diff options
| author | Pieter Wuille <pieter@wuille.net> | 2021-04-23 11:35:15 -0700 |
|---|---|---|
| committer | Pieter Wuille <pieter@wuille.net> | 2021-04-23 11:35:15 -0700 |
| commit | bdca9bcb6c9379707d09c63f02326884befbefb2 (patch) | |
| tree | f654bfaff4b5f042a6ecb001a5cf93fcb1dc8a0b | |
| parent | 6c0259fc2f8bd34ba83ad10a6a11d6d99e8d1fc7 (diff) | |
Squashed 'src/secp256k1/' changes from 3967d96bf1..efad3506a8
efad3506a8 Merge #906: Use modified divsteps with initial delta=1/2 for constant-time
cc2c09e3a7 Merge #918: Clean up configuration in gen_context
07067967ee add ECMULT_GEN_PREC_BITS to basic_config.h
a3aa2628c7 gen_context: Don't include basic-config.h
be0609fd54 Add unit tests for edge cases with delta=1/2 variant of divsteps
cd393ce228 Optimization: only do 59 hddivsteps per iteration instead of 62
277b224b6a Use modified divsteps with initial delta=1/2 for constant-time
376ca366db Fix typo in explanation
1e5d50fa93 Merge #889: fix uninitialized read in tests
c083cc6e52 Merge #903: Make argument of fe_normalizes_to_zero{_var} const
6e898534ff Merge #907: changed import to use brackets <> for openssl
4504472269 changed import to use brackets <> for openssl as they are not local to the project
26de4dfeb1 Merge #831: Safegcd inverses, drop Jacobi symbols, remove libgmp
23c3fb629b Make argument of fe_normalizes_to_zero{_var} const
24ad04fc06 Make scalar_inverse{,_var} benchmark scale with SECP256K1_BENCH_ITERS
ebc1af700f Optimization: track f,g limb count and pass to new variable-time update_fg_var
b306935ac1 Optimization: use formulas instead of lookup tables for cancelling g bits
9164a1b658 Optimization: special-case zero modulus limbs in modinv64
1f233b3fa0 Remove num/gmp support
20448b8d09 Remove unused Jacobi symbol support
5437e7bdfb Remove unused scalar_sqr
aa9cc52180 Improve field/scalar inverse tests
1e0e885c8a Make field/scalar code use the new modinv modules for inverses
436281afdc Move secp256k1_fe_inverse{_var} to per-impl files
aa404d53be Move secp256k1_scalar_{inverse{_var},is_even} to per-impl files
08d54964e5 Improve bounds checks in modinv modules
151aac00d3 Add tests for modinv modules
d8a92fcc4c Add extensive comments on the safegcd algorithm and implementation
8e415acba2 Add safegcd based modular inverse modules
de0a643c3d Add secp256k1_ctz{32,64}_var functions
4c3ba88c3a Merge #901: ci: Switch all Linux builds to Debian and more improvements
9361f360bb ci: Select number of parallel make jobs depending on CI environment
28eccdf806 ci: Split output of logs into multiple sections
c7f754fe4d ci: Run PRs on merge result instead of on the source branch
b994a8be3c ci: Print information about binaries using "file"
f24e122d13 ci: Switch all Linux builds to Debian
ebdba03cb5 Merge #891: build: Add workaround for automake 1.13 and older
3a8b47bc6d Merge #894: ctime_test: move context randomization test to the end
7d3497cdc4 ctime_test: move context randomization test to the end
99a1cfec17 print warnings for conditional-uninitialized
3d2cf6c5bd initialize variable in tests
f329bba244 build: Add workaround for automake 1.13 and older
24d1656c32 Merge #882: Use bit ops instead of int mult for constant-time logic in gej_add_ge
e491d06b98 Use bit ops instead of int mult for constant-time logic in gej_add_ge
f8c0b57e6b Merge #864: Add support for Cirrus CI
cc2a5451dc ci: Refactor Nix shell files
2480e55c8f ci: Remove support for Travis CI
2b359f1c1d ci: Enable simple cache for brewing valgrind on macOS
8c02e465c5 ci: Add support for Cirrus CI
659d0d4798 Merge #880: Add parens around ROUND_TO_ALIGN's parameter.
b6f649889a Add parens around ROUND_TO_ALIGN's parameter. This makes the macro robust against a hypothetical ROUND_TO_ALIGN(foo ? sizeA : size B) invocation.
a4abaab793 Merge #877: Add missing secp256k1_ge_set_gej_var decl.
5671e5f3fd Merge #874: Remove underscores from header defs.
db726782fa Merge #878: Remove unused secp256k1_fe_inv_all_var
b732701faa Merge #875: Avoid casting (void**) values.
75d2ae149e Remove unused secp256k1_fe_inv_all_var
482e4a9cfc Add missing secp256k1_ge_set_gej_var decl.
2730618604 Avoid casting (void**) values. Replaced with an expression that only casts (void*) values.
fb390c5299 Remove underscores from header defs. This makes them consistent with other files and avoids reserved identifiers.
f2d9aeae6d Merge #862: Autoconf improvements
328aaef22a Merge #845: Extract the secret key from a keypair
3c15130709 Improve CC_FOR_BUILD detection
47802a4762 Restructure and tidy configure.ac
252c19dfc6 Ask brew for valgrind include path
8c727b9087 Merge #860: fixed trivial typo
b7bc3a4aaa fixed typo
33cb3c2b1f Add secret key extraction from keypair to constant time tests
36d9dc1e8e Add seckey extraction from keypair to the extrakeys tests
fc96aa73f5 Add a function to extract the secretkey from a keypair
98dac87839 Merge #858: Fix insecure links
07aa4c70ff Fix insecure links
b61f9da54e Merge #857: docs: fix simple typo, dependecy -> dependency
18aadf9d28 docs: fix simple typo, dependecy -> dependency
2d9e7175c6 Merge #852: Add sage script for generating scalar_split_lambda constants
dc6e5c3a5c Merge #854: Rename msg32 to msghash32 in ecdsa_sign/verify and add explanation
6e85d675aa Rename tweak to tweak32 in public API
f587f04e35 Rename msg32 to msghash32 in ecdsa_sign/verify and add explanation
329a2e0a3f sage: Add script for generating scalar_split_lambda constants
8f0c6f1545 Merge #851: make test count iteration configurable by environment variable
f4fa8d226a forbid a test iteration of 0 or less
f554dfc708 sage: Reorganize files
3a106966aa Merge #849: Convert Sage code to Python 3 (as used by Sage >= 9)
13c88efed0 Convert Sage code to Python 3 (as used by Sage >= 9)
0ce4554881 make test count iteration configurable by environment variable
9e5939d284 Merge #835: Don't use reserved identifiers memczero and benchmark_verify_t
d0a83f7328 Merge #839: Prevent arithmetic on NULL pointer if the scratch space is too small
903b16aa6c Merge #840: Return NULL early in context_preallocated_create if flags invalid
1f4dd03838 Typedef (u)int128_t only when they're not provided by the compiler
ebfa2058e9 Return NULL early in context_preallocated_create if flags invalid
29a299e373 Run the undefined behaviour sanitizer on Travis
7506e064d7 Prevent arithmetic on NULL pointer if the scratch space is too small
e89278f211 Don't use reserved identifiers memczero and benchmark_verify_t
git-subtree-dir: src/secp256k1
git-subtree-split: efad3506a8937162e8010f5839fdf3771dfcf516
94 files changed, 4865 insertions, 2456 deletions
diff --git a/.cirrus.yml b/.cirrus.yml new file mode 100644 index 0000000000..506a860336 --- /dev/null +++ b/.cirrus.yml @@ -0,0 +1,198 @@ +env: + WIDEMUL: auto + STATICPRECOMPUTATION: yes + ECMULTGENPRECISION: auto + ASM: no + BUILD: check + WITH_VALGRIND: yes + RUN_VALGRIND: no + EXTRAFLAGS: + HOST: + ECDH: no + RECOVERY: no + SCHNORRSIG: no + EXPERIMENTAL: no + CTIMETEST: yes + BENCH: yes + ITERS: 2 + MAKEFLAGS: -j2 + +cat_logs_snippet: &CAT_LOGS + always: + cat_tests_log_script: + - cat tests.log || true + cat_exhaustive_tests_log_script: + - cat exhaustive_tests.log || true + cat_valgrind_ctime_test_log_script: + - cat valgrind_ctime_test.log || true + cat_bench_log_script: + - cat bench.log || true + on_failure: + 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 $CIRRUS_REPO_CLONE_URL $CIRRUS_BASE_BRANCH + - git config --global user.email "ci@ci.ci" + - git config --global user.name "ci" + - git merge FETCH_HEAD # Merge base to detect silent merge conflicts + +task: + name: "x86_64: Linux (Debian stable)" + container: + dockerfile: ci/linux-debian.Dockerfile + # Reduce number of CPUs to be able to do more builds in parallel. + cpu: 1 + # More than enough for our scripts. + memory: 1G + matrix: &ENV_MATRIX + - env: {WIDEMUL: int64, RECOVERY: yes} + - env: {WIDEMUL: int64, ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128} + - env: {WIDEMUL: int128, RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128, ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128, ASM: x86_64} + - env: { RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: { STATICPRECOMPUTATION: no} + - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETEST: no, BENCH: no} + - env: {CPPFLAGS: -DDETERMINISTIC} + - env: {CFLAGS: -O0, CTIMETEST: no} + - env: + CFLAGS: "-fsanitize=undefined -fno-omit-frame-pointer" + LDFLAGS: "-fsanitize=undefined -fno-omit-frame-pointer" + UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1" + ASM: x86_64 + ECDH: yes + RECOVERY: yes + EXPERIMENTAL: yes + SCHNORRSIG: yes + CTIMETEST: no + - env: { ECMULTGENPRECISION: 2 } + - env: { ECMULTGENPRECISION: 8 } + - env: + RUN_VALGRIND: yes + ASM: x86_64 + ECDH: yes + RECOVERY: yes + EXPERIMENTAL: yes + SCHNORRSIG: yes + EXTRAFLAGS: "--disable-openssl-tests" + BUILD: + matrix: + - env: + CC: gcc + - env: + CC: clang + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "i686: Linux (Debian stable)" + container: + dockerfile: ci/linux-debian.Dockerfile + cpu: 1 + memory: 1G + env: + HOST: i686-linux-gnu + ECDH: yes + RECOVERY: yes + EXPERIMENTAL: yes + SCHNORRSIG: yes + matrix: + - env: + CC: i686-linux-gnu-gcc + - env: + CC: clang --target=i686-pc-linux-gnu -isystem /usr/i686-linux-gnu/include + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "x86_64: macOS Catalina" + macos_instance: + image: catalina-base + env: + HOMEBREW_NO_AUTO_UPDATE: 1 + HOMEBREW_NO_INSTALL_CLEANUP: 1 + # Cirrus gives us a fixed number of 12 virtual CPUs. Not that we even have that many jobs at the moment... + MAKEFLAGS: -j13 + matrix: + << : *ENV_MATRIX + matrix: + - env: + CC: gcc-9 + - env: + CC: clang + # Update Command Line Tools + # Uncomment this if the Command Line Tools on the CirrusCI macOS image are too old to brew valgrind. + # See https://apple.stackexchange.com/a/195963 for the implementation. + ## update_clt_script: + ## - system_profiler SPSoftwareDataType + ## - touch /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress + ## - |- + ## PROD=$(softwareupdate -l | grep "*.*Command Line" | tail -n 1 | awk -F"*" '{print $2}' | sed -e 's/^ *//' | sed 's/Label: //g' | tr -d '\n') + ## # For debugging + ## - softwareupdate -l && echo "PROD: $PROD" + ## - softwareupdate -i "$PROD" --verbose + ## - rm /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress + ## + brew_valgrind_pre_script: + - brew config + - brew tap --shallow LouisBrunner/valgrind + # Fetch valgrind source but don't build it yet. + - brew fetch --HEAD LouisBrunner/valgrind/valgrind + brew_valgrind_cache: + # This is $(brew --cellar valgrind) but command substition does not work here. + folder: /usr/local/Cellar/valgrind + # Rebuild cache if ... + fingerprint_script: + # ... macOS version changes: + - sw_vers + # ... brew changes: + - brew config + # ... valgrind changes: + - git -C "$(brew --cache)/valgrind--git" rev-parse HEAD + populate_script: + # If there's no hit in the cache, build and install valgrind. + - brew install --HEAD LouisBrunner/valgrind/valgrind + brew_valgrind_post_script: + # If we have restored valgrind from the cache, tell brew to create symlink to the PATH. + # If we haven't restored from cached (and just run brew install), this is a no-op. + - brew link valgrind + brew_script: + - brew install automake libtool gcc@9 + << : *MERGE_BASE + test_script: + - ./ci/cirrus.sh + << : *CAT_LOGS + +task: + name: "s390x (big-endian): Linux (Debian stable, QEMU)" + container: + dockerfile: ci/linux-debian.Dockerfile + cpu: 1 + memory: 1G + env: + QEMU_CMD: qemu-s390x + HOST: s390x-linux-gnu + BUILD: + WITH_VALGRIND: no + ECDH: yes + RECOVERY: yes + EXPERIMENTAL: yes + SCHNORRSIG: yes + CTIMETEST: no + << : *MERGE_BASE + test_script: + # https://sourceware.org/bugzilla/show_bug.cgi?id=27008 + - rm /etc/ld.so.cache + - ./ci/cirrus.sh + << : *CAT_LOGS diff --git a/.travis.yml b/.travis.yml deleted file mode 100644 index ce8d6391b2..0000000000 --- a/.travis.yml +++ /dev/null @@ -1,108 +0,0 @@ -language: c -os: - - linux - - osx - -dist: bionic -# Valgrind currently supports upto macOS 10.13, the latest xcode of that version is 10.1 -osx_image: xcode10.1 -addons: - apt: - packages: - - libgmp-dev - - valgrind - - libtool-bin -compiler: - - clang - - gcc -env: - global: - - WIDEMUL=auto BIGNUM=auto STATICPRECOMPUTATION=yes ECMULTGENPRECISION=auto ASM=no BUILD=check WITH_VALGRIND=yes RUN_VALGRIND=no EXTRAFLAGS= HOST= ECDH=no RECOVERY=no SCHNORRSIG=no EXPERIMENTAL=no CTIMETEST=yes BENCH=yes ITERS=2 - matrix: - - WIDEMUL=int64 RECOVERY=yes - - WIDEMUL=int64 ECDH=yes EXPERIMENTAL=yes SCHNORRSIG=yes - - WIDEMUL=int128 - - WIDEMUL=int128 RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes - - WIDEMUL=int128 ECDH=yes EXPERIMENTAL=yes SCHNORRSIG=yes - - WIDEMUL=int128 ASM=x86_64 - - BIGNUM=no - - BIGNUM=no RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes - - BIGNUM=no STATICPRECOMPUTATION=no - - BUILD=distcheck WITH_VALGRIND=no CTIMETEST=no BENCH=no - - CPPFLAGS=-DDETERMINISTIC - - CFLAGS=-O0 CTIMETEST=no - - ECMULTGENPRECISION=2 - - ECMULTGENPRECISION=8 - - RUN_VALGRIND=yes BIGNUM=no ASM=x86_64 ECDH=yes RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes EXTRAFLAGS="--disable-openssl-tests" BUILD= -matrix: - fast_finish: true - include: - - compiler: clang - os: linux - env: HOST=i686-linux-gnu - addons: - apt: - packages: - - gcc-multilib - - libgmp-dev:i386 - - valgrind - - libtool-bin - - libc6-dbg:i386 - - compiler: clang - env: HOST=i686-linux-gnu - os: linux - addons: - apt: - packages: - - gcc-multilib - - valgrind - - libtool-bin - - libc6-dbg:i386 - - compiler: gcc - env: HOST=i686-linux-gnu - os: linux - addons: - apt: - packages: - - gcc-multilib - - valgrind - - libtool-bin - - libc6-dbg:i386 - - compiler: gcc - os: linux - env: HOST=i686-linux-gnu - addons: - apt: - packages: - - gcc-multilib - - libgmp-dev:i386 - - valgrind - - libtool-bin - - libc6-dbg:i386 - # S390x build (big endian system) - - compiler: gcc - env: HOST=s390x-unknown-linux-gnu ECDH=yes RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes CTIMETEST= - arch: s390x - -# We use this to install macOS dependencies instead of the built in `homebrew` plugin, -# because in xcode earlier than 11 they have a bug requiring updating the system which overall takes ~8 minutes. -# https://travis-ci.community/t/macos-build-fails-because-of-homebrew-bundle-unknown-command/7296 -before_install: - - if [ "${TRAVIS_OS_NAME}" = "osx" ]; then HOMEBREW_NO_AUTO_UPDATE=1 brew install gmp valgrind gcc@9; fi - -before_script: ./autogen.sh - -# travis auto terminates jobs that go for 10 minutes without printing to stdout, but travis_wait doesn't work well with forking programs like valgrind (https://docs.travis-ci.com/user/common-build-problems/#build-times-out-because-no-output-was-received https://github.com/bitcoin-core/secp256k1/pull/750#issuecomment-623476860) -script: - - function keep_alive() { while true; do echo -en "\a"; sleep 60; done } - - keep_alive & - - ./contrib/travis.sh - - kill %keep_alive - -after_script: - - cat ./tests.log - - cat ./exhaustive_tests.log - - cat ./valgrind_ctime_test.log - - cat ./bench.log - - $CC --version - - valgrind --version diff --git a/Makefile.am b/Makefile.am index 023fa6067f..58c9635e53 100644 --- a/Makefile.am +++ b/Makefile.am @@ -14,8 +14,6 @@ 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/num_gmp.h -noinst_HEADERS += src/num_gmp_impl.h noinst_HEADERS += src/ecdsa.h noinst_HEADERS += src/ecdsa_impl.h noinst_HEADERS += src/eckey.h @@ -26,14 +24,16 @@ 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/num.h -noinst_HEADERS += src/num_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/assumptions.h noinst_HEADERS += src/util.h noinst_HEADERS += src/scratch.h @@ -1,7 +1,7 @@ libsecp256k1 ============ -[](https://travis-ci.org/bitcoin-core/secp256k1) +[](https://cirrus-ci.com/github/bitcoin-core/secp256k1) Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1. @@ -34,11 +34,11 @@ Implementation details * 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). - * Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman). * 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. diff --git a/build-aux/m4/ax_prog_cc_for_build.m4 b/build-aux/m4/ax_prog_cc_for_build.m4 index 77fd346a79..7bcbf3200c 100644 --- a/build-aux/m4/ax_prog_cc_for_build.m4 +++ b/build-aux/m4/ax_prog_cc_for_build.m4 @@ -1,5 +1,5 @@ # =========================================================================== -# http://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html +# https://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html # =========================================================================== # # SYNOPSIS diff --git a/build-aux/m4/bitcoin_secp.m4 b/build-aux/m4/bitcoin_secp.m4 index ece3d655ed..e57888ca18 100644 --- a/build-aux/m4/bitcoin_secp.m4 +++ b/build-aux/m4/bitcoin_secp.m4 @@ -75,15 +75,10 @@ if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then fi ]) -dnl -AC_DEFUN([SECP_GMP_CHECK],[ -if test x"$has_gmp" != x"yes"; then +AC_DEFUN([SECP_VALGRIND_CHECK],[ +if test x"$has_valgrind" != x"yes"; then CPPFLAGS_TEMP="$CPPFLAGS" - CPPFLAGS="$GMP_CPPFLAGS $CPPFLAGS" - LIBS_TEMP="$LIBS" - LIBS="$GMP_LIBS $LIBS" - AC_CHECK_HEADER(gmp.h,[AC_CHECK_LIB(gmp, __gmpz_init,[has_gmp=yes; GMP_LIBS="$GMP_LIBS -lgmp"; AC_DEFINE(HAVE_LIBGMP,1,[Define this symbol if libgmp is installed])])]) - CPPFLAGS="$CPPFLAGS_TEMP" - LIBS="$LIBS_TEMP" + CPPFLAGS="$VALGRIND_CPPFLAGS $CPPFLAGS" + AC_CHECK_HEADER([valgrind/memcheck.h], [has_valgrind=yes; AC_DEFINE(HAVE_VALGRIND,1,[Define this symbol if valgrind is installed])]) fi ]) diff --git a/contrib/travis.sh b/ci/cirrus.sh index 24cc9315cb..f26ca98d1d 100755 --- a/contrib/travis.sh +++ b/ci/cirrus.sh @@ -3,45 +3,63 @@ set -e set -x -if [ "$HOST" = "i686-linux-gnu" ] -then - export CC="$CC -m32" -fi -if [ "$TRAVIS_OS_NAME" = "osx" ] && [ "$TRAVIS_COMPILER" = "gcc" ] -then - export CC="gcc-9" -fi +export LC_ALL=C + +env >> test_env.log + +$CC -v || true +valgrind --version || true + +./autogen.sh ./configure \ --enable-experimental="$EXPERIMENTAL" \ - --with-test-override-wide-multiply="$WIDEMUL" --with-bignum="$BIGNUM" --with-asm="$ASM" \ + --with-test-override-wide-multiply="$WIDEMUL" --with-asm="$ASM" \ --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \ --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \ --enable-module-schnorrsig="$SCHNORRSIG" \ --with-valgrind="$WITH_VALGRIND" \ --host="$HOST" $EXTRAFLAGS +# We have set "-j<n>" in MAKEFLAGS. +make + +# Print information about binaries so that we can see that the architecture is correct +file *tests || true +file bench_* || true +file .libs/* || true + if [ -n "$BUILD" ] then - make -j2 "$BUILD" + make "$BUILD" fi + if [ "$RUN_VALGRIND" = "yes" ] then - make -j2 - # the `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (http://valgrind.org/docs/manual/manual-core.html) + # the `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (https://www.valgrind.org/docs/manual/manual-core.html) valgrind --error-exitcode=42 ./tests 16 valgrind --error-exitcode=42 ./exhaustive_tests fi + +if [ -n "$QEMU_CMD" ] +then + $QEMU_CMD ./tests 16 + $QEMU_CMD ./exhaustive_tests +fi + if [ "$BENCH" = "yes" ] then + # Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool + EXEC='./libtool --mode=execute' + if [ -n "$QEMU_CMD" ] + then + EXEC="$EXEC $QEMU_CMD" + fi if [ "$RUN_VALGRIND" = "yes" ] then - # Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool - EXEC='./libtool --mode=execute valgrind --error-exitcode=42' - else - EXEC= + EXEC="$EXEC valgrind --error-exitcode=42" fi - # This limits the iterations in the benchmarks below to ITER(set in .travis.yml) iterations. + # This limits the iterations in the benchmarks below to ITER iterations. export SECP256K1_BENCH_ITERS="$ITERS" { $EXEC ./bench_ecmult diff --git a/ci/linux-debian.Dockerfile b/ci/linux-debian.Dockerfile new file mode 100644 index 0000000000..5967cf8b31 --- /dev/null +++ b/ci/linux-debian.Dockerfile @@ -0,0 +1,13 @@ +FROM debian:stable + +RUN dpkg --add-architecture i386 +RUN dpkg --add-architecture s390x +RUN apt-get update + +# dkpg-dev: to make pkg-config work in cross-builds +RUN apt-get install --no-install-recommends --no-upgrade -y \ + git ca-certificates \ + make automake libtool pkg-config dpkg-dev valgrind qemu-user \ + gcc clang libc6-dbg \ + gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 \ + gcc-s390x-linux-gnu libc6-dev-s390x-cross libc6-dbg:s390x diff --git a/configure.ac b/configure.ac index eb3b449bec..1ed991afa7 100644 --- a/configure.ac +++ b/configure.ac @@ -14,7 +14,7 @@ AM_INIT_AUTOMAKE([foreign subdir-objects]) : ${CFLAGS="-g"} LT_INIT -dnl make the compilation flags quiet unless V=1 is used +# Make the compilation flags quiet unless V=1 is used. m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])]) PKG_PROG_PKG_CONFIG @@ -22,9 +22,16 @@ PKG_PROG_PKG_CONFIG AC_PATH_TOOL(AR, ar) AC_PATH_TOOL(RANLIB, ranlib) AC_PATH_TOOL(STRIP, strip) -AX_PROG_CC_FOR_BUILD +# Save definition of AC_PROG_CC because AM_PROG_CC_C_O in automake<=1.13 will +# redefine AC_PROG_CC to exit with an error, which avoids the user calling it +# accidently and screwing up the effect of AM_PROG_CC_C_O. However, we'll need +# AC_PROG_CC later on in AX_PROG_CC_FOR_BUILD, where its usage is fine, and +# we'll carefully make sure not to call AC_PROG_CC anywhere else. +m4_copy([AC_PROG_CC], [saved_AC_PROG_CC]) AM_PROG_CC_C_O +# Restore AC_PROG_CC +m4_rename_force([saved_AC_PROG_CC], [AC_PROG_CC]) AC_PROG_CC_C89 if test x"$ac_cv_prog_cc_c89" = x"no"; then @@ -37,25 +44,23 @@ case $host_os in if test x$cross_compiling != xyes; then AC_PATH_PROG([BREW],brew,) if test x$BREW != x; then - dnl These Homebrew packages may be keg-only, meaning that they won't be found - dnl in expected paths because they may conflict with system files. Ask - dnl Homebrew where each one is located, then adjust paths accordingly. - + # These Homebrew packages may be keg-only, meaning that they won't be found + # in expected paths because they may conflict with system files. Ask + # Homebrew where each one is located, then adjust paths accordingly. openssl_prefix=`$BREW --prefix openssl 2>/dev/null` - gmp_prefix=`$BREW --prefix gmp 2>/dev/null` + valgrind_prefix=`$BREW --prefix valgrind 2>/dev/null` if test x$openssl_prefix != x; then PKG_CONFIG_PATH="$openssl_prefix/lib/pkgconfig:$PKG_CONFIG_PATH" export PKG_CONFIG_PATH CRYPTO_CPPFLAGS="-I$openssl_prefix/include" fi - if test x$gmp_prefix != x; then - GMP_CPPFLAGS="-I$gmp_prefix/include" - GMP_LIBS="-L$gmp_prefix/lib" + if test x$valgrind_prefix != x; then + VALGRIND_CPPFLAGS="-I$valgrind_prefix/include" fi else AC_PATH_PROG([PORT],port,) - dnl if homebrew isn't installed and macports is, add the macports default paths - dnl as a last resort. + # If homebrew isn't installed and macports is, add the macports default paths + # as a last resort. if test x$PORT != x; then CPPFLAGS="$CPPFLAGS -isystem /opt/local/include" LDFLAGS="$LDFLAGS -L/opt/local/lib" @@ -78,6 +83,15 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], ]) saved_CFLAGS="$CFLAGS" +CFLAGS="-Wconditional-uninitialized $CFLAGS" +AC_MSG_CHECKING([if ${CC} supports -Wconditional-uninitialized]) +AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], + [ AC_MSG_RESULT([yes]) ], + [ AC_MSG_RESULT([no]) + CFLAGS="$saved_CFLAGS" + ]) + +saved_CFLAGS="$CFLAGS" CFLAGS="-fvisibility=hidden $CFLAGS" AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden]) AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], @@ -86,6 +100,10 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], CFLAGS="$saved_CFLAGS" ]) +### +### Define config arguments +### + AC_ARG_ENABLE(benchmark, AS_HELP_STRING([--enable-benchmark],[compile benchmark [default=yes]]), [use_benchmark=$enableval], @@ -146,13 +164,10 @@ AC_ARG_ENABLE(external_default_callbacks, [use_external_default_callbacks=$enableval], [use_external_default_callbacks=no]) -dnl Test-only override of the (autodetected by the C code) "widemul" setting. -dnl Legal values are int64 (for [u]int64_t), int128 (for [unsigned] __int128), and auto (the default). +# Test-only override of the (autodetected by the C code) "widemul" setting. +# Legal values are int64 (for [u]int64_t), int128 (for [unsigned] __int128), and auto (the default). AC_ARG_WITH([test-override-wide-multiply], [] ,[set_widemul=$withval], [set_widemul=auto]) -AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto], -[bignum implementation to use [default=auto]])],[req_bignum=$withval], [req_bignum=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=$withval], [req_asm=auto]) @@ -177,15 +192,22 @@ AC_ARG_WITH([valgrind], [AS_HELP_STRING([--with-valgrind=yes|no|auto], )], [req_valgrind=$withval], [req_valgrind=auto]) +### +### Handle config options (except for modules) +### + if test x"$req_valgrind" = x"no"; then enable_valgrind=no else - AC_CHECK_HEADER([valgrind/memcheck.h], [enable_valgrind=yes], [ + SECP_VALGRIND_CHECK + if test x"$has_valgrind" != x"yes"; then if test x"$req_valgrind" = x"yes"; then AC_MSG_ERROR([Valgrind support explicitly requested but valgrind/memcheck.h header not available]) fi enable_valgrind=no - ], []) + else + enable_valgrind=yes + fi fi AM_CONDITIONAL([VALGRIND_ENABLED],[test "$enable_valgrind" = "yes"]) @@ -197,61 +219,6 @@ else CFLAGS="-O2 $CFLAGS" fi -if test x"$use_ecmult_static_precomputation" != x"no"; then - # Temporarily switch to an environment for the native compiler - save_cross_compiling=$cross_compiling - cross_compiling=no - SAVE_CC="$CC" - CC="$CC_FOR_BUILD" - SAVE_CFLAGS="$CFLAGS" - CFLAGS="$CFLAGS_FOR_BUILD" - SAVE_CPPFLAGS="$CPPFLAGS" - CPPFLAGS="$CPPFLAGS_FOR_BUILD" - SAVE_LDFLAGS="$LDFLAGS" - LDFLAGS="$LDFLAGS_FOR_BUILD" - - warn_CFLAGS_FOR_BUILD="-Wall -Wextra -Wno-unused-function" - saved_CFLAGS="$CFLAGS" - CFLAGS="$warn_CFLAGS_FOR_BUILD $CFLAGS" - AC_MSG_CHECKING([if native ${CC_FOR_BUILD} supports ${warn_CFLAGS_FOR_BUILD}]) - AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], - [ AC_MSG_RESULT([yes]) ], - [ AC_MSG_RESULT([no]) - CFLAGS="$saved_CFLAGS" - ]) - - AC_MSG_CHECKING([for working native compiler: ${CC_FOR_BUILD}]) - AC_RUN_IFELSE( - [AC_LANG_PROGRAM([], [])], - [working_native_cc=yes], - [working_native_cc=no],[:]) - - CFLAGS_FOR_BUILD="$CFLAGS" - - # Restore the environment - cross_compiling=$save_cross_compiling - CC="$SAVE_CC" - CFLAGS="$SAVE_CFLAGS" - CPPFLAGS="$SAVE_CPPFLAGS" - LDFLAGS="$SAVE_LDFLAGS" - - if test x"$working_native_cc" = x"no"; then - AC_MSG_RESULT([no]) - set_precomp=no - m4_define([please_set_for_build], [Please set CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD.]) - if test x"$use_ecmult_static_precomputation" = x"yes"; then - AC_MSG_ERROR([native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) - else - AC_MSG_WARN([Disabling statically generated ecmult table because the native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) - fi - else - AC_MSG_RESULT([yes]) - set_precomp=yes - fi -else - set_precomp=no -fi - if test x"$req_asm" = x"auto"; then SECP_64BIT_ASM_CHECK if test x"$has_64bit_asm" = x"yes"; then @@ -279,33 +246,7 @@ else esac fi -if test x"$req_bignum" = x"auto"; then - SECP_GMP_CHECK - if test x"$has_gmp" = x"yes"; then - set_bignum=gmp - fi - - if test x"$set_bignum" = x; then - set_bignum=no - fi -else - set_bignum=$req_bignum - case $set_bignum in - gmp) - SECP_GMP_CHECK - if test x"$has_gmp" != x"yes"; then - AC_MSG_ERROR([gmp bignum explicitly requested but libgmp not available]) - fi - ;; - no) - ;; - *) - AC_MSG_ERROR([invalid bignum implementation selection]) - ;; - esac -fi - -# select assembly optimization +# Select assembly optimization use_external_asm=no case $set_asm in @@ -322,7 +263,12 @@ no) ;; esac -# select wide multiplication implementation +if test x"$use_external_asm" = x"yes"; then + AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used]) +fi + + +# Select wide multiplication implementation case $set_widemul in int128) AC_DEFINE(USE_FORCE_WIDEMUL_INT128, 1, [Define this symbol to force the use of the (unsigned) __int128 based wide multiplication implementation]) @@ -337,25 +283,7 @@ auto) ;; esac -# select bignum implementation -case $set_bignum in -gmp) - AC_DEFINE(HAVE_LIBGMP, 1, [Define this symbol if libgmp is installed]) - AC_DEFINE(USE_NUM_GMP, 1, [Define this symbol to use the gmp implementation for num]) - AC_DEFINE(USE_FIELD_INV_NUM, 1, [Define this symbol to use the num-based field inverse implementation]) - AC_DEFINE(USE_SCALAR_INV_NUM, 1, [Define this symbol to use the num-based scalar inverse implementation]) - ;; -no) - AC_DEFINE(USE_NUM_NONE, 1, [Define this symbol to use no num implementation]) - AC_DEFINE(USE_FIELD_INV_BUILTIN, 1, [Define this symbol to use the native field inverse implementation]) - AC_DEFINE(USE_SCALAR_INV_BUILTIN, 1, [Define this symbol to use the native scalar inverse implementation]) - ;; -*) - AC_MSG_ERROR([invalid bignum implementation]) - ;; -esac - -#set ecmult window size +# Set ecmult window size if test x"$req_ecmult_window" = x"auto"; then set_ecmult_window=15 else @@ -377,7 +305,7 @@ case $set_ecmult_window in ;; esac -#set ecmult gen precision +# Set ecmult gen precision if test x"$req_ecmult_gen_precision" = x"auto"; then set_ecmult_gen_precision=4 else @@ -419,15 +347,93 @@ else enable_openssl_tests=no fi -if test x"$set_bignum" = x"gmp"; then - SECP_LIBS="$SECP_LIBS $GMP_LIBS" - SECP_INCLUDES="$SECP_INCLUDES $GMP_CPPFLAGS" +if test x"$enable_valgrind" = x"yes"; then + SECP_INCLUDES="$SECP_INCLUDES $VALGRIND_CPPFLAGS" +fi + +# Handle static precomputation (after everything which modifies CFLAGS and friends) +if test x"$use_ecmult_static_precomputation" != x"no"; then + if test x"$cross_compiling" = x"no"; then + set_precomp=yes + if test x"${CC_FOR_BUILD+x}${CFLAGS_FOR_BUILD+x}${CPPFLAGS_FOR_BUILD+x}${LDFLAGS_FOR_BUILD+x}" != x; then + AC_MSG_WARN([CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD is set but ignored because we are not cross-compiling.]) + fi + # If we're not cross-compiling, simply use the same compiler for building the static precompation code. + CC_FOR_BUILD="$CC" + CFLAGS_FOR_BUILD="$CFLAGS" + CPPFLAGS_FOR_BUILD="$CPPFLAGS" + LDFLAGS_FOR_BUILD="$LDFLAGS" + else + AX_PROG_CC_FOR_BUILD + + # Temporarily switch to an environment for the native compiler + save_cross_compiling=$cross_compiling + cross_compiling=no + SAVE_CC="$CC" + CC="$CC_FOR_BUILD" + SAVE_CFLAGS="$CFLAGS" + CFLAGS="$CFLAGS_FOR_BUILD" + SAVE_CPPFLAGS="$CPPFLAGS" + CPPFLAGS="$CPPFLAGS_FOR_BUILD" + SAVE_LDFLAGS="$LDFLAGS" + LDFLAGS="$LDFLAGS_FOR_BUILD" + + warn_CFLAGS_FOR_BUILD="-Wall -Wextra -Wno-unused-function" + saved_CFLAGS="$CFLAGS" + CFLAGS="$warn_CFLAGS_FOR_BUILD $CFLAGS" + AC_MSG_CHECKING([if native ${CC_FOR_BUILD} supports ${warn_CFLAGS_FOR_BUILD}]) + AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], + [ AC_MSG_RESULT([yes]) ], + [ AC_MSG_RESULT([no]) + CFLAGS="$saved_CFLAGS" + ]) + + AC_MSG_CHECKING([for working native compiler: ${CC_FOR_BUILD}]) + AC_RUN_IFELSE( + [AC_LANG_PROGRAM([], [])], + [working_native_cc=yes], + [working_native_cc=no],[:]) + + CFLAGS_FOR_BUILD="$CFLAGS" + + # Restore the environment + cross_compiling=$save_cross_compiling + CC="$SAVE_CC" + CFLAGS="$SAVE_CFLAGS" + CPPFLAGS="$SAVE_CPPFLAGS" + LDFLAGS="$SAVE_LDFLAGS" + + if test x"$working_native_cc" = x"no"; then + AC_MSG_RESULT([no]) + set_precomp=no + m4_define([please_set_for_build], [Please set CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD.]) + if test x"$use_ecmult_static_precomputation" = x"yes"; then + AC_MSG_ERROR([native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) + else + AC_MSG_WARN([Disabling statically generated ecmult table because the native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) + fi + else + AC_MSG_RESULT([yes]) + set_precomp=yes + fi + fi + + AC_SUBST(CC_FOR_BUILD) + AC_SUBST(CFLAGS_FOR_BUILD) + AC_SUBST(CPPFLAGS_FOR_BUILD) + AC_SUBST(LDFLAGS_FOR_BUILD) +else + set_precomp=no fi if test x"$set_precomp" = x"yes"; then AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table]) fi +### +### Handle module options +### + if test x"$enable_module_ecdh" = x"yes"; then AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module]) fi @@ -447,14 +453,14 @@ if test x"$enable_module_extrakeys" = x"yes"; then AC_DEFINE(ENABLE_MODULE_EXTRAKEYS, 1, [Define this symbol to enable the extrakeys module]) fi -if test x"$use_external_asm" = x"yes"; then - AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used]) -fi - if test x"$use_external_default_callbacks" = x"yes"; then AC_DEFINE(USE_EXTERNAL_DEFAULT_CALLBACKS, 1, [Define this symbol if an external implementation of the default callbacks is used]) fi +### +### Check for --enable-experimental if necessary +### + if test x"$enable_experimental" = x"yes"; then AC_MSG_NOTICE([******]) AC_MSG_NOTICE([WARNING: experimental build]) @@ -474,6 +480,10 @@ else fi fi +### +### Generate output +### + AC_CONFIG_HEADERS([src/libsecp256k1-config.h]) AC_CONFIG_FILES([Makefile libsecp256k1.pc]) AC_SUBST(SECP_INCLUDES) @@ -492,7 +502,7 @@ AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"]) AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"]) -dnl make sure nothing new is exported so that we don't break the cache +# Make sure nothing new is exported so that we don't break the cache. PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH" unset PKG_CONFIG_PATH PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP" @@ -513,10 +523,9 @@ echo " module extrakeys = $enable_module_extrakeys" echo " module schnorrsig = $enable_module_schnorrsig" echo echo " asm = $set_asm" -echo " bignum = $set_bignum" echo " ecmult window size = $set_ecmult_window" echo " ecmult gen prec. bits = $set_ecmult_gen_precision" -dnl Hide test-only options unless they're used. +# Hide test-only options unless they're used. if test x"$set_widemul" != xauto; then echo " wide multiplication = $set_widemul" fi @@ -527,3 +536,9 @@ echo " CFLAGS = $CFLAGS" echo " CPPFLAGS = $CPPFLAGS" echo " LDFLAGS = $LDFLAGS" echo +if test x"$set_precomp" = x"yes"; then +echo " CC_FOR_BUILD = $CC_FOR_BUILD" +echo " CFLAGS_FOR_BUILD = $CFLAGS_FOR_BUILD" +echo " CPPFLAGS_FOR_BUILD = $CPPFLAGS_FOR_BUILD" +echo " LDFLAGS_FOR_BUILD = $LDFLAGS_FOR_BUILD" +fi diff --git a/contrib/lax_der_parsing.c b/contrib/lax_der_parsing.c index f71db4b535..c1627e37e9 100644 --- a/contrib/lax_der_parsing.c +++ b/contrib/lax_der_parsing.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 <secp256k1.h> diff --git a/contrib/lax_der_parsing.h b/contrib/lax_der_parsing.h index 7eaf63bf6a..6b7255e28f 100644 --- a/contrib/lax_der_parsing.h +++ b/contrib/lax_der_parsing.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/contrib/lax_der_privatekey_parsing.c b/contrib/lax_der_privatekey_parsing.c index c2e63b4b8d..429760fbb6 100644 --- a/contrib/lax_der_privatekey_parsing.c +++ b/contrib/lax_der_privatekey_parsing.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014, 2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 <secp256k1.h> diff --git a/contrib/lax_der_privatekey_parsing.h b/contrib/lax_der_privatekey_parsing.h index fece261fb9..602c7c556a 100644 --- a/contrib/lax_der_privatekey_parsing.h +++ b/contrib/lax_der_privatekey_parsing.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014, 2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/doc/safegcd_implementation.md b/doc/safegcd_implementation.md new file mode 100644 index 0000000000..3ae556f9a7 --- /dev/null +++ b/doc/safegcd_implementation.md @@ -0,0 +1,765 @@ +# The safegcd implementation in libsecp256k1 explained + +This document explains the modular inverse implementation 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 +`valgrind_ctime_test.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): + """For a non-zero value v, find z such that v=(d<<z) for some odd d.""" + 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) +``` diff --git a/include/secp256k1.h b/include/secp256k1.h index 2178c8e2d6..d368488af2 100644 --- a/include/secp256k1.h +++ b/include/secp256k1.h @@ -11,7 +11,7 @@ extern "C" { * * 1. Context pointers go first, followed by output arguments, combined * output/input arguments, and finally input-only arguments. - * 2. Array lengths always immediately the follow the argument whose length + * 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, @@ -452,7 +452,14 @@ SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact( * 0: incorrect or unparseable signature * Args: ctx: a secp256k1 context object, initialized for verification. * In: sig: the signature being verified (cannot be NULL) - * msg32: the 32-byte message hash being verified (cannot be NULL) + * msghash32: the 32-byte message hash being verified (cannot be NULL). + * 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 (cannot be NULL) * * To avoid accepting malleable signatures, only ECDSA signatures in lower-S @@ -467,7 +474,7 @@ SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify( const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, - const unsigned char *msg32, + const unsigned char *msghash32, const secp256k1_pubkey *pubkey ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); @@ -532,12 +539,12 @@ SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_def * * Returns: 1: signature created * 0: the nonce generation function failed, or the secret key was invalid. - * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) - * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) - * In: msg32: the 32-byte message hash being signed (cannot be NULL) - * seckey: pointer to a 32-byte secret key (cannot be NULL) - * 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) + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msghash32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * 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) * * The created signature is always in lower-S form. See * secp256k1_ecdsa_signature_normalize for more details. @@ -545,7 +552,7 @@ SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_def SECP256K1_API int secp256k1_ecdsa_sign( const secp256k1_context* ctx, secp256k1_ecdsa_signature *sig, - const unsigned char *msg32, + const unsigned char *msghash32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void *ndata @@ -626,7 +633,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate( * invalid according to secp256k1_ec_seckey_verify, this * function returns 0. seckey will be set to some unspecified * value if this function returns 0. (cannot be NULL) - * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * 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) (cannot be NULL). @@ -634,7 +641,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add( const secp256k1_context* ctx, unsigned char *seckey, - const unsigned char *tweak + 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 @@ -642,7 +649,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( const secp256k1_context* ctx, unsigned char *seckey, - const unsigned char *tweak + const unsigned char *tweak32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); /** Tweak a public key by adding tweak times the generator to it. @@ -654,7 +661,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( * (cannot be NULL). * In/Out: pubkey: pointer to a public key object. pubkey will be set to an * invalid value if this function returns 0 (cannot be NULL). - * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * 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) (cannot be NULL). @@ -662,7 +669,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( const secp256k1_context* ctx, secp256k1_pubkey *pubkey, - const unsigned char *tweak + 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. @@ -673,7 +680,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( * invalid according to secp256k1_ec_seckey_verify, this * function returns 0. seckey will be set to some unspecified * value if this function returns 0. (cannot be NULL) - * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * 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) (cannot be NULL). @@ -681,7 +688,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul( const secp256k1_context* ctx, unsigned char *seckey, - const unsigned char *tweak + 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 @@ -689,7 +696,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( const secp256k1_context* ctx, unsigned char *seckey, - const unsigned char *tweak + const unsigned char *tweak32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); /** Tweak a public key by multiplying it by a tweak value. @@ -699,7 +706,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( * (cannot be NULL). * In/Out: pubkey: pointer to a public key object. pubkey will be set to an * invalid value if this function returns 0 (cannot be NULL). - * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * 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) (cannot be NULL). @@ -707,7 +714,7 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul( const secp256k1_context* ctx, secp256k1_pubkey *pubkey, - const unsigned char *tweak + const unsigned char *tweak32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); /** Updates the context randomization to protect against side-channel leakage. diff --git a/include/secp256k1_extrakeys.h b/include/secp256k1_extrakeys.h index 0c5dff2c94..6fc7b290f8 100644 --- a/include/secp256k1_extrakeys.h +++ b/include/secp256k1_extrakeys.h @@ -165,6 +165,19 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_create( const unsigned char *seckey ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); +/** Get the secret key from a keypair. + * + * Returns: 0 if the arguments are invalid. 1 otherwise. + * Args: ctx: pointer to a context object (cannot be NULL) + * Out: seckey: pointer to a 32-byte buffer for the secret key (cannot be NULL) + * In: keypair: pointer to a keypair (cannot be NULL) + */ +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: 0 if the arguments are invalid. 1 otherwise. diff --git a/include/secp256k1_recovery.h b/include/secp256k1_recovery.h index f8ccaecd3d..aa16532ce8 100644 --- a/include/secp256k1_recovery.h +++ b/include/secp256k1_recovery.h @@ -71,17 +71,17 @@ SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact( * * Returns: 1: signature created * 0: the nonce generation function failed, or the secret key was invalid. - * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) - * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) - * In: msg32: the 32-byte message hash being signed (cannot be NULL) - * seckey: pointer to a 32-byte secret key (cannot be NULL) - * 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) + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msghash32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * 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) */ SECP256K1_API int secp256k1_ecdsa_sign_recoverable( const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *sig, - const unsigned char *msg32, + const unsigned char *msghash32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void *ndata @@ -91,16 +91,16 @@ SECP256K1_API int secp256k1_ecdsa_sign_recoverable( * * Returns: 1: public key successfully recovered (which guarantees a correct signature). * 0: otherwise. - * Args: ctx: pointer to a context object, initialized for verification (cannot be NULL) - * Out: pubkey: pointer to the recovered public key (cannot be NULL) - * In: sig: pointer to initialized signature that supports pubkey recovery (cannot be NULL) - * msg32: the 32-byte message hash assumed to be signed (cannot be NULL) + * Args: ctx: pointer to a context object, initialized for verification (cannot be NULL) + * Out: pubkey: pointer to the recovered public key (cannot be NULL) + * In: sig: pointer to initialized signature that supports pubkey recovery (cannot be NULL) + * msghash32: the 32-byte message hash assumed to be signed (cannot be NULL) */ 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 *msg32 + const unsigned char *msghash32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); #ifdef __cplusplus diff --git a/sage/gen_exhaustive_groups.sage b/sage/gen_exhaustive_groups.sage index 3c3c984811..01d15dcdea 100644 --- a/sage/gen_exhaustive_groups.sage +++ b/sage/gen_exhaustive_groups.sage @@ -1,9 +1,4 @@ -# Define field size and field -P = 2^256 - 2^32 - 977 -F = GF(P) -BETA = F(0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee) - -assert(BETA != F(1) and BETA^3 == F(1)) +load("secp256k1_params.sage") orders_done = set() results = {} diff --git a/sage/gen_split_lambda_constants.sage b/sage/gen_split_lambda_constants.sage new file mode 100644 index 0000000000..7d4359e0f6 --- /dev/null +++ b/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/sage/group_prover.sage b/sage/group_prover.sage index 8521f07999..b200bfeae3 100644 --- a/sage/group_prover.sage +++ b/sage/group_prover.sage @@ -42,7 +42,7 @@ # 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 http://hyperelliptic.org/EFD +# by Tanja Lange and others, see https://hyperelliptic.org/EFD class fastfrac: """Fractions over rings.""" @@ -65,7 +65,7 @@ class fastfrac: return self.top in I and self.bot not in I def reduce(self,assumeZero): - zero = self.R.ideal(map(numerator, 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): @@ -100,7 +100,7 @@ class fastfrac: """Multiply something else with a fraction.""" return self.__mul__(other) - def __div__(self,other): + def __truediv__(self,other): """Divide two fractions.""" if parent(other) == ZZ: return fastfrac(self.R,self.top,self.bot * other) @@ -108,6 +108,11 @@ 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: @@ -175,7 +180,7 @@ class constraints: def conflicts(R, con): """Check whether any of the passed non-zero assumptions is implied by the zero assumptions""" - zero = R.ideal(map(numerator, con.zero)) + 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 @@ -195,7 +200,7 @@ def conflicts(R, con): def get_nonzero_set(R, assume): """Calculate a simple set of nonzero expressions""" - zero = R.ideal(map(numerator, assume.zero)) + zero = R.ideal(list(map(numerator, assume.zero))) nonzero = set() for nz in map(numerator, assume.nonzero): for (f,n) in nz.factor(): @@ -208,7 +213,7 @@ def get_nonzero_set(R, assume): def prove_nonzero(R, exprs, assume): """Check whether an expression is provably nonzero, given assumptions""" - zero = R.ideal(map(numerator, assume.zero)) + zero = R.ideal(list(map(numerator, assume.zero))) nonzero = get_nonzero_set(R, assume) expl = set() ok = True @@ -250,7 +255,7 @@ def prove_zero(R, exprs, assume): r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume) if not r: return (False, map(lambda x: "Possibly zero denominator: %s" % x, e)) - zero = R.ideal(map(numerator, assume.zero)) + zero = R.ideal(list(map(numerator, assume.zero))) nonzero = prod(x for x in assume.nonzero) expl = [] for expr in exprs: @@ -265,8 +270,8 @@ 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(map(numerator, assume.zero)) - zeroextra = R.ideal(map(numerator, zerox)) + 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 diff --git a/sage/secp256k1.sage b/sage/prove_group_implementations.sage index a97e732f7f..a97e732f7f 100644 --- a/sage/secp256k1.sage +++ b/sage/prove_group_implementations.sage diff --git a/sage/secp256k1_params.sage b/sage/secp256k1_params.sage new file mode 100644 index 0000000000..4e000726ed --- /dev/null +++ b/sage/secp256k1_params.sage @@ -0,0 +1,36 @@ +"""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) + +"""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/sage/weierstrass_prover.sage b/sage/weierstrass_prover.sage index 03ef2ec901..b770c6dafe 100644 --- a/sage/weierstrass_prover.sage +++ b/sage/weierstrass_prover.sage @@ -175,24 +175,24 @@ laws_jacobian_weierstrass = { 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) + print("Formula %s on Z%i:" % (name, p)) points = [] - for x in xrange(0, p): - for y in xrange(0, p): + 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) - for za in xrange(1, p): - for zb in xrange(1, p): + for za in range(1, p): + for zb in range(1, p): for pa in points: for pb in points: - for ia in xrange(2): - for ib in xrange(2): + 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 xrange(0, branches): + for branch in range(0, branches): assumeAssert, assumeBranch, pC = formula(branch, pA, pB) pC.X = F(pC.X) pC.Y = F(pC.Y) @@ -206,13 +206,13 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p): 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) + 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: - 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 + 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() def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC): @@ -242,9 +242,9 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): for key in laws_jacobian_weierstrass: res[key] = [] - print ("Formula " + name + ":") + print("Formula " + name + ":") count = 0 - for branch in xrange(branches): + for branch in range(branches): assumeFormula, assumeBranch, pC = formula(branch, pA, pB) pC.X = lift(pC.X) pC.Y = lift(pC.Y) @@ -255,10 +255,10 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch)) for key in res: - print " %s:" % key + 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(" branch %i: %s" % (x[1], x[0])) - print + print() diff --git a/src/asm/field_10x26_arm.s b/src/asm/field_10x26_arm.s index 9a5bd06721..5f68cefc46 100644 --- a/src/asm/field_10x26_arm.s +++ b/src/asm/field_10x26_arm.s @@ -1,9 +1,9 @@ @ 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 http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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. diff --git a/src/assumptions.h b/src/assumptions.h index 77204de2b8..6dc527b288 100644 --- a/src/assumptions.h +++ b/src/assumptions.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2020 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/basic-config.h b/src/basic-config.h index b0d82e89b4..6f7693cb8f 100644 --- a/src/basic-config.h +++ b/src/basic-config.h @@ -1,33 +1,16 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_BASIC_CONFIG_H #define SECP256K1_BASIC_CONFIG_H #ifdef USE_BASIC_CONFIG -#undef USE_ASM_X86_64 -#undef USE_ECMULT_STATIC_PRECOMPUTATION -#undef USE_EXTERNAL_ASM -#undef USE_EXTERNAL_DEFAULT_CALLBACKS -#undef USE_FIELD_INV_BUILTIN -#undef USE_FIELD_INV_NUM -#undef USE_NUM_GMP -#undef USE_NUM_NONE -#undef USE_SCALAR_INV_BUILTIN -#undef USE_SCALAR_INV_NUM -#undef USE_FORCE_WIDEMUL_INT64 -#undef USE_FORCE_WIDEMUL_INT128 -#undef ECMULT_WINDOW_SIZE - -#define USE_NUM_NONE 1 -#define USE_FIELD_INV_BUILTIN 1 -#define USE_SCALAR_INV_BUILTIN 1 -#define USE_WIDEMUL_64 1 #define ECMULT_WINDOW_SIZE 15 +#define ECMULT_GEN_PREC_BITS 4 #endif /* USE_BASIC_CONFIG */ diff --git a/src/bench.h b/src/bench.h index 9bfed903e0..63c55df44d 100644 --- a/src/bench.h +++ b/src/bench.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/bench_ecdh.c b/src/bench_ecdh.c index f099d33884..ab4b8f4244 100644 --- a/src/bench_ecdh.c +++ b/src/bench_ecdh.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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.* + ***********************************************************************/ #include <string.h> diff --git a/src/bench_ecmult.c b/src/bench_ecmult.c index facd07ef31..204e85a5dd 100644 --- a/src/bench_ecmult.c +++ b/src/bench_ecmult.c @@ -1,15 +1,14 @@ -/********************************************************************** - * Copyright (c) 2017 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "include/secp256k1.h" #include "util.h" #include "hash_impl.h" -#include "num_impl.h" #include "field_impl.h" #include "group_impl.h" #include "scalar_impl.h" diff --git a/src/bench_internal.c b/src/bench_internal.c index 5f2b7a9759..73b8a24ccb 100644 --- a/src/bench_internal.c +++ b/src/bench_internal.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "include/secp256k1.h" @@ -10,7 +10,6 @@ #include "assumptions.h" #include "util.h" #include "hash_impl.h" -#include "num_impl.h" #include "field_impl.h" #include "group_impl.h" #include "scalar_impl.h" @@ -99,15 +98,6 @@ void bench_scalar_negate(void* arg, int iters) { } } -void bench_scalar_sqr(void* arg, int iters) { - int i; - bench_inv *data = (bench_inv*)arg; - - for (i = 0; i < iters; i++) { - secp256k1_scalar_sqr(&data->scalar[0], &data->scalar[0]); - } -} - void bench_scalar_mul(void* arg, int iters) { int i; bench_inv *data = (bench_inv*)arg; @@ -255,26 +245,6 @@ void bench_group_add_affine_var(void* arg, int iters) { } } -void bench_group_jacobi_var(void* arg, int iters) { - int i, j = 0; - bench_inv *data = (bench_inv*)arg; - - for (i = 0; i < iters; i++) { - j += secp256k1_gej_has_quad_y_var(&data->gej[0]); - /* Vary the Y and Z coordinates of the input (the X coordinate doesn't matter to - secp256k1_gej_has_quad_y_var). 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].y, &data->fe[1]); - secp256k1_fe_add(&data->gej[0].z, &data->fe[2]); - secp256k1_fe_normalize_var(&data->gej[0].y); - secp256k1_fe_normalize_var(&data->gej[0].z); - } - CHECK(j <= iters); -} - void bench_group_to_affine_var(void* arg, int iters) { int i; bench_inv *data = (bench_inv*)arg; @@ -282,8 +252,10 @@ void bench_group_to_affine_var(void* arg, int iters) { 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. - Similar to bench_group_jacobi_var, this approach does not result in - coordinates of points on the curve. */ + 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); @@ -369,35 +341,16 @@ void bench_context_sign(void* arg, int iters) { } } -#ifndef USE_NUM_NONE -void bench_num_jacobi(void* arg, int iters) { - int i, j = 0; - bench_inv *data = (bench_inv*)arg; - secp256k1_num nx, na, norder; - - secp256k1_scalar_get_num(&nx, &data->scalar[0]); - secp256k1_scalar_order_get_num(&norder); - secp256k1_scalar_get_num(&na, &data->scalar[1]); - - for (i = 0; i < iters; i++) { - j += secp256k1_num_jacobi(&nx, &norder); - secp256k1_num_add(&nx, &nx, &na); - } - CHECK(j <= iters); -} -#endif - int main(int argc, char **argv) { bench_inv data; int iters = get_iters(20000); if (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 (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 (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, iters*10); if (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 (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters); - if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000); - if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000); + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, iters); + if (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 (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 (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); @@ -411,7 +364,6 @@ int main(int argc, char **argv) { if (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 (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 (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 (have_flag(argc, argv, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, iters); if (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 (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters); @@ -424,8 +376,5 @@ int main(int argc, char **argv) { if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 1 + iters/1000); if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 1 + iters/100); -#ifndef USE_NUM_NONE - if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, iters*10); -#endif return 0; } diff --git a/src/bench_recover.c b/src/bench_recover.c index e952ed1215..3f6270ce84 100644 --- a/src/bench_recover.c +++ b/src/bench_recover.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "include/secp256k1.h" #include "include/secp256k1_recovery.h" diff --git a/src/bench_schnorrsig.c b/src/bench_schnorrsig.c index 315f5af28e..f7f591c41d 100644 --- a/src/bench_schnorrsig.c +++ b/src/bench_schnorrsig.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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.* + ***********************************************************************/ #include <string.h> #include <stdlib.h> diff --git a/src/bench_sign.c b/src/bench_sign.c index c6b2942cc0..933f367c4b 100644 --- a/src/bench_sign.c +++ b/src/bench_sign.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "include/secp256k1.h" #include "util.h" @@ -12,11 +12,11 @@ typedef struct { secp256k1_context* ctx; unsigned char msg[32]; unsigned char key[32]; -} bench_sign; +} bench_sign_data; static void bench_sign_setup(void* arg) { int i; - bench_sign *data = (bench_sign*)arg; + bench_sign_data *data = (bench_sign_data*)arg; for (i = 0; i < 32; i++) { data->msg[i] = i + 1; @@ -28,7 +28,7 @@ static void bench_sign_setup(void* arg) { static void bench_sign_run(void* arg, int iters) { int i; - bench_sign *data = (bench_sign*)arg; + bench_sign_data *data = (bench_sign_data*)arg; unsigned char sig[74]; for (i = 0; i < iters; i++) { @@ -45,7 +45,7 @@ static void bench_sign_run(void* arg, int iters) { } int main(void) { - bench_sign data; + bench_sign_data data; int iters = get_iters(20000); diff --git a/src/bench_verify.c b/src/bench_verify.c index 272d3e5cc4..c56aefd369 100644 --- a/src/bench_verify.c +++ b/src/bench_verify.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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> @@ -29,11 +29,11 @@ typedef struct { #ifdef ENABLE_OPENSSL_TESTS EC_GROUP* ec_group; #endif -} benchmark_verify_t; +} bench_verify_data; -static void benchmark_verify(void* arg, int iters) { +static void bench_verify(void* arg, int iters) { int i; - benchmark_verify_t* data = (benchmark_verify_t*)arg; + bench_verify_data* data = (bench_verify_data*)arg; for (i = 0; i < iters; i++) { secp256k1_pubkey pubkey; @@ -51,9 +51,9 @@ static void benchmark_verify(void* arg, int iters) { } #ifdef ENABLE_OPENSSL_TESTS -static void benchmark_verify_openssl(void* arg, int iters) { +static void bench_verify_openssl(void* arg, int iters) { int i; - benchmark_verify_t* data = (benchmark_verify_t*)arg; + bench_verify_data* data = (bench_verify_data*)arg; for (i = 0; i < iters; i++) { data->sig[data->siglen - 1] ^= (i & 0xFF); @@ -84,7 +84,7 @@ int main(void) { int i; secp256k1_pubkey pubkey; secp256k1_ecdsa_signature sig; - benchmark_verify_t data; + bench_verify_data data; int iters = get_iters(20000); @@ -103,10 +103,10 @@ int main(void) { data.pubkeylen = 33; CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); - run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, iters); + run_benchmark("ecdsa_verify", bench_verify, NULL, NULL, &data, 10, iters); #ifdef ENABLE_OPENSSL_TESTS data.ec_group = EC_GROUP_new_by_curve_name(NID_secp256k1); - run_benchmark("ecdsa_verify_openssl", benchmark_verify_openssl, NULL, NULL, &data, 10, iters); + run_benchmark("ecdsa_verify_openssl", bench_verify_openssl, NULL, NULL, &data, 10, iters); EC_GROUP_free(data.ec_group); #endif diff --git a/src/ecdsa.h b/src/ecdsa.h index 80590c7cc8..d5e54d8ce6 100644 --- a/src/ecdsa.h +++ b/src/ecdsa.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/ecdsa_impl.h b/src/ecdsa_impl.h index 5f54b59faa..156a33d112 100644 --- a/src/ecdsa_impl.h +++ b/src/ecdsa_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/eckey.h b/src/eckey.h index b621f1e6c3..5be3a64b84 100644 --- a/src/eckey.h +++ b/src/eckey.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/eckey_impl.h b/src/eckey_impl.h index e2e72d9303..a39cb79653 100644 --- a/src/eckey_impl.h +++ b/src/eckey_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/ecmult.h b/src/ecmult.h index 09e8146414..7ab617e20e 100644 --- a/src/ecmult.h +++ b/src/ecmult.h @@ -1,13 +1,12 @@ -/********************************************************************** - * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "num.h" #include "group.h" #include "scalar.h" #include "scratch.h" diff --git a/src/ecmult_const.h b/src/ecmult_const.h index 03bb33257d..d6f0ea2227 100644 --- a/src/ecmult_const.h +++ b/src/ecmult_const.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h index bb9511108b..0e1fb965cb 100644 --- a/src/ecmult_const_impl.h +++ b/src/ecmult_const_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/ecmult_gen.h b/src/ecmult_gen.h index 30815e5aa1..539618dcbb 100644 --- a/src/ecmult_gen.h +++ b/src/ecmult_gen.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/ecmult_gen_impl.h b/src/ecmult_gen_impl.h index 30ac16518b..384a67faed 100644 --- a/src/ecmult_gen_impl.h +++ b/src/ecmult_gen_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -144,7 +144,7 @@ static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp25 * (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 - * (http://www.tau.ac.il/~tromer/papers/cache.pdf) + * (https://www.tau.ac.il/~tromer/papers/cache.pdf) */ secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits); } diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index a9e8b3c76c..5c2edac68f 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -1,8 +1,8 @@ -/***************************************************************************** - * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php. * - *****************************************************************************/ +/****************************************************************************** + * 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 @@ -595,11 +595,11 @@ static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callba scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar)); state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej)); state.zr = (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 * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); - state.pre_a_lam = state.pre_a + n_points * ECMULT_TABLE_SIZE(WINDOW_A); + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); + state.pre_a_lam = (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.prej == NULL || state.zr == NULL || state.pre_a == NULL) { + if (points == NULL || scalars == NULL || state.prej == NULL || state.zr == NULL || state.pre_a == NULL || state.pre_a_lam == NULL || state.ps == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } diff --git a/src/field.h b/src/field.h index aca1fb72c5..854aaebabc 100644 --- a/src/field.h +++ b/src/field.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -43,13 +43,12 @@ 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. The field - * implementation may optionally normalize the input, but this should not be relied upon. */ -static int secp256k1_fe_normalizes_to_zero(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. The field - * implementation may optionally normalize the input, but this should not be relied upon. */ -static int secp256k1_fe_normalizes_to_zero_var(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 integer. Resulting field element is normalized. */ static void secp256k1_fe_set_int(secp256k1_fe *r, int a); @@ -104,9 +103,6 @@ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a); * itself. */ static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a); -/** Checks whether a field element is a quadratic residue. */ -static int secp256k1_fe_is_quad_var(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); @@ -114,11 +110,6 @@ 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); -/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be - * at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and - * outputs must not overlap in memory. */ -static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len); - /** Convert a field element to the storage type. */ static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a); diff --git a/src/field_10x26.h b/src/field_10x26.h index 5ff03c8abc..9eb65607f1 100644 --- a/src/field_10x26.h +++ b/src/field_10x26.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h index 651500ee8e..7a38c117f1 100644 --- a/src/field_10x26_impl.h +++ b/src/field_10x26_impl.h @@ -1,14 +1,15 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "util.h" #include "field.h" +#include "modinv32_impl.h" #ifdef VERIFY static void secp256k1_fe_verify(const secp256k1_fe *a) { @@ -181,7 +182,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) { #endif } -static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { +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]; @@ -210,7 +211,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { return (z0 == 0) | (z1 == 0x3FFFFFFUL); } -static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { +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; @@ -1164,4 +1165,92 @@ static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const se #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); + + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +} + +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); + + VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); +} + #endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/field_5x52.h b/src/field_5x52.h index 6a068484c2..50ee3f9ec9 100644 --- a/src/field_5x52.h +++ b/src/field_5x52.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/field_5x52_asm_impl.h b/src/field_5x52_asm_impl.h index 1fc3171f6b..a2118044ab 100644 --- a/src/field_5x52_asm_impl.h +++ b/src/field_5x52_asm_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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: diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h index 71a38f915b..60ded927f6 100644 --- a/src/field_5x52_impl.h +++ b/src/field_5x52_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -13,6 +13,7 @@ #include "util.h" #include "field.h" +#include "modinv64_impl.h" #if defined(USE_ASM_X86_64) #include "field_5x52_asm_impl.h" @@ -161,7 +162,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) { #endif } -static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { +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 */ @@ -184,7 +185,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); } -static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { +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; @@ -498,4 +499,80 @@ static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const se #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 +} + #endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/field_5x52_int128_impl.h b/src/field_5x52_int128_impl.h index bcbfb92ac2..314002ee39 100644 --- a/src/field_5x52_int128_impl.h +++ b/src/field_5x52_int128_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/field_impl.h b/src/field_impl.h index 18e4d2f30e..374284a1f4 100644 --- a/src/field_impl.h +++ b/src/field_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -12,7 +12,6 @@ #endif #include "util.h" -#include "num.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "field_5x52_impl.h" @@ -136,185 +135,6 @@ static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) { return secp256k1_fe_equal(&t1, a); } -static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) { - secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; - int j; - - /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in - * { 1, 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<5; j++) { - secp256k1_fe_sqr(&t1, &t1); - } - secp256k1_fe_mul(&t1, &t1, a); - for (j=0; j<3; j++) { - secp256k1_fe_sqr(&t1, &t1); - } - secp256k1_fe_mul(&t1, &t1, &x2); - for (j=0; j<2; j++) { - secp256k1_fe_sqr(&t1, &t1); - } - secp256k1_fe_mul(r, a, &t1); -} - -static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) { -#if defined(USE_FIELD_INV_BUILTIN) - secp256k1_fe_inv(r, a); -#elif defined(USE_FIELD_INV_NUM) - secp256k1_num n, m; - static const secp256k1_fe negone = SECP256K1_FE_CONST( - 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, - 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL - ); - /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ - static const unsigned char prime[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,0x2F - }; - unsigned char b[32]; - int res; - secp256k1_fe c = *a; - secp256k1_fe_normalize_var(&c); - secp256k1_fe_get_b32(b, &c); - secp256k1_num_set_bin(&n, b, 32); - secp256k1_num_set_bin(&m, prime, 32); - secp256k1_num_mod_inverse(&n, &n, &m); - secp256k1_num_get_bin(b, 32, &n); - res = secp256k1_fe_set_b32(r, b); - (void)res; - VERIFY_CHECK(res); - /* Verify the result is the (unique) valid inverse using non-GMP code. */ - secp256k1_fe_mul(&c, &c, r); - secp256k1_fe_add(&c, &negone); - CHECK(secp256k1_fe_normalizes_to_zero_var(&c)); -#else -#error "Please select field inverse implementation" -#endif -} - -static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) { - secp256k1_fe u; - size_t i; - if (len < 1) { - return; - } - - VERIFY_CHECK((r + len <= a) || (a + len <= r)); - - r[0] = a[0]; - - i = 0; - while (++i < len) { - secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]); - } - - secp256k1_fe_inv_var(&u, &r[--i]); - - while (i > 0) { - size_t j = i--; - secp256k1_fe_mul(&r[j], &r[i], &u); - secp256k1_fe_mul(&u, &u, &a[j]); - } - - r[0] = u; -} - -static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) { -#ifndef USE_NUM_NONE - unsigned char b[32]; - secp256k1_num n; - secp256k1_num m; - /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ - static const unsigned char prime[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,0x2F - }; - - secp256k1_fe c = *a; - secp256k1_fe_normalize_var(&c); - secp256k1_fe_get_b32(b, &c); - secp256k1_num_set_bin(&n, b, 32); - secp256k1_num_set_bin(&m, prime, 32); - return secp256k1_num_jacobi(&n, &m) >= 0; -#else - secp256k1_fe r; - return secp256k1_fe_sqrt(&r, a); -#endif -} - static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); #endif /* SECP256K1_FIELD_IMPL_H */ diff --git a/src/gen_context.c b/src/gen_context.c index 8b7729aee4..024c557261 100644 --- a/src/gen_context.c +++ b/src/gen_context.c @@ -1,16 +1,17 @@ -/********************************************************************** - * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ -// Autotools creates libsecp256k1-config.h, of which ECMULT_GEN_PREC_BITS is needed. -// ifndef guard so downstream users can define their own if they do not use autotools. +/* Autotools creates libsecp256k1-config.h, of which ECMULT_GEN_PREC_BITS is needed. + ifndef guard so downstream users can define their own if they do not use autotools. */ #if !defined(ECMULT_GEN_PREC_BITS) #include "libsecp256k1-config.h" #endif -#define USE_BASIC_CONFIG 1 -#include "basic-config.h" + +/* We can't require the precomputed tables when creating them. */ +#undef USE_ECMULT_STATIC_PRECOMPUTATION #include "include/secp256k1.h" #include "assumptions.h" @@ -47,8 +48,8 @@ int main(int argc, char **argv) { return -1; } - fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n"); - fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n"); + fprintf(fp, "#ifndef SECP256K1_ECMULT_STATIC_CONTEXT_H\n"); + fprintf(fp, "#define SECP256K1_ECMULT_STATIC_CONTEXT_H\n"); fprintf(fp, "#include \"src/group.h\"\n"); fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n"); fprintf(fp, "#if ECMULT_GEN_PREC_N != %d || ECMULT_GEN_PREC_G != %d\n", ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G); diff --git a/src/group.h b/src/group.h index 36e39ecf0f..b9cd334dae 100644 --- a/src/group.h +++ b/src/group.h @@ -1,13 +1,12 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "num.h" #include "field.h" /** A group element of the secp256k1 curve, in affine coordinates. */ @@ -43,12 +42,6 @@ typedef struct { /** 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 a Y coordinate that is a quadratic residue modulo p. The return value - * is true iff a coordinate with the given X coordinate exists. - */ -static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x); - /** 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); @@ -62,9 +55,12 @@ 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 */ +/** 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); @@ -93,9 +89,6 @@ 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); -/** Check whether a group element's y coordinate is a quadratic residue. */ -static int secp256k1_gej_has_quad_y_var(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); diff --git a/src/group_impl.h b/src/group_impl.h index a5fbc91a0f..19ebd8f44e 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -1,13 +1,12 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "num.h" #include "field.h" #include "group.h" @@ -207,18 +206,14 @@ static void secp256k1_ge_clear(secp256k1_ge *r) { secp256k1_fe_clear(&r->y); } -static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) { +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(&x3, &secp256k1_fe_const_b); - return secp256k1_fe_sqrt(&r->y, &x3); -} - -static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) { - if (!secp256k1_ge_set_xquad(r, x)) { + if (!secp256k1_fe_sqrt(&r->y, &x3)) { return 0; } secp256k1_fe_normalize_var(&r->y); @@ -591,7 +586,7 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const 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 = Malt*Z (1) */ - infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity); + infinity = secp256k1_fe_normalizes_to_zero(&r->z) & ~a->infinity; secp256k1_fe_mul_int(&r->z, 2); /* r->z = Z3 = 2*Malt*Z (2) */ secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */ secp256k1_fe_add(&t, &q); /* t = Ralt^2-Q (3) */ @@ -655,26 +650,12 @@ static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) { secp256k1_fe_mul(&r->x, &r->x, &beta); } -static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) { - secp256k1_fe yz; - - if (a->infinity) { - return 0; - } - - /* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as - * that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z - is */ - secp256k1_fe_mul(&yz, &a->y, &a->z); - return secp256k1_fe_is_quad_var(&yz); -} - 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 dependecy on ecmult. */ + /* 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); diff --git a/src/hash.h b/src/hash.h index de26e4b89f..0947a09694 100644 --- a/src/hash.h +++ b/src/hash.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/hash_impl.h b/src/hash_impl.h index 409772587b..f8cd3a1634 100644 --- a/src/hash_impl.h +++ b/src/hash_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/modinv32.h b/src/modinv32.h new file mode 100644 index 0000000000..0efdda9ab5 --- /dev/null +++ b/src/modinv32.h @@ -0,0 +1,42 @@ +/*********************************************************************** + * 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 + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#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); + +#endif /* SECP256K1_MODINV32_H */ diff --git a/src/modinv32_impl.h b/src/modinv32_impl.h new file mode 100644 index 0000000000..661c5fc04c --- /dev/null +++ b/src/modinv32_impl.h @@ -0,0 +1,587 @@ +/*********************************************************************** + * 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; +} + +/* 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) { + /* inv256[i] = -(2*i+1)^-1 (mod 256) */ + static const uint8_t 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 + }; + + /* 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 * 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 (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) + labs(v)) >= 0); /* |u|+|v| doesn't overflow */ + VERIFY_CHECK((labs(q) + labs(r)) >= 0); /* |q|+|r| doesn't overflow */ + VERIFY_CHECK((labs(u) + labs(v)) <= M30 + 1); /* |u|+|v| <= 2^30 */ + VERIFY_CHECK((labs(q) + labs(r)) <= M30 + 1); /* |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; +} + +#endif /* SECP256K1_MODINV32_IMPL_H */ diff --git a/src/modinv64.h b/src/modinv64.h new file mode 100644 index 0000000000..da506dfa9f --- /dev/null +++ b/src/modinv64.h @@ -0,0 +1,46 @@ +/*********************************************************************** + * 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 + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#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); + +#endif /* SECP256K1_MODINV64_H */ diff --git a/src/modinv64_impl.h b/src/modinv64_impl.h new file mode 100644 index 0000000000..0743a9c821 --- /dev/null +++ b/src/modinv64_impl.h @@ -0,0 +1,593 @@ +/*********************************************************************** + * 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 "modinv64.h" + +#include "util.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. + */ + +#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 int64_t M62 = (int64_t)(UINT64_MAX >> 2); + int128_t c = 0; + int i; + for (i = 0; i < 4; ++i) { + if (i < alen) c += (int128_t)a->v[i] * factor; + r->v[i] = (int64_t)c & M62; c >>= 62; + } + if (4 < alen) c += (int128_t)a->v[4] * factor; + VERIFY_CHECK(c == (int64_t)c); + r->v[4] = (int64_t)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; +} +#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 +} + +/* 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; + +/* 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; + /* 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((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 65); + 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 + * 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; + /* 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((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 62); + 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 int64_t M62 = (int64_t)(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; + int128_t 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) + secp256k1_modinv64_abs(v)) >= 0); /* |u|+|v| doesn't overflow */ + VERIFY_CHECK((secp256k1_modinv64_abs(q) + secp256k1_modinv64_abs(r)) >= 0); /* |q|+|r| doesn't overflow */ + VERIFY_CHECK((secp256k1_modinv64_abs(u) + secp256k1_modinv64_abs(v)) <= M62 + 1); /* |u|+|v| <= 2^62 */ + VERIFY_CHECK((secp256k1_modinv64_abs(q) + secp256k1_modinv64_abs(r)) <= M62 + 1); /* |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]. */ + cd = (int128_t)u * d0 + (int128_t)v * e0; + ce = (int128_t)q * d0 + (int128_t)r * e0; + /* Correct md,me so that t*[d,e]+modulus*[md,me] has 62 zero bottom bits. */ + md -= (modinfo->modulus_inv62 * (uint64_t)cd + md) & M62; + me -= (modinfo->modulus_inv62 * (uint64_t)ce + me) & M62; + /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */ + cd += (int128_t)modinfo->modulus.v[0] * md; + ce += (int128_t)modinfo->modulus.v[0] * me; + /* Verify that the low 62 bits of the computation are indeed zero, and then throw them away. */ + VERIFY_CHECK(((int64_t)cd & M62) == 0); cd >>= 62; + VERIFY_CHECK(((int64_t)ce & M62) == 0); ce >>= 62; + /* Compute limb 1 of t*[d,e]+modulus*[md,me], and store it as output limb 0 (= down shift). */ + cd += (int128_t)u * d1 + (int128_t)v * e1; + ce += (int128_t)q * d1 + (int128_t)r * e1; + if (modinfo->modulus.v[1]) { /* Optimize for the case where limb of modulus is zero. */ + cd += (int128_t)modinfo->modulus.v[1] * md; + ce += (int128_t)modinfo->modulus.v[1] * me; + } + d->v[0] = (int64_t)cd & M62; cd >>= 62; + e->v[0] = (int64_t)ce & M62; ce >>= 62; + /* Compute limb 2 of t*[d,e]+modulus*[md,me], and store it as output limb 1. */ + cd += (int128_t)u * d2 + (int128_t)v * e2; + ce += (int128_t)q * d2 + (int128_t)r * e2; + if (modinfo->modulus.v[2]) { /* Optimize for the case where limb of modulus is zero. */ + cd += (int128_t)modinfo->modulus.v[2] * md; + ce += (int128_t)modinfo->modulus.v[2] * me; + } + d->v[1] = (int64_t)cd & M62; cd >>= 62; + e->v[1] = (int64_t)ce & M62; ce >>= 62; + /* Compute limb 3 of t*[d,e]+modulus*[md,me], and store it as output limb 2. */ + cd += (int128_t)u * d3 + (int128_t)v * e3; + ce += (int128_t)q * d3 + (int128_t)r * e3; + if (modinfo->modulus.v[3]) { /* Optimize for the case where limb of modulus is zero. */ + cd += (int128_t)modinfo->modulus.v[3] * md; + ce += (int128_t)modinfo->modulus.v[3] * me; + } + d->v[2] = (int64_t)cd & M62; cd >>= 62; + e->v[2] = (int64_t)ce & M62; ce >>= 62; + /* Compute limb 4 of t*[d,e]+modulus*[md,me], and store it as output limb 3. */ + cd += (int128_t)u * d4 + (int128_t)v * e4; + ce += (int128_t)q * d4 + (int128_t)r * e4; + cd += (int128_t)modinfo->modulus.v[4] * md; + ce += (int128_t)modinfo->modulus.v[4] * me; + d->v[3] = (int64_t)cd & M62; cd >>= 62; + e->v[3] = (int64_t)ce & M62; ce >>= 62; + /* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */ + d->v[4] = (int64_t)cd; + e->v[4] = (int64_t)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 int64_t M62 = (int64_t)(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; + int128_t cf, cg; + /* Start computing t*[f,g]. */ + cf = (int128_t)u * f0 + (int128_t)v * g0; + cg = (int128_t)q * f0 + (int128_t)r * g0; + /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK(((int64_t)cf & M62) == 0); cf >>= 62; + VERIFY_CHECK(((int64_t)cg & M62) == 0); cg >>= 62; + /* Compute limb 1 of t*[f,g], and store it as output limb 0 (= down shift). */ + cf += (int128_t)u * f1 + (int128_t)v * g1; + cg += (int128_t)q * f1 + (int128_t)r * g1; + f->v[0] = (int64_t)cf & M62; cf >>= 62; + g->v[0] = (int64_t)cg & M62; cg >>= 62; + /* Compute limb 2 of t*[f,g], and store it as output limb 1. */ + cf += (int128_t)u * f2 + (int128_t)v * g2; + cg += (int128_t)q * f2 + (int128_t)r * g2; + f->v[1] = (int64_t)cf & M62; cf >>= 62; + g->v[1] = (int64_t)cg & M62; cg >>= 62; + /* Compute limb 3 of t*[f,g], and store it as output limb 2. */ + cf += (int128_t)u * f3 + (int128_t)v * g3; + cg += (int128_t)q * f3 + (int128_t)r * g3; + f->v[2] = (int64_t)cf & M62; cf >>= 62; + g->v[2] = (int64_t)cg & M62; cg >>= 62; + /* Compute limb 4 of t*[f,g], and store it as output limb 3. */ + cf += (int128_t)u * f4 + (int128_t)v * g4; + cg += (int128_t)q * f4 + (int128_t)r * g4; + f->v[3] = (int64_t)cf & M62; cf >>= 62; + g->v[3] = (int64_t)cg & M62; cg >>= 62; + /* What remains is limb 5 of t*[f,g]; store it as output limb 4. */ + f->v[4] = (int64_t)cf; + g->v[4] = (int64_t)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 int64_t M62 = (int64_t)(UINT64_MAX >> 2); + const int64_t u = t->u, v = t->v, q = t->q, r = t->r; + int64_t fi, gi; + int128_t cf, cg; + int i; + VERIFY_CHECK(len > 0); + /* Start computing t*[f,g]. */ + fi = f->v[0]; + gi = g->v[0]; + cf = (int128_t)u * fi + (int128_t)v * gi; + cg = (int128_t)q * fi + (int128_t)r * gi; + /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ + VERIFY_CHECK(((int64_t)cf & M62) == 0); cf >>= 62; + VERIFY_CHECK(((int64_t)cg & M62) == 0); 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]; + cf += (int128_t)u * fi + (int128_t)v * gi; + cg += (int128_t)q * fi + (int128_t)r * gi; + f->v[i - 1] = (int64_t)cf & M62; cf >>= 62; + g->v[i - 1] = (int64_t)cg & M62; cg >>= 62; + } + /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */ + f->v[len - 1] = (int64_t)cf; + g->v[len - 1] = (int64_t)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; +} + +#endif /* SECP256K1_MODINV64_IMPL_H */ diff --git a/src/modules/ecdh/main_impl.h b/src/modules/ecdh/main_impl.h index 07a25b80d4..1ac67086be 100644 --- a/src/modules/ecdh/main_impl.h +++ b/src/modules/ecdh/main_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/modules/ecdh/tests_impl.h b/src/modules/ecdh/tests_impl.h index e8d2aeab9a..be07447a4b 100644 --- a/src/modules/ecdh/tests_impl.h +++ b/src/modules/ecdh/tests_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/modules/extrakeys/main_impl.h b/src/modules/extrakeys/main_impl.h index 5378d2f301..7390b22718 100644 --- a/src/modules/extrakeys/main_impl.h +++ b/src/modules/extrakeys/main_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2020 Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ -#define _SECP256K1_MODULE_EXTRAKEYS_MAIN_ +#ifndef SECP256K1_MODULE_EXTRAKEYS_MAIN_H +#define SECP256K1_MODULE_EXTRAKEYS_MAIN_H #include "include/secp256k1.h" #include "include/secp256k1_extrakeys.h" @@ -180,12 +180,22 @@ int secp256k1_keypair_create(const secp256k1_context* ctx, secp256k1_keypair *ke ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &sk, &pk, seckey32); secp256k1_keypair_save(keypair, &sk, &pk); - memczero(keypair, sizeof(*keypair), !ret); + 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); diff --git a/src/modules/extrakeys/tests_exhaustive_impl.h b/src/modules/extrakeys/tests_exhaustive_impl.h index 0e29bc6b09..0aca4fb72d 100644 --- a/src/modules/extrakeys/tests_exhaustive_impl.h +++ b/src/modules/extrakeys/tests_exhaustive_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2020 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ -#define _SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_ +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H #include "src/modules/extrakeys/main_impl.h" #include "include/secp256k1_extrakeys.h" diff --git a/src/modules/extrakeys/tests_impl.h b/src/modules/extrakeys/tests_impl.h index 5ee135849e..9473a7dd48 100644 --- a/src/modules/extrakeys/tests_impl.h +++ b/src/modules/extrakeys/tests_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2020 Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ -#define _SECP256K1_MODULE_EXTRAKEYS_TESTS_ +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_H #include "secp256k1_extrakeys.h" @@ -311,6 +311,7 @@ void test_xonly_pubkey_tweak_recursive(void) { 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; @@ -396,6 +397,28 @@ void test_keypair(void) { 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(none, sk_tmp, &keypair) == 1); + CHECK(secp256k1_keypair_sec(none, NULL, &keypair) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_keypair_sec(none, 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(sign, &keypair, sk) == 1); + CHECK(secp256k1_keypair_sec(none, 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(none, sk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0); + secp256k1_context_destroy(none); secp256k1_context_destroy(sign); secp256k1_context_destroy(verify); @@ -484,6 +507,7 @@ void test_keypair_add(void) { secp256k1_pubkey output_pk_xy; secp256k1_pubkey output_pk_expected; unsigned char pk32[32]; + unsigned char sk32[32]; int pk_parity; secp256k1_testrand256(tweak); @@ -501,7 +525,8 @@ void test_keypair_add(void) { 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_ec_pubkey_create(ctx, &output_pk_expected, &keypair.data[0]) == 1); + CHECK(secp256k1_keypair_sec(none, 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); } secp256k1_context_destroy(none); diff --git a/src/modules/recovery/main_impl.h b/src/modules/recovery/main_impl.h index e2576aa953..7a440a729b 100644 --- a/src/modules/recovery/main_impl.h +++ b/src/modules/recovery/main_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -120,34 +120,34 @@ static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, cons return !secp256k1_gej_is_infinity(&qj); } -int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { +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(msg32 != NULL); + ARG_CHECK(msghash32 != NULL); ARG_CHECK(signature != NULL); ARG_CHECK(seckey != NULL); - ret = secp256k1_ecdsa_sign_inner(ctx, &r, &s, &recid, msg32, seckey, noncefp, noncedata); + 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 *msg32) { +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(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); - ARG_CHECK(msg32 != 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, msg32, NULL); + secp256k1_scalar_set_b32(&m, msghash32, NULL); if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) { secp256k1_pubkey_save(pubkey, &q); return 1; diff --git a/src/modules/recovery/tests_exhaustive_impl.h b/src/modules/recovery/tests_exhaustive_impl.h index a2f381d77a..0ba9409c69 100644 --- a/src/modules/recovery/tests_exhaustive_impl.h +++ b/src/modules/recovery/tests_exhaustive_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2016 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/modules/recovery/tests_impl.h b/src/modules/recovery/tests_impl.h index 09cae38403..40dba87ce3 100644 --- a/src/modules/recovery/tests_impl.h +++ b/src/modules/recovery/tests_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/modules/schnorrsig/main_impl.h b/src/modules/schnorrsig/main_impl.h index b0d8481f9b..22e1b33a5a 100644 --- a/src/modules/schnorrsig/main_impl.h +++ b/src/modules/schnorrsig/main_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ -#define _SECP256K1_MODULE_SCHNORRSIG_MAIN_ +#ifndef SECP256K1_MODULE_SCHNORRSIG_MAIN_H +#define SECP256K1_MODULE_SCHNORRSIG_MAIN_H #include "include/secp256k1.h" #include "include/secp256k1_schnorrsig.h" @@ -179,7 +179,7 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64 secp256k1_scalar_add(&e, &e, &k); secp256k1_scalar_get_b32(&sig64[32], &e); - memczero(sig64, 64, !ret); + secp256k1_memczero(sig64, 64, !ret); secp256k1_scalar_clear(&k); secp256k1_scalar_clear(&sk); memset(seckey, 0, sizeof(seckey)); diff --git a/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/modules/schnorrsig/tests_exhaustive_impl.h index 4bf0bc1680..b4a428729f 100644 --- a/src/modules/schnorrsig/tests_exhaustive_impl.h +++ b/src/modules/schnorrsig/tests_exhaustive_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2020 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ -#define _SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_ +#ifndef SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H #include "include/secp256k1_schnorrsig.h" #include "src/modules/schnorrsig/main_impl.h" diff --git a/src/modules/schnorrsig/tests_impl.h b/src/modules/schnorrsig/tests_impl.h index f522fcb320..338462fc9d 100644 --- a/src/modules/schnorrsig/tests_impl.h +++ b/src/modules/schnorrsig/tests_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef _SECP256K1_MODULE_SCHNORRSIG_TESTS_ -#define _SECP256K1_MODULE_SCHNORRSIG_TESTS_ +/*********************************************************************** + * 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 "secp256k1_schnorrsig.h" diff --git a/src/num.h b/src/num.h deleted file mode 100644 index 49f2dd791d..0000000000 --- a/src/num.h +++ /dev/null @@ -1,74 +0,0 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef SECP256K1_NUM_H -#define SECP256K1_NUM_H - -#ifndef USE_NUM_NONE - -#if defined HAVE_CONFIG_H -#include "libsecp256k1-config.h" -#endif - -#if defined(USE_NUM_GMP) -#include "num_gmp.h" -#else -#error "Please select num implementation" -#endif - -/** Copy a number. */ -static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a); - -/** Convert a number's absolute value to a binary big-endian string. - * There must be enough place. */ -static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a); - -/** Set a number to the value of a binary big-endian string. */ -static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen); - -/** Compute a modular inverse. The input must be less than the modulus. */ -static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m); - -/** Compute the jacobi symbol (a|b). b must be positive and odd. */ -static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b); - -/** Compare the absolute value of two numbers. */ -static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b); - -/** Test whether two number are equal (including sign). */ -static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b); - -/** Add two (signed) numbers. */ -static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); - -/** Subtract two (signed) numbers. */ -static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); - -/** Multiply two (signed) numbers. */ -static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); - -/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1, - even if r was negative. */ -static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m); - -/** Right-shift the passed number by bits bits. */ -static void secp256k1_num_shift(secp256k1_num *r, int bits); - -/** Check whether a number is zero. */ -static int secp256k1_num_is_zero(const secp256k1_num *a); - -/** Check whether a number is one. */ -static int secp256k1_num_is_one(const secp256k1_num *a); - -/** Check whether a number is strictly negative. */ -static int secp256k1_num_is_neg(const secp256k1_num *a); - -/** Change a number's sign. */ -static void secp256k1_num_negate(secp256k1_num *r); - -#endif - -#endif /* SECP256K1_NUM_H */ diff --git a/src/num_gmp.h b/src/num_gmp.h deleted file mode 100644 index 3619844bd5..0000000000 --- a/src/num_gmp.h +++ /dev/null @@ -1,20 +0,0 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef SECP256K1_NUM_REPR_H -#define SECP256K1_NUM_REPR_H - -#include <gmp.h> - -#define NUM_LIMBS ((256+GMP_NUMB_BITS-1)/GMP_NUMB_BITS) - -typedef struct { - mp_limb_t data[2*NUM_LIMBS]; - int neg; - int limbs; -} secp256k1_num; - -#endif /* SECP256K1_NUM_REPR_H */ diff --git a/src/num_gmp_impl.h b/src/num_gmp_impl.h deleted file mode 100644 index 0ae2a8ba0e..0000000000 --- a/src/num_gmp_impl.h +++ /dev/null @@ -1,288 +0,0 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef SECP256K1_NUM_REPR_IMPL_H -#define SECP256K1_NUM_REPR_IMPL_H - -#include <string.h> -#include <stdlib.h> -#include <gmp.h> - -#include "util.h" -#include "num.h" - -#ifdef VERIFY -static void secp256k1_num_sanity(const secp256k1_num *a) { - VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0)); -} -#else -#define secp256k1_num_sanity(a) do { } while(0) -#endif - -static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) { - *r = *a; -} - -static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) { - unsigned char tmp[65]; - int len = 0; - int shift = 0; - if (a->limbs>1 || a->data[0] != 0) { - len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs); - } - while (shift < len && tmp[shift] == 0) shift++; - VERIFY_CHECK(len-shift <= (int)rlen); - memset(r, 0, rlen - len + shift); - if (len > shift) { - memcpy(r + rlen - len + shift, tmp + shift, len - shift); - } - memset(tmp, 0, sizeof(tmp)); -} - -static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) { - int len; - VERIFY_CHECK(alen > 0); - VERIFY_CHECK(alen <= 64); - len = mpn_set_str(r->data, a, alen, 256); - if (len == 0) { - r->data[0] = 0; - len = 1; - } - VERIFY_CHECK(len <= NUM_LIMBS*2); - r->limbs = len; - r->neg = 0; - while (r->limbs > 1 && r->data[r->limbs-1]==0) { - r->limbs--; - } -} - -static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { - mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs); - r->limbs = a->limbs; - if (c != 0) { - VERIFY_CHECK(r->limbs < 2*NUM_LIMBS); - r->data[r->limbs++] = c; - } -} - -static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { - mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs); - (void)c; - VERIFY_CHECK(c == 0); - r->limbs = a->limbs; - while (r->limbs > 1 && r->data[r->limbs-1]==0) { - r->limbs--; - } -} - -static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) { - secp256k1_num_sanity(r); - secp256k1_num_sanity(m); - - if (r->limbs >= m->limbs) { - mp_limb_t t[2*NUM_LIMBS]; - mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs); - memset(t, 0, sizeof(t)); - r->limbs = m->limbs; - while (r->limbs > 1 && r->data[r->limbs-1]==0) { - r->limbs--; - } - } - - if (r->neg && (r->limbs > 1 || r->data[0] != 0)) { - secp256k1_num_sub_abs(r, m, r); - r->neg = 0; - } -} - -static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) { - int i; - mp_limb_t g[NUM_LIMBS+1]; - mp_limb_t u[NUM_LIMBS+1]; - mp_limb_t v[NUM_LIMBS+1]; - mp_size_t sn; - mp_size_t gn; - secp256k1_num_sanity(a); - secp256k1_num_sanity(m); - - /** mpn_gcdext computes: (G,S) = gcdext(U,V), where - * * G = gcd(U,V) - * * G = U*S + V*T - * * U has equal or more limbs than V, and V has no padding - * If we set U to be (a padded version of) a, and V = m: - * G = a*S + m*T - * G = a*S mod m - * Assuming G=1: - * S = 1/a mod m - */ - VERIFY_CHECK(m->limbs <= NUM_LIMBS); - VERIFY_CHECK(m->data[m->limbs-1] != 0); - for (i = 0; i < m->limbs; i++) { - u[i] = (i < a->limbs) ? a->data[i] : 0; - v[i] = m->data[i]; - } - sn = NUM_LIMBS+1; - gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs); - (void)gn; - VERIFY_CHECK(gn == 1); - VERIFY_CHECK(g[0] == 1); - r->neg = a->neg ^ m->neg; - if (sn < 0) { - mpn_sub(r->data, m->data, m->limbs, r->data, -sn); - r->limbs = m->limbs; - while (r->limbs > 1 && r->data[r->limbs-1]==0) { - r->limbs--; - } - } else { - r->limbs = sn; - } - memset(g, 0, sizeof(g)); - memset(u, 0, sizeof(u)); - memset(v, 0, sizeof(v)); -} - -static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) { - int ret; - mpz_t ga, gb; - secp256k1_num_sanity(a); - secp256k1_num_sanity(b); - VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1)); - - mpz_inits(ga, gb, NULL); - - mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data); - mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data); - if (a->neg) { - mpz_neg(ga, ga); - } - - ret = mpz_jacobi(ga, gb); - - mpz_clears(ga, gb, NULL); - - return ret; -} - -static int secp256k1_num_is_one(const secp256k1_num *a) { - return (a->limbs == 1 && a->data[0] == 1); -} - -static int secp256k1_num_is_zero(const secp256k1_num *a) { - return (a->limbs == 1 && a->data[0] == 0); -} - -static int secp256k1_num_is_neg(const secp256k1_num *a) { - return (a->limbs > 1 || a->data[0] != 0) && a->neg; -} - -static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) { - if (a->limbs > b->limbs) { - return 1; - } - if (a->limbs < b->limbs) { - return -1; - } - return mpn_cmp(a->data, b->data, a->limbs); -} - -static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) { - if (a->limbs > b->limbs) { - return 0; - } - if (a->limbs < b->limbs) { - return 0; - } - if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) { - return 0; - } - return mpn_cmp(a->data, b->data, a->limbs) == 0; -} - -static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) { - if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */ - r->neg = a->neg; - if (a->limbs >= b->limbs) { - secp256k1_num_add_abs(r, a, b); - } else { - secp256k1_num_add_abs(r, b, a); - } - } else { - if (secp256k1_num_cmp(a, b) > 0) { - r->neg = a->neg; - secp256k1_num_sub_abs(r, a, b); - } else { - r->neg = b->neg ^ bneg; - secp256k1_num_sub_abs(r, b, a); - } - } -} - -static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { - secp256k1_num_sanity(a); - secp256k1_num_sanity(b); - secp256k1_num_subadd(r, a, b, 0); -} - -static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { - secp256k1_num_sanity(a); - secp256k1_num_sanity(b); - secp256k1_num_subadd(r, a, b, 1); -} - -static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { - mp_limb_t tmp[2*NUM_LIMBS+1]; - secp256k1_num_sanity(a); - secp256k1_num_sanity(b); - - VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1); - if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) { - r->limbs = 1; - r->neg = 0; - r->data[0] = 0; - return; - } - if (a->limbs >= b->limbs) { - mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs); - } else { - mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs); - } - r->limbs = a->limbs + b->limbs; - if (r->limbs > 1 && tmp[r->limbs - 1]==0) { - r->limbs--; - } - VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS); - mpn_copyi(r->data, tmp, r->limbs); - r->neg = a->neg ^ b->neg; - memset(tmp, 0, sizeof(tmp)); -} - -static void secp256k1_num_shift(secp256k1_num *r, int bits) { - if (bits % GMP_NUMB_BITS) { - /* Shift within limbs. */ - mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS); - } - if (bits >= GMP_NUMB_BITS) { - int i; - /* Shift full limbs. */ - for (i = 0; i < r->limbs; i++) { - int index = i + (bits / GMP_NUMB_BITS); - if (index < r->limbs && index < 2*NUM_LIMBS) { - r->data[i] = r->data[index]; - } else { - r->data[i] = 0; - } - } - } - while (r->limbs>1 && r->data[r->limbs-1]==0) { - r->limbs--; - } -} - -static void secp256k1_num_negate(secp256k1_num *r) { - r->neg ^= 1; -} - -#endif /* SECP256K1_NUM_REPR_IMPL_H */ diff --git a/src/num_impl.h b/src/num_impl.h deleted file mode 100644 index c45193b033..0000000000 --- a/src/num_impl.h +++ /dev/null @@ -1,24 +0,0 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef SECP256K1_NUM_IMPL_H -#define SECP256K1_NUM_IMPL_H - -#if defined HAVE_CONFIG_H -#include "libsecp256k1-config.h" -#endif - -#include "num.h" - -#if defined(USE_NUM_GMP) -#include "num_gmp_impl.h" -#elif defined(USE_NUM_NONE) -/* Nothing. */ -#else -#error "Please select num implementation" -#endif - -#endif /* SECP256K1_NUM_IMPL_H */ diff --git a/src/scalar.h b/src/scalar.h index fb3fb187ce..aaaa3d8827 100644 --- a/src/scalar.h +++ b/src/scalar.h @@ -1,13 +1,12 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "num.h" #include "util.h" #if defined HAVE_CONFIG_H @@ -63,9 +62,6 @@ static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, * the low bits that were shifted off */ static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); -/** Compute the square of a scalar (modulo the group order). */ -static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a); - /** Compute the inverse of a scalar (modulo the group order). */ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); @@ -91,14 +87,6 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar *a); * Returns -1 if the number was negated, 1 otherwise */ static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); -#ifndef USE_NUM_NONE -/** Convert a scalar to a number. */ -static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a); - -/** Get the order of the group as a number. */ -static void secp256k1_scalar_order_get_num(secp256k1_num *r); -#endif - /** Compare two scalars. */ static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); diff --git a/src/scalar_4x64.h b/src/scalar_4x64.h index 19c7495d1c..700964291e 100644 --- a/src/scalar_4x64.h +++ b/src/scalar_4x64.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/scalar_4x64_impl.h b/src/scalar_4x64_impl.h index 73cbd5e18a..a1def26fca 100644 --- a/src/scalar_4x64_impl.h +++ b/src/scalar_4x64_impl.h @@ -1,12 +1,14 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "modinv64_impl.h" + /* Limbs of the secp256k1 order. */ #define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL) #define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL) @@ -212,28 +214,6 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { VERIFY_CHECK(c1 >= th); \ } -/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ -#define muladd2(a,b) { \ - uint64_t tl, th, th2, tl2; \ - { \ - uint128_t t = (uint128_t)a * b; \ - th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ - tl = t; \ - } \ - th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \ - c2 += (th2 < th); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((th2 >= th) || (c2 != 0)); \ - tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \ - th2 += (tl2 < tl); /* at most 0xFFFFFFFFFFFFFFFF */ \ - c0 += tl2; /* overflow is handled on the next line */ \ - th2 += (c0 < tl2); /* second overflow is handled on the next line */ \ - c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \ - c1 += th2; /* overflow is handled on the next line */ \ - c2 += (c1 < th2); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \ -} - /** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ #define sumadd(a) { \ unsigned int over; \ @@ -743,148 +723,10 @@ static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, c #endif } -static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) { -#ifdef USE_ASM_X86_64 - __asm__ __volatile__( - /* Preload */ - "movq 0(%%rdi), %%r11\n" - "movq 8(%%rdi), %%r12\n" - "movq 16(%%rdi), %%r13\n" - "movq 24(%%rdi), %%r14\n" - /* (rax,rdx) = a0 * a0 */ - "movq %%r11, %%rax\n" - "mulq %%r11\n" - /* Extract l0 */ - "movq %%rax, 0(%%rsi)\n" - /* (r8,r9,r10) = (rdx,0) */ - "movq %%rdx, %%r8\n" - "xorq %%r9, %%r9\n" - "xorq %%r10, %%r10\n" - /* (r8,r9,r10) += 2 * a0 * a1 */ - "movq %%r11, %%rax\n" - "mulq %%r12\n" - "addq %%rax, %%r8\n" - "adcq %%rdx, %%r9\n" - "adcq $0, %%r10\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) += 2 * a0 * a2 */ - "movq %%r11, %%rax\n" - "mulq %%r13\n" - "addq %%rax, %%r9\n" - "adcq %%rdx, %%r10\n" - "adcq $0, %%r8\n" - "addq %%rax, %%r9\n" - "adcq %%rdx, %%r10\n" - "adcq $0, %%r8\n" - /* (r9,r10,r8) += a1 * a1 */ - "movq %%r12, %%rax\n" - "mulq %%r12\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) += 2 * a0 * a3 */ - "movq %%r11, %%rax\n" - "mulq %%r14\n" - "addq %%rax, %%r10\n" - "adcq %%rdx, %%r8\n" - "adcq $0, %%r9\n" - "addq %%rax, %%r10\n" - "adcq %%rdx, %%r8\n" - "adcq $0, %%r9\n" - /* (r10,r8,r9) += 2 * a1 * a2 */ - "movq %%r12, %%rax\n" - "mulq %%r13\n" - "addq %%rax, %%r10\n" - "adcq %%rdx, %%r8\n" - "adcq $0, %%r9\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) += 2 * a1 * a3 */ - "movq %%r12, %%rax\n" - "mulq %%r14\n" - "addq %%rax, %%r8\n" - "adcq %%rdx, %%r9\n" - "adcq $0, %%r10\n" - "addq %%rax, %%r8\n" - "adcq %%rdx, %%r9\n" - "adcq $0, %%r10\n" - /* (r8,r9,r10) += a2 * a2 */ - "movq %%r13, %%rax\n" - "mulq %%r13\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) += 2 * a2 * a3 */ - "movq %%r13, %%rax\n" - "mulq %%r14\n" - "addq %%rax, %%r9\n" - "adcq %%rdx, %%r10\n" - "adcq $0, %%r8\n" - "addq %%rax, %%r9\n" - "adcq %%rdx, %%r10\n" - "adcq $0, %%r8\n" - /* Extract l5 */ - "movq %%r9, 40(%%rsi)\n" - /* (r10,r8) += a3 * a3 */ - "movq %%r14, %%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" - : - : "S"(l), "D"(a->d) - : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "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], a->d[0]); - extract_fast(l[0]); - muladd2(a->d[0], a->d[1]); - extract(l[1]); - muladd2(a->d[0], a->d[2]); - muladd(a->d[1], a->d[1]); - extract(l[2]); - muladd2(a->d[0], a->d[3]); - muladd2(a->d[1], a->d[2]); - extract(l[3]); - muladd2(a->d[1], a->d[3]); - muladd(a->d[2], a->d[2]); - extract(l[4]); - muladd2(a->d[2], a->d[3]); - extract(l[5]); - muladd_fast(a->d[3], a->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 muladd2 #undef extract #undef extract_fast @@ -906,12 +748,6 @@ static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { return ret; } -static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { - uint64_t l[8]; - secp256k1_scalar_sqr_512(l, a); - secp256k1_scalar_reduce_512(r, l); -} - 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]; @@ -955,4 +791,78 @@ static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const se 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/scalar_8x32.h b/src/scalar_8x32.h index 2c9a348e24..17863ef937 100644 --- a/src/scalar_8x32.h +++ b/src/scalar_8x32.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/scalar_8x32_impl.h b/src/scalar_8x32_impl.h index 6853f79ecc..62c7ae7156 100644 --- a/src/scalar_8x32_impl.h +++ b/src/scalar_8x32_impl.h @@ -1,12 +1,14 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 "modinv32_impl.h" + /* Limbs of the secp256k1 order. */ #define SECP256K1_N_0 ((uint32_t)0xD0364141UL) #define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL) @@ -291,28 +293,6 @@ static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { VERIFY_CHECK(c1 >= th); \ } -/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ -#define muladd2(a,b) { \ - uint32_t tl, th, th2, tl2; \ - { \ - uint64_t t = (uint64_t)a * b; \ - th = t >> 32; /* at most 0xFFFFFFFE */ \ - tl = t; \ - } \ - th2 = th + th; /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \ - c2 += (th2 < th); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((th2 >= th) || (c2 != 0)); \ - tl2 = tl + tl; /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \ - th2 += (tl2 < tl); /* at most 0xFFFFFFFF */ \ - c0 += tl2; /* overflow is handled on the next line */ \ - th2 += (c0 < tl2); /* second overflow is handled on the next line */ \ - c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \ - c1 += th2; /* overflow is handled on the next line */ \ - c2 += (c1 < th2); /* never overflows by contract (verified the next line) */ \ - VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \ -} - /** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ #define sumadd(a) { \ unsigned int over; \ @@ -576,71 +556,10 @@ static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, con l[15] = c0; } -static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) { - /* 96 bit accumulator. */ - uint32_t c0 = 0, c1 = 0, c2 = 0; - - /* l[0..15] = a[0..7]^2. */ - muladd_fast(a->d[0], a->d[0]); - extract_fast(l[0]); - muladd2(a->d[0], a->d[1]); - extract(l[1]); - muladd2(a->d[0], a->d[2]); - muladd(a->d[1], a->d[1]); - extract(l[2]); - muladd2(a->d[0], a->d[3]); - muladd2(a->d[1], a->d[2]); - extract(l[3]); - muladd2(a->d[0], a->d[4]); - muladd2(a->d[1], a->d[3]); - muladd(a->d[2], a->d[2]); - extract(l[4]); - muladd2(a->d[0], a->d[5]); - muladd2(a->d[1], a->d[4]); - muladd2(a->d[2], a->d[3]); - extract(l[5]); - muladd2(a->d[0], a->d[6]); - muladd2(a->d[1], a->d[5]); - muladd2(a->d[2], a->d[4]); - muladd(a->d[3], a->d[3]); - extract(l[6]); - muladd2(a->d[0], a->d[7]); - muladd2(a->d[1], a->d[6]); - muladd2(a->d[2], a->d[5]); - muladd2(a->d[3], a->d[4]); - extract(l[7]); - muladd2(a->d[1], a->d[7]); - muladd2(a->d[2], a->d[6]); - muladd2(a->d[3], a->d[5]); - muladd(a->d[4], a->d[4]); - extract(l[8]); - muladd2(a->d[2], a->d[7]); - muladd2(a->d[3], a->d[6]); - muladd2(a->d[4], a->d[5]); - extract(l[9]); - muladd2(a->d[3], a->d[7]); - muladd2(a->d[4], a->d[6]); - muladd(a->d[5], a->d[5]); - extract(l[10]); - muladd2(a->d[4], a->d[7]); - muladd2(a->d[5], a->d[6]); - extract(l[11]); - muladd2(a->d[5], a->d[7]); - muladd(a->d[6], a->d[6]); - extract(l[12]); - muladd2(a->d[6], a->d[7]); - extract(l[13]); - muladd_fast(a->d[7], a->d[7]); - extract_fast(l[14]); - VERIFY_CHECK(c1 == 0); - l[15] = c0; -} - #undef sumadd #undef sumadd_fast #undef muladd #undef muladd_fast -#undef muladd2 #undef extract #undef extract_fast @@ -666,12 +585,6 @@ static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { return ret; } -static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { - uint32_t l[16]; - secp256k1_scalar_sqr_512(l, a); - secp256k1_scalar_reduce_512(r, l); -} - 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]; @@ -731,4 +644,92 @@ static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const se 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/scalar_impl.h b/src/scalar_impl.h index fc75891818..e124474773 100644 --- a/src/scalar_impl.h +++ b/src/scalar_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -31,231 +31,12 @@ 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); -#ifndef USE_NUM_NONE -static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) { - unsigned char c[32]; - secp256k1_scalar_get_b32(c, a); - secp256k1_num_set_bin(r, c, 32); -} - -/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */ -static void secp256k1_scalar_order_get_num(secp256k1_num *r) { -#if defined(EXHAUSTIVE_TEST_ORDER) - static const unsigned char order[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,EXHAUSTIVE_TEST_ORDER - }; -#else - static const unsigned char order[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 - }; -#endif - secp256k1_num_set_bin(r, order, 32); -} -#endif - 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)); } -static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { -#if defined(EXHAUSTIVE_TEST_ORDER) - 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); -} -#else - secp256k1_scalar *t; - int i; - /* First compute xN as x ^ (2^N - 1) for some values of N, - * and uM as x ^ M for some values of M. */ - secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126; - secp256k1_scalar u2, u5, u9, u11, u13; - - secp256k1_scalar_sqr(&u2, x); - secp256k1_scalar_mul(&x2, &u2, x); - secp256k1_scalar_mul(&u5, &u2, &x2); - secp256k1_scalar_mul(&x3, &u5, &u2); - secp256k1_scalar_mul(&u9, &x3, &u2); - secp256k1_scalar_mul(&u11, &u9, &u2); - secp256k1_scalar_mul(&u13, &u11, &u2); - - secp256k1_scalar_sqr(&x6, &u13); - secp256k1_scalar_sqr(&x6, &x6); - secp256k1_scalar_mul(&x6, &x6, &u11); - - secp256k1_scalar_sqr(&x8, &x6); - secp256k1_scalar_sqr(&x8, &x8); - secp256k1_scalar_mul(&x8, &x8, &x2); - - secp256k1_scalar_sqr(&x14, &x8); - for (i = 0; i < 5; i++) { - secp256k1_scalar_sqr(&x14, &x14); - } - secp256k1_scalar_mul(&x14, &x14, &x6); - - secp256k1_scalar_sqr(&x28, &x14); - for (i = 0; i < 13; i++) { - secp256k1_scalar_sqr(&x28, &x28); - } - secp256k1_scalar_mul(&x28, &x28, &x14); - - secp256k1_scalar_sqr(&x56, &x28); - for (i = 0; i < 27; i++) { - secp256k1_scalar_sqr(&x56, &x56); - } - secp256k1_scalar_mul(&x56, &x56, &x28); - - secp256k1_scalar_sqr(&x112, &x56); - for (i = 0; i < 55; i++) { - secp256k1_scalar_sqr(&x112, &x112); - } - secp256k1_scalar_mul(&x112, &x112, &x56); - - secp256k1_scalar_sqr(&x126, &x112); - for (i = 0; i < 13; i++) { - secp256k1_scalar_sqr(&x126, &x126); - } - secp256k1_scalar_mul(&x126, &x126, &x14); - - /* Then accumulate the final result (t starts at x126). */ - t = &x126; - for (i = 0; i < 3; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u5); /* 101 */ - for (i = 0; i < 4; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 4; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u5); /* 101 */ - for (i = 0; i < 5; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u11); /* 1011 */ - for (i = 0; i < 4; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u11); /* 1011 */ - for (i = 0; i < 4; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 5; i++) { /* 00 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 6; i++) { /* 00 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u13); /* 1101 */ - for (i = 0; i < 4; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u5); /* 101 */ - for (i = 0; i < 3; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 5; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u9); /* 1001 */ - for (i = 0; i < 6; i++) { /* 000 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u5); /* 101 */ - for (i = 0; i < 10; i++) { /* 0000000 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 4; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x3); /* 111 */ - for (i = 0; i < 9; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x8); /* 11111111 */ - for (i = 0; i < 5; i++) { /* 0 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u9); /* 1001 */ - for (i = 0; i < 6; i++) { /* 00 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u11); /* 1011 */ - for (i = 0; i < 4; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u13); /* 1101 */ - for (i = 0; i < 5; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &x2); /* 11 */ - for (i = 0; i < 6; i++) { /* 00 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u13); /* 1101 */ - for (i = 0; i < 10; i++) { /* 000000 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u13); /* 1101 */ - for (i = 0; i < 4; i++) { - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, &u9); /* 1001 */ - for (i = 0; i < 6; i++) { /* 00000 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(t, t, x); /* 1 */ - for (i = 0; i < 8; i++) { /* 00 */ - secp256k1_scalar_sqr(t, t); - } - secp256k1_scalar_mul(r, t, &x6); /* 111111 */ -} - -SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { - return !(a->d[0] & 1); -} -#endif - -static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { -#if defined(USE_SCALAR_INV_BUILTIN) - secp256k1_scalar_inverse(r, x); -#elif defined(USE_SCALAR_INV_NUM) - unsigned char b[32]; - secp256k1_num n, m; - secp256k1_scalar t = *x; - secp256k1_scalar_get_b32(b, &t); - secp256k1_num_set_bin(&n, b, 32); - secp256k1_scalar_order_get_num(&m); - secp256k1_num_mod_inverse(&n, &n, &m); - secp256k1_num_get_bin(b, 32, &n); - secp256k1_scalar_set_b32(r, b, NULL); - /* Verify that the inverse was computed correctly, without GMP code. */ - secp256k1_scalar_mul(&t, &t, r); - CHECK(secp256k1_scalar_is_one(&t)); -#else -#error "Please select scalar inverse implementation" -#endif -} - /* These parameters are generated using sage/gen_exhaustive_groups.sage. */ #if defined(EXHAUSTIVE_TEST_ORDER) # if EXHAUSTIVE_TEST_ORDER == 13 diff --git a/src/scalar_low.h b/src/scalar_low.h index 2794a7f171..67051bd30b 100644 --- a/src/scalar_low.h +++ b/src/scalar_low.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/scalar_low_impl.h b/src/scalar_low_impl.h index a615ec074b..7176f0b2ca 100644 --- a/src/scalar_low_impl.h +++ b/src/scalar_low_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2015 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -104,10 +104,6 @@ static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { return ret; } -static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { - *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER; -} - static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { *r1 = *a; *r2 = 0; @@ -125,4 +121,19 @@ static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const se *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/scratch.h b/src/scratch.h index 77b35d126b..9dcb7581f6 100644 --- a/src/scratch.h +++ b/src/scratch.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2017 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ - -#ifndef _SECP256K1_SCRATCH_ -#define _SECP256K1_SCRATCH_ +/*********************************************************************** + * 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) */ diff --git a/src/scratch_impl.h b/src/scratch_impl.h index f381e2e322..688e18eb66 100644 --- a/src/scratch_impl.h +++ b/src/scratch_impl.h @@ -1,11 +1,11 @@ -/********************************************************************** - * Copyright (c) 2017 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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_ +#ifndef SECP256K1_SCRATCH_IMPL_H +#define SECP256K1_SCRATCH_IMPL_H #include "util.h" #include "scratch.h" diff --git a/src/secp256k1.c b/src/secp256k1.c index dae506d08c..aef3f99ac3 100644 --- a/src/secp256k1.c +++ b/src/secp256k1.c @@ -1,15 +1,14 @@ -/********************************************************************** - * Copyright (c) 2013-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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.* + ***********************************************************************/ #include "include/secp256k1.h" #include "include/secp256k1_preallocated.h" #include "assumptions.h" #include "util.h" -#include "num_impl.h" #include "field_impl.h" #include "scalar_impl.h" #include "group_impl.h" @@ -86,6 +85,8 @@ const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_no_pr size_t secp256k1_context_preallocated_size(unsigned int flags) { size_t ret = ROUND_TO_ALIGN(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, @@ -122,21 +123,21 @@ secp256k1_context* secp256k1_context_preallocated_create(void* prealloc, unsigne if (!secp256k1_selftest()) { secp256k1_callback_call(&default_error_callback, "self test failed"); } - VERIFY_CHECK(prealloc != NULL); + prealloc_size = secp256k1_context_preallocated_size(flags); + if (prealloc_size == 0) { + return NULL; + } + VERIFY_CHECK(prealloc != NULL); ret = (secp256k1_context*)manual_alloc(&prealloc, sizeof(secp256k1_context), base, prealloc_size); ret->illegal_callback = default_illegal_callback; ret->error_callback = default_error_callback; - if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) { - secp256k1_callback_call(&ret->illegal_callback, - "Invalid flags"); - return NULL; - } - secp256k1_ecmult_context_init(&ret->ecmult_ctx); secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx); + /* Flags have been checked by secp256k1_context_preallocated_size. */ + VERIFY_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_CONTEXT); if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) { secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &prealloc); } @@ -420,17 +421,17 @@ int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ return ret; } -int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) { +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(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); - ARG_CHECK(msg32 != NULL); + ARG_CHECK(msghash32 != NULL); ARG_CHECK(sig != NULL); ARG_CHECK(pubkey != NULL); - secp256k1_scalar_set_b32(&m, msg32, 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) && @@ -531,16 +532,16 @@ static int secp256k1_ecdsa_sign_inner(const secp256k1_context* ctx, secp256k1_sc return ret; } -int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { +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(msg32 != NULL); + ARG_CHECK(msghash32 != NULL); ARG_CHECK(signature != NULL); ARG_CHECK(seckey != NULL); - ret = secp256k1_ecdsa_sign_inner(ctx, &r, &s, NULL, msg32, seckey, noncefp, noncedata); + ret = secp256k1_ecdsa_sign_inner(ctx, &r, &s, NULL, msghash32, seckey, noncefp, noncedata); secp256k1_ecdsa_signature_save(signature, &r, &s); return ret; } @@ -580,7 +581,7 @@ int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *p ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &seckey_scalar, &p, seckey); secp256k1_pubkey_save(pubkey, &p); - memczero(pubkey, sizeof(*pubkey), !ret); + secp256k1_memczero(pubkey, sizeof(*pubkey), !ret); secp256k1_scalar_clear(&seckey_scalar); return ret; @@ -621,26 +622,26 @@ int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *p } -static int secp256k1_ec_seckey_tweak_add_helper(secp256k1_scalar *sec, const unsigned char *tweak) { +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, tweak, &overflow); + 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 *tweak) { +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(tweak != NULL); + ARG_CHECK(tweak32 != NULL); ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); - ret &= secp256k1_ec_seckey_tweak_add_helper(&sec, tweak); + ret &= secp256k1_ec_seckey_tweak_add_helper(&sec, tweak32); secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); secp256k1_scalar_get_b32(seckey, &sec); @@ -648,28 +649,28 @@ int secp256k1_ec_seckey_tweak_add(const secp256k1_context* ctx, unsigned char *s return ret; } -int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { - return secp256k1_ec_seckey_tweak_add(ctx, seckey, tweak); +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(const secp256k1_ecmult_context* ecmult_ctx, secp256k1_ge *p, const unsigned char *tweak) { +static int secp256k1_ec_pubkey_tweak_add_helper(const secp256k1_ecmult_context* ecmult_ctx, secp256k1_ge *p, const unsigned char *tweak32) { secp256k1_scalar term; int overflow = 0; - secp256k1_scalar_set_b32(&term, tweak, &overflow); + secp256k1_scalar_set_b32(&term, tweak32, &overflow); return !overflow && secp256k1_eckey_pubkey_tweak_add(ecmult_ctx, p, &term); } -int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) { +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(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); ARG_CHECK(pubkey != NULL); - ARG_CHECK(tweak != 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(&ctx->ecmult_ctx, &p, tweak); + ret = ret && secp256k1_ec_pubkey_tweak_add_helper(&ctx->ecmult_ctx, &p, tweak32); if (ret) { secp256k1_pubkey_save(pubkey, &p); } @@ -677,16 +678,16 @@ int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey return ret; } -int secp256k1_ec_seckey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { +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(tweak != NULL); + ARG_CHECK(tweak32 != NULL); - secp256k1_scalar_set_b32(&factor, tweak, &overflow); + 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); @@ -697,11 +698,11 @@ int secp256k1_ec_seckey_tweak_mul(const secp256k1_context* ctx, unsigned char *s return ret; } -int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { - return secp256k1_ec_seckey_tweak_mul(ctx, seckey, tweak); +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 *tweak) { +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; @@ -709,9 +710,9 @@ int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey VERIFY_CHECK(ctx != NULL); ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); ARG_CHECK(pubkey != NULL); - ARG_CHECK(tweak != NULL); + ARG_CHECK(tweak32 != NULL); - secp256k1_scalar_set_b32(&factor, tweak, &overflow); + secp256k1_scalar_set_b32(&factor, tweak32, &overflow); ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); memset(pubkey, 0, sizeof(*pubkey)); if (ret) { diff --git a/src/selftest.h b/src/selftest.h index 0e37510c1e..52f1b8442e 100644 --- a/src/selftest.h +++ b/src/selftest.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2020 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/testrand.h b/src/testrand.h index a76003d5b8..667d1867bd 100644 --- a/src/testrand.h +++ b/src/testrand.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/testrand_impl.h b/src/testrand_impl.h index 3392566329..e643778f36 100644 --- a/src/testrand_impl.h +++ b/src/testrand_impl.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013-2015 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 diff --git a/src/tests.c b/src/tests.c index bb4b5b4c07..a146394305 100644 --- a/src/tests.c +++ b/src/tests.c @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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.* + ***********************************************************************/ #if defined HAVE_CONFIG_H #include "libsecp256k1-config.h" @@ -18,12 +18,13 @@ #include "include/secp256k1.h" #include "include/secp256k1_preallocated.h" #include "testrand_impl.h" +#include "util.h" #ifdef ENABLE_OPENSSL_TESTS -#include "openssl/bn.h" -#include "openssl/ec.h" -#include "openssl/ecdsa.h" -#include "openssl/obj_mac.h" +#include <openssl/bn.h> +#include <openssl/ec.h> +#include <openssl/ecdsa.h> +#include <openssl/obj_mac.h> # if OPENSSL_VERSION_NUMBER < 0x10100000L void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;} # endif @@ -32,6 +33,11 @@ void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) #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" +#endif + static int count = 64; static secp256k1_context *ctx = NULL; @@ -416,6 +422,25 @@ void run_scratch_tests(void) { secp256k1_context_destroy(none); } +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 *****/ void run_sha256_tests(void) { @@ -611,202 +636,924 @@ void run_rand_int(void) { } } -/***** NUM TESTS *****/ +/***** MODINV TESTS *****/ + +/* Compute the modular inverse of (odd) x mod 2^64. */ +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; +} -#ifndef USE_NUM_NONE -void random_num_negate(secp256k1_num *num) { - if (secp256k1_testrand_bits(1)) { - secp256k1_num_negate(num); +/* compute out = (a*b) mod m; if b=NULL, treat b=1. + * + * 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). */ +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; + } + } } -} -void random_num_order_test(secp256k1_num *num) { - secp256k1_scalar sc; - random_scalar_order_test(&sc); - secp256k1_scalar_get_num(num, &sc); + /* 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); } -void random_num_order(secp256k1_num *num) { - secp256k1_scalar sc; - random_scalar_order(&sc); - secp256k1_scalar_get_num(num, &sc); +/* Convert a 256-bit number represented as 16 uint16_t's to signed30 notation. */ +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); + } } -void test_num_negate(void) { - secp256k1_num n1; - secp256k1_num n2; - random_num_order_test(&n1); /* n1 = R */ - random_num_negate(&n1); - secp256k1_num_copy(&n2, &n1); /* n2 = R */ - secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */ - CHECK(secp256k1_num_is_zero(&n1)); - secp256k1_num_copy(&n1, &n2); /* n1 = R */ - secp256k1_num_negate(&n1); /* n1 = -R */ - CHECK(!secp256k1_num_is_zero(&n1)); - secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */ - CHECK(secp256k1_num_is_zero(&n1)); - secp256k1_num_copy(&n1, &n2); /* n1 = R */ - secp256k1_num_negate(&n1); /* n1 = -R */ - CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2)); - secp256k1_num_negate(&n1); /* n1 = R */ - CHECK(secp256k1_num_eq(&n1, &n2)); +/* Convert a 256-bit number in signed30 notation to a representation as 16 uint16_t's. */ +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); + } } -void test_num_add_sub(void) { +/* Randomly mutate the sign of limbs in signed30 representation, without changing the value. */ +void mutate_sign_signed30(secp256k1_modinv32_signed30* x) { int i; - secp256k1_scalar s; - secp256k1_num n1; - secp256k1_num n2; - secp256k1_num n1p2, n2p1, n1m2, n2m1; - random_num_order_test(&n1); /* n1 = R1 */ - if (secp256k1_testrand_bits(1)) { - random_num_negate(&n1); + for (i = 0; i < 16; ++i) { + int pos = secp256k1_testrand_int(8); + 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; + } } - random_num_order_test(&n2); /* n2 = R2 */ - if (secp256k1_testrand_bits(1)) { - random_num_negate(&n2); - } - secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */ - secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */ - secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */ - secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */ - CHECK(secp256k1_num_eq(&n1p2, &n2p1)); - CHECK(!secp256k1_num_eq(&n1p2, &n1m2)); - secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */ - CHECK(secp256k1_num_eq(&n2m1, &n1m2)); - CHECK(!secp256k1_num_eq(&n2m1, &n1)); - secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */ - CHECK(secp256k1_num_eq(&n2m1, &n1)); - CHECK(!secp256k1_num_eq(&n2p1, &n1)); - secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */ - CHECK(secp256k1_num_eq(&n2p1, &n1)); - - /* check is_one */ - secp256k1_scalar_set_int(&s, 1); - secp256k1_scalar_get_num(&n1, &s); - CHECK(secp256k1_num_is_one(&n1)); - /* check that 2^n + 1 is never 1 */ - secp256k1_scalar_get_num(&n2, &s); - for (i = 0; i < 250; ++i) { - secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */ - secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */ - CHECK(!secp256k1_num_is_one(&n1p2)); +} + +/* Test secp256k1_modinv32{_var}, using inputs in 16-bit limb format, and returning inverse. */ +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); + mutate_sign_signed30(&m.modulus); + + /* 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); + + 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]); } } -void test_num_mod(void) { +#ifdef SECP256K1_WIDEMUL_INT128 +/* Convert a 256-bit number represented as 16 uint16_t's to signed62 notation. */ +void uint16_to_signed62(secp256k1_modinv64_signed62* out, const uint16_t* in) { int i; - secp256k1_scalar s; - secp256k1_num order, n; - - /* check that 0 mod anything is 0 */ - random_scalar_order_test(&s); - secp256k1_scalar_get_num(&order, &s); - secp256k1_scalar_set_int(&s, 0); - secp256k1_scalar_get_num(&n, &s); - secp256k1_num_mod(&n, &order); - CHECK(secp256k1_num_is_zero(&n)); - - /* check that anything mod 1 is 0 */ - secp256k1_scalar_set_int(&s, 1); - secp256k1_scalar_get_num(&order, &s); - secp256k1_scalar_get_num(&n, &s); - secp256k1_num_mod(&n, &order); - CHECK(secp256k1_num_is_zero(&n)); - - /* check that increasing the number past 2^256 does not break this */ - random_scalar_order_test(&s); - secp256k1_scalar_get_num(&n, &s); - /* multiply by 2^8, which'll test this case with high probability */ - for (i = 0; i < 8; ++i) { - secp256k1_num_add(&n, &n, &n); + 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); } - secp256k1_num_mod(&n, &order); - CHECK(secp256k1_num_is_zero(&n)); } -void test_num_jacobi(void) { - secp256k1_scalar sqr; - secp256k1_scalar small; - secp256k1_scalar five; /* five is not a quadratic residue */ - secp256k1_num order, n; +/* Convert a 256-bit number in signed62 notation to a representation as 16 uint16_t's. */ +void signed62_to_uint16(uint16_t* out, const secp256k1_modinv64_signed62* in) { int i; - /* squares mod 5 are 1, 4 */ - const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 }; + memset(out, 0, 32); + for (i = 0; i < 256; ++i) { + out[i >> 4] |= (((in->v[i / 62]) >> (i % 62)) & 1) << (i & 15); + } +} - /* check some small values with 5 as the order */ - secp256k1_scalar_set_int(&five, 5); - secp256k1_scalar_get_num(&order, &five); - for (i = 0; i < 10; ++i) { - secp256k1_scalar_set_int(&small, i); - secp256k1_scalar_get_num(&n, &small); - CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]); +/* Randomly mutate the sign of limbs in signed62 representation, without changing the value. */ +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_int(4); + 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 large values with 5 as group order */ - secp256k1_scalar_get_num(&order, &five); - /* we first need a scalar which is not a multiple of 5 */ - do { - secp256k1_num fiven; - random_scalar_order_test(&sqr); - secp256k1_scalar_get_num(&fiven, &five); - secp256k1_scalar_get_num(&n, &sqr); - secp256k1_num_mod(&n, &fiven); - } while (secp256k1_num_is_zero(&n)); - /* next force it to be a residue. 2 is a nonresidue mod 5 so we can - * just multiply by two, i.e. add the number to itself */ - if (secp256k1_num_jacobi(&n, &order) == -1) { - secp256k1_num_add(&n, &n, &n); - } - - /* test residue */ - CHECK(secp256k1_num_jacobi(&n, &order) == 1); - /* test nonresidue */ - secp256k1_num_add(&n, &n, &n); - CHECK(secp256k1_num_jacobi(&n, &order) == -1); - - /** test with secp group order as order */ - secp256k1_scalar_order_get_num(&order); - random_scalar_order_test(&sqr); - secp256k1_scalar_sqr(&sqr, &sqr); - /* test residue */ - secp256k1_scalar_get_num(&n, &sqr); - CHECK(secp256k1_num_jacobi(&n, &order) == 1); - /* test nonresidue */ - secp256k1_scalar_mul(&sqr, &sqr, &five); - secp256k1_scalar_get_num(&n, &sqr); - CHECK(secp256k1_num_jacobi(&n, &order) == -1); - /* test multiple of the order*/ - CHECK(secp256k1_num_jacobi(&order, &order) == 0); - - /* check one less than the order */ - secp256k1_scalar_set_int(&small, 1); - secp256k1_scalar_get_num(&n, &small); - secp256k1_num_sub(&n, &order, &n); - CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */ +/* Test secp256k1_modinv64{_var}, using inputs in 16-bit limb format, and returning inverse. */ +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); + mutate_sign_signed62(&m.modulus); + + /* 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); + + 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 -void run_num_smalltests(void) { +/* test if a and b are coprime */ +int coprime(const uint16_t* a, const uint16_t* b) { + uint16_t x[16], y[16], t[16]; int i; - for (i = 0; i < 100*count; i++) { - test_num_negate(); - test_num_add_sub(); - test_num_mod(); - test_num_jacobi(); + 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; } + +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 + } + } +} /***** SCALAR TESTS *****/ + void scalar_test(void) { secp256k1_scalar s; secp256k1_scalar s1; secp256k1_scalar s2; -#ifndef USE_NUM_NONE - secp256k1_num snum, s1num, s2num; - secp256k1_num order, half_order; -#endif unsigned char c[32]; /* Set 's' to a random scalar, with value 'snum'. */ @@ -819,16 +1566,6 @@ void scalar_test(void) { random_scalar_order_test(&s2); secp256k1_scalar_get_b32(c, &s2); -#ifndef USE_NUM_NONE - secp256k1_scalar_get_num(&snum, &s); - secp256k1_scalar_get_num(&s1num, &s1); - secp256k1_scalar_get_num(&s2num, &s2); - - secp256k1_scalar_order_get_num(&order); - half_order = order; - secp256k1_num_shift(&half_order, 1); -#endif - { int i; /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */ @@ -868,80 +1605,6 @@ void scalar_test(void) { CHECK(secp256k1_scalar_eq(&n, &s)); } -#ifndef USE_NUM_NONE - { - /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */ - secp256k1_num rnum; - secp256k1_num r2num; - secp256k1_scalar r; - secp256k1_num_add(&rnum, &snum, &s2num); - secp256k1_num_mod(&rnum, &order); - secp256k1_scalar_add(&r, &s, &s2); - secp256k1_scalar_get_num(&r2num, &r); - CHECK(secp256k1_num_eq(&rnum, &r2num)); - } - - { - /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */ - secp256k1_scalar r; - secp256k1_num r2num; - secp256k1_num rnum; - secp256k1_num_mul(&rnum, &snum, &s2num); - secp256k1_num_mod(&rnum, &order); - secp256k1_scalar_mul(&r, &s, &s2); - secp256k1_scalar_get_num(&r2num, &r); - CHECK(secp256k1_num_eq(&rnum, &r2num)); - /* The result can only be zero if at least one of the factors was zero. */ - CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2))); - /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */ - CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2))); - CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s))); - } - - { - secp256k1_scalar neg; - secp256k1_num negnum; - secp256k1_num negnum2; - /* Check that comparison with zero matches comparison with zero on the number. */ - CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s)); - /* Check that comparison with the half order is equal to testing for high scalar. */ - CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0)); - secp256k1_scalar_negate(&neg, &s); - secp256k1_num_sub(&negnum, &order, &snum); - secp256k1_num_mod(&negnum, &order); - /* Check that comparison with the half order is equal to testing for high scalar after negation. */ - CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0)); - /* Negating should change the high property, unless the value was already zero. */ - CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s)); - secp256k1_scalar_get_num(&negnum2, &neg); - /* Negating a scalar should be equal to (order - n) mod order on the number. */ - CHECK(secp256k1_num_eq(&negnum, &negnum2)); - secp256k1_scalar_add(&neg, &neg, &s); - /* Adding a number to its negation should result in zero. */ - CHECK(secp256k1_scalar_is_zero(&neg)); - secp256k1_scalar_negate(&neg, &neg); - /* Negating zero should still result in zero. */ - CHECK(secp256k1_scalar_is_zero(&neg)); - } - - { - /* Test secp256k1_scalar_mul_shift_var. */ - secp256k1_scalar r; - secp256k1_num one; - secp256k1_num rnum; - secp256k1_num rnum2; - unsigned char cone[1] = {0x01}; - unsigned int shift = 256 + secp256k1_testrand_int(257); - secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift); - secp256k1_num_mul(&rnum, &s1num, &s2num); - secp256k1_num_shift(&rnum, shift - 1); - secp256k1_num_set_bin(&one, cone, 1); - secp256k1_num_add(&rnum, &rnum, &one); - secp256k1_num_shift(&rnum, 1); - secp256k1_scalar_get_num(&rnum2, &r); - CHECK(secp256k1_num_eq(&rnum, &rnum2)); - } - { /* test secp256k1_scalar_shr_int */ secp256k1_scalar r; @@ -955,34 +1618,6 @@ void scalar_test(void) { CHECK(expected == low); } } -#endif - - { - /* Test that scalar inverses are equal to the inverse of their number modulo the order. */ - if (!secp256k1_scalar_is_zero(&s)) { - secp256k1_scalar inv; -#ifndef USE_NUM_NONE - secp256k1_num invnum; - secp256k1_num invnum2; -#endif - secp256k1_scalar_inverse(&inv, &s); -#ifndef USE_NUM_NONE - secp256k1_num_mod_inverse(&invnum, &snum, &order); - secp256k1_scalar_get_num(&invnum2, &inv); - CHECK(secp256k1_num_eq(&invnum, &invnum2)); -#endif - secp256k1_scalar_mul(&inv, &inv, &s); - /* Multiplying a scalar with its inverse must result in one. */ - CHECK(secp256k1_scalar_is_one(&inv)); - secp256k1_scalar_inverse(&inv, &inv); - /* Inverting one must result in one. */ - CHECK(secp256k1_scalar_is_one(&inv)); -#ifndef USE_NUM_NONE - secp256k1_scalar_get_num(&invnum, &inv); - CHECK(secp256k1_num_is_one(&invnum)); -#endif - } - } { /* Test commutativity of add. */ @@ -1055,14 +1690,6 @@ void scalar_test(void) { } { - /* Test square. */ - secp256k1_scalar r1, r2; - secp256k1_scalar_sqr(&r1, &s1); - secp256k1_scalar_mul(&r2, &s1, &s1); - CHECK(secp256k1_scalar_eq(&r1, &r2)); - } - - { /* Test multiplicative identity. */ secp256k1_scalar r1, v1; secp256k1_scalar_set_int(&v1,1); @@ -1126,48 +1753,6 @@ void run_scalar_tests(void) { CHECK(secp256k1_scalar_is_zero(&o)); } -#ifndef USE_NUM_NONE - { - /* Test secp256k1_scalar_set_b32 boundary conditions */ - secp256k1_num order; - secp256k1_scalar scalar; - unsigned char bin[32]; - unsigned char bin_tmp[32]; - int overflow = 0; - /* 2^256-1 - order */ - static const secp256k1_scalar all_ones_minus_order = SECP256K1_SCALAR_CONST( - 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000001UL, - 0x45512319UL, 0x50B75FC4UL, 0x402DA173UL, 0x2FC9BEBEUL - ); - - /* A scalar set to 0s should be 0. */ - memset(bin, 0, 32); - secp256k1_scalar_set_b32(&scalar, bin, &overflow); - CHECK(overflow == 0); - CHECK(secp256k1_scalar_is_zero(&scalar)); - - /* A scalar with value of the curve order should be 0. */ - secp256k1_scalar_order_get_num(&order); - secp256k1_num_get_bin(bin, 32, &order); - secp256k1_scalar_set_b32(&scalar, bin, &overflow); - CHECK(overflow == 1); - CHECK(secp256k1_scalar_is_zero(&scalar)); - - /* A scalar with value of the curve order minus one should not overflow. */ - bin[31] -= 1; - secp256k1_scalar_set_b32(&scalar, bin, &overflow); - CHECK(overflow == 0); - secp256k1_scalar_get_b32(bin_tmp, &scalar); - CHECK(secp256k1_memcmp_var(bin, bin_tmp, 32) == 0); - - /* A scalar set to all 1s should overflow. */ - memset(bin, 0xFF, 32); - secp256k1_scalar_set_b32(&scalar, bin, &overflow); - CHECK(overflow == 1); - CHECK(secp256k1_scalar_eq(&scalar, &all_ones_minus_order)); - } -#endif - { /* Does check_overflow check catch all ones? */ static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST( @@ -1190,9 +1775,7 @@ void run_scalar_tests(void) { secp256k1_scalar one; secp256k1_scalar r1; secp256k1_scalar r2; -#if defined(USE_SCALAR_INV_NUM) secp256k1_scalar zzv; -#endif int overflow; unsigned char chal[33][2][32] = { {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00, @@ -1742,10 +2325,8 @@ void run_scalar_tests(void) { if (!secp256k1_scalar_is_zero(&y)) { secp256k1_scalar_inverse(&zz, &y); CHECK(!secp256k1_scalar_check_overflow(&zz)); -#if defined(USE_SCALAR_INV_NUM) secp256k1_scalar_inverse_var(&zzv, &y); CHECK(secp256k1_scalar_eq(&zzv, &zz)); -#endif secp256k1_scalar_mul(&z, &z, &zz); CHECK(!secp256k1_scalar_check_overflow(&z)); CHECK(secp256k1_scalar_eq(&x, &z)); @@ -1753,12 +2334,6 @@ void run_scalar_tests(void) { CHECK(!secp256k1_scalar_check_overflow(&zz)); CHECK(secp256k1_scalar_eq(&one, &zz)); } - secp256k1_scalar_mul(&z, &x, &x); - CHECK(!secp256k1_scalar_check_overflow(&z)); - secp256k1_scalar_sqr(&zz, &x); - CHECK(!secp256k1_scalar_check_overflow(&zz)); - CHECK(secp256k1_scalar_eq(&zz, &z)); - CHECK(secp256k1_scalar_eq(&r2, &zz)); } } } @@ -1814,13 +2389,6 @@ int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { return secp256k1_fe_equal_var(&an, &bn); } -int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) { - secp256k1_fe x; - secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); - secp256k1_fe_mul(&x, a, ai); - return check_fe_equal(&x, &one); -} - void run_field_convert(void) { static const unsigned char b32[32] = { 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, @@ -1940,52 +2508,6 @@ void run_field_misc(void) { } } -void run_field_inv(void) { - secp256k1_fe x, xi, xii; - int i; - for (i = 0; i < 10*count; i++) { - random_fe_non_zero(&x); - secp256k1_fe_inv(&xi, &x); - CHECK(check_fe_inverse(&x, &xi)); - secp256k1_fe_inv(&xii, &xi); - CHECK(check_fe_equal(&x, &xii)); - } -} - -void run_field_inv_var(void) { - secp256k1_fe x, xi, xii; - int i; - for (i = 0; i < 10*count; i++) { - random_fe_non_zero(&x); - secp256k1_fe_inv_var(&xi, &x); - CHECK(check_fe_inverse(&x, &xi)); - secp256k1_fe_inv_var(&xii, &xi); - CHECK(check_fe_equal(&x, &xii)); - } -} - -void run_field_inv_all_var(void) { - secp256k1_fe x[16], xi[16], xii[16]; - int i; - /* Check it's safe to call for 0 elements */ - secp256k1_fe_inv_all_var(xi, x, 0); - for (i = 0; i < count; i++) { - size_t j; - size_t len = secp256k1_testrand_int(15) + 1; - for (j = 0; j < len; j++) { - random_fe_non_zero(&x[j]); - } - secp256k1_fe_inv_all_var(xi, x, len); - for (j = 0; j < len; j++) { - CHECK(check_fe_inverse(&x[j], &xi[j])); - } - secp256k1_fe_inv_all_var(xii, xi, len); - for (j = 0; j < len; j++) { - CHECK(check_fe_equal(&x[j], &xii[j])); - } - } -} - void run_sqr(void) { secp256k1_fe x, s; @@ -2050,6 +2572,318 @@ void run_sqrt(void) { } } +/***** 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) + */ + +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_var)(&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_var)(&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_var)(&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 */ +} + +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(&l, &secp256k1_fe_one); /* 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 */ +} + +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 *****/ void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) { @@ -2111,7 +2945,6 @@ void test_ge(void) { */ 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 *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs)); secp256k1_fe zf; secp256k1_fe zfi2, zfi3; @@ -2145,23 +2978,6 @@ void test_ge(void) { } } - /* Compute z inverses. */ - { - secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs)); - for (i = 0; i < 4 * runs + 1; i++) { - if (i == 0) { - /* The point at infinity does not have a meaningful z inverse. Any should do. */ - do { - random_field_element_test(&zs[i]); - } while(secp256k1_fe_is_zero(&zs[i])); - } else { - zs[i] = gej[i].z; - } - } - secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1); - free(zs); - } - /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */ do { random_field_element_test(&zf); @@ -2270,16 +3086,9 @@ void test_ge(void) { free(gej_shuffled); } - /* Test batch gej -> ge conversion with and without known z ratios. */ + /* Test batch gej -> ge conversion without known z ratios. */ { - secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe)); secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge)); - for (i = 0; i < 4 * runs + 1; i++) { - /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */ - if (i < 4 * runs) { - secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z); - } - } secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1); for (i = 0; i < 4 * runs + 1; i++) { secp256k1_fe s; @@ -2288,7 +3097,6 @@ void test_ge(void) { ge_equals_gej(&ge_set_all[i], &gej[i]); } free(ge_set_all); - free(zr); } /* Test batch gej -> ge conversion with many infinities. */ @@ -2309,7 +3117,6 @@ void test_ge(void) { free(ge); free(gej); - free(zinv); } @@ -2456,64 +3263,35 @@ void run_ec_combine(void) { void test_group_decompress(const secp256k1_fe* x) { /* The input itself, normalized. */ secp256k1_fe fex = *x; - secp256k1_fe fez; - /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */ - secp256k1_ge ge_quad, ge_even, ge_odd; - secp256k1_gej gej_quad; + /* Results of set_xo_var(..., 0), set_xo_var(..., 1). */ + secp256k1_ge ge_even, ge_odd; /* Return values of the above calls. */ - int res_quad, res_even, res_odd; + int res_even, res_odd; secp256k1_fe_normalize_var(&fex); - res_quad = secp256k1_ge_set_xquad(&ge_quad, &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_quad == res_even); - CHECK(res_quad == res_odd); + CHECK(res_even == res_odd); - if (res_quad) { - secp256k1_fe_normalize_var(&ge_quad.x); + if (res_even) { secp256k1_fe_normalize_var(&ge_odd.x); secp256k1_fe_normalize_var(&ge_even.x); - secp256k1_fe_normalize_var(&ge_quad.y); secp256k1_fe_normalize_var(&ge_odd.y); secp256k1_fe_normalize_var(&ge_even.y); /* No infinity allowed. */ - CHECK(!ge_quad.infinity); CHECK(!ge_even.infinity); CHECK(!ge_odd.infinity); /* Check that the x coordinates check out. */ - CHECK(secp256k1_fe_equal_var(&ge_quad.x, x)); CHECK(secp256k1_fe_equal_var(&ge_even.x, x)); CHECK(secp256k1_fe_equal_var(&ge_odd.x, x)); - /* Check that the Y coordinate result in ge_quad is a square. */ - CHECK(secp256k1_fe_is_quad_var(&ge_quad.y)); - /* 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)); - - /* Check secp256k1_gej_has_quad_y_var. */ - secp256k1_gej_set_ge(&gej_quad, &ge_quad); - CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); - do { - random_fe_test(&fez); - } while (secp256k1_fe_is_zero(&fez)); - secp256k1_gej_rescale(&gej_quad, &fez); - CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); - secp256k1_gej_neg(&gej_quad, &gej_quad); - CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); - do { - random_fe_test(&fez); - } while (secp256k1_fe_is_zero(&fez)); - secp256k1_gej_rescale(&gej_quad, &fez); - CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); - secp256k1_gej_neg(&gej_quad, &gej_quad); - CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); } } @@ -4373,8 +5151,10 @@ void test_ecdsa_sign_verify(void) { secp256k1_scalar one; secp256k1_scalar msg, key; secp256k1_scalar sigr, sigs; - int recid; int getrec; + /* Initialize recid to suppress a false positive -Wconditional-uninitialized in clang. + VG_UNDEF ensures that valgrind will still treat the variable as uninitialized. */ + int recid = -1; VG_UNDEF(&recid, sizeof(recid)); random_scalar_order_test(&msg); random_scalar_order_test(&key); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key); @@ -5444,18 +6224,18 @@ void run_ecdsa_openssl(void) { # include "modules/schnorrsig/tests_impl.h" #endif -void run_memczero_test(void) { +void run_secp256k1_memczero_test(void) { unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; unsigned char buf2[sizeof(buf1)]; - /* memczero(..., ..., 0) is a noop. */ + /* secp256k1_memczero(..., ..., 0) is a noop. */ memcpy(buf2, buf1, sizeof(buf1)); - memczero(buf1, sizeof(buf1), 0); + secp256k1_memczero(buf1, sizeof(buf1), 0); CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); - /* memczero(..., ..., 1) zeros the buffer. */ + /* secp256k1_memczero(..., ..., 1) zeros the buffer. */ memset(buf2, 0, sizeof(buf2)); - memczero(buf1, sizeof(buf1) , 1); + secp256k1_memczero(buf1, sizeof(buf1) , 1); CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); } @@ -5626,6 +6406,15 @@ int main(int argc, char **argv) { /* find iteration count */ if (argc > 1) { count = strtol(argv[1], NULL, 0); + } else { + const char* env = getenv("SECP256K1_TEST_ITERS"); + if (env) { + 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); @@ -5646,22 +6435,18 @@ int main(int argc, char **argv) { run_rand_bits(); run_rand_int(); + run_ctz_tests(); + run_modinv_tests(); + run_inverse_tests(); + run_sha256_tests(); run_hmac_sha256_tests(); run_rfc6979_hmac_sha256_tests(); -#ifndef USE_NUM_NONE - /* num tests */ - run_num_smalltests(); -#endif - /* scalar tests */ run_scalar_tests(); /* field tests */ - run_field_inv(); - run_field_inv_var(); - run_field_inv_all_var(); run_field_misc(); run_field_convert(); run_sqr(); @@ -5723,7 +6508,7 @@ int main(int argc, char **argv) { #endif /* util tests */ - run_memczero_test(); + run_secp256k1_memczero_test(); run_cmov_tests(); diff --git a/src/tests_exhaustive.c b/src/tests_exhaustive.c index f4d5b8e176..2bb5381446 100644 --- a/src/tests_exhaustive.c +++ b/src/tests_exhaustive.c @@ -1,8 +1,8 @@ /*********************************************************************** - * Copyright (c) 2016 Andrew Poelstra * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ + * 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.* + ***********************************************************************/ #if defined HAVE_CONFIG_H #include "libsecp256k1-config.h" diff --git a/src/util.h b/src/util.h index 3a88a41bc6..f78846836c 100644 --- a/src/util.h +++ b/src/util.h @@ -1,8 +1,8 @@ -/********************************************************************** - * Copyright (c) 2013, 2014 Pieter Wuille * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 @@ -113,7 +113,7 @@ static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void #define ALIGNMENT 16 #endif -#define ROUND_TO_ALIGN(size) (((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT) +#define ROUND_TO_ALIGN(size) ((((size) + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT) /* Assume there is a contiguous memory object with bounds [base, base + max_size) * of which the memory range [base, *prealloc_ptr) is already allocated for usage, @@ -141,7 +141,7 @@ static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_siz VERIFY_CHECK(((unsigned char*)*prealloc_ptr - (unsigned char*)base) % ALIGNMENT == 0); VERIFY_CHECK((unsigned char*)*prealloc_ptr - (unsigned char*)base + aligned_alloc_size <= max_size); ret = *prealloc_ptr; - *((unsigned char**)prealloc_ptr) += aligned_alloc_size; + *prealloc_ptr = (unsigned char*)*prealloc_ptr + aligned_alloc_size; return ret; } @@ -202,7 +202,7 @@ static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_siz #endif /* Zero memory if flag == 1. Flag must be 0 or 1. Constant time. */ -static SECP256K1_INLINE void memczero(void *s, size_t len, int flag) { +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 @@ -260,14 +260,85 @@ static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag) # define SECP256K1_WIDEMUL_INT128 1 #elif defined(USE_FORCE_WIDEMUL_INT64) # define SECP256K1_WIDEMUL_INT64 1 -#elif defined(__SIZEOF_INT128__) +#elif defined(UINT128_MAX) || defined(__SIZEOF_INT128__) # define SECP256K1_WIDEMUL_INT128 1 #else # define SECP256K1_WIDEMUL_INT64 1 #endif #if defined(SECP256K1_WIDEMUL_INT128) +# 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 +#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[((x & -x) * 0x04D7651F) >> 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[((x & -x) * 0x022FDD63CC95386D) >> 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 +} #endif /* SECP256K1_UTIL_H */ diff --git a/src/valgrind_ctime_test.c b/src/valgrind_ctime_test.c index 3169e3651c..cfca5a196e 100644 --- a/src/valgrind_ctime_test.c +++ b/src/valgrind_ctime_test.c @@ -1,10 +1,12 @@ -/********************************************************************** - * Copyright (c) 2020 Gregory Maxwell * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or http://www.opensource.org/licenses/mit-license.php.* - **********************************************************************/ +/*********************************************************************** + * 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 <valgrind/memcheck.h> +#include <stdio.h> + #include "include/secp256k1.h" #include "assumptions.h" #include "util.h" @@ -25,8 +27,42 @@ #include "include/secp256k1_schnorrsig.h" #endif +void run_tests(secp256k1_context *ctx, unsigned char *key); + int main(void) { secp256k1_context* ctx; + unsigned char key[32]; + int ret, i; + + if (!RUNNING_ON_VALGRIND) { + fprintf(stderr, "This test can only usefully be run inside valgrind.\n"); + fprintf(stderr, "Usage: libtool --mode=execute valgrind ./valgrind_ctime_test\n"); + return 1; + } + ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN + | SECP256K1_CONTEXT_VERIFY + | 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. */ + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_context_randomize(ctx, key); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret); + + secp256k1_context_destroy(ctx); + return 0; +} + +void run_tests(secp256k1_context *ctx, unsigned char *key) { secp256k1_ecdsa_signature signature; secp256k1_pubkey pubkey; size_t siglen = 74; @@ -34,7 +70,6 @@ int main(void) { int i; int ret; unsigned char msg[32]; - unsigned char key[32]; unsigned char sig[74]; unsigned char spubkey[33]; #ifdef ENABLE_MODULE_RECOVERY @@ -45,26 +80,10 @@ int main(void) { secp256k1_keypair keypair; #endif - if (!RUNNING_ON_VALGRIND) { - fprintf(stderr, "This test can only usefully be run inside valgrind.\n"); - fprintf(stderr, "Usage: libtool --mode=execute valgrind ./valgrind_ctime_test\n"); - exit(1); - } - - /** 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; - } for (i = 0; i < 32; i++) { msg[i] = i + 1; } - ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN - | SECP256K1_CONTEXT_VERIFY - | SECP256K1_CONTEXT_DECLASSIFY); - /* Test keygen. */ VALGRIND_MAKE_MEM_UNDEFINED(key, 32); ret = secp256k1_ec_pubkey_create(ctx, &pubkey, key); @@ -122,12 +141,6 @@ int main(void) { VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); CHECK(ret == 1); - /* Test context randomisation. Do this last because it leaves the context tainted. */ - VALGRIND_MAKE_MEM_UNDEFINED(key, 32); - ret = secp256k1_context_randomize(ctx, key); - VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); - CHECK(ret); - /* Test keypair_create and keypair_xonly_tweak_add. */ #ifdef ENABLE_MODULE_EXTRAKEYS VALGRIND_MAKE_MEM_UNDEFINED(key, 32); @@ -140,6 +153,12 @@ int main(void) { ret = secp256k1_keypair_xonly_tweak_add(ctx, &keypair, msg); VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); CHECK(ret == 1); + + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + VALGRIND_MAKE_MEM_UNDEFINED(&keypair, sizeof(keypair)); + ret = secp256k1_keypair_sec(ctx, key, &keypair); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); #endif #ifdef ENABLE_MODULE_SCHNORRSIG @@ -151,7 +170,4 @@ int main(void) { VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); CHECK(ret == 1); #endif - - secp256k1_context_destroy(ctx); - return 0; } |