0; + secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1); +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint64_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d)); + mask0 = vflag + ~((uint64_t)0); + mask1 = ~mask0; + r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1); + r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1); + r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1); + r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1); +} + +static void secp256k1_scalar_from_signed62(secp256k1_scalar *r, const secp256k1_modinv64_signed62 *a) { + const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4]; + + /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and + * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4). + */ + VERIFY_CHECK(a0 >> 62 == 0); + VERIFY_CHECK(a1 >> 62 == 0); + VERIFY_CHECK(a2 >> 62 == 0); + VERIFY_CHECK(a3 >> 62 == 0); + VERIFY_CHECK(a4 >> 8 == 0); + + r->d[0] = a0 | a1 << 62; + r->d[1] = a1 >> 2 | a2 << 60; + r->d[2] = a2 >> 4 | a3 << 58; + r->d[3] = a3 >> 6 | a4 << 56; + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_scalar *a) { + const uint64_t M62 = UINT64_MAX >> 2; + const uint64_t a0 = a->d[0], a1 = a->d[1], a2 = a->d[2], a3 = a->d[3]; + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_check_overflow(a) == 0); +#endif + + r->v[0] = a0 & M62; + r->v[1] = (a0 >> 62 | a1 << 2) & M62; + r->v[2] = (a1 >> 60 | a2 << 4) & M62; + r->v[3] = (a2 >> 58 | a3 << 6) & M62; + r->v[4] = a3 >> 56; +} + +static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_scalar = { + {{0x3FD25E8CD0364141LL, 0x2ABB739ABD2280EELL, -0x15LL, 0, 256}}, + 0x34F20099AA774EC1LL +}; + +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { + secp256k1_modinv64_signed62 s; +#ifdef VERIFY + int zero_in = secp256k1_scalar_is_zero(x); +#endif + secp256k1_scalar_to_signed62(&s, x); + secp256k1_modinv64(&s, &secp256k1_const_modinfo_scalar); + secp256k1_scalar_from_signed62(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); +#endif +} + +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { + secp256k1_modinv64_signed62 s; +#ifdef VERIFY + int zero_in = secp256k1_scalar_is_zero(x); +#endif + secp256k1_scalar_to_signed62(&s, x); + secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_scalar); + secp256k1_scalar_from_signed62(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); +#endif +} + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(a->d[0] & 1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/src/secp256k1/src/scalar_8x32.h b/src/secp256k1/src/scalar_8x32.h new file mode 100644 index 0000000000..17863ef937 --- /dev/null +++ b/src/secp256k1/src/scalar_8x32.h @@ -0,0 +1,19 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include <stdint.h> + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef struct { + uint32_t d[8]; +} secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}} + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/src/secp256k1/src/scalar_8x32_impl.h b/src/secp256k1/src/scalar_8x32_impl.h new file mode 100644 index 0000000000..a2555cbbcd --- /dev/null +++ b/src/secp256k1/src/scalar_8x32_impl.h @@ -0,0 +1,737 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +#include "checkmem.h" +#include "modinv32_impl.h" + +/* Limbs of the secp256k1 order. */ +#define SECP256K1_N_0 ((uint32_t)0xD0364141UL) +#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL) +#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL) +#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL) +#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL) +#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL) + +/* Limbs of 2^256 minus the secp256k1 order. */ +#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) +#define SECP256K1_N_C_1 (~SECP256K1_N_1) +#define SECP256K1_N_C_2 (~SECP256K1_N_2) +#define SECP256K1_N_C_3 (~SECP256K1_N_3) +#define SECP256K1_N_C_4 (1) + +/* Limbs of half the secp256k1 order. */ +#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL) +#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL) +#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL) +#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL) +#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL) + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { + r->d[0] = 0; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; + r->d[4] = 0; + r->d[5] = 0; + r->d[6] = 0; + r->d[7] = 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { + r->d[0] = v; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; + r->d[4] = 0; + r->d[5] = 0; + r->d[6] = 0; + r->d[7] = 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5); + return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1); +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK(count < 32); + VERIFY_CHECK(offset + count <= 256); + if ((offset + count - 1) >> 5 == offset >> 5) { + return secp256k1_scalar_get_bits(a, offset, count); + } else { + VERIFY_CHECK((offset >> 5) + 1 < 8); + return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1); + } +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */ + no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */ + no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */ + no |= (a->d[4] < SECP256K1_N_4); + yes |= (a->d[4] > SECP256K1_N_4) & ~no; + no |= (a->d[3] < SECP256K1_N_3) & ~yes; + yes |= (a->d[3] > SECP256K1_N_3) & ~no; + no |= (a->d[2] < SECP256K1_N_2) & ~yes; + yes |= (a->d[2] > SECP256K1_N_2) & ~no; + no |= (a->d[1] < SECP256K1_N_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_1) & ~no; + yes |= (a->d[0] >= SECP256K1_N_0) & ~no; + return yes; +} + +SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) { + uint64_t t; + VERIFY_CHECK(overflow <= 1); + t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0; + r->d[0] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1; + r->d[1] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2; + r->d[2] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3; + r->d[3] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4; + r->d[4] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[5]; + r->d[5] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[6]; + r->d[6] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[7]; + r->d[7] = t & 0xFFFFFFFFUL; + return overflow; +} + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + int overflow; + uint64_t t = (uint64_t)a->d[0] + b->d[0]; + r->d[0] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[1] + b->d[1]; + r->d[1] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[2] + b->d[2]; + r->d[2] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[3] + b->d[3]; + r->d[3] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[4] + b->d[4]; + r->d[4] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[5] + b->d[5]; + r->d[5] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[6] + b->d[6]; + r->d[6] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[7] + b->d[7]; + r->d[7] = t & 0xFFFFFFFFULL; t >>= 32; + overflow = t + secp256k1_scalar_check_overflow(r); + VERIFY_CHECK(overflow == 0 || overflow == 1); + secp256k1_scalar_reduce(r, overflow); + return overflow; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + uint64_t t; + VERIFY_CHECK(bit < 256); + bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */ + t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F)); + r->d[0] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F)); + r->d[1] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F)); + r->d[2] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F)); + r->d[3] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F)); + r->d[4] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F)); + r->d[5] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F)); + r->d[6] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F)); + r->d[7] = t & 0xFFFFFFFFULL; +#ifdef VERIFY + VERIFY_CHECK((t >> 32) == 0); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int over; + r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24; + r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24; + r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24; + r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24; + r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24; + r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24; + r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24; + r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24; + over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); + if (overflow) { + *overflow = over; + } +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7]; + bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6]; + bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5]; + bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4]; + bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3]; + bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2]; + bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1]; + bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0); + uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1; + r->d[0] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[1]) + SECP256K1_N_1; + r->d[1] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[2]) + SECP256K1_N_2; + r->d[2] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[3]) + SECP256K1_N_3; + r->d[3] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[4]) + SECP256K1_N_4; + r->d[4] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[5]) + SECP256K1_N_5; + r->d[5] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[6]) + SECP256K1_N_6; + r->d[6] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[7]) + SECP256K1_N_7; + r->d[7] = t & nonzero; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[7] < SECP256K1_N_H_7); + yes |= (a->d[7] > SECP256K1_N_H_7) & ~no; + no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */ + no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */ + no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */ + no |= (a->d[3] < SECP256K1_N_H_3) & ~yes; + yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; + no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; + yes |= (a->d[2] > SECP256K1_N_H_2) & ~no; + no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; + yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; + return yes; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + /* If we are flag = 0, mask = 00...00 and this is a no-op; + * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ + uint32_t mask = !flag - 1; + uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0); + uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask); + r->d[0] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask); + r->d[1] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask); + r->d[2] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask); + r->d[3] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask); + r->d[4] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask); + r->d[5] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask); + r->d[6] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask); + r->d[7] = t & nonzero; + return 2 * (mask == 0) - 1; +} + + +/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ + +/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd(a,b) { \ + uint32_t tl, th; \ + { \ + uint64_t t = (uint64_t)a * b; \ + th = t >> 32; /* at most 0xFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl); /* at most 0xFFFFFFFF */ \ + c1 += th; /* overflow is handled on the next line */ \ + c2 += (c1 < th); /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ +} + +/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ +#define muladd_fast(a,b) { \ + uint32_t tl, th; \ + { \ + uint64_t t = (uint64_t)a * b; \ + th = t >> 32; /* at most 0xFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl); /* at most 0xFFFFFFFF */ \ + c1 += th; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK(c1 >= th); \ +} + +/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define sumadd(a) { \ + unsigned int over; \ + c0 += (a); /* overflow is handled on the next line */ \ + over = (c0 < (a)); \ + c1 += over; /* overflow is handled on the next line */ \ + c2 += (c1 < over); /* never overflows by contract */ \ +} + +/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ +#define sumadd_fast(a) { \ + c0 += (a); /* overflow is handled on the next line */ \ + c1 += (c0 < (a)); /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ + VERIFY_CHECK(c2 == 0); \ +} + +/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */ +#define extract(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = c2; \ + c2 = 0; \ +} + +/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */ +#define extract_fast(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = 0; \ + VERIFY_CHECK(c2 == 0); \ +} + +static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) { + uint64_t c; + uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15]; + uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12; + uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8; + + /* 96 bit accumulator. */ + uint32_t c0, c1, c2; + + /* Reduce 512 bits into 385. */ + /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */ + c0 = l[0]; c1 = 0; c2 = 0; + muladd_fast(n0, SECP256K1_N_C_0); + extract_fast(m0); + sumadd_fast(l[1]); + muladd(n1, SECP256K1_N_C_0); + muladd(n0, SECP256K1_N_C_1); + extract(m1); + sumadd(l[2]); + muladd(n2, SECP256K1_N_C_0); + muladd(n1, SECP256K1_N_C_1); + muladd(n0, SECP256K1_N_C_2); + extract(m2); + sumadd(l[3]); + muladd(n3, SECP256K1_N_C_0); + muladd(n2, SECP256K1_N_C_1); + muladd(n1, SECP256K1_N_C_2); + muladd(n0, SECP256K1_N_C_3); + extract(m3); + sumadd(l[4]); + muladd(n4, SECP256K1_N_C_0); + muladd(n3, SECP256K1_N_C_1); + muladd(n2, SECP256K1_N_C_2); + muladd(n1, SECP256K1_N_C_3); + sumadd(n0); + extract(m4); + sumadd(l[5]); + muladd(n5, SECP256K1_N_C_0); + muladd(n4, SECP256K1_N_C_1); + muladd(n3, SECP256K1_N_C_2); + muladd(n2, SECP256K1_N_C_3); + sumadd(n1); + extract(m5); + sumadd(l[6]); + muladd(n6, SECP256K1_N_C_0); + muladd(n5, SECP256K1_N_C_1); + muladd(n4, SECP256K1_N_C_2); + muladd(n3, SECP256K1_N_C_3); + sumadd(n2); + extract(m6); + sumadd(l[7]); + muladd(n7, SECP256K1_N_C_0); + muladd(n6, SECP256K1_N_C_1); + muladd(n5, SECP256K1_N_C_2); + muladd(n4, SECP256K1_N_C_3); + sumadd(n3); + extract(m7); + muladd(n7, SECP256K1_N_C_1); + muladd(n6, SECP256K1_N_C_2); + muladd(n5, SECP256K1_N_C_3); + sumadd(n4); + extract(m8); + muladd(n7, SECP256K1_N_C_2); + muladd(n6, SECP256K1_N_C_3); + sumadd(n5); + extract(m9); + muladd(n7, SECP256K1_N_C_3); + sumadd(n6); + extract(m10); + sumadd_fast(n7); + extract_fast(m11); + VERIFY_CHECK(c0 <= 1); + m12 = c0; + + /* Reduce 385 bits into 258. */ + /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */ + c0 = m0; c1 = 0; c2 = 0; + muladd_fast(m8, SECP256K1_N_C_0); + extract_fast(p0); + sumadd_fast(m1); + muladd(m9, SECP256K1_N_C_0); + muladd(m8, SECP256K1_N_C_1); + extract(p1); + sumadd(m2); + muladd(m10, SECP256K1_N_C_0); + muladd(m9, SECP256K1_N_C_1); + muladd(m8, SECP256K1_N_C_2); + extract(p2); + sumadd(m3); + muladd(m11, SECP256K1_N_C_0); + muladd(m10, SECP256K1_N_C_1); + muladd(m9, SECP256K1_N_C_2); + muladd(m8, SECP256K1_N_C_3); + extract(p3); + sumadd(m4); + muladd(m12, SECP256K1_N_C_0); + muladd(m11, SECP256K1_N_C_1); + muladd(m10, SECP256K1_N_C_2); + muladd(m9, SECP256K1_N_C_3); + sumadd(m8); + extract(p4); + sumadd(m5); + muladd(m12, SECP256K1_N_C_1); + muladd(m11, SECP256K1_N_C_2); + muladd(m10, SECP256K1_N_C_3); + sumadd(m9); + extract(p5); + sumadd(m6); + muladd(m12, SECP256K1_N_C_2); + muladd(m11, SECP256K1_N_C_3); + sumadd(m10); + extract(p6); + sumadd_fast(m7); + muladd_fast(m12, SECP256K1_N_C_3); + sumadd_fast(m11); + extract_fast(p7); + p8 = c0 + m12; + VERIFY_CHECK(p8 <= 2); + + /* Reduce 258 bits into 256. */ + /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */ + c = p0 + (uint64_t)SECP256K1_N_C_0 * p8; + r->d[0] = c & 0xFFFFFFFFUL; c >>= 32; + c += p1 + (uint64_t)SECP256K1_N_C_1 * p8; + r->d[1] = c & 0xFFFFFFFFUL; c >>= 32; + c += p2 + (uint64_t)SECP256K1_N_C_2 * p8; + r->d[2] = c & 0xFFFFFFFFUL; c >>= 32; + c += p3 + (uint64_t)SECP256K1_N_C_3 * p8; + r->d[3] = c & 0xFFFFFFFFUL; c >>= 32; + c += p4 + (uint64_t)p8; + r->d[4] = c & 0xFFFFFFFFUL; c >>= 32; + c += p5; + r->d[5] = c & 0xFFFFFFFFUL; c >>= 32; + c += p6; + r->d[6] = c & 0xFFFFFFFFUL; c >>= 32; + c += p7; + r->d[7] = c & 0xFFFFFFFFUL; c >>= 32; + + /* Final reduction of r. */ + secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); +} + +static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) { + /* 96 bit accumulator. */ + uint32_t c0 = 0, c1 = 0, c2 = 0; + + /* l[0..15] = a[0..7] * b[0..7]. */ + muladd_fast(a->d[0], b->d[0]); + extract_fast(l[0]); + muladd(a->d[0], b->d[1]); + muladd(a->d[1], b->d[0]); + extract(l[1]); + muladd(a->d[0], b->d[2]); + muladd(a->d[1], b->d[1]); + muladd(a->d[2], b->d[0]); + extract(l[2]); + muladd(a->d[0], b->d[3]); + muladd(a->d[1], b->d[2]); + muladd(a->d[2], b->d[1]); + muladd(a->d[3], b->d[0]); + extract(l[3]); + muladd(a->d[0], b->d[4]); + muladd(a->d[1], b->d[3]); + muladd(a->d[2], b->d[2]); + muladd(a->d[3], b->d[1]); + muladd(a->d[4], b->d[0]); + extract(l[4]); + muladd(a->d[0], b->d[5]); + muladd(a->d[1], b->d[4]); + muladd(a->d[2], b->d[3]); + muladd(a->d[3], b->d[2]); + muladd(a->d[4], b->d[1]); + muladd(a->d[5], b->d[0]); + extract(l[5]); + muladd(a->d[0], b->d[6]); + muladd(a->d[1], b->d[5]); + muladd(a->d[2], b->d[4]); + muladd(a->d[3], b->d[3]); + muladd(a->d[4], b->d[2]); + muladd(a->d[5], b->d[1]); + muladd(a->d[6], b->d[0]); + extract(l[6]); + muladd(a->d[0], b->d[7]); + muladd(a->d[1], b->d[6]); + muladd(a->d[2], b->d[5]); + muladd(a->d[3], b->d[4]); + muladd(a->d[4], b->d[3]); + muladd(a->d[5], b->d[2]); + muladd(a->d[6], b->d[1]); + muladd(a->d[7], b->d[0]); + extract(l[7]); + muladd(a->d[1], b->d[7]); + muladd(a->d[2], b->d[6]); + muladd(a->d[3], b->d[5]); + muladd(a->d[4], b->d[4]); + muladd(a->d[5], b->d[3]); + muladd(a->d[6], b->d[2]); + muladd(a->d[7], b->d[1]); + extract(l[8]); + muladd(a->d[2], b->d[7]); + muladd(a->d[3], b->d[6]); + muladd(a->d[4], b->d[5]); + muladd(a->d[5], b->d[4]); + muladd(a->d[6], b->d[3]); + muladd(a->d[7], b->d[2]); + extract(l[9]); + muladd(a->d[3], b->d[7]); + muladd(a->d[4], b->d[6]); + muladd(a->d[5], b->d[5]); + muladd(a->d[6], b->d[4]); + muladd(a->d[7], b->d[3]); + extract(l[10]); + muladd(a->d[4], b->d[7]); + muladd(a->d[5], b->d[6]); + muladd(a->d[6], b->d[5]); + muladd(a->d[7], b->d[4]); + extract(l[11]); + muladd(a->d[5], b->d[7]); + muladd(a->d[6], b->d[6]); + muladd(a->d[7], b->d[5]); + extract(l[12]); + muladd(a->d[6], b->d[7]); + muladd(a->d[7], b->d[6]); + extract(l[13]); + muladd_fast(a->d[7], b->d[7]); + extract_fast(l[14]); + VERIFY_CHECK(c1 == 0); + l[15] = c0; +} + +#undef sumadd +#undef sumadd_fast +#undef muladd +#undef muladd_fast +#undef extract +#undef extract_fast + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + uint32_t l[16]; + secp256k1_scalar_mul_512(l, a, b); + secp256k1_scalar_reduce_512(r, l); +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = r->d[0] & ((1 << n) - 1); + r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n)); + r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n)); + r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n)); + r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n)); + r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n)); + r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n)); + r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n)); + r->d[7] = (r->d[7] >> n); + return ret; +} + +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) { + r1->d[0] = k->d[0]; + r1->d[1] = k->d[1]; + r1->d[2] = k->d[2]; + r1->d[3] = k->d[3]; + r1->d[4] = 0; + r1->d[5] = 0; + r1->d[6] = 0; + r1->d[7] = 0; + r2->d[0] = k->d[4]; + r2->d[1] = k->d[5]; + r2->d[2] = k->d[6]; + r2->d[3] = k->d[7]; + r2->d[4] = 0; + r2->d[5] = 0; + r2->d[6] = 0; + r2->d[7] = 0; +} + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { + uint32_t l[16]; + unsigned int shiftlimbs; + unsigned int shiftlow; + unsigned int shifthigh; + VERIFY_CHECK(shift >= 256); + secp256k1_scalar_mul_512(l, a, b); + shiftlimbs = shift >> 5; + shiftlow = shift & 0x1F; + shifthigh = 32 - shiftlow; + r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0; + secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1); +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint32_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d)); + mask0 = vflag + ~((uint32_t)0); + mask1 = ~mask0; + r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1); + r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1); + r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1); + r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1); + r->d[4] = (r->d[4] & mask0) | (a->d[4] & mask1); + r->d[5] = (r->d[5] & mask0) | (a->d[5] & mask1); + r->d[6] = (r->d[6] & mask0) | (a->d[6] & mask1); + r->d[7] = (r->d[7] & mask0) | (a->d[7] & mask1); +} + +static void secp256k1_scalar_from_signed30(secp256k1_scalar *r, const secp256k1_modinv32_signed30 *a) { + const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4], + a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8]; + + /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and + * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8). + */ + VERIFY_CHECK(a0 >> 30 == 0); + VERIFY_CHECK(a1 >> 30 == 0); + VERIFY_CHECK(a2 >> 30 == 0); + VERIFY_CHECK(a3 >> 30 == 0); + VERIFY_CHECK(a4 >> 30 == 0); + VERIFY_CHECK(a5 >> 30 == 0); + VERIFY_CHECK(a6 >> 30 == 0); + VERIFY_CHECK(a7 >> 30 == 0); + VERIFY_CHECK(a8 >> 16 == 0); + + r->d[0] = a0 | a1 << 30; + r->d[1] = a1 >> 2 | a2 << 28; + r->d[2] = a2 >> 4 | a3 << 26; + r->d[3] = a3 >> 6 | a4 << 24; + r->d[4] = a4 >> 8 | a5 << 22; + r->d[5] = a5 >> 10 | a6 << 20; + r->d[6] = a6 >> 12 | a7 << 18; + r->d[7] = a7 >> 14 | a8 << 16; + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_scalar *a) { + const uint32_t M30 = UINT32_MAX >> 2; + const uint32_t a0 = a->d[0], a1 = a->d[1], a2 = a->d[2], a3 = a->d[3], + a4 = a->d[4], a5 = a->d[5], a6 = a->d[6], a7 = a->d[7]; + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_check_overflow(a) == 0); +#endif + + r->v[0] = a0 & M30; + r->v[1] = (a0 >> 30 | a1 << 2) & M30; + r->v[2] = (a1 >> 28 | a2 << 4) & M30; + r->v[3] = (a2 >> 26 | a3 << 6) & M30; + r->v[4] = (a3 >> 24 | a4 << 8) & M30; + r->v[5] = (a4 >> 22 | a5 << 10) & M30; + r->v[6] = (a5 >> 20 | a6 << 12) & M30; + r->v[7] = (a6 >> 18 | a7 << 14) & M30; + r->v[8] = a7 >> 16; +} + +static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_scalar = { + {{0x10364141L, 0x3F497A33L, 0x348A03BBL, 0x2BB739ABL, -0x146L, 0, 0, 0, 65536}}, + 0x2A774EC1L +}; + +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { + secp256k1_modinv32_signed30 s; +#ifdef VERIFY + int zero_in = secp256k1_scalar_is_zero(x); +#endif + secp256k1_scalar_to_signed30(&s, x); + secp256k1_modinv32(&s, &secp256k1_const_modinfo_scalar); + secp256k1_scalar_from_signed30(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); +#endif +} + +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { + secp256k1_modinv32_signed30 s; +#ifdef VERIFY + int zero_in = secp256k1_scalar_is_zero(x); +#endif + secp256k1_scalar_to_signed30(&s, x); + secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_scalar); + secp256k1_scalar_from_signed30(r, &s); + +#ifdef VERIFY + VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); +#endif +} + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(a->d[0] & 1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h new file mode 100644 index 0000000000..bed7f95fcb --- /dev/null +++ b/src/secp256k1/src/scalar_impl.h @@ -0,0 +1,300 @@ +/*********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_IMPL_H +#define SECP256K1_SCALAR_IMPL_H + +#ifdef VERIFY +#include <string.h> +#endif + +#include "scalar.h" +#include "util.h" + +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low_impl.h" +#elif defined(SECP256K1_WIDEMUL_INT128) +#include "scalar_4x64_impl.h" +#elif defined(SECP256K1_WIDEMUL_INT64) +#include "scalar_8x32_impl.h" +#else +#error "Please select wide multiplication implementation" +#endif + +static const secp256k1_scalar secp256k1_scalar_one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); +static const secp256k1_scalar secp256k1_scalar_zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + +static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin) { + int overflow; + secp256k1_scalar_set_b32(r, bin, &overflow); + return (!overflow) & (!secp256k1_scalar_is_zero(r)); +} + +#if defined(EXHAUSTIVE_TEST_ORDER) +/* Begin of section generated by sage/gen_exhaustive_groups.sage. */ +# if EXHAUSTIVE_TEST_ORDER == 7 +# define EXHAUSTIVE_TEST_LAMBDA 2 +# elif EXHAUSTIVE_TEST_ORDER == 13 +# define EXHAUSTIVE_TEST_LAMBDA 9 +# elif EXHAUSTIVE_TEST_ORDER == 199 +# define EXHAUSTIVE_TEST_LAMBDA 92 +# else +# error No known lambda for the specified exhaustive test group order. +# endif +/* End of section generated by sage/gen_exhaustive_groups.sage. */ + +/** + * Find r1 and r2 given k, such that r1 + r2 * lambda == k mod n; unlike in the + * full case we don't bother making r1 and r2 be small, we just want them to be + * nontrivial to get full test coverage for the exhaustive tests. We therefore + * (arbitrarily) set r2 = k + 5 (mod n) and r1 = k - r2 * lambda (mod n). + */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar * SECP256K1_RESTRICT r1, secp256k1_scalar * SECP256K1_RESTRICT r2, const secp256k1_scalar * SECP256K1_RESTRICT k) { + VERIFY_CHECK(r1 != k); + VERIFY_CHECK(r2 != k); + VERIFY_CHECK(r1 != r2); + *r2 = (*k + 5) % EXHAUSTIVE_TEST_ORDER; + *r1 = (*k + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER; +} +#else +/** + * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where + * lambda is: */ +static const secp256k1_scalar secp256k1_const_lambda = SECP256K1_SCALAR_CONST( + 0x5363AD4CUL, 0xC05C30E0UL, 0xA5261C02UL, 0x8812645AUL, + 0x122E22EAUL, 0x20816678UL, 0xDF02967CUL, 0x1B23BD72UL +); + +#ifdef VERIFY +static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k); +#endif + +/* + * Both lambda and beta are primitive cube roots of unity. That is lamba^3 == 1 mod n and + * beta^3 == 1 mod p, where n is the curve order and p is the field order. + * + * Furthermore, because (X^3 - 1) = (X - 1)(X^2 + X + 1), the primitive cube roots of unity are + * roots of X^2 + X + 1. Therefore lambda^2 + lamba == -1 mod n and beta^2 + beta == -1 mod p. + * (The other primitive cube roots of unity are lambda^2 and beta^2 respectively.) + * + * Let l = -1/2 + i*sqrt(3)/2, the complex root of X^2 + X + 1. We can define a ring + * homomorphism phi : Z[l] -> Z_n where phi(a + b*l) == a + b*lambda mod n. The kernel of phi + * is a lattice over Z[l] (considering Z[l] as a Z-module). This lattice is generated by a + * reduced basis {a1 + b1*l, a2 + b2*l} where + * + * - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3} + * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8} + * - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * + * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm + * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1 + * and k2 are small in absolute value. + * + * The algorithm computes c1 = round(b2 * k / n) and c2 = round((-b1) * k / n), and gives + * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and + * compute r2 = k2 mod n, and r1 = k1 mod n = (k - r2 * lambda) mod n, avoiding the need for + * the constants a1 and a2. + * + * g1, g2 are precomputed constants used to replace division with a rounded multiplication + * when decomposing the scalar for an endomorphism-based point multiplication. + * + * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve + * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5. + * + * The derivation is described in the paper "Efficient Software Implementation of Public-Key + * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez), + * Section 4.3 (here we use a somewhat higher-precision estimate): + * d = a1*b2 - b1*a2 + * g1 = round(2^384 * b2/d) + * g2 = round(2^384 * (-b1)/d) + * + * (Note that d is also equal to the curve order, n, here because [a1,b1] and [a2,b2] + * can be found as outputs of the Extended Euclidean Algorithm on inputs n and lambda). + * + * The function below splits k into r1 and r2, such that + * - r1 + lambda * r2 == k (mod n) + * - either r1 < 2^128 or -r1 mod n < 2^128 + * - either r2 < 2^128 or -r2 mod n < 2^128 + * + * See proof below. + */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar * SECP256K1_RESTRICT r1, secp256k1_scalar * SECP256K1_RESTRICT r2, const secp256k1_scalar * SECP256K1_RESTRICT k) { + secp256k1_scalar c1, c2; + static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, + 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL + ); + static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL + ); + static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST( + 0x3086D221UL, 0xA7D46BCDUL, 0xE86C90E4UL, 0x9284EB15UL, + 0x3DAA8A14UL, 0x71E8CA7FUL, 0xE893209AUL, 0x45DBB031UL + ); + static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST( + 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C4UL, + 0x221208ACUL, 0x9DF506C6UL, 0x1571B4AEUL, 0x8AC47F71UL + ); + VERIFY_CHECK(r1 != k); + VERIFY_CHECK(r2 != k); + VERIFY_CHECK(r1 != r2); + /* these _var calls are constant time since the shift amount is constant */ + secp256k1_scalar_mul_shift_var(&c1, k, &g1, 384); + secp256k1_scalar_mul_shift_var(&c2, k, &g2, 384); + secp256k1_scalar_mul(&c1, &c1, &minus_b1); + secp256k1_scalar_mul(&c2, &c2, &minus_b2); + secp256k1_scalar_add(r2, &c1, &c2); + secp256k1_scalar_mul(r1, r2, &secp256k1_const_lambda); + secp256k1_scalar_negate(r1, r1); + secp256k1_scalar_add(r1, r1, k); + +#ifdef VERIFY + secp256k1_scalar_split_lambda_verify(r1, r2, k); +#endif +} + +#ifdef VERIFY +/* + * Proof for secp256k1_scalar_split_lambda's bounds. + * + * Let + * - epsilon1 = 2^256 * |g1/2^384 - b2/d| + * - epsilon2 = 2^256 * |g2/2^384 - (-b1)/d| + * - c1 = round(k*g1/2^384) + * - c2 = round(k*g2/2^384) + * + * Lemma 1: |c1 - k*b2/d| < 2^-1 + epsilon1 + * + * |c1 - k*b2/d| + * = + * |c1 - k*g1/2^384 + k*g1/2^384 - k*b2/d| + * <= {triangle inequality} + * |c1 - k*g1/2^384| + |k*g1/2^384 - k*b2/d| + * = + * |c1 - k*g1/2^384| + k*|g1/2^384 - b2/d| + * < {rounding in c1 and 0 <= k < 2^256} + * 2^-1 + 2^256 * |g1/2^384 - b2/d| + * = {definition of epsilon1} + * 2^-1 + epsilon1 + * + * Lemma 2: |c2 - k*(-b1)/d| < 2^-1 + epsilon2 + * + * |c2 - k*(-b1)/d| + * = + * |c2 - k*g2/2^384 + k*g2/2^384 - k*(-b1)/d| + * <= {triangle inequality} + * |c2 - k*g2/2^384| + |k*g2/2^384 - k*(-b1)/d| + * = + * |c2 - k*g2/2^384| + k*|g2/2^384 - (-b1)/d| + * < {rounding in c2 and 0 <= k < 2^256} + * 2^-1 + 2^256 * |g2/2^384 - (-b1)/d| + * = {definition of epsilon2} + * 2^-1 + epsilon2 + * + * Let + * - k1 = k - c1*a1 - c2*a2 + * - k2 = - c1*b1 - c2*b2 + * + * Lemma 3: |k1| < (a1 + a2 + 1)/2 < 2^128 + * + * |k1| + * = {definition of k1} + * |k - c1*a1 - c2*a2| + * = {(a1*b2 - b1*a2)/n = 1} + * |k*(a1*b2 - b1*a2)/n - c1*a1 - c2*a2| + * = + * |a1*(k*b2/n - c1) + a2*(k*(-b1)/n - c2)| + * <= {triangle inequality} + * a1*|k*b2/n - c1| + a2*|k*(-b1)/n - c2| + * < {Lemma 1 and Lemma 2} + * a1*(2^-1 + epslion1) + a2*(2^-1 + epsilon2) + * < {rounding up to an integer} + * (a1 + a2 + 1)/2 + * < {rounding up to a power of 2} + * 2^128 + * + * Lemma 4: |k2| < (-b1 + b2)/2 + 1 < 2^128 + * + * |k2| + * = {definition of k2} + * |- c1*a1 - c2*a2| + * = {(b1*b2 - b1*b2)/n = 0} + * |k*(b1*b2 - b1*b2)/n - c1*b1 - c2*b2| + * = + * |b1*(k*b2/n - c1) + b2*(k*(-b1)/n - c2)| + * <= {triangle inequality} + * (-b1)*|k*b2/n - c1| + b2*|k*(-b1)/n - c2| + * < {Lemma 1 and Lemma 2} + * (-b1)*(2^-1 + epslion1) + b2*(2^-1 + epsilon2) + * < {rounding up to an integer} + * (-b1 + b2)/2 + 1 + * < {rounding up to a power of 2} + * 2^128 + * + * Let + * - r2 = k2 mod n + * - r1 = k - r2*lambda mod n. + * + * Notice that r1 is defined such that r1 + r2 * lambda == k (mod n). + * + * Lemma 5: r1 == k1 mod n. + * + * r1 + * == {definition of r1 and r2} + * k - k2*lambda + * == {definition of k2} + * k - (- c1*b1 - c2*b2)*lambda + * == + * k + c1*b1*lambda + c2*b2*lambda + * == {a1 + b1*lambda == 0 mod n and a2 + b2*lambda == 0 mod n} + * k - c1*a1 - c2*a2 + * == {definition of k1} + * k1 + * + * From Lemma 3, Lemma 4, Lemma 5 and the definition of r2, we can conclude that + * + * - either r1 < 2^128 or -r1 mod n < 2^128 + * - either r2 < 2^128 or -r2 mod n < 2^128. + * + * Q.E.D. + */ +static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k) { + secp256k1_scalar s; + unsigned char buf1[32]; + unsigned char buf2[32]; + + /* (a1 + a2 + 1)/2 is 0xa2a8918ca85bafe22016d0b917e4dd77 */ + static const unsigned char k1_bound[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xa2, 0xa8, 0x91, 0x8c, 0xa8, 0x5b, 0xaf, 0xe2, 0x20, 0x16, 0xd0, 0xb9, 0x17, 0xe4, 0xdd, 0x77 + }; + + /* (-b1 + b2)/2 + 1 is 0x8a65287bd47179fb2be08846cea267ed */ + static const unsigned char k2_bound[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x8a, 0x65, 0x28, 0x7b, 0xd4, 0x71, 0x79, 0xfb, 0x2b, 0xe0, 0x88, 0x46, 0xce, 0xa2, 0x67, 0xed + }; + + secp256k1_scalar_mul(&s, &secp256k1_const_lambda, r2); + secp256k1_scalar_add(&s, &s, r1); + VERIFY_CHECK(secp256k1_scalar_eq(&s, k)); + + secp256k1_scalar_negate(&s, r1); + secp256k1_scalar_get_b32(buf1, r1); + secp256k1_scalar_get_b32(buf2, &s); + VERIFY_CHECK(secp256k1_memcmp_var(buf1, k1_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k1_bound, 32) < 0); + + secp256k1_scalar_negate(&s, r2); + secp256k1_scalar_get_b32(buf1, r2); + secp256k1_scalar_get_b32(buf2, &s); + VERIFY_CHECK(secp256k1_memcmp_var(buf1, k2_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k2_bound, 32) < 0); +} +#endif /* VERIFY */ +#endif /* !defined(EXHAUSTIVE_TEST_ORDER) */ + +#endif /* SECP256K1_SCALAR_IMPL_H */ diff --git a/src/secp256k1/src/scalar_low.h b/src/secp256k1/src/scalar_low.h new file mode 100644 index 0000000000..67051bd30b --- /dev/null +++ b/src/secp256k1/src/scalar_low.h @@ -0,0 +1,17 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include <stdint.h> + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef uint32_t secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) (d0) + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/src/secp256k1/src/scalar_low_impl.h b/src/secp256k1/src/scalar_low_impl.h new file mode 100644 index 0000000000..bfd1139110 --- /dev/null +++ b/src/secp256k1/src/scalar_low_impl.h @@ -0,0 +1,141 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +#include "checkmem.h" +#include "scalar.h" + +#include <string.h> + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(*a & 1); +} + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; } +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; } + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + if (offset < 32) + return ((*a >> offset) & ((((uint32_t)1) << count) - 1)); + else + return 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + return secp256k1_scalar_get_bits(a, offset, count); +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; } + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER; + return *r < *b; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + if (flag && bit < 32) + *r += ((uint32_t)1 << bit); +#ifdef VERIFY + VERIFY_CHECK(bit < 32); + /* Verify that adding (1 << bit) will not overflow any in-range scalar *r by overflowing the underlying uint32_t. */ + VERIFY_CHECK(((uint32_t)1 << bit) - 1 <= UINT32_MAX - EXHAUSTIVE_TEST_ORDER); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int i; + int over = 0; + *r = 0; + for (i = 0; i < 32; i++) { + *r = (*r * 0x100) + b32[i]; + if (*r >= EXHAUSTIVE_TEST_ORDER) { + over = 1; + *r %= EXHAUSTIVE_TEST_ORDER; + } + } + if (overflow) *overflow = over; +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + memset(bin, 0, 32); + bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return *a == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + if (*a == 0) { + *r = 0; + } else { + *r = EXHAUSTIVE_TEST_ORDER - *a; + } +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return *a == 1; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + return *a > EXHAUSTIVE_TEST_ORDER / 2; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + if (flag) secp256k1_scalar_negate(r, r); + return flag ? -1 : 1; +} + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER; +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = *r & ((1 << n) - 1); + *r >>= n; + return ret; +} + +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r1 = *a; + *r2 = 0; +} + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return *a == *b; +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint32_t mask0, mask1; + volatile int vflag = flag; + SECP256K1_CHECKMEM_CHECK_VERIFY(r, sizeof(*r)); + mask0 = vflag + ~((uint32_t)0); + mask1 = ~mask0; + *r = (*r & mask0) | (*a & mask1); +} + +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { + int i; + *r = 0; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) + if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1) + *r = i; + /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus + * have a composite group order; fix it in exhaustive_tests.c). */ + VERIFY_CHECK(*r != 0); +} + +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { + secp256k1_scalar_inverse(r, x); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/src/secp256k1/src/scratch.h b/src/secp256k1/src/scratch.h new file mode 100644 index 0000000000..9dcb7581f6 --- /dev/null +++ b/src/secp256k1/src/scratch.h @@ -0,0 +1,42 @@ +/*********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCRATCH_H +#define SECP256K1_SCRATCH_H + +/* The typedef is used internally; the struct name is used in the public API + * (where it is exposed as a different typedef) */ +typedef struct secp256k1_scratch_space_struct { + /** guard against interpreting this object as other types */ + unsigned char magic[8]; + /** actual allocated data */ + void *data; + /** amount that has been allocated (i.e. `data + offset` is the next + * available pointer) */ + size_t alloc_size; + /** maximum size available to allocate */ + size_t max_size; +} secp256k1_scratch; + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size); + +static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch); + +/** Returns an opaque object used to "checkpoint" a scratch space. Used + * with `secp256k1_scratch_apply_checkpoint` to undo allocations. */ +static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch); + +/** Applies a check point received from `secp256k1_scratch_checkpoint`, + * undoing all allocations since that point. */ +static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t checkpoint); + +/** Returns the maximum allocation the scratch space will allow */ +static size_t secp256k1_scratch_max_allocation(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch, size_t n_objects); + +/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */ +static void *secp256k1_scratch_alloc(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t n); + +#endif diff --git a/src/secp256k1/src/scratch_impl.h b/src/secp256k1/src/scratch_impl.h new file mode 100644 index 0000000000..f71a20b963 --- /dev/null +++ b/src/secp256k1/src/scratch_impl.h @@ -0,0 +1,99 @@ +/*********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SCRATCH_IMPL_H +#define SECP256K1_SCRATCH_IMPL_H + +#include "util.h" +#include "scratch.h" + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t size) { + const size_t base_alloc = ROUND_TO_ALIGN(sizeof(secp256k1_scratch)); + void *alloc = checked_malloc(error_callback, base_alloc + size); + secp256k1_scratch* ret = (secp256k1_scratch *)alloc; + if (ret != NULL) { + memset(ret, 0, sizeof(*ret)); + memcpy(ret->magic, "scratch", 8); + ret->data = (void *) ((char *) alloc + base_alloc); + ret->max_size = size; + } + return ret; +} + +static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch) { + if (scratch != NULL) { + if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return; + } + VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */ + memset(scratch->magic, 0, sizeof(scratch->magic)); + free(scratch); + } +} + +static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch) { + if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return 0; + } + return scratch->alloc_size; +} + +static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t checkpoint) { + if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return; + } + if (checkpoint > scratch->alloc_size) { + secp256k1_callback_call(error_callback, "invalid checkpoint"); + return; + } + scratch->alloc_size = checkpoint; +} + +static size_t secp256k1_scratch_max_allocation(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch, size_t objects) { + if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return 0; + } + /* Ensure that multiplication will not wrap around */ + if (ALIGNMENT > 1 && objects > SIZE_MAX/(ALIGNMENT - 1)) { + return 0; + } + if (scratch->max_size - scratch->alloc_size <= objects * (ALIGNMENT - 1)) { + return 0; + } + return scratch->max_size - scratch->alloc_size - objects * (ALIGNMENT - 1); +} + +static void *secp256k1_scratch_alloc(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t size) { + void *ret; + size_t rounded_size; + + rounded_size = ROUND_TO_ALIGN(size); + /* Check that rounding did not wrap around */ + if (rounded_size < size) { + return NULL; + } + size = rounded_size; + + if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return NULL; + } + + if (size > scratch->max_size - scratch->alloc_size) { + return NULL; + } + ret = (void *) ((char *) scratch->data + scratch->alloc_size); + memset(ret, 0, size); + scratch->alloc_size += size; + + return ret; +} + +#endif diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c new file mode 100644 index 0000000000..7af333ca90 --- /dev/null +++ b/src/secp256k1/src/secp256k1.c @@ -0,0 +1,813 @@ +/*********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/* This is a C project. It should not be compiled with a C++ compiler, + * and we error out if we detect one. + * + * We still want to be able to test the project with a C++ compiler + * because it is still good to know if this will lead to real trouble, so + * there is a possibility to override the check. But be warned that + * compiling with a C++ compiler is not supported. */ +#if defined(__cplusplus) && !defined(SECP256K1_CPLUSPLUS_TEST_OVERRIDE) +#error Trying to compile a C project with a C++ compiler. +#endif + +#define SECP256K1_BUILD + +#include "../include/secp256k1.h" +#include "../include/secp256k1_preallocated.h" + +#include "assumptions.h" +#include "checkmem.h" +#include "util.h" + +#include "field_impl.h" +#include "scalar_impl.h" +#include "group_impl.h" +#include "ecmult_impl.h" +#include "ecmult_const_impl.h" +#include "ecmult_gen_impl.h" +#include "ecdsa_impl.h" +#include "eckey_impl.h" +#include "hash_impl.h" +#include "int128_impl.h" +#include "scratch_impl.h" +#include "selftest.h" + +#ifdef SECP256K1_NO_BUILD +# error "secp256k1.h processed without SECP256K1_BUILD defined while building secp256k1.c" +#endif + +#define ARG_CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + secp256k1_callback_call(&ctx->illegal_callback, #cond); \ + return 0; \ + } \ +} while(0) + +#define ARG_CHECK_VOID(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + secp256k1_callback_call(&ctx->illegal_callback, #cond); \ + return; \ + } \ +} while(0) + +/* Note that whenever you change the context struct, you must also change the + * context_eq function. */ +struct secp256k1_context_struct { + secp256k1_ecmult_gen_context ecmult_gen_ctx; + secp256k1_callback illegal_callback; + secp256k1_callback error_callback; + int declassify; +}; + +static const secp256k1_context secp256k1_context_static_ = { + { 0 }, + { secp256k1_default_illegal_callback_fn, 0 }, + { secp256k1_default_error_callback_fn, 0 }, + 0 +}; +const secp256k1_context *secp256k1_context_static = &secp256k1_context_static_; +const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_static_; + +/* Helper function that determines if a context is proper, i.e., is not the static context or a copy thereof. + * + * This is intended for "context" functions such as secp256k1_context_clone. Function which need specific + * features of a context should still check for these features directly. For example, a function that needs + * ecmult_gen should directly check for the existence of the ecmult_gen context. */ +static int secp256k1_context_is_proper(const secp256k1_context* ctx) { + return secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx); +} + +void secp256k1_selftest(void) { + if (!secp256k1_selftest_passes()) { + secp256k1_callback_call(&default_error_callback, "self test failed"); + } +} + +size_t secp256k1_context_preallocated_size(unsigned int flags) { + size_t ret = sizeof(secp256k1_context); + /* A return value of 0 is reserved as an indicator for errors when we call this function internally. */ + VERIFY_CHECK(ret != 0); + + if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) { + secp256k1_callback_call(&default_illegal_callback, + "Invalid flags"); + return 0; + } + + if (EXPECT(!SECP256K1_CHECKMEM_RUNNING() && (flags & SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY), 0)) { + secp256k1_callback_call(&default_illegal_callback, + "Declassify flag requires running with memory checking"); + return 0; + } + + return ret; +} + +size_t secp256k1_context_preallocated_clone_size(const secp256k1_context* ctx) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_context_is_proper(ctx)); + return sizeof(secp256k1_context); +} + +secp256k1_context* secp256k1_context_preallocated_create(void* prealloc, unsigned int flags) { + size_t prealloc_size; + secp256k1_context* ret; + + secp256k1_selftest(); + + prealloc_size = secp256k1_context_preallocated_size(flags); + if (prealloc_size == 0) { + return NULL; + } + VERIFY_CHECK(prealloc != NULL); + ret = (secp256k1_context*)prealloc; + ret->illegal_callback = default_illegal_callback; + ret->error_callback = default_error_callback; + + /* Flags have been checked by secp256k1_context_preallocated_size. */ + VERIFY_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_CONTEXT); + secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx); + ret->declassify = !!(flags & SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY); + + return ret; +} + +secp256k1_context* secp256k1_context_create(unsigned int flags) { + size_t const prealloc_size = secp256k1_context_preallocated_size(flags); + secp256k1_context* ctx = (secp256k1_context*)checked_malloc(&default_error_callback, prealloc_size); + if (EXPECT(secp256k1_context_preallocated_create(ctx, flags) == NULL, 0)) { + free(ctx); + return NULL; + } + + return ctx; +} + +secp256k1_context* secp256k1_context_preallocated_clone(const secp256k1_context* ctx, void* prealloc) { + secp256k1_context* ret; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(prealloc != NULL); + ARG_CHECK(secp256k1_context_is_proper(ctx)); + + ret = (secp256k1_context*)prealloc; + *ret = *ctx; + return ret; +} + +secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) { + secp256k1_context* ret; + size_t prealloc_size; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_context_is_proper(ctx)); + + prealloc_size = secp256k1_context_preallocated_clone_size(ctx); + ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, prealloc_size); + ret = secp256k1_context_preallocated_clone(ctx, ret); + return ret; +} + +void secp256k1_context_preallocated_destroy(secp256k1_context* ctx) { + ARG_CHECK_VOID(ctx == NULL || secp256k1_context_is_proper(ctx)); + + /* Defined as noop */ + if (ctx == NULL) { + return; + } + + secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx); +} + +void secp256k1_context_destroy(secp256k1_context* ctx) { + ARG_CHECK_VOID(ctx == NULL || secp256k1_context_is_proper(ctx)); + + /* Defined as noop */ + if (ctx == NULL) { + return; + } + + secp256k1_context_preallocated_destroy(ctx); + free(ctx); +} + +void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + /* We compare pointers instead of checking secp256k1_context_is_proper() here + because setting callbacks is allowed on *copies* of the static context: + it's harmless and makes testing easier. */ + ARG_CHECK_VOID(ctx != secp256k1_context_static); + if (fun == NULL) { + fun = secp256k1_default_illegal_callback_fn; + } + ctx->illegal_callback.fn = fun; + ctx->illegal_callback.data = data; +} + +void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + /* We compare pointers instead of checking secp256k1_context_is_proper() here + because setting callbacks is allowed on *copies* of the static context: + it's harmless and makes testing easier. */ + ARG_CHECK_VOID(ctx != secp256k1_context_static); + if (fun == NULL) { + fun = secp256k1_default_error_callback_fn; + } + ctx->error_callback.fn = fun; + ctx->error_callback.data = data; +} + +secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) { + VERIFY_CHECK(ctx != NULL); + return secp256k1_scratch_create(&ctx->error_callback, max_size); +} + +void secp256k1_scratch_space_destroy(const secp256k1_context *ctx, secp256k1_scratch_space* scratch) { + VERIFY_CHECK(ctx != NULL); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); +} + +/* Mark memory as no-longer-secret for the purpose of analysing constant-time behaviour + * of the software. + */ +static SECP256K1_INLINE void secp256k1_declassify(const secp256k1_context* ctx, const void *p, size_t len) { + if (EXPECT(ctx->declassify, 0)) SECP256K1_CHECKMEM_DEFINE(p, len); +} + +static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) { + if (sizeof(secp256k1_ge_storage) == 64) { + /* When the secp256k1_ge_storage type is exactly 64 byte, use its + * representation inside secp256k1_pubkey, as conversion is very fast. + * Note that secp256k1_pubkey_save must use the same representation. */ + secp256k1_ge_storage s; + memcpy(&s, &pubkey->data[0], sizeof(s)); + secp256k1_ge_from_storage(ge, &s); + } else { + /* Otherwise, fall back to 32-byte big endian for X and Y. */ + secp256k1_fe x, y; + secp256k1_fe_set_b32(&x, pubkey->data); + secp256k1_fe_set_b32(&y, pubkey->data + 32); + secp256k1_ge_set_xy(ge, &x, &y); + } + ARG_CHECK(!secp256k1_fe_is_zero(&ge->x)); + return 1; +} + +static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) { + if (sizeof(secp256k1_ge_storage) == 64) { + secp256k1_ge_storage s; + secp256k1_ge_to_storage(&s, ge); + memcpy(&pubkey->data[0], &s, sizeof(s)); + } else { + VERIFY_CHECK(!secp256k1_ge_is_infinity(ge)); + secp256k1_fe_normalize_var(&ge->x); + secp256k1_fe_normalize_var(&ge->y); + secp256k1_fe_get_b32(pubkey->data, &ge->x); + secp256k1_fe_get_b32(pubkey->data + 32, &ge->y); + } +} + +int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) { + secp256k1_ge Q; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(input != NULL); + if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) { + return 0; + } + if (!secp256k1_ge_is_in_correct_subgroup(&Q)) { + return 0; + } + secp256k1_pubkey_save(pubkey, &Q); + secp256k1_ge_clear(&Q); + return 1; +} + +int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) { + secp256k1_ge Q; + size_t len; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33u : 65u)); + len = *outputlen; + *outputlen = 0; + ARG_CHECK(output != NULL); + memset(output, 0, len); + ARG_CHECK(pubkey != NULL); + ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION); + if (secp256k1_pubkey_load(ctx, &Q, pubkey)) { + ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION); + if (ret) { + *outputlen = len; + } + } + return ret; +} + +int secp256k1_ec_pubkey_cmp(const secp256k1_context* ctx, const secp256k1_pubkey* pubkey0, const secp256k1_pubkey* pubkey1) { + unsigned char out[2][33]; + const secp256k1_pubkey* pk[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + pk[0] = pubkey0; pk[1] = pubkey1; + for (i = 0; i < 2; i++) { + size_t out_size = sizeof(out[i]); + /* If the public key is NULL or invalid, ec_pubkey_serialize will call + * the illegal_callback and return 0. In that case we will serialize the + * key as all zeros which is less than any valid public key. This + * results in consistent comparisons even if NULL or invalid pubkeys are + * involved and prevents edge cases such as sorting algorithms that use + * this function and do not terminate as a result. */ + if (!secp256k1_ec_pubkey_serialize(ctx, out[i], &out_size, pk[i], SECP256K1_EC_COMPRESSED)) { + /* Note that ec_pubkey_serialize should already set the output to + * zero in that case, but it's not guaranteed by the API, we can't + * test it and writing a VERIFY_CHECK is more complex than + * explicitly memsetting (again). */ + memset(out[i], 0, sizeof(out[i])); + } + } + return secp256k1_memcmp_var(out[0], out[1], sizeof(out[0])); +} + +static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) { + (void)ctx; + if (sizeof(secp256k1_scalar) == 32) { + /* When the secp256k1_scalar type is exactly 32 byte, use its + * representation inside secp256k1_ecdsa_signature, as conversion is very fast. + * Note that secp256k1_ecdsa_signature_save must use the same representation. */ + memcpy(r, &sig->data[0], 32); + memcpy(s, &sig->data[32], 32); + } else { + secp256k1_scalar_set_b32(r, &sig->data[0], NULL); + secp256k1_scalar_set_b32(s, &sig->data[32], NULL); + } +} + +static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) { + if (sizeof(secp256k1_scalar) == 32) { + memcpy(&sig->data[0], r, 32); + memcpy(&sig->data[32], s, 32); + } else { + secp256k1_scalar_get_b32(&sig->data[0], r); + secp256k1_scalar_get_b32(&sig->data[32], s); + } +} + +int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input != NULL); + + if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + return 1; + } else { + memset(sig, 0, sizeof(*sig)); + return 0; + } +} + +int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) { + secp256k1_scalar r, s; + int ret = 1; + int overflow = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input64 != NULL); + + secp256k1_scalar_set_b32(&r, &input64[0], &overflow); + ret &= !overflow; + secp256k1_scalar_set_b32(&s, &input64[32], &overflow); + ret &= !overflow; + if (ret) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + } else { + memset(sig, 0, sizeof(*sig)); + } + return ret; +} + +int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s); +} + +int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output64 != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + secp256k1_scalar_get_b32(&output64[0], &r); + secp256k1_scalar_get_b32(&output64[32], &s); + return 1; +} + +int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) { + secp256k1_scalar r, s; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sigin != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin); + ret = secp256k1_scalar_is_high(&s); + if (sigout != NULL) { + if (ret) { + secp256k1_scalar_negate(&s, &s); + } + secp256k1_ecdsa_signature_save(sigout, &r, &s); + } + + return ret; +} + +int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msghash32, const secp256k1_pubkey *pubkey) { + secp256k1_ge q; + secp256k1_scalar r, s; + secp256k1_scalar m; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(msghash32 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(pubkey != NULL); + + secp256k1_scalar_set_b32(&m, msghash32, NULL); + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return (!secp256k1_scalar_is_high(&s) && + secp256k1_pubkey_load(ctx, &q, pubkey) && + secp256k1_ecdsa_sig_verify(&r, &s, &q, &m)); +} + +static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *offset, const void *data, unsigned int len) { + memcpy(buf + *offset, data, len); + *offset += len; +} + +static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + unsigned char keydata[112]; + unsigned int offset = 0; + secp256k1_rfc6979_hmac_sha256 rng; + unsigned int i; + secp256k1_scalar msg; + unsigned char msgmod32[32]; + secp256k1_scalar_set_b32(&msg, msg32, NULL); + secp256k1_scalar_get_b32(msgmod32, &msg); + /* We feed a byte array to the PRNG as input, consisting of: + * - the private key (32 bytes) and reduced message (32 bytes), see RFC 6979 3.2d. + * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data. + * - optionally 16 extra bytes with the algorithm name. + * Because the arguments have distinct fixed lengths it is not possible for + * different argument mixtures to emulate each other and result in the same + * nonces. + */ + buffer_append(keydata, &offset, key32, 32); + buffer_append(keydata, &offset, msgmod32, 32); + if (data != NULL) { + buffer_append(keydata, &offset, data, 32); + } + if (algo16 != NULL) { + buffer_append(keydata, &offset, algo16, 16); + } + secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, offset); + memset(keydata, 0, sizeof(keydata)); + for (i = 0; i <= counter; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + return 1; +} + +const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979; +const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979; + +static int secp256k1_ecdsa_sign_inner(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar sec, non, msg; + int ret = 0; + int is_sec_valid; + unsigned char nonce32[32]; + unsigned int count = 0; + /* Default initialization here is important so we won't pass uninit values to the cmov in the end */ + *r = secp256k1_scalar_zero; + *s = secp256k1_scalar_zero; + if (recid) { + *recid = 0; + } + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_default; + } + + /* Fail if the secret key is invalid. */ + is_sec_valid = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_one, !is_sec_valid); + secp256k1_scalar_set_b32(&msg, msg32, NULL); + while (1) { + int is_nonce_valid; + ret = !!noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count); + if (!ret) { + break; + } + is_nonce_valid = secp256k1_scalar_set_b32_seckey(&non, nonce32); + /* The nonce is still secret here, but it being invalid is is less likely than 1:2^255. */ + secp256k1_declassify(ctx, &is_nonce_valid, sizeof(is_nonce_valid)); + if (is_nonce_valid) { + ret = secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, r, s, &sec, &msg, &non, recid); + /* The final signature is no longer a secret, nor is the fact that we were successful or not. */ + secp256k1_declassify(ctx, &ret, sizeof(ret)); + if (ret) { + break; + } + } + count++; + } + /* We don't want to declassify is_sec_valid and therefore the range of + * seckey. As a result is_sec_valid is included in ret only after ret was + * used as a branching variable. */ + ret &= is_sec_valid; + memset(nonce32, 0, 32); + secp256k1_scalar_clear(&msg); + secp256k1_scalar_clear(&non); + secp256k1_scalar_clear(&sec); + secp256k1_scalar_cmov(r, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_cmov(s, &secp256k1_scalar_zero, !ret); + if (recid) { + const int zero = 0; + secp256k1_int_cmov(recid, &zero, !ret); + } + return ret; +} + +int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msghash32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar r, s; + int ret; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(msghash32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_ecdsa_sign_inner(ctx, &r, &s, NULL, msghash32, seckey, noncefp, noncedata); + secp256k1_ecdsa_signature_save(signature, &r, &s); + return ret; +} + +int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) { + secp256k1_scalar sec; + int ret; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_clear(&sec); + return ret; +} + +static int secp256k1_ec_pubkey_create_helper(const secp256k1_ecmult_gen_context *ecmult_gen_ctx, secp256k1_scalar *seckey_scalar, secp256k1_ge *p, const unsigned char *seckey) { + secp256k1_gej pj; + int ret; + + ret = secp256k1_scalar_set_b32_seckey(seckey_scalar, seckey); + secp256k1_scalar_cmov(seckey_scalar, &secp256k1_scalar_one, !ret); + + secp256k1_ecmult_gen(ecmult_gen_ctx, &pj, seckey_scalar); + secp256k1_ge_set_gej(p, &pj); + return ret; +} + +int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) { + secp256k1_ge p; + secp256k1_scalar seckey_scalar; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &seckey_scalar, &p, seckey); + secp256k1_pubkey_save(pubkey, &p); + secp256k1_memczero(pubkey, sizeof(*pubkey), !ret); + + secp256k1_scalar_clear(&seckey_scalar); + return ret; +} + +int secp256k1_ec_seckey_negate(const secp256k1_context* ctx, unsigned char *seckey) { + secp256k1_scalar sec; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_negate(&sec, &sec); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) { + return secp256k1_ec_seckey_negate(ctx, seckey); +} + +int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *pubkey) { + int ret = 0; + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + + ret = secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + secp256k1_ge_neg(&p, &p); + secp256k1_pubkey_save(pubkey, &p); + } + return ret; +} + + +static int secp256k1_ec_seckey_tweak_add_helper(secp256k1_scalar *sec, const unsigned char *tweak32) { + secp256k1_scalar term; + int overflow = 0; + int ret = 0; + + secp256k1_scalar_set_b32(&term, tweak32, &overflow); + ret = (!overflow) & secp256k1_eckey_privkey_tweak_add(sec, &term); + secp256k1_scalar_clear(&term); + return ret; +} + +int secp256k1_ec_seckey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak32) { + secp256k1_scalar sec; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak32 != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + ret &= secp256k1_ec_seckey_tweak_add_helper(&sec, tweak32); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak32) { + return secp256k1_ec_seckey_tweak_add(ctx, seckey, tweak32); +} + +static int secp256k1_ec_pubkey_tweak_add_helper(secp256k1_ge *p, const unsigned char *tweak32) { + secp256k1_scalar term; + int overflow = 0; + secp256k1_scalar_set_b32(&term, tweak32, &overflow); + return !overflow && secp256k1_eckey_pubkey_tweak_add(p, &term); +} + +int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak32) { + secp256k1_ge p; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak32 != NULL); + + ret = secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + ret = ret && secp256k1_ec_pubkey_tweak_add_helper(&p, tweak32); + if (ret) { + secp256k1_pubkey_save(pubkey, &p); + } + + return ret; +} + +int secp256k1_ec_seckey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak32) { + secp256k1_scalar factor; + secp256k1_scalar sec; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak32 != NULL); + + secp256k1_scalar_set_b32(&factor, tweak32, &overflow); + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + ret &= (!overflow) & secp256k1_eckey_privkey_tweak_mul(&sec, &factor); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&factor); + return ret; +} + +int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak32) { + return secp256k1_ec_seckey_tweak_mul(ctx, seckey, tweak32); +} + +int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak32) { + secp256k1_ge p; + secp256k1_scalar factor; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak32 != NULL); + + secp256k1_scalar_set_b32(&factor, tweak32, &overflow); + ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + if (secp256k1_eckey_pubkey_tweak_mul(&p, &factor)) { + secp256k1_pubkey_save(pubkey, &p); + } else { + ret = 0; + } + } + + return ret; +} + +int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_context_is_proper(ctx)); + + if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) { + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32); + } + return 1; +} + +int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) { + size_t i; + secp256k1_gej Qj; + secp256k1_ge Q; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubnonce != NULL); + memset(pubnonce, 0, sizeof(*pubnonce)); + ARG_CHECK(n >= 1); + ARG_CHECK(pubnonces != NULL); + + secp256k1_gej_set_infinity(&Qj); + + for (i = 0; i < n; i++) { + ARG_CHECK(pubnonces[i] != NULL); + secp256k1_pubkey_load(ctx, &Q, pubnonces[i]); + secp256k1_gej_add_ge(&Qj, &Qj, &Q); + } + if (secp256k1_gej_is_infinity(&Qj)) { + return 0; + } + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(pubnonce, &Q); + return 1; +} + +int secp256k1_tagged_sha256(const secp256k1_context* ctx, unsigned char *hash32, const unsigned char *tag, size_t taglen, const unsigned char *msg, size_t msglen) { + secp256k1_sha256 sha; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(hash32 != NULL); + ARG_CHECK(tag != NULL); + ARG_CHECK(msg != NULL); + + secp256k1_sha256_initialize_tagged(&sha, tag, taglen); + secp256k1_sha256_write(&sha, msg, msglen); + secp256k1_sha256_finalize(&sha, hash32); + return 1; +} + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/main_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/main_impl.h" +#endif + +#ifdef ENABLE_MODULE_EXTRAKEYS +# include "modules/extrakeys/main_impl.h" +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG +# include "modules/schnorrsig/main_impl.h" +#endif diff --git a/src/secp256k1/src/selftest.h b/src/secp256k1/src/selftest.h new file mode 100644 index 0000000000..d083ac9524 --- /dev/null +++ b/src/secp256k1/src/selftest.h @@ -0,0 +1,32 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_SELFTEST_H +#define SECP256K1_SELFTEST_H + +#include "hash.h" + +#include <string.h> + +static int secp256k1_selftest_sha256(void) { + static const char *input63 = "For this sample, this 63-byte string will be used as input data"; + static const unsigned char output32[32] = { + 0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, + 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42, + }; + unsigned char out[32]; + secp256k1_sha256 hasher; + secp256k1_sha256_initialize(&hasher); + secp256k1_sha256_write(&hasher, (const unsigned char*)input63, 63); + secp256k1_sha256_finalize(&hasher, out); + return secp256k1_memcmp_var(out, output32, 32) == 0; +} + +static int secp256k1_selftest_passes(void) { + return secp256k1_selftest_sha256(); +} + +#endif /* SECP256K1_SELFTEST_H */ diff --git a/src/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h new file mode 100644 index 0000000000..d109bb9f8b --- /dev/null +++ b/src/secp256k1/src/testrand.h @@ -0,0 +1,46 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_TESTRAND_H +#define SECP256K1_TESTRAND_H + +/* A non-cryptographic RNG used only for test infrastructure. */ + +/** Seed the pseudorandom number generator for testing. */ +SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16); + +/** Generate a pseudorandom number in the range [0..2**32-1]. */ +SECP256K1_INLINE static uint32_t secp256k1_testrand32(void); + +/** Generate a pseudorandom number in the range [0..2**64-1]. */ +SECP256K1_INLINE static uint64_t secp256k1_testrand64(void); + +/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or + * more. */ +SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits); + +/** Generate a pseudorandom number in the range [0..range-1]. */ +static uint32_t secp256k1_testrand_int(uint32_t range); + +/** Generate a pseudorandom 32-byte array. */ +static void secp256k1_testrand256(unsigned char *b32); + +/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */ +static void secp256k1_testrand256_test(unsigned char *b32); + +/** Generate pseudorandom bytes with long sequences of zero and one bits. */ +static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len); + +/** Flip a single random bit in a byte array */ +static void secp256k1_testrand_flip(unsigned char *b, size_t len); + +/** Initialize the test RNG using (hex encoded) array up to 16 bytes, or randomly if hexseed is NULL. */ +static void secp256k1_testrand_init(const char* hexseed); + +/** Print final test information. */ +static void secp256k1_testrand_finish(void); + +#endif /* SECP256K1_TESTRAND_H */ diff --git a/src/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h new file mode 100644 index 0000000000..e9b9d7ded4 --- /dev/null +++ b/src/secp256k1/src/testrand_impl.h @@ -0,0 +1,197 @@ +/*********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_TESTRAND_IMPL_H +#define SECP256K1_TESTRAND_IMPL_H + +#include <stdint.h> +#include <stdio.h> +#include <string.h> + +#include "testrand.h" +#include "hash.h" + +static uint64_t secp256k1_test_state[4]; +static uint64_t secp256k1_test_rng_integer; +static int secp256k1_test_rng_integer_bits_left = 0; + +SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16) { + static const unsigned char PREFIX[19] = "secp256k1 test init"; + unsigned char out32[32]; + secp256k1_sha256 hash; + int i; + + /* Use SHA256(PREFIX || seed16) as initial state. */ + secp256k1_sha256_initialize(&hash); + secp256k1_sha256_write(&hash, PREFIX, sizeof(PREFIX)); + secp256k1_sha256_write(&hash, seed16, 16); + secp256k1_sha256_finalize(&hash, out32); + for (i = 0; i < 4; ++i) { + uint64_t s = 0; + int j; + for (j = 0; j < 8; ++j) s = (s << 8) | out32[8*i + j]; + secp256k1_test_state[i] = s; + } + secp256k1_test_rng_integer_bits_left = 0; +} + +SECP256K1_INLINE static uint64_t rotl(const uint64_t x, int k) { + return (x << k) | (x >> (64 - k)); +} + +SECP256K1_INLINE static uint64_t secp256k1_testrand64(void) { + /* Test-only Xoshiro256++ RNG. See https://prng.di.unimi.it/ */ + const uint64_t result = rotl(secp256k1_test_state[0] + secp256k1_test_state[3], 23) + secp256k1_test_state[0]; + const uint64_t t = secp256k1_test_state[1] << 17; + secp256k1_test_state[2] ^= secp256k1_test_state[0]; + secp256k1_test_state[3] ^= secp256k1_test_state[1]; + secp256k1_test_state[1] ^= secp256k1_test_state[2]; + secp256k1_test_state[0] ^= secp256k1_test_state[3]; + secp256k1_test_state[2] ^= t; + secp256k1_test_state[3] = rotl(secp256k1_test_state[3], 45); + return result; +} + +SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits) { + uint64_t ret; + if (secp256k1_test_rng_integer_bits_left < bits) { + secp256k1_test_rng_integer = secp256k1_testrand64(); + secp256k1_test_rng_integer_bits_left = 64; + } + ret = secp256k1_test_rng_integer; + secp256k1_test_rng_integer >>= bits; + secp256k1_test_rng_integer_bits_left -= bits; + ret &= ((~((uint64_t)0)) >> (64 - bits)); + return ret; +} + +SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) { + return secp256k1_testrand_bits(32); +} + +static uint32_t secp256k1_testrand_int(uint32_t range) { + /* We want a uniform integer between 0 and range-1, inclusive. + * B is the smallest number such that range <= 2**B. + * two mechanisms implemented here: + * - generate B bits numbers until one below range is found, and return it + * - find the largest multiple M of range that is <= 2**(B+A), generate B+A + * bits numbers until one below M is found, and return it modulo range + * The second mechanism consumes A more bits of entropy in every iteration, + * but may need fewer iterations due to M being closer to 2**(B+A) then + * range is to 2**B. The array below (indexed by B) contains a 0 when the + * first mechanism is to be used, and the number A otherwise. + */ + static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0}; + uint32_t trange, mult; + int bits = 0; + if (range <= 1) { + return 0; + } + trange = range - 1; + while (trange > 0) { + trange >>= 1; + bits++; + } + if (addbits[bits]) { + bits = bits + addbits[bits]; + mult = ((~((uint32_t)0)) >> (32 - bits)) / range; + trange = range * mult; + } else { + trange = range; + mult = 1; + } + while(1) { + uint32_t x = secp256k1_testrand_bits(bits); + if (x < trange) { + return (mult == 1) ? x : (x % range); + } + } +} + +static void secp256k1_testrand256(unsigned char *b32) { + int i; + for (i = 0; i < 4; ++i) { + uint64_t val = secp256k1_testrand64(); + b32[0] = val; + b32[1] = val >> 8; + b32[2] = val >> 16; + b32[3] = val >> 24; + b32[4] = val >> 32; + b32[5] = val >> 40; + b32[6] = val >> 48; + b32[7] = val >> 56; + b32 += 8; + } +} + +static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len) { + size_t bits = 0; + memset(bytes, 0, len); + while (bits < len * 8) { + int now; + uint32_t val; + now = 1 + (secp256k1_testrand_bits(6) * secp256k1_testrand_bits(5) + 16) / 31; + val = secp256k1_testrand_bits(1); + while (now > 0 && bits < len * 8) { + bytes[bits / 8] |= val << (bits % 8); + now--; + bits++; + } + } +} + +static void secp256k1_testrand256_test(unsigned char *b32) { + secp256k1_testrand_bytes_test(b32, 32); +} + +static void secp256k1_testrand_flip(unsigned char *b, size_t len) { + b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_bits(3)); +} + +static void secp256k1_testrand_init(const char* hexseed) { + unsigned char seed16[16] = {0}; + if (hexseed && strlen(hexseed) != 0) { + int pos = 0; + while (pos < 16 && hexseed[0] != 0 && hexseed[1] != 0) { + unsigned short sh; + if ((sscanf(hexseed, "%2hx", &sh)) == 1) { + seed16[pos] = sh; + } else { + break; + } + hexseed += 2; + pos++; + } + } else { + FILE *frand = fopen("/dev/urandom", "rb"); + if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) { + uint64_t t = time(NULL) * (uint64_t)1337; + fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n"); + seed16[0] ^= t; + seed16[1] ^= t >> 8; + seed16[2] ^= t >> 16; + seed16[3] ^= t >> 24; + seed16[4] ^= t >> 32; + seed16[5] ^= t >> 40; + seed16[6] ^= t >> 48; + seed16[7] ^= t >> 56; + } + if (frand) { + fclose(frand); + } + } + + printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]); + secp256k1_testrand_seed(seed16); +} + +static void secp256k1_testrand_finish(void) { + unsigned char run32[32]; + secp256k1_testrand256(run32); + printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]); +} + +#endif /* SECP256K1_TESTRAND_IMPL_H */ diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c new file mode 100644 index 0000000000..7f61f737c6 --- /dev/null +++ b/src/secp256k1/src/tests.c @@ -0,0 +1,7771 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <stdio.h> +#include <stdlib.h> +#include <string.h> + +#include <time.h> + +#include "secp256k1.c" +#include "../include/secp256k1.h" +#include "../include/secp256k1_preallocated.h" +#include "testrand_impl.h" +#include "checkmem.h" +#include "util.h" + +#include "../contrib/lax_der_parsing.c" +#include "../contrib/lax_der_privatekey_parsing.c" + +#include "modinv32_impl.h" +#ifdef SECP256K1_WIDEMUL_INT128 +#include "modinv64_impl.h" +#include "int128_impl.h" +#endif + +#define CONDITIONAL_TEST(cnt, nam) if (COUNT < (cnt)) { printf("Skipping %s (iteration count too low)\n", nam); } else + +static int COUNT = 64; +static secp256k1_context *CTX = NULL; +static secp256k1_context *STATIC_CTX = NULL; + +static int all_bytes_equal(const void* s, unsigned char value, size_t n) { + const unsigned char *p = s; + size_t i; + + for (i = 0; i < n; i++) { + if (p[i] != value) { + return 0; + } + } + return 1; +} + +/* TODO Use CHECK_ILLEGAL(_VOID) everywhere and get rid of the uncounting callback */ +/* CHECK that expr_or_stmt calls the illegal callback of ctx exactly once + * + * For checking functions that use ARG_CHECK_VOID */ +#define CHECK_ILLEGAL_VOID(ctx, expr_or_stmt) do { \ + int32_t _calls_to_illegal_callback = 0; \ + secp256k1_callback _saved_illegal_cb = ctx->illegal_callback; \ + secp256k1_context_set_illegal_callback(ctx, \ + counting_illegal_callback_fn, &_calls_to_illegal_callback); \ + { expr_or_stmt; } \ + ctx->illegal_callback = _saved_illegal_cb; \ + CHECK(_calls_to_illegal_callback == 1); \ +} while(0); + +/* CHECK that expr calls the illegal callback of ctx exactly once and that expr == 0 + * + * For checking functions that use ARG_CHECK */ +#define CHECK_ILLEGAL(ctx, expr) CHECK_ILLEGAL_VOID(ctx, CHECK((expr) == 0)) + +static void counting_illegal_callback_fn(const char* str, void* data) { + /* Dummy callback function that just counts. */ + int32_t *p; + (void)str; + p = data; + CHECK(*p != INT32_MAX); + (*p)++; +} + +static void uncounting_illegal_callback_fn(const char* str, void* data) { + /* Dummy callback function that just counts (backwards). */ + int32_t *p; + (void)str; + p = data; + CHECK(*p != INT32_MIN); + (*p)--; +} + +static void random_field_element_test(secp256k1_fe *fe) { + do { + unsigned char b32[32]; + secp256k1_testrand256_test(b32); + if (secp256k1_fe_set_b32(fe, b32)) { + break; + } + } while(1); +} + +static void random_field_element_magnitude(secp256k1_fe *fe) { + secp256k1_fe zero; + int n = secp256k1_testrand_int(9); + secp256k1_fe_normalize(fe); + if (n == 0) { + return; + } + secp256k1_fe_clear(&zero); + secp256k1_fe_negate(&zero, &zero, 0); + secp256k1_fe_mul_int(&zero, n - 1); + secp256k1_fe_add(fe, &zero); +#ifdef VERIFY + CHECK(fe->magnitude == n); +#endif +} + +static void random_group_element_test(secp256k1_ge *ge) { + secp256k1_fe fe; + do { + random_field_element_test(&fe); + if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_testrand_bits(1))) { + secp256k1_fe_normalize(&ge->y); + break; + } + } while(1); + ge->infinity = 0; +} + +static void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) { + secp256k1_fe z2, z3; + do { + random_field_element_test(&gej->z); + if (!secp256k1_fe_is_zero(&gej->z)) { + break; + } + } while(1); + secp256k1_fe_sqr(&z2, &gej->z); + secp256k1_fe_mul(&z3, &z2, &gej->z); + secp256k1_fe_mul(&gej->x, &ge->x, &z2); + secp256k1_fe_mul(&gej->y, &ge->y, &z3); + gej->infinity = ge->infinity; +} + +static void random_gej_test(secp256k1_gej *gej) { + secp256k1_ge ge; + random_group_element_test(&ge); + random_group_element_jacobian_test(gej, &ge); +} + +static void random_scalar_order_test(secp256k1_scalar *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_testrand256_test(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) { + continue; + } + break; + } while(1); +} + +static void random_scalar_order(secp256k1_scalar *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_testrand256(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) { + continue; + } + break; + } while(1); +} + +static void random_scalar_order_b32(unsigned char *b32) { + secp256k1_scalar num; + random_scalar_order(&num); + secp256k1_scalar_get_b32(b32, &num); +} + +static void run_selftest_tests(void) { + /* Test public API */ + secp256k1_selftest(); +} + +static int ecmult_gen_context_eq(const secp256k1_ecmult_gen_context *a, const secp256k1_ecmult_gen_context *b) { + return a->built == b->built + && secp256k1_scalar_eq(&a->blind, &b->blind) + && secp256k1_gej_eq_var(&a->initial, &b->initial); +} + +static int context_eq(const secp256k1_context *a, const secp256k1_context *b) { + return a->declassify == b->declassify + && ecmult_gen_context_eq(&a->ecmult_gen_ctx, &b->ecmult_gen_ctx) + && a->illegal_callback.fn == b->illegal_callback.fn + && a->illegal_callback.data == b->illegal_callback.data + && a->error_callback.fn == b->error_callback.fn + && a->error_callback.data == b->error_callback.data; +} + +static void run_deprecated_context_flags_test(void) { + /* Check that a context created with any of the flags in the flags array is + * identical to the NONE context. */ + unsigned int flags[] = { SECP256K1_CONTEXT_SIGN, + SECP256K1_CONTEXT_VERIFY, + SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY }; + secp256k1_context *none_ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + int i; + for (i = 0; i < (int)(sizeof(flags)/sizeof(flags[0])); i++) { + secp256k1_context *tmp_ctx; + CHECK(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE) == secp256k1_context_preallocated_size(flags[i])); + tmp_ctx = secp256k1_context_create(flags[i]); + CHECK(context_eq(none_ctx, tmp_ctx)); + secp256k1_context_destroy(tmp_ctx); + } + secp256k1_context_destroy(none_ctx); +} + +static void run_ec_illegal_argument_tests(void) { + int ecount = 0; + int ecount2 = 10; + secp256k1_pubkey pubkey; + secp256k1_pubkey zero_pubkey; + secp256k1_ecdsa_signature sig; + unsigned char ctmp[32]; + + /* Setup */ + secp256k1_context_set_illegal_callback(STATIC_CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount2); + memset(ctmp, 1, 32); + memset(&zero_pubkey, 0, sizeof(zero_pubkey)); + + /* Verify context-type checking illegal-argument errors. */ + CHECK(secp256k1_ec_pubkey_create(STATIC_CTX, &pubkey, ctmp) == 0); + CHECK(ecount == 1); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ecdsa_sign(STATIC_CTX, &sig, ctmp, ctmp, NULL, NULL) == 0); + CHECK(ecount == 2); + SECP256K1_CHECKMEM_UNDEFINE(&sig, sizeof(sig)); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, ctmp, ctmp, NULL, NULL) == 1); + SECP256K1_CHECKMEM_CHECK(&sig, sizeof(sig)); + CHECK(ecount2 == 10); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, ctmp, &pubkey) == 1); + CHECK(ecount2 == 10); + CHECK(secp256k1_ecdsa_verify(STATIC_CTX, &sig, ctmp, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp) == 1); + CHECK(ecount2 == 10); + CHECK(secp256k1_ec_pubkey_tweak_add(STATIC_CTX, &pubkey, ctmp) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, ctmp) == 1); + CHECK(ecount2 == 10); + CHECK(secp256k1_ec_pubkey_negate(STATIC_CTX, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_negate(STATIC_CTX, &zero_pubkey) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ec_pubkey_negate(CTX, NULL) == 0); + CHECK(ecount2 == 11); + CHECK(secp256k1_ec_pubkey_tweak_mul(STATIC_CTX, &pubkey, ctmp) == 1); + CHECK(ecount == 3); + + /* Clean up */ + secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL); + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); +} + +static void run_static_context_tests(int use_prealloc) { + /* Check that deprecated secp256k1_context_no_precomp is an alias to secp256k1_context_static. */ + CHECK(secp256k1_context_no_precomp == secp256k1_context_static); + + { + unsigned char seed[32] = {0x17}; + + /* Randomizing secp256k1_context_static is not supported. */ + CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_randomize(STATIC_CTX, seed)); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_randomize(STATIC_CTX, NULL)); + + /* Destroying or cloning secp256k1_context_static is not supported. */ + if (use_prealloc) { + CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_preallocated_clone_size(STATIC_CTX)); + { + secp256k1_context *my_static_ctx = malloc(sizeof(*STATIC_CTX)); + CHECK(my_static_ctx != NULL); + memset(my_static_ctx, 0x2a, sizeof(*my_static_ctx)); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_preallocated_clone(STATIC_CTX, my_static_ctx)); + CHECK(all_bytes_equal(my_static_ctx, 0x2a, sizeof(*my_static_ctx))); + free(my_static_ctx); + } + CHECK_ILLEGAL_VOID(STATIC_CTX, secp256k1_context_preallocated_destroy(STATIC_CTX)); + } else { + CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_clone(STATIC_CTX)); + CHECK_ILLEGAL_VOID(STATIC_CTX, secp256k1_context_destroy(STATIC_CTX)); + } + } + + { + /* Verify that setting and resetting illegal callback works */ + int32_t dummy = 0; + secp256k1_context_set_illegal_callback(STATIC_CTX, counting_illegal_callback_fn, &dummy); + CHECK(STATIC_CTX->illegal_callback.fn == counting_illegal_callback_fn); + CHECK(STATIC_CTX->illegal_callback.data == &dummy); + secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL); + CHECK(STATIC_CTX->illegal_callback.fn == secp256k1_default_illegal_callback_fn); + CHECK(STATIC_CTX->illegal_callback.data == NULL); + } +} + +static void run_proper_context_tests(int use_prealloc) { + int32_t dummy = 0; + secp256k1_context *my_ctx, *my_ctx_fresh; + void *my_ctx_prealloc = NULL; + unsigned char seed[32] = {0x17}; + + secp256k1_gej pubj; + secp256k1_ge pub; + secp256k1_scalar msg, key, nonce; + secp256k1_scalar sigr, sigs; + + /* Fresh reference context for comparison */ + my_ctx_fresh = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + + if (use_prealloc) { + my_ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + CHECK(my_ctx_prealloc != NULL); + my_ctx = secp256k1_context_preallocated_create(my_ctx_prealloc, SECP256K1_CONTEXT_NONE); + } else { + my_ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + } + + /* Randomize and reset randomization */ + CHECK(context_eq(my_ctx, my_ctx_fresh)); + CHECK(secp256k1_context_randomize(my_ctx, seed) == 1); + CHECK(!context_eq(my_ctx, my_ctx_fresh)); + CHECK(secp256k1_context_randomize(my_ctx, NULL) == 1); + CHECK(context_eq(my_ctx, my_ctx_fresh)); + + /* set error callback (to a function that still aborts in case malloc() fails in secp256k1_context_clone() below) */ + secp256k1_context_set_error_callback(my_ctx, secp256k1_default_illegal_callback_fn, NULL); + CHECK(my_ctx->error_callback.fn != secp256k1_default_error_callback_fn); + CHECK(my_ctx->error_callback.fn == secp256k1_default_illegal_callback_fn); + + /* check if sizes for cloning are consistent */ + CHECK(secp256k1_context_preallocated_clone_size(my_ctx) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + + /*** clone and destroy all of them to make sure cloning was complete ***/ + { + secp256k1_context *ctx_tmp; + + if (use_prealloc) { + /* clone into a non-preallocated context and then again into a new preallocated one. */ + ctx_tmp = my_ctx; + my_ctx = secp256k1_context_clone(my_ctx); + CHECK(context_eq(ctx_tmp, my_ctx)); + secp256k1_context_preallocated_destroy(ctx_tmp); + + free(my_ctx_prealloc); + my_ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + CHECK(my_ctx_prealloc != NULL); + ctx_tmp = my_ctx; + my_ctx = secp256k1_context_preallocated_clone(my_ctx, my_ctx_prealloc); + CHECK(context_eq(ctx_tmp, my_ctx)); + secp256k1_context_destroy(ctx_tmp); + } else { + /* clone into a preallocated context and then again into a new non-preallocated one. */ + void *prealloc_tmp; + + prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + CHECK(prealloc_tmp != NULL); + ctx_tmp = my_ctx; + my_ctx = secp256k1_context_preallocated_clone(my_ctx, prealloc_tmp); + CHECK(context_eq(ctx_tmp, my_ctx)); + secp256k1_context_destroy(ctx_tmp); + + ctx_tmp = my_ctx; + my_ctx = secp256k1_context_clone(my_ctx); + CHECK(context_eq(ctx_tmp, my_ctx)); + secp256k1_context_preallocated_destroy(ctx_tmp); + free(prealloc_tmp); + } + } + + /* Verify that the error callback makes it across the clone. */ + CHECK(my_ctx->error_callback.fn != secp256k1_default_error_callback_fn); + CHECK(my_ctx->error_callback.fn == secp256k1_default_illegal_callback_fn); + /* And that it resets back to default. */ + secp256k1_context_set_error_callback(my_ctx, NULL, NULL); + CHECK(my_ctx->error_callback.fn == secp256k1_default_error_callback_fn); + CHECK(context_eq(my_ctx, my_ctx_fresh)); + + /* Verify that setting and resetting illegal callback works */ + secp256k1_context_set_illegal_callback(my_ctx, counting_illegal_callback_fn, &dummy); + CHECK(my_ctx->illegal_callback.fn == counting_illegal_callback_fn); + CHECK(my_ctx->illegal_callback.data == &dummy); + secp256k1_context_set_illegal_callback(my_ctx, NULL, NULL); + CHECK(my_ctx->illegal_callback.fn == secp256k1_default_illegal_callback_fn); + CHECK(my_ctx->illegal_callback.data == NULL); + CHECK(context_eq(my_ctx, my_ctx_fresh)); + + /*** attempt to use them ***/ + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&my_ctx->ecmult_gen_ctx, &pubj, &key); + secp256k1_ge_set_gej(&pub, &pubj); + + /* obtain a working nonce */ + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(&my_ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); + + /* try signing */ + CHECK(secp256k1_ecdsa_sig_sign(&my_ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); + + /* try verifying */ + CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); + + /* cleanup */ + if (use_prealloc) { + secp256k1_context_preallocated_destroy(my_ctx); + free(my_ctx_prealloc); + } else { + secp256k1_context_destroy(my_ctx); + } + secp256k1_context_destroy(my_ctx_fresh); + + /* Defined as no-op. */ + secp256k1_context_destroy(NULL); + secp256k1_context_preallocated_destroy(NULL); +} + +static void run_scratch_tests(void) { + const size_t adj_alloc = ((500 + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT; + + int32_t ecount = 0; + size_t checkpoint; + size_t checkpoint_2; + secp256k1_scratch_space *scratch; + secp256k1_scratch_space local_scratch; + + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(CTX, counting_illegal_callback_fn, &ecount); + + /* Test public API */ + scratch = secp256k1_scratch_space_create(CTX, 1000); + CHECK(scratch != NULL); + CHECK(ecount == 0); + + /* Test internal API */ + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size == 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* Allocating 500 bytes succeeds */ + checkpoint = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch); + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500) != NULL); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000 - adj_alloc); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size != 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* Allocating another 501 bytes fails */ + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 501) == NULL); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000 - adj_alloc); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size != 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* ...but it succeeds once we apply the checkpoint to undo it */ + secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint); + CHECK(scratch->alloc_size == 0); + CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000); + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500) != NULL); + CHECK(scratch->alloc_size != 0); + + /* try to apply a bad checkpoint */ + checkpoint_2 = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch); + secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint); + CHECK(ecount == 0); + secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */ + CHECK(ecount == 1); + secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, (size_t) -1); /* this is just wildly invalid */ + CHECK(ecount == 2); + + /* try to use badly initialized scratch space */ + secp256k1_scratch_space_destroy(CTX, scratch); + memset(&local_scratch, 0, sizeof(local_scratch)); + scratch = &local_scratch; + CHECK(!secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0)); + CHECK(ecount == 3); + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500) == NULL); + CHECK(ecount == 4); + secp256k1_scratch_space_destroy(CTX, scratch); + CHECK(ecount == 5); + + /* Test that large integers do not wrap around in a bad way */ + scratch = secp256k1_scratch_space_create(CTX, 1000); + /* Try max allocation with a large number of objects. Only makes sense if + * ALIGNMENT is greater than 1 because otherwise the objects take no extra + * space. */ + CHECK(ALIGNMENT <= 1 || !secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, (SIZE_MAX / (ALIGNMENT - 1)) + 1)); + /* Try allocating SIZE_MAX to test wrap around which only happens if + * ALIGNMENT > 1, otherwise it returns NULL anyway because the scratch + * space is too small. */ + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, SIZE_MAX) == NULL); + secp256k1_scratch_space_destroy(CTX, scratch); + + /* cleanup */ + secp256k1_scratch_space_destroy(CTX, NULL); /* no-op */ + + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); + secp256k1_context_set_error_callback(CTX, NULL, NULL); +} + +static void run_ctz_tests(void) { + static const uint32_t b32[] = {1, 0xffffffff, 0x5e56968f, 0xe0d63129}; + static const uint64_t b64[] = {1, 0xffffffffffffffff, 0xbcd02462139b3fc3, 0x98b5f80c769693ef}; + int shift; + unsigned i; + for (i = 0; i < sizeof(b32) / sizeof(b32[0]); ++i) { + for (shift = 0; shift < 32; ++shift) { + CHECK(secp256k1_ctz32_var_debruijn(b32[i] << shift) == shift); + CHECK(secp256k1_ctz32_var(b32[i] << shift) == shift); + } + } + for (i = 0; i < sizeof(b64) / sizeof(b64[0]); ++i) { + for (shift = 0; shift < 64; ++shift) { + CHECK(secp256k1_ctz64_var_debruijn(b64[i] << shift) == shift); + CHECK(secp256k1_ctz64_var(b64[i] << shift) == shift); + } + } +} + +/***** HASH TESTS *****/ + +static void run_sha256_known_output_tests(void) { + static const char *inputs[] = { + "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe", + "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq", + "For this sample, this 63-byte string will be used as input data", + "This is exactly 64 bytes long, not counting the terminating byte", + "aaaaa", + }; + static const unsigned int repeat[] = { + 1, 1, 1, 1, 1, 1, 1, 1, 1000000/5 + }; + static const unsigned char outputs[][32] = { + {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}, + {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad}, + {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50}, + {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d}, + {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30}, + {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1}, + {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42}, + {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}, + {0xcd, 0xc7, 0x6e, 0x5c, 0x99, 0x14, 0xfb, 0x92, 0x81, 0xa1, 0xc7, 0xe2, 0x84, 0xd7, 0x3e, 0x67, 0xf1, 0x80, 0x9a, 0x48, 0xa4, 0x97, 0x20, 0x0e, 0x04, 0x6d, 0x39, 0xcc, 0xc7, 0x11, 0x2c, 0xd0}, + }; + unsigned int i, ninputs; + + /* Skip last input vector for low iteration counts */ + ninputs = sizeof(inputs)/sizeof(inputs[0]) - 1; + CONDITIONAL_TEST(16, "run_sha256_known_output_tests 1000000") ninputs++; + + for (i = 0; i < ninputs; i++) { + unsigned char out[32]; + secp256k1_sha256 hasher; + unsigned int j; + /* 1. Run: simply write the input bytestrings */ + j = repeat[i]; + secp256k1_sha256_initialize(&hasher); + while (j > 0) { + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + j--; + } + secp256k1_sha256_finalize(&hasher, out); + CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); + /* 2. Run: split the input bytestrings randomly before writing */ + if (strlen(inputs[i]) > 0) { + int split = secp256k1_testrand_int(strlen(inputs[i])); + secp256k1_sha256_initialize(&hasher); + j = repeat[i]; + while (j > 0) { + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + j--; + } + secp256k1_sha256_finalize(&hasher, out); + CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); + } + } +} + +/** SHA256 counter tests + +The tests verify that the SHA256 counter doesn't wrap around at message length +2^i bytes for i = 20, ..., 33. This wide range aims at being independent of the +implementation of the counter and it catches multiple natural 32-bit overflows +(e.g., counting bits, counting bytes, counting blocks, ...). + +The test vectors have been generated using following Python script which relies +on https://github.com/cloudtools/sha256/ (v0.3 on Python v3.10.2). + +``` +from sha256 import sha256 +from copy import copy + +def midstate_c_definition(hasher): + ret = ' {{0x' + hasher.state[0].hex('_', 4).replace('_', ', 0x') + '},\n' + ret += ' {0x00}, ' + str(hex(hasher.state[1])) + '}' + return ret + +def output_c_literal(hasher): + return '{0x' + hasher.digest().hex('_').replace('_', ', 0x') + '}' + +MESSAGE = b'abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno' +assert(len(MESSAGE) == 64) +BYTE_BOUNDARIES = [(2**b)//len(MESSAGE) - 1 for b in range(20, 34)] + +midstates = [] +digests = [] +hasher = sha256() +for i in range(BYTE_BOUNDARIES[-1] + 1): + if i in BYTE_BOUNDARIES: + midstates.append(midstate_c_definition(hasher)) + hasher_copy = copy(hasher) + hasher_copy.update(MESSAGE) + digests.append(output_c_literal(hasher_copy)) + hasher.update(MESSAGE) + +for x in midstates: + print(x + ',') + +for x in digests: + print(x + ',') +``` +*/ +static void run_sha256_counter_tests(void) { + static const char *input = "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno"; + static const secp256k1_sha256 midstates[] = { + {{0xa2b5c8bb, 0x26c88bb3, 0x2abdc3d2, 0x9def99a3, 0xdfd21a6e, 0x41fe585b, 0x7ef2c440, 0x2b79adda}, + {0x00}, 0xfffc0}, + {{0xa0d29445, 0x9287de66, 0x76aabd71, 0x41acd765, 0x0c7528b4, 0x84e14906, 0x942faec6, 0xcc5a7b26}, + {0x00}, 0x1fffc0}, + {{0x50449526, 0xb9f1d657, 0xa0fc13e9, 0x50860f10, 0xa550c431, 0x3fbc97c1, 0x7bbb2d89, 0xdb67bac1}, + {0x00}, 0x3fffc0}, + {{0x54a6efdc, 0x46762e7b, 0x88bfe73f, 0xbbd149c7, 0x41620c43, 0x1168da7b, 0x2c5960f9, 0xeccffda6}, + {0x00}, 0x7fffc0}, + {{0x2515a8f5, 0x5faa2977, 0x3a850486, 0xac858cad, 0x7b7276ee, 0x235c0385, 0xc53a157c, 0x7cb3e69c}, + {0x00}, 0xffffc0}, + {{0x34f39828, 0x409fedb7, 0x4bbdd0fb, 0x3b643634, 0x7806bf2e, 0xe0d1b713, 0xca3f2e1e, 0xe38722c2}, + {0x00}, 0x1ffffc0}, + {{0x389ef5c5, 0x38c54167, 0x8f5d56ab, 0x582a75cc, 0x8217caef, 0xf10947dd, 0x6a1998a8, 0x048f0b8c}, + {0x00}, 0x3ffffc0}, + {{0xd6c3f394, 0x0bee43b9, 0x6783f497, 0x29fa9e21, 0x6ce491c1, 0xa81fe45e, 0x2fc3859a, 0x269012d0}, + {0x00}, 0x7ffffc0}, + {{0x6dd3c526, 0x44d88aa0, 0x806a1bae, 0xfbcc0d32, 0x9d6144f3, 0x9d2bd757, 0x9851a957, 0xb50430ad}, + {0x00}, 0xfffffc0}, + {{0x2add4021, 0xdfe8a9e6, 0xa56317c6, 0x7a15f5bb, 0x4a48aacd, 0x5d368414, 0x4f00e6f0, 0xd9355023}, + {0x00}, 0x1fffffc0}, + {{0xb66666b4, 0xdbeac32b, 0x0ea351ae, 0xcba9da46, 0x6278b874, 0x8c508e23, 0xe16ca776, 0x8465bac1}, + {0x00}, 0x3fffffc0}, + {{0xb6744789, 0x9cce87aa, 0xc4c478b7, 0xf38404d8, 0x2e38ba62, 0xa3f7019b, 0x50458fe7, 0x3047dbec}, + {0x00}, 0x7fffffc0}, + {{0x8b1297ba, 0xba261a80, 0x2ba1b0dd, 0xfbc67d6d, 0x61072c4e, 0x4b5a2a0f, 0x52872760, 0x2dfeb162}, + {0x00}, 0xffffffc0}, + {{0x24f33cf7, 0x41ad6583, 0x41c8ff5d, 0xca7ef35f, 0x50395756, 0x021b743e, 0xd7126cd7, 0xd037473a}, + {0x00}, 0x1ffffffc0}, + }; + static const unsigned char outputs[][32] = { + {0x0e, 0x83, 0xe2, 0xc9, 0x4f, 0xb2, 0xb8, 0x2b, 0x89, 0x06, 0x92, 0x78, 0x04, 0x03, 0x48, 0x5c, 0x48, 0x44, 0x67, 0x61, 0x77, 0xa4, 0xc7, 0x90, 0x9e, 0x92, 0x55, 0x10, 0x05, 0xfe, 0x39, 0x15}, + {0x1d, 0x1e, 0xd7, 0xb8, 0xa3, 0xa7, 0x8a, 0x79, 0xfd, 0xa0, 0x05, 0x08, 0x9c, 0xeb, 0xf0, 0xec, 0x67, 0x07, 0x9f, 0x8e, 0x3c, 0x0d, 0x8e, 0xf9, 0x75, 0x55, 0x13, 0xc1, 0xe8, 0x77, 0xf8, 0xbb}, + {0x66, 0x95, 0x6c, 0xc9, 0xe0, 0x39, 0x65, 0xb6, 0xb0, 0x05, 0xd1, 0xaf, 0xaf, 0xf3, 0x1d, 0xb9, 0xa4, 0xda, 0x6f, 0x20, 0xcd, 0x3a, 0xae, 0x64, 0xc2, 0xdb, 0xee, 0xf5, 0xb8, 0x8d, 0x57, 0x0e}, + {0x3c, 0xbb, 0x1c, 0x12, 0x5e, 0x17, 0xfd, 0x54, 0x90, 0x45, 0xa7, 0x7b, 0x61, 0x6c, 0x1d, 0xfe, 0xe6, 0xcc, 0x7f, 0xee, 0xcf, 0xef, 0x33, 0x35, 0x50, 0x62, 0x16, 0x70, 0x2f, 0x87, 0xc3, 0xc9}, + {0x53, 0x4d, 0xa8, 0xe7, 0x1e, 0x98, 0x73, 0x8d, 0xd9, 0xa3, 0x54, 0xa5, 0x0e, 0x59, 0x2c, 0x25, 0x43, 0x6f, 0xaa, 0xa2, 0xf5, 0x21, 0x06, 0x3e, 0xc9, 0x82, 0x06, 0x94, 0x98, 0x72, 0x9d, 0xa7}, + {0xef, 0x7e, 0xe9, 0x6b, 0xd3, 0xe5, 0xb7, 0x41, 0x4c, 0xc8, 0xd3, 0x07, 0x52, 0x9a, 0x5a, 0x8b, 0x4e, 0x1e, 0x75, 0xa4, 0x17, 0x78, 0xc8, 0x36, 0xcd, 0xf8, 0x2e, 0xd9, 0x57, 0xe3, 0xd7, 0x07}, + {0x87, 0x16, 0xfb, 0xf9, 0xa5, 0xf8, 0xc4, 0x56, 0x2b, 0x48, 0x52, 0x8e, 0x2d, 0x30, 0x85, 0xb6, 0x4c, 0x56, 0xb5, 0xd1, 0x16, 0x9c, 0xcf, 0x32, 0x95, 0xad, 0x03, 0xe8, 0x05, 0x58, 0x06, 0x76}, + {0x75, 0x03, 0x80, 0x28, 0xf2, 0xa7, 0x63, 0x22, 0x1a, 0x26, 0x9c, 0x68, 0xe0, 0x58, 0xfc, 0x73, 0xeb, 0x42, 0xf6, 0x86, 0x16, 0x24, 0x4b, 0xbc, 0x24, 0xf7, 0x02, 0xc8, 0x3d, 0x90, 0xe2, 0xb0}, + {0xdf, 0x49, 0x0f, 0x15, 0x7b, 0x7d, 0xbf, 0xe0, 0xd4, 0xcf, 0x47, 0xc0, 0x80, 0x93, 0x4a, 0x61, 0xaa, 0x03, 0x07, 0x66, 0xb3, 0x38, 0x5d, 0xc8, 0xc9, 0x07, 0x61, 0xfb, 0x97, 0x10, 0x2f, 0xd8}, + {0x77, 0x19, 0x40, 0x56, 0x41, 0xad, 0xbc, 0x59, 0xda, 0x1e, 0xc5, 0x37, 0x14, 0x63, 0x7b, 0xfb, 0x79, 0xe2, 0x7a, 0xb1, 0x55, 0x42, 0x99, 0x42, 0x56, 0xfe, 0x26, 0x9d, 0x0f, 0x7e, 0x80, 0xc6}, + {0x50, 0xe7, 0x2a, 0x0e, 0x26, 0x44, 0x2f, 0xe2, 0x55, 0x2d, 0xc3, 0x93, 0x8a, 0xc5, 0x86, 0x58, 0x22, 0x8c, 0x0c, 0xbf, 0xb1, 0xd2, 0xca, 0x87, 0x2a, 0xe4, 0x35, 0x26, 0x6f, 0xcd, 0x05, 0x5e}, + {0xe4, 0x80, 0x6f, 0xdb, 0x3d, 0x7d, 0xba, 0xde, 0x50, 0x3f, 0xea, 0x00, 0x3d, 0x46, 0x59, 0x64, 0xfd, 0x58, 0x1c, 0xa1, 0xb8, 0x7d, 0x5f, 0xac, 0x94, 0x37, 0x9e, 0xa0, 0xc0, 0x9c, 0x93, 0x8b}, + {0x2c, 0xf3, 0xa9, 0xf6, 0x15, 0x25, 0x80, 0x70, 0x76, 0x99, 0x7d, 0xf1, 0xc3, 0x2f, 0xa3, 0x31, 0xff, 0x92, 0x35, 0x2e, 0x8d, 0x04, 0x13, 0x33, 0xd8, 0x0d, 0xdb, 0x4a, 0xf6, 0x8c, 0x03, 0x34}, + {0xec, 0x12, 0x24, 0x9f, 0x35, 0xa4, 0x29, 0x8b, 0x9e, 0x4a, 0x95, 0xf8, 0x61, 0xaf, 0x61, 0xc5, 0x66, 0x55, 0x3e, 0x3f, 0x2a, 0x98, 0xea, 0x71, 0x16, 0x6b, 0x1c, 0xd9, 0xe4, 0x09, 0xd2, 0x8e}, + }; + unsigned int i; + for (i = 0; i < sizeof(midstates)/sizeof(midstates[0]); i++) { + unsigned char out[32]; + secp256k1_sha256 hasher = midstates[i]; + secp256k1_sha256_write(&hasher, (const unsigned char*)input, strlen(input)); + secp256k1_sha256_finalize(&hasher, out); + CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); + } +} + +static void run_hmac_sha256_tests(void) { + static const char *keys[6] = { + "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b", + "\x4a\x65\x66\x65", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa" + }; + static const char *inputs[6] = { + "\x48\x69\x20\x54\x68\x65\x72\x65", + "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f", + "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd", + "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd", + "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74", + "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e" + }; + static const unsigned char outputs[6][32] = { + {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7}, + {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43}, + {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe}, + {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b}, + {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54}, + {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2} + }; + int i; + for (i = 0; i < 6; i++) { + secp256k1_hmac_sha256 hasher; + unsigned char out[32]; + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); + if (strlen(inputs[i]) > 0) { + int split = secp256k1_testrand_int(strlen(inputs[i])); + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); + } + } +} + +static void run_rfc6979_hmac_sha256_tests(void) { + static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0}; + static const unsigned char out1[3][32] = { + {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb}, + {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a}, + {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e} + }; + + static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}; + static const unsigned char out2[3][32] = { + {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95}, + {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9}, + {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94} + }; + + secp256k1_rfc6979_hmac_sha256 rng; + unsigned char out[32]; + int i; + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(secp256k1_memcmp_var(out, out1[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(secp256k1_memcmp_var(out, out1[i], 32) != 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(secp256k1_memcmp_var(out, out2[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); +} + +static void run_tagged_sha256_tests(void) { + int ecount = 0; + unsigned char tag[32] = { 0 }; + unsigned char msg[32] = { 0 }; + unsigned char hash32[32]; + unsigned char hash_expected[32] = { + 0x04, 0x7A, 0x5E, 0x17, 0xB5, 0x86, 0x47, 0xC1, + 0x3C, 0xC6, 0xEB, 0xC0, 0xAA, 0x58, 0x3B, 0x62, + 0xFB, 0x16, 0x43, 0x32, 0x68, 0x77, 0x40, 0x6C, + 0xE2, 0x76, 0x55, 0x9A, 0x3B, 0xDE, 0x55, 0xB3 + }; + + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + + /* API test */ + CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, sizeof(tag), msg, sizeof(msg)) == 1); + CHECK(secp256k1_tagged_sha256(CTX, NULL, tag, sizeof(tag), msg, sizeof(msg)) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_tagged_sha256(CTX, hash32, NULL, 0, msg, sizeof(msg)) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, sizeof(tag), NULL, 0) == 0); + CHECK(ecount == 3); + + /* Static test vector */ + memcpy(tag, "tag", 3); + memcpy(msg, "msg", 3); + CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, 3, msg, 3) == 1); + CHECK(secp256k1_memcmp_var(hash32, hash_expected, sizeof(hash32)) == 0); +} + +/***** RANDOM TESTS *****/ + +static void test_rand_bits(int rand32, int bits) { + /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to + * get a false negative chance below once in a billion */ + static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316}; + /* We try multiplying the results with various odd numbers, which shouldn't + * influence the uniform distribution modulo a power of 2. */ + static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011}; + /* We only select up to 6 bits from the output to analyse */ + unsigned int usebits = bits > 6 ? 6 : bits; + unsigned int maxshift = bits - usebits; + /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit + number, track all observed outcomes, one per bit in a uint64_t. */ + uint64_t x[6][27] = {{0}}; + unsigned int i, shift, m; + /* Multiply the output of all rand calls with the odd number m, which + should not change the uniformity of its distribution. */ + for (i = 0; i < rounds[usebits]; i++) { + uint32_t r = (rand32 ? secp256k1_testrand32() : secp256k1_testrand_bits(bits)); + CHECK((((uint64_t)r) >> bits) == 0); + for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) { + uint32_t rm = r * mults[m]; + for (shift = 0; shift <= maxshift; shift++) { + x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1))); + } + } + } + for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) { + for (shift = 0; shift <= maxshift; shift++) { + /* Test that the lower usebits bits of x[shift] are 1 */ + CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0); + } + } +} + +/* Subrange must be a whole divisor of range, and at most 64 */ +static void test_rand_int(uint32_t range, uint32_t subrange) { + /* (1-1/subrange)^rounds < 1/10^9 */ + int rounds = (subrange * 2073) / 100; + int i; + uint64_t x = 0; + CHECK((range % subrange) == 0); + for (i = 0; i < rounds; i++) { + uint32_t r = secp256k1_testrand_int(range); + CHECK(r < range); + r = r % subrange; + x |= (((uint64_t)1) << r); + } + /* Test that the lower subrange bits of x are 1. */ + CHECK(((~x) << (64 - subrange)) == 0); +} + +static void run_rand_bits(void) { + size_t b; + test_rand_bits(1, 32); + for (b = 1; b <= 32; b++) { + test_rand_bits(0, b); + } +} + +static void run_rand_int(void) { + static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432}; + static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64}; + unsigned int m, s; + for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) { + for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) { + test_rand_int(ms[m] * ss[s], ss[s]); + } + } +} + +/***** MODINV TESTS *****/ + +/* Compute the modular inverse of (odd) x mod 2^64. */ +static uint64_t modinv2p64(uint64_t x) { + /* If w = 1/x mod 2^(2^L), then w*(2 - w*x) = 1/x mod 2^(2^(L+1)). See + * Hacker's Delight second edition, Henry S. Warren, Jr., pages 245-247 for + * why. Start with L=0, for which it is true for every odd x that + * 1/x=1 mod 2. Iterating 6 times gives us 1/x mod 2^64. */ + int l; + uint64_t w = 1; + CHECK(x & 1); + for (l = 0; l < 6; ++l) w *= (2 - w*x); + return w; +} + + +/* compute out = (a*b) mod m; if b=NULL, treat b=1; if m=NULL, treat m=infinity. + * + * Out is a 512-bit number (represented as 32 uint16_t's in LE order). The other + * arguments are 256-bit numbers (represented as 16 uint16_t's in LE order). */ +static void mulmod256(uint16_t* out, const uint16_t* a, const uint16_t* b, const uint16_t* m) { + uint16_t mul[32]; + uint64_t c = 0; + int i, j; + int m_bitlen = 0; + int mul_bitlen = 0; + + if (b != NULL) { + /* Compute the product of a and b, and put it in mul. */ + for (i = 0; i < 32; ++i) { + for (j = i <= 15 ? 0 : i - 15; j <= i && j <= 15; j++) { + c += (uint64_t)a[j] * b[i - j]; + } + mul[i] = c & 0xFFFF; + c >>= 16; + } + CHECK(c == 0); + + /* compute the highest set bit in mul */ + for (i = 511; i >= 0; --i) { + if ((mul[i >> 4] >> (i & 15)) & 1) { + mul_bitlen = i; + break; + } + } + } else { + /* if b==NULL, set mul=a. */ + memcpy(mul, a, 32); + memset(mul + 16, 0, 32); + /* compute the highest set bit in mul */ + for (i = 255; i >= 0; --i) { + if ((mul[i >> 4] >> (i & 15)) & 1) { + mul_bitlen = i; + break; + } + } + } + + if (m) { + /* Compute the highest set bit in m. */ + for (i = 255; i >= 0; --i) { + if ((m[i >> 4] >> (i & 15)) & 1) { + m_bitlen = i; + break; + } + } + + /* Try do mul -= m<<i, for i going down to 0, whenever the result is not negative */ + for (i = mul_bitlen - m_bitlen; i >= 0; --i) { + uint16_t mul2[32]; + int64_t cs; + + /* Compute mul2 = mul - m<<i. */ + cs = 0; /* accumulator */ + for (j = 0; j < 32; ++j) { /* j loops over the output limbs in mul2. */ + /* Compute sub: the 16 bits in m that will be subtracted from mul2[j]. */ + uint16_t sub = 0; + int p; + for (p = 0; p < 16; ++p) { /* p loops over the bit positions in mul2[j]. */ + int bitpos = j * 16 - i + p; /* bitpos is the correspond bit position in m. */ + if (bitpos >= 0 && bitpos < 256) { + sub |= ((m[bitpos >> 4] >> (bitpos & 15)) & 1) << p; + } + } + /* Add mul[j]-sub to accumulator, and shift bottom 16 bits out to mul2[j]. */ + cs += mul[j]; + cs -= sub; + mul2[j] = (cs & 0xFFFF); + cs >>= 16; + } + /* If remainder of subtraction is 0, set mul = mul2. */ + if (cs == 0) { + memcpy(mul, mul2, sizeof(mul)); + } + } + /* Sanity check: test that all limbs higher than m's highest are zero */ + for (i = (m_bitlen >> 4) + 1; i < 32; ++i) { + CHECK(mul[i] == 0); + } + } + memcpy(out, mul, 32); +} + +/* Convert a 256-bit number represented as 16 uint16_t's to signed30 notation. */ +static void uint16_to_signed30(secp256k1_modinv32_signed30* out, const uint16_t* in) { + int i; + memset(out->v, 0, sizeof(out->v)); + for (i = 0; i < 256; ++i) { + out->v[i / 30] |= (int32_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 30); + } +} + +/* Convert a 256-bit number in signed30 notation to a representation as 16 uint16_t's. */ +static void signed30_to_uint16(uint16_t* out, const secp256k1_modinv32_signed30* in) { + int i; + memset(out, 0, 32); + for (i = 0; i < 256; ++i) { + out[i >> 4] |= (((in->v[i / 30]) >> (i % 30)) & 1) << (i & 15); + } +} + +/* Randomly mutate the sign of limbs in signed30 representation, without changing the value. */ +static void mutate_sign_signed30(secp256k1_modinv32_signed30* x) { + int i; + for (i = 0; i < 16; ++i) { + int pos = secp256k1_testrand_bits(3); + if (x->v[pos] > 0 && x->v[pos + 1] <= 0x3fffffff) { + x->v[pos] -= 0x40000000; + x->v[pos + 1] += 1; + } else if (x->v[pos] < 0 && x->v[pos + 1] >= 0x3fffffff) { + x->v[pos] += 0x40000000; + x->v[pos + 1] -= 1; + } + } +} + +/* Test secp256k1_modinv32{_var}, using inputs in 16-bit limb format, and returning inverse. */ +static void test_modinv32_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) { + uint16_t tmp[16]; + secp256k1_modinv32_signed30 x; + secp256k1_modinv32_modinfo m; + int i, vartime, nonzero; + + uint16_to_signed30(&x, in); + nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4] | x.v[5] | x.v[6] | x.v[7] | x.v[8]) != 0; + uint16_to_signed30(&m.modulus, mod); + + /* compute 1/modulus mod 2^30 */ + m.modulus_inv30 = modinv2p64(m.modulus.v[0]) & 0x3fffffff; + CHECK(((m.modulus_inv30 * m.modulus.v[0]) & 0x3fffffff) == 1); + + /* Test secp256k1_jacobi32_maybe_var. */ + if (nonzero) { + int jac; + uint16_t sqr[16], negone[16]; + mulmod256(sqr, in, in, mod); + uint16_to_signed30(&x, sqr); + /* Compute jacobi symbol of in^2, which must be 1 (or uncomputable). */ + jac = secp256k1_jacobi32_maybe_var(&x, &m); + CHECK(jac == 0 || jac == 1); + /* Then compute the jacobi symbol of -(in^2). x and -x have opposite + * jacobi symbols if and only if (mod % 4) == 3. */ + negone[0] = mod[0] - 1; + for (i = 1; i < 16; ++i) negone[i] = mod[i]; + mulmod256(sqr, sqr, negone, mod); + uint16_to_signed30(&x, sqr); + jac = secp256k1_jacobi32_maybe_var(&x, &m); + CHECK(jac == 0 || jac == 1 - (mod[0] & 2)); + } + + uint16_to_signed30(&x, in); + mutate_sign_signed30(&m.modulus); + for (vartime = 0; vartime < 2; ++vartime) { + /* compute inverse */ + (vartime ? secp256k1_modinv32_var : secp256k1_modinv32)(&x, &m); + + /* produce output */ + signed30_to_uint16(out, &x); + + /* check if the inverse times the input is 1 (mod m), unless x is 0. */ + mulmod256(tmp, out, in, mod); + CHECK(tmp[0] == nonzero); + for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0); + + /* invert again */ + (vartime ? secp256k1_modinv32_var : secp256k1_modinv32)(&x, &m); + + /* check if the result is equal to the input */ + signed30_to_uint16(tmp, &x); + for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]); + } +} + +#ifdef SECP256K1_WIDEMUL_INT128 +/* Convert a 256-bit number represented as 16 uint16_t's to signed62 notation. */ +static void uint16_to_signed62(secp256k1_modinv64_signed62* out, const uint16_t* in) { + int i; + memset(out->v, 0, sizeof(out->v)); + for (i = 0; i < 256; ++i) { + out->v[i / 62] |= (int64_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 62); + } +} + +/* Convert a 256-bit number in signed62 notation to a representation as 16 uint16_t's. */ +static void signed62_to_uint16(uint16_t* out, const secp256k1_modinv64_signed62* in) { + int i; + memset(out, 0, 32); + for (i = 0; i < 256; ++i) { + out[i >> 4] |= (((in->v[i / 62]) >> (i % 62)) & 1) << (i & 15); + } +} + +/* Randomly mutate the sign of limbs in signed62 representation, without changing the value. */ +static void mutate_sign_signed62(secp256k1_modinv64_signed62* x) { + static const int64_t M62 = (int64_t)(UINT64_MAX >> 2); + int i; + for (i = 0; i < 8; ++i) { + int pos = secp256k1_testrand_bits(2); + if (x->v[pos] > 0 && x->v[pos + 1] <= M62) { + x->v[pos] -= (M62 + 1); + x->v[pos + 1] += 1; + } else if (x->v[pos] < 0 && x->v[pos + 1] >= -M62) { + x->v[pos] += (M62 + 1); + x->v[pos + 1] -= 1; + } + } +} + +/* Test secp256k1_modinv64{_var}, using inputs in 16-bit limb format, and returning inverse. */ +static void test_modinv64_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) { + static const int64_t M62 = (int64_t)(UINT64_MAX >> 2); + uint16_t tmp[16]; + secp256k1_modinv64_signed62 x; + secp256k1_modinv64_modinfo m; + int i, vartime, nonzero; + + uint16_to_signed62(&x, in); + nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4]) != 0; + uint16_to_signed62(&m.modulus, mod); + + /* compute 1/modulus mod 2^62 */ + m.modulus_inv62 = modinv2p64(m.modulus.v[0]) & M62; + CHECK(((m.modulus_inv62 * m.modulus.v[0]) & M62) == 1); + + /* Test secp256k1_jacobi64_maybe_var. */ + if (nonzero) { + int jac; + uint16_t sqr[16], negone[16]; + mulmod256(sqr, in, in, mod); + uint16_to_signed62(&x, sqr); + /* Compute jacobi symbol of in^2, which must be 1 (or uncomputable). */ + jac = secp256k1_jacobi64_maybe_var(&x, &m); + CHECK(jac == 0 || jac == 1); + /* Then compute the jacobi symbol of -(in^2). x and -x have opposite + * jacobi symbols if and only if (mod % 4) == 3. */ + negone[0] = mod[0] - 1; + for (i = 1; i < 16; ++i) negone[i] = mod[i]; + mulmod256(sqr, sqr, negone, mod); + uint16_to_signed62(&x, sqr); + jac = secp256k1_jacobi64_maybe_var(&x, &m); + CHECK(jac == 0 || jac == 1 - (mod[0] & 2)); + } + + uint16_to_signed62(&x, in); + mutate_sign_signed62(&m.modulus); + for (vartime = 0; vartime < 2; ++vartime) { + /* compute inverse */ + (vartime ? secp256k1_modinv64_var : secp256k1_modinv64)(&x, &m); + + /* produce output */ + signed62_to_uint16(out, &x); + + /* check if the inverse times the input is 1 (mod m), unless x is 0. */ + mulmod256(tmp, out, in, mod); + CHECK(tmp[0] == nonzero); + for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0); + + /* invert again */ + (vartime ? secp256k1_modinv64_var : secp256k1_modinv64)(&x, &m); + + /* check if the result is equal to the input */ + signed62_to_uint16(tmp, &x); + for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]); + } +} +#endif + +/* test if a and b are coprime */ +static int coprime(const uint16_t* a, const uint16_t* b) { + uint16_t x[16], y[16], t[16]; + int i; + int iszero; + memcpy(x, a, 32); + memcpy(y, b, 32); + + /* simple gcd loop: while x!=0, (x,y)=(y%x,x) */ + while (1) { + iszero = 1; + for (i = 0; i < 16; ++i) { + if (x[i] != 0) { + iszero = 0; + break; + } + } + if (iszero) break; + mulmod256(t, y, NULL, x); + memcpy(y, x, 32); + memcpy(x, t, 32); + } + + /* return whether y=1 */ + if (y[0] != 1) return 0; + for (i = 1; i < 16; ++i) { + if (y[i] != 0) return 0; + } + return 1; +} + +static void run_modinv_tests(void) { + /* Fixed test cases. Each tuple is (input, modulus, output), each as 16x16 bits in LE order. */ + static const uint16_t CASES[][3][16] = { + /* Test cases triggering edge cases in divsteps */ + + /* Test case known to need 713 divsteps */ + {{0x1513, 0x5389, 0x54e9, 0x2798, 0x1957, 0x66a0, 0x8057, 0x3477, + 0x7784, 0x1052, 0x326a, 0x9331, 0x6506, 0xa95c, 0x91f3, 0xfb5e}, + {0x2bdd, 0x8df4, 0xcc61, 0x481f, 0xdae5, 0x5ca7, 0xf43b, 0x7d54, + 0x13d6, 0x469b, 0x2294, 0x20f4, 0xb2a4, 0xa2d1, 0x3ff1, 0xfd4b}, + {0xffd8, 0xd9a0, 0x456e, 0x81bb, 0xbabd, 0x6cea, 0x6dbd, 0x73ab, + 0xbb94, 0x3d3c, 0xdf08, 0x31c4, 0x3e32, 0xc179, 0x2486, 0xb86b}}, + /* Test case known to need 589 divsteps, reaching delta=-140 and + delta=141. */ + {{0x3fb1, 0x903b, 0x4eb7, 0x4813, 0xd863, 0x26bf, 0xd89f, 0xa8a9, + 0x02fe, 0x57c6, 0x554a, 0x4eab, 0x165e, 0x3d61, 0xee1e, 0x456c}, + {0x9295, 0x823b, 0x5c1f, 0x5386, 0x48e0, 0x02ff, 0x4c2a, 0xa2da, + 0xe58f, 0x967c, 0xc97e, 0x3f5a, 0x69fb, 0x52d9, 0x0a86, 0xb4a3}, + {0x3d30, 0xb893, 0xa809, 0xa7a8, 0x26f5, 0x5b42, 0x55be, 0xf4d0, + 0x12c2, 0x7e6a, 0xe41a, 0x90c7, 0xebfa, 0xf920, 0x304e, 0x1419}}, + /* Test case known to need 650 divsteps, and doing 65 consecutive (f,g/2) steps. */ + {{0x8583, 0x5058, 0xbeae, 0xeb69, 0x48bc, 0x52bb, 0x6a9d, 0xcc94, + 0x2a21, 0x87d5, 0x5b0d, 0x42f6, 0x5b8a, 0x2214, 0xe9d6, 0xa040}, + {0x7531, 0x27cb, 0x7e53, 0xb739, 0x6a5f, 0x83f5, 0xa45c, 0xcb1d, + 0x8a87, 0x1c9c, 0x51d7, 0x851c, 0xb9d8, 0x1fbe, 0xc241, 0xd4a3}, + {0xcdb4, 0x275c, 0x7d22, 0xa906, 0x0173, 0xc054, 0x7fdf, 0x5005, + 0x7fb8, 0x9059, 0xdf51, 0x99df, 0x2654, 0x8f6e, 0x070f, 0xb347}}, + /* example needing 713 divsteps; delta=-2..3 */ + {{0xe2e9, 0xee91, 0x4345, 0xe5ad, 0xf3ec, 0x8f42, 0x0364, 0xd5c9, + 0xff49, 0xbef5, 0x4544, 0x4c7c, 0xae4b, 0xfd9d, 0xb35b, 0xda9d}, + {0x36e7, 0x8cca, 0x2ed0, 0x47b3, 0xaca4, 0xb374, 0x7d2a, 0x0772, + 0x6bdb, 0xe0a7, 0x900b, 0xfe10, 0x788c, 0x6f22, 0xd909, 0xf298}, + {0xd8c6, 0xba39, 0x13ed, 0x198c, 0x16c8, 0xb837, 0xa5f2, 0x9797, + 0x0113, 0x882a, 0x15b5, 0x324c, 0xabee, 0xe465, 0x8170, 0x85ac}}, + /* example needing 713 divsteps; delta=-2..3 */ + {{0xd5b7, 0x2966, 0x040e, 0xf59a, 0x0387, 0xd96d, 0xbfbc, 0xd850, + 0x2d96, 0x872a, 0xad81, 0xc03c, 0xbb39, 0xb7fa, 0xd904, 0xef78}, + {0x6279, 0x4314, 0xfdd3, 0x1568, 0x0982, 0x4d13, 0x625f, 0x010c, + 0x22b1, 0x0cc3, 0xf22d, 0x5710, 0x1109, 0x5751, 0x7714, 0xfcf2}, + {0xdb13, 0x5817, 0x232e, 0xe456, 0xbbbc, 0x6fbe, 0x4572, 0xa358, + 0xc76d, 0x928e, 0x0162, 0x5314, 0x8325, 0x5683, 0xe21b, 0xda88}}, + /* example needing 713 divsteps; delta=-2..3 */ + {{0xa06f, 0x71ee, 0x3bac, 0x9ebb, 0xdeaa, 0x09ed, 0x1cf7, 0x9ec9, + 0x7158, 0x8b72, 0x5d53, 0x5479, 0x5c75, 0xbb66, 0x9125, 0xeccc}, + {0x2941, 0xd46c, 0x3cd4, 0x4a9d, 0x5c4a, 0x256b, 0xbd6c, 0x9b8e, + 0x8fe0, 0x8a14, 0xffe8, 0x2496, 0x618d, 0xa9d7, 0x5018, 0xfb29}, + {0x437c, 0xbd60, 0x7590, 0x94bb, 0x0095, 0xd35e, 0xd4fe, 0xd6da, + 0x0d4e, 0x5342, 0x4cd2, 0x169b, 0x661c, 0x1380, 0xed2d, 0x85c1}}, + /* example reaching delta=-64..65; 661 divsteps */ + {{0xfde4, 0x68d6, 0x6c48, 0x7f77, 0x1c78, 0x96de, 0x2fd9, 0xa6c2, + 0xbbb5, 0xd319, 0x69cf, 0xd4b3, 0xa321, 0xcda0, 0x172e, 0xe530}, + {0xd9e3, 0x0f60, 0x3d86, 0xeeab, 0x25ee, 0x9582, 0x2d50, 0xfe16, + 0xd4e2, 0xe3ba, 0x94e2, 0x9833, 0x6c5e, 0x8982, 0x13b6, 0xe598}, + {0xe675, 0xf55a, 0x10f6, 0xabde, 0x5113, 0xecaa, 0x61ae, 0xad9f, + 0x0c27, 0xef33, 0x62e5, 0x211d, 0x08fa, 0xa78d, 0xc675, 0x8bae}}, + /* example reaching delta=-64..65; 661 divsteps */ + {{0x21bf, 0x52d5, 0x8fd4, 0xaa18, 0x156a, 0x7247, 0xebb8, 0x5717, + 0x4eb5, 0x1421, 0xb58f, 0x3b0b, 0x5dff, 0xe533, 0xb369, 0xd28a}, + {0x9f6b, 0xe463, 0x2563, 0xc74d, 0x6d81, 0x636a, 0x8fc8, 0x7a94, + 0x9429, 0x1585, 0xf35e, 0x7ff5, 0xb64f, 0x9720, 0xba74, 0xe108}, + {0xa5ab, 0xea7b, 0xfe5e, 0x8a85, 0x13be, 0x7934, 0xe8a0, 0xa187, + 0x86b5, 0xe477, 0xb9a4, 0x75d7, 0x538f, 0xdd70, 0xc781, 0xb67d}}, + /* example reaching delta=-64..65; 661 divsteps */ + {{0xa41a, 0x3e8d, 0xf1f5, 0x9493, 0x868c, 0x5103, 0x2725, 0x3ceb, + 0x6032, 0x3624, 0xdc6b, 0x9120, 0xbf4c, 0x8821, 0x91ad, 0xb31a}, + {0x5c0b, 0xdda5, 0x20f8, 0x32a1, 0xaf73, 0x6ec5, 0x4779, 0x43d6, + 0xd454, 0x9573, 0xbf84, 0x5a58, 0xe04e, 0x307e, 0xd1d5, 0xe230}, + {0xda15, 0xbcd6, 0x7180, 0xabd3, 0x04e6, 0x6986, 0xc0d7, 0x90bb, + 0x3a4d, 0x7c95, 0xaaab, 0x9ab3, 0xda34, 0xa7f6, 0x9636, 0x6273}}, + /* example doing 123 consecutive (f,g/2) steps; 615 divsteps */ + {{0xb4d6, 0xb38f, 0x00aa, 0xebda, 0xd4c2, 0x70b8, 0x9dad, 0x58ee, + 0x68f8, 0x48d3, 0xb5ff, 0xf422, 0x9e46, 0x2437, 0x18d0, 0xd9cc}, + {0x5c83, 0xfed7, 0x97f5, 0x3f07, 0xcaad, 0x95b1, 0xb4a4, 0xb005, + 0x23af, 0xdd27, 0x6c0d, 0x932c, 0xe2b2, 0xe3ae, 0xfb96, 0xdf67}, + {0x3105, 0x0127, 0xfd48, 0x039b, 0x35f1, 0xbc6f, 0x6c0a, 0xb572, + 0xe4df, 0xebad, 0x8edc, 0xb89d, 0x9555, 0x4c26, 0x1fef, 0x997c}}, + /* example doing 123 consecutive (f,g/2) steps; 614 divsteps */ + {{0x5138, 0xd474, 0x385f, 0xc964, 0x00f2, 0x6df7, 0x862d, 0xb185, + 0xb264, 0xe9e1, 0x466c, 0xf39e, 0xafaf, 0x5f41, 0x47e2, 0xc89d}, + {0x8607, 0x9c81, 0x46a2, 0x7dcc, 0xcb0c, 0x9325, 0xe149, 0x2bde, + 0x6632, 0x2869, 0xa261, 0xb163, 0xccee, 0x22ae, 0x91e0, 0xcfd5}, + {0x831c, 0xda22, 0xb080, 0xba7a, 0x26e2, 0x54b0, 0x073b, 0x5ea0, + 0xed4b, 0xcb3d, 0xbba1, 0xbec8, 0xf2ad, 0xae0d, 0x349b, 0x17d1}}, + /* example doing 123 consecutive (f,g/2) steps; 614 divsteps */ + {{0xe9a5, 0xb4ad, 0xd995, 0x9953, 0xcdff, 0x50d7, 0xf715, 0x9dc7, + 0x3e28, 0x15a9, 0x95a3, 0x8554, 0x5b5e, 0xad1d, 0x6d57, 0x3d50}, + {0x3ad9, 0xbd60, 0x5cc7, 0x6b91, 0xadeb, 0x71f6, 0x7cc4, 0xa58a, + 0x2cce, 0xf17c, 0x38c9, 0x97ed, 0x65fb, 0x3fa6, 0xa6bc, 0xeb24}, + {0xf96c, 0x1963, 0x8151, 0xa0cc, 0x299b, 0xf277, 0x001a, 0x16bb, + 0xfd2e, 0x532d, 0x0410, 0xe117, 0x6b00, 0x44ec, 0xca6a, 0x1745}}, + /* example doing 446 (f,g/2) steps; 523 divsteps */ + {{0x3758, 0xa56c, 0xe41e, 0x4e47, 0x0975, 0xa82b, 0x107c, 0x89cf, + 0x2093, 0x5a0c, 0xda37, 0xe007, 0x6074, 0x4f68, 0x2f5a, 0xbb8a}, + {0x4beb, 0xa40f, 0x2c42, 0xd9d6, 0x97e8, 0xca7c, 0xd395, 0x894f, + 0x1f50, 0x8067, 0xa233, 0xb850, 0x1746, 0x1706, 0xbcda, 0xdf32}, + {0x762a, 0xceda, 0x4c45, 0x1ca0, 0x8c37, 0xd8c5, 0xef57, 0x7a2c, + 0x6e98, 0xe38a, 0xc50e, 0x2ca9, 0xcb85, 0x24d5, 0xc29c, 0x61f6}}, + /* example doing 446 (f,g/2) steps; 523 divsteps */ + {{0x6f38, 0x74ad, 0x7332, 0x4073, 0x6521, 0xb876, 0xa370, 0xa6bd, + 0xcea5, 0xbd06, 0x969f, 0x77c6, 0x1e69, 0x7c49, 0x7d51, 0xb6e7}, + {0x3f27, 0x4be4, 0xd81e, 0x1396, 0xb21f, 0x92aa, 0x6dc3, 0x6283, + 0x6ada, 0x3ca2, 0xc1e5, 0x8b9b, 0xd705, 0x5598, 0x8ba1, 0xe087}, + {0x6a22, 0xe834, 0xbc8d, 0xcee9, 0x42fc, 0xfc77, 0x9c45, 0x1ca8, + 0xeb66, 0xed74, 0xaaf9, 0xe75f, 0xfe77, 0x46d2, 0x179b, 0xbf3e}}, + /* example doing 336 (f,(f+g)/2) steps; 693 divsteps */ + {{0x7ea7, 0x444e, 0x84ea, 0xc447, 0x7c1f, 0xab97, 0x3de6, 0x5878, + 0x4e8b, 0xc017, 0x03e0, 0xdc40, 0xbbd0, 0x74ce, 0x0169, 0x7ab5}, + {0x4023, 0x154f, 0xfbe4, 0x8195, 0xfda0, 0xef54, 0x9e9a, 0xc703, + 0x2803, 0xf760, 0x6302, 0xed5b, 0x7157, 0x6456, 0xdd7d, 0xf14b}, + {0xb6fb, 0xe3b3, 0x0733, 0xa77e, 0x44c5, 0x3003, 0xc937, 0xdd4d, + 0x5355, 0x14e9, 0x184e, 0xcefe, 0xe6b5, 0xf2e0, 0x0a28, 0x5b74}}, + /* example doing 336 (f,(f+g)/2) steps; 687 divsteps */ + {{0xa893, 0xb5f4, 0x1ede, 0xa316, 0x242c, 0xbdcc, 0xb017, 0x0836, + 0x3a37, 0x27fb, 0xfb85, 0x251e, 0xa189, 0xb15d, 0xa4b8, 0xc24c}, + {0xb0b7, 0x57ba, 0xbb6d, 0x9177, 0xc896, 0xc7f2, 0x43b4, 0x85a6, + 0xe6c4, 0xe50e, 0x3109, 0x7ca5, 0xd73d, 0x13ff, 0x0c3d, 0xcd62}, + {0x48ca, 0xdb34, 0xe347, 0x2cef, 0x4466, 0x10fb, 0x7ee1, 0x6344, + 0x4308, 0x966d, 0xd4d1, 0xb099, 0x994f, 0xd025, 0x2187, 0x5866}}, + /* example doing 267 (g,(g-f)/2) steps; 678 divsteps */ + {{0x0775, 0x1754, 0x01f6, 0xdf37, 0xc0be, 0x8197, 0x072f, 0x6cf5, + 0x8b36, 0x8069, 0x5590, 0xb92d, 0x6084, 0x47a4, 0x23fe, 0xddd5}, + {0x8e1b, 0xda37, 0x27d9, 0x312e, 0x3a2f, 0xef6d, 0xd9eb, 0x8153, + 0xdcba, 0x9fa3, 0x9f80, 0xead5, 0x134d, 0x2ebb, 0x5ec0, 0xe032}, + {0x1cb6, 0x5a61, 0x1bed, 0x77d6, 0xd5d1, 0x7498, 0xef33, 0x2dd2, + 0x1089, 0xedbd, 0x6958, 0x16ae, 0x336c, 0x45e6, 0x4361, 0xbadc}}, + /* example doing 267 (g,(g-f)/2) steps; 676 divsteps */ + {{0x0207, 0xf948, 0xc430, 0xf36b, 0xf0a7, 0x5d36, 0x751f, 0x132c, + 0x6f25, 0xa630, 0xca1f, 0xc967, 0xaf9c, 0x34e7, 0xa38f, 0xbe9f}, + {0x5fb9, 0x7321, 0x6561, 0x5fed, 0x54ec, 0x9c3a, 0xee0e, 0x6717, + 0x49af, 0xb896, 0xf4f5, 0x451c, 0x722a, 0xf116, 0x64a9, 0xcf0b}, + {0xf4d7, 0xdb47, 0xfef2, 0x4806, 0x4cb8, 0x18c7, 0xd9a7, 0x4951, + 0x14d8, 0x5c3a, 0xd22d, 0xd7b2, 0x750c, 0x3de7, 0x8b4a, 0x19aa}}, + + /* Test cases triggering edge cases in divsteps variant starting with delta=1/2 */ + + /* example needing 590 divsteps; delta=-5/2..7/2 */ + {{0x9118, 0xb640, 0x53d7, 0x30ab, 0x2a23, 0xd907, 0x9323, 0x5b3a, + 0xb6d4, 0x538a, 0x7637, 0xfe97, 0xfd05, 0x3cc0, 0x453a, 0xfb7e}, + {0x6983, 0x4f75, 0x4ad1, 0x48ad, 0xb2d9, 0x521d, 0x3dbc, 0x9cc0, + 0x4b60, 0x0ac6, 0xd3be, 0x0fb6, 0xd305, 0x3895, 0x2da5, 0xfdf8}, + {0xcec1, 0x33ac, 0xa801, 0x8194, 0xe36c, 0x65ef, 0x103b, 0xca54, + 0xfa9b, 0xb41d, 0x9b52, 0xb6f7, 0xa611, 0x84aa, 0x3493, 0xbf54}}, + /* example needing 590 divsteps; delta=-3/2..5/2 */ + {{0xb5f2, 0x42d0, 0x35e8, 0x8ca0, 0x4b62, 0x6e1d, 0xbdf3, 0x890e, + 0x8c82, 0x23d8, 0xc79a, 0xc8e8, 0x789e, 0x353d, 0x9766, 0xea9d}, + {0x6fa1, 0xacba, 0x4b7a, 0x5de1, 0x95d0, 0xc845, 0xebbf, 0x6f5a, + 0x30cf, 0x52db, 0x69b7, 0xe278, 0x4b15, 0x8411, 0x2ab2, 0xf3e7}, + {0xf12c, 0x9d6d, 0x95fa, 0x1878, 0x9f13, 0x4fb5, 0x3c8b, 0xa451, + 0x7182, 0xc4b6, 0x7e2a, 0x7bb7, 0x6e0e, 0x5b68, 0xde55, 0x9927}}, + /* example needing 590 divsteps; delta=-3/2..5/2 */ + {{0x229c, 0x4ef8, 0x1e93, 0xe5dc, 0xcde5, 0x6d62, 0x263b, 0xad11, + 0xced0, 0x88ff, 0xae8e, 0x3183, 0x11d2, 0xa50b, 0x350d, 0xeb40}, + {0x3157, 0xe2ea, 0x8a02, 0x0aa3, 0x5ae1, 0xb26c, 0xea27, 0x6805, + 0x87e2, 0x9461, 0x37c1, 0x2f8d, 0x85d2, 0x77a8, 0xf805, 0xeec9}, + {0x6f4e, 0x2748, 0xf7e5, 0xd8d3, 0xabe2, 0x7270, 0xc4e0, 0xedc7, + 0xf196, 0x78ca, 0x9139, 0xd8af, 0x72c6, 0xaf2f, 0x85d2, 0x6cd3}}, + /* example needing 590 divsteps; delta=-5/2..7/2 */ + {{0xdce8, 0xf1fe, 0x6708, 0x021e, 0xf1ca, 0xd609, 0x5443, 0x85ce, + 0x7a05, 0x8f9c, 0x90c3, 0x52e7, 0x8e1d, 0x97b8, 0xc0bf, 0xf2a1}, + {0xbd3d, 0xed11, 0x1625, 0xb4c5, 0x844c, 0xa413, 0x2569, 0xb9ba, + 0xcd35, 0xff84, 0xcd6e, 0x7f0b, 0x7d5d, 0x10df, 0x3efe, 0xfbe5}, + {0xa9dd, 0xafef, 0xb1b7, 0x4c8d, 0x50e4, 0xafbf, 0x2d5a, 0xb27c, + 0x0653, 0x66b6, 0x5d36, 0x4694, 0x7e35, 0xc47c, 0x857f, 0x32c5}}, + /* example needing 590 divsteps; delta=-3/2..5/2 */ + {{0x7902, 0xc9f8, 0x926b, 0xaaeb, 0x90f8, 0x1c89, 0xcce3, 0x96b7, + 0x28b2, 0x87a2, 0x136d, 0x695a, 0xa8df, 0x9061, 0x9e31, 0xee82}, + {0xd3a9, 0x3c02, 0x818c, 0x6b81, 0x34b3, 0xebbb, 0xe2c8, 0x7712, + 0xbfd6, 0x8248, 0xa6f4, 0xba6f, 0x03bb, 0xfb54, 0x7575, 0xfe89}, + {0x8246, 0x0d63, 0x478e, 0xf946, 0xf393, 0x0451, 0x08c2, 0x5919, + 0x5fd6, 0x4c61, 0xbeb7, 0x9a15, 0x30e1, 0x55fc, 0x6a01, 0x3724}}, + /* example reaching delta=-127/2..129/2; 571 divsteps */ + {{0x3eff, 0x926a, 0x77f5, 0x1fff, 0x1a5b, 0xf3ef, 0xf64b, 0x8681, + 0xf800, 0xf9bc, 0x761d, 0xe268, 0x62b0, 0xa032, 0xba9c, 0xbe56}, + {0xb8f9, 0x00e7, 0x47b7, 0xdffc, 0xfd9d, 0x5abb, 0xa19b, 0x1868, + 0x31fd, 0x3b29, 0x3674, 0x5449, 0xf54d, 0x1d19, 0x6ac7, 0xff6f}, + {0xf1d7, 0x3551, 0x5682, 0x9adf, 0xe8aa, 0x19a5, 0x8340, 0x71db, + 0xb7ab, 0x4cfd, 0xf661, 0x632c, 0xc27e, 0xd3c6, 0xdf42, 0xd306}}, + /* example reaching delta=-127/2..129/2; 571 divsteps */ + {{0x0000, 0x0000, 0x0000, 0x0000, 0x3aff, 0x2ed7, 0xf2e0, 0xabc7, + 0x8aee, 0x166e, 0x7ed0, 0x9ac7, 0x714a, 0xb9c5, 0x4d58, 0xad6c}, + {0x9cf9, 0x47e2, 0xa421, 0xb277, 0xffc2, 0x2747, 0x6486, 0x94c1, + 0x1d99, 0xd49b, 0x1096, 0x991a, 0xe986, 0xae02, 0xe89b, 0xea36}, + {0x1fb4, 0x98d8, 0x19b7, 0x80e9, 0xcdac, 0xaa5a, 0xf1e6, 0x0074, + 0xe393, 0xed8b, 0x8d5c, 0xe17d, 0x81b3, 0xc16d, 0x54d3, 0x9be3}}, + /* example reaching delta=-127/2..129/2; 571 divsteps */ + {{0xd047, 0x7e36, 0x3157, 0x7ab6, 0xb4d9, 0x8dae, 0x7534, 0x4f5d, + 0x489e, 0xa8ab, 0x8a3d, 0xd52c, 0x62af, 0xa032, 0xba9c, 0xbe56}, + {0xb1f1, 0x737f, 0x5964, 0x5afb, 0x3712, 0x8ef9, 0x19f7, 0x9669, + 0x664d, 0x03ad, 0xc352, 0xf7a5, 0xf545, 0x1d19, 0x6ac7, 0xff6f}, + {0xa834, 0x5256, 0x27bc, 0x33bd, 0xba11, 0x5a7b, 0x791e, 0xe6c0, + 0x9ac4, 0x9370, 0x1130, 0x28b4, 0x2b2e, 0x231b, 0x082a, 0x796e}}, + /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ + {{0x6ab1, 0x6ea0, 0x1a99, 0xe0c2, 0xdd45, 0x645d, 0x8dbc, 0x466a, + 0xfa64, 0x4289, 0xd3f7, 0xfc8f, 0x2894, 0xe3c5, 0xa008, 0xcc14}, + {0xc75f, 0xc083, 0x4cc2, 0x64f2, 0x2aff, 0x4c12, 0x8461, 0xc4ae, + 0xbbfa, 0xb336, 0xe4b2, 0x3ac5, 0x2c22, 0xf56c, 0x5381, 0xe943}, + {0xcd80, 0x760d, 0x4395, 0xb3a6, 0xd497, 0xf583, 0x82bd, 0x1daa, + 0xbe92, 0x2613, 0xfdfb, 0x869b, 0x0425, 0xa333, 0x7056, 0xc9c5}}, + /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ + {{0x71d4, 0x64df, 0xec4f, 0x74d8, 0x7e0c, 0x40d3, 0x7073, 0x4cc8, + 0x2a2a, 0xb1ff, 0x8518, 0x6513, 0xb0ea, 0x640a, 0x62d9, 0xd5f4}, + {0xdc75, 0xd937, 0x3b13, 0x1d36, 0xdf83, 0xd034, 0x1c1c, 0x4332, + 0x4cc3, 0xeeec, 0x7d94, 0x6771, 0x3384, 0x74b0, 0x947d, 0xf2c4}, + {0x0a82, 0x37a4, 0x12d5, 0xec97, 0x972c, 0xe6bf, 0xc348, 0xa0a9, + 0xc50c, 0xdc7c, 0xae30, 0x19d1, 0x0fca, 0x35e1, 0xd6f6, 0x81ee}}, + /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ + {{0xa6b1, 0xabc5, 0x5bbc, 0x7f65, 0xdd32, 0xaa73, 0xf5a3, 0x1982, + 0xced4, 0xe949, 0x0fd6, 0x2bc4, 0x2bd7, 0xe3c5, 0xa008, 0xcc14}, + {0x4b5f, 0x8f96, 0xa375, 0xfbcf, 0x1c7d, 0xf1ec, 0x03f5, 0xb35d, + 0xb999, 0xdb1f, 0xc9a1, 0xb4c7, 0x1dd5, 0xf56c, 0x5381, 0xe943}, + {0xaa3d, 0x38b9, 0xf17d, 0xeed9, 0x9988, 0x69ee, 0xeb88, 0x1495, + 0x203f, 0x18c8, 0x82b7, 0xdcb2, 0x34a7, 0x6b00, 0x6998, 0x589a}}, + /* example doing 453 (f,g/2) steps; 514 divsteps */ + {{0xa478, 0xe60d, 0x3244, 0x60e6, 0xada3, 0xfe50, 0xb6b1, 0x2eae, + 0xd0ef, 0xa7b1, 0xef63, 0x05c0, 0xe213, 0x443e, 0x4427, 0x2448}, + {0x258f, 0xf9ef, 0xe02b, 0x92dd, 0xd7f3, 0x252b, 0xa503, 0x9089, + 0xedff, 0x96c1, 0xfe3a, 0x3a39, 0x198a, 0x981d, 0x0627, 0xedb7}, + {0x595a, 0x45be, 0x8fb0, 0x2265, 0xc210, 0x02b8, 0xdce9, 0xe241, + 0xcab6, 0xbf0d, 0x0049, 0x8d9a, 0x2f51, 0xae54, 0x5785, 0xb411}}, + /* example doing 453 (f,g/2) steps; 514 divsteps */ + {{0x48f0, 0x7db3, 0xdafe, 0x1c92, 0x5912, 0xe11a, 0xab52, 0xede1, + 0x3182, 0x8980, 0x5d2b, 0x9b5b, 0x8718, 0xda27, 0x1683, 0x1de2}, + {0x168f, 0x6f36, 0xce7a, 0xf435, 0x19d4, 0xda5e, 0x2351, 0x9af5, + 0xb003, 0x0ef5, 0x3b4c, 0xecec, 0xa9f0, 0x78e1, 0xdfef, 0xe823}, + {0x5f55, 0xfdcc, 0xb233, 0x2914, 0x84f0, 0x97d1, 0x9cf4, 0x2159, + 0xbf56, 0xb79c, 0x17a3, 0x7cef, 0xd5de, 0x34f0, 0x5311, 0x4c54}}, + /* example doing 510 (f,(f+g)/2) steps; 512 divsteps */ + {{0x2789, 0x2e04, 0x6e0e, 0xb6cd, 0xe4de, 0x4dbf, 0x228d, 0x7877, + 0xc335, 0x806b, 0x38cd, 0x8049, 0xa73b, 0xcfa2, 0x82f7, 0x9e19}, + {0xc08d, 0xb99d, 0xb8f3, 0x663d, 0xbbb3, 0x1284, 0x1485, 0x1d49, + 0xc98f, 0x9e78, 0x1588, 0x11e3, 0xd91a, 0xa2c7, 0xfff1, 0xc7b9}, + {0x1e1f, 0x411d, 0x7c49, 0x0d03, 0xe789, 0x2f8e, 0x5d55, 0xa95e, + 0x826e, 0x8de5, 0x52a0, 0x1abc, 0x4cd7, 0xd13a, 0x4395, 0x63e1}}, + /* example doing 510 (f,(f+g)/2) steps; 512 divsteps */ + {{0xd5a1, 0xf786, 0x555c, 0xb14b, 0x44ae, 0x535f, 0x4a49, 0xffc3, + 0xf497, 0x70d1, 0x57c8, 0xa933, 0xc85a, 0x1910, 0x75bf, 0x960b}, + {0xfe53, 0x5058, 0x496d, 0xfdff, 0x6fb8, 0x4100, 0x92bd, 0xe0c4, + 0xda89, 0xe0a4, 0x841b, 0x43d4, 0xa388, 0x957f, 0x99ca, 0x9abf}, + {0xe530, 0x05bc, 0xfeec, 0xfc7e, 0xbcd3, 0x1239, 0x54cb, 0x7042, + 0xbccb, 0x139e, 0x9076, 0x0203, 0x6068, 0x90c7, 0x1ddf, 0x488d}}, + /* example doing 228 (g,(g-f)/2) steps; 538 divsteps */ + {{0x9488, 0xe54b, 0x0e43, 0x81d2, 0x06e7, 0x4b66, 0x36d0, 0x53d6, + 0x2b68, 0x22ec, 0x3fa9, 0xc1a7, 0x9ad2, 0xa596, 0xb3ac, 0xdf42}, + {0xe31f, 0x0b28, 0x5f3b, 0xc1ff, 0x344c, 0xbf5f, 0xd2ec, 0x2936, + 0x9995, 0xdeb2, 0xae6c, 0x2852, 0xa2c6, 0xb306, 0x8120, 0xe305}, + {0xa56e, 0xfb98, 0x1537, 0x4d85, 0x619e, 0x866c, 0x3cd4, 0x779a, + 0xdd66, 0xa80d, 0xdc2f, 0xcae4, 0xc74c, 0x5175, 0xa65d, 0x605e}}, + /* example doing 228 (g,(g-f)/2) steps; 537 divsteps */ + {{0x8cd5, 0x376d, 0xd01b, 0x7176, 0x19ef, 0xcf09, 0x8403, 0x5e52, + 0x83c1, 0x44de, 0xb91e, 0xb33d, 0xe15c, 0x51e7, 0xbad8, 0x6359}, + {0x3b75, 0xf812, 0x5f9e, 0xa04e, 0x92d3, 0x226e, 0x540e, 0x7c9a, + 0x31c6, 0x46d2, 0x0b7b, 0xdb4a, 0xe662, 0x4950, 0x0265, 0xf76f}, + {0x09ed, 0x692f, 0xe8f1, 0x3482, 0xab54, 0x36b4, 0x8442, 0x6ae9, + 0x4329, 0x6505, 0x183b, 0x1c1d, 0x482d, 0x7d63, 0xb44f, 0xcc09}}, + + /* Test cases with the group order as modulus. */ + + /* Test case with the group order as modulus, needing 635 divsteps. */ + {{0x95ed, 0x6c01, 0xd113, 0x5ff1, 0xd7d0, 0x29cc, 0x5817, 0x6120, + 0xca8e, 0xaad1, 0x25ae, 0x8e84, 0x9af6, 0x30bf, 0xf0ed, 0x1686}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x1631, 0xbf4a, 0x286a, 0x2716, 0x469f, 0x2ac8, 0x1312, 0xe9bc, + 0x04f4, 0x304b, 0x9931, 0x113b, 0xd932, 0xc8f4, 0x0d0d, 0x01a1}}, + /* example with group size as modulus needing 631 divsteps */ + {{0x85ed, 0xc284, 0x9608, 0x3c56, 0x19b6, 0xbb5b, 0x2850, 0xdab7, + 0xa7f5, 0xe9ab, 0x06a4, 0x5bbb, 0x1135, 0xa186, 0xc424, 0xc68b}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x8479, 0x450a, 0x8fa3, 0xde05, 0xb2f5, 0x7793, 0x7269, 0xbabb, + 0xc3b3, 0xd49b, 0x3377, 0x03c6, 0xe694, 0xc760, 0xd3cb, 0x2811}}, + /* example with group size as modulus needing 565 divsteps starting at delta=1/2 */ + {{0x8432, 0x5ceb, 0xa847, 0x6f1e, 0x51dd, 0x535a, 0x6ddc, 0x70ce, + 0x6e70, 0xc1f6, 0x18f2, 0x2a7e, 0xc8e7, 0x39f8, 0x7e96, 0xebbf}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x257e, 0x449f, 0x689f, 0x89aa, 0x3989, 0xb661, 0x376c, 0x1e32, + 0x654c, 0xee2e, 0xf4e2, 0x33c8, 0x3f2f, 0x9716, 0x6046, 0xcaa3}}, + /* Test case with the group size as modulus, needing 981 divsteps with + broken eta handling. */ + {{0xfeb9, 0xb877, 0xee41, 0x7fa3, 0x87da, 0x94c4, 0x9d04, 0xc5ae, + 0x5708, 0x0994, 0xfc79, 0x0916, 0xbf32, 0x3ad8, 0xe11c, 0x5ca2}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0f12, 0x075e, 0xce1c, 0x6f92, 0xc80f, 0xca92, 0x9a04, 0x6126, + 0x4b6c, 0x57d6, 0xca31, 0x97f3, 0x1f99, 0xf4fd, 0xda4d, 0x42ce}}, + /* Test case with the group size as modulus, input = 0. */ + {{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, + /* Test case with the group size as modulus, input = 1. */ + {{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, + /* Test case with the group size as modulus, input = 2. */ + {{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x20a1, 0x681b, 0x2f46, 0xdfe9, 0x501d, 0x57a4, 0x6e73, 0x5d57, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}}, + /* Test case with the group size as modulus, input = group - 1. */ + {{0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, + 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}}, + + /* Test cases with the field size as modulus. */ + + /* Test case with the field size as modulus, needing 637 divsteps. */ + {{0x9ec3, 0x1919, 0xca84, 0x7c11, 0xf996, 0x06f3, 0x5408, 0x6688, + 0x1320, 0xdb8a, 0x632a, 0x0dcb, 0x8a84, 0x6bee, 0x9c95, 0xe34e}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x18e5, 0x19b6, 0xdf92, 0x1aaa, 0x09fb, 0x8a3f, 0x52b0, 0x8701, + 0xac0c, 0x2582, 0xda44, 0x9bcc, 0x6828, 0x1c53, 0xbd8f, 0xbd2c}}, + /* example with field size as modulus needing 637 divsteps */ + {{0xaec3, 0xa7cf, 0x2f2d, 0x0693, 0x5ad5, 0xa8ff, 0x7ec7, 0x30ff, + 0x0c8b, 0xc242, 0xcab2, 0x063a, 0xf86e, 0x6057, 0x9cbd, 0xf6d8}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0310, 0x579d, 0xcb38, 0x9030, 0x3ded, 0x9bb9, 0x1234, 0x63ce, + 0x0c63, 0x8e3d, 0xacfe, 0x3c20, 0xdc85, 0xf859, 0x919e, 0x1d45}}, + /* example with field size as modulus needing 564 divsteps starting at delta=1/2 */ + {{0x63ae, 0x8d10, 0x0071, 0xdb5c, 0xb454, 0x78d1, 0x744a, 0x5f8e, + 0xe4d8, 0x87b1, 0x8e62, 0x9590, 0xcede, 0xa070, 0x36b4, 0x7f6f}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0xfdc8, 0xe8d5, 0xbe15, 0x9f86, 0xa5fe, 0xf18e, 0xa7ff, 0xd291, + 0xf4c2, 0x9c87, 0xf150, 0x073e, 0x69b8, 0xf7c4, 0xee4b, 0xc7e6}}, + /* Test case with the field size as modulus, needing 935 divsteps with + broken eta handling. */ + {{0x1b37, 0xbdc3, 0x8bcd, 0x25e3, 0x1eae, 0x567d, 0x30b6, 0xf0d8, + 0x9277, 0x0cf8, 0x9c2e, 0xecd7, 0x631d, 0xe38f, 0xd4f8, 0x5c93}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x1622, 0xe05b, 0xe880, 0x7de9, 0x3e45, 0xb682, 0xee6c, 0x67ed, + 0xa179, 0x15db, 0x6b0d, 0xa656, 0x7ccb, 0x8ef7, 0xa2ff, 0xe279}}, + /* Test case with the field size as modulus, input = 0. */ + {{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, + /* Test case with the field size as modulus, input = 1. */ + {{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, + /* Test case with the field size as modulus, input = 2. */ + {{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0xfe18, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}}, + /* Test case with the field size as modulus, input = field - 1. */ + {{0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, + {0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}}, + + /* Selected from a large number of random inputs to reach small/large + * d/e values in various configurations. */ + {{0x3a08, 0x23e1, 0x4d8c, 0xe606, 0x3263, 0x67af, 0x9bf1, 0x9d70, + 0xf5fd, 0x12e4, 0x03c8, 0xb9ca, 0xe847, 0x8c5d, 0x6322, 0xbd30}, + {0x8359, 0x59dd, 0x1831, 0x7c1a, 0x1e83, 0xaee1, 0x770d, 0xcea8, + 0xfbb1, 0xeed6, 0x10b5, 0xe2c6, 0x36ea, 0xee17, 0xe32c, 0xffff}, + {0x1727, 0x0f36, 0x6f85, 0x5d0c, 0xca6c, 0x3072, 0x9628, 0x5842, + 0xcb44, 0x7c2b, 0xca4f, 0x62e5, 0x29b1, 0x6ffd, 0x9055, 0xc196}}, + {{0x905d, 0x41c8, 0xa2ff, 0x295b, 0x72bb, 0x4679, 0x6d01, 0x2c98, + 0xb3e0, 0xc537, 0xa310, 0xe07e, 0xe72f, 0x4999, 0x1148, 0xf65e}, + {0x5b41, 0x4239, 0x3c37, 0x5130, 0x30e3, 0xff35, 0xc51f, 0x1a43, + 0xdb23, 0x13cf, 0x9f49, 0xf70c, 0x5e70, 0xd411, 0x3005, 0xf8c6}, + {0xc30e, 0x68f0, 0x201a, 0xe10c, 0x864a, 0x6243, 0xe946, 0x43ae, + 0xf3f1, 0x52dc, 0x1f7f, 0x50d4, 0x2797, 0x064c, 0x5ca4, 0x90e3}}, + {{0xf1b5, 0xc6e5, 0xd2c4, 0xff95, 0x27c5, 0x0c92, 0x5d19, 0x7ae5, + 0x4fbe, 0x5438, 0x99e1, 0x880d, 0xd892, 0xa05c, 0x6ffd, 0x7eac}, + {0x2153, 0xcc9d, 0xfc6c, 0x8358, 0x49a1, 0x01e2, 0xcef0, 0x4969, + 0xd69a, 0x8cef, 0xf5b2, 0xfd95, 0xdcc2, 0x71f4, 0x6ae2, 0xceeb}, + {0x9b2e, 0xcdc6, 0x0a5c, 0x7317, 0x9084, 0xe228, 0x56cf, 0xd512, + 0x628a, 0xce21, 0x3473, 0x4e13, 0x8823, 0x1ed0, 0x34d0, 0xbfa3}}, + {{0x5bae, 0x53e5, 0x5f4d, 0x21ca, 0xb875, 0x8ecf, 0x9aa6, 0xbe3c, + 0x9f96, 0x7b82, 0x375d, 0x4d3e, 0x491c, 0xb1eb, 0x04c9, 0xb6c8}, + {0xfcfd, 0x10b7, 0x73b2, 0xd23b, 0xa357, 0x67da, 0x0d9f, 0x8702, + 0xa037, 0xff8e, 0x0e8b, 0x1801, 0x2c5c, 0x4e6e, 0x4558, 0xfff2}, + {0xc50f, 0x5654, 0x6713, 0x5ef5, 0xa7ce, 0xa647, 0xc832, 0x69ce, + 0x1d5c, 0x4310, 0x0746, 0x5a01, 0x96ea, 0xde4b, 0xa88b, 0x5543}}, + {{0xdc7f, 0x5e8c, 0x89d1, 0xb077, 0xd521, 0xcf90, 0x32fa, 0x5737, + 0x839e, 0x1464, 0x007c, 0x09c6, 0x9371, 0xe8ea, 0xc1cb, 0x75c4}, + {0xe3a3, 0x107f, 0xa82a, 0xa375, 0x4578, 0x60f4, 0x75c9, 0x5ee4, + 0x3fd7, 0x2736, 0x2871, 0xd3d2, 0x5f1d, 0x1abb, 0xa764, 0xffff}, + {0x45c6, 0x1f2e, 0xb14c, 0x84d7, 0x7bb7, 0x5a04, 0x0504, 0x3f33, + 0x5cc1, 0xb07a, 0x6a6c, 0x786f, 0x647f, 0xe1d7, 0x78a2, 0x4cf4}}, + {{0xc006, 0x356f, 0x8cd2, 0x967b, 0xb49e, 0x2d4e, 0x14bf, 0x4bcb, + 0xddab, 0xd3f9, 0xa068, 0x2c1c, 0xd242, 0xa56d, 0xf2c7, 0x5f97}, + {0x465b, 0xb745, 0x0e0d, 0x69a9, 0x987d, 0xcb37, 0xf637, 0xb311, + 0xc4d6, 0x2ddb, 0xf68f, 0x2af9, 0x959d, 0x3f53, 0x98f2, 0xf640}, + {0xc0f2, 0x6bfb, 0xf5c3, 0x91c1, 0x6b05, 0x0825, 0x5ca0, 0x7df7, + 0x9d55, 0x6d9e, 0xfe94, 0x2ad9, 0xd9f0, 0xe68b, 0xa72b, 0xd1b2}}, + {{0x2279, 0x61ba, 0x5bc6, 0x136b, 0xf544, 0x717c, 0xafda, 0x02bd, + 0x79af, 0x1fad, 0xea09, 0x81bb, 0x932b, 0x32c9, 0xdf1d, 0xe576}, + {0x8215, 0x7817, 0xca82, 0x43b0, 0x9b06, 0xea65, 0x1291, 0x0621, + 0x0089, 0x46fe, 0xc5a6, 0xddd7, 0x8065, 0xc6a0, 0x214b, 0xfc64}, + {0x04bf, 0x6f2a, 0x86b2, 0x841a, 0x4a95, 0xc632, 0x97b7, 0x5821, + 0x2b18, 0x1bb0, 0x3e97, 0x935e, 0xcc7d, 0x066b, 0xd513, 0xc251}}, + {{0x76e8, 0x5bc2, 0x3eaa, 0x04fc, 0x9974, 0x92c1, 0x7c15, 0xfa89, + 0x1151, 0x36ee, 0x48b2, 0x049c, 0x5f16, 0xcee4, 0x925b, 0xe98e}, + {0x913f, 0x0a2d, 0xa185, 0x9fea, 0xda5a, 0x4025, 0x40d7, 0x7cfa, + 0x88ca, 0xbbe8, 0xb265, 0xb7e4, 0x6cb1, 0xed64, 0xc6f9, 0xffb5}, + {0x6ab1, 0x1a86, 0x5009, 0x152b, 0x1cc4, 0xe2c8, 0x960b, 0x19d0, + 0x3554, 0xc562, 0xd013, 0xcf91, 0x10e1, 0x7933, 0xe195, 0xcf49}}, + {{0x9cb5, 0xd2d7, 0xc6ed, 0xa818, 0xb495, 0x06ee, 0x0f4a, 0x06e3, + 0x4c5a, 0x80ce, 0xd49a, 0x4cd7, 0x7487, 0x92af, 0xe516, 0x676c}, + {0xd6e9, 0x6b85, 0x619a, 0xb52c, 0x20a0, 0x2f79, 0x3545, 0x1edd, + 0x5a6f, 0x8082, 0x9b80, 0xf8f8, 0xc78a, 0xd0a3, 0xadf4, 0xffff}, + {0x01c2, 0x2118, 0xef5e, 0xa877, 0x046a, 0xd2c2, 0x2ad5, 0x951c, + 0x8900, 0xa5c9, 0x8d0f, 0x6b61, 0x55d3, 0xd572, 0x48de, 0x9219}}, + {{0x5114, 0x0644, 0x23dd, 0x01d3, 0xc101, 0xa659, 0xea17, 0x640f, + 0xf767, 0x2644, 0x9cec, 0xd8ba, 0xd6da, 0x9156, 0x8aeb, 0x875a}, + {0xc1bf, 0xdae9, 0xe96b, 0xce77, 0xf7a1, 0x3e99, 0x5c2e, 0x973b, + 0xd048, 0x5bd0, 0x4e8a, 0xcb85, 0xce39, 0x37f5, 0x815d, 0xffff}, + {0x48cc, 0x35b6, 0x26d4, 0x2ea6, 0x50d6, 0xa2f9, 0x64b6, 0x03bf, + 0xd00c, 0xe057, 0x3343, 0xfb79, 0x3ce5, 0xf717, 0xc5af, 0xe185}}, + {{0x13ff, 0x6c76, 0x2077, 0x16e0, 0xd5ca, 0xf2ad, 0x8dba, 0x8f49, + 0x7887, 0x16f9, 0xb646, 0xfc87, 0xfa31, 0x5096, 0xf08c, 0x3fbe}, + {0x8139, 0x6fd7, 0xf6df, 0xa7bf, 0x6699, 0x5361, 0x6f65, 0x13c8, + 0xf4d1, 0xe28f, 0xc545, 0x0a8c, 0x5274, 0xb0a6, 0xffff, 0xffff}, + {0x22ca, 0x0cd6, 0xc1b5, 0xb064, 0x44a7, 0x297b, 0x495f, 0x34ac, + 0xfa95, 0xec62, 0xf08d, 0x621c, 0x66a6, 0xba94, 0x84c6, 0x8ee0}}, + {{0xaa30, 0x312e, 0x439c, 0x4e88, 0x2e2f, 0x32dc, 0xb880, 0xa28e, + 0xf795, 0xc910, 0xb406, 0x8dd7, 0xb187, 0xa5a5, 0x38f1, 0xe49e}, + {0xfb19, 0xf64a, 0xba6a, 0x8ec2, 0x7255, 0xce89, 0x2cf9, 0x9cba, + 0xe1fe, 0x50da, 0x1705, 0xac52, 0xe3d4, 0x4269, 0x0648, 0xfd77}, + {0xb4c8, 0x6e8a, 0x2b5f, 0x4c2d, 0x5a67, 0xa7bb, 0x7d6d, 0x5569, + 0xa0ea, 0x244a, 0xc0f2, 0xf73d, 0x58cf, 0xac7f, 0xd32b, 0x3018}}, + {{0xc953, 0x1ae1, 0xae46, 0x8709, 0x19c2, 0xa986, 0x9abe, 0x1611, + 0x0395, 0xd5ab, 0xf0f6, 0xb5b0, 0x5b2b, 0x0317, 0x80ba, 0x376d}, + {0xfe77, 0xbc03, 0xac2f, 0x9d00, 0xa175, 0x293d, 0x3b56, 0x0e3a, + 0x0a9c, 0xf40c, 0x690e, 0x1508, 0x95d4, 0xddc4, 0xe805, 0xffff}, + {0xb1ce, 0x0929, 0xa5fe, 0x4b50, 0x9d5d, 0x8187, 0x2557, 0x4376, + 0x11ba, 0xdcef, 0xc1f3, 0xd531, 0x1824, 0x93f6, 0xd81f, 0x8f83}}, + {{0xb8d2, 0xb900, 0x4a0c, 0x7188, 0xa5bf, 0x1b0b, 0x2ae5, 0xa35b, + 0x98e0, 0x610c, 0x86db, 0x2487, 0xa267, 0x002c, 0xebb6, 0xc5f4}, + {0x9cdd, 0x1c1b, 0x2f06, 0x43d1, 0xce47, 0xc334, 0x6e60, 0xc016, + 0x989e, 0x0ab2, 0x0cac, 0x1196, 0xe2d9, 0x2e04, 0xc62b, 0xffff}, + {0xdc36, 0x1f05, 0x6aa9, 0x7a20, 0x944f, 0x2fd3, 0xa553, 0xdb4f, + 0xbd5c, 0x3a75, 0x25d4, 0xe20e, 0xa387, 0x1410, 0xdbb1, 0x1b60}}, + {{0x76b3, 0x2207, 0x4930, 0x5dd7, 0x65a0, 0xd55c, 0xb443, 0x53b7, + 0x5c22, 0x818a, 0xb2e7, 0x9de8, 0x9985, 0xed45, 0x33b1, 0x53e8}, + {0x7913, 0x44e1, 0xf15b, 0x5edd, 0x34f3, 0x4eba, 0x0758, 0x7104, + 0x32d9, 0x28f3, 0x4401, 0x85c5, 0xb695, 0xb899, 0xc0f2, 0xffff}, + {0x7f43, 0xd202, 0x24c9, 0x69f3, 0x74dc, 0x1a69, 0xeaee, 0x5405, + 0x1755, 0x4bb8, 0x04e3, 0x2fd2, 0xada8, 0x39eb, 0x5b4d, 0x96ca}}, + {{0x807b, 0x7112, 0xc088, 0xdafd, 0x02fa, 0x9d95, 0x5e42, 0xc033, + 0xde0a, 0xeecf, 0x8e90, 0x8da1, 0xb17e, 0x9a5b, 0x4c6d, 0x1914}, + {0x4871, 0xd1cb, 0x47d7, 0x327f, 0x09ec, 0x97bb, 0x2fae, 0xd346, + 0x6b78, 0x3707, 0xfeb2, 0xa6ab, 0x13df, 0x76b0, 0x8fb9, 0xffb3}, + {0x179e, 0xb63b, 0x4784, 0x231e, 0x9f42, 0x7f1a, 0xa3fb, 0xdd8c, + 0xd1eb, 0xb4c9, 0x8ca7, 0x018c, 0xf691, 0x576c, 0xa7d6, 0xce27}}, + {{0x5f45, 0x7c64, 0x083d, 0xedd5, 0x08a0, 0x0c64, 0x6c6f, 0xec3c, + 0xe2fb, 0x352c, 0x9303, 0x75e4, 0xb4e0, 0x8b09, 0xaca4, 0x7025}, + {0x1025, 0xb482, 0xfed5, 0xa678, 0x8966, 0x9359, 0x5329, 0x98bb, + 0x85b2, 0x73ba, 0x9982, 0x6fdc, 0xf190, 0xbe8c, 0xdc5c, 0xfd93}, + {0x83a2, 0x87a4, 0xa680, 0x52a1, 0x1ba1, 0x8848, 0x5db7, 0x9744, + 0x409c, 0x0745, 0x0e1e, 0x1cfc, 0x00cd, 0xf573, 0x2071, 0xccaa}}, + {{0xf61f, 0x63d4, 0x536c, 0x9eb9, 0x5ddd, 0xbb11, 0x9014, 0xe904, + 0xfe01, 0x6b45, 0x1858, 0xcb5b, 0x4c38, 0x43e1, 0x381d, 0x7f94}, + {0xf61f, 0x63d4, 0xd810, 0x7ca3, 0x8a04, 0x4b83, 0x11fc, 0xdf94, + 0x4169, 0xbd05, 0x608e, 0x7151, 0x4fbf, 0xb31a, 0x38a7, 0xa29b}, + {0xe621, 0xdfa5, 0x3d06, 0x1d03, 0x81e6, 0x00da, 0x53a6, 0x965e, + 0x93e5, 0x2164, 0x5b61, 0x59b8, 0xa629, 0x8d73, 0x699a, 0x6111}}, + {{0x4cc3, 0xd29e, 0xf4a3, 0x3428, 0x2048, 0xeec9, 0x5f50, 0x99a4, + 0x6de9, 0x05f2, 0x5aa9, 0x5fd2, 0x98b4, 0x1adc, 0x225f, 0x777f}, + {0xe649, 0x37da, 0x5ba6, 0x5765, 0x3f4a, 0x8a1c, 0x2e79, 0xf550, + 0x1a54, 0xcd1e, 0x7218, 0x3c3c, 0x6311, 0xfe28, 0x95fb, 0xed97}, + {0xe9b6, 0x0c47, 0x3f0e, 0x849b, 0x11f8, 0xe599, 0x5e4d, 0xd618, + 0xa06d, 0x33a0, 0x9a3e, 0x44db, 0xded8, 0x10f0, 0x94d2, 0x81fb}}, + {{0x2e59, 0x7025, 0xd413, 0x455a, 0x1ce3, 0xbd45, 0x7263, 0x27f7, + 0x23e3, 0x518e, 0xbe06, 0xc8c4, 0xe332, 0x4276, 0x68b4, 0xb166}, + {0x596f, 0x0cf6, 0xc8ec, 0x787b, 0x04c1, 0x473c, 0xd2b8, 0x8d54, + 0x9cdf, 0x77f2, 0xd3f3, 0x6735, 0x0638, 0xf80e, 0x9467, 0xc6aa}, + {0xc7e7, 0x1822, 0xb62a, 0xec0d, 0x89cd, 0x7846, 0xbfa2, 0x35d5, + 0xfa38, 0x870f, 0x494b, 0x1697, 0x8b17, 0xf904, 0x10b6, 0x9822}}, + {{0x6d5b, 0x1d4f, 0x0aaf, 0x807b, 0x35fb, 0x7ee8, 0x00c6, 0x059a, + 0xddf0, 0x1fb1, 0xc38a, 0xd78e, 0x2aa4, 0x79e7, 0xad28, 0xc3f1}, + {0xe3bb, 0x174e, 0xe0a8, 0x74b6, 0xbd5b, 0x35f6, 0x6d23, 0x6328, + 0xc11f, 0x83e1, 0xf928, 0xa918, 0x838e, 0xbf43, 0xe243, 0xfffb}, + {0x9cf2, 0x6b8b, 0x3476, 0x9d06, 0xdcf2, 0xdb8a, 0x89cd, 0x4857, + 0x75c2, 0xabb8, 0x490b, 0xc9bd, 0x890e, 0xe36e, 0xd552, 0xfffa}}, + {{0x2f09, 0x9d62, 0xa9fc, 0xf090, 0xd6d1, 0x9d1d, 0x1828, 0xe413, + 0xc92b, 0x3d5a, 0x1373, 0x368c, 0xbaf2, 0x2158, 0x71eb, 0x08a3}, + {0x2f09, 0x1d62, 0x4630, 0x0de1, 0x06dc, 0xf7f1, 0xc161, 0x1e92, + 0x7495, 0x97e4, 0x94b6, 0xa39e, 0x4f1b, 0x18f8, 0x7bd4, 0x0c4c}, + {0xeb3d, 0x723d, 0x0907, 0x525b, 0x463a, 0x49a8, 0xc6b8, 0xce7f, + 0x740c, 0x0d7d, 0xa83b, 0x457f, 0xae8e, 0xc6af, 0xd331, 0x0475}}, + {{0x6abd, 0xc7af, 0x3e4e, 0x95fd, 0x8fc4, 0xee25, 0x1f9c, 0x0afe, + 0x291d, 0xcde0, 0x48f4, 0xb2e8, 0xf7af, 0x8f8d, 0x0bd6, 0x078d}, + {0x4037, 0xbf0e, 0x2081, 0xf363, 0x13b2, 0x381e, 0xfb6e, 0x818e, + 0x27e4, 0x5662, 0x18b0, 0x0cd2, 0x81f5, 0x9415, 0x0d6c, 0xf9fb}, + {0xd205, 0x0981, 0x0498, 0x1f08, 0xdb93, 0x1732, 0x0579, 0x1424, + 0xad95, 0x642f, 0x050c, 0x1d6d, 0xfc95, 0xfc4a, 0xd41b, 0x3521}}, + {{0xf23a, 0x4633, 0xaef4, 0x1a92, 0x3c8b, 0x1f09, 0x30f3, 0x4c56, + 0x2a2f, 0x4f62, 0xf5e4, 0x8329, 0x63cc, 0xb593, 0xec6a, 0xc428}, + {0x93a7, 0xfcf6, 0x606d, 0xd4b2, 0x2aad, 0x28b4, 0xc65b, 0x8998, + 0x4e08, 0xd178, 0x0900, 0xc82b, 0x7470, 0xa342, 0x7c0f, 0xffff}, + {0x315f, 0xf304, 0xeb7b, 0xe5c3, 0x1451, 0x6311, 0x8f37, 0x93a8, + 0x4a38, 0xa6c6, 0xe393, 0x1087, 0x6301, 0xd673, 0x4ec4, 0xffff}}, + {{0x892e, 0xeed0, 0x1165, 0xcbc1, 0x5545, 0xa280, 0x7243, 0x10c9, + 0x9536, 0x36af, 0xb3fc, 0x2d7c, 0xe8a5, 0x09d6, 0xe1d4, 0xe85d}, + {0xae09, 0xc28a, 0xd777, 0xbd80, 0x23d6, 0xf980, 0xeb7c, 0x4e0e, + 0xf7dc, 0x6475, 0xf10a, 0x2d33, 0x5dfd, 0x797a, 0x7f1c, 0xf71a}, + {0x4064, 0x8717, 0xd091, 0x80b0, 0x4527, 0x8442, 0xac8b, 0x9614, + 0xc633, 0x35f5, 0x7714, 0x2e83, 0x4aaa, 0xd2e4, 0x1acd, 0x0562}}, + {{0xdb64, 0x0937, 0x308b, 0x53b0, 0x00e8, 0xc77f, 0x2f30, 0x37f7, + 0x79ce, 0xeb7f, 0xde81, 0x9286, 0xafda, 0x0e62, 0xae00, 0x0067}, + {0x2cc7, 0xd362, 0xb161, 0x0557, 0x4ff2, 0xb9c8, 0x06fe, 0x5f2b, + 0xde33, 0x0190, 0x28c6, 0xb886, 0xee2b, 0x5a4e, 0x3289, 0x0185}, + {0x4215, 0x923e, 0xf34f, 0xb362, 0x88f8, 0xceec, 0xafdd, 0x7f42, + 0x0c57, 0x56b2, 0xa366, 0x6a08, 0x0826, 0xfb8f, 0x1b03, 0x0163}}, + {{0xa4ba, 0x8408, 0x810a, 0xdeba, 0x47a3, 0x853a, 0xeb64, 0x2f74, + 0x3039, 0x038c, 0x7fbb, 0x498e, 0xd1e9, 0x46fb, 0x5691, 0x32a4}, + {0xd749, 0xb49d, 0x20b7, 0x2af6, 0xd34a, 0xd2da, 0x0a10, 0xf781, + 0x58c9, 0x171f, 0x3cb6, 0x6337, 0x88cd, 0xcf1e, 0xb246, 0x7351}, + {0xf729, 0xcf0a, 0x96ea, 0x032c, 0x4a8f, 0x42fe, 0xbac8, 0xec65, + 0x1510, 0x0d75, 0x4c17, 0x8d29, 0xa03f, 0x8b7e, 0x2c49, 0x0000}}, + {{0x0fa4, 0x8e1c, 0x3788, 0xba3c, 0x8d52, 0xd89d, 0x12c8, 0xeced, + 0x9fe6, 0x9b88, 0xecf3, 0xe3c8, 0xac48, 0x76ed, 0xf23e, 0xda79}, + {0x1103, 0x227c, 0x5b00, 0x3fcf, 0xc5d0, 0x2d28, 0x8020, 0x4d1c, + 0xc6b9, 0x67f9, 0x6f39, 0x989a, 0xda53, 0x3847, 0xd416, 0xe0d0}, + {0xdd8e, 0xcf31, 0x3710, 0x7e44, 0xa511, 0x933c, 0x0cc3, 0x5145, + 0xf632, 0x5e1d, 0x038f, 0x5ce7, 0x7265, 0xda9d, 0xded6, 0x08f8}}, + {{0xe2c8, 0x91d5, 0xa5f5, 0x735f, 0x6b58, 0x56dc, 0xb39d, 0x5c4a, + 0x57d0, 0xa1c2, 0xd92f, 0x9ad4, 0xf7c4, 0x51dd, 0xaf5c, 0x0096}, + {0x1739, 0x7207, 0x7505, 0xbf35, 0x42de, 0x0a29, 0xa962, 0xdedf, + 0x53e8, 0x12bf, 0xcde7, 0xd8e2, 0x8d4d, 0x2c4b, 0xb1b1, 0x0628}, + {0x992d, 0xe3a7, 0xb422, 0xc198, 0x23ab, 0xa6ef, 0xb45d, 0x50da, + 0xa738, 0x014a, 0x2310, 0x85fb, 0x5fe8, 0x1b18, 0x1774, 0x03a7}}, + {{0x1f16, 0x2b09, 0x0236, 0xee90, 0xccf9, 0x9775, 0x8130, 0x4c91, + 0x9091, 0x310b, 0x6dc4, 0x86f6, 0xc2e8, 0xef60, 0xfc0e, 0xf3a4}, + {0x9f49, 0xac15, 0x02af, 0x110f, 0xc59d, 0x5677, 0xa1a9, 0x38d5, + 0x914f, 0xa909, 0x3a3a, 0x4a39, 0x3703, 0xea30, 0x73da, 0xffad}, + {0x15ed, 0xdd16, 0x83c7, 0x270a, 0x862f, 0xd8ad, 0xcaa1, 0x5f41, + 0x99a9, 0x3fc8, 0x7bb2, 0x360a, 0xb06d, 0xfadc, 0x1b36, 0xffa8}}, + {{0xc4e0, 0xb8fd, 0x5106, 0xe169, 0x754c, 0xa58c, 0xc413, 0x8224, + 0x5483, 0x63ec, 0xd477, 0x8473, 0x4778, 0x9281, 0x0000, 0x0000}, + {0x85e1, 0xff54, 0xb200, 0xe413, 0xf4f4, 0x4c0f, 0xfcec, 0xc183, + 0x60d3, 0x1b0c, 0x3834, 0x601c, 0x943c, 0xbe6e, 0x0002, 0x0000}, + {0xf4f8, 0xfd5e, 0x61ef, 0xece8, 0x9199, 0xe5c4, 0x05a6, 0xe6c3, + 0xc4ae, 0x8b28, 0x66b1, 0x8a95, 0x9ece, 0x8f4a, 0x0001, 0x0000}}, + {{0xeae9, 0xa1b4, 0xc6d8, 0x2411, 0x2b5a, 0x1dd0, 0x2dc9, 0xb57b, + 0x5ccd, 0x4957, 0xaf59, 0xa04b, 0x5f42, 0xab7c, 0x2826, 0x526f}, + {0xf407, 0x165a, 0xb724, 0x2f12, 0x2ea1, 0x470b, 0x4464, 0xbd35, + 0x606f, 0xd73e, 0x50d3, 0x8a7f, 0x8029, 0x7ffc, 0xbe31, 0x6cfb}, + {0x8171, 0x1f4c, 0xced2, 0x9c99, 0x6d7e, 0x5a0f, 0xfefb, 0x59e3, + 0xa0c8, 0xabd9, 0xc4c5, 0x57d3, 0xbfa3, 0x4f11, 0x96a2, 0x5a7d}}, + {{0xe068, 0x4cc0, 0x8bcd, 0xc903, 0x9e52, 0xb3e1, 0xd745, 0x0995, + 0xdd8f, 0xf14b, 0xd2ac, 0xd65a, 0xda1d, 0xa742, 0xbac5, 0x474c}, + {0x7481, 0xf2ad, 0x9757, 0x2d82, 0xb683, 0xb16b, 0x0002, 0x7b60, + 0x8f0c, 0x2594, 0x8f64, 0x3b7a, 0x3552, 0x8d9d, 0xb9d7, 0x67eb}, + {0xcaab, 0xb9a1, 0xf966, 0xe311, 0x5b34, 0x0fa0, 0x6abc, 0x8134, + 0xab3d, 0x90f6, 0x1984, 0x9232, 0xec17, 0x74e5, 0x2ceb, 0x434e}}, + {{0x0fb1, 0x7a55, 0x1a5c, 0x53eb, 0xd7b3, 0x7a01, 0xca32, 0x31f6, + 0x3b74, 0x679e, 0x1501, 0x6c57, 0xdb20, 0x8b7c, 0xd7d0, 0x8097}, + {0xb127, 0xb20c, 0xe3a2, 0x96f3, 0xe0d8, 0xd50c, 0x14b4, 0x0b40, + 0x6eeb, 0xa258, 0x99db, 0x3c8c, 0x0f51, 0x4198, 0x3887, 0xffd0}, + {0x0273, 0x9f8c, 0x9669, 0xbbba, 0x1c49, 0x767c, 0xc2af, 0x59f0, + 0x1366, 0xd397, 0x63ac, 0x6fe8, 0x1a9a, 0x1259, 0x01d0, 0x0016}}, + {{0x7876, 0x2a35, 0xa24a, 0x433e, 0x5501, 0x573c, 0xd76d, 0xcb82, + 0x1334, 0xb4a6, 0xf290, 0xc797, 0xeae9, 0x2b83, 0x1e2b, 0x8b14}, + {0x3885, 0x8aef, 0x9dea, 0x2b8c, 0xdd7c, 0xd7cd, 0xb0cc, 0x05ee, + 0x361b, 0x3800, 0xb0d4, 0x4c23, 0xbd3f, 0x5180, 0x9783, 0xff80}, + {0xab36, 0x3104, 0xdae8, 0x0704, 0x4a28, 0x6714, 0x824b, 0x0051, + 0x8134, 0x1f6a, 0x712d, 0x1f03, 0x03b2, 0xecac, 0x377d, 0xfef9}} + }; + + int i, j, ok; + + /* Test known inputs/outputs */ + for (i = 0; (size_t)i < sizeof(CASES) / sizeof(CASES[0]); ++i) { + uint16_t out[16]; + test_modinv32_uint16(out, CASES[i][0], CASES[i][1]); + for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]); +#ifdef SECP256K1_WIDEMUL_INT128 + test_modinv64_uint16(out, CASES[i][0], CASES[i][1]); + for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]); +#endif + } + + for (i = 0; i < 100 * COUNT; ++i) { + /* 256-bit numbers in 16-uint16_t's notation */ + static const uint16_t ZERO[16] = {0}; + uint16_t xd[16]; /* the number (in range [0,2^256)) to be inverted */ + uint16_t md[16]; /* the modulus (odd, in range [3,2^256)) */ + uint16_t id[16]; /* the inverse of xd mod md */ + + /* generate random xd and md, so that md is odd, md>1, xd<md, and gcd(xd,md)=1 */ + do { + /* generate random xd and md (with many subsequent 0s and 1s) */ + secp256k1_testrand256_test((unsigned char*)xd); + secp256k1_testrand256_test((unsigned char*)md); + md[0] |= 1; /* modulus must be odd */ + /* If modulus is 1, find another one. */ + ok = md[0] != 1; + for (j = 1; j < 16; ++j) ok |= md[j] != 0; + mulmod256(xd, xd, NULL, md); /* Make xd = xd mod md */ + } while (!(ok && coprime(xd, md))); + + test_modinv32_uint16(id, xd, md); +#ifdef SECP256K1_WIDEMUL_INT128 + test_modinv64_uint16(id, xd, md); +#endif + + /* In a few cases, also test with input=0 */ + if (i < COUNT) { + test_modinv32_uint16(id, ZERO, md); +#ifdef SECP256K1_WIDEMUL_INT128 + test_modinv64_uint16(id, ZERO, md); +#endif + } + } +} + +/***** INT128 TESTS *****/ + +#ifdef SECP256K1_WIDEMUL_INT128 +/* Add two 256-bit numbers (represented as 16 uint16_t's in LE order) together mod 2^256. */ +static void add256(uint16_t* out, const uint16_t* a, const uint16_t* b) { + int i; + uint32_t carry = 0; + for (i = 0; i < 16; ++i) { + carry += a[i]; + carry += b[i]; + out[i] = carry; + carry >>= 16; + } +} + +/* Negate a 256-bit number (represented as 16 uint16_t's in LE order) mod 2^256. */ +static void neg256(uint16_t* out, const uint16_t* a) { + int i; + uint32_t carry = 1; + for (i = 0; i < 16; ++i) { + carry += (uint16_t)~a[i]; + out[i] = carry; + carry >>= 16; + } +} + +/* Right-shift a 256-bit number (represented as 16 uint16_t's in LE order). */ +static void rshift256(uint16_t* out, const uint16_t* a, int n, int sign_extend) { + uint16_t sign = sign_extend && (a[15] >> 15); + int i, j; + for (i = 15; i >= 0; --i) { + uint16_t v = 0; + for (j = 0; j < 16; ++j) { + int frompos = i*16 + j + n; + if (frompos >= 256) { + v |= sign << j; + } else { + v |= ((uint16_t)((a[frompos >> 4] >> (frompos & 15)) & 1)) << j; + } + } + out[i] = v; + } +} + +/* Load a 64-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */ +static void load256u64(uint16_t* out, uint64_t v, int is_signed) { + int i; + uint64_t sign = is_signed && (v >> 63) ? UINT64_MAX : 0; + for (i = 0; i < 4; ++i) { + out[i] = v >> (16 * i); + } + for (i = 4; i < 16; ++i) { + out[i] = sign; + } +} + +/* Load a 128-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */ +static void load256two64(uint16_t* out, uint64_t hi, uint64_t lo, int is_signed) { + int i; + uint64_t sign = is_signed && (hi >> 63) ? UINT64_MAX : 0; + for (i = 0; i < 4; ++i) { + out[i] = lo >> (16 * i); + } + for (i = 4; i < 8; ++i) { + out[i] = hi >> (16 * (i - 4)); + } + for (i = 8; i < 16; ++i) { + out[i] = sign; + } +} + +/* Check whether the 256-bit value represented by array of 16-bit values is in range -2^127 < v < 2^127. */ +static int int256is127(const uint16_t* v) { + int all_0 = ((v[7] & 0x8000) == 0), all_1 = ((v[7] & 0x8000) == 0x8000); + int i; + for (i = 8; i < 16; ++i) { + if (v[i] != 0) all_0 = 0; + if (v[i] != 0xffff) all_1 = 0; + } + return all_0 || all_1; +} + +static void load256u128(uint16_t* out, const secp256k1_uint128* v) { + uint64_t lo = secp256k1_u128_to_u64(v), hi = secp256k1_u128_hi_u64(v); + load256two64(out, hi, lo, 0); +} + +static void load256i128(uint16_t* out, const secp256k1_int128* v) { + uint64_t lo; + int64_t hi; + secp256k1_int128 c = *v; + lo = secp256k1_i128_to_u64(&c); + secp256k1_i128_rshift(&c, 64); + hi = secp256k1_i128_to_i64(&c); + load256two64(out, hi, lo, 1); +} + +static void run_int128_test_case(void) { + unsigned char buf[32]; + uint64_t v[4]; + secp256k1_int128 swa, swz; + secp256k1_uint128 uwa, uwz; + uint64_t ub, uc; + int64_t sb, sc; + uint16_t rswa[16], rswz[32], rswr[32], ruwa[16], ruwz[32], ruwr[32]; + uint16_t rub[16], ruc[16], rsb[16], rsc[16]; + int i; + + /* Generate 32-byte random value. */ + secp256k1_testrand256_test(buf); + /* Convert into 4 64-bit integers. */ + for (i = 0; i < 4; ++i) { + uint64_t vi = 0; + int j; + for (j = 0; j < 8; ++j) vi = (vi << 8) + buf[8*i + j]; + v[i] = vi; + } + /* Convert those into a 128-bit value and two 64-bit values (signed and unsigned). */ + secp256k1_u128_load(&uwa, v[1], v[0]); + secp256k1_i128_load(&swa, v[1], v[0]); + ub = v[2]; + sb = v[2]; + uc = v[3]; + sc = v[3]; + /* Load those also into 16-bit array representations. */ + load256u128(ruwa, &uwa); + load256i128(rswa, &swa); + load256u64(rub, ub, 0); + load256u64(rsb, sb, 1); + load256u64(ruc, uc, 0); + load256u64(rsc, sc, 1); + /* test secp256k1_u128_mul */ + mulmod256(ruwr, rub, ruc, NULL); + secp256k1_u128_mul(&uwz, ub, uc); + load256u128(ruwz, &uwz); + CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0); + /* test secp256k1_u128_accum_mul */ + mulmod256(ruwr, rub, ruc, NULL); + add256(ruwr, ruwr, ruwa); + uwz = uwa; + secp256k1_u128_accum_mul(&uwz, ub, uc); + load256u128(ruwz, &uwz); + CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0); + /* test secp256k1_u128_accum_u64 */ + add256(ruwr, rub, ruwa); + uwz = uwa; + secp256k1_u128_accum_u64(&uwz, ub); + load256u128(ruwz, &uwz); + CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0); + /* test secp256k1_u128_rshift */ + rshift256(ruwr, ruwa, uc % 128, 0); + uwz = uwa; + secp256k1_u128_rshift(&uwz, uc % 128); + load256u128(ruwz, &uwz); + CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0); + /* test secp256k1_u128_to_u64 */ + CHECK(secp256k1_u128_to_u64(&uwa) == v[0]); + /* test secp256k1_u128_hi_u64 */ + CHECK(secp256k1_u128_hi_u64(&uwa) == v[1]); + /* test secp256k1_u128_from_u64 */ + secp256k1_u128_from_u64(&uwz, ub); + load256u128(ruwz, &uwz); + CHECK(secp256k1_memcmp_var(rub, ruwz, 16) == 0); + /* test secp256k1_u128_check_bits */ + { + int uwa_bits = 0; + int j; + for (j = 0; j < 128; ++j) { + if (ruwa[j / 16] >> (j % 16)) uwa_bits = 1 + j; + } + for (j = 0; j < 128; ++j) { + CHECK(secp256k1_u128_check_bits(&uwa, j) == (uwa_bits <= j)); + } + } + /* test secp256k1_i128_mul */ + mulmod256(rswr, rsb, rsc, NULL); + secp256k1_i128_mul(&swz, sb, sc); + load256i128(rswz, &swz); + CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0); + /* test secp256k1_i128_accum_mul */ + mulmod256(rswr, rsb, rsc, NULL); + add256(rswr, rswr, rswa); + if (int256is127(rswr)) { + swz = swa; + secp256k1_i128_accum_mul(&swz, sb, sc); + load256i128(rswz, &swz); + CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0); + } + /* test secp256k1_i128_det */ + { + uint16_t rsd[16], rse[16], rst[32]; + int64_t sd = v[0], se = v[1]; + load256u64(rsd, sd, 1); + load256u64(rse, se, 1); + mulmod256(rst, rsc, rsd, NULL); + neg256(rst, rst); + mulmod256(rswr, rsb, rse, NULL); + add256(rswr, rswr, rst); + secp256k1_i128_det(&swz, sb, sc, sd, se); + load256i128(rswz, &swz); + CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0); + } + /* test secp256k1_i128_rshift */ + rshift256(rswr, rswa, uc % 127, 1); + swz = swa; + secp256k1_i128_rshift(&swz, uc % 127); + load256i128(rswz, &swz); + CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0); + /* test secp256k1_i128_to_u64 */ + CHECK(secp256k1_i128_to_u64(&swa) == v[0]); + /* test secp256k1_i128_from_i64 */ + secp256k1_i128_from_i64(&swz, sb); + load256i128(rswz, &swz); + CHECK(secp256k1_memcmp_var(rsb, rswz, 16) == 0); + /* test secp256k1_i128_to_i64 */ + CHECK(secp256k1_i128_to_i64(&swz) == sb); + /* test secp256k1_i128_eq_var */ + { + int expect = (uc & 1); + swz = swa; + if (!expect) { + /* Make sure swz != swa */ + uint64_t v0c = v[0], v1c = v[1]; + if (ub & 64) { + v1c ^= (((uint64_t)1) << (ub & 63)); + } else { + v0c ^= (((uint64_t)1) << (ub & 63)); + } + secp256k1_i128_load(&swz, v1c, v0c); + } + CHECK(secp256k1_i128_eq_var(&swa, &swz) == expect); + } + /* test secp256k1_i128_check_pow2 (sign == 1) */ + { + int expect = (uc & 1); + int pos = ub % 127; + if (expect) { + /* If expect==1, set swz to exactly 2^pos. */ + uint64_t hi = 0; + uint64_t lo = 0; + if (pos >= 64) { + hi = (((uint64_t)1) << (pos & 63)); + } else { + lo = (((uint64_t)1) << (pos & 63)); + } + secp256k1_i128_load(&swz, hi, lo); + } else { + /* If expect==0, set swz = swa, but update expect=1 if swa happens to equal 2^pos. */ + if (pos >= 64) { + if ((v[1] == (((uint64_t)1) << (pos & 63))) && v[0] == 0) expect = 1; + } else { + if ((v[0] == (((uint64_t)1) << (pos & 63))) && v[1] == 0) expect = 1; + } + swz = swa; + } + CHECK(secp256k1_i128_check_pow2(&swz, pos, 1) == expect); + } + /* test secp256k1_i128_check_pow2 (sign == -1) */ + { + int expect = (uc & 1); + int pos = ub % 127; + if (expect) { + /* If expect==1, set swz to exactly -2^pos. */ + uint64_t hi = ~(uint64_t)0; + uint64_t lo = ~(uint64_t)0; + if (pos >= 64) { + hi <<= (pos & 63); + lo = 0; + } else { + lo <<= (pos & 63); + } + secp256k1_i128_load(&swz, hi, lo); + } else { + /* If expect==0, set swz = swa, but update expect=1 if swa happens to equal -2^pos. */ + if (pos >= 64) { + if ((v[1] == ((~(uint64_t)0) << (pos & 63))) && v[0] == 0) expect = 1; + } else { + if ((v[0] == ((~(uint64_t)0) << (pos & 63))) && v[1] == ~(uint64_t)0) expect = 1; + } + swz = swa; + } + CHECK(secp256k1_i128_check_pow2(&swz, pos, -1) == expect); + } +} + +static void run_int128_tests(void) { + { /* secp256k1_u128_accum_mul */ + secp256k1_uint128 res; + + /* Check secp256k1_u128_accum_mul overflow */ + secp256k1_u128_mul(&res, UINT64_MAX, UINT64_MAX); + secp256k1_u128_accum_mul(&res, UINT64_MAX, UINT64_MAX); + CHECK(secp256k1_u128_to_u64(&res) == 2); + CHECK(secp256k1_u128_hi_u64(&res) == 18446744073709551612U); + } + { /* secp256k1_u128_accum_mul */ + secp256k1_int128 res; + + /* Compute INT128_MAX = 2^127 - 1 with secp256k1_i128_accum_mul */ + secp256k1_i128_mul(&res, INT64_MAX, INT64_MAX); + secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MAX); + CHECK(secp256k1_i128_to_u64(&res) == 2); + secp256k1_i128_accum_mul(&res, 4, 9223372036854775807); + secp256k1_i128_accum_mul(&res, 1, 1); + CHECK(secp256k1_i128_to_u64(&res) == UINT64_MAX); + secp256k1_i128_rshift(&res, 64); + CHECK(secp256k1_i128_to_i64(&res) == INT64_MAX); + + /* Compute INT128_MIN = - 2^127 with secp256k1_i128_accum_mul */ + secp256k1_i128_mul(&res, INT64_MAX, INT64_MIN); + CHECK(secp256k1_i128_to_u64(&res) == (uint64_t)INT64_MIN); + secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MIN); + CHECK(secp256k1_i128_to_u64(&res) == 0); + secp256k1_i128_accum_mul(&res, 2, INT64_MIN); + CHECK(secp256k1_i128_to_u64(&res) == 0); + secp256k1_i128_rshift(&res, 64); + CHECK(secp256k1_i128_to_i64(&res) == INT64_MIN); + } + { + /* Randomized tests. */ + int i; + for (i = 0; i < 256 * COUNT; ++i) run_int128_test_case(); + } +} +#endif + +/***** SCALAR TESTS *****/ + +static void scalar_test(void) { + secp256k1_scalar s; + secp256k1_scalar s1; + secp256k1_scalar s2; + unsigned char c[32]; + + /* Set 's' to a random scalar, with value 'snum'. */ + random_scalar_order_test(&s); + + /* Set 's1' to a random scalar, with value 's1num'. */ + random_scalar_order_test(&s1); + + /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */ + random_scalar_order_test(&s2); + secp256k1_scalar_get_b32(c, &s2); + + { + int i; + /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar n; + secp256k1_scalar_set_int(&n, 0); + for (i = 0; i < 256; i += 4) { + secp256k1_scalar t; + int j; + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4)); + for (j = 0; j < 4; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + + { + /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar n; + int i = 0; + secp256k1_scalar_set_int(&n, 0); + while (i < 256) { + secp256k1_scalar t; + int j; + int now = secp256k1_testrand_int(15) + 1; + if (now + i > 256) { + now = 256 - i; + } + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now)); + for (j = 0; j < now; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + i += now; + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + + { + /* test secp256k1_scalar_shr_int */ + secp256k1_scalar r; + int i; + random_scalar_order_test(&r); + for (i = 0; i < 100; ++i) { + int low; + int shift = 1 + secp256k1_testrand_int(15); + int expected = r.d[0] % (1 << shift); + low = secp256k1_scalar_shr_int(&r, shift); + CHECK(expected == low); + } + } + + { + /* Test commutativity of add. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + secp256k1_scalar r1, r2; + secp256k1_scalar b; + int i; + /* Test add_bit. */ + int bit = secp256k1_testrand_bits(8); + secp256k1_scalar_set_int(&b, 1); + CHECK(secp256k1_scalar_is_one(&b)); + for (i = 0; i < bit; i++) { + secp256k1_scalar_add(&b, &b, &b); + } + r1 = s1; + r2 = s1; + if (!secp256k1_scalar_add(&r1, &r1, &b)) { + /* No overflow happened. */ + secp256k1_scalar_cadd_bit(&r2, bit, 1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + /* cadd is a noop when flag is zero */ + secp256k1_scalar_cadd_bit(&r2, bit, 0); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + } + + { + /* Test commutativity of mul. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of add. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r1, &r1, &s); + secp256k1_scalar_add(&r2, &s2, &s); + secp256k1_scalar_add(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of mul. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s2, &s); + secp256k1_scalar_mul(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test distributitivity of mul over add. */ + secp256k1_scalar r1, r2, t; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s1, &s); + secp256k1_scalar_mul(&t, &s2, &s); + secp256k1_scalar_add(&r2, &r2, &t); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test multiplicative identity. */ + secp256k1_scalar r1, v1; + secp256k1_scalar_set_int(&v1,1); + secp256k1_scalar_mul(&r1, &s1, &v1); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test additive identity. */ + secp256k1_scalar r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_add(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test zero product property. */ + secp256k1_scalar r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_mul(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &v0)); + } + +} + +static void run_scalar_set_b32_seckey_tests(void) { + unsigned char b32[32]; + secp256k1_scalar s1; + secp256k1_scalar s2; + + /* Usually set_b32 and set_b32_seckey give the same result */ + random_scalar_order_b32(b32); + secp256k1_scalar_set_b32(&s1, b32, NULL); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 1); + CHECK(secp256k1_scalar_eq(&s1, &s2) == 1); + + memset(b32, 0, sizeof(b32)); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); + memset(b32, 0xFF, sizeof(b32)); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); +} + +static void run_scalar_tests(void) { + int i; + for (i = 0; i < 128 * COUNT; i++) { + scalar_test(); + } + for (i = 0; i < COUNT; i++) { + run_scalar_set_b32_seckey_tests(); + } + + { + /* (-1)+1 should be zero. */ + secp256k1_scalar s, o; + secp256k1_scalar_set_int(&s, 1); + CHECK(secp256k1_scalar_is_one(&s)); + secp256k1_scalar_negate(&o, &s); + secp256k1_scalar_add(&o, &o, &s); + CHECK(secp256k1_scalar_is_zero(&o)); + secp256k1_scalar_negate(&o, &o); + CHECK(secp256k1_scalar_is_zero(&o)); + } + + { + /* Does check_overflow check catch all ones? */ + static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + CHECK(secp256k1_scalar_check_overflow(&overflowed)); + } + + { + /* Static test vectors. + * These were reduced from ~10^12 random vectors based on comparison-decision + * and edge-case coverage on 32-bit and 64-bit implementations. + * The responses were generated with Sage 5.9. + */ + secp256k1_scalar x; + secp256k1_scalar y; + secp256k1_scalar z; + secp256k1_scalar zz; + secp256k1_scalar one; + secp256k1_scalar r1; + secp256k1_scalar r2; + secp256k1_scalar zzv; + int overflow; + unsigned char chal[33][2][32] = { + {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}}, + {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, + 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00}, + {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, + 0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff, + 0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, + 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f, + 0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f, + 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00, + 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff, + 0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0}, + {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00, + 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, + 0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f}, + {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, + 0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff, + 0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, + 0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff}, + {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff, + 0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, + 0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f, + 0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}}, + {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00}, + {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}}, + {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00, + 0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}}, + {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00}, + {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80, + 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, + 0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}}, + {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}}, + {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, + 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00}, + {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, + 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f, + 0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}}, + {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, + 0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00, + 0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f, + 0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}}, + {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83, + 0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0}, + {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, + 0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}}, + {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, + 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}, + {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, + 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}} + }; + unsigned char res[33][2][32] = { + {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9, + 0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1, + 0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6, + 0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35}, + {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d, + 0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c, + 0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49, + 0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}}, + {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22, + 0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c, + 0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f, + 0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8}, + {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77, + 0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4, + 0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59, + 0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}}, + {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef, + 0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab, + 0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55, + 0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c}, + {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96, + 0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f, + 0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12, + 0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}}, + {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c, + 0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf, + 0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9, + 0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48}, + {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42, + 0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5, + 0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c, + 0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}}, + {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb, + 0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74, + 0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6, + 0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63}, + {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3, + 0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99, + 0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58, + 0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}}, + {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b, + 0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7, + 0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f, + 0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0}, + {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d, + 0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d, + 0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9, + 0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}}, + {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7, + 0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70, + 0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06, + 0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e}, + {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9, + 0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79, + 0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e, + 0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}}, + {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb, + 0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5, + 0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a, + 0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe}, + {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48, + 0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e, + 0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc, + 0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}}, + {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b, + 0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0, + 0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53, + 0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8}, + {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c, + 0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01, + 0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f, + 0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}}, + {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7, + 0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c, + 0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92, + 0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30}, + {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62, + 0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e, + 0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb, + 0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}}, + {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25, + 0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d, + 0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0, + 0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13}, + {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60, + 0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00, + 0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4, + 0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}}, + {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31, + 0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4, + 0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88, + 0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa}, + {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57, + 0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38, + 0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51, + 0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}}, + {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c, + 0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f, + 0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2, + 0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4}, + {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01, + 0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4, + 0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86, + 0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}}, + {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5, + 0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51, + 0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3, + 0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62}, + {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c, + 0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91, + 0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c, + 0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}}, + {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e, + 0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56, + 0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58, + 0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4}, + {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41, + 0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7, + 0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92, + 0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}}, + {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec, + 0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19, + 0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3, + 0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4}, + {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87, + 0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a, + 0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92, + 0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}}, + {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64, + 0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3, + 0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f, + 0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33}, + {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c, + 0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d, + 0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea, + 0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}}, + {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7, + 0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a, + 0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae, + 0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe}, + {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc, + 0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39, + 0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14, + 0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}}, + {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23, + 0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d, + 0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2, + 0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16}, + {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c, + 0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84, + 0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0, + 0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}}, + {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb, + 0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94, + 0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b, + 0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e}, + {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54, + 0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00, + 0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb, + 0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}, + {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, + {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0, + 0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b, + 0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94, + 0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8}, + {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26, + 0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d, + 0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a, + 0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd}, + {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39, + 0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea, + 0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf, + 0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae}, + {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b, + 0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb, + 0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6, + 0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}}, + {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a, + 0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f, + 0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9, + 0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56}, + {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93, + 0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07, + 0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71, + 0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}}, + {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87, + 0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9, + 0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55, + 0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73}, + {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d, + 0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86, + 0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb, + 0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}}, + {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2, + 0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7, + 0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41, + 0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7}, + {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06, + 0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04, + 0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08, + 0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}}, + {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2, + 0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b, + 0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40, + 0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68}, + {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e, + 0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a, + 0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b, + 0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}}, + {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67, + 0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f, + 0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a, + 0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51}, + {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2, + 0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38, + 0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34, + 0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}}, + {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, + 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, + 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, + 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}, + {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, + 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, + 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, + 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}} + }; + secp256k1_scalar_set_int(&one, 1); + for (i = 0; i < 33; i++) { + secp256k1_scalar_set_b32(&x, chal[i][0], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&y, chal[i][1], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&r1, res[i][0], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&r2, res[i][1], &overflow); + CHECK(!overflow); + secp256k1_scalar_mul(&z, &x, &y); + CHECK(!secp256k1_scalar_check_overflow(&z)); + CHECK(secp256k1_scalar_eq(&r1, &z)); + if (!secp256k1_scalar_is_zero(&y)) { + secp256k1_scalar_inverse(&zz, &y); + CHECK(!secp256k1_scalar_check_overflow(&zz)); + secp256k1_scalar_inverse_var(&zzv, &y); + CHECK(secp256k1_scalar_eq(&zzv, &zz)); + secp256k1_scalar_mul(&z, &z, &zz); + CHECK(!secp256k1_scalar_check_overflow(&z)); + CHECK(secp256k1_scalar_eq(&x, &z)); + secp256k1_scalar_mul(&zz, &zz, &y); + CHECK(!secp256k1_scalar_check_overflow(&zz)); + CHECK(secp256k1_scalar_eq(&one, &zz)); + } + } + } +} + +/***** FIELD TESTS *****/ + +static void random_fe(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_testrand256(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +static void random_fe_test(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_testrand256_test(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +static void random_fe_non_zero(secp256k1_fe *nz) { + int tries = 10; + while (--tries >= 0) { + random_fe(nz); + secp256k1_fe_normalize(nz); + if (!secp256k1_fe_is_zero(nz)) { + break; + } + } + /* Infinitesimal probability of spurious failure here */ + CHECK(tries >= 0); +} + +static void random_fe_non_square(secp256k1_fe *ns) { + secp256k1_fe r; + random_fe_non_zero(ns); + if (secp256k1_fe_sqrt(&r, ns)) { + secp256k1_fe_negate(ns, ns, 1); + } +} + +static int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe an = *a; + secp256k1_fe bn = *b; + secp256k1_fe_normalize_weak(&an); + secp256k1_fe_normalize_var(&bn); + return secp256k1_fe_equal_var(&an, &bn); +} + +static void run_field_convert(void) { + static const unsigned char b32[32] = { + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, + 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40 + }; + static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + static const secp256k1_fe fe = SECP256K1_FE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + secp256k1_fe fe2; + unsigned char b322[32]; + secp256k1_fe_storage fes2; + /* Check conversions to fe. */ + CHECK(secp256k1_fe_set_b32(&fe2, b32)); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + secp256k1_fe_from_storage(&fe2, &fes); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + /* Check conversion from fe. */ + secp256k1_fe_get_b32(b322, &fe); + CHECK(secp256k1_memcmp_var(b322, b32, 32) == 0); + secp256k1_fe_to_storage(&fes2, &fe); + CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0); +} + +/* Returns true if two field elements have the same representation. */ +static int fe_identical(const secp256k1_fe *a, const secp256k1_fe *b) { + int ret = 1; +#ifdef VERIFY + ret &= (a->magnitude == b->magnitude); + ret &= (a->normalized == b->normalized); +#endif + /* Compare the struct member that holds the limbs. */ + ret &= (secp256k1_memcmp_var(a->n, b->n, sizeof(a->n)) == 0); + return ret; +} + +static void run_field_half(void) { + secp256k1_fe t, u; + int m; + + /* Check magnitude 0 input */ + secp256k1_fe_get_bounds(&t, 0); + secp256k1_fe_half(&t); +#ifdef VERIFY + CHECK(t.magnitude == 1); + CHECK(t.normalized == 0); +#endif + CHECK(secp256k1_fe_normalizes_to_zero(&t)); + + /* Check non-zero magnitudes in the supported range */ + for (m = 1; m < 32; m++) { + /* Check max-value input */ + secp256k1_fe_get_bounds(&t, m); + + u = t; + secp256k1_fe_half(&u); +#ifdef VERIFY + CHECK(u.magnitude == (m >> 1) + 1); + CHECK(u.normalized == 0); +#endif + secp256k1_fe_normalize_weak(&u); + secp256k1_fe_add(&u, &u); + CHECK(check_fe_equal(&t, &u)); + + /* Check worst-case input: ensure the LSB is 1 so that P will be added, + * which will also cause all carries to be 1, since all limbs that can + * generate a carry are initially even and all limbs of P are odd in + * every existing field implementation. */ + secp256k1_fe_get_bounds(&t, m); + CHECK(t.n[0] > 0); + CHECK((t.n[0] & 1) == 0); + --t.n[0]; + + u = t; + secp256k1_fe_half(&u); +#ifdef VERIFY + CHECK(u.magnitude == (m >> 1) + 1); + CHECK(u.normalized == 0); +#endif + secp256k1_fe_normalize_weak(&u); + secp256k1_fe_add(&u, &u); + CHECK(check_fe_equal(&t, &u)); + } +} + +static void run_field_misc(void) { + secp256k1_fe x; + secp256k1_fe y; + secp256k1_fe z; + secp256k1_fe q; + int v; + secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5); + int i, j; + for (i = 0; i < 1000 * COUNT; i++) { + secp256k1_fe_storage xs, ys, zs; + if (i & 1) { + random_fe(&x); + } else { + random_fe_test(&x); + } + random_fe_non_zero(&y); + v = secp256k1_testrand_bits(15); + /* Test that fe_add_int is equivalent to fe_set_int + fe_add. */ + secp256k1_fe_set_int(&q, v); /* q = v */ + z = x; /* z = x */ + secp256k1_fe_add(&z, &q); /* z = x+v */ + q = x; /* q = x */ + secp256k1_fe_add_int(&q, v); /* q = x+v */ + CHECK(check_fe_equal(&q, &z)); + /* Test the fe equality and comparison operations. */ + CHECK(secp256k1_fe_cmp_var(&x, &x) == 0); + CHECK(secp256k1_fe_equal_var(&x, &x)); + z = x; + secp256k1_fe_add(&z,&y); + /* Test fe conditional move; z is not normalized here. */ + q = x; + secp256k1_fe_cmov(&x, &z, 0); +#ifdef VERIFY + CHECK(x.normalized && x.magnitude == 1); +#endif + secp256k1_fe_cmov(&x, &x, 1); + CHECK(!fe_identical(&x, &z)); + CHECK(fe_identical(&x, &q)); + secp256k1_fe_cmov(&q, &z, 1); +#ifdef VERIFY + CHECK(!q.normalized && q.magnitude == z.magnitude); +#endif + CHECK(fe_identical(&q, &z)); + secp256k1_fe_normalize_var(&x); + secp256k1_fe_normalize_var(&z); + CHECK(!secp256k1_fe_equal_var(&x, &z)); + secp256k1_fe_normalize_var(&q); + secp256k1_fe_cmov(&q, &z, (i&1)); +#ifdef VERIFY + CHECK(q.normalized && q.magnitude == 1); +#endif + for (j = 0; j < 6; j++) { + secp256k1_fe_negate(&z, &z, j+1); + secp256k1_fe_normalize_var(&q); + secp256k1_fe_cmov(&q, &z, (j&1)); +#ifdef VERIFY + CHECK((q.normalized != (j&1)) && q.magnitude == ((j&1) ? z.magnitude : 1)); +#endif + } + secp256k1_fe_normalize_var(&z); + /* Test storage conversion and conditional moves. */ + secp256k1_fe_to_storage(&xs, &x); + secp256k1_fe_to_storage(&ys, &y); + secp256k1_fe_to_storage(&zs, &z); + secp256k1_fe_storage_cmov(&zs, &xs, 0); + secp256k1_fe_storage_cmov(&zs, &zs, 1); + CHECK(secp256k1_memcmp_var(&xs, &zs, sizeof(xs)) != 0); + secp256k1_fe_storage_cmov(&ys, &xs, 1); + CHECK(secp256k1_memcmp_var(&xs, &ys, sizeof(xs)) == 0); + secp256k1_fe_from_storage(&x, &xs); + secp256k1_fe_from_storage(&y, &ys); + secp256k1_fe_from_storage(&z, &zs); + /* Test that mul_int, mul, and add agree. */ + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&y, &x); + z = x; + secp256k1_fe_mul_int(&z, 3); + CHECK(check_fe_equal(&y, &z)); + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&z, &x); + CHECK(check_fe_equal(&z, &y)); + z = x; + secp256k1_fe_mul_int(&z, 5); + secp256k1_fe_mul(&q, &x, &fe5); + CHECK(check_fe_equal(&z, &q)); + secp256k1_fe_negate(&x, &x, 1); + secp256k1_fe_add(&z, &x); + secp256k1_fe_add(&q, &x); + CHECK(check_fe_equal(&y, &z)); + CHECK(check_fe_equal(&q, &y)); + /* Check secp256k1_fe_half. */ + z = x; + secp256k1_fe_half(&z); + secp256k1_fe_add(&z, &z); + CHECK(check_fe_equal(&x, &z)); + secp256k1_fe_add(&z, &z); + secp256k1_fe_half(&z); + CHECK(check_fe_equal(&x, &z)); + } +} + +static void test_fe_mul(const secp256k1_fe* a, const secp256k1_fe* b, int use_sqr) +{ + secp256k1_fe c, an, bn; + /* Variables in BE 32-byte format. */ + unsigned char a32[32], b32[32], c32[32]; + /* Variables in LE 16x uint16_t format. */ + uint16_t a16[16], b16[16], c16[16]; + /* Field modulus in LE 16x uint16_t format. */ + static const uint16_t m16[16] = { + 0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, + }; + uint16_t t16[32]; + int i; + + /* Compute C = A * B in fe format. */ + c = *a; + if (use_sqr) { + secp256k1_fe_sqr(&c, &c); + } else { + secp256k1_fe_mul(&c, &c, b); + } + + /* Convert A, B, C into LE 16x uint16_t format. */ + an = *a; + bn = *b; + secp256k1_fe_normalize_var(&c); + secp256k1_fe_normalize_var(&an); + secp256k1_fe_normalize_var(&bn); + secp256k1_fe_get_b32(a32, &an); + secp256k1_fe_get_b32(b32, &bn); + secp256k1_fe_get_b32(c32, &c); + for (i = 0; i < 16; ++i) { + a16[i] = a32[31 - 2*i] + ((uint16_t)a32[30 - 2*i] << 8); + b16[i] = b32[31 - 2*i] + ((uint16_t)b32[30 - 2*i] << 8); + c16[i] = c32[31 - 2*i] + ((uint16_t)c32[30 - 2*i] << 8); + } + /* Compute T = A * B in LE 16x uint16_t format. */ + mulmod256(t16, a16, b16, m16); + /* Compare */ + CHECK(secp256k1_memcmp_var(t16, c16, 32) == 0); +} + +static void run_fe_mul(void) { + int i; + for (i = 0; i < 100 * COUNT; ++i) { + secp256k1_fe a, b, c, d; + random_fe(&a); + random_field_element_magnitude(&a); + random_fe(&b); + random_field_element_magnitude(&b); + random_fe_test(&c); + random_field_element_magnitude(&c); + random_fe_test(&d); + random_field_element_magnitude(&d); + test_fe_mul(&a, &a, 1); + test_fe_mul(&c, &c, 1); + test_fe_mul(&a, &b, 0); + test_fe_mul(&a, &c, 0); + test_fe_mul(&c, &b, 0); + test_fe_mul(&c, &d, 0); + } +} + +static void run_sqr(void) { + secp256k1_fe x, s; + + { + int i; + secp256k1_fe_set_int(&x, 1); + secp256k1_fe_negate(&x, &x, 1); + + for (i = 1; i <= 512; ++i) { + secp256k1_fe_mul_int(&x, 2); + secp256k1_fe_normalize(&x); + secp256k1_fe_sqr(&s, &x); + } + } +} + +static void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) { + secp256k1_fe r1, r2; + int v = secp256k1_fe_sqrt(&r1, a); + CHECK((v == 0) == (k == NULL)); + + if (k != NULL) { + /* Check that the returned root is +/- the given known answer */ + secp256k1_fe_negate(&r2, &r1, 1); + secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k); + secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2); + CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2)); + } +} + +static void run_sqrt(void) { + secp256k1_fe ns, x, s, t; + int i; + + /* Check sqrt(0) is 0 */ + secp256k1_fe_set_int(&x, 0); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + + /* Check sqrt of small squares (and their negatives) */ + for (i = 1; i <= 100; i++) { + secp256k1_fe_set_int(&x, i); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + } + + /* Consistency checks for large random values */ + for (i = 0; i < 10; i++) { + int j; + random_fe_non_square(&ns); + for (j = 0; j < COUNT; j++) { + random_fe(&x); + secp256k1_fe_sqr(&s, &x); + CHECK(secp256k1_fe_is_square_var(&s)); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + CHECK(!secp256k1_fe_is_square_var(&t)); + test_sqrt(&t, NULL); + secp256k1_fe_mul(&t, &s, &ns); + test_sqrt(&t, NULL); + } + } +} + +/***** FIELD/SCALAR INVERSE TESTS *****/ + +static const secp256k1_scalar scalar_minus_one = SECP256K1_SCALAR_CONST( + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, + 0xBAAEDCE6, 0xAF48A03B, 0xBFD25E8C, 0xD0364140 +); + +static const secp256k1_fe fe_minus_one = SECP256K1_FE_CONST( + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, + 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFC2E +); + +/* These tests test the following identities: + * + * for x==0: 1/x == 0 + * for x!=0: x*(1/x) == 1 + * for x!=0 and x!=1: 1/(1/x - 1) + 1 == -1/(x-1) + */ + +static void test_inverse_scalar(secp256k1_scalar* out, const secp256k1_scalar* x, int var) +{ + secp256k1_scalar l, r, t; + + (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, x); /* l = 1/x */ + if (out) *out = l; + if (secp256k1_scalar_is_zero(x)) { + CHECK(secp256k1_scalar_is_zero(&l)); + return; + } + secp256k1_scalar_mul(&t, x, &l); /* t = x*(1/x) */ + CHECK(secp256k1_scalar_is_one(&t)); /* x*(1/x) == 1 */ + secp256k1_scalar_add(&r, x, &scalar_minus_one); /* r = x-1 */ + if (secp256k1_scalar_is_zero(&r)) return; + (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&r, &r); /* r = 1/(x-1) */ + secp256k1_scalar_add(&l, &scalar_minus_one, &l); /* l = 1/x-1 */ + (var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, &l); /* l = 1/(1/x-1) */ + secp256k1_scalar_add(&l, &l, &secp256k1_scalar_one); /* l = 1/(1/x-1)+1 */ + secp256k1_scalar_add(&l, &r, &l); /* l = 1/(1/x-1)+1 + 1/(x-1) */ + CHECK(secp256k1_scalar_is_zero(&l)); /* l == 0 */ +} + +static void test_inverse_field(secp256k1_fe* out, const secp256k1_fe* x, int var) +{ + secp256k1_fe l, r, t; + + (var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&l, x) ; /* l = 1/x */ + if (out) *out = l; + t = *x; /* t = x */ + if (secp256k1_fe_normalizes_to_zero_var(&t)) { + CHECK(secp256k1_fe_normalizes_to_zero(&l)); + return; + } + secp256k1_fe_mul(&t, x, &l); /* t = x*(1/x) */ + secp256k1_fe_add(&t, &fe_minus_one); /* t = x*(1/x)-1 */ + CHECK(secp256k1_fe_normalizes_to_zero(&t)); /* x*(1/x)-1 == 0 */ + r = *x; /* r = x */ + secp256k1_fe_add(&r, &fe_minus_one); /* r = x-1 */ + if (secp256k1_fe_normalizes_to_zero_var(&r)) return; + (var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&r, &r); /* r = 1/(x-1) */ + secp256k1_fe_add(&l, &fe_minus_one); /* l = 1/x-1 */ + (var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&l, &l); /* l = 1/(1/x-1) */ + secp256k1_fe_add_int(&l, 1); /* l = 1/(1/x-1)+1 */ + secp256k1_fe_add(&l, &r); /* l = 1/(1/x-1)+1 + 1/(x-1) */ + CHECK(secp256k1_fe_normalizes_to_zero_var(&l)); /* l == 0 */ +} + +static void run_inverse_tests(void) +{ + /* Fixed test cases for field inverses: pairs of (x, 1/x) mod p. */ + static const secp256k1_fe fe_cases[][2] = { + /* 0 */ + {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), + SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}, + /* 1 */ + {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), + SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1)}, + /* -1 */ + {SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e), + SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e)}, + /* 2 */ + {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2), + SECP256K1_FE_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7ffffe18)}, + /* 2**128 */ + {SECP256K1_FE_CONST(0, 0, 0, 1, 0, 0, 0, 0), + SECP256K1_FE_CONST(0xbcb223fe, 0xdc24a059, 0xd838091d, 0xd2253530, 0xffffffff, 0xffffffff, 0xffffffff, 0x434dd931)}, + /* Input known to need 637 divsteps */ + {SECP256K1_FE_CONST(0xe34e9c95, 0x6bee8a84, 0x0dcb632a, 0xdb8a1320, 0x66885408, 0x06f3f996, 0x7c11ca84, 0x19199ec3), + SECP256K1_FE_CONST(0xbd2cbd8f, 0x1c536828, 0x9bccda44, 0x2582ac0c, 0x870152b0, 0x8a3f09fb, 0x1aaadf92, 0x19b618e5)}, + /* Input known to need 567 divsteps starting with delta=1/2. */ + {SECP256K1_FE_CONST(0xf6bc3ba3, 0x636451c4, 0x3e46357d, 0x2c21d619, 0x0988e234, 0x15985661, 0x6672982b, 0xa7549bfc), + SECP256K1_FE_CONST(0xb024fdc7, 0x5547451e, 0x426c585f, 0xbd481425, 0x73df6b75, 0xeef6d9d0, 0x389d87d4, 0xfbb440ba)}, + /* Input known to need 566 divsteps starting with delta=1/2. */ + {SECP256K1_FE_CONST(0xb595d81b, 0x2e3c1e2f, 0x482dbc65, 0xe4865af7, 0x9a0a50aa, 0x29f9e618, 0x6f87d7a5, 0x8d1063ae), + SECP256K1_FE_CONST(0xc983337c, 0x5d5c74e1, 0x49918330, 0x0b53afb5, 0xa0428a0b, 0xce6eef86, 0x059bd8ef, 0xe5b908de)}, + /* Set of 10 inputs accessing all 128 entries in the modinv32 divsteps_var table */ + {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0xe0ff1f80, 0x1f000000, 0x00000000, 0x00000000, 0xfeff0100, 0x00000000), + SECP256K1_FE_CONST(0x9faf9316, 0x77e5049d, 0x0b5e7a1b, 0xef70b893, 0x18c9e30c, 0x045e7fd7, 0x29eddf8c, 0xd62e9e3d)}, + {SECP256K1_FE_CONST(0x621a538d, 0x511b2780, 0x35688252, 0x53f889a4, 0x6317c3ac, 0x32ba0a46, 0x6277c0d1, 0xccd31192), + SECP256K1_FE_CONST(0x38513b0c, 0x5eba856f, 0xe29e882e, 0x9b394d8c, 0x34bda011, 0xeaa66943, 0x6a841a4c, 0x6ae8bcff)}, + {SECP256K1_FE_CONST(0x00000200, 0xf0ffff1f, 0x00000000, 0x0000e0ff, 0xffffffff, 0xfffcffff, 0xffffffff, 0xffff0100), + SECP256K1_FE_CONST(0x5da42a52, 0x3640de9e, 0x13e64343, 0x0c7591b7, 0x6c1e3519, 0xf048c5b6, 0x0484217c, 0xedbf8b2f)}, + {SECP256K1_FE_CONST(0xd1343ef9, 0x4b952621, 0x7c52a2ee, 0x4ea1281b, 0x4ab46410, 0x9f26998d, 0xa686a8ff, 0x9f2103e8), + SECP256K1_FE_CONST(0x84044385, 0x9a4619bf, 0x74e35b6d, 0xa47e0c46, 0x6b7fb47d, 0x9ffab128, 0xb0775aa3, 0xcb318bd1)}, + {SECP256K1_FE_CONST(0xb27235d2, 0xc56a52be, 0x210db37a, 0xd50d23a4, 0xbe621bdd, 0x5df22c6a, 0xe926ba62, 0xd2e4e440), + SECP256K1_FE_CONST(0x67a26e54, 0x483a9d3c, 0xa568469e, 0xd258ab3d, 0xb9ec9981, 0xdca9b1bd, 0x8d2775fe, 0x53ae429b)}, + {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00e0ffff, 0xffffff83, 0xffffffff, 0x3f00f00f, 0x000000e0, 0xffffffff), + SECP256K1_FE_CONST(0x310e10f8, 0x23bbfab0, 0xac94907d, 0x076c9a45, 0x8d357d7f, 0xc763bcee, 0x00d0e615, 0x5a6acef6)}, + {SECP256K1_FE_CONST(0xfeff0300, 0x001c0000, 0xf80700c0, 0x0ff0ffff, 0xffffffff, 0x0fffffff, 0xffff0100, 0x7f0000fe), + SECP256K1_FE_CONST(0x28e2fdb4, 0x0709168b, 0x86f598b0, 0x3453a370, 0x530cf21f, 0x32f978d5, 0x1d527a71, 0x59269b0c)}, + {SECP256K1_FE_CONST(0xc2591afa, 0x7bb98ef7, 0x090bb273, 0x85c14f87, 0xbb0b28e0, 0x54d3c453, 0x85c66753, 0xd5574d2f), + SECP256K1_FE_CONST(0xfdca70a2, 0x70ce627c, 0x95e66fae, 0x848a6dbb, 0x07ffb15c, 0x5f63a058, 0xba4140ed, 0x6113b503)}, + {SECP256K1_FE_CONST(0xf5475db3, 0xedc7b5a3, 0x411c047e, 0xeaeb452f, 0xc625828e, 0x1cf5ad27, 0x8eec1060, 0xc7d3e690), + SECP256K1_FE_CONST(0x5eb756c0, 0xf963f4b9, 0xdc6a215e, 0xec8cc2d8, 0x2e9dec01, 0xde5eb88d, 0x6aba7164, 0xaecb2c5a)}, + {SECP256K1_FE_CONST(0x00000000, 0x00f8ffff, 0xffffffff, 0x01000000, 0xe0ff1f00, 0x00000000, 0xffffff7f, 0x00000000), + SECP256K1_FE_CONST(0xe0d2e3d8, 0x49b6157d, 0xe54e88c2, 0x1a7f02ca, 0x7dd28167, 0xf1125d81, 0x7bfa444e, 0xbe110037)}, + /* Selection of randomly generated inputs that reach high/low d/e values in various configurations. */ + {SECP256K1_FE_CONST(0x13cc08a4, 0xd8c41f0f, 0x179c3e67, 0x54c46c67, 0xc4109221, 0x09ab3b13, 0xe24d9be1, 0xffffe950), + SECP256K1_FE_CONST(0xb80c8006, 0xd16abaa7, 0xcabd71e5, 0xcf6714f4, 0x966dd3d0, 0x64767a2d, 0xe92c4441, 0x51008cd1)}, + {SECP256K1_FE_CONST(0xaa6db990, 0x95efbca1, 0x3cc6ff71, 0x0602e24a, 0xf49ff938, 0x99fffc16, 0x46f40993, 0xc6e72057), + SECP256K1_FE_CONST(0xd5d3dd69, 0xb0c195e5, 0x285f1d49, 0xe639e48c, 0x9223f8a9, 0xca1d731d, 0x9ca482f9, 0xa5b93e06)}, + {SECP256K1_FE_CONST(0x1c680eac, 0xaeabffd8, 0x9bdc4aee, 0x1781e3de, 0xa3b08108, 0x0015f2e0, 0x94449e1b, 0x2f67a058), + SECP256K1_FE_CONST(0x7f083f8d, 0x31254f29, 0x6510f475, 0x245c373d, 0xc5622590, 0x4b323393, 0x32ed1719, 0xc127444b)}, + {SECP256K1_FE_CONST(0x147d44b3, 0x012d83f8, 0xc160d386, 0x1a44a870, 0x9ba6be96, 0x8b962707, 0x267cbc1a, 0xb65b2f0a), + SECP256K1_FE_CONST(0x555554ff, 0x170aef1e, 0x50a43002, 0xe51fbd36, 0xafadb458, 0x7a8aded1, 0x0ca6cd33, 0x6ed9087c)}, + {SECP256K1_FE_CONST(0x12423796, 0x22f0fe61, 0xf9ca017c, 0x5384d107, 0xa1fbf3b2, 0x3b018013, 0x916a3c37, 0x4000b98c), + SECP256K1_FE_CONST(0x20257700, 0x08668f94, 0x1177e306, 0x136c01f5, 0x8ed1fbd2, 0x95ec4589, 0xae38edb9, 0xfd19b6d7)}, + {SECP256K1_FE_CONST(0xdcf2d030, 0x9ab42cb4, 0x93ffa181, 0xdcd23619, 0x39699b52, 0x08909a20, 0xb5a17695, 0x3a9dcf21), + SECP256K1_FE_CONST(0x1f701dea, 0xe211fb1f, 0x4f37180d, 0x63a0f51c, 0x29fe1e40, 0xa40b6142, 0x2e7b12eb, 0x982b06b6)}, + {SECP256K1_FE_CONST(0x79a851f6, 0xa6314ed3, 0xb35a55e6, 0xca1c7d7f, 0xe32369ea, 0xf902432e, 0x375308c5, 0xdfd5b600), + SECP256K1_FE_CONST(0xcaae00c5, 0xe6b43851, 0x9dabb737, 0x38cba42c, 0xa02c8549, 0x7895dcbf, 0xbd183d71, 0xafe4476a)}, + {SECP256K1_FE_CONST(0xede78fdd, 0xcfc92bf1, 0x4fec6c6c, 0xdb8d37e2, 0xfb66bc7b, 0x28701870, 0x7fa27c9a, 0x307196ec), + SECP256K1_FE_CONST(0x68193a6c, 0x9a8b87a7, 0x2a760c64, 0x13e473f6, 0x23ae7bed, 0x1de05422, 0x88865427, 0xa3418265)}, + {SECP256K1_FE_CONST(0xa40b2079, 0xb8f88e89, 0xa7617997, 0x89baf5ae, 0x174df343, 0x75138eae, 0x2711595d, 0x3fc3e66c), + SECP256K1_FE_CONST(0x9f99c6a5, 0x6d685267, 0xd4b87c37, 0x9d9c4576, 0x358c692b, 0x6bbae0ed, 0x3389c93d, 0x7fdd2655)}, + {SECP256K1_FE_CONST(0x7c74c6b6, 0xe98d9151, 0x72645cf1, 0x7f06e321, 0xcefee074, 0x15b2113a, 0x10a9be07, 0x08a45696), + SECP256K1_FE_CONST(0x8c919a88, 0x898bc1e0, 0x77f26f97, 0x12e655b7, 0x9ba0ac40, 0xe15bb19e, 0x8364cc3b, 0xe227a8ee)}, + {SECP256K1_FE_CONST(0x109ba1ce, 0xdafa6d4a, 0xa1cec2b2, 0xeb1069f4, 0xb7a79e5b, 0xec6eb99b, 0xaec5f643, 0xee0e723e), + SECP256K1_FE_CONST(0x93d13eb8, 0x4bb0bcf9, 0xe64f5a71, 0xdbe9f359, 0x7191401c, 0x6f057a4a, 0xa407fe1b, 0x7ecb65cc)}, + {SECP256K1_FE_CONST(0x3db076cd, 0xec74a5c9, 0xf61dd138, 0x90e23e06, 0xeeedd2d0, 0x74cbc4e0, 0x3dbe1e91, 0xded36a78), + SECP256K1_FE_CONST(0x3f07f966, 0x8e2a1e09, 0x706c71df, 0x02b5e9d5, 0xcb92ddbf, 0xcdd53010, 0x16545564, 0xe660b107)}, + {SECP256K1_FE_CONST(0xe31c73ed, 0xb4c4b82c, 0x02ae35f7, 0x4cdec153, 0x98b522fd, 0xf7d2460c, 0x6bf7c0f8, 0x4cf67b0d), + SECP256K1_FE_CONST(0x4b8f1faf, 0x94e8b070, 0x19af0ff6, 0xa319cd31, 0xdf0a7ffb, 0xefaba629, 0x59c50666, 0x1fe5b843)}, + {SECP256K1_FE_CONST(0x4c8b0e6e, 0x83392ab6, 0xc0e3e9f1, 0xbbd85497, 0x16698897, 0xf552d50d, 0x79652ddb, 0x12f99870), + SECP256K1_FE_CONST(0x56d5101f, 0xd23b7949, 0x17dc38d6, 0xf24022ef, 0xcf18e70a, 0x5cc34424, 0x438544c3, 0x62da4bca)}, + {SECP256K1_FE_CONST(0xb0e040e2, 0x40cc35da, 0x7dd5c611, 0x7fccb178, 0x28888137, 0xbc930358, 0xea2cbc90, 0x775417dc), + SECP256K1_FE_CONST(0xca37f0d4, 0x016dd7c8, 0xab3ae576, 0x96e08d69, 0x68ed9155, 0xa9b44270, 0x900ae35d, 0x7c7800cd)}, + {SECP256K1_FE_CONST(0x8a32ea49, 0x7fbb0bae, 0x69724a9d, 0x8e2105b2, 0xbdf69178, 0x862577ef, 0x35055590, 0x667ddaef), + SECP256K1_FE_CONST(0xd02d7ead, 0xc5e190f0, 0x559c9d72, 0xdaef1ffc, 0x64f9f425, 0xf43645ea, 0x7341e08d, 0x11768e96)}, + {SECP256K1_FE_CONST(0xa3592d98, 0x9abe289d, 0x579ebea6, 0xbb0857a8, 0xe242ab73, 0x85f9a2ce, 0xb6998f0f, 0xbfffbfc6), + SECP256K1_FE_CONST(0x093c1533, 0x32032efa, 0x6aa46070, 0x0039599e, 0x589c35f4, 0xff525430, 0x7fe3777a, 0x44b43ddc)}, + {SECP256K1_FE_CONST(0x647178a3, 0x229e607b, 0xcc98521a, 0xcce3fdd9, 0x1e1bc9c9, 0x97fb7c6a, 0x61b961e0, 0x99b10709), + SECP256K1_FE_CONST(0x98217c13, 0xd51ddf78, 0x96310e77, 0xdaebd908, 0x602ca683, 0xcb46d07a, 0xa1fcf17e, 0xc8e2feb3)}, + {SECP256K1_FE_CONST(0x7334627c, 0x73f98968, 0x99464b4b, 0xf5964958, 0x1b95870d, 0xc658227e, 0x5e3235d8, 0xdcab5787), + SECP256K1_FE_CONST(0x000006fd, 0xc7e9dd94, 0x40ae367a, 0xe51d495c, 0x07603b9b, 0x2d088418, 0x6cc5c74c, 0x98514307)}, + {SECP256K1_FE_CONST(0x82e83876, 0x96c28938, 0xa50dd1c5, 0x605c3ad1, 0xc048637d, 0x7a50825f, 0x335ed01a, 0x00005760), + SECP256K1_FE_CONST(0xb0393f9f, 0x9f2aa55e, 0xf5607e2e, 0x5287d961, 0x60b3e704, 0xf3e16e80, 0xb4f9a3ea, 0xfec7f02d)}, + {SECP256K1_FE_CONST(0xc97b6cec, 0x3ee6b8dc, 0x98d24b58, 0x3c1970a1, 0xfe06297a, 0xae813529, 0xe76bb6bd, 0x771ae51d), + SECP256K1_FE_CONST(0x0507c702, 0xd407d097, 0x47ddeb06, 0xf6625419, 0x79f48f79, 0x7bf80d0b, 0xfc34b364, 0x253a5db1)}, + {SECP256K1_FE_CONST(0xd559af63, 0x77ea9bc4, 0x3cf1ad14, 0x5c7a4bbb, 0x10e7d18b, 0x7ce0dfac, 0x380bb19d, 0x0bb99bd3), + SECP256K1_FE_CONST(0x00196119, 0xb9b00d92, 0x34edfdb5, 0xbbdc42fc, 0xd2daa33a, 0x163356ca, 0xaa8754c8, 0xb0ec8b0b)}, + {SECP256K1_FE_CONST(0x8ddfa3dc, 0x52918da0, 0x640519dc, 0x0af8512a, 0xca2d33b2, 0xbde52514, 0xda9c0afc, 0xcb29fce4), + SECP256K1_FE_CONST(0xb3e4878d, 0x5cb69148, 0xcd54388b, 0xc23acce0, 0x62518ba8, 0xf09def92, 0x7b31e6aa, 0x6ba35b02)}, + {SECP256K1_FE_CONST(0xf8207492, 0xe3049f0a, 0x65285f2b, 0x0bfff996, 0x00ca112e, 0xc05da837, 0x546d41f9, 0x5194fb91), + SECP256K1_FE_CONST(0x7b7ee50b, 0xa8ed4bbd, 0xf6469930, 0x81419a5c, 0x071441c7, 0x290d046e, 0x3b82ea41, 0x611c5f95)}, + {SECP256K1_FE_CONST(0x050f7c80, 0x5bcd3c6b, 0x823cb724, 0x5ce74db7, 0xa4e39f5c, 0xbd8828d7, 0xfd4d3e07, 0x3ec2926a), + SECP256K1_FE_CONST(0x000d6730, 0xb0171314, 0x4764053d, 0xee157117, 0x48fd61da, 0xdea0b9db, 0x1d5e91c6, 0xbdc3f59e)}, + {SECP256K1_FE_CONST(0x3e3ea8eb, 0x05d760cf, 0x23009263, 0xb3cb3ac9, 0x088f6f0d, 0x3fc182a3, 0xbd57087c, 0xe67c62f9), + SECP256K1_FE_CONST(0xbe988716, 0xa29c1bf6, 0x4456aed6, 0xab1e4720, 0x49929305, 0x51043bf4, 0xebd833dd, 0xdd511e8b)}, + {SECP256K1_FE_CONST(0x6964d2a9, 0xa7fa6501, 0xa5959249, 0x142f4029, 0xea0c1b5f, 0x2f487ef6, 0x301ac80a, 0x768be5cd), + SECP256K1_FE_CONST(0x3918ffe4, 0x07492543, 0xed24d0b7, 0x3df95f8f, 0xaffd7cb4, 0x0de2191c, 0x9ec2f2ad, 0x2c0cb3c6)}, + {SECP256K1_FE_CONST(0x37c93520, 0xf6ddca57, 0x2b42fd5e, 0xb5c7e4de, 0x11b5b81c, 0xb95e91f3, 0x95c4d156, 0x39877ccb), + SECP256K1_FE_CONST(0x9a94b9b5, 0x57eb71ee, 0x4c975b8b, 0xac5262a8, 0x077b0595, 0xe12a6b1f, 0xd728edef, 0x1a6bf956)} + }; + /* Fixed test cases for scalar inverses: pairs of (x, 1/x) mod n. */ + static const secp256k1_scalar scalar_cases[][2] = { + /* 0 */ + {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0), + SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0)}, + /* 1 */ + {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1), + SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1)}, + /* -1 */ + {SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140), + SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140)}, + /* 2 */ + {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 2), + SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x5d576e73, 0x57a4501d, 0xdfe92f46, 0x681b20a1)}, + /* 2**128 */ + {SECP256K1_SCALAR_CONST(0, 0, 0, 1, 0, 0, 0, 0), + SECP256K1_SCALAR_CONST(0x50a51ac8, 0x34b9ec24, 0x4b0dff66, 0x5588b13e, 0x9984d5b3, 0xcf80ef0f, 0xd6a23766, 0xa3ee9f22)}, + /* Input known to need 635 divsteps */ + {SECP256K1_SCALAR_CONST(0xcb9f1d35, 0xdd4416c2, 0xcd71bf3f, 0x6365da66, 0x3c9b3376, 0x8feb7ae9, 0x32a5ef60, 0x19199ec3), + SECP256K1_SCALAR_CONST(0x1d7c7bba, 0xf1893d53, 0xb834bd09, 0x36b411dc, 0x42c2e42f, 0xec72c428, 0x5e189791, 0x8e9bc708)}, + /* Input known to need 566 divsteps starting with delta=1/2. */ + {SECP256K1_SCALAR_CONST(0x7e3c993d, 0xa4272488, 0xbc015b49, 0x2db54174, 0xd382083a, 0xebe6db35, 0x80f82eff, 0xcd132c72), + SECP256K1_SCALAR_CONST(0x086f34a0, 0x3e631f76, 0x77418f28, 0xcc84ac95, 0x6304439d, 0x365db268, 0x312c6ded, 0xd0b934f8)}, + /* Input known to need 565 divsteps starting with delta=1/2. */ + {SECP256K1_SCALAR_CONST(0xbad7e587, 0x3f307859, 0x60d93147, 0x8a18491e, 0xb38a9fd5, 0x254350d3, 0x4b1f0e4b, 0x7dd6edc4), + SECP256K1_SCALAR_CONST(0x89f2df26, 0x39e2b041, 0xf19bd876, 0xd039c8ac, 0xc2223add, 0x29c4943e, 0x6632d908, 0x515f467b)}, + /* Selection of randomly generated inputs that reach low/high d/e values in various configurations. */ + {SECP256K1_SCALAR_CONST(0x1950d757, 0xb37a5809, 0x435059bb, 0x0bb8997e, 0x07e1e3c8, 0x5e5d7d2c, 0x6a0ed8e3, 0xdbde180e), + SECP256K1_SCALAR_CONST(0xbf72af9b, 0x750309e2, 0x8dda230b, 0xfe432b93, 0x7e25e475, 0x4388251e, 0x633d894b, 0x3bcb6f8c)}, + {SECP256K1_SCALAR_CONST(0x9bccf4e7, 0xc5a515e3, 0x50637aa9, 0xbb65a13f, 0x391749a1, 0x62de7d4e, 0xf6d7eabb, 0x3cd10ce0), + SECP256K1_SCALAR_CONST(0xaf2d5623, 0xb6385a33, 0xcd0365be, 0x5e92a70d, 0x7f09179c, 0x3baaf30f, 0x8f9cc83b, 0x20092f67)}, + {SECP256K1_SCALAR_CONST(0x73a57111, 0xb242952a, 0x5c5dee59, 0xf3be2ace, 0xa30a7659, 0xa46e5f47, 0xd21267b1, 0x39e642c9), + SECP256K1_SCALAR_CONST(0xa711df07, 0xcbcf13ef, 0xd61cc6be, 0xbcd058ce, 0xb02cf157, 0x272d4a18, 0x86d0feb3, 0xcd5fa004)}, + {SECP256K1_SCALAR_CONST(0x04884963, 0xce0580b1, 0xba547030, 0x3c691db3, 0x9cd2c84f, 0x24c7cebd, 0x97ebfdba, 0x3e785ec2), + SECP256K1_SCALAR_CONST(0xaaaaaf14, 0xd7c99ba7, 0x517ce2c1, 0x78a28b4c, 0x3769a851, 0xe5c5a03d, 0x4cc28f33, 0x0ec4dc5d)}, + {SECP256K1_SCALAR_CONST(0x1679ed49, 0x21f537b1, 0x815cb8ae, 0x9efc511c, 0x5b9fa037, 0x0b0f275e, 0x6c985281, 0x6c4a9905), + SECP256K1_SCALAR_CONST(0xb14ac3d5, 0x62b52999, 0xef34ead1, 0xffca4998, 0x0294341a, 0x1f8172aa, 0xea1624f9, 0x302eea62)}, + {SECP256K1_SCALAR_CONST(0x626b37c0, 0xf0057c35, 0xee982f83, 0x452a1fd3, 0xea826506, 0x48b08a9d, 0x1d2c4799, 0x4ad5f6ec), + SECP256K1_SCALAR_CONST(0xe38643b7, 0x567bfc2f, 0x5d2f1c15, 0xe327239c, 0x07112443, 0x69509283, 0xfd98e77a, 0xdb71c1e8)}, + {SECP256K1_SCALAR_CONST(0x1850a3a7, 0x759efc56, 0x54f287b2, 0x14d1234b, 0xe263bbc9, 0xcf4d8927, 0xd5f85f27, 0x965bd816), + SECP256K1_SCALAR_CONST(0x3b071831, 0xcac9619a, 0xcceb0596, 0xf614d63b, 0x95d0db2f, 0xc6a00901, 0x8eaa2621, 0xabfa0009)}, + {SECP256K1_SCALAR_CONST(0x94ae5d06, 0xa27dc400, 0x487d72be, 0xaa51ebed, 0xe475b5c0, 0xea675ffc, 0xf4df627a, 0xdca4222f), + SECP256K1_SCALAR_CONST(0x01b412ed, 0xd7830956, 0x1532537e, 0xe5e3dc99, 0x8fd3930a, 0x54f8d067, 0x32ef5760, 0x594438a5)}, + {SECP256K1_SCALAR_CONST(0x1f24278a, 0xb5bfe374, 0xa328dbbc, 0xebe35f48, 0x6620e009, 0xd58bb1b4, 0xb5a6bf84, 0x8815f63a), + SECP256K1_SCALAR_CONST(0xfe928416, 0xca5ba2d3, 0xfde513da, 0x903a60c7, 0x9e58ad8a, 0x8783bee4, 0x083a3843, 0xa608c914)}, + {SECP256K1_SCALAR_CONST(0xdc107d58, 0x274f6330, 0x67dba8bc, 0x26093111, 0x5201dfb8, 0x968ce3f5, 0xf34d1bd4, 0xf2146504), + SECP256K1_SCALAR_CONST(0x660cfa90, 0x13c3d93e, 0x7023b1e5, 0xedd09e71, 0x6d9c9d10, 0x7a3d2cdb, 0xdd08edc3, 0xaa78fcfb)}, + {SECP256K1_SCALAR_CONST(0x7cd1e905, 0xc6f02776, 0x2f551cc7, 0x5da61cff, 0x7da05389, 0x1119d5a4, 0x631c7442, 0x894fd4f7), + SECP256K1_SCALAR_CONST(0xff20862a, 0x9d3b1a37, 0x1628803b, 0x3004ccae, 0xaa23282a, 0xa89a1109, 0xd94ece5e, 0x181bdc46)}, + {SECP256K1_SCALAR_CONST(0x5b9dade8, 0x23d26c58, 0xcd12d818, 0x25b8ae97, 0x3dea04af, 0xf482c96b, 0xa062f254, 0x9e453640), + SECP256K1_SCALAR_CONST(0x50c38800, 0x15fa53f4, 0xbe1e5392, 0x5c9b120a, 0x262c22c7, 0x18fa0816, 0x5f2baab4, 0x8cb5db46)}, + {SECP256K1_SCALAR_CONST(0x11cdaeda, 0x969c464b, 0xef1f4ab0, 0x5b01d22e, 0x656fd098, 0x882bea84, 0x65cdbe7a, 0x0c19ff03), + SECP256K1_SCALAR_CONST(0x1968d0fa, 0xac46f103, 0xb55f1f72, 0xb3820bed, 0xec6b359a, 0x4b1ae0ad, 0x7e38e1fb, 0x295ccdfb)}, + {SECP256K1_SCALAR_CONST(0x2c351aa1, 0x26e91589, 0x194f8a1e, 0x06561f66, 0x0cb97b7f, 0x10914454, 0x134d1c03, 0x157266b4), + SECP256K1_SCALAR_CONST(0xbe49ada6, 0x92bd8711, 0x41b176c4, 0xa478ba95, 0x14883434, 0x9d1cd6f3, 0xcc4b847d, 0x22af80f5)}, + {SECP256K1_SCALAR_CONST(0x6ba07c6e, 0x13a60edb, 0x6247f5c3, 0x84b5fa56, 0x76fe3ec5, 0x80426395, 0xf65ec2ae, 0x623ba730), + SECP256K1_SCALAR_CONST(0x25ac23f7, 0x418cd747, 0x98376f9d, 0x4a11c7bf, 0x24c8ebfe, 0x4c8a8655, 0x345f4f52, 0x1c515595)}, + {SECP256K1_SCALAR_CONST(0x9397a712, 0x8abb6951, 0x2d4a3d54, 0x703b1c2a, 0x0661dca8, 0xd75c9b31, 0xaed4d24b, 0xd2ab2948), + SECP256K1_SCALAR_CONST(0xc52e8bef, 0xd55ce3eb, 0x1c897739, 0xeb9fb606, 0x36b9cd57, 0x18c51cc2, 0x6a87489e, 0xffd0dcf3)}, + {SECP256K1_SCALAR_CONST(0xe6a808cc, 0xeb437888, 0xe97798df, 0x4e224e44, 0x7e3b380a, 0x207c1653, 0x889f3212, 0xc6738b6f), + SECP256K1_SCALAR_CONST(0x31f9ae13, 0xd1e08b20, 0x757a2e5e, 0x5243a0eb, 0x8ae35f73, 0x19bb6122, 0xb910f26b, 0xda70aa55)}, + {SECP256K1_SCALAR_CONST(0xd0320548, 0xab0effe7, 0xa70779e0, 0x61a347a6, 0xb8c1e010, 0x9d5281f8, 0x2ee588a6, 0x80000000), + SECP256K1_SCALAR_CONST(0x1541897e, 0x78195c90, 0x7583dd9e, 0x728b6100, 0xbce8bc6d, 0x7a53b471, 0x5dcd9e45, 0x4425fcaf)}, + {SECP256K1_SCALAR_CONST(0x93d623f1, 0xd45b50b0, 0x796e9186, 0x9eac9407, 0xd30edc20, 0xef6304cf, 0x250494e7, 0xba503de9), + SECP256K1_SCALAR_CONST(0x7026d638, 0x1178b548, 0x92043952, 0x3c7fb47c, 0xcd3ea236, 0x31d82b01, 0x612fc387, 0x80b9b957)}, + {SECP256K1_SCALAR_CONST(0xf860ab39, 0x55f5d412, 0xa4d73bcc, 0x3b48bd90, 0xc248ffd3, 0x13ca10be, 0x8fba84cc, 0xdd28d6a3), + SECP256K1_SCALAR_CONST(0x5c32fc70, 0xe0b15d67, 0x76694700, 0xfe62be4d, 0xeacdb229, 0x7a4433d9, 0x52155cd0, 0x7649ab59)}, + {SECP256K1_SCALAR_CONST(0x4e41311c, 0x0800af58, 0x7a690a8e, 0xe175c9ba, 0x6981ab73, 0xac532ea8, 0x5c1f5e63, 0x6ac1f189), + SECP256K1_SCALAR_CONST(0xfffffff9, 0xd075982c, 0x7fbd3825, 0xc05038a2, 0x4533b91f, 0x94ec5f45, 0xb280b28f, 0x842324dc)}, + {SECP256K1_SCALAR_CONST(0x48e473bf, 0x3555eade, 0xad5d7089, 0x2424c4e4, 0x0a99397c, 0x2dc796d8, 0xb7a43a69, 0xd0364141), + SECP256K1_SCALAR_CONST(0x634976b2, 0xa0e47895, 0x1ec38593, 0x266d6fd0, 0x6f602644, 0x9bb762f1, 0x7180c704, 0xe23a4daa)}, + {SECP256K1_SCALAR_CONST(0xbe83878d, 0x3292fc54, 0x26e71c62, 0x556ccedc, 0x7cbb8810, 0x4032a720, 0x34ead589, 0xe4d6bd13), + SECP256K1_SCALAR_CONST(0x6cd150ad, 0x25e59d0f, 0x74cbae3d, 0x6377534a, 0x1e6562e8, 0xb71b9d18, 0xe1e5d712, 0x8480abb3)}, + {SECP256K1_SCALAR_CONST(0xcdddf2e5, 0xefc15f88, 0xc9ee06de, 0x8a846ca9, 0x28561581, 0x68daa5fb, 0xd1cf3451, 0xeb1782d0), + SECP256K1_SCALAR_CONST(0xffffffd9, 0xed8d2af4, 0x993c865a, 0x23e9681a, 0x3ca3a3dc, 0xe6d5a46e, 0xbd86bd87, 0x61b55c70)}, + {SECP256K1_SCALAR_CONST(0xb6a18f1f, 0x04872df9, 0x08165ec4, 0x319ca19c, 0x6c0359ab, 0x1f7118fb, 0xc2ef8082, 0xca8b7785), + SECP256K1_SCALAR_CONST(0xff55b19b, 0x0f1ac78c, 0x0f0c88c2, 0x2358d5ad, 0x5f455e4e, 0x3330b72f, 0x274dc153, 0xffbf272b)}, + {SECP256K1_SCALAR_CONST(0xea4898e5, 0x30eba3e8, 0xcf0e5c3d, 0x06ec6844, 0x01e26fb6, 0x75636225, 0xc5d08f4c, 0x1decafa0), + SECP256K1_SCALAR_CONST(0xe5a014a8, 0xe3c4ec1e, 0xea4f9b32, 0xcfc7b386, 0x00630806, 0x12c08d02, 0x6407ccc2, 0xb067d90e)}, + {SECP256K1_SCALAR_CONST(0x70e9aea9, 0x7e933af0, 0x8a23bfab, 0x23e4b772, 0xff951863, 0x5ffcf47d, 0x6bebc918, 0x2ca58265), + SECP256K1_SCALAR_CONST(0xf4e00006, 0x81bc6441, 0x4eb6ec02, 0xc194a859, 0x80ad7c48, 0xba4e9afb, 0x8b6bdbe0, 0x989d8f77)}, + {SECP256K1_SCALAR_CONST(0x3c56c774, 0x46efe6f0, 0xe93618b8, 0xf9b5a846, 0xd247df61, 0x83b1e215, 0x06dc8bcc, 0xeefc1bf5), + SECP256K1_SCALAR_CONST(0xfff8937a, 0x2cd9586b, 0x43c25e57, 0xd1cefa7a, 0x9fb91ed3, 0x95b6533d, 0x8ad0de5b, 0xafb93f00)}, + {SECP256K1_SCALAR_CONST(0xfb5c2772, 0x5cb30e83, 0xe38264df, 0xe4e3ebf3, 0x392aa92e, 0xa68756a1, 0x51279ac5, 0xb50711a8), + SECP256K1_SCALAR_CONST(0x000013af, 0x1105bfe7, 0xa6bbd7fb, 0x3d638f99, 0x3b266b02, 0x072fb8bc, 0x39251130, 0x2e0fd0ea)} + }; + int i, var, testrand; + unsigned char b32[32]; + secp256k1_fe x_fe; + secp256k1_scalar x_scalar; + memset(b32, 0, sizeof(b32)); + /* Test fixed test cases through test_inverse_{scalar,field}, both ways. */ + for (i = 0; (size_t)i < sizeof(fe_cases)/sizeof(fe_cases[0]); ++i) { + for (var = 0; var <= 1; ++var) { + test_inverse_field(&x_fe, &fe_cases[i][0], var); + check_fe_equal(&x_fe, &fe_cases[i][1]); + test_inverse_field(&x_fe, &fe_cases[i][1], var); + check_fe_equal(&x_fe, &fe_cases[i][0]); + } + } + for (i = 0; (size_t)i < sizeof(scalar_cases)/sizeof(scalar_cases[0]); ++i) { + for (var = 0; var <= 1; ++var) { + test_inverse_scalar(&x_scalar, &scalar_cases[i][0], var); + CHECK(secp256k1_scalar_eq(&x_scalar, &scalar_cases[i][1])); + test_inverse_scalar(&x_scalar, &scalar_cases[i][1], var); + CHECK(secp256k1_scalar_eq(&x_scalar, &scalar_cases[i][0])); + } + } + /* Test inputs 0..999 and their respective negations. */ + for (i = 0; i < 1000; ++i) { + b32[31] = i & 0xff; + b32[30] = (i >> 8) & 0xff; + secp256k1_scalar_set_b32(&x_scalar, b32, NULL); + secp256k1_fe_set_b32(&x_fe, b32); + for (var = 0; var <= 1; ++var) { + test_inverse_scalar(NULL, &x_scalar, var); + test_inverse_field(NULL, &x_fe, var); + } + secp256k1_scalar_negate(&x_scalar, &x_scalar); + secp256k1_fe_negate(&x_fe, &x_fe, 1); + for (var = 0; var <= 1; ++var) { + test_inverse_scalar(NULL, &x_scalar, var); + test_inverse_field(NULL, &x_fe, var); + } + } + /* test 128*count random inputs; half with testrand256_test, half with testrand256 */ + for (testrand = 0; testrand <= 1; ++testrand) { + for (i = 0; i < 64 * COUNT; ++i) { + (testrand ? secp256k1_testrand256_test : secp256k1_testrand256)(b32); + secp256k1_scalar_set_b32(&x_scalar, b32, NULL); + secp256k1_fe_set_b32(&x_fe, b32); + for (var = 0; var <= 1; ++var) { + test_inverse_scalar(NULL, &x_scalar, var); + test_inverse_field(NULL, &x_fe, var); + } + } + } +} + +/***** GROUP TESTS *****/ + +static void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) { + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + CHECK(secp256k1_fe_equal_var(&a->x, &b->x)); + CHECK(secp256k1_fe_equal_var(&a->y, &b->y)); +} + +/* This compares jacobian points including their Z, not just their geometric meaning. */ +static int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) { + secp256k1_gej a2; + secp256k1_gej b2; + int ret = 1; + ret &= a->infinity == b->infinity; + if (ret && !a->infinity) { + a2 = *a; + b2 = *b; + secp256k1_fe_normalize(&a2.x); + secp256k1_fe_normalize(&a2.y); + secp256k1_fe_normalize(&a2.z); + secp256k1_fe_normalize(&b2.x); + secp256k1_fe_normalize(&b2.y); + secp256k1_fe_normalize(&b2.z); + ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0; + ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0; + ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0; + } + return ret; +} + +static void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) { + secp256k1_fe z2s; + secp256k1_fe u1, u2, s1, s2; + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */ + secp256k1_fe_sqr(&z2s, &b->z); + secp256k1_fe_mul(&u1, &a->x, &z2s); + u2 = b->x; secp256k1_fe_normalize_weak(&u2); + secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z); + s2 = b->y; secp256k1_fe_normalize_weak(&s2); + CHECK(secp256k1_fe_equal_var(&u1, &u2)); + CHECK(secp256k1_fe_equal_var(&s1, &s2)); +} + +static void test_ge(void) { + int i, i1; + int runs = 6; + /* 25 points are used: + * - infinity + * - for each of four random points p1 p2 p3 p4, we add the point, its + * negation, and then those two again but with randomized Z coordinate. + * - The same is then done for lambda*p1 and lambda^2*p1. + */ + secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs)); + secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs)); + secp256k1_fe zf; + secp256k1_fe zfi2, zfi3; + + secp256k1_gej_set_infinity(&gej[0]); + secp256k1_ge_clear(&ge[0]); + secp256k1_ge_set_gej_var(&ge[0], &gej[0]); + for (i = 0; i < runs; i++) { + int j; + secp256k1_ge g; + random_group_element_test(&g); + if (i >= runs - 2) { + secp256k1_ge_mul_lambda(&g, &ge[1]); + } + if (i >= runs - 1) { + secp256k1_ge_mul_lambda(&g, &g); + } + ge[1 + 4 * i] = g; + ge[2 + 4 * i] = g; + secp256k1_ge_neg(&ge[3 + 4 * i], &g); + secp256k1_ge_neg(&ge[4 + 4 * i], &g); + secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]); + random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]); + secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]); + random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]); + for (j = 0; j < 4; j++) { + random_field_element_magnitude(&ge[1 + j + 4 * i].x); + random_field_element_magnitude(&ge[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].x); + random_field_element_magnitude(&gej[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].z); + } + } + + /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */ + do { + random_field_element_test(&zf); + } while(secp256k1_fe_is_zero(&zf)); + random_field_element_magnitude(&zf); + secp256k1_fe_inv_var(&zfi3, &zf); + secp256k1_fe_sqr(&zfi2, &zfi3); + secp256k1_fe_mul(&zfi3, &zfi3, &zfi2); + + for (i1 = 0; i1 < 1 + 4 * runs; i1++) { + int i2; + for (i2 = 0; i2 < 1 + 4 * runs; i2++) { + /* Compute reference result using gej + gej (var). */ + secp256k1_gej refj, resj; + secp256k1_ge ref; + secp256k1_fe zr; + secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr); + /* Check Z ratio. */ + if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) { + secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zrz, &refj.z)); + } + secp256k1_ge_set_gej_var(&ref, &refj); + + /* Test gej + ge with Z ratio result (var). */ + secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr); + ge_equals_gej(&ref, &resj); + if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) { + secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zrz, &resj.z)); + } + + /* Test gej + ge (var, with additional Z factor). */ + { + secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */ + secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2); + secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3); + random_field_element_magnitude(&ge2_zfi.x); + random_field_element_magnitude(&ge2_zfi.y); + secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf); + ge_equals_gej(&ref, &resj); + } + + /* Test gej + ge (const). */ + if (i2 != 0) { + /* secp256k1_gej_add_ge does not support its second argument being infinity. */ + secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]); + ge_equals_gej(&ref, &resj); + } + + /* Test doubling (var). */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) { + secp256k1_fe zr2; + /* Normal doubling with Z ratio result. */ + secp256k1_gej_double_var(&resj, &gej[i1], &zr2); + ge_equals_gej(&ref, &resj); + /* Check Z ratio. */ + secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zr2, &resj.z)); + /* Normal doubling. */ + secp256k1_gej_double_var(&resj, &gej[i2], NULL); + ge_equals_gej(&ref, &resj); + /* Constant-time doubling. */ + secp256k1_gej_double(&resj, &gej[i2]); + ge_equals_gej(&ref, &resj); + } + + /* Test adding opposites. */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) { + CHECK(secp256k1_ge_is_infinity(&ref)); + } + + /* Test adding infinity. */ + if (i1 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i1])); + CHECK(secp256k1_gej_is_infinity(&gej[i1])); + ge_equals_gej(&ref, &gej[i2]); + } + if (i2 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i2])); + CHECK(secp256k1_gej_is_infinity(&gej[i2])); + ge_equals_gej(&ref, &gej[i1]); + } + } + } + + /* Test adding all points together in random order equals infinity. */ + { + secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY; + secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&CTX->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej)); + for (i = 0; i < 4 * runs + 1; i++) { + gej_shuffled[i] = gej[i]; + } + for (i = 0; i < 4 * runs + 1; i++) { + int swap = i + secp256k1_testrand_int(4 * runs + 1 - i); + if (swap != i) { + secp256k1_gej t = gej_shuffled[i]; + gej_shuffled[i] = gej_shuffled[swap]; + gej_shuffled[swap] = t; + } + } + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL); + } + CHECK(secp256k1_gej_is_infinity(&sum)); + free(gej_shuffled); + } + + /* Test batch gej -> ge conversion without known z ratios. */ + { + secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&CTX->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge)); + secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1); + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_fe s; + random_fe_non_zero(&s); + secp256k1_gej_rescale(&gej[i], &s); + ge_equals_gej(&ge_set_all[i], &gej[i]); + } + free(ge_set_all); + } + + /* Test batch gej -> ge conversion with many infinities. */ + for (i = 0; i < 4 * runs + 1; i++) { + int odd; + random_group_element_test(&ge[i]); + odd = secp256k1_fe_is_odd(&ge[i].x); + CHECK(odd == 0 || odd == 1); + /* randomly set half the points to infinity */ + if (odd == i % 2) { + secp256k1_ge_set_infinity(&ge[i]); + } + secp256k1_gej_set_ge(&gej[i], &ge[i]); + } + /* batch convert */ + secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1); + /* check result */ + for (i = 0; i < 4 * runs + 1; i++) { + ge_equals_gej(&ge[i], &gej[i]); + } + + /* Test batch gej -> ge conversion with all infinities. */ + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_gej_set_infinity(&gej[i]); + } + /* batch convert */ + secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1); + /* check result */ + for (i = 0; i < 4 * runs + 1; i++) { + CHECK(secp256k1_ge_is_infinity(&ge[i])); + } + + free(ge); + free(gej); +} + +static void test_intialized_inf(void) { + secp256k1_ge p; + secp256k1_gej pj, npj, infj1, infj2, infj3; + secp256k1_fe zinv; + + /* Test that adding P+(-P) results in a fully initialized infinity*/ + random_group_element_test(&p); + secp256k1_gej_set_ge(&pj, &p); + secp256k1_gej_neg(&npj, &pj); + + secp256k1_gej_add_var(&infj1, &pj, &npj, NULL); + CHECK(secp256k1_gej_is_infinity(&infj1)); + CHECK(secp256k1_fe_is_zero(&infj1.x)); + CHECK(secp256k1_fe_is_zero(&infj1.y)); + CHECK(secp256k1_fe_is_zero(&infj1.z)); + + secp256k1_gej_add_ge_var(&infj2, &npj, &p, NULL); + CHECK(secp256k1_gej_is_infinity(&infj2)); + CHECK(secp256k1_fe_is_zero(&infj2.x)); + CHECK(secp256k1_fe_is_zero(&infj2.y)); + CHECK(secp256k1_fe_is_zero(&infj2.z)); + + secp256k1_fe_set_int(&zinv, 1); + secp256k1_gej_add_zinv_var(&infj3, &npj, &p, &zinv); + CHECK(secp256k1_gej_is_infinity(&infj3)); + CHECK(secp256k1_fe_is_zero(&infj3.x)); + CHECK(secp256k1_fe_is_zero(&infj3.y)); + CHECK(secp256k1_fe_is_zero(&infj3.z)); + + +} + +static void test_add_neg_y_diff_x(void) { + /* The point of this test is to check that we can add two points + * whose y-coordinates are negatives of each other but whose x + * coordinates differ. If the x-coordinates were the same, these + * points would be negatives of each other and their sum is + * infinity. This is cool because it "covers up" any degeneracy + * in the addition algorithm that would cause the xy coordinates + * of the sum to be wrong (since infinity has no xy coordinates). + * HOWEVER, if the x-coordinates are different, infinity is the + * wrong answer, and such degeneracies are exposed. This is the + * root of https://github.com/bitcoin-core/secp256k1/issues/257 + * which this test is a regression test for. + * + * These points were generated in sage as + * # secp256k1 params + * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F) + * C = EllipticCurve ([F (0), F (7)]) + * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798) + * N = FiniteField(G.order()) + * + * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F) + * x = polygen(N) + * lam = (1 - x^3).roots()[1][0] + * + * # random "bad pair" + * P = C.random_element() + * Q = -int(lam) * P + * print " P: %x %x" % P.xy() + * print " Q: %x %x" % Q.xy() + * print "P + Q: %x %x" % (P + Q).xy() + */ + secp256k1_gej aj = SECP256K1_GEJ_CONST( + 0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30, + 0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb, + 0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8, + 0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d + ); + secp256k1_gej bj = SECP256K1_GEJ_CONST( + 0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86, + 0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7, + 0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57, + 0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2 + ); + secp256k1_gej sumj = SECP256K1_GEJ_CONST( + 0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027, + 0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a, + 0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08, + 0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe + ); + secp256k1_ge b; + secp256k1_gej resj; + secp256k1_ge res; + secp256k1_ge_set_gej(&b, &bj); + + secp256k1_gej_add_var(&resj, &aj, &bj, NULL); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); + + secp256k1_gej_add_ge(&resj, &aj, &b); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); + + secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); +} + +static void run_ge(void) { + int i; + for (i = 0; i < COUNT * 32; i++) { + test_ge(); + } + test_add_neg_y_diff_x(); + test_intialized_inf(); +} + +static void test_gej_cmov(const secp256k1_gej *a, const secp256k1_gej *b) { + secp256k1_gej t = *a; + secp256k1_gej_cmov(&t, b, 0); + CHECK(gej_xyz_equals_gej(&t, a)); + secp256k1_gej_cmov(&t, b, 1); + CHECK(gej_xyz_equals_gej(&t, b)); +} + +static void run_gej(void) { + int i; + secp256k1_gej a, b; + + /* Tests for secp256k1_gej_cmov */ + for (i = 0; i < COUNT; i++) { + secp256k1_gej_set_infinity(&a); + secp256k1_gej_set_infinity(&b); + test_gej_cmov(&a, &b); + + random_gej_test(&a); + test_gej_cmov(&a, &b); + test_gej_cmov(&b, &a); + + b = a; + test_gej_cmov(&a, &b); + + random_gej_test(&b); + test_gej_cmov(&a, &b); + test_gej_cmov(&b, &a); + } + + /* Tests for secp256k1_gej_eq_var */ + for (i = 0; i < COUNT; i++) { + secp256k1_fe fe; + random_gej_test(&a); + random_gej_test(&b); + CHECK(!secp256k1_gej_eq_var(&a, &b)); + + b = a; + random_field_element_test(&fe); + if (secp256k1_fe_is_zero(&fe)) { + continue; + } + secp256k1_gej_rescale(&a, &fe); + CHECK(secp256k1_gej_eq_var(&a, &b)); + } +} + +static void test_ec_combine(void) { + secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_pubkey data[6]; + const secp256k1_pubkey* d[6]; + secp256k1_pubkey sd; + secp256k1_pubkey sd2; + secp256k1_gej Qj; + secp256k1_ge Q; + int i; + for (i = 1; i <= 6; i++) { + secp256k1_scalar s; + random_scalar_order_test(&s); + secp256k1_scalar_add(&sum, &sum, &s); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &Qj, &s); + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(&data[i - 1], &Q); + d[i - 1] = &data[i - 1]; + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &Qj, &sum); + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(&sd, &Q); + CHECK(secp256k1_ec_pubkey_combine(CTX, &sd2, d, i) == 1); + CHECK(secp256k1_memcmp_var(&sd, &sd2, sizeof(sd)) == 0); + } +} + +static void run_ec_combine(void) { + int i; + for (i = 0; i < COUNT * 8; i++) { + test_ec_combine(); + } +} + +static void test_group_decompress(const secp256k1_fe* x) { + /* The input itself, normalized. */ + secp256k1_fe fex = *x; + /* Results of set_xo_var(..., 0), set_xo_var(..., 1). */ + secp256k1_ge ge_even, ge_odd; + /* Return values of the above calls. */ + int res_even, res_odd; + + secp256k1_fe_normalize_var(&fex); + + res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0); + res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1); + + CHECK(res_even == res_odd); + + if (res_even) { + secp256k1_fe_normalize_var(&ge_odd.x); + secp256k1_fe_normalize_var(&ge_even.x); + secp256k1_fe_normalize_var(&ge_odd.y); + secp256k1_fe_normalize_var(&ge_even.y); + + /* No infinity allowed. */ + CHECK(!ge_even.infinity); + CHECK(!ge_odd.infinity); + + /* Check that the x coordinates check out. */ + CHECK(secp256k1_fe_equal_var(&ge_even.x, x)); + CHECK(secp256k1_fe_equal_var(&ge_odd.x, x)); + + /* Check odd/even Y in ge_odd, ge_even. */ + CHECK(secp256k1_fe_is_odd(&ge_odd.y)); + CHECK(!secp256k1_fe_is_odd(&ge_even.y)); + } +} + +static void run_group_decompress(void) { + int i; + for (i = 0; i < COUNT * 4; i++) { + secp256k1_fe fe; + random_fe_test(&fe); + test_group_decompress(&fe); + } +} + +/***** ECMULT TESTS *****/ + +static void test_pre_g_table(const secp256k1_ge_storage * pre_g, size_t n) { + /* Tests the pre_g / pre_g_128 tables for consistency. + * For independent verification we take a "geometric" approach to verification. + * We check that every entry is on-curve. + * We check that for consecutive entries p and q, that p + gg - q = 0 by checking + * (1) p, gg, and -q are colinear. + * (2) p, gg, and -q are all distinct. + * where gg is twice the generator, where the generator is the first table entry. + * + * Checking the table's generators are correct is done in run_ecmult_pre_g. + */ + secp256k1_gej g2; + secp256k1_ge p, q, gg; + secp256k1_fe dpx, dpy, dqx, dqy; + size_t i; + + CHECK(0 < n); + + secp256k1_ge_from_storage(&p, &pre_g[0]); + CHECK(secp256k1_ge_is_valid_var(&p)); + + secp256k1_gej_set_ge(&g2, &p); + secp256k1_gej_double_var(&g2, &g2, NULL); + secp256k1_ge_set_gej_var(&gg, &g2); + for (i = 1; i < n; ++i) { + secp256k1_fe_negate(&dpx, &p.x, 1); secp256k1_fe_add(&dpx, &gg.x); secp256k1_fe_normalize_weak(&dpx); + secp256k1_fe_negate(&dpy, &p.y, 1); secp256k1_fe_add(&dpy, &gg.y); secp256k1_fe_normalize_weak(&dpy); + /* Check that p is not equal to gg */ + CHECK(!secp256k1_fe_normalizes_to_zero_var(&dpx) || !secp256k1_fe_normalizes_to_zero_var(&dpy)); + + secp256k1_ge_from_storage(&q, &pre_g[i]); + CHECK(secp256k1_ge_is_valid_var(&q)); + + secp256k1_fe_negate(&dqx, &q.x, 1); secp256k1_fe_add(&dqx, &gg.x); secp256k1_fe_normalize_weak(&dqx); + dqy = q.y; secp256k1_fe_add(&dqy, &gg.y); secp256k1_fe_normalize_weak(&dqy); + /* Check that -q is not equal to gg */ + CHECK(!secp256k1_fe_normalizes_to_zero_var(&dqx) || !secp256k1_fe_normalizes_to_zero_var(&dqy)); + + /* Check that -q is not equal to p */ + CHECK(!secp256k1_fe_equal_var(&dpx, &dqx) || !secp256k1_fe_equal_var(&dpy, &dqy)); + + /* Check that p, -q and gg are colinear */ + secp256k1_fe_mul(&dpx, &dpx, &dqy); + secp256k1_fe_mul(&dpy, &dpy, &dqx); + CHECK(secp256k1_fe_equal_var(&dpx, &dpy)); + + p = q; + } +} + +static void run_ecmult_pre_g(void) { + secp256k1_ge_storage gs; + secp256k1_gej gj; + secp256k1_ge g; + size_t i; + + /* Check that the pre_g and pre_g_128 tables are consistent. */ + test_pre_g_table(secp256k1_pre_g, ECMULT_TABLE_SIZE(WINDOW_G)); + test_pre_g_table(secp256k1_pre_g_128, ECMULT_TABLE_SIZE(WINDOW_G)); + + /* Check the first entry from the pre_g table. */ + secp256k1_ge_to_storage(&gs, &secp256k1_ge_const_g); + CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g[0], sizeof(gs)) == 0); + + /* Check the first entry from the pre_g_128 table. */ + secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g); + for (i = 0; i < 128; ++i) { + secp256k1_gej_double_var(&gj, &gj, NULL); + } + secp256k1_ge_set_gej(&g, &gj); + secp256k1_ge_to_storage(&gs, &g); + CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g_128[0], sizeof(gs)) == 0); +} + +static void run_ecmult_chain(void) { + /* random starting point A (on the curve) */ + secp256k1_gej a = SECP256K1_GEJ_CONST( + 0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3, + 0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004, + 0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f, + 0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f + ); + /* two random initial factors xn and gn */ + secp256k1_scalar xn = SECP256K1_SCALAR_CONST( + 0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c, + 0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407 + ); + secp256k1_scalar gn = SECP256K1_SCALAR_CONST( + 0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9, + 0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de + ); + /* two small multipliers to be applied to xn and gn in every iteration: */ + static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337); + static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113); + /* accumulators with the resulting coefficients to A and G */ + secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + /* actual points */ + secp256k1_gej x; + secp256k1_gej x2; + int i; + + /* the point being computed */ + x = a; + for (i = 0; i < 200*COUNT; i++) { + /* in each iteration, compute X = xn*X + gn*G; */ + secp256k1_ecmult(&x, &x, &xn, &gn); + /* also compute ae and ge: the actual accumulated factors for A and G */ + /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */ + secp256k1_scalar_mul(&ae, &ae, &xn); + secp256k1_scalar_mul(&ge, &ge, &xn); + secp256k1_scalar_add(&ge, &ge, &gn); + /* modify xn and gn */ + secp256k1_scalar_mul(&xn, &xn, &xf); + secp256k1_scalar_mul(&gn, &gn, &gf); + + /* verify */ + if (i == 19999) { + /* expected result after 19999 iterations */ + secp256k1_gej rp = SECP256K1_GEJ_CONST( + 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE, + 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830, + 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D, + 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88 + ); + CHECK(secp256k1_gej_eq_var(&rp, &x)); + } + } + /* redo the computation, but directly with the resulting ae and ge coefficients: */ + secp256k1_ecmult(&x2, &a, &ae, &ge); + CHECK(secp256k1_gej_eq_var(&x, &x2)); +} + +static void test_point_times_order(const secp256k1_gej *point) { + /* X * (point + G) + (order-X) * (pointer + G) = 0 */ + secp256k1_scalar x; + secp256k1_scalar nx; + secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_gej res1, res2; + secp256k1_ge res3; + unsigned char pub[65]; + size_t psize = 65; + random_scalar_order_test(&x); + secp256k1_scalar_negate(&nx, &x); + secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */ + secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */ + secp256k1_gej_add_var(&res1, &res1, &res2, NULL); + CHECK(secp256k1_gej_is_infinity(&res1)); + secp256k1_ge_set_gej(&res3, &res1); + CHECK(secp256k1_ge_is_infinity(&res3)); + CHECK(secp256k1_ge_is_valid_var(&res3) == 0); + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0); + psize = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0); + /* check zero/one edge cases */ + secp256k1_ecmult(&res1, point, &zero, &zero); + secp256k1_ge_set_gej(&res3, &res1); + CHECK(secp256k1_ge_is_infinity(&res3)); + secp256k1_ecmult(&res1, point, &one, &zero); + secp256k1_ge_set_gej(&res3, &res1); + ge_equals_gej(&res3, point); + secp256k1_ecmult(&res1, point, &zero, &one); + secp256k1_ge_set_gej(&res3, &res1); + ge_equals_ge(&res3, &secp256k1_ge_const_g); +} + +/* These scalars reach large (in absolute value) outputs when fed to secp256k1_scalar_split_lambda. + * + * They are computed as: + * - For a in [-2, -1, 0, 1, 2]: + * - For b in [-3, -1, 1, 3]: + * - Output (a*LAMBDA + (ORDER+b)/2) % ORDER + */ +static const secp256k1_scalar scalars_near_split_bounds[20] = { + SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fc), + SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fd), + SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fe), + SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6ff), + SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632d), + SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632e), + SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632f), + SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf76330), + SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b209f), + SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a0), + SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a1), + SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a2), + SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede11), + SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede12), + SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede13), + SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede14), + SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a42), + SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a43), + SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a44), + SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a45) +}; + +static void test_ecmult_target(const secp256k1_scalar* target, int mode) { + /* Mode: 0=ecmult_gen, 1=ecmult, 2=ecmult_const */ + secp256k1_scalar n1, n2; + secp256k1_ge p; + secp256k1_gej pj, p1j, p2j, ptj; + static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + + /* Generate random n1,n2 such that n1+n2 = -target. */ + random_scalar_order_test(&n1); + secp256k1_scalar_add(&n2, &n1, target); + secp256k1_scalar_negate(&n2, &n2); + + /* Generate a random input point. */ + if (mode != 0) { + random_group_element_test(&p); + secp256k1_gej_set_ge(&pj, &p); + } + + /* EC multiplications */ + if (mode == 0) { + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &p1j, &n1); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &p2j, &n2); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &ptj, target); + } else if (mode == 1) { + secp256k1_ecmult(&p1j, &pj, &n1, &zero); + secp256k1_ecmult(&p2j, &pj, &n2, &zero); + secp256k1_ecmult(&ptj, &pj, target, &zero); + } else { + secp256k1_ecmult_const(&p1j, &p, &n1, 256); + secp256k1_ecmult_const(&p2j, &p, &n2, 256); + secp256k1_ecmult_const(&ptj, &p, target, 256); + } + + /* Add them all up: n1*P + n2*P + target*P = (n1+n2+target)*P = (n1+n1-n1-n2)*P = 0. */ + secp256k1_gej_add_var(&ptj, &ptj, &p1j, NULL); + secp256k1_gej_add_var(&ptj, &ptj, &p2j, NULL); + CHECK(secp256k1_gej_is_infinity(&ptj)); +} + +static void run_ecmult_near_split_bound(void) { + int i; + unsigned j; + for (i = 0; i < 4*COUNT; ++i) { + for (j = 0; j < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++j) { + test_ecmult_target(&scalars_near_split_bounds[j], 0); + test_ecmult_target(&scalars_near_split_bounds[j], 1); + test_ecmult_target(&scalars_near_split_bounds[j], 2); + } + } +} + +static void run_point_times_order(void) { + int i; + secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2); + static const secp256k1_fe xr = SECP256K1_FE_CONST( + 0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C, + 0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45 + ); + for (i = 0; i < 500; i++) { + secp256k1_ge p; + if (secp256k1_ge_set_xo_var(&p, &x, 1)) { + secp256k1_gej j; + CHECK(secp256k1_ge_is_valid_var(&p)); + secp256k1_gej_set_ge(&j, &p); + test_point_times_order(&j); + } + secp256k1_fe_sqr(&x, &x); + } + secp256k1_fe_normalize_var(&x); + CHECK(secp256k1_fe_equal_var(&x, &xr)); +} + +static void ecmult_const_random_mult(void) { + /* random starting point A (on the curve) */ + secp256k1_ge a = SECP256K1_GE_CONST( + 0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b, + 0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a, + 0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c, + 0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d + ); + /* random initial factor xn */ + secp256k1_scalar xn = SECP256K1_SCALAR_CONST( + 0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327, + 0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b + ); + /* expected xn * A (from sage) */ + secp256k1_ge expected_b = SECP256K1_GE_CONST( + 0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd, + 0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786, + 0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f, + 0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956 + ); + secp256k1_gej b; + secp256k1_ecmult_const(&b, &a, &xn, 256); + + CHECK(secp256k1_ge_is_valid_var(&a)); + ge_equals_gej(&expected_b, &b); +} + +static void ecmult_const_commutativity(void) { + secp256k1_scalar a; + secp256k1_scalar b; + secp256k1_gej res1; + secp256k1_gej res2; + secp256k1_ge mid1; + secp256k1_ge mid2; + random_scalar_order_test(&a); + random_scalar_order_test(&b); + + secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256); + secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256); + secp256k1_ge_set_gej(&mid1, &res1); + secp256k1_ge_set_gej(&mid2, &res2); + secp256k1_ecmult_const(&res1, &mid1, &b, 256); + secp256k1_ecmult_const(&res2, &mid2, &a, 256); + secp256k1_ge_set_gej(&mid1, &res1); + secp256k1_ge_set_gej(&mid2, &res2); + ge_equals_ge(&mid1, &mid2); +} + +static void ecmult_const_mult_zero_one(void) { + secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_scalar negone; + secp256k1_gej res1; + secp256k1_ge res2; + secp256k1_ge point; + secp256k1_scalar_negate(&negone, &one); + + random_group_element_test(&point); + secp256k1_ecmult_const(&res1, &point, &zero, 3); + secp256k1_ge_set_gej(&res2, &res1); + CHECK(secp256k1_ge_is_infinity(&res2)); + secp256k1_ecmult_const(&res1, &point, &one, 2); + secp256k1_ge_set_gej(&res2, &res1); + ge_equals_ge(&res2, &point); + secp256k1_ecmult_const(&res1, &point, &negone, 256); + secp256k1_gej_neg(&res1, &res1); + secp256k1_ge_set_gej(&res2, &res1); + ge_equals_ge(&res2, &point); +} + +static void ecmult_const_mult_xonly(void) { + int i; + + /* Test correspondence between secp256k1_ecmult_const and secp256k1_ecmult_const_xonly. */ + for (i = 0; i < 2*COUNT; ++i) { + secp256k1_ge base; + secp256k1_gej basej, resj; + secp256k1_fe n, d, resx, v; + secp256k1_scalar q; + int res; + /* Random base point. */ + random_group_element_test(&base); + /* Random scalar to multiply it with. */ + random_scalar_order_test(&q); + /* If i is odd, n=d*base.x for random non-zero d */ + if (i & 1) { + do { + random_field_element_test(&d); + } while (secp256k1_fe_normalizes_to_zero_var(&d)); + secp256k1_fe_mul(&n, &base.x, &d); + } else { + n = base.x; + } + /* Perform x-only multiplication. */ + res = secp256k1_ecmult_const_xonly(&resx, &n, (i & 1) ? &d : NULL, &q, 256, i & 2); + CHECK(res); + /* Perform normal multiplication. */ + secp256k1_gej_set_ge(&basej, &base); + secp256k1_ecmult(&resj, &basej, &q, NULL); + /* Check that resj's X coordinate corresponds with resx. */ + secp256k1_fe_sqr(&v, &resj.z); + secp256k1_fe_mul(&v, &v, &resx); + CHECK(check_fe_equal(&v, &resj.x)); + } + + /* Test that secp256k1_ecmult_const_xonly correctly rejects X coordinates not on curve. */ + for (i = 0; i < 2*COUNT; ++i) { + secp256k1_fe x, n, d, c, r; + int res; + secp256k1_scalar q; + random_scalar_order_test(&q); + /* Generate random X coordinate not on the curve. */ + do { + random_field_element_test(&x); + secp256k1_fe_sqr(&c, &x); + secp256k1_fe_mul(&c, &c, &x); + secp256k1_fe_add(&c, &secp256k1_fe_const_b); + } while (secp256k1_fe_is_square_var(&c)); + /* If i is odd, n=d*x for random non-zero d. */ + if (i & 1) { + do { + random_field_element_test(&d); + } while (secp256k1_fe_normalizes_to_zero_var(&d)); + secp256k1_fe_mul(&n, &x, &d); + } else { + n = x; + } + res = secp256k1_ecmult_const_xonly(&r, &n, (i & 1) ? &d : NULL, &q, 256, 0); + CHECK(res == 0); + } +} + +static void ecmult_const_chain_multiply(void) { + /* Check known result (randomly generated test problem from sage) */ + const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST( + 0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d, + 0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b + ); + const secp256k1_gej expected_point = SECP256K1_GEJ_CONST( + 0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd, + 0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f, + 0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196, + 0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435 + ); + secp256k1_gej point; + secp256k1_ge res; + int i; + + secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g); + for (i = 0; i < 100; ++i) { + secp256k1_ge tmp; + secp256k1_ge_set_gej(&tmp, &point); + secp256k1_ecmult_const(&point, &tmp, &scalar, 256); + } + secp256k1_ge_set_gej(&res, &point); + ge_equals_gej(&res, &expected_point); +} + +static void run_ecmult_const_tests(void) { + ecmult_const_mult_zero_one(); + ecmult_const_random_mult(); + ecmult_const_commutativity(); + ecmult_const_chain_multiply(); + ecmult_const_mult_xonly(); +} + +typedef struct { + secp256k1_scalar *sc; + secp256k1_ge *pt; +} ecmult_multi_data; + +static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + ecmult_multi_data *data = (ecmult_multi_data*) cbdata; + *sc = data->sc[idx]; + *pt = data->pt[idx]; + return 1; +} + +static int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + (void)sc; + (void)pt; + (void)idx; + (void)cbdata; + return 0; +} + +static void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) { + int ncount; + secp256k1_scalar szero; + secp256k1_scalar sc[32]; + secp256k1_ge pt[32]; + secp256k1_gej r; + secp256k1_gej r2; + ecmult_multi_data data; + + data.sc = sc; + data.pt = pt; + secp256k1_scalar_set_int(&szero, 0); + + /* No points to multiply */ + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, NULL, ecmult_multi_callback, &data, 0)); + + /* Check 1- and 2-point multiplies against ecmult */ + for (ncount = 0; ncount < COUNT; ncount++) { + secp256k1_ge ptg; + secp256k1_gej ptgj; + random_scalar_order(&sc[0]); + random_scalar_order(&sc[1]); + + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + pt[0] = ptg; + pt[1] = secp256k1_ge_const_g; + + /* only G scalar */ + secp256k1_ecmult(&r2, &ptgj, &szero, &sc[0]); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + + /* 1-point */ + secp256k1_ecmult(&r2, &ptgj, &sc[0], &szero); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 1)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + + /* Try to multiply 1 point, but callback returns false */ + CHECK(!ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1)); + + /* 2-point */ + secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 2)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + + /* 2-point with G scalar */ + secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + } + + /* Check infinite outputs of various forms */ + for (ncount = 0; ncount < COUNT; ncount++) { + secp256k1_ge ptg; + size_t i, j; + size_t sizes[] = { 2, 10, 32 }; + + for (j = 0; j < 3; j++) { + for (i = 0; i < 32; i++) { + random_scalar_order(&sc[i]); + secp256k1_ge_set_infinity(&pt[i]); + } + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + for (j = 0; j < 3; j++) { + for (i = 0; i < 32; i++) { + random_group_element_test(&ptg); + pt[i] = ptg; + secp256k1_scalar_set_int(&sc[i], 0); + } + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + for (j = 0; j < 3; j++) { + random_group_element_test(&ptg); + for (i = 0; i < 16; i++) { + random_scalar_order(&sc[2*i]); + secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]); + pt[2 * i] = ptg; + pt[2 * i + 1] = ptg; + } + + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + + random_scalar_order(&sc[0]); + for (i = 0; i < 16; i++) { + random_group_element_test(&ptg); + + sc[2*i] = sc[0]; + sc[2*i+1] = sc[0]; + pt[2 * i] = ptg; + secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]); + } + + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + random_group_element_test(&ptg); + secp256k1_scalar_set_int(&sc[0], 0); + pt[0] = ptg; + for (i = 1; i < 32; i++) { + pt[i] = ptg; + + random_scalar_order(&sc[i]); + secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]); + secp256k1_scalar_negate(&sc[i], &sc[i]); + } + + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 32)); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + /* Check random points, constant scalar */ + for (ncount = 0; ncount < COUNT; ncount++) { + size_t i; + secp256k1_gej_set_infinity(&r); + + random_scalar_order(&sc[0]); + for (i = 0; i < 20; i++) { + secp256k1_ge ptg; + sc[i] = sc[0]; + random_group_element_test(&ptg); + pt[i] = ptg; + secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL); + } + + secp256k1_ecmult(&r2, &r, &sc[0], &szero); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + } + + /* Check random scalars, constant point */ + for (ncount = 0; ncount < COUNT; ncount++) { + size_t i; + secp256k1_ge ptg; + secp256k1_gej p0j; + secp256k1_scalar rs; + secp256k1_scalar_set_int(&rs, 0); + + random_group_element_test(&ptg); + for (i = 0; i < 20; i++) { + random_scalar_order(&sc[i]); + pt[i] = ptg; + secp256k1_scalar_add(&rs, &rs, &sc[i]); + } + + secp256k1_gej_set_ge(&p0j, &pt[0]); + secp256k1_ecmult(&r2, &p0j, &rs, &szero); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + CHECK(secp256k1_gej_eq_var(&r, &r2)); + } + + /* Sanity check that zero scalars don't cause problems */ + for (ncount = 0; ncount < 20; ncount++) { + random_scalar_order(&sc[ncount]); + random_group_element_test(&pt[ncount]); + } + + secp256k1_scalar_clear(&sc[0]); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + secp256k1_scalar_clear(&sc[1]); + secp256k1_scalar_clear(&sc[2]); + secp256k1_scalar_clear(&sc[3]); + secp256k1_scalar_clear(&sc[4]); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 6)); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 5)); + CHECK(secp256k1_gej_is_infinity(&r)); + + /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */ + { + const size_t TOP = 8; + size_t s0i, s1i; + size_t t0i, t1i; + secp256k1_ge ptg; + secp256k1_gej ptgj; + + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + + for(t0i = 0; t0i < TOP; t0i++) { + for(t1i = 0; t1i < TOP; t1i++) { + secp256k1_gej t0p, t1p; + secp256k1_scalar t0, t1; + + secp256k1_scalar_set_int(&t0, (t0i + 1) / 2); + secp256k1_scalar_cond_negate(&t0, t0i & 1); + secp256k1_scalar_set_int(&t1, (t1i + 1) / 2); + secp256k1_scalar_cond_negate(&t1, t1i & 1); + + secp256k1_ecmult(&t0p, &ptgj, &t0, &szero); + secp256k1_ecmult(&t1p, &ptgj, &t1, &szero); + + for(s0i = 0; s0i < TOP; s0i++) { + for(s1i = 0; s1i < TOP; s1i++) { + secp256k1_scalar tmp1, tmp2; + secp256k1_gej expected, actual; + + secp256k1_ge_set_gej(&pt[0], &t0p); + secp256k1_ge_set_gej(&pt[1], &t1p); + + secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2); + secp256k1_scalar_cond_negate(&sc[0], s0i & 1); + secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2); + secp256k1_scalar_cond_negate(&sc[1], s1i & 1); + + secp256k1_scalar_mul(&tmp1, &t0, &sc[0]); + secp256k1_scalar_mul(&tmp2, &t1, &sc[1]); + secp256k1_scalar_add(&tmp1, &tmp1, &tmp2); + + secp256k1_ecmult(&expected, &ptgj, &tmp1, &szero); + CHECK(ecmult_multi(&CTX->error_callback, scratch, &actual, &szero, ecmult_multi_callback, &data, 2)); + CHECK(secp256k1_gej_eq_var(&actual, &expected)); + } + } + } + } + } +} + +static int test_ecmult_multi_random(secp256k1_scratch *scratch) { + /* Large random test for ecmult_multi_* functions which exercises: + * - Few or many inputs (0 up to 128, roughly exponentially distributed). + * - Few or many 0*P or a*INF inputs (roughly uniformly distributed). + * - Including or excluding an nonzero a*G term (or such a term at all). + * - Final expected result equal to infinity or not (roughly 50%). + * - ecmult_multi_var, ecmult_strauss_single_batch, ecmult_pippenger_single_batch + */ + + /* These 4 variables define the eventual input to the ecmult_multi function. + * g_scalar is the G scalar fed to it (or NULL, possibly, if g_scalar=0), and + * scalars[0..filled-1] and gejs[0..filled-1] are the scalars and points + * which form its normal inputs. */ + int filled = 0; + secp256k1_scalar g_scalar = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar scalars[128]; + secp256k1_gej gejs[128]; + /* The expected result, and the computed result. */ + secp256k1_gej expected, computed; + /* Temporaries. */ + secp256k1_scalar sc_tmp; + secp256k1_ge ge_tmp; + /* Variables needed for the actual input to ecmult_multi. */ + secp256k1_ge ges[128]; + ecmult_multi_data data; + + int i; + /* Which multiplication function to use */ + int fn = secp256k1_testrand_int(3); + secp256k1_ecmult_multi_func ecmult_multi = fn == 0 ? secp256k1_ecmult_multi_var : + fn == 1 ? secp256k1_ecmult_strauss_batch_single : + secp256k1_ecmult_pippenger_batch_single; + /* Simulate exponentially distributed num. */ + int num_bits = 2 + secp256k1_testrand_int(6); + /* Number of (scalar, point) inputs (excluding g). */ + int num = secp256k1_testrand_int((1 << num_bits) + 1); + /* Number of those which are nonzero. */ + int num_nonzero = secp256k1_testrand_int(num + 1); + /* Whether we're aiming to create an input with nonzero expected result. */ + int nonzero_result = secp256k1_testrand_bits(1); + /* Whether we will provide nonzero g multiplicand. In some cases our hand + * is forced here based on num_nonzero and nonzero_result. */ + int g_nonzero = num_nonzero == 0 ? nonzero_result : + num_nonzero == 1 && !nonzero_result ? 1 : + (int)secp256k1_testrand_bits(1); + /* Which g_scalar pointer to pass into ecmult_multi(). */ + const secp256k1_scalar* g_scalar_ptr = (g_nonzero || secp256k1_testrand_bits(1)) ? &g_scalar : NULL; + /* How many EC multiplications were performed in this function. */ + int mults = 0; + /* How many randomization steps to apply to the input list. */ + int rands = (int)secp256k1_testrand_bits(3); + if (rands > num_nonzero) rands = num_nonzero; + + secp256k1_gej_set_infinity(&expected); + secp256k1_gej_set_infinity(&gejs[0]); + secp256k1_scalar_set_int(&scalars[0], 0); + + if (g_nonzero) { + /* If g_nonzero, set g_scalar to nonzero value r. */ + random_scalar_order_test(&g_scalar); + if (!nonzero_result) { + /* If expected=0 is desired, add a (a*r, -(1/a)*g) term to compensate. */ + CHECK(num_nonzero > filled); + random_scalar_order_test(&sc_tmp); + secp256k1_scalar_mul(&scalars[filled], &sc_tmp, &g_scalar); + secp256k1_scalar_inverse_var(&sc_tmp, &sc_tmp); + secp256k1_scalar_negate(&sc_tmp, &sc_tmp); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &gejs[filled], &sc_tmp); + ++filled; + ++mults; + } + } + + if (nonzero_result && filled < num_nonzero) { + /* If a nonzero result is desired, and there is space, add a random nonzero term. */ + random_scalar_order_test(&scalars[filled]); + random_group_element_test(&ge_tmp); + secp256k1_gej_set_ge(&gejs[filled], &ge_tmp); + ++filled; + } + + if (nonzero_result) { + /* Compute the expected result using normal ecmult. */ + CHECK(filled <= 1); + secp256k1_ecmult(&expected, &gejs[0], &scalars[0], &g_scalar); + mults += filled + g_nonzero; + } + + /* At this point we have expected = scalar_g*G + sum(scalars[i]*gejs[i] for i=0..filled-1). */ + CHECK(filled <= 1 + !nonzero_result); + CHECK(filled <= num_nonzero); + + /* Add entries to scalars,gejs so that there are num of them. All the added entries + * either have scalar=0 or point=infinity, so these do not change the expected result. */ + while (filled < num) { + if (secp256k1_testrand_bits(1)) { + secp256k1_gej_set_infinity(&gejs[filled]); + random_scalar_order_test(&scalars[filled]); + } else { + secp256k1_scalar_set_int(&scalars[filled], 0); + random_group_element_test(&ge_tmp); + secp256k1_gej_set_ge(&gejs[filled], &ge_tmp); + } + ++filled; + } + + /* Now perform cheapish transformations on gejs and scalars, for indices + * 0..num_nonzero-1, which do not change the expected result, but may + * convert some of them to be both non-0-scalar and non-infinity-point. */ + for (i = 0; i < rands; ++i) { + int j; + secp256k1_scalar v, iv; + /* Shuffle the entries. */ + for (j = 0; j < num_nonzero; ++j) { + int k = secp256k1_testrand_int(num_nonzero - j); + if (k != 0) { + secp256k1_gej gej = gejs[j]; + secp256k1_scalar sc = scalars[j]; + gejs[j] = gejs[j + k]; + scalars[j] = scalars[j + k]; + gejs[j + k] = gej; + scalars[j + k] = sc; + } + } + /* Perturb all consecutive pairs of inputs: + * a*P + b*Q -> (a+b)*P + b*(Q-P). */ + for (j = 0; j + 1 < num_nonzero; j += 2) { + secp256k1_gej gej; + secp256k1_scalar_add(&scalars[j], &scalars[j], &scalars[j+1]); + secp256k1_gej_neg(&gej, &gejs[j]); + secp256k1_gej_add_var(&gejs[j+1], &gejs[j+1], &gej, NULL); + } + /* Transform the last input: a*P -> (v*a) * ((1/v)*P). */ + CHECK(num_nonzero >= 1); + random_scalar_order_test(&v); + secp256k1_scalar_inverse(&iv, &v); + secp256k1_scalar_mul(&scalars[num_nonzero - 1], &scalars[num_nonzero - 1], &v); + secp256k1_ecmult(&gejs[num_nonzero - 1], &gejs[num_nonzero - 1], &iv, NULL); + ++mults; + } + + /* Shuffle all entries (0..num-1). */ + for (i = 0; i < num; ++i) { + int j = secp256k1_testrand_int(num - i); + if (j != 0) { + secp256k1_gej gej = gejs[i]; + secp256k1_scalar sc = scalars[i]; + gejs[i] = gejs[i + j]; + scalars[i] = scalars[i + j]; + gejs[i + j] = gej; + scalars[i + j] = sc; + } + } + + /* Compute affine versions of all inputs. */ + secp256k1_ge_set_all_gej_var(ges, gejs, filled); + /* Invoke ecmult_multi code. */ + data.sc = scalars; + data.pt = ges; + CHECK(ecmult_multi(&CTX->error_callback, scratch, &computed, g_scalar_ptr, ecmult_multi_callback, &data, filled)); + mults += num_nonzero + g_nonzero; + /* Compare with expected result. */ + CHECK(secp256k1_gej_eq_var(&computed, &expected)); + return mults; +} + +static void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) { + secp256k1_scalar szero; + secp256k1_scalar sc; + secp256k1_ge pt; + secp256k1_gej r; + ecmult_multi_data data; + secp256k1_scratch *scratch_empty; + + random_group_element_test(&pt); + random_scalar_order(&sc); + data.sc = ≻ + data.pt = &pt; + secp256k1_scalar_set_int(&szero, 0); + + /* Try to multiply 1 point, but scratch space is empty.*/ + scratch_empty = secp256k1_scratch_create(&CTX->error_callback, 0); + CHECK(!ecmult_multi(&CTX->error_callback, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1)); + secp256k1_scratch_destroy(&CTX->error_callback, scratch_empty); +} + +static void test_secp256k1_pippenger_bucket_window_inv(void) { + int i; + + CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0); + for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) { + /* Bucket_window of 8 is not used with endo */ + if (i == 8) { + continue; + } + CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i); + if (i != PIPPENGER_MAX_BUCKET_WINDOW) { + CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i); + } + } +} + +/** + * Probabilistically test the function returning the maximum number of possible points + * for a given scratch space. + */ +static void test_ecmult_multi_pippenger_max_points(void) { + size_t scratch_size = secp256k1_testrand_bits(8); + size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12); + secp256k1_scratch *scratch; + size_t n_points_supported; + int bucket_window = 0; + + for(; scratch_size < max_size; scratch_size+=256) { + size_t i; + size_t total_alloc; + size_t checkpoint; + scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size); + CHECK(scratch != NULL); + checkpoint = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch); + n_points_supported = secp256k1_pippenger_max_points(&CTX->error_callback, scratch); + if (n_points_supported == 0) { + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + continue; + } + bucket_window = secp256k1_pippenger_bucket_window(n_points_supported); + /* allocate `total_alloc` bytes over `PIPPENGER_SCRATCH_OBJECTS` many allocations */ + total_alloc = secp256k1_pippenger_scratch_size(n_points_supported, bucket_window); + for (i = 0; i < PIPPENGER_SCRATCH_OBJECTS - 1; i++) { + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 1)); + total_alloc--; + } + CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, total_alloc)); + secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint); + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + } + CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW); +} + +static void test_ecmult_multi_batch_size_helper(void) { + size_t n_batches, n_batch_points, max_n_batch_points, n; + + max_n_batch_points = 0; + n = 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0); + + max_n_batch_points = 1; + n = 0; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 0); + CHECK(n_batch_points == 0); + + max_n_batch_points = 2; + n = 5; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 3); + CHECK(n_batch_points == 2); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + n = ECMULT_MAX_POINTS_PER_BATCH; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 1); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1; + n = ECMULT_MAX_POINTS_PER_BATCH + 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 2); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1); + + max_n_batch_points = 1; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX); + CHECK(n_batch_points == 1); + + max_n_batch_points = 2; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX/2 + 1); + CHECK(n_batch_points == 2); +} + +/** + * Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to + * 1 <= i <= num points. + */ +static void test_ecmult_multi_batching(void) { + static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD; + secp256k1_scalar scG; + secp256k1_scalar szero; + secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_scalar) * n_points); + secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_ge) * n_points); + secp256k1_gej r; + secp256k1_gej r2; + ecmult_multi_data data; + int i; + secp256k1_scratch *scratch; + + secp256k1_gej_set_infinity(&r2); + secp256k1_scalar_set_int(&szero, 0); + + /* Get random scalars and group elements and compute result */ + random_scalar_order(&scG); + secp256k1_ecmult(&r2, &r2, &szero, &scG); + for(i = 0; i < n_points; i++) { + secp256k1_ge ptg; + secp256k1_gej ptgj; + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + pt[i] = ptg; + random_scalar_order(&sc[i]); + secp256k1_ecmult(&ptgj, &ptgj, &sc[i], NULL); + secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL); + } + data.sc = sc; + data.pt = pt; + secp256k1_gej_neg(&r2, &r2); + + /* Test with empty scratch space. It should compute the correct result using + * ecmult_mult_simple algorithm which doesn't require a scratch space. */ + scratch = secp256k1_scratch_create(&CTX->error_callback, 0); + CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + + /* Test with space for 1 point in pippenger. That's not enough because + * ecmult_multi selects strauss which requires more memory. It should + * therefore select the simple algorithm. */ + scratch = secp256k1_scratch_create(&CTX->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); + CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + + for(i = 1; i <= n_points; i++) { + if (i > ECMULT_PIPPENGER_THRESHOLD) { + int bucket_window = secp256k1_pippenger_bucket_window(i); + size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window); + scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); + } else { + size_t scratch_size = secp256k1_strauss_scratch_size(i); + scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); + } + CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + } + free(sc); + free(pt); +} + +static void run_ecmult_multi_tests(void) { + secp256k1_scratch *scratch; + int64_t todo = (int64_t)320 * COUNT; + + test_secp256k1_pippenger_bucket_window_inv(); + test_ecmult_multi_pippenger_max_points(); + scratch = secp256k1_scratch_create(&CTX->error_callback, 819200); + test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); + test_ecmult_multi(NULL, secp256k1_ecmult_multi_var); + test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single); + test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single); + test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single); + test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single); + while (todo > 0) { + todo -= test_ecmult_multi_random(scratch); + } + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + + /* Run test_ecmult_multi with space for exactly one point */ + scratch = secp256k1_scratch_create(&CTX->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); + test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); + secp256k1_scratch_destroy(&CTX->error_callback, scratch); + + test_ecmult_multi_batch_size_helper(); + test_ecmult_multi_batching(); +} + +static void test_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, two, t; + int wnaf[256]; + int zeroes = -1; + int i; + int bits; + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&two, 2); + bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w); + CHECK(bits <= 256); + for (i = bits-1; i >= 0; i--) { + int v = wnaf[i]; + secp256k1_scalar_mul(&x, &x, &two); + if (v) { + CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */ + zeroes=0; + CHECK((v & 1) == 1); /* check non-zero elements are odd */ + CHECK(v <= (1 << (w-1)) - 1); /* check range below */ + CHECK(v >= -(1 << (w-1)) - 1); /* check range above */ + } else { + CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */ + zeroes++; + } + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */ +} + +static void test_constant_wnaf_negate(const secp256k1_scalar *number) { + secp256k1_scalar neg1 = *number; + secp256k1_scalar neg2 = *number; + int sign1 = 1; + int sign2 = 1; + + if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) { + secp256k1_scalar_negate(&neg1, &neg1); + sign1 = -1; + } + sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2)); + CHECK(sign1 == sign2); + CHECK(secp256k1_scalar_eq(&neg1, &neg2)); +} + +static void test_constant_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, shift; + int wnaf[256] = {0}; + int i; + int skew; + int bits = 256; + secp256k1_scalar num = *number; + secp256k1_scalar scalar_skew; + + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&shift, 1 << w); + for (i = 0; i < 16; ++i) { + secp256k1_scalar_shr_int(&num, 8); + } + bits = 128; + skew = secp256k1_wnaf_const(wnaf, &num, w, bits); + + for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) { + secp256k1_scalar t; + int v = wnaf[i]; + CHECK(v != 0); /* check nonzero */ + CHECK(v & 1); /* check parity */ + CHECK(v > -(1 << w)); /* check range above */ + CHECK(v < (1 << w)); /* check range below */ + + secp256k1_scalar_mul(&x, &x, &shift); + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + /* Skew num because when encoding numbers as odd we use an offset */ + secp256k1_scalar_set_int(&scalar_skew, skew); + secp256k1_scalar_add(&num, &num, &scalar_skew); + CHECK(secp256k1_scalar_eq(&x, &num)); +} + +static void test_fixed_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, shift; + int wnaf[256] = {0}; + int i; + int skew; + secp256k1_scalar num = *number; + + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&shift, 1 << w); + for (i = 0; i < 16; ++i) { + secp256k1_scalar_shr_int(&num, 8); + } + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + + for (i = WNAF_SIZE(w)-1; i >= 0; --i) { + secp256k1_scalar t; + int v = wnaf[i]; + CHECK(v == 0 || v & 1); /* check parity */ + CHECK(v > -(1 << w)); /* check range above */ + CHECK(v < (1 << w)); /* check range below */ + + secp256k1_scalar_mul(&x, &x, &shift); + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + /* If skew is 1 then add 1 to num */ + secp256k1_scalar_cadd_bit(&num, 0, skew == 1); + CHECK(secp256k1_scalar_eq(&x, &num)); +} + +/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the + * rest is 0.*/ +static void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) { + int i; + for (i = WNAF_SIZE(w)-1; i >= 8; --i) { + CHECK(wnaf[i] == 0); + } + for (i = 7; i >= 0; --i) { + CHECK(wnaf[i] == wnaf_expected[i]); + } +} + +static void test_fixed_wnaf_small(void) { + int w = 4; + int wnaf[256] = {0}; + int i; + int skew; + secp256k1_scalar num; + + secp256k1_scalar_set_int(&num, 0); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + for (i = WNAF_SIZE(w)-1; i >= 0; --i) { + int v = wnaf[i]; + CHECK(v == 0); + } + CHECK(skew == 0); + + secp256k1_scalar_set_int(&num, 1); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + for (i = WNAF_SIZE(w)-1; i >= 1; --i) { + int v = wnaf[i]; + CHECK(v == 0); + } + CHECK(wnaf[0] == 1); + CHECK(skew == 0); + + { + int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf }; + secp256k1_scalar_set_int(&num, 0xffffffff); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } + { + int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf }; + secp256k1_scalar_set_int(&num, 0xeeeeeeee); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 1); + } + { + int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 }; + secp256k1_scalar_set_int(&num, 0x01010101); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } + { + int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 }; + secp256k1_scalar_set_int(&num, 0x01ef1ef1); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } +} + +static void run_wnaf(void) { + int i; + secp256k1_scalar n = {{0}}; + + test_constant_wnaf(&n, 4); + /* Sanity check: 1 and 2 are the smallest odd and even numbers and should + * have easier-to-diagnose failure modes */ + n.d[0] = 1; + test_constant_wnaf(&n, 4); + n.d[0] = 2; + test_constant_wnaf(&n, 4); + /* Test -1, because it's a special case in wnaf_const */ + n = secp256k1_scalar_one; + secp256k1_scalar_negate(&n, &n); + test_constant_wnaf(&n, 4); + + /* Test -2, which may not lead to overflows in wnaf_const */ + secp256k1_scalar_add(&n, &secp256k1_scalar_one, &secp256k1_scalar_one); + secp256k1_scalar_negate(&n, &n); + test_constant_wnaf(&n, 4); + + /* Test (1/2) - 1 = 1/-2 and 1/2 = (1/-2) + 1 + as corner cases of negation handling in wnaf_const */ + secp256k1_scalar_inverse(&n, &n); + test_constant_wnaf(&n, 4); + + secp256k1_scalar_add(&n, &n, &secp256k1_scalar_one); + test_constant_wnaf(&n, 4); + + /* Test 0 for fixed wnaf */ + test_fixed_wnaf_small(); + /* Random tests */ + for (i = 0; i < COUNT; i++) { + random_scalar_order(&n); + test_wnaf(&n, 4+(i%10)); + test_constant_wnaf_negate(&n); + test_constant_wnaf(&n, 4 + (i % 10)); + test_fixed_wnaf(&n, 4 + (i % 10)); + } + secp256k1_scalar_set_int(&n, 0); + CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1); + CHECK(secp256k1_scalar_is_zero(&n)); + CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1); + CHECK(secp256k1_scalar_is_zero(&n)); +} + +static int test_ecmult_accumulate_cb(secp256k1_scalar* sc, secp256k1_ge* pt, size_t idx, void* data) { + const secp256k1_scalar* indata = (const secp256k1_scalar*)data; + *sc = *indata; + *pt = secp256k1_ge_const_g; + CHECK(idx == 0); + return 1; +} + +static void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar* x, secp256k1_scratch* scratch) { + /* Compute x*G in 6 different ways, serialize it uncompressed, and feed it into acc. */ + secp256k1_gej rj1, rj2, rj3, rj4, rj5, rj6, gj, infj; + secp256k1_ge r; + const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + unsigned char bytes[65]; + size_t size = 65; + secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g); + secp256k1_gej_set_infinity(&infj); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &rj1, x); + secp256k1_ecmult(&rj2, &gj, x, &zero); + secp256k1_ecmult(&rj3, &infj, &zero, x); + secp256k1_ecmult_multi_var(NULL, scratch, &rj4, x, NULL, NULL, 0); + secp256k1_ecmult_multi_var(NULL, scratch, &rj5, &zero, test_ecmult_accumulate_cb, (void*)x, 1); + secp256k1_ecmult_const(&rj6, &secp256k1_ge_const_g, x, 256); + secp256k1_ge_set_gej_var(&r, &rj1); + ge_equals_gej(&r, &rj2); + ge_equals_gej(&r, &rj3); + ge_equals_gej(&r, &rj4); + ge_equals_gej(&r, &rj5); + ge_equals_gej(&r, &rj6); + if (secp256k1_ge_is_infinity(&r)) { + /* Store infinity as 0x00 */ + const unsigned char zerobyte[1] = {0}; + secp256k1_sha256_write(acc, zerobyte, 1); + } else { + /* Store other points using their uncompressed serialization. */ + secp256k1_eckey_pubkey_serialize(&r, bytes, &size, 0); + CHECK(size == 65); + secp256k1_sha256_write(acc, bytes, size); + } +} + +static void test_ecmult_constants_2bit(void) { + /* Using test_ecmult_accumulate, test ecmult for: + * - For i in 0..36: + * - Key i + * - Key -i + * - For i in 0..255: + * - For j in 1..255 (only odd values): + * - Key (j*2^i) mod order + */ + secp256k1_scalar x; + secp256k1_sha256 acc; + unsigned char b32[32]; + int i, j; + secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(CTX, 65536); + + /* Expected hash of all the computed points; created with an independent + * implementation. */ + static const unsigned char expected32[32] = { + 0xe4, 0x71, 0x1b, 0x4d, 0x14, 0x1e, 0x68, 0x48, + 0xb7, 0xaf, 0x47, 0x2b, 0x4c, 0xd2, 0x04, 0x14, + 0x3a, 0x75, 0x87, 0x60, 0x1a, 0xf9, 0x63, 0x60, + 0xd0, 0xcb, 0x1f, 0xaa, 0x85, 0x9a, 0xb7, 0xb4 + }; + secp256k1_sha256_initialize(&acc); + for (i = 0; i <= 36; ++i) { + secp256k1_scalar_set_int(&x, i); + test_ecmult_accumulate(&acc, &x, scratch); + secp256k1_scalar_negate(&x, &x); + test_ecmult_accumulate(&acc, &x, scratch); + }; + for (i = 0; i < 256; ++i) { + for (j = 1; j < 256; j += 2) { + int k; + secp256k1_scalar_set_int(&x, j); + for (k = 0; k < i; ++k) secp256k1_scalar_add(&x, &x, &x); + test_ecmult_accumulate(&acc, &x, scratch); + } + } + secp256k1_sha256_finalize(&acc, b32); + CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0); + + secp256k1_scratch_space_destroy(CTX, scratch); +} + +static void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsigned char* expected32) { + /* Using test_ecmult_accumulate, test ecmult for: + * - Key 0 + * - Key 1 + * - Key -1 + * - For i in range(iter): + * - Key SHA256(LE32(prefix) || LE16(i)) + */ + secp256k1_scalar x; + secp256k1_sha256 acc; + unsigned char b32[32]; + unsigned char inp[6]; + size_t i; + secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(CTX, 65536); + + inp[0] = prefix & 0xFF; + inp[1] = (prefix >> 8) & 0xFF; + inp[2] = (prefix >> 16) & 0xFF; + inp[3] = (prefix >> 24) & 0xFF; + secp256k1_sha256_initialize(&acc); + secp256k1_scalar_set_int(&x, 0); + test_ecmult_accumulate(&acc, &x, scratch); + secp256k1_scalar_set_int(&x, 1); + test_ecmult_accumulate(&acc, &x, scratch); + secp256k1_scalar_negate(&x, &x); + test_ecmult_accumulate(&acc, &x, scratch); + + for (i = 0; i < iter; ++i) { + secp256k1_sha256 gen; + inp[4] = i & 0xff; + inp[5] = (i >> 8) & 0xff; + secp256k1_sha256_initialize(&gen); + secp256k1_sha256_write(&gen, inp, sizeof(inp)); + secp256k1_sha256_finalize(&gen, b32); + secp256k1_scalar_set_b32(&x, b32, NULL); + test_ecmult_accumulate(&acc, &x, scratch); + } + secp256k1_sha256_finalize(&acc, b32); + CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0); + + secp256k1_scratch_space_destroy(CTX, scratch); +} + +static void run_ecmult_constants(void) { + /* Expected hashes of all points in the tests below. Computed using an + * independent implementation. */ + static const unsigned char expected32_6bit20[32] = { + 0x68, 0xb6, 0xed, 0x6f, 0x28, 0xca, 0xc9, 0x7f, + 0x8e, 0x8b, 0xd6, 0xc0, 0x61, 0x79, 0x34, 0x6e, + 0x5a, 0x8f, 0x2b, 0xbc, 0x3e, 0x1f, 0xc5, 0x2e, + 0x2a, 0xd0, 0x45, 0x67, 0x7f, 0x95, 0x95, 0x8e + }; + static const unsigned char expected32_8bit8[32] = { + 0x8b, 0x65, 0x8e, 0xea, 0x86, 0xae, 0x3c, 0x95, + 0x90, 0xb6, 0x77, 0xa4, 0x8c, 0x76, 0xd9, 0xec, + 0xf5, 0xab, 0x8a, 0x2f, 0xfd, 0xdb, 0x19, 0x12, + 0x1a, 0xee, 0xe6, 0xb7, 0x6e, 0x05, 0x3f, 0xc6 + }; + /* For every combination of 6 bit positions out of 256, restricted to + * 20-bit windows (i.e., the first and last bit position are no more than + * 19 bits apart), all 64 bit patterns occur in the input scalars used in + * this test. */ + CONDITIONAL_TEST(1, "test_ecmult_constants_sha 1024") { + test_ecmult_constants_sha(4808378u, 1024, expected32_6bit20); + } + + /* For every combination of 8 consecutive bit positions, all 256 bit + * patterns occur in the input scalars used in this test. */ + CONDITIONAL_TEST(3, "test_ecmult_constants_sha 2048") { + test_ecmult_constants_sha(1607366309u, 2048, expected32_8bit8); + } + + CONDITIONAL_TEST(35, "test_ecmult_constants_2bit") { + test_ecmult_constants_2bit(); + } +} + +static void test_ecmult_gen_blind(void) { + /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */ + secp256k1_scalar key; + secp256k1_scalar b; + unsigned char seed32[32]; + secp256k1_gej pgej; + secp256k1_gej pgej2; + secp256k1_gej i; + secp256k1_ge pge; + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pgej, &key); + secp256k1_testrand256(seed32); + b = CTX->ecmult_gen_ctx.blind; + i = CTX->ecmult_gen_ctx.initial; + secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, seed32); + CHECK(!secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.blind)); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pgej2, &key); + CHECK(!gej_xyz_equals_gej(&pgej, &pgej2)); + CHECK(!gej_xyz_equals_gej(&i, &CTX->ecmult_gen_ctx.initial)); + secp256k1_ge_set_gej(&pge, &pgej); + ge_equals_gej(&pge, &pgej2); +} + +static void test_ecmult_gen_blind_reset(void) { + /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */ + secp256k1_scalar b; + secp256k1_gej initial; + secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0); + b = CTX->ecmult_gen_ctx.blind; + initial = CTX->ecmult_gen_ctx.initial; + secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0); + CHECK(secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.blind)); + CHECK(gej_xyz_equals_gej(&initial, &CTX->ecmult_gen_ctx.initial)); +} + +static void run_ecmult_gen_blind(void) { + int i; + test_ecmult_gen_blind_reset(); + for (i = 0; i < 10; i++) { + test_ecmult_gen_blind(); + } +} + +/***** ENDOMORPHISH TESTS *****/ +static void test_scalar_split(const secp256k1_scalar* full) { + secp256k1_scalar s, s1, slam; + const unsigned char zero[32] = {0}; + unsigned char tmp[32]; + + secp256k1_scalar_split_lambda(&s1, &slam, full); + + /* check slam*lambda + s1 == full */ + secp256k1_scalar_mul(&s, &secp256k1_const_lambda, &slam); + secp256k1_scalar_add(&s, &s, &s1); + CHECK(secp256k1_scalar_eq(&s, full)); + + /* check that both are <= 128 bits in size */ + if (secp256k1_scalar_is_high(&s1)) { + secp256k1_scalar_negate(&s1, &s1); + } + if (secp256k1_scalar_is_high(&slam)) { + secp256k1_scalar_negate(&slam, &slam); + } + + secp256k1_scalar_get_b32(tmp, &s1); + CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0); + secp256k1_scalar_get_b32(tmp, &slam); + CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0); +} + + +static void run_endomorphism_tests(void) { + unsigned i; + static secp256k1_scalar s; + test_scalar_split(&secp256k1_scalar_zero); + test_scalar_split(&secp256k1_scalar_one); + secp256k1_scalar_negate(&s,&secp256k1_scalar_one); + test_scalar_split(&s); + test_scalar_split(&secp256k1_const_lambda); + secp256k1_scalar_add(&s, &secp256k1_const_lambda, &secp256k1_scalar_one); + test_scalar_split(&s); + + for (i = 0; i < 100U * COUNT; ++i) { + secp256k1_scalar full; + random_scalar_order_test(&full); + test_scalar_split(&full); + } + for (i = 0; i < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++i) { + test_scalar_split(&scalars_near_split_bounds[i]); + } +} + +static void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) { + unsigned char pubkeyc[65]; + secp256k1_pubkey pubkey; + secp256k1_ge ge; + size_t pubkeyclen; + int32_t ecount; + ecount = 0; + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) { + /* Smaller sizes are tested exhaustively elsewhere. */ + int32_t i; + memcpy(&pubkeyc[1], input, 64); + SECP256K1_CHECKMEM_UNDEFINE(&pubkeyc[pubkeyclen], 65 - pubkeyclen); + for (i = 0; i < 256; i++) { + /* Try all type bytes. */ + int xpass; + int ypass; + int ysign; + pubkeyc[0] = i; + /* What sign does this point have? */ + ysign = (input[63] & 1) + 2; + /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */ + xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2); + /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */ + ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) && + ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65)); + if (xpass || ypass) { + /* These cases must parse. */ + unsigned char pubkeyo[65]; + size_t outl; + memset(&pubkey, 0, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + ecount = 0; + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + outl = 65; + SECP256K1_CHECKMEM_UNDEFINE(pubkeyo, 65); + CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + SECP256K1_CHECKMEM_CHECK(pubkeyo, outl); + CHECK(outl == 33); + CHECK(secp256k1_memcmp_var(&pubkeyo[1], &pubkeyc[1], 32) == 0); + CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0])); + if (ypass) { + /* This test isn't always done because we decode with alternative signs, so the y won't match. */ + CHECK(pubkeyo[0] == ysign); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + secp256k1_pubkey_save(&pubkey, &ge); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + outl = 65; + SECP256K1_CHECKMEM_UNDEFINE(pubkeyo, 65); + CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); + SECP256K1_CHECKMEM_CHECK(pubkeyo, outl); + CHECK(outl == 65); + CHECK(pubkeyo[0] == 4); + CHECK(secp256k1_memcmp_var(&pubkeyo[1], input, 64) == 0); + } + CHECK(ecount == 0); + } else { + /* These cases must fail to parse. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + } + } + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); +} + +static void run_ec_pubkey_parse_test(void) { +#define SECP256K1_EC_PARSE_TEST_NVALID (12) + const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = { + { + /* Point with leading and trailing zeros in x and y serialization. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83, + 0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00 + }, + { + /* Point with x equal to a 3rd root of unity.*/ + 0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9, + 0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Point with largest x. (1/2) */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c, + 0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e, + 0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d, + }, + { + /* Point with largest x. (2/2) */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c, + 0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1, + 0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2, + }, + { + /* Point with smallest x. (1/2) */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Point with smallest x. (2/2) */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, + 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41, + }, + { + /* Point with largest y. (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with largest y. (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with largest y. (3/3) */ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with smallest y. (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Point with smallest y. (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Point with smallest y. (3/3) */ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 + } + }; +#define SECP256K1_EC_PARSE_TEST_NXVALID (4) + const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = { + { + /* Valid if y overflow ignored (y = 1 mod p). (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* Valid if y overflow ignored (y = 1 mod p). (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* x on curve, y is from y^2 = x^3 + 8. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03 + } + }; +#define SECP256K1_EC_PARSE_TEST_NINVALID (7) + const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = { + { + /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */ + 0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, + 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Valid if x overflow ignored (x = 1 mod p). */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Valid if x overflow ignored (x = 1 mod p). */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, + 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41, + }, + { + /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + 0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f, + 0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28, + }, + { + /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + 0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0, + 0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07, + }, + { + /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d, + 0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc, + }, + { + /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2, + 0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53 + } + }; + const unsigned char pubkeyc[66] = { + /* Serialization of G. */ + 0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, + 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, + 0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08, + 0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4, + 0xB8, 0x00 + }; + unsigned char sout[65]; + unsigned char shortkey[2]; + secp256k1_ge ge; + secp256k1_pubkey pubkey; + size_t len; + int32_t i; + int32_t ecount; + int32_t ecount2; + ecount = 0; + /* Nothing should be reading this far into pubkeyc. */ + SECP256K1_CHECKMEM_UNDEFINE(&pubkeyc[65], 1); + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + /* Zero length claimed, fail, zeroize, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(shortkey, 2); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 0) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* Length one claimed, fail, zeroize, no illegal arg error. */ + for (i = 0; i < 256 ; i++) { + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + shortkey[0] = i; + SECP256K1_CHECKMEM_UNDEFINE(&shortkey[1], 1); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 1) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + /* Length two claimed, fail, zeroize, no illegal arg error. */ + for (i = 0; i < 65536 ; i++) { + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + shortkey[0] = i & 255; + shortkey[1] = i >> 8; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 2) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */ + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 33) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */ + CHECK(secp256k1_ec_pubkey_parse(CTX, NULL, pubkeyc, 65) == 0); + CHECK(ecount == 2); + /* NULL input string. Illegal arg and zeroize output. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, NULL, 65) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 1); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 2); + /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 64) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 66) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* Valid parse. */ + memset(&pubkey, 0, sizeof(pubkey)); + ecount = 0; + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 65) == 1); + CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, pubkeyc, 65) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + SECP256K1_CHECKMEM_UNDEFINE(&ge, sizeof(ge)); + CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 1); + SECP256K1_CHECKMEM_CHECK(&ge.x, sizeof(ge.x)); + SECP256K1_CHECKMEM_CHECK(&ge.y, sizeof(ge.y)); + SECP256K1_CHECKMEM_CHECK(&ge.infinity, sizeof(ge.infinity)); + ge_equals_ge(&secp256k1_ge_const_g, &ge); + CHECK(ecount == 0); + /* secp256k1_ec_pubkey_serialize illegal args. */ + ecount = 0; + len = 65; + CHECK(secp256k1_ec_pubkey_serialize(CTX, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); + CHECK(ecount == 1); + CHECK(len == 0); + CHECK(secp256k1_ec_pubkey_serialize(CTX, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); + CHECK(ecount == 2); + len = 65; + SECP256K1_CHECKMEM_UNDEFINE(sout, 65); + CHECK(secp256k1_ec_pubkey_serialize(CTX, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0); + SECP256K1_CHECKMEM_CHECK(sout, 65); + CHECK(ecount == 3); + CHECK(len == 0); + len = 65; + CHECK(secp256k1_ec_pubkey_serialize(CTX, sout, &len, &pubkey, ~0) == 0); + CHECK(ecount == 4); + CHECK(len == 0); + len = 65; + SECP256K1_CHECKMEM_UNDEFINE(sout, 65); + CHECK(secp256k1_ec_pubkey_serialize(CTX, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); + SECP256K1_CHECKMEM_CHECK(sout, 65); + CHECK(ecount == 4); + CHECK(len == 65); + /* Multiple illegal args. Should still set arg error only once. */ + ecount = 0; + ecount2 = 11; + CHECK(secp256k1_ec_pubkey_parse(CTX, NULL, NULL, 65) == 0); + CHECK(ecount == 1); + /* Does the illegal arg callback actually change the behavior? */ + secp256k1_context_set_illegal_callback(CTX, uncounting_illegal_callback_fn, &ecount2); + CHECK(secp256k1_ec_pubkey_parse(CTX, NULL, NULL, 65) == 0); + CHECK(ecount == 1); + CHECK(ecount2 == 10); + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); + /* Try a bunch of prefabbed points with all possible encodings. */ + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) { + ec_pubkey_parse_pointtest(valid[i], 1, 1); + } + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) { + ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0); + } + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) { + ec_pubkey_parse_pointtest(invalid[i], 0, 0); + } +} + +static void run_eckey_edge_case_test(void) { + const unsigned char orderc[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 + }; + const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00}; + unsigned char ctmp[33]; + unsigned char ctmp2[33]; + secp256k1_pubkey pubkey; + secp256k1_pubkey pubkey2; + secp256k1_pubkey pubkey_one; + secp256k1_pubkey pubkey_negone; + const secp256k1_pubkey *pubkeys[3]; + size_t len; + int32_t ecount; + /* Group order is too large, reject. */ + CHECK(secp256k1_ec_seckey_verify(CTX, orderc) == 0); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, orderc) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* Maximum value is too large, reject. */ + memset(ctmp, 255, 32); + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* Zero is too small, reject. */ + memset(ctmp, 0, 32); + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* One must be accepted. */ + ctmp[31] = 0x01; + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + pubkey_one = pubkey; + /* Group order + 1 is too large, reject. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x42; + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* -1 must be accepted. */ + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + pubkey_negone = pubkey; + /* Tweak of zero leaves the value unchanged. */ + memset(ctmp2, 0, 32); + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, ctmp2) == 1); + CHECK(secp256k1_memcmp_var(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40); + memcpy(&pubkey2, &pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Multiply tweak of zero zeroizes the output. */ + CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, ctmp2) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, ctmp2) == 0); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing + seckey, the seckey is zeroized. */ + memcpy(ctmp, orderc, 32); + memset(ctmp2, 0, 32); + ctmp2[31] = 0x01; + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp2) == 1); + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0); + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, ctmp2) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, ctmp2) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); + /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing + tweak, the seckey is zeroized. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, orderc) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, orderc) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + /* If pubkey_tweak_add or pubkey_tweak_mul are called with an overflowing + tweak, the pubkey is zeroized. */ + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, orderc) == 0); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, orderc) == 0); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* If the resulting key in secp256k1_ec_seckey_tweak_add and + * secp256k1_ec_pubkey_tweak_add is 0 the functions fail and in the latter + * case the pubkey is zeroized. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + memset(ctmp2, 0, 32); + ctmp2[31] = 1; + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp2, ctmp) == 0); + CHECK(secp256k1_memcmp_var(zeros, ctmp2, 32) == 0); + ctmp2[31] = 1; + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 0); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* Tweak computation wraps and results in a key of 1. */ + ctmp2[31] = 2; + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp2, ctmp) == 1); + CHECK(secp256k1_memcmp_var(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1); + ctmp2[31] = 2; + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1); + ctmp2[31] = 1; + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, ctmp2) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Tweak mul * 2 = 1+1. */ + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1); + ctmp2[31] = 2; + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey2, ctmp2) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Test argument errors. */ + ecount = 0; + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + CHECK(ecount == 0); + /* Zeroize pubkey on parse error. */ + memset(&pubkey, 0, 32); + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + memset(&pubkey2, 0, 32); + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey2, ctmp2) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_memcmp_var(&pubkey2, zeros, sizeof(pubkey2)) == 0); + /* Plain argument errors. */ + ecount = 0; + CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ec_seckey_verify(CTX, NULL) == 0); + CHECK(ecount == 1); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 4; + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 4; + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + CHECK(secp256k1_ec_seckey_tweak_add(CTX, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 1; + CHECK(secp256k1_ec_seckey_tweak_mul(CTX, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + CHECK(secp256k1_ec_pubkey_create(CTX, NULL, ctmp) == 0); + CHECK(ecount == 1); + memset(&pubkey, 1, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* secp256k1_ec_pubkey_combine tests. */ + ecount = 0; + pubkeys[0] = &pubkey_one; + SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[0], sizeof(secp256k1_pubkey *)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[1], sizeof(secp256k1_pubkey *)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[2], sizeof(secp256k1_pubkey *)); + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 0) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_combine(CTX, NULL, pubkeys, 1) == 0); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 2); + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, NULL, 1) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 3); + pubkeys[0] = &pubkey_negone; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 1) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + len = 33; + CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0); + /* Result is infinity. */ + pubkeys[0] = &pubkey_one; + pubkeys[1] = &pubkey_negone; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 2) == 0); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 3); + /* Passes through infinity but comes out one. */ + pubkeys[2] = &pubkey_one; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 3) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + len = 33; + CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0); + /* Adds to two. */ + pubkeys[1] = &pubkey_one; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 2) == 1); + SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); +} + +static void run_eckey_negate_test(void) { + unsigned char seckey[32]; + unsigned char seckey_tmp[32]; + + random_scalar_order_b32(seckey); + memcpy(seckey_tmp, seckey, 32); + + /* Verify negation changes the key and changes it back */ + CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 1); + CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) != 0); + CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 1); + CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); + + /* Check that privkey alias gives same result */ + CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 1); + CHECK(secp256k1_ec_privkey_negate(CTX, seckey_tmp) == 1); + CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); + + /* Negating all 0s fails */ + memset(seckey, 0, 32); + memset(seckey_tmp, 0, 32); + CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 0); + /* Check that seckey is not modified */ + CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); + + /* Negating an overflowing seckey fails and the seckey is zeroed. In this + * test, the seckey has 16 random bytes to ensure that ec_seckey_negate + * doesn't just set seckey to a constant value in case of failure. */ + random_scalar_order_b32(seckey); + memset(seckey, 0xFF, 16); + memset(seckey_tmp, 0, 32); + CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 0); + CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); +} + +static void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) { + secp256k1_scalar nonce; + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(&CTX->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid)); +} + +static void test_ecdsa_sign_verify(void) { + secp256k1_gej pubj; + secp256k1_ge pub; + secp256k1_scalar one; + secp256k1_scalar msg, key; + secp256k1_scalar sigr, sigs; + int getrec; + int recid; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pubj, &key); + secp256k1_ge_set_gej(&pub, &pubj); + getrec = secp256k1_testrand_bits(1); + /* The specific way in which this conditional is written sidesteps a potential bug in clang. + See the commit messages of the commit that introduced this comment for details. */ + if (getrec) { + random_sign(&sigr, &sigs, &key, &msg, &recid); + CHECK(recid >= 0 && recid < 4); + } else { + random_sign(&sigr, &sigs, &key, &msg, NULL); + } + CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); + secp256k1_scalar_set_int(&one, 1); + secp256k1_scalar_add(&msg, &msg, &one); + CHECK(!secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); +} + +static void run_ecdsa_sign_verify(void) { + int i; + for (i = 0; i < 10*COUNT; i++) { + test_ecdsa_sign_verify(); + } +} + +/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */ +static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + (void)msg32; + (void)key32; + (void)algo16; + memcpy(nonce32, data, 32); + return (counter == 0); +} + +static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + /* Dummy nonce generator that has a fatal error on the first counter value. */ + if (counter == 0) { + return 0; + } + return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1); +} + +static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */ + if (counter < 3) { + memset(nonce32, counter==0 ? 0 : 255, 32); + if (counter == 2) { + nonce32[31]--; + } + return 1; + } + if (counter < 5) { + static const unsigned char order[] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41 + }; + memcpy(nonce32, order, 32); + if (counter == 4) { + nonce32[31]++; + } + return 1; + } + /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */ + /* If someone does fine a case where it retries for secp256k1, we'd like to know. */ + if (counter > 5) { + return 0; + } + return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5); +} + +static int is_empty_signature(const secp256k1_ecdsa_signature *sig) { + static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0}; + return secp256k1_memcmp_var(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0; +} + +static void test_ecdsa_end_to_end(void) { + unsigned char extra[32] = {0x00}; + unsigned char privkey[32]; + unsigned char message[32]; + unsigned char privkey2[32]; + secp256k1_ecdsa_signature signature[6]; + secp256k1_scalar r, s; + unsigned char sig[74]; + size_t siglen = 74; + unsigned char pubkeyc[65]; + size_t pubkeyclen = 65; + secp256k1_pubkey pubkey; + secp256k1_pubkey pubkey_tmp; + unsigned char seckey[300]; + size_t seckeylen = 300; + + /* Generate a random key and message. */ + { + secp256k1_scalar msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(privkey, &key); + secp256k1_scalar_get_b32(message, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(CTX, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, privkey) == 1); + + /* Verify exporting and importing public key. */ + CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyc, &pubkeyclen, &pubkey, secp256k1_testrand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED)); + memset(&pubkey, 0, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 1); + + /* Verify negation changes the key and changes it back */ + memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey_tmp) == 1); + CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0); + CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey_tmp) == 1); + CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0); + + /* Verify private key import and export. */ + CHECK(ec_privkey_export_der(CTX, seckey, &seckeylen, privkey, secp256k1_testrand_bits(1) == 1)); + CHECK(ec_privkey_import_der(CTX, privkey2, seckey, seckeylen) == 1); + CHECK(secp256k1_memcmp_var(privkey, privkey2, 32) == 0); + + /* Optionally tweak the keys using addition. */ + if (secp256k1_testrand_int(3) == 0) { + int ret1; + int ret2; + int ret3; + unsigned char rnd[32]; + unsigned char privkey_tmp[32]; + secp256k1_pubkey pubkey2; + secp256k1_testrand256_test(rnd); + memcpy(privkey_tmp, privkey, 32); + ret1 = secp256k1_ec_seckey_tweak_add(CTX, privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, rnd); + /* Check that privkey alias gives same result */ + ret3 = secp256k1_ec_privkey_tweak_add(CTX, privkey_tmp, rnd); + CHECK(ret1 == ret2); + CHECK(ret2 == ret3); + if (ret1 == 0) { + return; + } + CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, privkey) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + } + + /* Optionally tweak the keys using multiplication. */ + if (secp256k1_testrand_int(3) == 0) { + int ret1; + int ret2; + int ret3; + unsigned char rnd[32]; + unsigned char privkey_tmp[32]; + secp256k1_pubkey pubkey2; + secp256k1_testrand256_test(rnd); + memcpy(privkey_tmp, privkey, 32); + ret1 = secp256k1_ec_seckey_tweak_mul(CTX, privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, rnd); + /* Check that privkey alias gives same result */ + ret3 = secp256k1_ec_privkey_tweak_mul(CTX, privkey_tmp, rnd); + CHECK(ret1 == ret2); + CHECK(ret2 == ret3); + if (ret1 == 0) { + return; + } + CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, privkey) == 1); + CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + } + + /* Sign. */ + CHECK(secp256k1_ecdsa_sign(CTX, &signature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(CTX, &signature[4], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(CTX, &signature[1], message, privkey, NULL, extra) == 1); + extra[31] = 1; + CHECK(secp256k1_ecdsa_sign(CTX, &signature[2], message, privkey, NULL, extra) == 1); + extra[31] = 0; + extra[0] = 1; + CHECK(secp256k1_ecdsa_sign(CTX, &signature[3], message, privkey, NULL, extra) == 1); + CHECK(secp256k1_memcmp_var(&signature[0], &signature[4], sizeof(signature[0])) == 0); + CHECK(secp256k1_memcmp_var(&signature[0], &signature[1], sizeof(signature[0])) != 0); + CHECK(secp256k1_memcmp_var(&signature[0], &signature[2], sizeof(signature[0])) != 0); + CHECK(secp256k1_memcmp_var(&signature[0], &signature[3], sizeof(signature[0])) != 0); + CHECK(secp256k1_memcmp_var(&signature[1], &signature[2], sizeof(signature[0])) != 0); + CHECK(secp256k1_memcmp_var(&signature[1], &signature[3], sizeof(signature[0])) != 0); + CHECK(secp256k1_memcmp_var(&signature[2], &signature[3], sizeof(signature[0])) != 0); + /* Verify. */ + CHECK(secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[1], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[2], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[3], message, &pubkey) == 1); + /* Test lower-S form, malleate, verify and fail, test again, malleate again */ + CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[0])); + secp256k1_ecdsa_signature_load(CTX, &r, &s, &signature[0]); + secp256k1_scalar_negate(&s, &s); + secp256k1_ecdsa_signature_save(&signature[5], &r, &s); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 0); + CHECK(secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5])); + CHECK(secp256k1_ecdsa_signature_normalize(CTX, &signature[5], &signature[5])); + CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5])); + CHECK(!secp256k1_ecdsa_signature_normalize(CTX, &signature[5], &signature[5])); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 1); + secp256k1_scalar_negate(&s, &s); + secp256k1_ecdsa_signature_save(&signature[5], &r, &s); + CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5])); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 1); + CHECK(secp256k1_memcmp_var(&signature[5], &signature[0], 64) == 0); + + /* Serialize/parse DER and verify again */ + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, sig, &siglen, &signature[0]) == 1); + memset(&signature[0], 0, sizeof(signature[0])); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &signature[0], sig, siglen) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 1); + /* Serialize/destroy/parse DER and verify again. */ + siglen = 74; + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, sig, &siglen, &signature[0]) == 1); + sig[secp256k1_testrand_int(siglen)] += 1 + secp256k1_testrand_int(255); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &signature[0], sig, siglen) == 0 || + secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 0); +} + +static void test_random_pubkeys(void) { + secp256k1_ge elem; + secp256k1_ge elem2; + unsigned char in[65]; + /* Generate some randomly sized pubkeys. */ + size_t len = secp256k1_testrand_bits(2) == 0 ? 65 : 33; + if (secp256k1_testrand_bits(2) == 0) { + len = secp256k1_testrand_bits(6); + } + if (len == 65) { + in[0] = secp256k1_testrand_bits(1) ? 4 : (secp256k1_testrand_bits(1) ? 6 : 7); + } else { + in[0] = secp256k1_testrand_bits(1) ? 2 : 3; + } + if (secp256k1_testrand_bits(3) == 0) { + in[0] = secp256k1_testrand_bits(8); + } + if (len > 1) { + secp256k1_testrand256(&in[1]); + } + if (len > 33) { + secp256k1_testrand256(&in[33]); + } + if (secp256k1_eckey_pubkey_parse(&elem, in, len)) { + unsigned char out[65]; + unsigned char firstb; + int res; + size_t size = len; + firstb = in[0]; + /* If the pubkey can be parsed, it should round-trip... */ + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33)); + CHECK(size == len); + CHECK(secp256k1_memcmp_var(&in[1], &out[1], len-1) == 0); + /* ... except for the type of hybrid inputs. */ + if ((in[0] != 6) && (in[0] != 7)) { + CHECK(in[0] == out[0]); + } + size = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0)); + CHECK(size == 65); + CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size)); + ge_equals_ge(&elem,&elem2); + /* Check that the X9.62 hybrid type is checked. */ + in[0] = secp256k1_testrand_bits(1) ? 6 : 7; + res = secp256k1_eckey_pubkey_parse(&elem2, in, size); + if (firstb == 2 || firstb == 3) { + if (in[0] == firstb + 4) { + CHECK(res); + } else { + CHECK(!res); + } + } + if (res) { + ge_equals_ge(&elem,&elem2); + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0)); + CHECK(secp256k1_memcmp_var(&in[1], &out[1], 64) == 0); + } + } +} + +static void run_pubkey_comparison(void) { + unsigned char pk1_ser[33] = { + 0x02, + 0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11, + 0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23 + }; + const unsigned char pk2_ser[33] = { + 0x02, + 0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d, + 0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c + }; + secp256k1_pubkey pk1; + secp256k1_pubkey pk2; + int32_t ecount = 0; + + CHECK(secp256k1_ec_pubkey_parse(CTX, &pk1, pk1_ser, sizeof(pk1_ser)) == 1); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pk2, pk2_ser, sizeof(pk2_ser)) == 1); + + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + CHECK(secp256k1_ec_pubkey_cmp(CTX, NULL, &pk2) < 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, NULL) > 0); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk2) < 0); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk1) > 0); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk1) == 0); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk2) == 0); + CHECK(ecount == 2); + { + secp256k1_pubkey pk_tmp; + memset(&pk_tmp, 0, sizeof(pk_tmp)); /* illegal pubkey */ + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk_tmp, &pk2) < 0); + CHECK(ecount == 3); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk_tmp, &pk_tmp) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk_tmp) > 0); + CHECK(ecount == 6); + } + + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); + + /* Make pk2 the same as pk1 but with 3 rather than 2. Note that in + * an uncompressed encoding, these would have the opposite ordering */ + pk1_ser[0] = 3; + CHECK(secp256k1_ec_pubkey_parse(CTX, &pk2, pk1_ser, sizeof(pk1_ser)) == 1); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk2) < 0); + CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk1) > 0); +} + +static void run_random_pubkeys(void) { + int i; + for (i = 0; i < 10*COUNT; i++) { + test_random_pubkeys(); + } +} + +static void run_ecdsa_end_to_end(void) { + int i; + for (i = 0; i < 64*COUNT; i++) { + test_ecdsa_end_to_end(); + } +} + +static int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) { + static const unsigned char zeroes[32] = {0}; + + int ret = 0; + + secp256k1_ecdsa_signature sig_der; + unsigned char roundtrip_der[2048]; + unsigned char compact_der[64]; + size_t len_der = 2048; + int parsed_der = 0, valid_der = 0, roundtrips_der = 0; + + secp256k1_ecdsa_signature sig_der_lax; + unsigned char roundtrip_der_lax[2048]; + unsigned char compact_der_lax[64]; + size_t len_der_lax = 2048; + int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0; + + parsed_der = secp256k1_ecdsa_signature_parse_der(CTX, &sig_der, sig, siglen); + if (parsed_der) { + ret |= (!secp256k1_ecdsa_signature_serialize_compact(CTX, compact_der, &sig_der)) << 0; + valid_der = (secp256k1_memcmp_var(compact_der, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der + 32, zeroes, 32) != 0); + } + if (valid_der) { + ret |= (!secp256k1_ecdsa_signature_serialize_der(CTX, roundtrip_der, &len_der, &sig_der)) << 1; + roundtrips_der = (len_der == siglen) && secp256k1_memcmp_var(roundtrip_der, sig, siglen) == 0; + } + + parsed_der_lax = ecdsa_signature_parse_der_lax(CTX, &sig_der_lax, sig, siglen); + if (parsed_der_lax) { + ret |= (!secp256k1_ecdsa_signature_serialize_compact(CTX, compact_der_lax, &sig_der_lax)) << 10; + valid_der_lax = (secp256k1_memcmp_var(compact_der_lax, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der_lax + 32, zeroes, 32) != 0); + } + if (valid_der_lax) { + ret |= (!secp256k1_ecdsa_signature_serialize_der(CTX, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11; + roundtrips_der_lax = (len_der_lax == siglen) && secp256k1_memcmp_var(roundtrip_der_lax, sig, siglen) == 0; + } + + if (certainly_der) { + ret |= (!parsed_der) << 2; + } + if (certainly_not_der) { + ret |= (parsed_der) << 17; + } + if (valid_der) { + ret |= (!roundtrips_der) << 3; + } + + if (valid_der) { + ret |= (!roundtrips_der_lax) << 12; + ret |= (len_der != len_der_lax) << 13; + ret |= ((len_der != len_der_lax) || (secp256k1_memcmp_var(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14; + } + ret |= (roundtrips_der != roundtrips_der_lax) << 15; + if (parsed_der) { + ret |= (!parsed_der_lax) << 16; + } + + return ret; +} + +static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) { + size_t i; + for (i = 0; i < ptrlen; i++) { + int shift = ptrlen - 1 - i; + if (shift >= 4) { + ptr[i] = 0; + } else { + ptr[i] = (val >> shift) & 0xFF; + } + } +} + +static void damage_array(unsigned char *sig, size_t *len) { + int pos; + int action = secp256k1_testrand_bits(3); + if (action < 1 && *len > 3) { + /* Delete a byte. */ + pos = secp256k1_testrand_int(*len); + memmove(sig + pos, sig + pos + 1, *len - pos - 1); + (*len)--; + return; + } else if (action < 2 && *len < 2048) { + /* Insert a byte. */ + pos = secp256k1_testrand_int(1 + *len); + memmove(sig + pos + 1, sig + pos, *len - pos); + sig[pos] = secp256k1_testrand_bits(8); + (*len)++; + return; + } else if (action < 4) { + /* Modify a byte. */ + sig[secp256k1_testrand_int(*len)] += 1 + secp256k1_testrand_int(255); + return; + } else { /* action < 8 */ + /* Modify a bit. */ + sig[secp256k1_testrand_int(*len)] ^= 1 << secp256k1_testrand_bits(3); + return; + } +} + +static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) { + int der; + int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2]; + size_t tlen, elen, glen; + int indet; + int n; + + *len = 0; + der = secp256k1_testrand_bits(2) == 0; + *certainly_der = der; + *certainly_not_der = 0; + indet = der ? 0 : secp256k1_testrand_int(10) == 0; + + for (n = 0; n < 2; n++) { + /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */ + nlow[n] = der ? 1 : (secp256k1_testrand_bits(3) != 0); + /* The length of the number in bytes (the first byte of which will always be nonzero) */ + nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_bits(3) / 8; + CHECK(nlen[n] <= 232); + /* The top bit of the number. */ + nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_testrand_bits(1)); + /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */ + nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_testrand_bits(7) : 1 + secp256k1_testrand_int(127)); + /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */ + nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_bits(3) / 8); + if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) { + *certainly_not_der = 1; + } + CHECK(nlen[n] + nzlen[n] <= 300); + /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */ + nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2); + if (!der) { + /* nlenlen[n] max 127 bytes */ + int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256; + nlenlen[n] += add; + if (add != 0) { + *certainly_not_der = 1; + } + } + CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427); + } + + /* The total length of the data to go, so far */ + tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1]; + CHECK(tlen <= 856); + + /* The length of the garbage inside the tuple. */ + elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_bits(3) / 8; + if (elen != 0) { + *certainly_not_der = 1; + } + tlen += elen; + CHECK(tlen <= 980); + + /* The length of the garbage after the end of the tuple. */ + glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_bits(3) / 8; + if (glen != 0) { + *certainly_not_der = 1; + } + CHECK(tlen + glen <= 990); + + /* Write the tuple header. */ + sig[(*len)++] = 0x30; + if (indet) { + /* Indeterminate length */ + sig[(*len)++] = 0x80; + *certainly_not_der = 1; + } else { + int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2); + if (!der) { + int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256; + tlenlen += add; + if (add != 0) { + *certainly_not_der = 1; + } + } + if (tlenlen == 0) { + /* Short length notation */ + sig[(*len)++] = tlen; + } else { + /* Long length notation */ + sig[(*len)++] = 128 + tlenlen; + assign_big_endian(sig + *len, tlenlen, tlen); + *len += tlenlen; + } + tlen += tlenlen; + } + tlen += 2; + CHECK(tlen + glen <= 1119); + + for (n = 0; n < 2; n++) { + /* Write the integer header. */ + sig[(*len)++] = 0x02; + if (nlenlen[n] == 0) { + /* Short length notation */ + sig[(*len)++] = nlen[n] + nzlen[n]; + } else { + /* Long length notation. */ + sig[(*len)++] = 128 + nlenlen[n]; + assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]); + *len += nlenlen[n]; + } + /* Write zero padding */ + while (nzlen[n] > 0) { + sig[(*len)++] = 0x00; + nzlen[n]--; + } + if (nlen[n] == 32 && !nlow[n]) { + /* Special extra 16 0xFF bytes in "high" 32-byte numbers */ + int i; + for (i = 0; i < 16; i++) { + sig[(*len)++] = 0xFF; + } + nlen[n] -= 16; + } + /* Write first byte of number */ + if (nlen[n] > 0) { + sig[(*len)++] = nhbyte[n]; + nlen[n]--; + } + /* Generate remaining random bytes of number */ + secp256k1_testrand_bytes_test(sig + *len, nlen[n]); + *len += nlen[n]; + nlen[n] = 0; + } + + /* Generate random garbage inside tuple. */ + secp256k1_testrand_bytes_test(sig + *len, elen); + *len += elen; + + /* Generate end-of-contents bytes. */ + if (indet) { + sig[(*len)++] = 0; + sig[(*len)++] = 0; + tlen += 2; + } + CHECK(tlen + glen <= 1121); + + /* Generate random garbage outside tuple. */ + secp256k1_testrand_bytes_test(sig + *len, glen); + *len += glen; + tlen += glen; + CHECK(tlen <= 1121); + CHECK(tlen == *len); +} + +static void run_ecdsa_der_parse(void) { + int i,j; + for (i = 0; i < 200 * COUNT; i++) { + unsigned char buffer[2048]; + size_t buflen = 0; + int certainly_der = 0; + int certainly_not_der = 0; + random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der); + CHECK(buflen <= 2048); + for (j = 0; j < 16; j++) { + int ret = 0; + if (j > 0) { + damage_array(buffer, &buflen); + /* We don't know anything anymore about the DERness of the result */ + certainly_der = 0; + certainly_not_der = 0; + } + ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der); + if (ret != 0) { + size_t k; + fprintf(stderr, "Failure %x on ", ret); + for (k = 0; k < buflen; k++) { + fprintf(stderr, "%02x ", buffer[k]); + } + fprintf(stderr, "\n"); + } + CHECK(ret == 0); + } + } +} + +/* Tests several edge cases. */ +static void test_ecdsa_edge_cases(void) { + int t; + secp256k1_ecdsa_signature sig; + + /* Test the case where ECDSA recomputes a point that is infinity. */ + { + secp256k1_gej keyj; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_negate(&ss, &ss); + secp256k1_scalar_inverse(&ss, &ss); + secp256k1_scalar_set_int(&sr, 1); + secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &keyj, &sr); + secp256k1_ge_set_gej(&key, &keyj); + msg = ss; + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with r of zero fails. */ + { + const unsigned char pubkey_mods_zero[33] = { + 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, + 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, + 0x41 + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 0); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33)); + CHECK(secp256k1_ecdsa_sig_verify( &sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with s of zero fails. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01 + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 0); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 1); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with message 0 passes. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x02 + }; + const unsigned char pubkey2[33] = { + 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, + 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, + 0x43 + }; + secp256k1_ge key; + secp256k1_ge key2; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 2); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 2); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_set_int(&ss, 1); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0); + } + + /* Verify signature with message 1 passes. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22, + 0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05, + 0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c, + 0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76, + 0x25 + }; + const unsigned char pubkey2[33] = { + 0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40, + 0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae, + 0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f, + 0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10, + 0x62 + }; + const unsigned char csr[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb + }; + secp256k1_ge key; + secp256k1_ge key2; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 1); + secp256k1_scalar_set_b32(&sr, csr, NULL); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_set_int(&ss, 2); + secp256k1_scalar_inverse_var(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0); + } + + /* Verify signature with message -1 passes. */ + { + const unsigned char pubkey[33] = { + 0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0, + 0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52, + 0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27, + 0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20, + 0xf1 + }; + const unsigned char csr[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 1); + secp256k1_scalar_negate(&msg, &msg); + secp256k1_scalar_set_b32(&sr, csr, NULL); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); + secp256k1_scalar_set_int(&ss, 3); + secp256k1_scalar_inverse_var(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); + } + + /* Signature where s would be zero. */ + { + secp256k1_pubkey pubkey; + size_t siglen; + int32_t ecount; + unsigned char signature[72]; + static const unsigned char nonce[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + static const unsigned char nonce2[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40 + }; + const unsigned char key[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + unsigned char msg[32] = { + 0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53, + 0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7, + 0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62, + 0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9, + }; + ecount = 0; + secp256k1_context_set_illegal_callback(CTX, counting_illegal_callback_fn, &ecount); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, precomputed_nonce_function, nonce) == 0); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, precomputed_nonce_function, nonce2) == 0); + msg[31] = 0xaa; + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, precomputed_nonce_function, nonce) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdsa_sign(CTX, NULL, msg, key, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, precomputed_nonce_function, nonce2) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, key) == 1); + CHECK(secp256k1_ecdsa_verify(CTX, NULL, msg, &pubkey) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, NULL, &pubkey) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg, NULL) == 0); + CHECK(ecount == 6); + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg, &pubkey) == 1); + CHECK(ecount == 6); + CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, NULL) == 0); + CHECK(ecount == 7); + /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */ + CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg, &pubkey) == 0); + CHECK(ecount == 8); + siglen = 72; + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, NULL, &siglen, &sig) == 0); + CHECK(ecount == 9); + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, signature, NULL, &sig) == 0); + CHECK(ecount == 10); + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, signature, &siglen, NULL) == 0); + CHECK(ecount == 11); + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, signature, &siglen, &sig) == 1); + CHECK(ecount == 11); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, NULL, signature, siglen) == 0); + CHECK(ecount == 12); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, NULL, siglen) == 0); + CHECK(ecount == 13); + CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, signature, siglen) == 1); + CHECK(ecount == 13); + siglen = 10; + /* Too little room for a signature does not fail via ARGCHECK. */ + CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, signature, &siglen, &sig) == 0); + CHECK(ecount == 13); + ecount = 0; + CHECK(secp256k1_ecdsa_signature_normalize(CTX, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_signature_serialize_compact(CTX, NULL, &sig) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_signature_serialize_compact(CTX, signature, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_signature_serialize_compact(CTX, signature, &sig) == 1); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, NULL, signature) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, &sig, NULL) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, &sig, signature) == 1); + CHECK(ecount == 5); + memset(signature, 255, 64); + CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, &sig, signature) == 0); + CHECK(ecount == 5); + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); + } + + /* Nonce function corner cases. */ + for (t = 0; t < 2; t++) { + static const unsigned char zero[32] = {0x00}; + int i; + unsigned char key[32]; + unsigned char msg[32]; + secp256k1_ecdsa_signature sig2; + secp256k1_scalar sr[512], ss; + const unsigned char *extra; + extra = t == 0 ? NULL : zero; + memset(msg, 0, 32); + msg[31] = 1; + /* High key results in signature failure. */ + memset(key, 0xFF, 32); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, NULL, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* Zero key results in signature failure. */ + memset(key, 0, 32); + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, NULL, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* Nonce function failure results in signature failure. */ + key[31] = 1; + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, nonce_function_test_fail, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* The retry loop successfully makes its way to the first good value. */ + CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, nonce_function_test_retry, extra) == 1); + CHECK(!is_empty_signature(&sig)); + CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, nonce_function_rfc6979, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0); + /* The default nonce function is deterministic. */ + CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0); + /* The default nonce function changes output with different messages. */ + for(i = 0; i < 256; i++) { + int j; + msg[0] = i; + CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + secp256k1_ecdsa_signature_load(CTX, &sr[i], &ss, &sig2); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); + } + } + msg[0] = 0; + msg[31] = 2; + /* The default nonce function changes output with different keys. */ + for(i = 256; i < 512; i++) { + int j; + key[0] = i - 256; + CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + secp256k1_ecdsa_signature_load(CTX, &sr[i], &ss, &sig2); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); + } + } + key[0] = 0; + } + + { + /* Check that optional nonce arguments do not have equivalent effect. */ + const unsigned char zeros[32] = {0}; + unsigned char nonce[32]; + unsigned char nonce2[32]; + unsigned char nonce3[32]; + unsigned char nonce4[32]; + SECP256K1_CHECKMEM_UNDEFINE(nonce,32); + SECP256K1_CHECKMEM_UNDEFINE(nonce2,32); + SECP256K1_CHECKMEM_UNDEFINE(nonce3,32); + SECP256K1_CHECKMEM_UNDEFINE(nonce4,32); + CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1); + SECP256K1_CHECKMEM_CHECK(nonce,32); + CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1); + SECP256K1_CHECKMEM_CHECK(nonce2,32); + CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1); + SECP256K1_CHECKMEM_CHECK(nonce3,32); + CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1); + SECP256K1_CHECKMEM_CHECK(nonce4,32); + CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); + CHECK(secp256k1_memcmp_var(nonce, nonce3, 32) != 0); + CHECK(secp256k1_memcmp_var(nonce, nonce4, 32) != 0); + CHECK(secp256k1_memcmp_var(nonce2, nonce3, 32) != 0); + CHECK(secp256k1_memcmp_var(nonce2, nonce4, 32) != 0); + CHECK(secp256k1_memcmp_var(nonce3, nonce4, 32) != 0); + } + + + /* Privkey export where pubkey is the point at infinity. */ + { + unsigned char privkey[300]; + unsigned char seckey[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41, + }; + size_t outlen = 300; + CHECK(!ec_privkey_export_der(CTX, privkey, &outlen, seckey, 0)); + outlen = 300; + CHECK(!ec_privkey_export_der(CTX, privkey, &outlen, seckey, 1)); + } +} + +static void run_ecdsa_edge_cases(void) { + test_ecdsa_edge_cases(); +} + +/** Wycheproof tests + +The tests check for known attacks (range checks in (r,s), arithmetic errors, malleability). +*/ +static void test_ecdsa_wycheproof(void) { + #include "wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h" + + int t; + for (t = 0; t < SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS; t++) { + secp256k1_ecdsa_signature signature; + secp256k1_sha256 hasher; + secp256k1_pubkey pubkey; + const unsigned char *msg, *sig, *pk; + unsigned char out[32] = {0}; + int actual_verify = 0; + + memset(&pubkey, 0, sizeof(pubkey)); + pk = &wycheproof_ecdsa_public_keys[testvectors[t].pk_offset]; + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pk, 65) == 1); + + secp256k1_sha256_initialize(&hasher); + msg = &wycheproof_ecdsa_messages[testvectors[t].msg_offset]; + secp256k1_sha256_write(&hasher, msg, testvectors[t].msg_len); + secp256k1_sha256_finalize(&hasher, out); + + sig = &wycheproof_ecdsa_signatures[testvectors[t].sig_offset]; + if (secp256k1_ecdsa_signature_parse_der(CTX, &signature, sig, testvectors[t].sig_len) == 1) { + actual_verify = secp256k1_ecdsa_verify(CTX, (const secp256k1_ecdsa_signature *)&signature, out, &pubkey); + } + CHECK(testvectors[t].expected_verify == actual_verify); + } +} + +/* Tests cases from Wycheproof test suite. */ +static void run_ecdsa_wycheproof(void) { + test_ecdsa_wycheproof(); +} + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/tests_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/tests_impl.h" +#endif + +#ifdef ENABLE_MODULE_EXTRAKEYS +# include "modules/extrakeys/tests_impl.h" +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG +# include "modules/schnorrsig/tests_impl.h" +#endif + +static void run_secp256k1_memczero_test(void) { + unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; + unsigned char buf2[sizeof(buf1)]; + + /* secp256k1_memczero(..., ..., 0) is a noop. */ + memcpy(buf2, buf1, sizeof(buf1)); + secp256k1_memczero(buf1, sizeof(buf1), 0); + CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); + + /* secp256k1_memczero(..., ..., 1) zeros the buffer. */ + memset(buf2, 0, sizeof(buf2)); + secp256k1_memczero(buf1, sizeof(buf1) , 1); + CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); +} + +static void run_secp256k1_byteorder_tests(void) { + const uint32_t x = 0xFF03AB45; + const unsigned char x_be[4] = {0xFF, 0x03, 0xAB, 0x45}; + unsigned char buf[4]; + uint32_t x_; + + secp256k1_write_be32(buf, x); + CHECK(secp256k1_memcmp_var(buf, x_be, sizeof(buf)) == 0); + + x_ = secp256k1_read_be32(buf); + CHECK(x == x_); +} + +static void int_cmov_test(void) { + int r = INT_MAX; + int a = 0; + + secp256k1_int_cmov(&r, &a, 0); + CHECK(r == INT_MAX); + + r = 0; a = INT_MAX; + secp256k1_int_cmov(&r, &a, 1); + CHECK(r == INT_MAX); + + a = 0; + secp256k1_int_cmov(&r, &a, 1); + CHECK(r == 0); + + a = 1; + secp256k1_int_cmov(&r, &a, 1); + CHECK(r == 1); + + r = 1; a = 0; + secp256k1_int_cmov(&r, &a, 0); + CHECK(r == 1); + +} + +static void fe_cmov_test(void) { + static const secp256k1_fe zero = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0); + static const secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + static const secp256k1_fe max = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + secp256k1_fe r = max; + secp256k1_fe a = zero; + + secp256k1_fe_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + r = zero; a = max; + secp256k1_fe_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + a = zero; + secp256k1_fe_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); + + a = one; + secp256k1_fe_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); + + r = one; a = zero; + secp256k1_fe_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); +} + +static void fe_storage_cmov_test(void) { + static const secp256k1_fe_storage zero = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0); + static const secp256k1_fe_storage one = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + static const secp256k1_fe_storage max = SECP256K1_FE_STORAGE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + secp256k1_fe_storage r = max; + secp256k1_fe_storage a = zero; + + secp256k1_fe_storage_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + r = zero; a = max; + secp256k1_fe_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + a = zero; + secp256k1_fe_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); + + a = one; + secp256k1_fe_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); + + r = one; a = zero; + secp256k1_fe_storage_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); +} + +static void scalar_cmov_test(void) { + static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + static const secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + static const secp256k1_scalar max = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + secp256k1_scalar r = max; + secp256k1_scalar a = zero; + + secp256k1_scalar_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + r = zero; a = max; + secp256k1_scalar_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + a = zero; + secp256k1_scalar_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); + + a = one; + secp256k1_scalar_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); + + r = one; a = zero; + secp256k1_scalar_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); +} + +static void ge_storage_cmov_test(void) { + static const secp256k1_ge_storage zero = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); + static const secp256k1_ge_storage one = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1); + static const secp256k1_ge_storage max = SECP256K1_GE_STORAGE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + secp256k1_ge_storage r = max; + secp256k1_ge_storage a = zero; + + secp256k1_ge_storage_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + r = zero; a = max; + secp256k1_ge_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); + + a = zero; + secp256k1_ge_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); + + a = one; + secp256k1_ge_storage_cmov(&r, &a, 1); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); + + r = one; a = zero; + secp256k1_ge_storage_cmov(&r, &a, 0); + CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); +} + +static void run_cmov_tests(void) { + int_cmov_test(); + fe_cmov_test(); + fe_storage_cmov_test(); + scalar_cmov_test(); + ge_storage_cmov_test(); +} + +int main(int argc, char **argv) { + /* Disable buffering for stdout to improve reliability of getting + * diagnostic information. Happens right at the start of main because + * setbuf must be used before any other operation on the stream. */ + setbuf(stdout, NULL); + /* Also disable buffering for stderr because it's not guaranteed that it's + * unbuffered on all systems. */ + setbuf(stderr, NULL); + + /* find iteration count */ + if (argc > 1) { + COUNT = strtol(argv[1], NULL, 0); + } else { + const char* env = getenv("SECP256K1_TEST_ITERS"); + if (env && strlen(env) > 0) { + COUNT = strtol(env, NULL, 0); + } + } + if (COUNT <= 0) { + fputs("An iteration count of 0 or less is not allowed.\n", stderr); + return EXIT_FAILURE; + } + printf("test count = %i\n", COUNT); + + /* find random seed */ + secp256k1_testrand_init(argc > 2 ? argv[2] : NULL); + + /*** Setup test environment ***/ + + /* Create a global context available to all tests */ + CTX = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + /* Randomize the context only with probability 15/16 + to make sure we test without context randomization from time to time. + TODO Reconsider this when recalibrating the tests. */ + if (secp256k1_testrand_bits(4)) { + unsigned char rand32[32]; + secp256k1_testrand256(rand32); + CHECK(secp256k1_context_randomize(CTX, rand32)); + } + /* Make a writable copy of secp256k1_context_static in order to test the effect of API functions + that write to the context. The API does not support cloning the static context, so we use + memcpy instead. The user is not supposed to copy a context but we should still ensure that + the API functions handle copies of the static context gracefully. */ + STATIC_CTX = malloc(sizeof(*secp256k1_context_static)); + CHECK(STATIC_CTX != NULL); + memcpy(STATIC_CTX, secp256k1_context_static, sizeof(secp256k1_context)); + CHECK(!secp256k1_context_is_proper(STATIC_CTX)); + + /*** Run actual tests ***/ + + /* selftest tests */ + run_selftest_tests(); + + /* context tests */ + run_proper_context_tests(0); run_proper_context_tests(1); + run_static_context_tests(0); run_static_context_tests(1); + run_deprecated_context_flags_test(); + + /* scratch tests */ + run_scratch_tests(); + + /* randomness tests */ + run_rand_bits(); + run_rand_int(); + + /* integer arithmetic tests */ +#ifdef SECP256K1_WIDEMUL_INT128 + run_int128_tests(); +#endif + run_ctz_tests(); + run_modinv_tests(); + run_inverse_tests(); + + /* hash tests */ + run_sha256_known_output_tests(); + run_sha256_counter_tests(); + run_hmac_sha256_tests(); + run_rfc6979_hmac_sha256_tests(); + run_tagged_sha256_tests(); + + /* scalar tests */ + run_scalar_tests(); + + /* field tests */ + run_field_half(); + run_field_misc(); + run_field_convert(); + run_fe_mul(); + run_sqr(); + run_sqrt(); + + /* group tests */ + run_ge(); + run_gej(); + run_group_decompress(); + + /* ecmult tests */ + run_ecmult_pre_g(); + run_wnaf(); + run_point_times_order(); + run_ecmult_near_split_bound(); + run_ecmult_chain(); + run_ecmult_constants(); + run_ecmult_gen_blind(); + run_ecmult_const_tests(); + run_ecmult_multi_tests(); + run_ec_combine(); + + /* endomorphism tests */ + run_endomorphism_tests(); + + /* EC point parser test */ + run_ec_pubkey_parse_test(); + + /* EC key edge cases */ + run_eckey_edge_case_test(); + + /* EC key arithmetic test */ + run_eckey_negate_test(); + +#ifdef ENABLE_MODULE_ECDH + /* ecdh tests */ + run_ecdh_tests(); +#endif + + /* ecdsa tests */ + run_ec_illegal_argument_tests(); + run_pubkey_comparison(); + run_random_pubkeys(); + run_ecdsa_der_parse(); + run_ecdsa_sign_verify(); + run_ecdsa_end_to_end(); + run_ecdsa_edge_cases(); + run_ecdsa_wycheproof(); + +#ifdef ENABLE_MODULE_RECOVERY + /* ECDSA pubkey recovery tests */ + run_recovery_tests(); +#endif + +#ifdef ENABLE_MODULE_EXTRAKEYS + run_extrakeys_tests(); +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG + run_schnorrsig_tests(); +#endif + + /* util tests */ + run_secp256k1_memczero_test(); + run_secp256k1_byteorder_tests(); + + run_cmov_tests(); + + /*** Tear down test environment ***/ + free(STATIC_CTX); + secp256k1_context_destroy(CTX); + + secp256k1_testrand_finish(); + + printf("no problems found\n"); + return 0; +} diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c new file mode 100644 index 0000000000..63b6ef03af --- /dev/null +++ b/src/secp256k1/src/tests_exhaustive.c @@ -0,0 +1,495 @@ +/*********************************************************************** + * Copyright (c) 2016 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include <stdio.h> +#include <stdlib.h> +#include <time.h> + +#ifndef EXHAUSTIVE_TEST_ORDER +/* see group_impl.h for allowable values */ +#define EXHAUSTIVE_TEST_ORDER 13 +#endif + +#include "secp256k1.c" +#include "../include/secp256k1.h" +#include "assumptions.h" +#include "group.h" +#include "testrand_impl.h" +#include "ecmult_compute_table_impl.h" +#include "ecmult_gen_compute_table_impl.h" + +static int count = 2; + +/** stolen from tests.c */ +static void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) { + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + CHECK(secp256k1_fe_equal_var(&a->x, &b->x)); + CHECK(secp256k1_fe_equal_var(&a->y, &b->y)); +} + +static void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) { + secp256k1_fe z2s; + secp256k1_fe u1, u2, s1, s2; + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */ + secp256k1_fe_sqr(&z2s, &b->z); + secp256k1_fe_mul(&u1, &a->x, &z2s); + u2 = b->x; secp256k1_fe_normalize_weak(&u2); + secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z); + s2 = b->y; secp256k1_fe_normalize_weak(&s2); + CHECK(secp256k1_fe_equal_var(&u1, &u2)); + CHECK(secp256k1_fe_equal_var(&s1, &s2)); +} + +static void random_fe(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_testrand256(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +static void random_fe_non_zero(secp256k1_fe *nz) { + int tries = 10; + while (--tries >= 0) { + random_fe(nz); + secp256k1_fe_normalize(nz); + if (!secp256k1_fe_is_zero(nz)) { + break; + } + } + /* Infinitesimal probability of spurious failure here */ + CHECK(tries >= 0); +} +/** END stolen from tests.c */ + +static uint32_t num_cores = 1; +static uint32_t this_core = 0; + +SECP256K1_INLINE static int skip_section(uint64_t* iter) { + if (num_cores == 1) return 0; + *iter += 0xe7037ed1a0b428dbULL; + return ((((uint32_t)*iter ^ (*iter >> 32)) * num_cores) >> 32) != this_core; +} + +static int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32, + const unsigned char *key32, const unsigned char *algo16, + void *data, unsigned int attempt) { + secp256k1_scalar s; + int *idata = data; + (void)msg32; + (void)key32; + (void)algo16; + /* Some nonces cannot be used because they'd cause s and/or r to be zero. + * The signing function has retry logic here that just re-calls the nonce + * function with an increased `attempt`. So if attempt > 0 this means we + * need to change the nonce to avoid an infinite loop. */ + if (attempt > 0) { + *idata = (*idata + 1) % EXHAUSTIVE_TEST_ORDER; + } + secp256k1_scalar_set_int(&s, *idata); + secp256k1_scalar_get_b32(nonce32, &s); + return 1; +} + +static void test_exhaustive_endomorphism(const secp256k1_ge *group) { + int i; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_ge res; + secp256k1_ge_mul_lambda(&res, &group[i]); + ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res); + } +} + +static void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj) { + int i, j; + uint64_t iter = 0; + + /* Sanity-check (and check infinity functions) */ + CHECK(secp256k1_ge_is_infinity(&group[0])); + CHECK(secp256k1_gej_is_infinity(&groupj[0])); + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + CHECK(!secp256k1_ge_is_infinity(&group[i])); + CHECK(!secp256k1_gej_is_infinity(&groupj[i])); + } + + /* Check all addition formulae */ + for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) { + secp256k1_fe fe_inv; + if (skip_section(&iter)) continue; + secp256k1_fe_inv(&fe_inv, &groupj[j].z); + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_ge zless_gej; + secp256k1_gej tmp; + /* add_var */ + secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL); + ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp); + /* add_ge */ + if (j > 0) { + secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]); + ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp); + } + /* add_ge_var */ + secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL); + ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp); + /* add_zinv_var */ + zless_gej.infinity = groupj[j].infinity; + zless_gej.x = groupj[j].x; + zless_gej.y = groupj[j].y; + secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv); + ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp); + } + } + + /* Check doubling */ + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_gej tmp; + secp256k1_gej_double(&tmp, &groupj[i]); + ge_equals_gej(&group[(2 * i) % EXHAUSTIVE_TEST_ORDER], &tmp); + secp256k1_gej_double_var(&tmp, &groupj[i], NULL); + ge_equals_gej(&group[(2 * i) % EXHAUSTIVE_TEST_ORDER], &tmp); + } + + /* Check negation */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_ge tmp; + secp256k1_gej tmpj; + secp256k1_ge_neg(&tmp, &group[i]); + ge_equals_ge(&group[EXHAUSTIVE_TEST_ORDER - i], &tmp); + secp256k1_gej_neg(&tmpj, &groupj[i]); + ge_equals_gej(&group[EXHAUSTIVE_TEST_ORDER - i], &tmpj); + } +} + +static void test_exhaustive_ecmult(const secp256k1_ge *group, const secp256k1_gej *groupj) { + int i, j, r_log; + uint64_t iter = 0; + for (r_log = 1; r_log < EXHAUSTIVE_TEST_ORDER; r_log++) { + for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) { + if (skip_section(&iter)) continue; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_gej tmp; + secp256k1_scalar na, ng; + secp256k1_scalar_set_int(&na, i); + secp256k1_scalar_set_int(&ng, j); + + secp256k1_ecmult(&tmp, &groupj[r_log], &na, &ng); + ge_equals_gej(&group[(i * r_log + j) % EXHAUSTIVE_TEST_ORDER], &tmp); + + } + } + } + + for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) { + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + int ret; + secp256k1_gej tmp; + secp256k1_fe xn, xd, tmpf; + secp256k1_scalar ng; + + if (skip_section(&iter)) continue; + + secp256k1_scalar_set_int(&ng, j); + + /* Test secp256k1_ecmult_const. */ + secp256k1_ecmult_const(&tmp, &group[i], &ng, 256); + ge_equals_gej(&group[(i * j) % EXHAUSTIVE_TEST_ORDER], &tmp); + + if (j != 0) { + /* Test secp256k1_ecmult_const_xonly with all curve X coordinates, and xd=NULL. */ + ret = secp256k1_ecmult_const_xonly(&tmpf, &group[i].x, NULL, &ng, 256, 0); + CHECK(ret); + CHECK(secp256k1_fe_equal_var(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x)); + + /* Test secp256k1_ecmult_const_xonly with all curve X coordinates, with random xd. */ + random_fe_non_zero(&xd); + secp256k1_fe_mul(&xn, &xd, &group[i].x); + ret = secp256k1_ecmult_const_xonly(&tmpf, &xn, &xd, &ng, 256, 0); + CHECK(ret); + CHECK(secp256k1_fe_equal_var(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x)); + } + } + } +} + +typedef struct { + secp256k1_scalar sc[2]; + secp256k1_ge pt[2]; +} ecmult_multi_data; + +static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + ecmult_multi_data *data = (ecmult_multi_data*) cbdata; + *sc = data->sc[idx]; + *pt = data->pt[idx]; + return 1; +} + +static void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group) { + int i, j, k, x, y; + uint64_t iter = 0; + secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096); + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) { + for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) { + for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) { + for (x = 0; x < EXHAUSTIVE_TEST_ORDER; x++) { + if (skip_section(&iter)) continue; + for (y = 0; y < EXHAUSTIVE_TEST_ORDER; y++) { + secp256k1_gej tmp; + secp256k1_scalar g_sc; + ecmult_multi_data data; + + secp256k1_scalar_set_int(&data.sc[0], i); + secp256k1_scalar_set_int(&data.sc[1], j); + secp256k1_scalar_set_int(&g_sc, k); + data.pt[0] = group[x]; + data.pt[1] = group[y]; + + secp256k1_ecmult_multi_var(&ctx->error_callback, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2); + ge_equals_gej(&group[(i * x + j * y + k) % EXHAUSTIVE_TEST_ORDER], &tmp); + } + } + } + } + } + secp256k1_scratch_destroy(&ctx->error_callback, scratch); +} + +static void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k, int* overflow) { + secp256k1_fe x; + unsigned char x_bin[32]; + k %= EXHAUSTIVE_TEST_ORDER; + x = group[k].x; + secp256k1_fe_normalize(&x); + secp256k1_fe_get_b32(x_bin, &x); + secp256k1_scalar_set_b32(r, x_bin, overflow); +} + +static void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group) { + int s, r, msg, key; + uint64_t iter = 0; + for (s = 1; s < EXHAUSTIVE_TEST_ORDER; s++) { + for (r = 1; r < EXHAUSTIVE_TEST_ORDER; r++) { + for (msg = 1; msg < EXHAUSTIVE_TEST_ORDER; msg++) { + for (key = 1; key < EXHAUSTIVE_TEST_ORDER; key++) { + secp256k1_ge nonconst_ge; + secp256k1_ecdsa_signature sig; + secp256k1_pubkey pk; + secp256k1_scalar sk_s, msg_s, r_s, s_s; + secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s; + int k, should_verify; + unsigned char msg32[32]; + + if (skip_section(&iter)) continue; + + secp256k1_scalar_set_int(&s_s, s); + secp256k1_scalar_set_int(&r_s, r); + secp256k1_scalar_set_int(&msg_s, msg); + secp256k1_scalar_set_int(&sk_s, key); + + /* Verify by hand */ + /* Run through every k value that gives us this r and check that *one* works. + * Note there could be none, there could be multiple, ECDSA is weird. */ + should_verify = 0; + for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) { + secp256k1_scalar check_x_s; + r_from_k(&check_x_s, group, k, NULL); + if (r_s == check_x_s) { + secp256k1_scalar_set_int(&s_times_k_s, k); + secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s); + secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s); + secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s); + should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s); + } + } + /* nb we have a "high s" rule */ + should_verify &= !secp256k1_scalar_is_high(&s_s); + + /* Verify by calling verify */ + secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s); + memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge)); + secp256k1_pubkey_save(&pk, &nonconst_ge); + secp256k1_scalar_get_b32(msg32, &msg_s); + CHECK(should_verify == + secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk)); + } + } + } + } +} + +static void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group) { + int i, j, k; + uint64_t iter = 0; + + /* Loop */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { /* message */ + for (j = 1; j < EXHAUSTIVE_TEST_ORDER; j++) { /* key */ + if (skip_section(&iter)) continue; + for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) { /* nonce */ + const int starting_k = k; + int ret; + secp256k1_ecdsa_signature sig; + secp256k1_scalar sk, msg, r, s, expected_r; + unsigned char sk32[32], msg32[32]; + secp256k1_scalar_set_int(&msg, i); + secp256k1_scalar_set_int(&sk, j); + secp256k1_scalar_get_b32(sk32, &sk); + secp256k1_scalar_get_b32(msg32, &msg); + + ret = secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k); + CHECK(ret == 1); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig); + /* Note that we compute expected_r *after* signing -- this is important + * because our nonce-computing function function might change k during + * signing. */ + r_from_k(&expected_r, group, k, NULL); + CHECK(r == expected_r); + CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER); + + /* Overflow means we've tried every possible nonce */ + if (k < starting_k) { + break; + } + } + } + } + + /* We would like to verify zero-knowledge here by counting how often every + * possible (s, r) tuple appears, but because the group order is larger + * than the field order, when coercing the x-values to scalar values, some + * appear more often than others, so we are actually not zero-knowledge. + * (This effect also appears in the real code, but the difference is on the + * order of 1/2^128th the field order, so the deviation is not useful to a + * computationally bounded attacker.) + */ +} + +#ifdef ENABLE_MODULE_RECOVERY +#include "modules/recovery/tests_exhaustive_impl.h" +#endif + +#ifdef ENABLE_MODULE_EXTRAKEYS +#include "modules/extrakeys/tests_exhaustive_impl.h" +#endif + +#ifdef ENABLE_MODULE_SCHNORRSIG +#include "modules/schnorrsig/tests_exhaustive_impl.h" +#endif + +int main(int argc, char** argv) { + int i; + secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER]; + secp256k1_ge group[EXHAUSTIVE_TEST_ORDER]; + unsigned char rand32[32]; + secp256k1_context *ctx; + + /* Disable buffering for stdout to improve reliability of getting + * diagnostic information. Happens right at the start of main because + * setbuf must be used before any other operation on the stream. */ + setbuf(stdout, NULL); + /* Also disable buffering for stderr because it's not guaranteed that it's + * unbuffered on all systems. */ + setbuf(stderr, NULL); + + printf("Exhaustive tests for order %lu\n", (unsigned long)EXHAUSTIVE_TEST_ORDER); + + /* find iteration count */ + if (argc > 1) { + count = strtol(argv[1], NULL, 0); + } + printf("test count = %i\n", count); + + /* find random seed */ + secp256k1_testrand_init(argc > 2 ? argv[2] : NULL); + + /* set up split processing */ + if (argc > 4) { + num_cores = strtol(argv[3], NULL, 0); + this_core = strtol(argv[4], NULL, 0); + if (num_cores < 1 || this_core >= num_cores) { + fprintf(stderr, "Usage: %s [count] [seed] [numcores] [thiscore]\n", argv[0]); + return 1; + } + printf("running tests for core %lu (out of [0..%lu])\n", (unsigned long)this_core, (unsigned long)num_cores - 1); + } + + /* Recreate the ecmult{,_gen} tables using the right generator (as selected via EXHAUSTIVE_TEST_ORDER) */ + secp256k1_ecmult_gen_compute_table(&secp256k1_ecmult_gen_prec_table[0][0], &secp256k1_ge_const_g, ECMULT_GEN_PREC_BITS); + secp256k1_ecmult_compute_two_tables(secp256k1_pre_g, secp256k1_pre_g_128, WINDOW_G, &secp256k1_ge_const_g); + + while (count--) { + /* Build context */ + ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + secp256k1_testrand256(rand32); + CHECK(secp256k1_context_randomize(ctx, rand32)); + + /* Generate the entire group */ + secp256k1_gej_set_infinity(&groupj[0]); + secp256k1_ge_set_gej(&group[0], &groupj[0]); + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g); + secp256k1_ge_set_gej(&group[i], &groupj[i]); + if (count != 0) { + /* Set a different random z-value for each Jacobian point, except z=1 + is used in the last iteration. */ + secp256k1_fe z; + random_fe(&z); + secp256k1_gej_rescale(&groupj[i], &z); + } + + /* Verify against ecmult_gen */ + { + secp256k1_scalar scalar_i; + secp256k1_gej generatedj; + secp256k1_ge generated; + + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i); + secp256k1_ge_set_gej(&generated, &generatedj); + + CHECK(group[i].infinity == 0); + CHECK(generated.infinity == 0); + CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x)); + CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y)); + } + } + + /* Run the tests */ + test_exhaustive_endomorphism(group); + test_exhaustive_addition(group, groupj); + test_exhaustive_ecmult(group, groupj); + test_exhaustive_ecmult_multi(ctx, group); + test_exhaustive_sign(ctx, group); + test_exhaustive_verify(ctx, group); + +#ifdef ENABLE_MODULE_RECOVERY + test_exhaustive_recovery(ctx, group); +#endif +#ifdef ENABLE_MODULE_EXTRAKEYS + test_exhaustive_extrakeys(ctx, group); +#endif +#ifdef ENABLE_MODULE_SCHNORRSIG + test_exhaustive_schnorrsig(ctx); +#endif + + secp256k1_context_destroy(ctx); + } + + secp256k1_testrand_finish(); + + printf("no problems found\n"); + return 0; +} diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h new file mode 100644 index 0000000000..e75c5ad552 --- /dev/null +++ b/src/secp256k1/src/util.h @@ -0,0 +1,322 @@ +/*********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_UTIL_H +#define SECP256K1_UTIL_H + +#include <stdlib.h> +#include <stdint.h> +#include <stdio.h> +#include <limits.h> + +#define STR_(x) #x +#define STR(x) STR_(x) +#define DEBUG_CONFIG_MSG(x) "DEBUG_CONFIG: " x +#define DEBUG_CONFIG_DEF(x) DEBUG_CONFIG_MSG(#x "=" STR(x)) + +typedef struct { + void (*fn)(const char *text, void* data); + const void* data; +} secp256k1_callback; + +static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) { + cb->fn(text, (void*)cb->data); +} + +#ifndef USE_EXTERNAL_DEFAULT_CALLBACKS +static void secp256k1_default_illegal_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str); + abort(); +} +static void secp256k1_default_error_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str); + abort(); +} +#else +void secp256k1_default_illegal_callback_fn(const char* str, void* data); +void secp256k1_default_error_callback_fn(const char* str, void* data); +#endif + +static const secp256k1_callback default_illegal_callback = { + secp256k1_default_illegal_callback_fn, + NULL +}; + +static const secp256k1_callback default_error_callback = { + secp256k1_default_error_callback_fn, + NULL +}; + + +#ifdef DETERMINISTIC +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s\n", msg); \ + abort(); \ +} while(0); +#else +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ + abort(); \ +} while(0) +#endif + +#if SECP256K1_GNUC_PREREQ(3, 0) +#define EXPECT(x,c) __builtin_expect((x),(c)) +#else +#define EXPECT(x,c) (x) +#endif + +#ifdef DETERMINISTIC +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed"); \ + } \ +} while(0) +#else +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed: " #cond); \ + } \ +} while(0) +#endif + +/* Like assert(), but when VERIFY is defined, and side-effect safe. */ +#if defined(COVERAGE) +#define VERIFY_CHECK(check) +#define VERIFY_SETUP(stmt) +#elif defined(VERIFY) +#define VERIFY_CHECK CHECK +#define VERIFY_SETUP(stmt) do { stmt; } while(0) +#else +#define VERIFY_CHECK(cond) do { (void)(cond); } while(0) +#define VERIFY_SETUP(stmt) +#endif + +static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) { + void *ret = malloc(size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) { + void *ret = realloc(ptr, size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +#if defined(__BIGGEST_ALIGNMENT__) +#define ALIGNMENT __BIGGEST_ALIGNMENT__ +#else +/* Using 16 bytes alignment because common architectures never have alignment + * requirements above 8 for any of the types we care about. In addition we + * leave some room because currently we don't care about a few bytes. */ +#define ALIGNMENT 16 +#endif + +#define ROUND_TO_ALIGN(size) ((((size) + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT) + +/* Macro for restrict, when available and not in a VERIFY build. */ +#if defined(SECP256K1_BUILD) && defined(VERIFY) +# define SECP256K1_RESTRICT +#else +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(3,0) +# define SECP256K1_RESTRICT __restrict__ +# elif (defined(_MSC_VER) && _MSC_VER >= 1400) +# define SECP256K1_RESTRICT __restrict +# else +# define SECP256K1_RESTRICT +# endif +# else +# define SECP256K1_RESTRICT restrict +# endif +#endif + +#if defined(_WIN32) +# define I64FORMAT "I64d" +# define I64uFORMAT "I64u" +#else +# define I64FORMAT "lld" +# define I64uFORMAT "llu" +#endif + +#if defined(__GNUC__) +# define SECP256K1_GNUC_EXT __extension__ +#else +# define SECP256K1_GNUC_EXT +#endif + +/* Zero memory if flag == 1. Flag must be 0 or 1. Constant time. */ +static SECP256K1_INLINE void secp256k1_memczero(void *s, size_t len, int flag) { + unsigned char *p = (unsigned char *)s; + /* Access flag with a volatile-qualified lvalue. + This prevents clang from figuring out (after inlining) that flag can + take only be 0 or 1, which leads to variable time code. */ + volatile int vflag = flag; + unsigned char mask = -(unsigned char) vflag; + while (len) { + *p &= ~mask; + p++; + len--; + } +} + +/** Semantics like memcmp. Variable-time. + * + * We use this to avoid possible compiler bugs with memcmp, e.g. + * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=95189 + */ +static SECP256K1_INLINE int secp256k1_memcmp_var(const void *s1, const void *s2, size_t n) { + const unsigned char *p1 = s1, *p2 = s2; + size_t i; + + for (i = 0; i < n; i++) { + int diff = p1[i] - p2[i]; + if (diff != 0) { + return diff; + } + } + return 0; +} + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized and non-negative.*/ +static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag) { + unsigned int mask0, mask1, r_masked, a_masked; + /* Access flag with a volatile-qualified lvalue. + This prevents clang from figuring out (after inlining) that flag can + take only be 0 or 1, which leads to variable time code. */ + volatile int vflag = flag; + + /* Casting a negative int to unsigned and back to int is implementation defined behavior */ + VERIFY_CHECK(*r >= 0 && *a >= 0); + + mask0 = (unsigned int)vflag + ~0u; + mask1 = ~mask0; + r_masked = ((unsigned int)*r & mask0); + a_masked = ((unsigned int)*a & mask1); + + *r = (int)(r_masked | a_masked); +} + +#if defined(USE_FORCE_WIDEMUL_INT128_STRUCT) +/* If USE_FORCE_WIDEMUL_INT128_STRUCT is set, use int128_struct. */ +# define SECP256K1_WIDEMUL_INT128 1 +# define SECP256K1_INT128_STRUCT 1 +#elif defined(USE_FORCE_WIDEMUL_INT128) +/* If USE_FORCE_WIDEMUL_INT128 is set, use int128. */ +# define SECP256K1_WIDEMUL_INT128 1 +# define SECP256K1_INT128_NATIVE 1 +#elif defined(USE_FORCE_WIDEMUL_INT64) +/* If USE_FORCE_WIDEMUL_INT64 is set, use int64. */ +# define SECP256K1_WIDEMUL_INT64 1 +#elif defined(UINT128_MAX) || defined(__SIZEOF_INT128__) +/* If a native 128-bit integer type exists, use int128. */ +# define SECP256K1_WIDEMUL_INT128 1 +# define SECP256K1_INT128_NATIVE 1 +#elif defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) +/* On 64-bit MSVC targets (x86_64 and arm64), use int128_struct + * (which has special logic to implement using intrinsics on those systems). */ +# define SECP256K1_WIDEMUL_INT128 1 +# define SECP256K1_INT128_STRUCT 1 +#elif SIZE_MAX > 0xffffffff +/* Systems with 64-bit pointers (and thus registers) very likely benefit from + * using 64-bit based arithmetic (even if we need to fall back to 32x32->64 based + * multiplication logic). */ +# define SECP256K1_WIDEMUL_INT128 1 +# define SECP256K1_INT128_STRUCT 1 +#else +/* Lastly, fall back to int64 based arithmetic. */ +# define SECP256K1_WIDEMUL_INT64 1 +#endif + +#ifndef __has_builtin +#define __has_builtin(x) 0 +#endif + +/* Determine the number of trailing zero bits in a (non-zero) 32-bit x. + * This function is only intended to be used as fallback for + * secp256k1_ctz32_var, but permits it to be tested separately. */ +static SECP256K1_INLINE int secp256k1_ctz32_var_debruijn(uint32_t x) { + static const uint8_t debruijn[32] = { + 0x00, 0x01, 0x02, 0x18, 0x03, 0x13, 0x06, 0x19, 0x16, 0x04, 0x14, 0x0A, + 0x10, 0x07, 0x0C, 0x1A, 0x1F, 0x17, 0x12, 0x05, 0x15, 0x09, 0x0F, 0x0B, + 0x1E, 0x11, 0x08, 0x0E, 0x1D, 0x0D, 0x1C, 0x1B + }; + return debruijn[(uint32_t)((x & -x) * 0x04D7651FU) >> 27]; +} + +/* Determine the number of trailing zero bits in a (non-zero) 64-bit x. + * This function is only intended to be used as fallback for + * secp256k1_ctz64_var, but permits it to be tested separately. */ +static SECP256K1_INLINE int secp256k1_ctz64_var_debruijn(uint64_t x) { + static const uint8_t debruijn[64] = { + 0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28, + 62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11, + 63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10, + 51, 25, 36, 32, 60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12 + }; + return debruijn[(uint64_t)((x & -x) * 0x022FDD63CC95386DU) >> 58]; +} + +/* Determine the number of trailing zero bits in a (non-zero) 32-bit x. */ +static SECP256K1_INLINE int secp256k1_ctz32_var(uint32_t x) { + VERIFY_CHECK(x != 0); +#if (__has_builtin(__builtin_ctz) || SECP256K1_GNUC_PREREQ(3,4)) + /* If the unsigned type is sufficient to represent the largest uint32_t, consider __builtin_ctz. */ + if (((unsigned)UINT32_MAX) == UINT32_MAX) { + return __builtin_ctz(x); + } +#endif +#if (__has_builtin(__builtin_ctzl) || SECP256K1_GNUC_PREREQ(3,4)) + /* Otherwise consider __builtin_ctzl (the unsigned long type is always at least 32 bits). */ + return __builtin_ctzl(x); +#else + /* If no suitable CTZ builtin is available, use a (variable time) software emulation. */ + return secp256k1_ctz32_var_debruijn(x); +#endif +} + +/* Determine the number of trailing zero bits in a (non-zero) 64-bit x. */ +static SECP256K1_INLINE int secp256k1_ctz64_var(uint64_t x) { + VERIFY_CHECK(x != 0); +#if (__has_builtin(__builtin_ctzl) || SECP256K1_GNUC_PREREQ(3,4)) + /* If the unsigned long type is sufficient to represent the largest uint64_t, consider __builtin_ctzl. */ + if (((unsigned long)UINT64_MAX) == UINT64_MAX) { + return __builtin_ctzl(x); + } +#endif +#if (__has_builtin(__builtin_ctzll) || SECP256K1_GNUC_PREREQ(3,4)) + /* Otherwise consider __builtin_ctzll (the unsigned long long type is always at least 64 bits). */ + return __builtin_ctzll(x); +#else + /* If no suitable CTZ builtin is available, use a (variable time) software emulation. */ + return secp256k1_ctz64_var_debruijn(x); +#endif +} + +/* Read a uint32_t in big endian */ +SECP256K1_INLINE static uint32_t secp256k1_read_be32(const unsigned char* p) { + return (uint32_t)p[0] << 24 | + (uint32_t)p[1] << 16 | + (uint32_t)p[2] << 8 | + (uint32_t)p[3]; +} + +/* Write a uint32_t in big endian */ +SECP256K1_INLINE static void secp256k1_write_be32(unsigned char* p, uint32_t x) { + p[3] = x; + p[2] = x >> 8; + p[1] = x >> 16; + p[0] = x >> 24; +} + +#endif /* SECP256K1_UTIL_H */ diff --git a/src/secp256k1/src/wycheproof/WYCHEPROOF_COPYING b/src/secp256k1/src/wycheproof/WYCHEPROOF_COPYING new file mode 100644 index 0000000000..cddf9d9182 --- /dev/null +++ b/src/secp256k1/src/wycheproof/WYCHEPROOF_COPYING @@ -0,0 +1,212 @@ +* The file `ecdsa_secp256k1_sha256_bitcoin_test.json` in this directory + comes from Google's project Wycheproof with git commit + `b063b4aedae951c69df014cd25fa6d69ae9e8cb9`, see + https://github.com/google/wycheproof/blob/b063b4aedae951c69df014cd25fa6d69ae9e8cb9/testvectors_v1/ecdsa_secp256k1_sha256_bitcoin_test.json + +* The file `ecdsa_secp256k1_sha256_bitcoin_test.h` is generated from + `ecdsa_secp256k1_sha256_bitcoin_test.json` using the script + `tests_wycheproof_generate.py`. + +------------------------------------------------------------------------------- + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h b/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h new file mode 100644 index 0000000000..736737fd61 --- /dev/null +++ b/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h @@ -0,0 +1,1564 @@ +/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */ +#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS (463) + +typedef struct { + size_t pk_offset; + size_t msg_offset; + size_t msg_len; + size_t sig_offset; + size_t sig_len; + int expected_verify; +} wycheproof_ecdsa_testvector; + +static const unsigned char wycheproof_ecdsa_messages[] = { 0x31,0x32,0x33,0x34,0x30,0x30, + 0x32,0x35,0x35,0x38,0x35, + 0x34,0x32,0x36,0x34,0x37,0x39,0x37,0x32,0x34, + 0x37,0x31,0x33,0x38,0x36,0x38,0x34,0x38,0x39,0x31, + 0x31,0x30,0x33,0x35,0x39,0x33,0x33,0x31,0x36,0x36,0x38, + 0x33,0x39,0x34,0x39,0x34,0x30,0x31,0x32,0x31,0x35, + 0x31,0x33,0x34,0x34,0x32,0x39,0x33,0x30,0x37,0x39, + 0x33,0x37,0x30,0x36,0x32,0x31,0x31,0x37,0x31,0x32, + 0x33,0x34,0x33,0x36,0x38,0x38,0x37,0x31,0x32, + 0x31,0x33,0x35,0x31,0x35,0x33,0x30,0x33,0x37,0x30, + 0x36,0x35,0x35,0x33,0x32,0x30,0x33,0x31,0x32,0x36, + 0x31,0x35,0x36,0x34,0x33,0x34,0x36,0x36,0x30,0x33, + 0x34,0x34,0x32,0x39,0x35,0x33,0x39,0x31,0x31,0x37, + 0x31,0x30,0x39,0x35,0x33,0x32,0x36,0x31,0x33,0x35,0x31, + 0x35,0x39,0x38,0x37,0x33,0x35,0x30,0x30,0x34,0x31, + 0x33,0x34,0x36,0x33,0x30,0x30,0x36,0x38,0x37,0x38, + 0x39,0x38,0x31,0x37,0x33,0x32,0x30,0x32,0x38,0x37, + 0x33,0x32,0x32,0x32,0x30,0x34,0x31,0x30,0x34,0x36, + 0x36,0x36,0x36,0x36,0x33,0x30,0x37,0x31,0x30,0x34, + 0x31,0x30,0x33,0x35,0x39,0x35,0x31,0x38,0x39,0x38, + 0x31,0x38,0x34,0x36,0x35,0x39,0x37,0x31,0x39,0x35, + 0x33,0x31,0x33,0x36,0x30,0x34,0x36,0x31,0x38,0x39, + 0x32,0x36,0x36,0x33,0x37,0x38,0x34,0x32,0x35,0x34, + 0x31,0x36,0x35,0x32,0x31,0x30,0x30,0x35,0x32,0x34, + 0x35,0x37,0x34,0x38,0x30,0x38,0x31,0x36,0x39,0x36, + 0x36,0x33,0x34,0x33,0x39,0x31,0x33,0x34,0x36,0x38, + 0x31,0x35,0x34,0x31,0x31,0x30,0x33,0x35,0x39,0x38, + 0x31,0x30,0x34,0x37,0x38,0x35,0x38,0x30,0x31,0x32,0x38, + 0x31,0x30,0x35,0x33,0x36,0x32,0x38,0x35,0x35,0x36,0x38, + 0x39,0x35,0x33,0x39,0x30,0x34,0x31,0x30,0x35, + 0x39,0x37,0x38,0x38,0x34,0x38,0x30,0x33,0x39, + 0x33,0x36,0x31,0x30,0x36,0x37,0x32,0x34,0x34,0x32, + 0x31,0x30,0x35,0x34,0x32,0x34,0x30,0x37,0x30,0x35, + 0x35,0x31,0x37,0x34,0x34,0x34,0x38,0x31,0x39,0x37, + 0x31,0x39,0x36,0x37,0x35,0x36,0x31,0x32,0x35,0x31, + 0x33,0x34,0x34,0x37,0x32,0x35,0x33,0x33,0x34,0x33, + 0x33,0x36,0x38,0x32,0x36,0x34,0x33,0x31,0x38, + 0x33,0x32,0x36,0x31,0x31,0x39,0x38,0x36,0x30,0x38, + 0x39,0x36,0x37,0x38,0x37,0x38,0x31,0x30,0x39,0x34, + 0x34,0x39,0x35,0x38,0x38,0x32,0x33,0x38,0x32,0x33, + 0x38,0x32,0x34,0x36,0x33,0x37,0x38,0x33,0x37, + 0x31,0x31,0x30,0x32,0x30,0x38,0x33,0x33,0x37,0x37,0x36, + 0x31,0x33,0x33,0x38,0x37,0x31,0x36,0x34,0x38, + 0x33,0x32,0x32,0x31,0x34,0x34,0x31,0x36,0x32, + 0x31,0x30,0x36,0x38,0x36,0x36,0x35,0x35,0x35,0x34,0x36, + 0x36,0x32,0x31,0x35,0x35,0x32,0x34,0x36, + 0x37,0x30,0x33,0x30,0x38,0x31,0x38,0x37,0x37,0x34, + 0x35,0x39,0x32,0x34,0x35,0x32,0x33,0x37,0x34,0x34, + 0x31,0x34,0x39,0x35,0x35,0x38,0x36,0x36,0x32,0x31, + 0x34,0x30,0x30,0x35,0x33,0x31,0x34,0x34,0x30,0x36, + 0x33,0x30,0x39,0x36,0x34,0x35,0x37,0x35,0x31,0x32, + 0x32,0x37,0x38,0x34,0x30,0x32,0x35,0x36,0x32,0x30, + 0x32,0x36,0x31,0x38,0x37,0x38,0x37,0x34,0x31,0x38, + 0x31,0x36,0x34,0x32,0x36,0x32,0x35,0x32,0x36,0x32, + 0x36,0x38,0x32,0x34,0x31,0x38,0x39,0x34,0x33,0x36, + 0x34,0x38,0x34,0x32,0x34,0x35,0x34,0x32,0x35, + 0x4d,0x73,0x67, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x4d,0x65,0x73,0x73,0x61,0x67,0x65}; + +static const unsigned char wycheproof_ecdsa_public_keys[] = { 0x04,0xb8,0x38,0xff,0x44,0xe5,0xbc,0x17,0x7b,0xf2,0x11,0x89,0xd0,0x76,0x60,0x82,0xfc,0x9d,0x84,0x32,0x26,0x88,0x7f,0xc9,0x76,0x03,0x71,0x10,0x0b,0x7e,0xe2,0x0a,0x6f,0xf0,0xc9,0xd7,0x5b,0xfb,0xa7,0xb3,0x1a,0x6b,0xca,0x19,0x74,0x49,0x6e,0xeb,0x56,0xde,0x35,0x70,0x71,0x95,0x5d,0x83,0xc4,0xb1,0xba,0xda,0xa0,0xb2,0x18,0x32,0xe9, + 0x04,0x07,0x31,0x0f,0x90,0xa9,0xea,0xe1,0x49,0xa0,0x84,0x02,0xf5,0x41,0x94,0xa0,0xf7,0xb4,0xac,0x42,0x7b,0xf8,0xd9,0xbd,0x6c,0x76,0x81,0x07,0x1d,0xc4,0x7d,0xc3,0x62,0x26,0xa6,0xd3,0x7a,0xc4,0x6d,0x61,0xfd,0x60,0x0c,0x0b,0xf1,0xbf,0xf8,0x76,0x89,0xed,0x11,0x7d,0xda,0x6b,0x0e,0x59,0x31,0x8a,0xe0,0x10,0xa1,0x97,0xa2,0x6c,0xa0, + 0x04,0xbc,0x97,0xe7,0x58,0x5e,0xec,0xad,0x48,0xe1,0x66,0x83,0xbc,0x40,0x91,0x70,0x8e,0x1a,0x93,0x0c,0x68,0x3f,0xc4,0x70,0x01,0xd4,0xb3,0x83,0x59,0x4f,0x2c,0x4e,0x22,0x70,0x59,0x89,0xcf,0x69,0xda,0xea,0xdd,0x4e,0x4e,0x4b,0x81,0x51,0xed,0x88,0x8d,0xfe,0xc2,0x0f,0xb0,0x17,0x28,0xd8,0x9d,0x56,0xb3,0xf3,0x8f,0x2a,0xe9,0xc8,0xc5, + 0x04,0x44,0xad,0x33,0x9a,0xfb,0xc2,0x1e,0x9a,0xbf,0x7b,0x60,0x2a,0x5c,0xa5,0x35,0xea,0x37,0x81,0x35,0xb6,0xd1,0x0d,0x81,0x31,0x0b,0xdd,0x82,0x93,0xd1,0xdf,0x32,0x52,0xb6,0x3f,0xf7,0xd0,0x77,0x47,0x70,0xf8,0xfe,0x1d,0x17,0x22,0xfa,0x83,0xac,0xd0,0x2f,0x43,0x4e,0x4f,0xc1,0x10,0xa0,0xcc,0x8f,0x6d,0xdd,0xd3,0x7d,0x56,0xc4,0x63, + 0x04,0x12,0x60,0xc2,0x12,0x2c,0x9e,0x24,0x4e,0x1a,0xf5,0x15,0x1b,0xed,0xe0,0xc3,0xae,0x23,0xb5,0x4d,0x7c,0x59,0x68,0x81,0xd3,0xee,0xba,0xd2,0x1f,0x37,0xdd,0x87,0x8c,0x5c,0x9a,0x0c,0x1a,0x9a,0xde,0x76,0x73,0x7a,0x88,0x11,0xbd,0x6a,0x7f,0x92,0x87,0xc9,0x78,0xee,0x39,0x6a,0xa8,0x9c,0x11,0xe4,0x72,0x29,0xd2,0xcc,0xb5,0x52,0xf0, + 0x04,0x18,0x77,0x04,0x5b,0xe2,0x5d,0x34,0xa1,0xd0,0x60,0x0f,0x9d,0x5c,0x00,0xd0,0x64,0x5a,0x2a,0x54,0x37,0x9b,0x6c,0xee,0xfa,0xd2,0xe6,0xbf,0x5c,0x2a,0x33,0x52,0xce,0x82,0x1a,0x53,0x2c,0xc1,0x75,0x1e,0xe1,0xd3,0x6d,0x41,0xc3,0xd6,0xab,0x4e,0x9b,0x14,0x3e,0x44,0xec,0x46,0xd7,0x34,0x78,0xea,0x6a,0x79,0xa5,0xc0,0xe5,0x41,0x59, + 0x04,0x45,0x54,0x39,0xfc,0xc3,0xd2,0xde,0xec,0xed,0xde,0xae,0xce,0x60,0xe7,0xbd,0x17,0x30,0x4f,0x36,0xeb,0xb6,0x02,0xad,0xf5,0xa2,0x2e,0x0b,0x8f,0x1d,0xb4,0x6a,0x50,0xae,0xc3,0x8f,0xb2,0xba,0xf2,0x21,0xe9,0xa8,0xd1,0x88,0x7c,0x7b,0xf6,0x22,0x2d,0xd1,0x83,0x46,0x34,0xe7,0x72,0x63,0x31,0x5a,0xf6,0xd2,0x36,0x09,0xd0,0x4f,0x77, + 0x04,0x2e,0x1f,0x46,0x6b,0x02,0x4c,0x0c,0x3a,0xce,0x24,0x37,0xde,0x09,0x12,0x7f,0xed,0x04,0xb7,0x06,0xf9,0x4b,0x19,0xa2,0x1b,0xb1,0xc2,0xac,0xf3,0x5c,0xec,0xe7,0x18,0x04,0x49,0xae,0x35,0x23,0xd7,0x25,0x34,0xe9,0x64,0x97,0x2c,0xfd,0x3b,0x38,0xaf,0x0b,0xdd,0xd9,0x61,0x9e,0x5a,0xf2,0x23,0xe4,0xd1,0xa4,0x0f,0x34,0xcf,0x9f,0x1d, + 0x04,0x8e,0x7a,0xbd,0xbb,0xd1,0x8d,0xe7,0x45,0x23,0x74,0xc1,0x87,0x9a,0x1c,0x3b,0x01,0xd1,0x32,0x61,0xe7,0xd4,0x57,0x1c,0x3b,0x47,0xa1,0xc7,0x6c,0x55,0xa2,0x33,0x73,0x26,0xed,0x89,0x7c,0xd5,0x17,0xa4,0xf5,0x34,0x9d,0xb8,0x09,0x78,0x0f,0x6d,0x2f,0x2b,0x9f,0x62,0x99,0xd8,0xb5,0xa8,0x90,0x77,0xf1,0x11,0x9a,0x71,0x8f,0xd7,0xb3, + 0x04,0x7b,0x33,0x3d,0x43,0x40,0xd3,0xd7,0x18,0xdd,0x3e,0x6a,0xff,0x7d,0xe7,0xbb,0xf8,0xb7,0x2b,0xfd,0x61,0x6c,0x84,0x20,0x05,0x60,0x52,0x84,0x23,0x76,0xb9,0xaf,0x19,0x42,0x11,0x7c,0x5a,0xfe,0xac,0x75,0x5d,0x6f,0x37,0x6f,0xc6,0x32,0x9a,0x7d,0x76,0x05,0x1b,0x87,0x12,0x3a,0x4a,0x5d,0x0b,0xc4,0xa5,0x39,0x38,0x0f,0x03,0xde,0x7b, + 0x04,0xd3,0x0c,0xa4,0xa0,0xdd,0xb6,0x61,0x6c,0x85,0x1d,0x30,0xce,0xd6,0x82,0xc4,0x0f,0x83,0xc6,0x27,0x58,0xa1,0xf2,0x75,0x99,0x88,0xd6,0x76,0x3a,0x88,0xf1,0xc0,0xe5,0x03,0xa8,0x0d,0x54,0x15,0x65,0x0d,0x41,0x23,0x97,0x84,0xe8,0xe2,0xfb,0x12,0x35,0xe9,0xfe,0x99,0x1d,0x11,0x2e,0xbb,0x81,0x18,0x6c,0xbf,0x0d,0xa2,0xde,0x3a,0xff, + 0x04,0x48,0x96,0x9b,0x39,0x99,0x12,0x97,0xb3,0x32,0xa6,0x52,0xd3,0xee,0x6e,0x01,0xe9,0x09,0xb3,0x99,0x04,0xe7,0x1f,0xa2,0x35,0x4a,0x78,0x30,0xc7,0x75,0x0b,0xaf,0x24,0xb4,0x01,0x2d,0x1b,0x83,0x0d,0x19,0x9c,0xcb,0x1f,0xc9,0x72,0xb3,0x2b,0xfd,0xed,0x55,0xf0,0x9c,0xd6,0x2d,0x25,0x7e,0x5e,0x84,0x4e,0x27,0xe5,0x7a,0x15,0x94,0xec, + 0x04,0x02,0xef,0x4d,0x6d,0x6c,0xfd,0x5a,0x94,0xf1,0xd7,0x78,0x42,0x26,0xe3,0xe2,0xa6,0xc0,0xa4,0x36,0xc5,0x58,0x39,0x61,0x9f,0x38,0xfb,0x44,0x72,0xb5,0xf9,0xee,0x77,0x7e,0xb4,0xac,0xd4,0xee,0xbd,0xa5,0xcd,0x72,0x87,0x5f,0xfd,0x2a,0x2f,0x26,0x22,0x9c,0x2d,0xc6,0xb4,0x65,0x00,0x91,0x9a,0x43,0x2c,0x86,0x73,0x9f,0x3a,0xe8,0x66, + 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0x04,0x1f,0x57,0x99,0xc9,0x5b,0xe8,0x90,0x63,0xb2,0x4f,0x26,0xe4,0x0c,0xb9,0x28,0xc1,0xa8,0x68,0xa7,0x6f,0xb0,0x09,0x46,0x07,0xe8,0x04,0x3d,0xb4,0x09,0xc9,0x1c,0x32,0xe7,0x57,0x24,0xe8,0x13,0xa4,0x19,0x1e,0x3a,0x83,0x90,0x07,0xf0,0x8e,0x2e,0x89,0x73,0x88,0xb0,0x6d,0x4a,0x00,0xde,0x6d,0xe6,0x0e,0x53,0x6d,0x91,0xfa,0xb5,0x66, + 0x04,0xa3,0x33,0x1a,0x4e,0x1b,0x42,0x23,0xec,0x2c,0x02,0x7e,0xdd,0x48,0x2c,0x92,0x8a,0x14,0xed,0x35,0x8d,0x93,0xf1,0xd4,0x21,0x7d,0x39,0xab,0xf6,0x9f,0xcb,0x5c,0xcc,0x28,0xd6,0x84,0xd2,0xaa,0xab,0xcd,0x63,0x83,0x77,0x5c,0xaa,0x62,0x39,0xde,0x26,0xd4,0xc6,0x93,0x7b,0xb6,0x03,0xec,0xb4,0x19,0x60,0x82,0xf4,0xcf,0xfd,0x50,0x9d, + 0x04,0x3f,0x39,0x52,0x19,0x97,0x74,0xc7,0xcf,0x39,0xb3,0x8b,0x66,0xcb,0x10,0x42,0xa6,0x26,0x0d,0x86,0x80,0x80,0x38,0x45,0xe4,0xd4,0x33,0xad,0xba,0x3b,0xb2,0x48,0x18,0x5e,0xa4,0x95,0xb6,0x8c,0xbc,0x7e,0xd4,0x17,0x3e,0xe6,0x3c,0x90,0x42,0xdc,0x50,0x26,0x25,0xc7,0xeb,0x7e,0x21,0xfb,0x02,0xca,0x9a,0x91,0x14,0xe0,0xa3,0xa1,0x8d, + 0x04,0xcd,0xfb,0x8c,0x0f,0x42,0x2e,0x14,0x4e,0x13,0x7c,0x24,0x12,0xc8,0x6c,0x17,0x1f,0x5f,0xe3,0xfa,0x3f,0x5b,0xbb,0x54,0x4e,0x90,0x76,0x28,0x8f,0x3c,0xed,0x78,0x6e,0x05,0x4f,0xd0,0x72,0x1b,0x77,0xc1,0x1c,0x79,0xbe,0xac,0xb3,0xc9,0x42,0x11,0xb0,0xa1,0x9b,0xda,0x08,0x65,0x2e,0xfe,0xaf,0x92,0x51,0x3a,0x3b,0x0a,0x16,0x36,0x98, + 0x04,0x73,0x59,0x8a,0x6a,0x1c,0x68,0x27,0x8f,0xa6,0xbf,0xd0,0xce,0x40,0x64,0xe6,0x82,0x35,0xbc,0x1c,0x0f,0x6b,0x20,0xa9,0x28,0x10,0x8b,0xe3,0x36,0x73,0x0f,0x87,0xe3,0xcb,0xae,0x61,0x25,0x19,0xb5,0x03,0x2e,0xcc,0x85,0xae,0xd8,0x11,0x27,0x1a,0x95,0xfe,0x79,0x39,0xd5,0xd3,0x46,0x01,0x40,0xba,0x31,0x8f,0x4d,0x14,0xab,0xa3,0x1d, + 0x04,0x58,0xde,0xbd,0x9a,0x7e,0xe2,0xc9,0xd5,0x91,0x32,0x47,0x8a,0x54,0x40,0xae,0x4d,0x5d,0x7e,0xd4,0x37,0x30,0x83,0x69,0xf9,0x2e,0xa8,0x6c,0x82,0x18,0x3f,0x10,0xa1,0x67,0x73,0xe7,0x6f,0x5e,0xdb,0xf4,0xda,0x0e,0x4f,0x1b,0xdf,0xfa,0xc0,0xf5,0x72,0x57,0xe1,0xdf,0xa4,0x65,0x84,0x29,0x31,0x30,0x9a,0x24,0x24,0x5f,0xda,0x6a,0x5d, + 0x04,0x8b,0x90,0x4d,0xe4,0x79,0x67,0x34,0x0c,0x5f,0x8c,0x35,0x72,0xa7,0x20,0x92,0x4e,0xf7,0x57,0x86,0x37,0xfe,0xab,0x19,0x49,0xac,0xb2,0x41,0xa5,0xa6,0xac,0x3f,0x5b,0x95,0x09,0x04,0x49,0x6f,0x98,0x24,0xb1,0xd6,0x3f,0x33,0x13,0xba,0xe2,0x1b,0x89,0xfa,0xe8,0x9a,0xfd,0xfc,0x81,0x1b,0x5e,0xce,0x03,0xfd,0x5a,0xa3,0x01,0x86,0x4f, + 0x04,0xf4,0x89,0x2b,0x6d,0x52,0x5c,0x77,0x1e,0x03,0x5f,0x2a,0x25,0x27,0x08,0xf3,0x78,0x4e,0x48,0x23,0x86,0x04,0xb4,0xf9,0x4d,0xc5,0x6e,0xaa,0x1e,0x54,0x6d,0x94,0x1a,0x34,0x6b,0x1a,0xa0,0xbc,0xe6,0x8b,0x1c,0x50,0xe5,0xb5,0x2f,0x50,0x9f,0xb5,0x52,0x2e,0x5c,0x25,0xe0,0x28,0xbc,0x8f,0x86,0x34,0x02,0xed,0xb7,0xbc,0xad,0x8b,0x1b, + 0x04,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x48,0x3a,0xda,0x77,0x26,0xa3,0xc4,0x65,0x5d,0xa4,0xfb,0xfc,0x0e,0x11,0x08,0xa8,0xfd,0x17,0xb4,0x48,0xa6,0x85,0x54,0x19,0x9c,0x47,0xd0,0x8f,0xfb,0x10,0xd4,0xb8, + 0x04,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0xb7,0xc5,0x25,0x88,0xd9,0x5c,0x3b,0x9a,0xa2,0x5b,0x04,0x03,0xf1,0xee,0xf7,0x57,0x02,0xe8,0x4b,0xb7,0x59,0x7a,0xab,0xe6,0x63,0xb8,0x2f,0x6f,0x04,0xef,0x27,0x77, + 0x04,0x78,0x2c,0x8e,0xd1,0x7e,0x3b,0x2a,0x78,0x3b,0x54,0x64,0xf3,0x3b,0x09,0x65,0x2a,0x71,0xc6,0x78,0xe0,0x5e,0xc5,0x1e,0x84,0xe2,0xbc,0xfc,0x66,0x3a,0x3d,0xe9,0x63,0xaf,0x9a,0xcb,0x42,0x80,0xb8,0xc7,0xf7,0xc4,0x2f,0x4e,0xf9,0xab,0xa6,0x24,0x5e,0xc1,0xec,0x17,0x12,0xfd,0x38,0xa0,0xfa,0x96,0x41,0x8d,0x8c,0xd6,0xaa,0x61,0x52, + 0x04,0x6e,0x82,0x35,0x55,0x45,0x29,0x14,0x09,0x91,0x82,0xc6,0xb2,0xc1,0xd6,0xf0,0xb5,0xd2,0x8d,0x50,0xcc,0xd0,0x05,0xaf,0x2c,0xe1,0xbb,0xa5,0x41,0xaa,0x40,0xca,0xff,0x00,0x00,0x00,0x01,0x06,0x04,0x92,0xd5,0xa5,0x67,0x3e,0x0f,0x25,0xd8,0xd5,0x0f,0xb7,0xe5,0x8c,0x49,0xd8,0x6d,0x46,0xd4,0x21,0x69,0x55,0xe0,0xaa,0x3d,0x40,0xe1, + 0x04,0x6e,0x82,0x35,0x55,0x45,0x29,0x14,0x09,0x91,0x82,0xc6,0xb2,0xc1,0xd6,0xf0,0xb5,0xd2,0x8d,0x50,0xcc,0xd0,0x05,0xaf,0x2c,0xe1,0xbb,0xa5,0x41,0xaa,0x40,0xca,0xff,0xff,0xff,0xff,0xfe,0xf9,0xfb,0x6d,0x2a,0x5a,0x98,0xc1,0xf0,0xda,0x27,0x2a,0xf0,0x48,0x1a,0x73,0xb6,0x27,0x92,0xb9,0x2b,0xde,0x96,0xaa,0x1e,0x55,0xc2,0xbb,0x4e, + 0x04,0x00,0x00,0x00,0x01,0x3f,0xd2,0x22,0x48,0xd6,0x4d,0x95,0xf7,0x3c,0x29,0xb4,0x8a,0xb4,0x86,0x31,0x85,0x0b,0xe5,0x03,0xfd,0x00,0xf8,0x46,0x8b,0x5f,0x0f,0x70,0xe0,0xf6,0xee,0x7a,0xa4,0x3b,0xc2,0xc6,0xfd,0x25,0xb1,0xd8,0x26,0x92,0x41,0xcb,0xdd,0x9d,0xbb,0x0d,0xac,0x96,0xdc,0x96,0x23,0x1f,0x43,0x07,0x05,0xf8,0x38,0x71,0x7d, + 0x04,0x25,0xaf,0xd6,0x89,0xac,0xab,0xae,0xd6,0x7c,0x1f,0x29,0x6d,0xe5,0x94,0x06,0xf8,0xc5,0x50,0xf5,0x71,0x46,0xa0,0xb4,0xec,0x2c,0x97,0x87,0x6d,0xff,0xff,0xff,0xff,0xfa,0x46,0xa7,0x6e,0x52,0x03,0x22,0xdf,0xbc,0x49,0x1e,0xc4,0xf0,0xcc,0x19,0x74,0x20,0xfc,0x4e,0xa5,0x88,0x3d,0x8f,0x6d,0xd5,0x3c,0x35,0x4b,0xc4,0xf6,0x7c,0x35, + 0x04,0xd1,0x2e,0x6c,0x66,0xb6,0x77,0x34,0xc3,0xc8,0x4d,0x26,0x01,0xcf,0x5d,0x35,0xdc,0x09,0x7e,0x27,0x63,0x7f,0x0a,0xca,0x4a,0x4f,0xdb,0x74,0xb6,0xaa,0xdd,0x3b,0xb9,0x3f,0x5b,0xdf,0xf8,0x8b,0xd5,0x73,0x6d,0xf8,0x98,0xe6,0x99,0x00,0x6e,0xd7,0x50,0xf1,0x1c,0xf0,0x7c,0x58,0x66,0xcd,0x7a,0xd7,0x0c,0x71,0x21,0xff,0xff,0xff,0xff, + 0x04,0x6d,0x4a,0x7f,0x60,0xd4,0x77,0x4a,0x4f,0x0a,0xa8,0xbb,0xde,0xdb,0x95,0x3c,0x7e,0xea,0x79,0x09,0x40,0x7e,0x31,0x64,0x75,0x56,0x64,0xbc,0x28,0x00,0x00,0x00,0x00,0xe6,0x59,0xd3,0x4e,0x4d,0xf3,0x8d,0x9e,0x8c,0x9e,0xaa,0xdf,0xba,0x36,0x61,0x2c,0x76,0x91,0x95,0xbe,0x86,0xc7,0x7a,0xac,0x3f,0x36,0xe7,0x8b,0x53,0x86,0x80,0xfb}; + +static const unsigned char wycheproof_ecdsa_signatures[] = { 0x30,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x21,0x00,0x90,0x0e,0x75,0xad,0x23,0x3f,0xcc,0x90,0x85,0x09,0xdb,0xff,0x59,0x22,0x64,0x7d,0xb3,0x7c,0x21,0xf4,0xaf,0xd3,0x20,0x3a,0xe8,0xdc,0x4a,0xe7,0x79,0x4b,0x0f,0x87, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 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0x30,0x45,0x02,0x21,0x00,0xb6,0x15,0x69,0x8c,0x35,0x8b,0x35,0x92,0x0d,0xd8,0x83,0xec,0xa6,0x25,0xa6,0xc5,0xf7,0x56,0x39,0x70,0xcd,0xfc,0x37,0x8f,0x8f,0xe0,0xce,0xe1,0x70,0x92,0x14,0x4c,0x02,0x20,0x25,0xf4,0x7b,0x32,0x6b,0x5b,0xe1,0xfb,0x61,0x0b,0x88,0x51,0x53,0xea,0x84,0xd4,0x1e,0xb4,0x71,0x6b,0xe6,0x6a,0x99,0x4e,0x87,0x79,0x98,0x9d,0xf1,0xc8,0x63,0xd4, + 0x30,0x45,0x02,0x21,0x00,0x87,0xcf,0x8c,0x0e,0xb8,0x2d,0x44,0xf6,0x9c,0x60,0xa2,0xff,0x54,0x57,0xd3,0xaa,0xa3,0x22,0xe7,0xec,0x61,0xae,0x5a,0xec,0xfd,0x67,0x8a,0xe1,0xc1,0x93,0x2b,0x0e,0x02,0x20,0x3a,0xdd,0x3b,0x11,0x58,0x15,0x04,0x7d,0x6e,0xb3,0x40,0xa3,0xe0,0x08,0x98,0x9e,0xaa,0x0f,0x87,0x08,0xd1,0x79,0x48,0x14,0x72,0x90,0x94,0xd0,0x8d,0x24,0x60,0xd3, + 0x30,0x44,0x02,0x20,0x62,0xf4,0x8e,0xf7,0x1a,0xce,0x27,0xbf,0x5a,0x01,0x83,0x4d,0xe1,0xf7,0xe3,0xf9,0x48,0xb9,0xdc,0xe1,0xca,0x1e,0x91,0x1d,0x5e,0x13,0xd3,0xb1,0x04,0x47,0x1d,0x82,0x02,0x20,0x5e,0xa8,0xf3,0x3f,0x0c,0x77,0x89,0x72,0xc4,0x58,0x20,0x80,0xde,0xda,0x9b,0x34,0x18,0x57,0xdd,0x64,0x51,0x4f,0x08,0x49,0xa0,0x5f,0x69,0x64,0xc2,0xe3,0x40,0x22, + 0x30,0x45,0x02,0x21,0x00,0xf6,0xb0,0xe2,0xf6,0xfe,0x02,0x0c,0xf7,0xc0,0xc2,0x01,0x37,0x43,0x43,0x44,0xed,0x7a,0xdd,0x6c,0x4b,0xe5,0x18,0x61,0xe2,0xd1,0x4c,0xbd,0xa4,0x72,0xa6,0xff,0xb4,0x02,0x20,0x64,0x16,0xc8,0xdd,0x3e,0x5c,0x52,0x82,0xb3,0x06,0xe8,0xdc,0x8f,0xf3,0x4a,0xb6,0x4c,0xc9,0x95,0x49,0x23,0x2d,0x67,0x8d,0x71,0x44,0x02,0xeb,0x6c,0xa7,0xaa,0x0f, + 0x30,0x45,0x02,0x21,0x00,0xdb,0x09,0xd8,0x46,0x0f,0x05,0xef,0xf2,0x3b,0xc7,0xe4,0x36,0xb6,0x7d,0xa5,0x63,0xfa,0x4b,0x4e,0xdb,0x58,0xac,0x24,0xce,0x20,0x1f,0xa8,0xa3,0x58,0x12,0x50,0x57,0x02,0x20,0x46,0xda,0x11,0x67,0x54,0x60,0x29,0x40,0xc8,0x99,0x9c,0x8d,0x66,0x5f,0x78,0x6c,0x50,0xf5,0x77,0x2c,0x0a,0x3c,0xdb,0xda,0x07,0x5e,0x77,0xea,0xbc,0x64,0xdf,0x16, + 0x30,0x44,0x02,0x20,0x59,0x2c,0x41,0xe1,0x65,0x17,0xf1,0x2f,0xca,0xbd,0x98,0x26,0x76,0x74,0xf9,0x74,0xb5,0x88,0xe9,0xf3,0x5d,0x35,0x40,0x6c,0x1a,0x7b,0xb2,0xed,0x1d,0x19,0xb7,0xb8,0x02,0x20,0x3e,0x65,0xa0,0x6b,0xd9,0xf8,0x3c,0xaa,0xeb,0x7b,0x00,0xf2,0x36,0x8d,0x7e,0x0d,0xec,0xe6,0xb1,0x22,0x21,0x26,0x9a,0x9b,0x5b,0x76,0x51,0x98,0xf8,0x40,0xa3,0xa1, + 0x30,0x45,0x02,0x21,0x00,0xbe,0x0d,0x70,0x88,0x7d,0x5e,0x40,0x82,0x1a,0x61,0xb6,0x80,0x47,0xde,0x4e,0xa0,0x3d,0xeb,0xfd,0xf5,0x1c,0xdf,0x4d,0x4b,0x19,0x55,0x58,0xb9,0x59,0xa0,0x32,0xb2,0x02,0x20,0x7d,0x99,0x4b,0x2d,0x8f,0x1d,0xbb,0xeb,0x13,0x53,0x4e,0xb3,0xf6,0xe5,0xdc,0xcd,0x85,0xf5,0xc4,0x13,0x3c,0x27,0xd9,0xe6,0x42,0x71,0xb1,0x82,0x6c,0xe1,0xf6,0x7d, + 0x30,0x45,0x02,0x21,0x00,0xfa,0xe9,0x2d,0xfc,0xb2,0xee,0x39,0x2d,0x27,0x0a,0xf3,0xa5,0x73,0x9f,0xaa,0x26,0xd4,0xf9,0x7b,0xfd,0x39,0xed,0x3c,0xbe,0xe4,0xd2,0x9e,0x26,0xaf,0x3b,0x20,0x6a,0x02,0x20,0x6c,0x9b,0xa3,0x7f,0x9f,0xaa,0x6a,0x1f,0xd3,0xf6,0x5f,0x23,0xb4,0xe8,0x53,0xd4,0x69,0x2a,0x72,0x74,0x24,0x0a,0x12,0xdb,0x7b,0xa3,0x88,0x48,0x30,0x63,0x0d,0x16, + 0x30,0x44,0x02,0x20,0x17,0x6a,0x25,0x57,0x56,0x6f,0xfa,0x51,0x8b,0x11,0x22,0x66,0x94,0xeb,0x98,0x02,0xed,0x20,0x98,0xbf,0xe2,0x78,0xe5,0x57,0x0f,0xe1,0xd5,0xd7,0xaf,0x18,0xa9,0x43,0x02,0x20,0x12,0x91,0xdf,0x6a,0x0e,0xd5,0xfc,0x0d,0x15,0x09,0x8e,0x70,0xbc,0xf1,0x3a,0x00,0x92,0x84,0xdf,0xd0,0x68,0x9d,0x3b,0xb4,0xbe,0x6c,0xee,0xb9,0xbe,0x14,0x87,0xc4, + 0x30,0x44,0x02,0x20,0x60,0xbe,0x20,0xc3,0xdb,0xc1,0x62,0xdd,0x34,0xd2,0x67,0x80,0x62,0x1c,0x10,0x4b,0xbe,0x5d,0xac,0xe6,0x30,0x17,0x1b,0x2d,0xae,0xf0,0xd8,0x26,0x40,0x9e,0xe5,0xc2,0x02,0x20,0x42,0x7f,0x7e,0x4d,0x88,0x9d,0x54,0x91,0x70,0xbd,0xa6,0xa9,0x40,0x9f,0xb1,0xcb,0x8b,0x0e,0x76,0x3d,0x13,0xee,0xa7,0xbd,0x97,0xf6,0x4c,0xf4,0x1d,0xc6,0xe4,0x97, + 0x30,0x45,0x02,0x21,0x00,0xed,0xf0,0x3c,0xf6,0x3f,0x65,0x88,0x83,0x28,0x9a,0x1a,0x59,0x3d,0x10,0x07,0x89,0x5b,0x9f,0x23,0x6d,0x27,0xc9,0xc1,0xf1,0x31,0x30,0x89,0xaa,0xed,0x6b,0x16,0xae,0x02,0x20,0x1a,0x4d,0xd6,0xfc,0x08,0x14,0xdc,0x52,0x3d,0x1f,0xef,0xa8,0x1c,0x64,0xfb,0xf5,0xe6,0x18,0xe6,0x51,0xe7,0x09,0x6f,0xcc,0xad,0xbb,0x94,0xcd,0x48,0xe5,0xe0,0xcd}; + +static const wycheproof_ecdsa_testvector testvectors[SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS] = { + /* tcId: 1. Signature malleability */ + {0, 0, 6, 0, 72, 0 }, + /* tcId: 2. valid */ + {0, 0, 6, 72, 71, 1 }, + /* tcId: 3. length of sequence [r, s] uses long form encoding */ + {0, 0, 6, 143, 72, 0 }, + /* tcId: 4. length of sequence [r, s] contains a leading 0 */ + {0, 0, 6, 215, 73, 0 }, + /* tcId: 5. length of sequence [r, s] uses 70 instead of 69 */ + {0, 0, 6, 288, 71, 0 }, + /* tcId: 6. length of sequence [r, s] uses 68 instead of 69 */ + {0, 0, 6, 359, 71, 0 }, + /* tcId: 7. uint32 overflow in length of sequence [r, s] */ + {0, 0, 6, 430, 76, 0 }, + /* tcId: 8. uint64 overflow in length of sequence [r, s] */ + {0, 0, 6, 506, 80, 0 }, + /* tcId: 9. length of sequence [r, s] = 2**31 - 1 */ + {0, 0, 6, 586, 75, 0 }, + /* tcId: 10. length of sequence [r, s] = 2**31 */ + {0, 0, 6, 661, 75, 0 }, + /* tcId: 11. length of sequence [r, s] = 2**32 - 1 */ + {0, 0, 6, 736, 75, 0 }, + /* tcId: 12. length of sequence [r, s] = 2**40 - 1 */ + {0, 0, 6, 811, 76, 0 }, + /* tcId: 13. length of sequence [r, s] = 2**64 - 1 */ + {0, 0, 6, 887, 79, 0 }, + /* tcId: 14. incorrect length of sequence [r, s] */ + {0, 0, 6, 966, 71, 0 }, + /* tcId: 15. replaced sequence [r, s] by an indefinite length tag without termination */ + {0, 0, 6, 1037, 71, 0 }, + /* tcId: 16. removing sequence [r, s] */ + {0, 0, 6, 1108, 0, 0 }, + /* tcId: 17. lonely sequence tag */ + {0, 0, 6, 1108, 1, 0 }, + /* tcId: 18. appending 0's to sequence [r, s] */ + {0, 0, 6, 1109, 73, 0 }, + /* tcId: 19. prepending 0's to sequence [r, s] */ + {0, 0, 6, 1182, 73, 0 }, + /* tcId: 20. appending unused 0's to sequence [r, s] */ + {0, 0, 6, 1255, 73, 0 }, + /* tcId: 21. appending null value to sequence [r, s] */ + {0, 0, 6, 1328, 73, 0 }, + /* tcId: 22. prepending garbage to sequence [r, s] */ + {0, 0, 6, 1401, 76, 0 }, + /* tcId: 23. prepending garbage to sequence [r, s] */ + {0, 0, 6, 1477, 75, 0 }, + /* tcId: 24. appending garbage to sequence [r, s] */ + {0, 0, 6, 1552, 79, 0 }, + /* tcId: 25. including undefined tags */ + {0, 0, 6, 1631, 79, 0 }, + /* tcId: 26. including undefined tags */ + {0, 0, 6, 1710, 79, 0 }, + /* tcId: 27. including undefined tags */ + {0, 0, 6, 1789, 79, 0 }, + /* tcId: 28. truncated length of sequence [r, s] */ + {0, 0, 6, 1868, 2, 0 }, + /* tcId: 29. including undefined tags to sequence [r, s] */ + {0, 0, 6, 1870, 77, 0 }, + /* tcId: 30. using composition with indefinite length for sequence [r, s] */ + {0, 0, 6, 1947, 75, 0 }, + /* tcId: 31. using composition with wrong tag for sequence [r, s] */ + {0, 0, 6, 2022, 75, 0 }, + /* tcId: 32. Replacing sequence [r, s] with NULL */ + {0, 0, 6, 2097, 2, 0 }, + /* tcId: 33. changing tag value of sequence [r, s] */ + {0, 0, 6, 2099, 71, 0 }, + /* tcId: 34. changing tag value of sequence [r, s] */ + {0, 0, 6, 2170, 71, 0 }, + /* tcId: 35. changing tag value of sequence [r, s] */ + {0, 0, 6, 2241, 71, 0 }, + /* tcId: 36. changing tag value of sequence [r, s] */ + {0, 0, 6, 2312, 71, 0 }, + /* tcId: 37. changing tag value of sequence [r, s] */ + {0, 0, 6, 2383, 71, 0 }, + /* tcId: 38. dropping value of sequence [r, s] */ + {0, 0, 6, 2454, 2, 0 }, + /* tcId: 39. using composition for sequence [r, s] */ + {0, 0, 6, 2456, 75, 0 }, + /* tcId: 40. truncated sequence [r, s] */ + {0, 0, 6, 2531, 70, 0 }, + /* tcId: 41. truncated sequence [r, s] */ + {0, 0, 6, 2601, 70, 0 }, + /* tcId: 42. sequence [r, s] of size 4166 to check for overflows */ + {0, 0, 6, 2671, 4170, 0 }, + /* tcId: 43. indefinite length */ + {0, 0, 6, 6841, 73, 0 }, + /* tcId: 44. indefinite length with truncated delimiter */ + {0, 0, 6, 6914, 72, 0 }, + /* tcId: 45. indefinite length with additional element */ + {0, 0, 6, 6986, 75, 0 }, + /* tcId: 46. indefinite length with truncated element */ + {0, 0, 6, 7061, 77, 0 }, + /* tcId: 47. indefinite length with garbage */ + {0, 0, 6, 7138, 77, 0 }, + /* tcId: 48. indefinite length with nonempty EOC */ + {0, 0, 6, 7215, 75, 0 }, + /* tcId: 49. prepend empty sequence */ + {0, 0, 6, 7290, 73, 0 }, + /* tcId: 50. append empty sequence */ + {0, 0, 6, 7363, 73, 0 }, + /* tcId: 51. append zero */ + {0, 0, 6, 7436, 74, 0 }, + /* tcId: 52. append garbage with high tag number */ + {0, 0, 6, 7510, 74, 0 }, + /* tcId: 53. append null with explicit tag */ + {0, 0, 6, 7584, 75, 0 }, + /* tcId: 54. append null with implicit tag */ + {0, 0, 6, 7659, 73, 0 }, + /* tcId: 55. sequence of sequence */ + {0, 0, 6, 7732, 73, 0 }, + /* tcId: 56. truncated sequence: removed last 1 elements */ + {0, 0, 6, 7805, 37, 0 }, + /* tcId: 57. repeating element in sequence */ + {0, 0, 6, 7842, 105, 0 }, + /* tcId: 58. flipped bit 0 in r */ + {0, 0, 6, 7947, 69, 0 }, + /* tcId: 59. flipped bit 32 in r */ + {0, 0, 6, 8016, 69, 0 }, + /* tcId: 60. flipped bit 48 in r */ + {0, 0, 6, 8085, 69, 0 }, + /* tcId: 61. flipped bit 64 in r */ + {0, 0, 6, 8154, 69, 0 }, + /* tcId: 62. length of r uses long form encoding */ + {0, 0, 6, 8223, 72, 0 }, + /* tcId: 63. length of r contains a leading 0 */ + {0, 0, 6, 8295, 73, 0 }, + /* tcId: 64. length of r uses 34 instead of 33 */ + {0, 0, 6, 8368, 71, 0 }, + /* tcId: 65. length of r uses 32 instead of 33 */ + {0, 0, 6, 8439, 71, 0 }, + /* tcId: 66. uint32 overflow in length of r */ + {0, 0, 6, 8510, 76, 0 }, + /* tcId: 67. uint64 overflow in length of r */ + {0, 0, 6, 8586, 80, 0 }, + /* tcId: 68. length of r = 2**31 - 1 */ + {0, 0, 6, 8666, 75, 0 }, + /* tcId: 69. length of r = 2**31 */ + {0, 0, 6, 8741, 75, 0 }, + /* tcId: 70. length of r = 2**32 - 1 */ + {0, 0, 6, 8816, 75, 0 }, + /* tcId: 71. length of r = 2**40 - 1 */ + {0, 0, 6, 8891, 76, 0 }, + /* tcId: 72. length of r = 2**64 - 1 */ + {0, 0, 6, 8967, 79, 0 }, + /* tcId: 73. incorrect length of r */ + {0, 0, 6, 9046, 71, 0 }, + /* tcId: 74. replaced r by an indefinite length tag without termination */ + {0, 0, 6, 9117, 71, 0 }, + /* tcId: 75. removing r */ + {0, 0, 6, 9188, 36, 0 }, + /* tcId: 76. lonely integer tag */ + {0, 0, 6, 9224, 37, 0 }, + /* tcId: 77. lonely integer tag */ + {0, 0, 6, 9261, 38, 0 }, + /* tcId: 78. appending 0's to r */ + {0, 0, 6, 9299, 73, 0 }, + /* tcId: 79. prepending 0's to r */ + {0, 0, 6, 9372, 73, 0 }, + /* tcId: 80. appending unused 0's to r */ + {0, 0, 6, 9445, 73, 0 }, + /* tcId: 81. appending null value to r */ + {0, 0, 6, 9518, 73, 0 }, + /* tcId: 82. prepending garbage to r */ + {0, 0, 6, 9591, 76, 0 }, + /* tcId: 83. prepending garbage to r */ + {0, 0, 6, 9667, 75, 0 }, + /* tcId: 84. appending garbage to r */ + {0, 0, 6, 9742, 79, 0 }, + /* tcId: 85. truncated length of r */ + {0, 0, 6, 9821, 38, 0 }, + /* tcId: 86. including undefined tags to r */ + {0, 0, 6, 9859, 77, 0 }, + /* tcId: 87. using composition with indefinite length for r */ + {0, 0, 6, 9936, 75, 0 }, + /* tcId: 88. using composition with wrong tag for r */ + {0, 0, 6, 10011, 75, 0 }, + /* tcId: 89. Replacing r with NULL */ + {0, 0, 6, 10086, 38, 0 }, + /* tcId: 90. changing tag value of r */ + {0, 0, 6, 10124, 71, 0 }, + /* tcId: 91. changing tag value of r */ + {0, 0, 6, 10195, 71, 0 }, + /* tcId: 92. changing tag value of r */ + {0, 0, 6, 10266, 71, 0 }, + /* tcId: 93. changing tag value of r */ + {0, 0, 6, 10337, 71, 0 }, + /* tcId: 94. changing tag value of r */ + {0, 0, 6, 10408, 71, 0 }, + /* tcId: 95. dropping value of r */ + {0, 0, 6, 10479, 38, 0 }, + /* tcId: 96. using composition for r */ + {0, 0, 6, 10517, 75, 0 }, + /* tcId: 97. modifying first byte of r */ + {0, 0, 6, 10592, 71, 0 }, + /* tcId: 98. modifying last byte of r */ + {0, 0, 6, 10663, 71, 0 }, + /* tcId: 99. truncated r */ + {0, 0, 6, 10734, 70, 0 }, + /* tcId: 100. truncated r */ + {0, 0, 6, 10804, 70, 0 }, + /* tcId: 101. r of size 4130 to check for overflows */ + {0, 0, 6, 10874, 4172, 0 }, + /* tcId: 102. leading ff in r */ + {0, 0, 6, 15046, 72, 0 }, + /* tcId: 103. replaced r by infinity */ + {0, 0, 6, 15118, 39, 0 }, + /* tcId: 104. replacing r with zero */ + {0, 0, 6, 15157, 39, 0 }, + /* tcId: 105. flipped bit 0 in s */ + {0, 0, 6, 15196, 69, 0 }, + /* tcId: 106. flipped bit 32 in s */ + {0, 0, 6, 15265, 69, 0 }, + /* tcId: 107. flipped bit 48 in s */ + {0, 0, 6, 15334, 69, 0 }, + /* tcId: 108. flipped bit 64 in s */ + {0, 0, 6, 15403, 69, 0 }, + /* tcId: 109. length of s uses long form encoding */ + {0, 0, 6, 15472, 72, 0 }, + /* tcId: 110. length of s contains a leading 0 */ + {0, 0, 6, 15544, 73, 0 }, + /* tcId: 111. length of s uses 33 instead of 32 */ + {0, 0, 6, 15617, 71, 0 }, + /* tcId: 112. length of s uses 31 instead of 32 */ + {0, 0, 6, 15688, 71, 0 }, + /* tcId: 113. uint32 overflow in length of s */ + {0, 0, 6, 15759, 76, 0 }, + /* tcId: 114. uint64 overflow in length of s */ + {0, 0, 6, 15835, 80, 0 }, + /* tcId: 115. length of s = 2**31 - 1 */ + {0, 0, 6, 15915, 75, 0 }, + /* tcId: 116. length of s = 2**31 */ + {0, 0, 6, 15990, 75, 0 }, + /* tcId: 117. length of s = 2**32 - 1 */ + {0, 0, 6, 16065, 75, 0 }, + /* tcId: 118. length of s = 2**40 - 1 */ + {0, 0, 6, 16140, 76, 0 }, + /* tcId: 119. length of s = 2**64 - 1 */ + {0, 0, 6, 16216, 79, 0 }, + /* tcId: 120. incorrect length of s */ + {0, 0, 6, 16295, 71, 0 }, + /* tcId: 121. replaced s by an indefinite length tag without termination */ + {0, 0, 6, 16366, 71, 0 }, + /* tcId: 122. appending 0's to s */ + {0, 0, 6, 16437, 73, 0 }, + /* tcId: 123. prepending 0's to s */ + {0, 0, 6, 16510, 73, 0 }, + /* tcId: 124. appending null value to s */ + {0, 0, 6, 16583, 73, 0 }, + /* tcId: 125. prepending garbage to s */ + {0, 0, 6, 16656, 76, 0 }, + /* tcId: 126. prepending garbage to s */ + {0, 0, 6, 16732, 75, 0 }, + /* tcId: 127. appending garbage to s */ + {0, 0, 6, 16807, 79, 0 }, + /* tcId: 128. truncated length of s */ + {0, 0, 6, 16886, 39, 0 }, + /* tcId: 129. including undefined tags to s */ + {0, 0, 6, 16925, 77, 0 }, + /* tcId: 130. using composition with indefinite length for s */ + {0, 0, 6, 17002, 75, 0 }, + /* tcId: 131. using composition with wrong tag for s */ + {0, 0, 6, 17077, 75, 0 }, + /* tcId: 132. Replacing s with NULL */ + {0, 0, 6, 17152, 39, 0 }, + /* tcId: 133. changing tag value of s */ + {0, 0, 6, 17191, 71, 0 }, + /* tcId: 134. changing tag value of s */ + {0, 0, 6, 17262, 71, 0 }, + /* tcId: 135. changing tag value of s */ + {0, 0, 6, 17333, 71, 0 }, + /* tcId: 136. changing tag value of s */ + {0, 0, 6, 17404, 71, 0 }, + /* tcId: 137. changing tag value of s */ + {0, 0, 6, 17475, 71, 0 }, + /* tcId: 138. dropping value of s */ + {0, 0, 6, 17546, 39, 0 }, + /* tcId: 139. using composition for s */ + {0, 0, 6, 17585, 75, 0 }, + /* tcId: 140. modifying first byte of s */ + {0, 0, 6, 17660, 71, 0 }, + /* tcId: 141. modifying last byte of s */ + {0, 0, 6, 17731, 71, 0 }, + /* tcId: 142. truncated s */ + {0, 0, 6, 17802, 70, 0 }, + /* tcId: 143. truncated s */ + {0, 0, 6, 17872, 70, 0 }, + /* tcId: 144. s of size 4129 to check for overflows */ + {0, 0, 6, 17942, 4172, 0 }, + /* tcId: 145. leading ff in s */ + {0, 0, 6, 22114, 72, 0 }, + /* tcId: 146. replaced s by infinity */ + {0, 0, 6, 22186, 40, 0 }, + /* tcId: 147. replacing s with zero */ + {0, 0, 6, 22226, 40, 0 }, + /* tcId: 148. replaced r by r + n */ + {0, 0, 6, 22266, 71, 0 }, + /* tcId: 149. replaced r by r - n */ + {0, 0, 6, 22337, 70, 0 }, + /* tcId: 150. replaced r by r + 256 * n */ + {0, 0, 6, 22407, 72, 0 }, + /* tcId: 151. replaced r by -r */ + {0, 0, 6, 22479, 71, 0 }, + /* tcId: 152. replaced r by n - r */ + {0, 0, 6, 22550, 70, 0 }, + /* tcId: 153. replaced r by -n - r */ + {0, 0, 6, 22620, 71, 0 }, + /* tcId: 154. replaced r by r + 2**256 */ + {0, 0, 6, 22691, 71, 0 }, + /* tcId: 155. replaced r by r + 2**320 */ + {0, 0, 6, 22762, 79, 0 }, + /* tcId: 156. replaced s by s + n */ + {0, 0, 6, 22841, 71, 0 }, + /* tcId: 157. replaced s by s - n */ + {0, 0, 6, 22912, 71, 0 }, + /* tcId: 158. replaced s by s + 256 * n */ + {0, 0, 6, 22983, 72, 0 }, + /* tcId: 159. replaced s by -s */ + {0, 0, 6, 23055, 70, 0 }, + /* tcId: 160. replaced s by -n - s */ + {0, 0, 6, 23125, 71, 0 }, + /* tcId: 161. replaced s by s + 2**256 */ + {0, 0, 6, 23196, 71, 0 }, + /* tcId: 162. replaced s by s - 2**256 */ + {0, 0, 6, 23267, 71, 0 }, + /* tcId: 163. replaced s by s + 2**320 */ + {0, 0, 6, 23338, 79, 0 }, + /* tcId: 164. Signature with special case values r=0 and s=0 */ + {0, 0, 6, 23417, 8, 0 }, + /* tcId: 165. Signature with special case values r=0 and s=1 */ + {0, 0, 6, 23425, 8, 0 }, + /* tcId: 166. Signature with special case values r=0 and s=-1 */ + {0, 0, 6, 23433, 8, 0 }, + /* tcId: 167. Signature with special case values r=0 and s=n */ + {0, 0, 6, 23441, 40, 0 }, + /* tcId: 168. Signature with special case values r=0 and s=n - 1 */ + {0, 0, 6, 23481, 40, 0 }, + /* tcId: 169. Signature with special case values r=0 and s=n + 1 */ + {0, 0, 6, 23521, 40, 0 }, + /* tcId: 170. Signature with special case values r=0 and s=p */ + {0, 0, 6, 23561, 40, 0 }, + /* tcId: 171. Signature with special case values r=0 and s=p + 1 */ + {0, 0, 6, 23601, 40, 0 }, + /* tcId: 172. Signature with special case values r=1 and s=0 */ + {0, 0, 6, 23641, 8, 0 }, + /* tcId: 173. Signature with special case values r=1 and s=1 */ + {0, 0, 6, 23649, 8, 0 }, + /* tcId: 174. Signature with special case values r=1 and s=-1 */ + {0, 0, 6, 23657, 8, 0 }, + /* tcId: 175. Signature with special case values r=1 and s=n */ + {0, 0, 6, 23665, 40, 0 }, + /* tcId: 176. Signature with special case values r=1 and s=n - 1 */ + {0, 0, 6, 23705, 40, 0 }, + /* tcId: 177. Signature with special case values r=1 and s=n + 1 */ + {0, 0, 6, 23745, 40, 0 }, + /* tcId: 178. Signature with special case values r=1 and s=p */ + {0, 0, 6, 23785, 40, 0 }, + /* tcId: 179. Signature with special case values r=1 and s=p + 1 */ + {0, 0, 6, 23825, 40, 0 }, + /* tcId: 180. Signature with special case values r=-1 and s=0 */ + {0, 0, 6, 23865, 8, 0 }, + /* tcId: 181. Signature with special case values r=-1 and s=1 */ + {0, 0, 6, 23873, 8, 0 }, + /* tcId: 182. Signature with special case values r=-1 and s=-1 */ + {0, 0, 6, 23881, 8, 0 }, + /* tcId: 183. Signature with special case values r=-1 and s=n */ + {0, 0, 6, 23889, 40, 0 }, + /* tcId: 184. Signature with special case values r=-1 and s=n - 1 */ + {0, 0, 6, 23929, 40, 0 }, + /* tcId: 185. Signature with special case values r=-1 and s=n + 1 */ + {0, 0, 6, 23969, 40, 0 }, + /* tcId: 186. Signature with special case values r=-1 and s=p */ + {0, 0, 6, 24009, 40, 0 }, + /* tcId: 187. Signature with special case values r=-1 and s=p + 1 */ + {0, 0, 6, 24049, 40, 0 }, + /* tcId: 188. Signature with special case values r=n and s=0 */ + {0, 0, 6, 24089, 40, 0 }, + /* tcId: 189. Signature with special case values r=n and s=1 */ + {0, 0, 6, 24129, 40, 0 }, + /* tcId: 190. Signature with special case values r=n and s=-1 */ + {0, 0, 6, 24169, 40, 0 }, + /* tcId: 191. Signature with special case values r=n and s=n */ + {0, 0, 6, 24209, 72, 0 }, + /* tcId: 192. Signature with special case values r=n and s=n - 1 */ + {0, 0, 6, 24281, 72, 0 }, + /* tcId: 193. Signature with special case values r=n and s=n + 1 */ + {0, 0, 6, 24353, 72, 0 }, + /* tcId: 194. Signature with special case values r=n and s=p */ + {0, 0, 6, 24425, 72, 0 }, + /* tcId: 195. Signature with special case values r=n and s=p + 1 */ + {0, 0, 6, 24497, 72, 0 }, + /* tcId: 196. Signature with special case values r=n - 1 and s=0 */ + {0, 0, 6, 24569, 40, 0 }, + /* tcId: 197. Signature with special case values r=n - 1 and s=1 */ + {0, 0, 6, 24609, 40, 0 }, + /* tcId: 198. Signature with special case values r=n - 1 and s=-1 */ + {0, 0, 6, 24649, 40, 0 }, + /* tcId: 199. Signature with special case values r=n - 1 and s=n */ + {0, 0, 6, 24689, 72, 0 }, + /* tcId: 200. Signature with special case values r=n - 1 and s=n - 1 */ + {0, 0, 6, 24761, 72, 0 }, + /* tcId: 201. Signature with special case values r=n - 1 and s=n + 1 */ + {0, 0, 6, 24833, 72, 0 }, + /* tcId: 202. Signature with special case values r=n - 1 and s=p */ + {0, 0, 6, 24905, 72, 0 }, + /* tcId: 203. Signature with special case values r=n - 1 and s=p + 1 */ + {0, 0, 6, 24977, 72, 0 }, + /* tcId: 204. Signature with special case values r=n + 1 and s=0 */ + {0, 0, 6, 25049, 40, 0 }, + /* tcId: 205. Signature with special case values r=n + 1 and s=1 */ + {0, 0, 6, 25089, 40, 0 }, + /* tcId: 206. Signature with special case values r=n + 1 and s=-1 */ + {0, 0, 6, 25129, 40, 0 }, + /* tcId: 207. Signature with special case values r=n + 1 and s=n */ + {0, 0, 6, 25169, 72, 0 }, + /* tcId: 208. Signature with special case values r=n + 1 and s=n - 1 */ + {0, 0, 6, 25241, 72, 0 }, + /* tcId: 209. Signature with special case values r=n + 1 and s=n + 1 */ + {0, 0, 6, 25313, 72, 0 }, + /* tcId: 210. Signature with special case values r=n + 1 and s=p */ + {0, 0, 6, 25385, 72, 0 }, + /* tcId: 211. Signature with special case values r=n + 1 and s=p + 1 */ + {0, 0, 6, 25457, 72, 0 }, + /* tcId: 212. Signature with special case values r=p and s=0 */ + {0, 0, 6, 25529, 40, 0 }, + /* tcId: 213. Signature with special case values r=p and s=1 */ + {0, 0, 6, 25569, 40, 0 }, + /* tcId: 214. Signature with special case values r=p and s=-1 */ + {0, 0, 6, 25609, 40, 0 }, + /* tcId: 215. Signature with special case values r=p and s=n */ + {0, 0, 6, 25649, 72, 0 }, + /* tcId: 216. Signature with special case values r=p and s=n - 1 */ + {0, 0, 6, 25721, 72, 0 }, + /* tcId: 217. Signature with special case values r=p and s=n + 1 */ + {0, 0, 6, 25793, 72, 0 }, + /* tcId: 218. Signature with special case values r=p and s=p */ + {0, 0, 6, 25865, 72, 0 }, + /* tcId: 219. Signature with special case values r=p and s=p + 1 */ + {0, 0, 6, 25937, 72, 0 }, + /* tcId: 220. Signature with special case values r=p + 1 and s=0 */ + {0, 0, 6, 26009, 40, 0 }, + /* tcId: 221. Signature with special case values r=p + 1 and s=1 */ + {0, 0, 6, 26049, 40, 0 }, + /* tcId: 222. Signature with special case values r=p + 1 and s=-1 */ + {0, 0, 6, 26089, 40, 0 }, + /* tcId: 223. Signature with special case values r=p + 1 and s=n */ + {0, 0, 6, 26129, 72, 0 }, + /* tcId: 224. Signature with special case values r=p + 1 and s=n - 1 */ + {0, 0, 6, 26201, 72, 0 }, + /* tcId: 225. Signature with special case values r=p + 1 and s=n + 1 */ + {0, 0, 6, 26273, 72, 0 }, + /* tcId: 226. Signature with special case values r=p + 1 and s=p */ + {0, 0, 6, 26345, 72, 0 }, + /* tcId: 227. Signature with special case values r=p + 1 and s=p + 1 */ + {0, 0, 6, 26417, 72, 0 }, + /* tcId: 228. Signature encoding contains incorrect types: r=0, s=0.25 */ + {0, 0, 6, 26489, 10, 0 }, + /* tcId: 229. Signature encoding contains incorrect types: r=0, s=nan */ + {0, 0, 6, 26499, 8, 0 }, + /* tcId: 230. Signature encoding contains incorrect types: r=0, s=True */ + {0, 0, 6, 26507, 8, 0 }, + /* tcId: 231. Signature encoding contains incorrect types: r=0, s=False */ + {0, 0, 6, 26515, 8, 0 }, + /* tcId: 232. Signature encoding contains incorrect types: r=0, s=Null */ + {0, 0, 6, 26523, 7, 0 }, + /* tcId: 233. Signature encoding contains incorrect types: r=0, s=empyt UTF-8 string */ + {0, 0, 6, 26530, 7, 0 }, + /* tcId: 234. Signature encoding contains incorrect types: r=0, s="0" */ + {0, 0, 6, 26537, 8, 0 }, + /* tcId: 235. Signature encoding contains incorrect types: r=0, s=empty list */ + {0, 0, 6, 26545, 7, 0 }, + /* tcId: 236. Signature encoding contains incorrect types: r=0, s=list containing 0 */ + {0, 0, 6, 26552, 10, 0 }, + /* tcId: 237. Signature encoding contains incorrect types: r=1, s=0.25 */ + {0, 0, 6, 26562, 10, 0 }, + /* tcId: 238. Signature encoding contains incorrect types: r=1, s=nan */ + {0, 0, 6, 26572, 8, 0 }, + /* tcId: 239. Signature encoding contains incorrect types: r=1, s=True */ + {0, 0, 6, 26580, 8, 0 }, + /* tcId: 240. Signature encoding contains incorrect types: r=1, s=False */ + {0, 0, 6, 26588, 8, 0 }, + /* tcId: 241. Signature encoding contains incorrect types: r=1, s=Null */ + {0, 0, 6, 26596, 7, 0 }, + /* tcId: 242. Signature encoding contains incorrect types: r=1, s=empyt UTF-8 string */ + {0, 0, 6, 26603, 7, 0 }, + /* tcId: 243. Signature encoding contains incorrect types: r=1, s="0" */ + {0, 0, 6, 26610, 8, 0 }, + /* tcId: 244. Signature encoding contains incorrect types: r=1, s=empty list */ + {0, 0, 6, 26618, 7, 0 }, + /* tcId: 245. Signature encoding contains incorrect types: r=1, s=list containing 0 */ + {0, 0, 6, 26625, 10, 0 }, + /* tcId: 246. Signature encoding contains incorrect types: r=-1, s=0.25 */ + {0, 0, 6, 26635, 10, 0 }, + /* tcId: 247. Signature encoding contains incorrect types: r=-1, s=nan */ + {0, 0, 6, 26645, 8, 0 }, + /* tcId: 248. Signature encoding contains incorrect types: r=-1, s=True */ + {0, 0, 6, 26653, 8, 0 }, + /* tcId: 249. Signature encoding contains incorrect types: r=-1, s=False */ + {0, 0, 6, 26661, 8, 0 }, + /* tcId: 250. Signature encoding contains incorrect types: r=-1, s=Null */ + {0, 0, 6, 26669, 7, 0 }, + /* tcId: 251. Signature encoding contains incorrect types: r=-1, s=empyt UTF-8 string */ + {0, 0, 6, 26676, 7, 0 }, + /* tcId: 252. Signature encoding contains incorrect types: r=-1, s="0" */ + {0, 0, 6, 26683, 8, 0 }, + /* tcId: 253. Signature encoding contains incorrect types: r=-1, s=empty list */ + {0, 0, 6, 26691, 7, 0 }, + /* tcId: 254. Signature encoding contains incorrect types: r=-1, s=list containing 0 */ + {0, 0, 6, 26698, 10, 0 }, + /* tcId: 255. Signature encoding contains incorrect types: r=n, s=0.25 */ + {0, 0, 6, 26708, 42, 0 }, + /* tcId: 256. Signature encoding contains incorrect types: r=n, s=nan */ + {0, 0, 6, 26750, 40, 0 }, + /* tcId: 257. Signature encoding contains incorrect types: r=n, s=True */ + {0, 0, 6, 26790, 40, 0 }, + /* tcId: 258. Signature encoding contains incorrect types: r=n, s=False */ + {0, 0, 6, 26830, 40, 0 }, + /* tcId: 259. Signature encoding contains incorrect types: r=n, s=Null */ + {0, 0, 6, 26870, 39, 0 }, + /* tcId: 260. Signature encoding contains incorrect types: r=n, s=empyt UTF-8 string */ + {0, 0, 6, 26909, 39, 0 }, + /* tcId: 261. Signature encoding contains incorrect types: r=n, s="0" */ + {0, 0, 6, 26948, 40, 0 }, + /* tcId: 262. Signature encoding contains incorrect types: r=n, s=empty list */ + {0, 0, 6, 26988, 39, 0 }, + /* tcId: 263. Signature encoding contains incorrect types: r=n, s=list containing 0 */ + {0, 0, 6, 27027, 42, 0 }, + /* tcId: 264. Signature encoding contains incorrect types: r=p, s=0.25 */ + {0, 0, 6, 27069, 42, 0 }, + /* tcId: 265. Signature encoding contains incorrect types: r=p, s=nan */ + {0, 0, 6, 27111, 40, 0 }, + /* tcId: 266. Signature encoding contains incorrect types: r=p, s=True */ + {0, 0, 6, 27151, 40, 0 }, + /* tcId: 267. Signature encoding contains incorrect types: r=p, s=False */ + {0, 0, 6, 27191, 40, 0 }, + /* tcId: 268. Signature encoding contains incorrect types: r=p, s=Null */ + {0, 0, 6, 27231, 39, 0 }, + /* tcId: 269. Signature encoding contains incorrect types: r=p, s=empyt UTF-8 string */ + {0, 0, 6, 27270, 39, 0 }, + /* tcId: 270. Signature encoding contains incorrect types: r=p, s="0" */ + {0, 0, 6, 27309, 40, 0 }, + /* tcId: 271. Signature encoding contains incorrect types: r=p, s=empty list */ + {0, 0, 6, 27349, 39, 0 }, + /* tcId: 272. Signature encoding contains incorrect types: r=p, s=list containing 0 */ + {0, 0, 6, 27388, 42, 0 }, + /* tcId: 273. Signature encoding contains incorrect types: r=0.25, s=0.25 */ + {0, 0, 6, 27430, 12, 0 }, + /* tcId: 274. Signature encoding contains incorrect types: r=nan, s=nan */ + {0, 0, 6, 27442, 8, 0 }, + /* tcId: 275. Signature encoding contains incorrect types: r=True, s=True */ + {0, 0, 6, 27450, 8, 0 }, + /* tcId: 276. Signature encoding contains incorrect types: r=False, s=False */ + {0, 0, 6, 27458, 8, 0 }, + /* tcId: 277. Signature encoding contains incorrect types: r=Null, s=Null */ + {0, 0, 6, 27466, 6, 0 }, + /* tcId: 278. Signature encoding contains incorrect types: r=empyt UTF-8 string, s=empyt UTF-8 string */ + {0, 0, 6, 27472, 6, 0 }, + /* tcId: 279. Signature encoding contains incorrect types: r="0", s="0" */ + {0, 0, 6, 27478, 8, 0 }, + /* tcId: 280. Signature encoding contains incorrect types: r=empty list, s=empty list */ + {0, 0, 6, 27486, 6, 0 }, + /* tcId: 281. Signature encoding contains incorrect types: r=list containing 0, s=list containing 0 */ + {0, 0, 6, 27492, 12, 0 }, + /* tcId: 282. Signature encoding contains incorrect types: r=0.25, s=0 */ + {0, 0, 6, 27504, 10, 0 }, + /* tcId: 283. Signature encoding contains incorrect types: r=nan, s=0 */ + {0, 0, 6, 27514, 8, 0 }, + /* tcId: 284. Signature encoding contains incorrect types: r=True, s=0 */ + {0, 0, 6, 27522, 8, 0 }, + /* tcId: 285. Signature encoding contains incorrect types: r=False, s=0 */ + {0, 0, 6, 27530, 8, 0 }, + /* tcId: 286. Signature encoding contains incorrect types: r=Null, s=0 */ + {0, 0, 6, 27538, 7, 0 }, + /* tcId: 287. Signature encoding contains incorrect types: r=empyt UTF-8 string, s=0 */ + {0, 0, 6, 27545, 7, 0 }, + /* tcId: 288. Signature encoding contains incorrect types: r="0", s=0 */ + {0, 0, 6, 27552, 8, 0 }, + /* tcId: 289. Signature encoding contains incorrect types: r=empty list, s=0 */ + {0, 0, 6, 27560, 7, 0 }, + /* tcId: 290. Signature encoding contains incorrect types: r=list containing 0, s=0 */ + {0, 0, 6, 27567, 10, 0 }, + /* tcId: 291. Edge case for Shamir multiplication */ + {0, 6, 5, 27577, 71, 1 }, + /* tcId: 292. special case hash */ + {0, 11, 9, 27648, 71, 1 }, + /* tcId: 293. special case hash */ + {0, 20, 10, 27719, 70, 1 }, + /* tcId: 294. special case hash */ + {0, 30, 11, 27789, 71, 1 }, + /* tcId: 295. special case hash */ + {0, 41, 10, 27860, 71, 1 }, + /* tcId: 296. special case hash */ + {0, 51, 10, 27931, 70, 1 }, + /* tcId: 297. special case hash */ + {0, 61, 10, 28001, 71, 1 }, + /* tcId: 298. special case hash */ + {0, 71, 9, 28072, 70, 1 }, + /* tcId: 299. special case hash */ + {0, 80, 10, 28142, 71, 1 }, + /* tcId: 300. special case hash */ + {0, 90, 10, 28213, 71, 1 }, + /* tcId: 301. special case hash */ + {0, 100, 10, 28284, 71, 1 }, + /* tcId: 302. special case hash */ + {0, 110, 10, 28355, 71, 1 }, + /* tcId: 303. special case hash */ + {0, 120, 11, 28426, 70, 1 }, + /* tcId: 304. special case hash */ + {0, 131, 10, 28496, 71, 1 }, + /* tcId: 305. special case hash */ + {0, 141, 10, 28567, 71, 1 }, + /* tcId: 306. special case hash */ + {0, 151, 10, 28638, 70, 1 }, + /* tcId: 307. special case hash */ + {0, 161, 10, 28708, 71, 1 }, + /* tcId: 308. special case hash */ + {0, 171, 10, 28779, 71, 1 }, + /* tcId: 309. special case hash */ + {0, 181, 10, 28850, 70, 1 }, + /* tcId: 310. special case hash */ + {0, 191, 10, 28920, 71, 1 }, + /* tcId: 311. special case hash */ + {0, 201, 10, 28991, 71, 1 }, + /* tcId: 312. special case hash */ + {0, 211, 10, 29062, 71, 1 }, + /* tcId: 313. special case hash */ + {0, 221, 10, 29133, 70, 1 }, + /* tcId: 314. special case hash */ + {0, 231, 10, 29203, 71, 1 }, + /* tcId: 315. special case hash */ + {0, 241, 10, 29274, 71, 1 }, + /* tcId: 316. special case hash */ + {0, 251, 10, 29345, 71, 1 }, + /* tcId: 317. special case hash */ + {0, 261, 11, 29416, 71, 1 }, + /* tcId: 318. special case hash */ + {0, 272, 11, 29487, 70, 1 }, + /* tcId: 319. special case hash */ + {0, 283, 9, 29557, 71, 1 }, + /* tcId: 320. special case hash */ + {0, 292, 9, 29628, 71, 1 }, + /* tcId: 321. special case hash */ + {0, 301, 10, 29699, 71, 1 }, + /* tcId: 322. special case hash */ + {0, 311, 10, 29770, 71, 1 }, + /* tcId: 323. special case hash */ + {0, 321, 10, 29841, 70, 1 }, + /* tcId: 324. special case hash */ + {0, 331, 10, 29911, 70, 1 }, + /* tcId: 325. special case hash */ + {0, 341, 10, 29981, 71, 1 }, + /* tcId: 326. special case hash */ + {0, 351, 9, 30052, 70, 1 }, + /* tcId: 327. special case hash */ + {0, 360, 10, 30122, 70, 1 }, + /* tcId: 328. special case hash */ + {0, 370, 10, 30192, 70, 1 }, + /* tcId: 329. special case hash */ + {0, 380, 10, 30262, 70, 1 }, + /* tcId: 330. special case hash */ + {0, 390, 9, 30332, 71, 1 }, + /* tcId: 331. special case hash */ + {0, 399, 11, 30403, 70, 1 }, + /* tcId: 332. special case hash */ + {0, 410, 9, 30473, 71, 1 }, + /* tcId: 333. special case hash */ + {0, 419, 9, 30544, 71, 1 }, + /* tcId: 334. special case hash */ + {0, 428, 11, 30615, 70, 1 }, + /* tcId: 335. special case hash */ + {0, 439, 8, 30685, 71, 1 }, + /* tcId: 336. special case hash */ + {0, 447, 10, 30756, 70, 1 }, + /* tcId: 337. special case hash */ + {0, 457, 10, 30826, 71, 1 }, + /* tcId: 338. special case hash */ + {0, 467, 10, 30897, 70, 1 }, + /* tcId: 339. special case hash */ + {0, 477, 10, 30967, 70, 1 }, + /* tcId: 340. special case hash */ + {0, 487, 10, 31037, 70, 1 }, + /* tcId: 341. special case hash */ + {0, 497, 10, 31107, 71, 1 }, + /* tcId: 342. special case hash */ + {0, 507, 10, 31178, 70, 1 }, + /* tcId: 343. special case hash */ + {0, 517, 10, 31248, 70, 1 }, + /* tcId: 344. special case hash */ + {0, 527, 10, 31318, 71, 1 }, + /* tcId: 345. special case hash */ + {0, 537, 9, 31389, 70, 1 }, + /* tcId: 346. k*G has a large x-coordinate */ + {65, 0, 6, 31459, 24, 1 }, + /* tcId: 347. r too large */ + {65, 0, 6, 31483, 40, 0 }, + /* tcId: 348. r,s are large */ + {130, 0, 6, 31523, 40, 1 }, + /* tcId: 349. r and s^-1 have a large Hamming weight */ + {195, 0, 6, 31563, 70, 1 }, + /* tcId: 350. r and s^-1 have a large Hamming weight */ + {260, 0, 6, 31633, 70, 1 }, + /* tcId: 351. small r and s */ + {325, 0, 6, 31703, 8, 1 }, + /* tcId: 352. small r and s */ + {390, 0, 6, 31711, 8, 1 }, + /* tcId: 353. small r and s */ + {455, 0, 6, 31719, 8, 1 }, + /* tcId: 354. small r and s */ + {520, 0, 6, 31727, 8, 1 }, + /* tcId: 355. small r and s */ + {585, 0, 6, 31735, 8, 1 }, + /* tcId: 356. small r and s */ + {650, 0, 6, 31743, 8, 1 }, + /* tcId: 357. r is larger than n */ + {650, 0, 6, 31751, 40, 0 }, + /* tcId: 358. s is larger than n */ + {715, 0, 6, 31791, 10, 0 }, + /* tcId: 359. small r and s^-1 */ + {780, 0, 6, 31801, 40, 1 }, + /* tcId: 360. smallish r and s^-1 */ + {845, 0, 6, 31841, 45, 1 }, + /* tcId: 361. 100-bit r and small s^-1 */ + {910, 0, 6, 31886, 51, 1 }, + /* tcId: 362. small r and 100 bit s^-1 */ + {975, 0, 6, 31937, 40, 1 }, + /* tcId: 363. 100-bit r and s^-1 */ + {1040, 0, 6, 31977, 51, 1 }, + /* tcId: 364. r and s^-1 are close to n */ + {1105, 0, 6, 32028, 71, 1 }, + /* tcId: 365. r and s are 64-bit integer */ + {1170, 0, 6, 32099, 24, 1 }, + /* tcId: 366. r and s are 100-bit integer */ + {1235, 0, 6, 32123, 32, 1 }, + /* tcId: 367. r and s are 128-bit integer */ + {1300, 0, 6, 32155, 40, 1 }, + /* tcId: 368. r and s are 160-bit integer */ + {1365, 0, 6, 32195, 48, 1 }, + /* tcId: 369. s == 1 */ + {1430, 0, 6, 32243, 39, 1 }, + /* tcId: 370. s == 0 */ + {1430, 0, 6, 32282, 39, 0 }, + /* tcId: 371. edge case modular inverse */ + {1495, 0, 6, 32321, 70, 1 }, + /* tcId: 372. edge case modular inverse */ + {1560, 0, 6, 32391, 70, 1 }, + /* tcId: 373. edge case modular inverse */ + {1625, 0, 6, 32461, 70, 1 }, + /* tcId: 374. edge case modular inverse */ + {1690, 0, 6, 32531, 70, 1 }, + /* tcId: 375. edge case modular inverse */ + {1755, 0, 6, 32601, 70, 1 }, + /* tcId: 376. edge case modular inverse */ + {1820, 0, 6, 32671, 70, 1 }, + /* tcId: 377. edge case modular inverse */ + {1885, 0, 6, 32741, 70, 1 }, + /* tcId: 378. edge case modular inverse */ + {1950, 0, 6, 32811, 70, 1 }, + /* tcId: 379. edge case modular inverse */ + {2015, 0, 6, 32881, 70, 1 }, + /* tcId: 380. edge case modular inverse */ + {2080, 0, 6, 32951, 70, 1 }, + /* tcId: 381. edge case modular inverse */ + {2145, 0, 6, 33021, 70, 1 }, + /* tcId: 382. edge case modular inverse */ + {2210, 0, 6, 33091, 70, 1 }, + /* tcId: 383. edge case modular inverse */ + {2275, 0, 6, 33161, 70, 1 }, + /* tcId: 384. edge case modular inverse */ + {2340, 0, 6, 33231, 70, 1 }, + /* tcId: 385. edge case modular inverse */ + {2405, 0, 6, 33301, 70, 1 }, + /* tcId: 386. point at infinity during verify */ + {2470, 0, 6, 33371, 70, 0 }, + /* tcId: 387. edge case for signature malleability */ + {2535, 0, 6, 33441, 70, 1 }, + /* tcId: 388. edge case for signature malleability */ + {2600, 0, 6, 33511, 70, 0 }, + /* tcId: 389. u1 == 1 */ + {2665, 0, 6, 33581, 70, 1 }, + /* tcId: 390. u1 == n - 1 */ + {2730, 0, 6, 33651, 70, 1 }, + /* tcId: 391. u2 == 1 */ + {2795, 0, 6, 33721, 70, 1 }, + /* tcId: 392. u2 == n - 1 */ + {2860, 0, 6, 33791, 70, 1 }, + /* tcId: 393. edge case for u1 */ + {2925, 0, 6, 33861, 70, 1 }, + /* tcId: 394. edge case for u1 */ + {2990, 0, 6, 33931, 70, 1 }, + /* tcId: 395. edge case for u1 */ + {3055, 0, 6, 34001, 70, 1 }, + /* tcId: 396. edge case for u1 */ + {3120, 0, 6, 34071, 70, 1 }, + /* tcId: 397. edge case for u1 */ + {3185, 0, 6, 34141, 70, 1 }, + /* tcId: 398. edge case for u1 */ + {3250, 0, 6, 34211, 70, 1 }, + /* tcId: 399. edge case for u1 */ + {3315, 0, 6, 34281, 70, 1 }, + /* tcId: 400. edge case for u1 */ + {3380, 0, 6, 34351, 70, 1 }, + /* tcId: 401. edge case for u1 */ + {3445, 0, 6, 34421, 70, 1 }, + /* tcId: 402. edge case for u1 */ + {3510, 0, 6, 34491, 70, 1 }, + /* tcId: 403. edge case for u1 */ + {3575, 0, 6, 34561, 70, 1 }, + /* tcId: 404. edge case for u1 */ + {3640, 0, 6, 34631, 70, 1 }, + /* tcId: 405. edge case for u1 */ + {3705, 0, 6, 34701, 70, 1 }, + /* tcId: 406. edge case for u1 */ + {3770, 0, 6, 34771, 70, 1 }, + /* tcId: 407. edge case for u1 */ + {3835, 0, 6, 34841, 70, 1 }, + /* tcId: 408. edge case for u2 */ + {3900, 0, 6, 34911, 70, 1 }, + /* tcId: 409. edge case for u2 */ + {3965, 0, 6, 34981, 70, 1 }, + /* tcId: 410. edge case for u2 */ + {4030, 0, 6, 35051, 70, 1 }, + /* tcId: 411. edge case for u2 */ + {4095, 0, 6, 35121, 70, 1 }, + /* tcId: 412. edge case for u2 */ + {4160, 0, 6, 35191, 70, 1 }, + /* tcId: 413. edge case for u2 */ + {4225, 0, 6, 35261, 69, 1 }, + /* tcId: 414. edge case for u2 */ + {4290, 0, 6, 35330, 70, 1 }, + /* tcId: 415. edge case for u2 */ + {4355, 0, 6, 35400, 70, 1 }, + /* tcId: 416. edge case for u2 */ + {4420, 0, 6, 35470, 70, 1 }, + /* tcId: 417. edge case for u2 */ + {4485, 0, 6, 35540, 70, 1 }, + /* tcId: 418. edge case for u2 */ + {4550, 0, 6, 35610, 70, 1 }, + /* tcId: 419. edge case for u2 */ + {4615, 0, 6, 35680, 70, 1 }, + /* tcId: 420. edge case for u2 */ + {4680, 0, 6, 35750, 70, 1 }, + /* tcId: 421. edge case for u2 */ + {4745, 0, 6, 35820, 70, 1 }, + /* tcId: 422. edge case for u2 */ + {4810, 0, 6, 35890, 70, 1 }, + /* tcId: 423. point duplication during verification */ + {4875, 0, 6, 35960, 70, 1 }, + /* tcId: 424. duplication bug */ + {4940, 0, 6, 36030, 70, 0 }, + /* tcId: 425. comparison with point at infinity */ + {5005, 0, 6, 36100, 70, 0 }, + /* tcId: 426. extreme value for k and edgecase s */ + {5070, 0, 6, 36170, 71, 1 }, + /* tcId: 427. extreme value for k and s^-1 */ + {5135, 0, 6, 36241, 71, 1 }, + /* tcId: 428. extreme value for k and s^-1 */ + {5200, 0, 6, 36312, 71, 1 }, + /* tcId: 429. extreme value for k and s^-1 */ + {5265, 0, 6, 36383, 71, 1 }, + /* tcId: 430. extreme value for k and s^-1 */ + {5330, 0, 6, 36454, 71, 1 }, + /* tcId: 431. extreme value for k */ + {5395, 0, 6, 36525, 71, 1 }, + /* tcId: 432. extreme value for k and edgecase s */ + {5460, 0, 6, 36596, 70, 1 }, + /* tcId: 433. extreme value for k and s^-1 */ + {5525, 0, 6, 36666, 70, 1 }, + /* tcId: 434. extreme value for k and s^-1 */ + {5590, 0, 6, 36736, 70, 1 }, + /* tcId: 435. extreme value for k and s^-1 */ + {5655, 0, 6, 36806, 70, 1 }, + /* tcId: 436. extreme value for k and s^-1 */ + {5720, 0, 6, 36876, 70, 1 }, + /* tcId: 437. extreme value for k */ + {5785, 0, 6, 36946, 70, 1 }, + /* tcId: 438. public key shares x-coordinate with generator */ + {5850, 0, 6, 37016, 71, 0 }, + /* tcId: 439. public key shares x-coordinate with generator */ + {5850, 0, 6, 37087, 70, 0 }, + /* tcId: 440. public key shares x-coordinate with generator */ + {5915, 0, 6, 37157, 71, 0 }, + /* tcId: 441. public key shares x-coordinate with generator */ + {5915, 0, 6, 37228, 70, 0 }, + /* tcId: 442. pseudorandom signature */ + {5980, 546, 0, 37298, 71, 1 }, + /* tcId: 443. pseudorandom signature */ + {5980, 546, 3, 37369, 70, 1 }, + /* tcId: 444. pseudorandom signature */ + {5980, 0, 6, 37439, 71, 1 }, + /* tcId: 445. pseudorandom signature */ + {5980, 549, 20, 37510, 70, 1 }, + /* tcId: 446. y-coordinate of the public key is small */ + {6045, 569, 7, 37580, 70, 1 }, + /* tcId: 447. y-coordinate of the public key is small */ + {6045, 569, 7, 37650, 70, 1 }, + /* tcId: 448. y-coordinate of the public key is small */ + {6045, 569, 7, 37720, 71, 1 }, + /* tcId: 449. y-coordinate of the public key is large */ + {6110, 569, 7, 37791, 70, 1 }, + /* tcId: 450. y-coordinate of the public key is large */ + {6110, 569, 7, 37861, 71, 1 }, + /* tcId: 451. y-coordinate of the public key is large */ + {6110, 569, 7, 37932, 70, 1 }, + /* tcId: 452. x-coordinate of the public key is small */ + {6175, 569, 7, 38002, 70, 1 }, + /* tcId: 453. x-coordinate of the public key is small */ + {6175, 569, 7, 38072, 71, 1 }, + /* tcId: 454. x-coordinate of the public key is small */ + {6175, 569, 7, 38143, 71, 1 }, + /* tcId: 455. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38214, 70, 1 }, + /* tcId: 456. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38284, 71, 1 }, + /* tcId: 457. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38355, 71, 1 }, + /* tcId: 458. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38426, 70, 1 }, + /* tcId: 459. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38496, 71, 1 }, + /* tcId: 460. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38567, 71, 1 }, + /* tcId: 461. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38638, 70, 1 }, + /* tcId: 462. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38708, 70, 1 }, + /* tcId: 463. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38778, 71, 1 }, + +}; diff --git a/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json b/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json new file mode 100644 index 0000000000..9c90747993 --- /dev/null +++ b/src/secp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json @@ -0,0 +1,6360 @@ +{ + "algorithm" : "ECDSA", + "schema" : "ecdsa_bitcoin_verify_schema.json", + "generatorVersion" : "0.9rc5", + "numberOfTests" : 463, + "header" : [ + "Test vectors of type EcdsaBitcoinVerify are meant for the verification", + "of a ECDSA variant used for bitcoin, that add signature non-malleability." + ], + "notes" : { + "ArithmeticError" : { + "bugType" : "EDGE_CASE", + "description" : "Some implementations of ECDSA have arithmetic errors that occur when intermediate results have extreme values. This test vector has been constructed to test such occurences.", + "cves" : [ + "CVE-2017-18146" + ] + }, + "BerEncodedSignature" : { + "bugType" : "BER_ENCODING", + "description" : "ECDSA signatures are usually DER encoded. This signature contains valid values for r and s, but it uses alternative BER encoding.", + "effect" : "Accepting alternative BER encodings may be benign in some cases, or be an issue if protocol requires signature malleability.", + "cves" : [ + "CVE-2020-14966", + "CVE-2020-13822", + "CVE-2019-14859", + "CVE-2016-1000342" + ] + }, + "EdgeCasePublicKey" : { + "bugType" : "EDGE_CASE", + "description" : "The test vector uses a special case public key. " + }, + "EdgeCaseShamirMultiplication" : { + "bugType" : "EDGE_CASE", + "description" : "Shamir proposed a fast method for computing the sum of two scalar multiplications efficiently. This test vector has been constructed so that an intermediate result is the point at infinity if Shamir's method is used." + }, + "IntegerOverflow" : { + "bugType" : "CAN_OF_WORMS", + "description" : "The test vector contains an r and s that has been modified, so that the original value is restored if the implementation ignores the most significant bits.", + "effect" : "Without further analysis it is unclear if the modification can be used to forge signatures." + }, + "InvalidEncoding" : { + "bugType" : "CAN_OF_WORMS", + "description" : "ECDSA signatures are encoded using ASN.1. This test vector contains an incorrectly encoded signature. The test vector itself was generated from a valid signature by modifying its encoding.", + "effect" : "Without further analysis it is unclear if the modification can be used to forge signatures." + }, + "InvalidSignature" : { + "bugType" : "AUTH_BYPASS", + "description" : "The signature contains special case values such as r=0 and s=0. Buggy implementations may accept such values, if the implementation does not check boundaries and computes s^(-1) == 0.", + "effect" : "Accepting such signatures can have the effect that an adversary can forge signatures without even knowning the message to sign.", + "cves" : [ + "CVE-2022-21449", + "CVE-2021-43572", + "CVE-2022-24884" + ] + }, + "InvalidTypesInSignature" : { + "bugType" : "AUTH_BYPASS", + "description" : "The signature contains invalid types. Dynamic typed languages sometime coerce such values of different types into integers. If an implementation is careless and has additional bugs, such as not checking integer boundaries then it may be possible that such signatures are accepted.", + "effect" : "Accepting such signatures can have the effect that an adversary can forge signatures without even knowning the message to sign.", + "cves" : [ + "CVE-2022-21449" + ] + }, + "ModifiedInteger" : { + "bugType" : "CAN_OF_WORMS", + "description" : "The test vector contains an r and s that has been modified. The goal is to check for arithmetic errors.", + "effect" : "Without further analysis it is unclear if the modification can be used to forge signatures." + }, + "ModifiedSignature" : { + "bugType" : "CAN_OF_WORMS", + "description" : "The test vector contains an invalid signature that was generated from a valid signature by modifying it.", + "effect" : "Without further analysis it is unclear if the modification can be used to forge signatures." + }, + "ModularInverse" : { + "bugType" : "EDGE_CASE", + "description" : "The test vectors contains a signature where computing the modular inverse of s hits an edge case.", + "effect" : "While the signature in this test vector is constructed and similar cases are unlikely to occur, it is important to determine if the underlying arithmetic error can be used to forge signatures.", + "cves" : [ + "CVE-2019-0865" + ] + }, + "PointDuplication" : { + "bugType" : "EDGE_CASE", + "description" : "Some implementations of ECDSA do not handle duplication and points at infinity correctly. This is a test vector that has been specially crafted to check for such an omission.", + "cves" : [ + "2020-12607", + "CVE-2015-2730" + ] + }, + "RangeCheck" : { + "bugType" : "CAN_OF_WORMS", + "description" : "The test vector contains an r and s that has been modified. By adding or subtracting the order of the group (or other values) the test vector checks whether signature verification verifies the range of r and s.", + "effect" : "Without further analysis it is unclear if the modification can be used to forge signatures." + }, + "SignatureMalleabilityBitcoin" : { + "bugType" : "SIGNATURE_MALLEABILITY", + "description" : "\"BitCoins\"-curves are curves where signature malleability can be a serious issue. An implementation should only accept a signature s where s < n/2. If an implementation is not meant for uses cases that require signature malleability then this implemenation should be tested with another set of test vectors.", + "effect" : "In bitcoin exchanges, it may be used to make a double deposits or double withdrawals", + "links" : [ + "https://en.bitcoin.it/wiki/Transaction_malleability", + "https://en.bitcoinwiki.org/wiki/Transaction_Malleability" + ] + }, + "SmallRandS" : { + "bugType" : "EDGE_CASE", + "description" : "The test vectors contains a signature where both r and s are small integers. Some libraries cannot verify such signatures.", + "effect" : "While the signature in this test vector is constructed and similar cases are unlikely to occur, it is important to determine if the underlying arithmetic error can be used to forge signatures.", + "cves" : [ + "2020-13895" + ] + }, + "SpecialCaseHash" : { + "bugType" : "EDGE_CASE", + "description" : "The test vector contains a signature where the hash of the message is a special case, e.g., contains a long run of 0 or 1 bits." + }, + "ValidSignature" : { + "bugType" : "BASIC", + "description" : "The test vector contains a valid signature that was generated pseudorandomly. Such signatures should not fail to verify unless some of the parameters (e.g. curve or hash function) are not supported." + } + }, + "testGroups" : [ + { + "type" : "EcdsaBitcoinVerify", + "publicKey" : { + "type" : "EcPublicKey", + "curve" : "secp256k1", + "keySize" : 256, + "uncompressed" : "04b838ff44e5bc177bf21189d0766082fc9d843226887fc9760371100b7ee20a6ff0c9d75bfba7b31a6bca1974496eeb56de357071955d83c4b1badaa0b21832e9", + "wx" : "00b838ff44e5bc177bf21189d0766082fc9d843226887fc9760371100b7ee20a6f", + "wy" : "00f0c9d75bfba7b31a6bca1974496eeb56de357071955d83c4b1badaa0b21832e9" + }, + "publicKeyDer" : "3056301006072a8648ce3d020106052b8104000a03420004b838ff44e5bc177bf21189d0766082fc9d843226887fc9760371100b7ee20a6ff0c9d75bfba7b31a6bca1974496eeb56de357071955d83c4b1badaa0b21832e9", + "publicKeyPem" : "-----BEGIN PUBLIC KEY-----\nMFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAEuDj/ROW8F3vyEYnQdmCC/J2EMiaIf8l2\nA3EQC37iCm/wyddb+6ezGmvKGXRJbutW3jVwcZVdg8Sxutqgshgy6Q==\n-----END PUBLIC KEY-----\n", + "sha" : 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"3045022100f6b0e2f6fe020cf7c0c20137434344ed7add6c4be51861e2d14cbda472a6ffb402206416c8dd3e5c5282b306e8dc8ff34ab64cc99549232d678d714402eb6ca7aa0f", + "result" : "valid" + }, + { + "tcId" : 457, + "comment" : "x-coordinate of the public key has many trailing 1's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "3045022100db09d8460f05eff23bc7e436b67da563fa4b4edb58ac24ce201fa8a358125057022046da116754602940c8999c8d665f786c50f5772c0a3cdbda075e77eabc64df16", + "result" : "valid" + } + ] + }, + { + "type" : "EcdsaBitcoinVerify", + "publicKey" : { + "type" : "EcPublicKey", + "curve" : "secp256k1", + "keySize" : 256, + "uncompressed" : "04d12e6c66b67734c3c84d2601cf5d35dc097e27637f0aca4a4fdb74b6aadd3bb93f5bdff88bd5736df898e699006ed750f11cf07c5866cd7ad70c7121ffffffff", + "wx" : "00d12e6c66b67734c3c84d2601cf5d35dc097e27637f0aca4a4fdb74b6aadd3bb9", + "wy" : "3f5bdff88bd5736df898e699006ed750f11cf07c5866cd7ad70c7121ffffffff" + }, + "publicKeyDer" : "3056301006072a8648ce3d020106052b8104000a03420004d12e6c66b67734c3c84d2601cf5d35dc097e27637f0aca4a4fdb74b6aadd3bb93f5bdff88bd5736df898e699006ed750f11cf07c5866cd7ad70c7121ffffffff", + "publicKeyPem" : "-----BEGIN PUBLIC KEY-----\nMFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAE0S5sZrZ3NMPITSYBz1013Al+J2N/CspK\nT9t0tqrdO7k/W9/4i9VzbfiY5pkAbtdQ8RzwfFhmzXrXDHEh/////w==\n-----END PUBLIC KEY-----\n", + "sha" : "SHA-256", + "tests" : [ + { + "tcId" : 458, + "comment" : "y-coordinate of the public key has many trailing 1's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "30440220592c41e16517f12fcabd98267674f974b588e9f35d35406c1a7bb2ed1d19b7b802203e65a06bd9f83caaeb7b00f2368d7e0dece6b12221269a9b5b765198f840a3a1", + "result" : "valid" + }, + { + "tcId" : 459, + "comment" : "y-coordinate of the public key has many trailing 1's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "3045022100be0d70887d5e40821a61b68047de4ea03debfdf51cdf4d4b195558b959a032b202207d994b2d8f1dbbeb13534eb3f6e5dccd85f5c4133c27d9e64271b1826ce1f67d", + "result" : "valid" + }, + { + "tcId" : 460, + "comment" : "y-coordinate of the public key has many trailing 1's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "3045022100fae92dfcb2ee392d270af3a5739faa26d4f97bfd39ed3cbee4d29e26af3b206a02206c9ba37f9faa6a1fd3f65f23b4e853d4692a7274240a12db7ba3884830630d16", + "result" : "valid" + } + ] + }, + { + "type" : "EcdsaBitcoinVerify", + "publicKey" : { + "type" : "EcPublicKey", + "curve" : "secp256k1", + "keySize" : 256, + "uncompressed" : "046d4a7f60d4774a4f0aa8bbdedb953c7eea7909407e3164755664bc2800000000e659d34e4df38d9e8c9eaadfba36612c769195be86c77aac3f36e78b538680fb", + "wx" : "6d4a7f60d4774a4f0aa8bbdedb953c7eea7909407e3164755664bc2800000000", + "wy" : "00e659d34e4df38d9e8c9eaadfba36612c769195be86c77aac3f36e78b538680fb" + }, + "publicKeyDer" : "3056301006072a8648ce3d020106052b8104000a034200046d4a7f60d4774a4f0aa8bbdedb953c7eea7909407e3164755664bc2800000000e659d34e4df38d9e8c9eaadfba36612c769195be86c77aac3f36e78b538680fb", + "publicKeyPem" : "-----BEGIN PUBLIC KEY-----\nMFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAEbUp/YNR3Sk8KqLve25U8fup5CUB+MWR1\nVmS8KAAAAADmWdNOTfONnoyeqt+6NmEsdpGVvobHeqw/NueLU4aA+w==\n-----END PUBLIC KEY-----\n", + "sha" : "SHA-256", + "tests" : [ + { + "tcId" : 461, + "comment" : "x-coordinate of the public key has many trailing 0's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "30440220176a2557566ffa518b11226694eb9802ed2098bfe278e5570fe1d5d7af18a94302201291df6a0ed5fc0d15098e70bcf13a009284dfd0689d3bb4be6ceeb9be1487c4", + "result" : "valid" + }, + { + "tcId" : 462, + "comment" : "x-coordinate of the public key has many trailing 0's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "3044022060be20c3dbc162dd34d26780621c104bbe5dace630171b2daef0d826409ee5c20220427f7e4d889d549170bda6a9409fb1cb8b0e763d13eea7bd97f64cf41dc6e497", + "result" : "valid" + }, + { + "tcId" : 463, + "comment" : "x-coordinate of the public key has many trailing 0's", + "flags" : [ + "EdgeCasePublicKey" + ], + "msg" : "4d657373616765", + "sig" : "3045022100edf03cf63f658883289a1a593d1007895b9f236d27c9c1f1313089aaed6b16ae02201a4dd6fc0814dc523d1fefa81c64fbf5e618e651e7096fccadbb94cd48e5e0cd", + "result" : "valid" + } + ] + } + ] +} diff --git a/src/secp256k1/tools/tests_wycheproof_generate.py b/src/secp256k1/tools/tests_wycheproof_generate.py new file mode 100755 index 0000000000..333f6fbef0 --- /dev/null +++ b/src/secp256k1/tools/tests_wycheproof_generate.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +# Copyright (c) 2023 Random "Randy" Lattice and Sean Andersen +# Distributed under the MIT software license, see the accompanying +# file COPYING or https://www.opensource.org/licenses/mit-license.php. +''' +Generate a C file with ECDSA testvectors from the Wycheproof project. +''' + +import json +import hashlib +import urllib.request +import sys + +filename_input = sys.argv[1] + +with open(filename_input) as f: + doc = json.load(f) + +num_groups = len(doc['testGroups']) + +def to_c_array(x): + if x == "": return "" + s = ',0x'.join(a+b for a,b in zip(x[::2], x[1::2])) + return "0x" + s + + +num_vectors = 0 +offset_msg_running, offset_pk_running, offset_sig = 0, 0, 0 +out = "" +messages = "" +signatures = "" +public_keys = "" +cache_msgs = {} +cache_public_keys = {} + +for i in range(num_groups): + group = doc['testGroups'][i] + num_tests = len(group['tests']) + public_key = group['publicKey'] + for j in range(num_tests): + test_vector = group['tests'][j] + # // 2 to convert hex to byte length + sig_size = len(test_vector['sig']) // 2 + msg_size = len(test_vector['msg']) // 2 + + if test_vector['result'] == "invalid": expected_verify = 0 + elif test_vector['result'] == "valid": expected_verify = 1 + else: raise ValueError("invalid result field") + + if num_vectors != 0 and sig_size != 0: signatures += ",\n " + + new_msg = False + msg = to_c_array(test_vector['msg']) + msg_offset = offset_msg_running + # check for repeated msg + if msg not in cache_msgs.keys(): + if num_vectors != 0 and msg_size != 0: messages += ",\n " + cache_msgs[msg] = offset_msg_running + messages += msg + new_msg = True + else: + msg_offset = cache_msgs[msg] + + new_pk = False + pk = to_c_array(public_key['uncompressed']) + pk_offset = offset_pk_running + # check for repeated pk + if pk not in cache_public_keys.keys(): + if num_vectors != 0: public_keys += ",\n " + cache_public_keys[pk] = offset_pk_running + public_keys += pk + new_pk = True + else: + pk_offset = cache_public_keys[pk] + + signatures += to_c_array(test_vector['sig']) + + out += " /" + "* tcId: " + str(test_vector['tcId']) + ". " + test_vector['comment'] + " *" + "/\n" + out += " {" + "{0}, {1}, {2}, {3}, {4}, {5}".format( + pk_offset, + msg_offset, + msg_size, + offset_sig, + sig_size, + expected_verify) + " },\n" + if new_msg: offset_msg_running += msg_size + if new_pk: offset_pk_running += 65 + offset_sig += sig_size + num_vectors += 1 + +struct_definition = """ +typedef struct { + size_t pk_offset; + size_t msg_offset; + size_t msg_len; + size_t sig_offset; + size_t sig_len; + int expected_verify; +} wycheproof_ecdsa_testvector; +""" + + +print("/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */") +print("#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS ({})".format(num_vectors)) + +print(struct_definition) + +print("static const unsigned char wycheproof_ecdsa_messages[] = { " + messages + "};\n") +print("static const unsigned char wycheproof_ecdsa_public_keys[] = { " + public_keys + "};\n") +print("static const unsigned char wycheproof_ecdsa_signatures[] = { " + signatures + "};\n") + +print("static const wycheproof_ecdsa_testvector testvectors[SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS] = {") +print(out) +print("};") |