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authorPieter Wuille <pieter@wuille.net>2021-04-23 11:35:15 -0700
committerPieter Wuille <pieter@wuille.net>2021-04-23 11:35:15 -0700
commita5a447a352463c7b75752aa08b6d9cb46aa051ea (patch)
tree16b3dcf91f6f1fe7b8e9ec62ed76b12631edbf6f /src
parentcabb5661234f8d832dbc3b65bf80b0acc02db0a0 (diff)
parentbdca9bcb6c9379707d09c63f02326884befbefb2 (diff)
Update libsecp256k1 subtree to latest upstream master
Diffstat (limited to 'src')
-rw-r--r--src/secp256k1/.cirrus.yml198
-rw-r--r--src/secp256k1/.travis.yml108
-rw-r--r--src/secp256k1/Makefile.am8
-rw-r--r--src/secp256k1/README.md4
-rw-r--r--src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m42
-rw-r--r--src/secp256k1/build-aux/m4/bitcoin_secp.m413
-rwxr-xr-xsrc/secp256k1/ci/cirrus.sh (renamed from src/secp256k1/contrib/travis.sh)52
-rw-r--r--src/secp256k1/ci/linux-debian.Dockerfile13
-rw-r--r--src/secp256k1/configure.ac279
-rw-r--r--src/secp256k1/contrib/lax_der_parsing.c10
-rw-r--r--src/secp256k1/contrib/lax_der_parsing.h10
-rw-r--r--src/secp256k1/contrib/lax_der_privatekey_parsing.c10
-rw-r--r--src/secp256k1/contrib/lax_der_privatekey_parsing.h10
-rw-r--r--src/secp256k1/doc/safegcd_implementation.md765
-rw-r--r--src/secp256k1/include/secp256k1.h47
-rw-r--r--src/secp256k1/include/secp256k1_extrakeys.h13
-rw-r--r--src/secp256k1/include/secp256k1_recovery.h24
-rw-r--r--src/secp256k1/sage/gen_exhaustive_groups.sage7
-rw-r--r--src/secp256k1/sage/gen_split_lambda_constants.sage114
-rw-r--r--src/secp256k1/sage/group_prover.sage23
-rw-r--r--src/secp256k1/sage/prove_group_implementations.sage (renamed from src/secp256k1/sage/secp256k1.sage)0
-rw-r--r--src/secp256k1/sage/secp256k1_params.sage36
-rw-r--r--src/secp256k1/sage/weierstrass_prover.sage32
-rw-r--r--src/secp256k1/src/asm/field_10x26_arm.s10
-rw-r--r--src/secp256k1/src/assumptions.h10
-rw-r--r--src/secp256k1/src/basic-config.h29
-rw-r--r--src/secp256k1/src/bench.h10
-rw-r--r--src/secp256k1/src/bench_ecdh.c10
-rw-r--r--src/secp256k1/src/bench_ecmult.c11
-rw-r--r--src/secp256k1/src/bench_internal.c73
-rw-r--r--src/secp256k1/src/bench_recover.c10
-rw-r--r--src/secp256k1/src/bench_schnorrsig.c10
-rw-r--r--src/secp256k1/src/bench_sign.c18
-rw-r--r--src/secp256k1/src/bench_verify.c26
-rw-r--r--src/secp256k1/src/ecdsa.h10
-rw-r--r--src/secp256k1/src/ecdsa_impl.h10
-rw-r--r--src/secp256k1/src/eckey.h10
-rw-r--r--src/secp256k1/src/eckey_impl.h10
-rw-r--r--src/secp256k1/src/ecmult.h11
-rw-r--r--src/secp256k1/src/ecmult_const.h10
-rw-r--r--src/secp256k1/src/ecmult_const_impl.h10
-rw-r--r--src/secp256k1/src/ecmult_gen.h10
-rw-r--r--src/secp256k1/src/ecmult_gen_impl.h12
-rw-r--r--src/secp256k1/src/ecmult_impl.h16
-rw-r--r--src/secp256k1/src/field.h29
-rw-r--r--src/secp256k1/src/field_10x26.h10
-rw-r--r--src/secp256k1/src/field_10x26_impl.h103
-rw-r--r--src/secp256k1/src/field_5x52.h10
-rw-r--r--src/secp256k1/src/field_5x52_asm_impl.h10
-rw-r--r--src/secp256k1/src/field_5x52_impl.h91
-rw-r--r--src/secp256k1/src/field_5x52_int128_impl.h10
-rw-r--r--src/secp256k1/src/field_impl.h190
-rw-r--r--src/secp256k1/src/gen_context.c23
-rw-r--r--src/secp256k1/src/group.h25
-rw-r--r--src/secp256k1/src/group_impl.h37
-rw-r--r--src/secp256k1/src/hash.h10
-rw-r--r--src/secp256k1/src/hash_impl.h10
-rw-r--r--src/secp256k1/src/modinv32.h42
-rw-r--r--src/secp256k1/src/modinv32_impl.h587
-rw-r--r--src/secp256k1/src/modinv64.h46
-rw-r--r--src/secp256k1/src/modinv64_impl.h593
-rw-r--r--src/secp256k1/src/modules/ecdh/main_impl.h10
-rw-r--r--src/secp256k1/src/modules/ecdh/tests_impl.h10
-rw-r--r--src/secp256k1/src/modules/extrakeys/main_impl.h26
-rw-r--r--src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h14
-rw-r--r--src/secp256k1/src/modules/extrakeys/tests_impl.h41
-rw-r--r--src/secp256k1/src/modules/recovery/main_impl.h22
-rw-r--r--src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h10
-rw-r--r--src/secp256k1/src/modules/recovery/tests_impl.h10
-rw-r--r--src/secp256k1/src/modules/schnorrsig/main_impl.h16
-rw-r--r--src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h14
-rw-r--r--src/secp256k1/src/modules/schnorrsig/tests_impl.h16
-rw-r--r--src/secp256k1/src/num.h74
-rw-r--r--src/secp256k1/src/num_gmp.h20
-rw-r--r--src/secp256k1/src/num_gmp_impl.h288
-rw-r--r--src/secp256k1/src/num_impl.h24
-rw-r--r--src/secp256k1/src/scalar.h22
-rw-r--r--src/secp256k1/src/scalar_4x64.h10
-rw-r--r--src/secp256k1/src/scalar_4x64_impl.h252
-rw-r--r--src/secp256k1/src/scalar_8x32.h10
-rw-r--r--src/secp256k1/src/scalar_8x32_impl.h189
-rw-r--r--src/secp256k1/src/scalar_impl.h229
-rw-r--r--src/secp256k1/src/scalar_low.h10
-rw-r--r--src/secp256k1/src/scalar_low_impl.h29
-rw-r--r--src/secp256k1/src/scratch.h16
-rw-r--r--src/secp256k1/src/scratch_impl.h14
-rw-r--r--src/secp256k1/src/secp256k1.c81
-rw-r--r--src/secp256k1/src/selftest.h10
-rw-r--r--src/secp256k1/src/testrand.h10
-rw-r--r--src/secp256k1/src/testrand_impl.h10
-rw-r--r--src/secp256k1/src/tests.c1729
-rw-r--r--src/secp256k1/src/tests_exhaustive.c8
-rw-r--r--src/secp256k1/src/util.h89
-rw-r--r--src/secp256k1/src/valgrind_ctime_test.c78
94 files changed, 4865 insertions, 2456 deletions
diff --git a/src/secp256k1/.cirrus.yml b/src/secp256k1/.cirrus.yml
new file mode 100644
index 0000000000..506a860336
--- /dev/null
+++ b/src/secp256k1/.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/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
deleted file mode 100644
index ce8d6391b2..0000000000
--- a/src/secp256k1/.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/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am
index 023fa6067f..58c9635e53 100644
--- a/src/secp256k1/Makefile.am
+++ b/src/secp256k1/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
diff --git a/src/secp256k1/README.md b/src/secp256k1/README.md
index e070937235..197a56fff8 100644
--- a/src/secp256k1/README.md
+++ b/src/secp256k1/README.md
@@ -1,7 +1,7 @@
libsecp256k1
============
-[![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1)
+[![Build Status](https://api.cirrus-ci.com/github/bitcoin-core/secp256k1.svg?branch=master)](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/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4 b/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
index 77fd346a79..7bcbf3200c 100644
--- a/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
+++ b/src/secp256k1/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/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
index ece3d655ed..e57888ca18 100644
--- a/src/secp256k1/build-aux/m4/bitcoin_secp.m4
+++ b/src/secp256k1/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 $CPPFLAGS"
+ AC_CHECK_HEADER([valgrind/memcheck.h], [has_valgrind=yes; AC_DEFINE(HAVE_VALGRIND,1,[Define this symbol if valgrind is installed])])
fi
])
diff --git a/src/secp256k1/contrib/travis.sh b/src/secp256k1/ci/cirrus.sh
index 24cc9315cb..f26ca98d1d 100755
--- a/src/secp256k1/contrib/travis.sh
+++ b/src/secp256k1/ci/cirrus.sh
@@ -3,45 +3,63 @@
set -e
set -x
-if [ "$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/src/secp256k1/ci/linux-debian.Dockerfile b/src/secp256k1/ci/linux-debian.Dockerfile
new file mode 100644
index 0000000000..5967cf8b31
--- /dev/null
+++ b/src/secp256k1/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/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index eb3b449bec..1ed991afa7 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/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/src/secp256k1/contrib/lax_der_parsing.c b/src/secp256k1/contrib/lax_der_parsing.c
index f71db4b535..c1627e37e9 100644
--- a/src/secp256k1/contrib/lax_der_parsing.c
+++ b/src/secp256k1/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/src/secp256k1/contrib/lax_der_parsing.h b/src/secp256k1/contrib/lax_der_parsing.h
index 7eaf63bf6a..6b7255e28f 100644
--- a/src/secp256k1/contrib/lax_der_parsing.h
+++ b/src/secp256k1/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/src/secp256k1/contrib/lax_der_privatekey_parsing.c b/src/secp256k1/contrib/lax_der_privatekey_parsing.c
index c2e63b4b8d..429760fbb6 100644
--- a/src/secp256k1/contrib/lax_der_privatekey_parsing.c
+++ b/src/secp256k1/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/src/secp256k1/contrib/lax_der_privatekey_parsing.h b/src/secp256k1/contrib/lax_der_privatekey_parsing.h
index fece261fb9..602c7c556a 100644
--- a/src/secp256k1/contrib/lax_der_privatekey_parsing.h
+++ b/src/secp256k1/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/src/secp256k1/doc/safegcd_implementation.md b/src/secp256k1/doc/safegcd_implementation.md
new file mode 100644
index 0000000000..3ae556f9a7
--- /dev/null
+++ b/src/secp256k1/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 *&delta;* 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 *&delta;=1 f=21 g=14*
+- Take the third branch: *&delta;=2 f=21 g=7*
+- Take the first branch: *&delta;=-1 f=7 g=-7*
+- Take the second branch: *&delta;=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&thinsp;c* and *g=b&thinsp;c* for some integers *a*
+ and *b*. As *(g,g-f)=(b&thinsp;c,(b-a)c)* and *(f,f+g)=(a&thinsp;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 *&delta;* 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 *&delta;*.
+
+
+## 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&thinsp;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&thinsp;x + b&thinsp;M = 1*.
+Taking that expression *mod M* gives *a&thinsp;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&thinsp;[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 *&delta;* 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&thinsp;M* and *ce* by *q&thinsp;M*. Similarly,
+increasing *e* by *M* is equal to incrementing *cd* by *v&thinsp;M* and *ce* by *r&thinsp;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&thinsp;M* and *me&thinsp;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 &ne; 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
+*&lceil;724/N&rceil;* 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 *&delta;>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
+*&eta;=-&delta;*. In this representation, negating *&delta;* corresponds to negating *&eta;*, and incrementing
+*&delta;* corresponds to decrementing *&eta;*. 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 *&delta;* 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 *&zeta;=-(&delta;+1/2)*
+is used instead to keep the variable integral. Incrementing *&delta;* by *1* still translates to
+decrementing *&zeta;* by *1*, but negating *&delta;* now corresponds to going from *&zeta;* to *-(&zeta;+1)*, or
+*~&zeta;*. 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 *&delta;=1* and *&eta;=-&delta;* 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 *&eta;*. 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 *&eta; &geq; 0*, the loop does not modify *f*. Instead, it cancels out bottom
+bits of *g* and shifts them out, and decreases *&eta;* and *i* accordingly - interrupting only when *&eta;*
+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&thinsp;f* has a few bottom
+zero bits. If that number of bits is *L*, we want *g+w&thinsp;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 *&eta;+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&thinsp;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 *&zeta;* instead of *&delta;*, 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/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
index 2178c8e2d6..d368488af2 100644
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/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/src/secp256k1/include/secp256k1_extrakeys.h b/src/secp256k1/include/secp256k1_extrakeys.h
index 0c5dff2c94..6fc7b290f8 100644
--- a/src/secp256k1/include/secp256k1_extrakeys.h
+++ b/src/secp256k1/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/src/secp256k1/include/secp256k1_recovery.h b/src/secp256k1/include/secp256k1_recovery.h
index f8ccaecd3d..aa16532ce8 100644
--- a/src/secp256k1/include/secp256k1_recovery.h
+++ b/src/secp256k1/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/src/secp256k1/sage/gen_exhaustive_groups.sage b/src/secp256k1/sage/gen_exhaustive_groups.sage
index 3c3c984811..01d15dcdea 100644
--- a/src/secp256k1/sage/gen_exhaustive_groups.sage
+++ b/src/secp256k1/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/src/secp256k1/sage/gen_split_lambda_constants.sage b/src/secp256k1/sage/gen_split_lambda_constants.sage
new file mode 100644
index 0000000000..7d4359e0f6
--- /dev/null
+++ b/src/secp256k1/sage/gen_split_lambda_constants.sage
@@ -0,0 +1,114 @@
+""" Generates the constants used in secp256k1_scalar_split_lambda.
+
+See the comments for secp256k1_scalar_split_lambda in src/scalar_impl.h for detailed explanations.
+"""
+
+load("secp256k1_params.sage")
+
+def inf_norm(v):
+ """Returns the infinity norm of a vector."""
+ return max(map(abs, v))
+
+def gauss_reduction(i1, i2):
+ v1, v2 = i1.copy(), i2.copy()
+ while True:
+ if inf_norm(v2) < inf_norm(v1):
+ v1, v2 = v2, v1
+ # This is essentially
+ # m = round((v1[0]*v2[0] + v1[1]*v2[1]) / (inf_norm(v1)**2))
+ # (rounding to the nearest integer) without relying on floating point arithmetic.
+ m = ((v1[0]*v2[0] + v1[1]*v2[1]) + (inf_norm(v1)**2) // 2) // (inf_norm(v1)**2)
+ if m == 0:
+ return v1, v2
+ v2[0] -= m*v1[0]
+ v2[1] -= m*v1[1]
+
+def find_split_constants_gauss():
+ """Find constants for secp256k1_scalar_split_lamdba using gauss reduction."""
+ (v11, v12), (v21, v22) = gauss_reduction([0, N], [1, int(LAMBDA)])
+
+ # We use related vectors in secp256k1_scalar_split_lambda.
+ A1, B1 = -v21, -v11
+ A2, B2 = v22, -v21
+
+ return A1, B1, A2, B2
+
+def find_split_constants_explicit_tof():
+ """Find constants for secp256k1_scalar_split_lamdba using the trace of Frobenius.
+
+ See Benjamin Smith: "Easy scalar decompositions for efficient scalar multiplication on
+ elliptic curves and genus 2 Jacobians" (https://eprint.iacr.org/2013/672), Example 2
+ """
+ assert P % 3 == 1 # The paper says P % 3 == 2 but that appears to be a mistake, see [10].
+ assert C.j_invariant() == 0
+
+ t = C.trace_of_frobenius()
+
+ c = Integer(sqrt((4*P - t**2)/3))
+ A1 = Integer((t - c)/2 - 1)
+ B1 = c
+
+ A2 = Integer((t + c)/2 - 1)
+ B2 = Integer(1 - (t - c)/2)
+
+ # We use a negated b values in secp256k1_scalar_split_lambda.
+ B1, B2 = -B1, -B2
+
+ return A1, B1, A2, B2
+
+A1, B1, A2, B2 = find_split_constants_explicit_tof()
+
+# For extra fun, use an independent method to recompute the constants.
+assert (A1, B1, A2, B2) == find_split_constants_gauss()
+
+# PHI : Z[l] -> Z_n where phi(a + b*l) == a + b*lambda mod n.
+def PHI(a,b):
+ return Z(a + LAMBDA*b)
+
+# Check that (A1, B1) and (A2, B2) are in the kernel of PHI.
+assert PHI(A1, B1) == Z(0)
+assert PHI(A2, B2) == Z(0)
+
+# Check that the parallelogram generated by (A1, A2) and (B1, B2)
+# is a fundamental domain by containing exactly N points.
+# Since the LHS is the determinant and N != 0, this also checks that
+# (A1, A2) and (B1, B2) are linearly independent. By the previous
+# assertions, (A1, A2) and (B1, B2) are a basis of the kernel.
+assert A1*B2 - B1*A2 == N
+
+# Check that their components are short enough.
+assert (A1 + A2)/2 < sqrt(N)
+assert B1 < sqrt(N)
+assert B2 < sqrt(N)
+
+G1 = round((2**384)*B2/N)
+G2 = round((2**384)*(-B1)/N)
+
+def rnddiv2(v):
+ if v & 1:
+ v += 1
+ return v >> 1
+
+def scalar_lambda_split(k):
+ """Equivalent to secp256k1_scalar_lambda_split()."""
+ c1 = rnddiv2((k * G1) >> 383)
+ c2 = rnddiv2((k * G2) >> 383)
+ c1 = (c1 * -B1) % N
+ c2 = (c2 * -B2) % N
+ r2 = (c1 + c2) % N
+ r1 = (k + r2 * -LAMBDA) % N
+ return (r1, r2)
+
+# The result of scalar_lambda_split can depend on the representation of k (mod n).
+SPECIAL = (2**383) // G2 + 1
+assert scalar_lambda_split(SPECIAL) != scalar_lambda_split(SPECIAL + N)
+
+print(' A1 =', hex(A1))
+print(' -B1 =', hex(-B1))
+print(' A2 =', hex(A2))
+print(' -B2 =', hex(-B2))
+print(' =', hex(Z(-B2)))
+print(' -LAMBDA =', hex(-LAMBDA))
+
+print(' G1 =', hex(G1))
+print(' G2 =', hex(G2))
diff --git a/src/secp256k1/sage/group_prover.sage b/src/secp256k1/sage/group_prover.sage
index 8521f07999..b200bfeae3 100644
--- a/src/secp256k1/sage/group_prover.sage
+++ b/src/secp256k1/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/src/secp256k1/sage/secp256k1.sage b/src/secp256k1/sage/prove_group_implementations.sage
index a97e732f7f..a97e732f7f 100644
--- a/src/secp256k1/sage/secp256k1.sage
+++ b/src/secp256k1/sage/prove_group_implementations.sage
diff --git a/src/secp256k1/sage/secp256k1_params.sage b/src/secp256k1/sage/secp256k1_params.sage
new file mode 100644
index 0000000000..4e000726ed
--- /dev/null
+++ b/src/secp256k1/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/src/secp256k1/sage/weierstrass_prover.sage b/src/secp256k1/sage/weierstrass_prover.sage
index 03ef2ec901..b770c6dafe 100644
--- a/src/secp256k1/sage/weierstrass_prover.sage
+++ b/src/secp256k1/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/secp256k1/src/asm/field_10x26_arm.s b/src/secp256k1/src/asm/field_10x26_arm.s
index 9a5bd06721..5f68cefc46 100644
--- a/src/secp256k1/src/asm/field_10x26_arm.s
+++ b/src/secp256k1/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/secp256k1/src/assumptions.h b/src/secp256k1/src/assumptions.h
index 77204de2b8..6dc527b288 100644
--- a/src/secp256k1/src/assumptions.h
+++ b/src/secp256k1/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/secp256k1/src/basic-config.h b/src/secp256k1/src/basic-config.h
index b0d82e89b4..6f7693cb8f 100644
--- a/src/secp256k1/src/basic-config.h
+++ b/src/secp256k1/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/secp256k1/src/bench.h b/src/secp256k1/src/bench.h
index 9bfed903e0..63c55df44d 100644
--- a/src/secp256k1/src/bench.h
+++ b/src/secp256k1/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/secp256k1/src/bench_ecdh.c b/src/secp256k1/src/bench_ecdh.c
index f099d33884..ab4b8f4244 100644
--- a/src/secp256k1/src/bench_ecdh.c
+++ b/src/secp256k1/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/secp256k1/src/bench_ecmult.c b/src/secp256k1/src/bench_ecmult.c
index facd07ef31..204e85a5dd 100644
--- a/src/secp256k1/src/bench_ecmult.c
+++ b/src/secp256k1/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/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index 5f2b7a9759..73b8a24ccb 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/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/secp256k1/src/bench_recover.c b/src/secp256k1/src/bench_recover.c
index e952ed1215..3f6270ce84 100644
--- a/src/secp256k1/src/bench_recover.c
+++ b/src/secp256k1/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/secp256k1/src/bench_schnorrsig.c b/src/secp256k1/src/bench_schnorrsig.c
index 315f5af28e..f7f591c41d 100644
--- a/src/secp256k1/src/bench_schnorrsig.c
+++ b/src/secp256k1/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/secp256k1/src/bench_sign.c b/src/secp256k1/src/bench_sign.c
index c6b2942cc0..933f367c4b 100644
--- a/src/secp256k1/src/bench_sign.c
+++ b/src/secp256k1/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/secp256k1/src/bench_verify.c b/src/secp256k1/src/bench_verify.c
index 272d3e5cc4..c56aefd369 100644
--- a/src/secp256k1/src/bench_verify.c
+++ b/src/secp256k1/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/secp256k1/src/ecdsa.h b/src/secp256k1/src/ecdsa.h
index 80590c7cc8..d5e54d8ce6 100644
--- a/src/secp256k1/src/ecdsa.h
+++ b/src/secp256k1/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/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h
index 5f54b59faa..156a33d112 100644
--- a/src/secp256k1/src/ecdsa_impl.h
+++ b/src/secp256k1/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/secp256k1/src/eckey.h b/src/secp256k1/src/eckey.h
index b621f1e6c3..5be3a64b84 100644
--- a/src/secp256k1/src/eckey.h
+++ b/src/secp256k1/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/secp256k1/src/eckey_impl.h b/src/secp256k1/src/eckey_impl.h
index e2e72d9303..a39cb79653 100644
--- a/src/secp256k1/src/eckey_impl.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h
index 09e8146414..7ab617e20e 100644
--- a/src/secp256k1/src/ecmult.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult_const.h b/src/secp256k1/src/ecmult_const.h
index 03bb33257d..d6f0ea2227 100644
--- a/src/secp256k1/src/ecmult_const.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
index bb9511108b..0e1fb965cb 100644
--- a/src/secp256k1/src/ecmult_const_impl.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult_gen.h b/src/secp256k1/src/ecmult_gen.h
index 30815e5aa1..539618dcbb 100644
--- a/src/secp256k1/src/ecmult_gen.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h
index 30ac16518b..384a67faed 100644
--- a/src/secp256k1/src/ecmult_gen_impl.h
+++ b/src/secp256k1/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/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index a9e8b3c76c..5c2edac68f 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/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/secp256k1/src/field.h b/src/secp256k1/src/field.h
index aca1fb72c5..854aaebabc 100644
--- a/src/secp256k1/src/field.h
+++ b/src/secp256k1/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/secp256k1/src/field_10x26.h b/src/secp256k1/src/field_10x26.h
index 5ff03c8abc..9eb65607f1 100644
--- a/src/secp256k1/src/field_10x26.h
+++ b/src/secp256k1/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/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h
index 651500ee8e..7a38c117f1 100644
--- a/src/secp256k1/src/field_10x26_impl.h
+++ b/src/secp256k1/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/secp256k1/src/field_5x52.h b/src/secp256k1/src/field_5x52.h
index 6a068484c2..50ee3f9ec9 100644
--- a/src/secp256k1/src/field_5x52.h
+++ b/src/secp256k1/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/secp256k1/src/field_5x52_asm_impl.h b/src/secp256k1/src/field_5x52_asm_impl.h
index 1fc3171f6b..a2118044ab 100644
--- a/src/secp256k1/src/field_5x52_asm_impl.h
+++ b/src/secp256k1/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/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h
index 71a38f915b..60ded927f6 100644
--- a/src/secp256k1/src/field_5x52_impl.h
+++ b/src/secp256k1/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/secp256k1/src/field_5x52_int128_impl.h b/src/secp256k1/src/field_5x52_int128_impl.h
index bcbfb92ac2..314002ee39 100644
--- a/src/secp256k1/src/field_5x52_int128_impl.h
+++ b/src/secp256k1/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/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h
index 18e4d2f30e..374284a1f4 100644
--- a/src/secp256k1/src/field_impl.h
+++ b/src/secp256k1/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/secp256k1/src/gen_context.c b/src/secp256k1/src/gen_context.c
index 8b7729aee4..024c557261 100644
--- a/src/secp256k1/src/gen_context.c
+++ b/src/secp256k1/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/secp256k1/src/group.h b/src/secp256k1/src/group.h
index 36e39ecf0f..b9cd334dae 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/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/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index a5fbc91a0f..19ebd8f44e 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/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/secp256k1/src/hash.h b/src/secp256k1/src/hash.h
index de26e4b89f..0947a09694 100644
--- a/src/secp256k1/src/hash.h
+++ b/src/secp256k1/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/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h
index 409772587b..f8cd3a1634 100644
--- a/src/secp256k1/src/hash_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modinv32.h b/src/secp256k1/src/modinv32.h
new file mode 100644
index 0000000000..0efdda9ab5
--- /dev/null
+++ b/src/secp256k1/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/secp256k1/src/modinv32_impl.h b/src/secp256k1/src/modinv32_impl.h
new file mode 100644
index 0000000000..661c5fc04c
--- /dev/null
+++ b/src/secp256k1/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/secp256k1/src/modinv64.h b/src/secp256k1/src/modinv64.h
new file mode 100644
index 0000000000..da506dfa9f
--- /dev/null
+++ b/src/secp256k1/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/secp256k1/src/modinv64_impl.h b/src/secp256k1/src/modinv64_impl.h
new file mode 100644
index 0000000000..0743a9c821
--- /dev/null
+++ b/src/secp256k1/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/secp256k1/src/modules/ecdh/main_impl.h b/src/secp256k1/src/modules/ecdh/main_impl.h
index 07a25b80d4..1ac67086be 100644
--- a/src/secp256k1/src/modules/ecdh/main_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h
index e8d2aeab9a..be07447a4b 100644
--- a/src/secp256k1/src/modules/ecdh/tests_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/extrakeys/main_impl.h b/src/secp256k1/src/modules/extrakeys/main_impl.h
index 5378d2f301..7390b22718 100644
--- a/src/secp256k1/src/modules/extrakeys/main_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
index 0e29bc6b09..0aca4fb72d 100644
--- a/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/extrakeys/tests_impl.h b/src/secp256k1/src/modules/extrakeys/tests_impl.h
index 5ee135849e..9473a7dd48 100644
--- a/src/secp256k1/src/modules/extrakeys/tests_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h
index e2576aa953..7a440a729b 100644
--- a/src/secp256k1/src/modules/recovery/main_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/recovery/tests_exhaustive_impl.h b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
index a2f381d77a..0ba9409c69 100644
--- a/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h
index 09cae38403..40dba87ce3 100644
--- a/src/secp256k1/src/modules/recovery/tests_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/schnorrsig/main_impl.h b/src/secp256k1/src/modules/schnorrsig/main_impl.h
index b0d8481f9b..22e1b33a5a 100644
--- a/src/secp256k1/src/modules/schnorrsig/main_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
index 4bf0bc1680..b4a428729f 100644
--- a/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
+++ b/src/secp256k1/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/secp256k1/src/modules/schnorrsig/tests_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_impl.h
index f522fcb320..338462fc9d 100644
--- a/src/secp256k1/src/modules/schnorrsig/tests_impl.h
+++ b/src/secp256k1/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/secp256k1/src/num.h b/src/secp256k1/src/num.h
deleted file mode 100644
index 49f2dd791d..0000000000
--- a/src/secp256k1/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/secp256k1/src/num_gmp.h b/src/secp256k1/src/num_gmp.h
deleted file mode 100644
index 3619844bd5..0000000000
--- a/src/secp256k1/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/secp256k1/src/num_gmp_impl.h b/src/secp256k1/src/num_gmp_impl.h
deleted file mode 100644
index 0ae2a8ba0e..0000000000
--- a/src/secp256k1/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/secp256k1/src/num_impl.h b/src/secp256k1/src/num_impl.h
deleted file mode 100644
index c45193b033..0000000000
--- a/src/secp256k1/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/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h
index fb3fb187ce..aaaa3d8827 100644
--- a/src/secp256k1/src/scalar.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_4x64.h b/src/secp256k1/src/scalar_4x64.h
index 19c7495d1c..700964291e 100644
--- a/src/secp256k1/src/scalar_4x64.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h
index 73cbd5e18a..a1def26fca 100644
--- a/src/secp256k1/src/scalar_4x64_impl.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_8x32.h b/src/secp256k1/src/scalar_8x32.h
index 2c9a348e24..17863ef937 100644
--- a/src/secp256k1/src/scalar_8x32.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_8x32_impl.h b/src/secp256k1/src/scalar_8x32_impl.h
index 6853f79ecc..62c7ae7156 100644
--- a/src/secp256k1/src/scalar_8x32_impl.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index fc75891818..e124474773 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_low.h b/src/secp256k1/src/scalar_low.h
index 2794a7f171..67051bd30b 100644
--- a/src/secp256k1/src/scalar_low.h
+++ b/src/secp256k1/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/secp256k1/src/scalar_low_impl.h b/src/secp256k1/src/scalar_low_impl.h
index a615ec074b..7176f0b2ca 100644
--- a/src/secp256k1/src/scalar_low_impl.h
+++ b/src/secp256k1/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/secp256k1/src/scratch.h b/src/secp256k1/src/scratch.h
index 77b35d126b..9dcb7581f6 100644
--- a/src/secp256k1/src/scratch.h
+++ b/src/secp256k1/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/secp256k1/src/scratch_impl.h b/src/secp256k1/src/scratch_impl.h
index f381e2e322..688e18eb66 100644
--- a/src/secp256k1/src/scratch_impl.h
+++ b/src/secp256k1/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/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
index dae506d08c..aef3f99ac3 100644
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/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/secp256k1/src/selftest.h b/src/secp256k1/src/selftest.h
index 0e37510c1e..52f1b8442e 100644
--- a/src/secp256k1/src/selftest.h
+++ b/src/secp256k1/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/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h
index a76003d5b8..667d1867bd 100644
--- a/src/secp256k1/src/testrand.h
+++ b/src/secp256k1/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/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h
index 3392566329..e643778f36 100644
--- a/src/secp256k1/src/testrand_impl.h
+++ b/src/secp256k1/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/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index bb4b5b4c07..a146394305 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/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/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
index f4d5b8e176..2bb5381446 100644
--- a/src/secp256k1/src/tests_exhaustive.c
+++ b/src/secp256k1/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/secp256k1/src/util.h b/src/secp256k1/src/util.h
index 3a88a41bc6..f78846836c 100644
--- a/src/secp256k1/src/util.h
+++ b/src/secp256k1/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/secp256k1/src/valgrind_ctime_test.c b/src/secp256k1/src/valgrind_ctime_test.c
index 3169e3651c..cfca5a196e 100644
--- a/src/secp256k1/src/valgrind_ctime_test.c
+++ b/src/secp256k1/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;
}