Browse Source

Merge commit 'b2135359b3ad37cf2ac09b008079ddb237eff2c9'

pull/1/head
Wladimir J. van der Laan 6 years ago
parent
commit
0237096df5
  1. 19
      src/secp256k1/.gitignore
  2. 19
      src/secp256k1/.travis.yml
  3. 72
      src/secp256k1/Makefile.am
  4. 2
      src/secp256k1/README.md
  5. 140
      src/secp256k1/build-aux/m4/ax_jni_include_dir.m4
  6. 4
      src/secp256k1/build-aux/m4/bitcoin_secp.m4
  7. 146
      src/secp256k1/configure.ac
  8. 2
      src/secp256k1/libsecp256k1.pc.in
  9. 322
      src/secp256k1/sage/group_prover.sage
  10. 306
      src/secp256k1/sage/secp256k1.sage
  11. 264
      src/secp256k1/sage/weierstrass_prover.sage
  12. 919
      src/secp256k1/src/asm/field_10x26_arm.s
  13. 3
      src/secp256k1/src/bench_ecdh.c
  14. 34
      src/secp256k1/src/bench_internal.c
  15. 44
      src/secp256k1/src/bench_verify.c
  16. 67
      src/secp256k1/src/ecmult_const_impl.h
  17. 2
      src/secp256k1/src/ecmult_impl.h
  18. 8
      src/secp256k1/src/field.h
  19. 12
      src/secp256k1/src/field_10x26_impl.h
  20. 1
      src/secp256k1/src/field_5x52_impl.h
  21. 4
      src/secp256k1/src/field_5x52_int128_impl.h
  22. 36
      src/secp256k1/src/field_impl.h
  23. 5
      src/secp256k1/src/group.h
  24. 36
      src/secp256k1/src/group_impl.h
  25. 2
      src/secp256k1/src/hash.h
  26. 10
      src/secp256k1/src/hash_impl.h
  27. 472
      src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java
  28. 247
      src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java
  29. 45
      src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java
  30. 51
      src/secp256k1/src/java/org/bitcoin/Secp256k1Context.java
  31. 412
      src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c
  32. 112
      src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h
  33. 15
      src/secp256k1/src/java/org_bitcoin_Secp256k1Context.c
  34. 22
      src/secp256k1/src/java/org_bitcoin_Secp256k1Context.h
  35. 2
      src/secp256k1/src/modules/ecdh/Makefile.am.include
  36. 2
      src/secp256k1/src/modules/recovery/Makefile.am.include
  37. 2
      src/secp256k1/src/modules/schnorr/Makefile.am.include
  38. 6
      src/secp256k1/src/num.h
  39. 26
      src/secp256k1/src/num_gmp_impl.h
  40. 2
      src/secp256k1/src/scalar_impl.h
  41. 15
      src/secp256k1/src/secp256k1.c
  42. 190
      src/secp256k1/src/tests.c

19
src/secp256k1/.gitignore vendored

@ -25,17 +25,24 @@ config.status @@ -25,17 +25,24 @@ config.status
libtool
.deps/
.dirstamp
build-aux/
*.lo
*.o
*~
src/libsecp256k1-config.h
src/libsecp256k1-config.h.in
src/ecmult_static_context.h
m4/libtool.m4
m4/ltoptions.m4
m4/ltsugar.m4
m4/ltversion.m4
m4/lt~obsolete.m4
build-aux/config.guess
build-aux/config.sub
build-aux/depcomp
build-aux/install-sh
build-aux/ltmain.sh
build-aux/m4/libtool.m4
build-aux/m4/lt~obsolete.m4
build-aux/m4/ltoptions.m4
build-aux/m4/ltsugar.m4
build-aux/m4/ltversion.m4
build-aux/missing
build-aux/compile
build-aux/test-driver
src/stamp-h1
libsecp256k1.pc

19
src/secp256k1/.travis.yml

@ -6,26 +6,31 @@ addons: @@ -6,26 +6,31 @@ addons:
compiler:
- clang
- gcc
cache:
directories:
- src/java/guava/
env:
global:
- FIELD=auto BIGNUM=auto SCALAR=auto ENDOMORPHISM=no STATICPRECOMPUTATION=yes ASM=no BUILD=check EXTRAFLAGS= HOST= ECDH=no schnorr=no RECOVERY=no
- FIELD=auto BIGNUM=auto SCALAR=auto ENDOMORPHISM=no STATICPRECOMPUTATION=yes ASM=no BUILD=check EXTRAFLAGS= HOST= ECDH=no schnorr=no RECOVERY=no EXPERIMENTAL=no
- GUAVA_URL=https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar GUAVA_JAR=src/java/guava/guava-18.0.jar
matrix:
- SCALAR=32bit RECOVERY=yes
- SCALAR=32bit FIELD=32bit ECDH=yes
- SCALAR=32bit FIELD=32bit ECDH=yes EXPERIMENTAL=yes
- SCALAR=64bit
- FIELD=64bit RECOVERY=yes
- FIELD=64bit ENDOMORPHISM=yes
- FIELD=64bit ENDOMORPHISM=yes ECDH=yes
- FIELD=64bit ENDOMORPHISM=yes ECDH=yes EXPERIMENTAL=yes
- FIELD=64bit ASM=x86_64
- FIELD=64bit ENDOMORPHISM=yes ASM=x86_64
- FIELD=32bit SCHNORR=yes
- FIELD=32bit SCHNORR=yes EXPERIMENTAL=yes
- FIELD=32bit ENDOMORPHISM=yes
- BIGNUM=no
- BIGNUM=no ENDOMORPHISM=yes SCHNORR=yes RECOVERY=yes
- BIGNUM=no ENDOMORPHISM=yes SCHNORR=yes RECOVERY=yes EXPERIMENTAL=yes
- BIGNUM=no STATICPRECOMPUTATION=no
- BUILD=distcheck
- EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
- EXTRAFLAGS=CFLAGS=-O0
- BUILD=check-java ECDH=yes SCHNORR=yes EXPERIMENTAL=yes
matrix:
fast_finish: true
include:
@ -55,9 +60,11 @@ matrix: @@ -55,9 +60,11 @@ matrix:
packages:
- gcc-multilib
- libgmp-dev:i386
before_install: mkdir -p `dirname $GUAVA_JAR`
install: if [ ! -f $GUAVA_JAR ]; then wget $GUAVA_URL -O $GUAVA_JAR; fi
before_script: ./autogen.sh
script:
- if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
- if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
- ./configure --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
- ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
os: linux

72
src/secp256k1/Makefile.am

@ -1,6 +1,12 @@ @@ -1,6 +1,12 @@
ACLOCAL_AMFLAGS = -I build-aux/m4
lib_LTLIBRARIES = libsecp256k1.la
if USE_JNI
JNI_LIB = libsecp256k1_jni.la
noinst_LTLIBRARIES = $(JNI_LIB)
else
JNI_LIB =
endif
include_HEADERS = include/secp256k1.h
noinst_HEADERS =
noinst_HEADERS += src/scalar.h
@ -32,6 +38,7 @@ noinst_HEADERS += src/field_5x52_impl.h @@ -32,6 +38,7 @@ 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/java/org_bitcoin_NativeSecp256k1.h
noinst_HEADERS += src/java/org_bitcoin_Secp256k1Context.h
noinst_HEADERS += src/util.h
noinst_HEADERS += src/testrand.h
noinst_HEADERS += src/testrand_impl.h
@ -45,35 +52,80 @@ noinst_HEADERS += contrib/lax_der_parsing.c @@ -45,35 +52,80 @@ noinst_HEADERS += contrib/lax_der_parsing.c
noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
if USE_EXTERNAL_ASM
COMMON_LIB = libsecp256k1_common.la
noinst_LTLIBRARIES = $(COMMON_LIB)
else
COMMON_LIB =
endif
pkgconfigdir = $(libdir)/pkgconfig
pkgconfig_DATA = libsecp256k1.pc
if USE_EXTERNAL_ASM
if USE_ASM_ARM
libsecp256k1_common_la_SOURCES = src/asm/field_10x26_arm.s
endif
endif
libsecp256k1_la_SOURCES = src/secp256k1.c
libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
libsecp256k1_la_LIBADD = $(SECP_LIBS)
libsecp256k1_la_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
libsecp256k1_la_LIBADD = $(JNI_LIB) $(SECP_LIBS) $(COMMON_LIB)
libsecp256k1_jni_la_SOURCES = src/java/org_bitcoin_NativeSecp256k1.c src/java/org_bitcoin_Secp256k1Context.c
libsecp256k1_jni_la_CPPFLAGS = -DSECP256K1_BUILD $(JNI_INCLUDES)
noinst_PROGRAMS =
if USE_BENCHMARK
noinst_PROGRAMS += bench_verify bench_sign bench_internal
bench_verify_SOURCES = src/bench_verify.c
bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
bench_sign_SOURCES = src/bench_sign.c
bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
bench_internal_SOURCES = src/bench_internal.c
bench_internal_LDADD = $(SECP_LIBS)
bench_internal_CPPFLAGS = $(SECP_INCLUDES)
bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
endif
if USE_TESTS
noinst_PROGRAMS += tests
tests_SOURCES = src/tests.c
tests_CPPFLAGS = -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS)
tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
tests_LDFLAGS = -static
TESTS = tests
endif
JAVAROOT=src/java
JAVAORG=org/bitcoin
JAVA_GUAVA=$(srcdir)/$(JAVAROOT)/guava/guava-18.0.jar
CLASSPATH_ENV=CLASSPATH=$(JAVA_GUAVA)
JAVA_FILES= \
$(JAVAROOT)/$(JAVAORG)/NativeSecp256k1.java \
$(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Test.java \
$(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Util.java \
$(JAVAROOT)/$(JAVAORG)/Secp256k1Context.java
if USE_JNI
$(JAVA_GUAVA):
@echo Guava is missing. Fetch it via: \
wget https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar -O $(@)
@false
.stamp-java: $(JAVA_FILES)
@echo Compiling $^
$(AM_V_at)$(CLASSPATH_ENV) javac $^
@touch $@
if USE_TESTS
check-java: libsecp256k1.la $(JAVA_GUAVA) .stamp-java
$(AM_V_at)java -Djava.library.path="./:./src:./src/.libs:.libs/" -cp "$(JAVA_GUAVA):$(JAVAROOT)" $(JAVAORG)/NativeSecp256k1Test
endif
endif
if USE_ECMULT_STATIC_PRECOMPUTATION
CPPFLAGS_FOR_BUILD +=-I$(top_srcdir)
CFLAGS_FOR_BUILD += -Wall -Wextra -Wno-unused-function
@ -93,10 +145,10 @@ $(bench_internal_OBJECTS): src/ecmult_static_context.h @@ -93,10 +145,10 @@ $(bench_internal_OBJECTS): src/ecmult_static_context.h
src/ecmult_static_context.h: $(gen_context_BIN)
./$(gen_context_BIN)
CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h
CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h $(JAVAROOT)/$(JAVAORG)/*.class .stamp-java
endif
EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h
EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h $(JAVA_FILES)
if ENABLE_MODULE_ECDH
include src/modules/ecdh/Makefile.am.include

2
src/secp256k1/README.md

@ -1,7 +1,7 @@ @@ -1,7 +1,7 @@
libsecp256k1
============
[![Build Status](https://travis-ci.org/bitcoin/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin/secp256k1)
[![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1)
Optimized C library for EC operations on curve secp256k1.

140
src/secp256k1/build-aux/m4/ax_jni_include_dir.m4

@ -0,0 +1,140 @@ @@ -0,0 +1,140 @@
# ===========================================================================
# http://www.gnu.org/software/autoconf-archive/ax_jni_include_dir.html
# ===========================================================================
#
# SYNOPSIS
#
# AX_JNI_INCLUDE_DIR
#
# DESCRIPTION
#
# AX_JNI_INCLUDE_DIR finds include directories needed for compiling
# programs using the JNI interface.
#
# JNI include directories are usually in the Java distribution. This is
# deduced from the value of $JAVA_HOME, $JAVAC, or the path to "javac", in
# that order. When this macro completes, a list of directories is left in
# the variable JNI_INCLUDE_DIRS.
#
# Example usage follows:
#
# AX_JNI_INCLUDE_DIR
#
# for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS
# do
# CPPFLAGS="$CPPFLAGS -I$JNI_INCLUDE_DIR"
# done
#
# If you want to force a specific compiler:
#
# - at the configure.in level, set JAVAC=yourcompiler before calling
# AX_JNI_INCLUDE_DIR
#
# - at the configure level, setenv JAVAC
#
# Note: This macro can work with the autoconf M4 macros for Java programs.
# This particular macro is not part of the original set of macros.
#
# LICENSE
#
# Copyright (c) 2008 Don Anderson <dda@sleepycat.com>
#
# Copying and distribution of this file, with or without modification, are
# permitted in any medium without royalty provided the copyright notice
# and this notice are preserved. This file is offered as-is, without any
# warranty.
#serial 10
AU_ALIAS([AC_JNI_INCLUDE_DIR], [AX_JNI_INCLUDE_DIR])
AC_DEFUN([AX_JNI_INCLUDE_DIR],[
JNI_INCLUDE_DIRS=""
if test "x$JAVA_HOME" != x; then
_JTOPDIR="$JAVA_HOME"
else
if test "x$JAVAC" = x; then
JAVAC=javac
fi
AC_PATH_PROG([_ACJNI_JAVAC], [$JAVAC], [no])
if test "x$_ACJNI_JAVAC" = xno; then
AC_MSG_WARN([cannot find JDK; try setting \$JAVAC or \$JAVA_HOME])
fi
_ACJNI_FOLLOW_SYMLINKS("$_ACJNI_JAVAC")
_JTOPDIR=`echo "$_ACJNI_FOLLOWED" | sed -e 's://*:/:g' -e 's:/[[^/]]*$::'`
fi
case "$host_os" in
darwin*) _JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
_JINC="$_JTOPDIR/Headers";;
*) _JINC="$_JTOPDIR/include";;
esac
_AS_ECHO_LOG([_JTOPDIR=$_JTOPDIR])
_AS_ECHO_LOG([_JINC=$_JINC])
# On Mac OS X 10.6.4, jni.h is a symlink:
# /System/Library/Frameworks/JavaVM.framework/Versions/Current/Headers/jni.h
# -> ../../CurrentJDK/Headers/jni.h.
AC_CACHE_CHECK(jni headers, ac_cv_jni_header_path,
[
if test -f "$_JINC/jni.h"; then
ac_cv_jni_header_path="$_JINC"
JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
else
_JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
if test -f "$_JTOPDIR/include/jni.h"; then
ac_cv_jni_header_path="$_JTOPDIR/include"
JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
else
ac_cv_jni_header_path=none
fi
fi
])
# get the likely subdirectories for system specific java includes
case "$host_os" in
bsdi*) _JNI_INC_SUBDIRS="bsdos";;
darwin*) _JNI_INC_SUBDIRS="darwin";;
freebsd*) _JNI_INC_SUBDIRS="freebsd";;
linux*) _JNI_INC_SUBDIRS="linux genunix";;
osf*) _JNI_INC_SUBDIRS="alpha";;
solaris*) _JNI_INC_SUBDIRS="solaris";;
mingw*) _JNI_INC_SUBDIRS="win32";;
cygwin*) _JNI_INC_SUBDIRS="win32";;
*) _JNI_INC_SUBDIRS="genunix";;
esac
if test "x$ac_cv_jni_header_path" != "xnone"; then
# add any subdirectories that are present
for JINCSUBDIR in $_JNI_INC_SUBDIRS
do
if test -d "$_JTOPDIR/include/$JINCSUBDIR"; then
JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $_JTOPDIR/include/$JINCSUBDIR"
fi
done
fi
])
# _ACJNI_FOLLOW_SYMLINKS <path>
# Follows symbolic links on <path>,
# finally setting variable _ACJNI_FOLLOWED
# ----------------------------------------
AC_DEFUN([_ACJNI_FOLLOW_SYMLINKS],[
# find the include directory relative to the javac executable
_cur="$1"
while ls -ld "$_cur" 2>/dev/null | grep " -> " >/dev/null; do
AC_MSG_CHECKING([symlink for $_cur])
_slink=`ls -ld "$_cur" | sed 's/.* -> //'`
case "$_slink" in
/*) _cur="$_slink";;
# 'X' avoids triggering unwanted echo options.
*) _cur=`echo "X$_cur" | sed -e 's/^X//' -e 's:[[^/]]*$::'`"$_slink";;
esac
AC_MSG_RESULT([$_cur])
done
_ACJNI_FOLLOWED="$_cur"
])# _ACJNI

4
src/secp256k1/build-aux/m4/bitcoin_secp.m4

@ -3,13 +3,13 @@ AC_DEFUN([SECP_INT128_CHECK],[ @@ -3,13 +3,13 @@ AC_DEFUN([SECP_INT128_CHECK],[
has_int128=$ac_cv_type___int128
])
dnl
dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
AC_DEFUN([SECP_64BIT_ASM_CHECK],[
AC_MSG_CHECKING(for x86_64 assembly availability)
AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
#include <stdint.h>]],[[
uint64_t a = 11, tmp;
__asm__ __volatile__("movq $0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
__asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
]])],[has_64bit_asm=yes],[has_64bit_asm=no])
AC_MSG_RESULT([$has_64bit_asm])
])

146
src/secp256k1/configure.ac

@ -29,6 +29,7 @@ AC_PROG_CC_C89 @@ -29,6 +29,7 @@ AC_PROG_CC_C89
if test x"$ac_cv_prog_cc_c89" = x"no"; then
AC_MSG_ERROR([c89 compiler support required])
fi
AM_PROG_AS
case $host_os in
*darwin*)
@ -93,23 +94,33 @@ AC_ARG_ENABLE(tests, @@ -93,23 +94,33 @@ AC_ARG_ENABLE(tests,
[use_tests=$enableval],
[use_tests=yes])
AC_ARG_ENABLE(openssl_tests,
AS_HELP_STRING([--enable-openssl-tests],[enable OpenSSL tests, if OpenSSL is available (default is auto)]),
[enable_openssl_tests=$enableval],
[enable_openssl_tests=auto])
AC_ARG_ENABLE(experimental,
AS_HELP_STRING([--enable-experimental],[allow experimental configure options (default is no)]),
[use_experimental=$enableval],
[use_experimental=no])
AC_ARG_ENABLE(endomorphism,
AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
[use_endomorphism=$enableval],
[use_endomorphism=no])
AC_ARG_ENABLE(ecmult_static_precomputation,
AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing (default is yes)]),
[use_ecmult_static_precomputation=$enableval],
[use_ecmult_static_precomputation=yes])
[use_ecmult_static_precomputation=auto])
AC_ARG_ENABLE(module_ecdh,
AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (default is no)]),
AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (experimental)]),
[enable_module_ecdh=$enableval],
[enable_module_ecdh=no])
AC_ARG_ENABLE(module_schnorr,
AS_HELP_STRING([--enable-module-schnorr],[enable Schnorr signature module (default is no)]),
AS_HELP_STRING([--enable-module-schnorr],[enable Schnorr signature module (experimental)]),
[enable_module_schnorr=$enableval],
[enable_module_schnorr=no])
@ -118,6 +129,11 @@ AC_ARG_ENABLE(module_recovery, @@ -118,6 +129,11 @@ AC_ARG_ENABLE(module_recovery,
[enable_module_recovery=$enableval],
[enable_module_recovery=no])
AC_ARG_ENABLE(jni,
AS_HELP_STRING([--enable-jni],[enable libsecp256k1_jni (default is auto)]),
[use_jni=$enableval],
[use_jni=auto])
AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
[Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
@ -127,8 +143,8 @@ AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto], @@ -127,8 +143,8 @@ AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto],
AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
[Specify scalar implementation. Default is auto])],[req_scalar=$withval], [req_scalar=auto])
AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|no|auto]
[Specify assembly optimizations to use. Default is auto])],[req_asm=$withval], [req_asm=auto])
AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto]
[Specify assembly optimizations to use. Default is auto (experimental: arm)])],[req_asm=$withval], [req_asm=auto])
AC_CHECK_TYPES([__int128])
@ -138,6 +154,34 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])], @@ -138,6 +154,34 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])],
[ AC_MSG_RESULT([no])
])
if test x"$use_ecmult_static_precomputation" != x"no"; then
save_cross_compiling=$cross_compiling
cross_compiling=no
TEMP_CC="$CC"
CC="$CC_FOR_BUILD"
AC_MSG_CHECKING([native compiler: ${CC_FOR_BUILD}])
AC_RUN_IFELSE(
[AC_LANG_PROGRAM([], [return 0])],
[working_native_cc=yes],
[working_native_cc=no],[dnl])
CC="$TEMP_CC"
cross_compiling=$save_cross_compiling
if test x"$working_native_cc" = x"no"; then
set_precomp=no
if test x"$use_ecmult_static_precomputation" = x"yes"; then
AC_MSG_ERROR([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
else
AC_MSG_RESULT([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
fi
else
AC_MSG_RESULT([ok])
set_precomp=yes
fi
else
set_precomp=no
fi
if test x"$req_asm" = x"auto"; then
SECP_64BIT_ASM_CHECK
if test x"$has_64bit_asm" = x"yes"; then
@ -155,6 +199,8 @@ else @@ -155,6 +199,8 @@ else
AC_MSG_ERROR([x86_64 assembly optimization requested but not available])
fi
;;
arm)
;;
no)
;;
*)
@ -247,10 +293,15 @@ else @@ -247,10 +293,15 @@ else
fi
# select assembly optimization
use_external_asm=no
case $set_asm in
x86_64)
AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations])
;;
arm)
use_external_asm=yes
;;
no)
;;
*)
@ -305,16 +356,51 @@ esac @@ -305,16 +356,51 @@ esac
if test x"$use_tests" = x"yes"; then
SECP_OPENSSL_CHECK
if test x"$has_openssl_ec" = x"yes"; then
AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS"
SECP_TEST_LIBS="$CRYPTO_LIBS"
case $host in
*mingw*)
SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
;;
esac
if test x"$enable_openssl_tests" != x"no"; then
AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS"
SECP_TEST_LIBS="$CRYPTO_LIBS"
case $host in
*mingw*)
SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
;;
esac
fi
else
if test x"$enable_openssl_tests" = x"yes"; then
AC_MSG_ERROR([OpenSSL tests requested but OpenSSL with EC support is not available])
fi
fi
else
if test x"$enable_openssl_tests" = x"yes"; then
AC_MSG_ERROR([OpenSSL tests requested but tests are not enabled])
fi
fi
if test x"$use_jni" != x"no"; then
AX_JNI_INCLUDE_DIR
have_jni_dependencies=yes
if test x"$enable_module_schnorr" = x"no"; then
have_jni_dependencies=no
fi
if test x"$enable_module_ecdh" = x"no"; then
have_jni_dependencies=no
fi
if test "x$JNI_INCLUDE_DIRS" = "x"; then
have_jni_dependencies=no
fi
if test "x$have_jni_dependencies" = "xno"; then
if test x"$use_jni" = x"yes"; then
AC_MSG_ERROR([jni support explicitly requested but headers/dependencies were not found. Enable ECDH and Schnorr and try again.])
fi
AC_MSG_WARN([jni headers/dependencies not found. jni support disabled])
use_jni=no
else
use_jni=yes
for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS; do
JNI_INCLUDES="$JNI_INCLUDES -I$JNI_INCLUDE_DIR"
done
fi
fi
@ -345,18 +431,43 @@ fi @@ -345,18 +431,43 @@ fi
AC_C_BIGENDIAN()
if test x"$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
AC_MSG_NOTICE([Using static precomputation: $set_precomp])
AC_MSG_NOTICE([Using assembly optimizations: $set_asm])
AC_MSG_NOTICE([Using field implementation: $set_field])
AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
AC_MSG_NOTICE([Using jni: $use_jni])
if test x"$enable_experimental" = x"yes"; then
AC_MSG_NOTICE([******])
AC_MSG_NOTICE([WARNING: experimental build])
AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
AC_MSG_NOTICE([******])
else
if test x"$enable_module_schnorr" = x"yes"; then
AC_MSG_ERROR([Schnorr signature module is experimental. Use --enable-experimental to allow.])
fi
if test x"$enable_module_ecdh" = x"yes"; then
AC_MSG_ERROR([ECDH module is experimental. Use --enable-experimental to allow.])
fi
if test x"$set_asm" = x"arm"; then
AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
fi
fi
AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
AC_CONFIG_FILES([Makefile libsecp256k1.pc])
AC_SUBST(JNI_INCLUDES)
AC_SUBST(SECP_INCLUDES)
AC_SUBST(SECP_LIBS)
AC_SUBST(SECP_TEST_LIBS)
@ -367,6 +478,9 @@ AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$use_ecmult_static_pr @@ -367,6 +478,9 @@ AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$use_ecmult_static_pr
AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
AM_CONDITIONAL([ENABLE_MODULE_SCHNORR], [test x"$enable_module_schnorr" = x"yes"])
AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
AM_CONDITIONAL([USE_JNI], [test x"$use_jni" == x"yes"])
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
PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"

2
src/secp256k1/libsecp256k1.pc.in

@ -5,7 +5,7 @@ includedir=@includedir@ @@ -5,7 +5,7 @@ includedir=@includedir@
Name: libsecp256k1
Description: Optimized C library for EC operations on curve secp256k1
URL: https://github.com/bitcoin/secp256k1
URL: https://github.com/bitcoin-core/secp256k1
Version: @PACKAGE_VERSION@
Cflags: -I${includedir}
Libs.private: @SECP_LIBS@

322
src/secp256k1/sage/group_prover.sage

@ -0,0 +1,322 @@ @@ -0,0 +1,322 @@
# This code supports verifying group implementations which have branches
# or conditional statements (like cmovs), by allowing each execution path
# to independently set assumptions on input or intermediary variables.
#
# The general approach is:
# * A constraint is a tuple of two sets of of symbolic expressions:
# the first of which are required to evaluate to zero, the second of which
# are required to evaluate to nonzero.
# - A constraint is said to be conflicting if any of its nonzero expressions
# is in the ideal with basis the zero expressions (in other words: when the
# zero expressions imply that one of the nonzero expressions are zero).
# * There is a list of laws that describe the intended behaviour, including
# laws for addition and doubling. Each law is called with the symbolic point
# coordinates as arguments, and returns:
# - A constraint describing the assumptions under which it is applicable,
# called "assumeLaw"
# - A constraint describing the requirements of the law, called "require"
# * Implementations are transliterated into functions that operate as well on
# algebraic input points, and are called once per combination of branches
# exectured. Each execution returns:
# - A constraint describing the assumptions this implementation requires
# (such as Z1=1), called "assumeFormula"
# - A constraint describing the assumptions this specific branch requires,
# but which is by construction guaranteed to cover the entire space by
# merging the results from all branches, called "assumeBranch"
# - The result of the computation
# * All combinations of laws with implementation branches are tried, and:
# - If the combination of assumeLaw, assumeFormula, and assumeBranch results
# in a conflict, it means this law does not apply to this branch, and it is
# skipped.
# - For others, we try to prove the require constraints hold, assuming the
# information in assumeLaw + assumeFormula + assumeBranch, and if this does
# not succeed, we fail.
# + To prove an expression is zero, we check whether it belongs to the
# ideal with the assumed zero expressions as basis. This test is exact.
# + To prove an expression is nonzero, we check whether each of its
# factors is contained in the set of nonzero assumptions' factors.
# This test is not exact, so various combinations of original and
# reduced expressions' factors are tried.
# - If we succeed, we print out the assumptions from assumeFormula that
# weren't implied by assumeLaw already. Those from assumeBranch are skipped,
# as we assume that all constraints in it are complementary with each other.
#
# Based on the sage verification scripts used in the Explicit-Formulas Database
# by Tanja Lange and others, see http://hyperelliptic.org/EFD
class fastfrac:
"""Fractions over rings."""
def __init__(self,R,top,bot=1):
"""Construct a fractional, given a ring, a numerator, and denominator."""
self.R = R
if parent(top) == ZZ or parent(top) == R:
self.top = R(top)
self.bot = R(bot)
elif top.__class__ == fastfrac:
self.top = top.top
self.bot = top.bot * bot
else:
self.top = R(numerator(top))
self.bot = R(denominator(top)) * bot
def iszero(self,I):
"""Return whether this fraction is zero given an ideal."""
return self.top in I and self.bot not in I
def reduce(self,assumeZero):
zero = self.R.ideal(map(numerator, assumeZero))
return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot))
def __add__(self,other):
"""Add two fractions."""
if parent(other) == ZZ:
return fastfrac(self.R,self.top + self.bot * other,self.bot)
if other.__class__ == fastfrac:
return fastfrac(self.R,self.top * other.bot + self.bot * other.top,self.bot * other.bot)
return NotImplemented
def __sub__(self,other):
"""Subtract two fractions."""
if parent(other) == ZZ:
return fastfrac(self.R,self.top - self.bot * other,self.bot)
if other.__class__ == fastfrac:
return fastfrac(self.R,self.top * other.bot - self.bot * other.top,self.bot * other.bot)
return NotImplemented
def __neg__(self):
"""Return the negation of a fraction."""
return fastfrac(self.R,-self.top,self.bot)
def __mul__(self,other):
"""Multiply two fractions."""
if parent(other) == ZZ:
return fastfrac(self.R,self.top * other,self.bot)
if other.__class__ == fastfrac:
return fastfrac(self.R,self.top * other.top,self.bot * other.bot)
return NotImplemented
def __rmul__(self,other):
"""Multiply something else with a fraction."""
return self.__mul__(other)
def __div__(self,other):
"""Divide two fractions."""
if parent(other) == ZZ:
return fastfrac(self.R,self.top,self.bot * other)
if other.__class__ == fastfrac:
return fastfrac(self.R,self.top * other.bot,self.bot * other.top)
return NotImplemented
def __pow__(self,other):
"""Compute a power of a fraction."""
if parent(other) == ZZ:
if other < 0:
# Negative powers require flipping top and bottom
return fastfrac(self.R,self.bot ^ (-other),self.top ^ (-other))
else:
return fastfrac(self.R,self.top ^ other,self.bot ^ other)
return NotImplemented
def __str__(self):
return "fastfrac((" + str(self.top) + ") / (" + str(self.bot) + "))"
def __repr__(self):
return "%s" % self
def numerator(self):
return self.top
class constraints:
"""A set of constraints, consisting of zero and nonzero expressions.
Constraints can either be used to express knowledge or a requirement.
Both the fields zero and nonzero are maps from expressions to description
strings. The expressions that are the keys in zero are required to be zero,
and the expressions that are the keys in nonzero are required to be nonzero.
Note that (a != 0) and (b != 0) is the same as (a*b != 0), so all keys in
nonzero could be multiplied into a single key. This is often much less
efficient to work with though, so we keep them separate inside the
constraints. This allows higher-level code to do fast checks on the individual
nonzero elements, or combine them if needed for stronger checks.
We can't multiply the different zero elements, as it would suffice for one of
the factors to be zero, instead of all of them. Instead, the zero elements are
typically combined into an ideal first.
"""
def __init__(self, **kwargs):
if 'zero' in kwargs:
self.zero = dict(kwargs['zero'])
else:
self.zero = dict()
if 'nonzero' in kwargs:
self.nonzero = dict(kwargs['nonzero'])
else:
self.nonzero = dict()
def negate(self):
return constraints(zero=self.nonzero, nonzero=self.zero)
def __add__(self, other):
zero = self.zero.copy()
zero.update(other.zero)
nonzero = self.nonzero.copy()
nonzero.update(other.nonzero)
return constraints(zero=zero, nonzero=nonzero)
def __str__(self):
return "constraints(zero=%s,nonzero=%s)" % (self.zero, self.nonzero)
def __repr__(self):
return "%s" % self
def 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))
if 1 in zero:
return True
# First a cheap check whether any of the individual nonzero terms conflict on
# their own.
for nonzero in con.nonzero:
if nonzero.iszero(zero):
return True
# It can be the case that entries in the nonzero set do not individually
# conflict with the zero set, but their combination does. For example, knowing
# that either x or y is zero is equivalent to having x*y in the zero set.
# Having x or y individually in the nonzero set is not a conflict, but both
# simultaneously is, so that is the right thing to check for.
if reduce(lambda a,b: a * b, con.nonzero, fastfrac(R, 1)).iszero(zero):
return True
return False
def get_nonzero_set(R, assume):
"""Calculate a simple set of nonzero expressions"""
zero = R.ideal(map(numerator, assume.zero))
nonzero = set()
for nz in map(numerator, assume.nonzero):
for (f,n) in nz.factor():
nonzero.add(f)
rnz = zero.reduce(nz)
for (f,n) in rnz.factor():
nonzero.add(f)
return nonzero
def prove_nonzero(R, exprs, assume):
"""Check whether an expression is provably nonzero, given assumptions"""
zero = R.ideal(map(numerator, assume.zero))
nonzero = get_nonzero_set(R, assume)
expl = set()
ok = True
for expr in exprs:
if numerator(expr) in zero:
return (False, [exprs[expr]])
allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
for (f, n) in allexprs.factor():
if f not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for (f, n) in zero.reduce(numerator(allexprs)).factor():
if f not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for expr in exprs:
for (f,n) in numerator(expr).factor():
if f not in nonzero:
ok = False
if ok:
return (True, None)
ok = True
for expr in exprs:
for (f,n) in zero.reduce(numerator(expr)).factor():
if f not in nonzero:
expl.add(exprs[expr])
if expl:
return (False, list(expl))
else:
return (True, None)
def prove_zero(R, exprs, assume):
"""Check whether all of the passed expressions are provably zero, given assumptions"""
r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
if not r:
return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
zero = R.ideal(map(numerator, assume.zero))
nonzero = prod(x for x in assume.nonzero)
expl = []
for expr in exprs:
if not expr.iszero(zero):
expl.append(exprs[expr])
if not expl:
return (True, None)
return (False, expl)
def describe_extra(R, assume, assumeExtra):
"""Describe what assumptions are added, given existing assumptions"""
zerox = assume.zero.copy()
zerox.update(assumeExtra.zero)
zero = R.ideal(map(numerator, assume.zero))
zeroextra = R.ideal(map(numerator, zerox))
nonzero = get_nonzero_set(R, assume)
ret = set()
# Iterate over the extra zero expressions
for base in assumeExtra.zero:
if base not in zero:
add = []
for (f, n) in numerator(base).factor():
if f not in nonzero:
add += ["%s" % f]
if add:
ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
# Iterate over the extra nonzero expressions
for nz in assumeExtra.nonzero:
nzr = zeroextra.reduce(numerator(nz))
if nzr not in zeroextra:
for (f,n) in nzr.factor():
if zeroextra.reduce(f) not in nonzero:
ret.add("%s != 0" % zeroextra.reduce(f))
return ", ".join(x for x in ret)
def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require):
"""Check a set of zero and nonzero requirements, given a set of zero and nonzero assumptions"""
assume = assumeLaw + assumeAssert + assumeBranch
if conflicts(R, assume):
# This formula does not apply
return None
describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert)
ok, msg = prove_zero(R, require.zero, assume)
if not ok:
return "FAIL, %s fails (assuming %s)" % (str(msg), describe)
res, expl = prove_nonzero(R, require.nonzero, assume)
if not res:
return "FAIL, %s fails (assuming %s)" % (str(expl), describe)
if describe != "":
return "OK (assuming %s)" % describe
else:
return "OK"
def concrete_verify(c):
for k in c.zero:
if k != 0:
return (False, c.zero[k])
for k in c.nonzero:
if k == 0:
return (False, c.nonzero[k])
return (True, None)

306
src/secp256k1/sage/secp256k1.sage

@ -0,0 +1,306 @@ @@ -0,0 +1,306 @@
# Test libsecp256k1' group operation implementations using prover.sage
import sys
load("group_prover.sage")
load("weierstrass_prover.sage")
def formula_secp256k1_gej_double_var(a):
"""libsecp256k1's secp256k1_gej_double_var, used by various addition functions"""
rz = a.Z * a.Y
rz = rz * 2
t1 = a.X^2
t1 = t1 * 3
t2 = t1^2
t3 = a.Y^2
t3 = t3 * 2
t4 = t3^2
t4 = t4 * 2
t3 = t3 * a.X
rx = t3
rx = rx * 4
rx = -rx
rx = rx + t2
t2 = -t2
t3 = t3 * 6
t3 = t3 + t2
ry = t1 * t3
t2 = -t4
ry = ry + t2
return jacobianpoint(rx, ry, rz)
def formula_secp256k1_gej_add_var(branch, a, b):
"""libsecp256k1's secp256k1_gej_add_var"""
if branch == 0:
return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
if branch == 1:
return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
z22 = b.Z^2
z12 = a.Z^2
u1 = a.X * z22
u2 = b.X * z12
s1 = a.Y * z22
s1 = s1 * b.Z
s2 = b.Y * z12
s2 = s2 * a.Z
h = -u1
h = h + u2
i = -s1
i = i + s2
if branch == 2:
r = formula_secp256k1_gej_double_var(a)
return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
if branch == 3:
return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
i2 = i^2
h2 = h^2
h3 = h2 * h
h = h * b.Z
rz = a.Z * h
t = u1 * h2
rx = t
rx = rx * 2
rx = rx + h3
rx = -rx
rx = rx + i2
ry = -rx
ry = ry + t
ry = ry * i
h3 = h3 * s1
h3 = -h3
ry = ry + h3
return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
def formula_secp256k1_gej_add_ge_var(branch, a, b):
"""libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1"""
if branch == 0:
return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
if branch == 1:
return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
z12 = a.Z^2
u1 = a.X
u2 = b.X * z12
s1 = a.Y
s2 = b.Y * z12
s2 = s2 * a.Z
h = -u1
h = h + u2
i = -s1
i = i + s2
if (branch == 2):
r = formula_secp256k1_gej_double_var(a)
return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
if (branch == 3):
return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
i2 = i^2
h2 = h^2
h3 = h * h2
rz = a.Z * h
t = u1 * h2
rx = t
rx = rx * 2
rx = rx + h3
rx = -rx
rx = rx + i2
ry = -rx
ry = ry + t
ry = ry * i
h3 = h3 * s1
h3 = -h3
ry = ry + h3
return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
def formula_secp256k1_gej_add_zinv_var(branch, a, b):
"""libsecp256k1's secp256k1_gej_add_zinv_var"""
bzinv = b.Z^(-1)
if branch == 0:
return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
if branch == 1:
bzinv2 = bzinv^2
bzinv3 = bzinv2 * bzinv
rx = b.X * bzinv2
ry = b.Y * bzinv3
rz = 1
return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
azz = a.Z * bzinv
z12 = azz^2
u1 = a.X
u2 = b.X * z12
s1 = a.Y
s2 = b.Y * z12
s2 = s2 * azz
h = -u1
h = h + u2
i = -s1
i = i + s2
if branch == 2:
r = formula_secp256k1_gej_double_var(a)
return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
if branch == 3:
return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
i2 = i^2
h2 = h^2
h3 = h * h2
rz = a.Z
rz = rz * h
t = u1 * h2
rx = t
rx = rx * 2
rx = rx + h3
rx = -rx
rx = rx + i2
ry = -rx
ry = ry + t
ry = ry * i
h3 = h3 * s1
h3 = -h3
ry = ry + h3
return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
def formula_secp256k1_gej_add_ge(branch, a, b):
"""libsecp256k1's secp256k1_gej_add_ge"""
zeroes = {}
nonzeroes = {}
a_infinity = False
if (branch & 4) != 0:
nonzeroes.update({a.Infinity : 'a_infinite'})
a_infinity = True
else:
zeroes.update({a.Infinity : 'a_finite'})
zz = a.Z^2
u1 = a.X
u2 = b.X * zz
s1 = a.Y
s2 = b.Y * zz
s2 = s2 * a.Z
t = u1
t = t + u2
m = s1
m = m + s2
rr = t^2
m_alt = -u2
tt = u1 * m_alt
rr = rr + tt
degenerate = (branch & 3) == 3
if (branch & 1) != 0:
zeroes.update({m : 'm_zero'})
else:
nonzeroes.update({m : 'm_nonzero'})
if (branch & 2) != 0:
zeroes.update({rr : 'rr_zero'})
else:
nonzeroes.update({rr : 'rr_nonzero'})
rr_alt = s1
rr_alt = rr_alt * 2
m_alt = m_alt + u1
if not degenerate:
rr_alt = rr
m_alt = m
n = m_alt^2
q = n * t
n = n^2
if degenerate:
n = m
t = rr_alt^2
rz = a.Z * m_alt
infinity = False
if (branch & 8) != 0:
if not a_infinity:
infinity = True
zeroes.update({rz : 'r.z=0'})
else:
nonzeroes.update({rz : 'r.z!=0'})
rz = rz * 2
q = -q
t = t + q
rx = t
t = t * 2
t = t + q
t = t * rr_alt
t = t + n
ry = -t
rx = rx * 4
ry = ry * 4
if a_infinity:
rx = b.X
ry = b.Y
rz = 1
if infinity:
return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity())
return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz))
def formula_secp256k1_gej_add_ge_old(branch, a, b):
"""libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx"""
a_infinity = (branch & 1) != 0
zero = {}
nonzero = {}
if a_infinity:
nonzero.update({a.Infinity : 'a_infinite'})
else:
zero.update({a.Infinity : 'a_finite'})
zz = a.Z^2
u1 = a.X
u2 = b.X * zz
s1 = a.Y
s2 = b.Y * zz
s2 = s2 * a.Z
z = a.Z
t = u1
t = t + u2
m = s1
m = m + s2
n = m^2
q = n * t
n = n^2
rr = t^2
t = u1 * u2
t = -t
rr = rr + t
t = rr^2
rz = m * z
infinity = False
if (branch & 2) != 0:
if not a_infinity:
infinity = True
else:
return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity())
zero.update({rz : 'r.z=0'})
else:
nonzero.update({rz : 'r.z!=0'})
rz = rz * (0 if a_infinity else 2)
rx = t
q = -q
rx = rx + q
q = q * 3
t = t * 2
t = t + q
t = t * rr
t = t + n
ry = -t
rx = rx * (0 if a_infinity else 4)
ry = ry * (0 if a_infinity else 4)
t = b.X
t = t * (1 if a_infinity else 0)
rx = rx + t
t = b.Y
t = t * (1 if a_infinity else 0)
ry = ry + t
t = (1 if a_infinity else 0)
rz = rz + t
if infinity:
return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity())
return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
if __name__ == "__main__":
check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)

264
src/secp256k1/sage/weierstrass_prover.sage

@ -0,0 +1,264 @@ @@ -0,0 +1,264 @@
# Prover implementation for Weierstrass curves of the form
# y^2 = x^3 + A * x + B, specifically with a = 0 and b = 7, with group laws
# operating on affine and Jacobian coordinates, including the point at infinity
# represented by a 4th variable in coordinates.
load("group_prover.sage")
class affinepoint:
def __init__(self, x, y, infinity=0):
self.x = x
self.y = y
self.infinity = infinity
def __str__(self):
return "affinepoint(x=%s,y=%s,inf=%s)" % (self.x, self.y, self.infinity)
class jacobianpoint:
def __init__(self, x, y, z, infinity=0):
self.X = x
self.Y = y
self.Z = z
self.Infinity = infinity
def __str__(self):
return "jacobianpoint(X=%s,Y=%s,Z=%s,inf=%s)" % (self.X, self.Y, self.Z, self.Infinity)
def point_at_infinity():
return jacobianpoint(1, 1, 1, 1)
def negate(p):
if p.__class__ == affinepoint:
return affinepoint(p.x, -p.y)
if p.__class__ == jacobianpoint:
return jacobianpoint(p.X, -p.Y, p.Z)
assert(False)
def on_weierstrass_curve(A, B, p):
"""Return a set of zero-expressions for an affine point to be on the curve"""
return constraints(zero={p.x^3 + A*p.x + B - p.y^2: 'on_curve'})
def tangential_to_weierstrass_curve(A, B, p12, p3):
"""Return a set of zero-expressions for ((x12,y12),(x3,y3)) to be a line that is tangential to the curve at (x12,y12)"""
return constraints(zero={
(p12.y - p3.y) * (p12.y * 2) - (p12.x^2 * 3 + A) * (p12.x - p3.x): 'tangential_to_curve'
})
def colinear(p1, p2, p3):
"""Return a set of zero-expressions for ((x1,y1),(x2,y2),(x3,y3)) to be collinear"""
return constraints(zero={
(p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x): 'colinear_1',
(p2.y - p3.y) * (p2.x - p1.x) - (p2.y - p1.y) * (p2.x - p3.x): 'colinear_2',
(p3.y - p1.y) * (p3.x - p2.x) - (p3.y - p2.y) * (p3.x - p1.x): 'colinear_3'
})
def good_affine_point(p):
return constraints(nonzero={p.x : 'nonzero_x', p.y : 'nonzero_y'})
def good_jacobian_point(p):
return constraints(nonzero={p.X : 'nonzero_X', p.Y : 'nonzero_Y', p.Z^6 : 'nonzero_Z'})
def good_point(p):
return constraints(nonzero={p.Z^6 : 'nonzero_X'})
def finite(p, *affine_fns):
con = good_point(p) + constraints(zero={p.Infinity : 'finite_point'})
if p.Z != 0:
return con + reduce(lambda a, b: a + b, (f(affinepoint(p.X / p.Z^2, p.Y / p.Z^3)) for f in affine_fns), con)
else:
return con
def infinite(p):
return constraints(nonzero={p.Infinity : 'infinite_point'})
def law_jacobian_weierstrass_add(A, B, pa, pb, pA, pB, pC):
"""Check whether the passed set of coordinates is a valid Jacobian add, given assumptions"""
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
on_weierstrass_curve(A, B, pa) +
on_weierstrass_curve(A, B, pb) +
finite(pA) +
finite(pB) +
constraints(nonzero={pa.x - pb.x : 'different_x'}))
require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
colinear(pa, pb, negate(pc))))
return (assumeLaw, require)
def law_jacobian_weierstrass_double(A, B, pa, pb, pA, pB, pC):
"""Check whether the passed set of coordinates is a valid Jacobian doubling, given assumptions"""
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
on_weierstrass_curve(A, B, pa) +
on_weierstrass_curve(A, B, pb) +
finite(pA) +
finite(pB) +
constraints(zero={pa.x - pb.x : 'equal_x', pa.y - pb.y : 'equal_y'}))
require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
tangential_to_weierstrass_curve(A, B, pa, negate(pc))))
return (assumeLaw, require)
def law_jacobian_weierstrass_add_opposites(A, B, pa, pb, pA, pB, pC):
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
on_weierstrass_curve(A, B, pa) +
on_weierstrass_curve(A, B, pb) +
finite(pA) +
finite(pB) +
constraints(zero={pa.x - pb.x : 'equal_x', pa.y + pb.y : 'opposite_y'}))
require = infinite(pC)
return (assumeLaw, require)
def law_jacobian_weierstrass_add_infinite_a(A, B, pa, pb, pA, pB, pC):
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
on_weierstrass_curve(A, B, pb) +
infinite(pA) +
finite(pB))
require = finite(pC, lambda pc: constraints(zero={pc.x - pb.x : 'c.x=b.x', pc.y - pb.y : 'c.y=b.y'}))
return (assumeLaw, require)
def law_jacobian_weierstrass_add_infinite_b(A, B, pa, pb, pA, pB, pC):
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
on_weierstrass_curve(A, B, pa) +
infinite(pB) +
finite(pA))
require = finite(pC, lambda pc: constraints(zero={pc.x - pa.x : 'c.x=a.x', pc.y - pa.y : 'c.y=a.y'}))
return (assumeLaw, require)
def law_jacobian_weierstrass_add_infinite_ab(A, B, pa, pb, pA, pB, pC):
assumeLaw = (good_affine_point(pa) +
good_affine_point(pb) +
good_jacobian_point(pA) +
good_jacobian_point(pB) +
infinite(pA) +
infinite(pB))
require = infinite(pC)
return (assumeLaw, require)
laws_jacobian_weierstrass = {
'add': law_jacobian_weierstrass_add,
'double': law_jacobian_weierstrass_double,
'add_opposite': law_jacobian_weierstrass_add_opposites,
'add_infinite_a': law_jacobian_weierstrass_add_infinite_a,
'add_infinite_b': law_jacobian_weierstrass_add_infinite_b,
'add_infinite_ab': law_jacobian_weierstrass_add_infinite_ab
}