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Update bitcoin secp256k1 lib

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This commit is contained in:
Gustav Simonsson 2015-04-07 12:13:37 +02:00
parent 9c55576c7b
commit f4d4f1ccb2
74 changed files with 10526 additions and 4978 deletions
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32
crypto/secp256k1/secp256k1/.travis.yml Normal file
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language: c
compiler:
- clang
- gcc
install:
- sudo apt-get install -qq libssl-dev
- if [ "$BIGNUM" = "gmp" -o "$BIGNUM" = "auto" ]; then sudo apt-get install --no-install-recommends --no-upgrade -qq libgmp-dev; fi
- if [ -n "$EXTRAPACKAGES" ]; then sudo apt-get update && sudo apt-get install --no-install-recommends --no-upgrade $EXTRAPACKAGES; fi
env:
global:
- FIELD=auto BIGNUM=auto SCALAR=auto ENDOMORPHISM=no ASM=no BUILD=check EXTRAFLAGS= HOST= EXTRAPACKAGES=
matrix:
- SCALAR=32bit
- SCALAR=64bit
- FIELD=64bit
- FIELD=64bit ENDOMORPHISM=yes
- FIELD=64bit ASM=x86_64
- FIELD=64bit ENDOMORPHISM=yes ASM=x86_64
- FIELD=32bit
- FIELD=32bit ENDOMORPHISM=yes
- BIGNUM=no
- BIGNUM=no ENDOMORPHISM=yes
- BUILD=distcheck
- EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
- HOST=i686-linux-gnu EXTRAPACKAGES="gcc-multilib"
- HOST=i686-linux-gnu EXTRAPACKAGES="gcc-multilib" ENDOMORPHISM=yes
before_script: ./autogen.sh
script:
- if [ -n "$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 $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
os: linux

55
crypto/secp256k1/secp256k1/Makefile
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$(shell CC=$(CC) YASM=$(YASM) ./configure)
include config.mk
FILES := src/*.h src/impl/*.h
JAVA_FILES := src/java/org_bitcoin_NativeSecp256k1.h src/java/org_bitcoin_NativeSecp256k1.c
OBJS :=
ifeq ($(USE_ASM), 1)
OBJS := $(OBJS) obj/field_5x$(HAVE_LIMB)_asm.o
endif
STD="gnu99"
default: tests libsecp256k1.a libsecp256k1.so
clean:
rm -rf obj/*.o bench tests *.a *.so config.mk
obj/field_5x52_asm.o: src/field_5x52_asm.asm
$(YASM) -f elf64 -o obj/field_5x52_asm.o src/field_5x52_asm.asm
obj/field_5x64_asm.o: src/field_5x64_asm.asm
$(YASM) -f elf64 -o obj/field_5x64_asm.o src/field_5x64_asm.asm
obj/secp256k1.o: $(FILES) src/secp256k1.c include/secp256k1.h
$(CC) -fPIC -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) -DNDEBUG -$(OPTLEVEL) src/secp256k1.c -c -o obj/secp256k1.o
bench: $(FILES) src/bench.c $(OBJS)
$(CC) -fPIC -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) $(CFLAGS_TEST_EXTRA) -DNDEBUG -$(OPTLEVEL) src/bench.c $(OBJS) $(LDFLAGS_EXTRA) $(LDFLAGS_TEST_EXTRA) -o bench
tests: $(FILES) src/tests.c $(OBJS)
$(CC) -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) $(CFLAGS_TEST_EXTRA) -DVERIFY -fstack-protector-all -$(OPTLEVEL) -ggdb3 src/tests.c $(OBJS) $(LDFLAGS_EXTRA) $(LDFLAGS_TEST_EXTRA) -o tests
tests_fuzzer: $(FILES) src/tests_fuzzer.c obj/secp256k1.o $(OBJS)
$(CC) -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) $(CFLAGS_TEST_EXTRA) -DVERIFY -fstack-protector-all -$(OPTLEVEL) -ggdb3 src/tests_fuzzer.c $(OBJS) obj/secp256k1.o $(LDFLAGS_EXTRA) $(LDFLAGS_TEST_EXTRA) -o tests_fuzzer
coverage: $(FILES) src/tests.c $(OBJS)
rm -rf tests.gcno tests.gcda tests_cov
$(CC) -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) $(CFLAGS_TEST_EXTRA) -DVERIFY --coverage -$(OPTLEVEL) -g src/tests.c $(OBJS) $(LDFLAGS_EXTRA) $(LDFLAGS_TEST_EXTRA) -o tests_cov
rm -rf lcov
mkdir -p lcov
cd lcov; lcov --directory ../ --zerocounters
cd lcov; ../tests_cov
cd lcov; lcov --directory ../ --capture --output-file secp256k1.info
cd lcov; genhtml -o . secp256k1.info
libsecp256k1.a: obj/secp256k1.o $(OBJS)
$(AR) -rs $@ $(OBJS) obj/secp256k1.o
libsecp256k1.so: obj/secp256k1.o $(OBJS)
$(CC) -std=$(STD) $(LDFLAGS_EXTRA) $(OBJS) obj/secp256k1.o -shared -o libsecp256k1.so
libjavasecp256k1.so: $(OBJS) obj/secp256k1.o $(JAVA_FILES)
$(CC) -fPIC -std=$(STD) $(CFLAGS) $(CFLAGS_EXTRA) -DNDEBUG -$(OPTLEVEL) -I. src/java/org_bitcoin_NativeSecp256k1.c $(LDFLAGS_EXTRA) $(OBJS) obj/secp256k1.o -shared -o libjavasecp256k1.so

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crypto/secp256k1/secp256k1/Makefile.am Normal file
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ACLOCAL_AMFLAGS = -I build-aux/m4
lib_LTLIBRARIES = libsecp256k1.la
include_HEADERS = include/secp256k1.h
noinst_HEADERS =
noinst_HEADERS += src/scalar.h
noinst_HEADERS += src/scalar_4x64.h
noinst_HEADERS += src/scalar_8x32.h
noinst_HEADERS += src/scalar_impl.h
noinst_HEADERS += src/scalar_4x64_impl.h
noinst_HEADERS += src/scalar_8x32_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
noinst_HEADERS += src/eckey_impl.h
noinst_HEADERS += src/ecmult.h
noinst_HEADERS += src/ecmult_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/java/org_bitcoin_NativeSecp256k1.h
noinst_HEADERS += src/util.h
noinst_HEADERS += src/testrand.h
noinst_HEADERS += src/testrand_impl.h
noinst_HEADERS += src/hash.h
noinst_HEADERS += src/hash_impl.h
noinst_HEADERS += src/field.h
noinst_HEADERS += src/field_impl.h
noinst_HEADERS += src/bench.h
pkgconfigdir = $(libdir)/pkgconfig
pkgconfig_DATA = libsecp256k1.pc
libsecp256k1_la_SOURCES = src/secp256k1.c
libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include $(SECP_INCLUDES)
libsecp256k1_la_LIBADD = $(SECP_LIBS)
noinst_PROGRAMS =
if USE_BENCHMARK
noinst_PROGRAMS += bench_verify bench_recover bench_sign bench_internal
bench_verify_SOURCES = src/bench_verify.c
bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_verify_LDFLAGS = -static
bench_recover_SOURCES = src/bench_recover.c
bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_recover_LDFLAGS = -static
bench_sign_SOURCES = src/bench_sign.c
bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_sign_LDFLAGS = -static
bench_internal_SOURCES = src/bench_internal.c
bench_internal_LDADD = $(SECP_LIBS)
bench_internal_LDFLAGS = -static
bench_internal_CPPFLAGS = $(SECP_INCLUDES)
endif
if USE_TESTS
noinst_PROGRAMS += tests
tests_SOURCES = src/tests.c
tests_CPPFLAGS = -DVERIFY $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS)
tests_LDFLAGS = -static
TESTS = tests
endif
EXTRA_DIST = autogen.sh

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crypto/secp256k1/secp256k1/README.md Normal file
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libsecp256k1
============
[![Build Status](https://travis-ci.org/bitcoin/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin/secp256k1)
Optimized C library for EC operations on curve secp256k1.
This library is a work in progress and is being used to research best practices. Use at your own risk.
Features:
* secp256k1 ECDSA signing/verification and key generation.
* Adding/multiplying private/public keys.
* Serialization/parsing of private keys, public keys, signatures.
* Constant time, constant memory access signing and pubkey generation.
* Derandomized DSA (via RFC6979 or with a caller provided function.)
* Very efficient implementation.
Implementation details
----------------------
* General
* No runtime heap allocation.
* Extensive testing infrastructure.
* Structured to facilitate review and analysis.
* Intended to be portable to any system with a C89 compiler and uint64_t support.
* Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
* Field operations
* Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
* Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
* Using 10 26-bit limbs.
* 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.
* Group operations
* Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
* Use addition between points in Jacobian and affine coordinates where possible.
* Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
* Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
* Point multiplication for verification (a*P + b*G).
* Use wNAF notation for point multiplicands.
* Use a much larger window for multiples of G, using precomputed multiples.
* Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
* Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
* Point multiplication for signing
* Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
* Access the table with branch-free conditional moves so memory access is uniform.
* No data-dependent branches
* The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally.
Build steps
-----------
libsecp256k1 is built using autotools:
$ ./autogen.sh
$ ./configure
$ make
$ ./tests
$ sudo make install # optional

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crypto/secp256k1/secp256k1/autogen.sh Executable file
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#!/bin/sh
set -e
autoreconf -if --warnings=all

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crypto/secp256k1/secp256k1/build-aux/m4/bitcoin_secp.m4 Normal file
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dnl libsecp25k1 helper checks
AC_DEFUN([SECP_INT128_CHECK],[
has_int128=$ac_cv_type___int128
])
dnl
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 $0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
]])],[has_64bit_asm=yes],[has_64bit_asm=no])
AC_MSG_RESULT([$has_64bit_asm])
])
dnl
AC_DEFUN([SECP_OPENSSL_CHECK],[
if test x"$use_pkgconfig" = x"yes"; then
: #NOP
m4_ifdef([PKG_CHECK_MODULES],[
PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no])
if test x"$has_libcrypto" = x"yes"; then
TEMP_LIBS="$LIBS"
LIBS="$LIBS $CRYPTO_LIBS"
AC_CHECK_LIB(crypto, main,[AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])],[has_libcrypto=no])
LIBS="$TEMP_LIBS"
fi
])
else
AC_CHECK_HEADER(openssl/crypto.h,[AC_CHECK_LIB(crypto, main,[has_libcrypto=yes; CRYPTO_LIBS=-lcrypto; AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])]
)])
LIBS=
fi
if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
AC_MSG_CHECKING(for EC functions in libcrypto)
AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
#include <openssl/ec.h>
#include <openssl/ecdsa.h>
#include <openssl/obj_mac.h>]],[[
EC_KEY *eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
EC_KEY_free(eckey);
]])],[has_openssl_ec=yes],[has_openssl_ec=no])
AC_MSG_RESULT([$has_openssl_ec])
fi
])
dnl
AC_DEFUN([SECP_GMP_CHECK],[
if test x"$has_gmp" != 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"
fi
])

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crypto/secp256k1/secp256k1/config.mk
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CC=cc
YASM=yasm
CFLAGS_EXTRA=-DUSE_FIELD_5X52 -DUSE_FIELD_5X52_ASM -DUSE_NUM_GMP -DUSE_FIELD_INV_NUM
CFLAGS_TEST_EXTRA=-DENABLE_OPENSSL_TESTS
LDFLAGS_EXTRA=-lgmp
LDFLAGS_TEST_EXTRA=-lcrypto
USE_ASM=1
HAVE_LIMB=52
OPTLEVEL=O2

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crypto/secp256k1/secp256k1/configure vendored
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#!/bin/sh
if test -f config.mk; then
exit 0
fi
if test -z "$CC"; then
CC=cc
fi
if test -z "$YASM"; then
YASM=yasm
fi
# test yasm
$YASM -f elf64 -o /tmp/secp256k1-$$.o - <<EOF
BITS 64
GLOBAL testyasm
ALIGN 32
testyasm:
xor r9,r9
EOF
if [ "$?" = 0 ]; then
$CC $CFLAGS -std=c99 -x c -c - -o /tmp/secp256k1-$$-2.o 2>/dev/null <<EOF
void __attribute__ ((sysv_abi)) testyasm(void);
int main() {
testyasm();
return 0;
}
EOF
$CC $CFLAGS -std=c99 /tmp/secp256k1-$$-2.o /tmp/secp256k1-$$.o -o /dev/null 2>/dev/null
if [ "$?" = 0 ]; then
HAVE_YASM=1
fi
rm -rf /tmp/secp256k1-$$-2.o /tmp/secp256k1-$$.o
fi
# test openssl
HAVE_OPENSSL=0
$CC $CFLAGS -std=c99 -x c - -o /dev/null -lcrypto 2>/dev/null <<EOF
#include <openssl/bn.h>
int main() {
BN_CTX *ctx = BN_CTX_new();
BN_CTX_free(ctx);
return 0;
}
EOF
if [ "$?" = 0 ]; then
HAVE_OPENSSL=1
fi
# test openssl/EC
HAVE_OPENSSL_EC=0
if [ "$HAVE_OPENSSL" = "1" ]; then
$CC $CFLAGS -std=c99 -x c - -o /dev/null -lcrypto 2>/dev/null <<EOF
#include <openssl/ec.h>
#include <openssl/ecdsa.h>
#include <openssl/obj_mac.h>
int main() {
EC_KEY *eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
EC_KEY_free(eckey);
return 0;
}
EOF
if [ "$?" = 0 ]; then
HAVE_OPENSSL_EC=1
fi
fi
# test gmp
HAVE_GMP=0
$CC $CFLAGS -std=c99 -x c - -o /dev/null -lgmp 2>/dev/null <<EOF
#include <gmp.h>
int main() {
mpz_t n;
mpz_init(n);
mpz_clear(n);
return 0;
}
EOF
if [ "$?" = 0 ]; then
HAVE_GMP=1
fi
# test __int128
HAVE_INT128=0
$CC $CFLAGS -std=c99 -x c - -o /dev/null 2>/dev/null <<EOF
#include <stdint.h>
int main() {
__int128 x = 0;
return 0;
}
EOF
if [ "$?" = 0 ]; then
HAVE_INT128=1
fi
#default limb size
HAVE_LIMB=52
for arg in "$@"; do
case "$arg" in
--no-yasm)
HAVE_YASM=0
;;
--no-gmp)
HAVE_GMP=0
;;
--no-openssl)
HAVE_OPENSSL=0
;;
--use-5x64)
HAVE_LIMB=64
;;
esac
done
LINK_OPENSSL=0
LINK_GMP=0
USE_ASM=0
# select field implementation
if [ "$HAVE_YASM" = "1" ]; then
CFLAGS_FIELD="-DUSE_FIELD_5X$HAVE_LIMB -DUSE_FIELD_5X${HAVE_LIMB}_ASM"
USE_ASM=1
elif [ "$HAVE_INT128" = "1" ]; then
CFLAGS_FIELD="-DUSE_FIELD_5X$HAVE_LIMB -DUSE_FIELD_5X${HAVE_LIMB}_INT128"
elif [ "$HAVE_GMP" = "1" ]; then
CFLAGS_FIELD="-DUSE_FIELD_GMP"
LINK_GMP=1
else
CFLAGS_FIELD="-DUSE_FIELD_10X26"
fi
# select num implementation
if [ "$HAVE_GMP" = "1" ]; then
CFLAGS_NUM="-DUSE_NUM_GMP -DUSE_FIELD_INV_NUM"
LINK_GMP=1
elif [ "$HAVE_OPENSSL" = "1" ]; then
CFLAGS_NUM="-DUSE_NUM_OPENSSL -DUSE_FIELD_INV_BUILTIN"
LINK_OPENSSL=1
else
echo "No usable num implementation found" >&2
exit 1
fi
CFLAGS_EXTRA="$CFLAGS_FIELD $CFLAGS_NUM"
LDFLAGS_EXTRA=""
if [ "$LINK_GMP" = "1" ]; then
LDFLAGS_EXTRA="-lgmp"
fi
if [ "$LINK_OPENSSL" = "1" ]; then
LDFLAGS_EXTRA="-lcrypto"
else
if [ "$HAVE_OPENSSL_EC" = "1" ]; then
LDFLAGS_TEST_EXTRA="-lcrypto"
fi
fi
CFLAGS_TEST_EXTRA=""
if [ "$HAVE_OPENSSL_EC" = "1" ]; then
CFLAGS_TEST_EXTRA="-DENABLE_OPENSSL_TESTS"
fi
echo "CC=$CC" > config.mk
echo "YASM=$YASM" >>config.mk
echo "CFLAGS_EXTRA=$CFLAGS_EXTRA" >> config.mk
echo "CFLAGS_TEST_EXTRA=$CFLAGS_TEST_EXTRA" >> config.mk
echo "LDFLAGS_EXTRA=$LDFLAGS_EXTRA" >> config.mk
echo "LDFLAGS_TEST_EXTRA=$LDFLAGS_TEST_EXTRA" >> config.mk
echo "USE_ASM=$USE_ASM" >>config.mk
echo "HAVE_LIMB=$HAVE_LIMB" >>config.mk
echo "OPTLEVEL=O2" >>config.mk

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AC_PREREQ([2.60])
AC_INIT([libsecp256k1],[0.1])
AC_CONFIG_AUX_DIR([build-aux])
AC_CONFIG_MACRO_DIR([build-aux/m4])
AC_CANONICAL_HOST
AH_TOP([#ifndef LIBSECP256K1_CONFIG_H])
AH_TOP([#define LIBSECP256K1_CONFIG_H])
AH_BOTTOM([#endif /*LIBSECP256K1_CONFIG_H*/])
AM_INIT_AUTOMAKE([foreign subdir-objects])
LT_INIT
dnl make the compilation flags quiet unless V=1 is used
m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])])
PKG_PROG_PKG_CONFIG
AC_PATH_TOOL(AR, ar)
AC_PATH_TOOL(RANLIB, ranlib)
AC_PATH_TOOL(STRIP, strip)
if test "x$CFLAGS" = "x"; then
CFLAGS="-O3 -g"
fi
AC_PROG_CC_C89
if test x"$ac_cv_prog_cc_c89" = x"no"; then
AC_MSG_ERROR([c89 compiler support required])
fi
case $host in
*mingw*)
use_pkgconfig=no
;;
*)
use_pkgconfig=yes
;;
esac
case $host_os in
*darwin*)
if test x$cross_compiling != xyes; then
AC_PATH_PROG([BREW],brew,)
if test x$BREW != x; then
dnl These Homebrew packages may be keg-only, meaning that they won't be found
dnl in expected paths because they may conflict with system files. Ask
dnl Homebrew where each one is located, then adjust paths accordingly.
openssl_prefix=`$BREW --prefix openssl 2>/dev/null`
gmp_prefix=`$BREW --prefix gmp 2>/dev/null`
if test x$openssl_prefix != x; then
PKG_CONFIG_PATH="$openssl_prefix/lib/pkgconfig:$PKG_CONFIG_PATH"
export PKG_CONFIG_PATH
fi
if test x$gmp_prefix != x; then
GMP_CPPFLAGS="-I$gmp_prefix/include"
GMP_LIBS="-L$gmp_prefix/lib"
fi
else
AC_PATH_PROG([PORT],port,)
dnl if homebrew isn't installed and macports is, add the macports default paths
dnl as a last resort.
if test x$PORT != x; then
CPPFLAGS="$CPPFLAGS -isystem /opt/local/include"
LDFLAGS="$LDFLAGS -L/opt/local/lib"
fi
fi
fi
;;
esac
CFLAGS="$CFLAGS -W"
warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
saved_CFLAGS="$CFLAGS"
CFLAGS="$CFLAGS $warn_CFLAGS"
AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
[ AC_MSG_RESULT([yes]) ],
[ AC_MSG_RESULT([no])
CFLAGS="$saved_CFLAGS"
])
AC_ARG_ENABLE(benchmark,
AS_HELP_STRING([--enable-benchmark],[compile benchmark (default is no)]),
[use_benchmark=$enableval],
[use_benchmark=no])
AC_ARG_ENABLE(tests,
AS_HELP_STRING([--enable-tests],[compile tests (default is yes)]),
[use_tests=$enableval],
[use_tests=yes])
AC_ARG_ENABLE(endomorphism,
AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
[use_endomorphism=$enableval],
[use_endomorphism=no])
AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
[Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto],
[Specify Bignum Implementation. Default is auto])],[req_bignum=$withval], [req_bignum=auto])
AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
[Specify scalar implementation. Default is auto])],[req_scalar=$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=$withval], [req_asm=auto])
AC_CHECK_TYPES([__int128])
AC_MSG_CHECKING([for __builtin_expect])
AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])],
[ AC_MSG_RESULT([yes]);AC_DEFINE(HAVE_BUILTIN_EXPECT,1,[Define this symbol if __builtin_expect is available]) ],
[ AC_MSG_RESULT([no])
])
if test x"$req_asm" = x"auto"; then
SECP_64BIT_ASM_CHECK
if test x"$has_64bit_asm" = x"yes"; then
set_asm=x86_64
fi
if test x"$set_asm" = x; then
set_asm=no
fi
else
set_asm=$req_asm
case $set_asm in
x86_64)
SECP_64BIT_ASM_CHECK
if test x"$has_64bit_asm" != x"yes"; then
AC_MSG_ERROR([x86_64 assembly optimization requested but not available])
fi
;;
no)
;;
*)
AC_MSG_ERROR([invalid assembly optimization selection])
;;
esac
fi
if test x"$req_field" = x"auto"; then
if test x"set_asm" = x"x86_64"; then
set_field=64bit
fi
if test x"$set_field" = x; then
SECP_INT128_CHECK
if test x"$has_int128" = x"yes"; then
set_field=64bit
fi
fi
if test x"$set_field" = x; then
set_field=32bit
fi
else
set_field=$req_field
case $set_field in
64bit)
if test x"$set_asm" != x"x86_64"; then
SECP_INT128_CHECK
if test x"$has_int128" != x"yes"; then
AC_MSG_ERROR([64bit field explicitly requested but neither __int128 support or x86_64 assembly available])
fi
fi
;;
32bit)
;;
*)
AC_MSG_ERROR([invalid field implementation selection])
;;
esac
fi
if test x"$req_scalar" = x"auto"; then
SECP_INT128_CHECK
if test x"$has_int128" = x"yes"; then
set_scalar=64bit
fi
if test x"$set_scalar" = x; then
set_scalar=32bit
fi
else
set_scalar=$req_scalar
case $set_scalar in
64bit)
SECP_INT128_CHECK
if test x"$has_int128" != x"yes"; then
AC_MSG_ERROR([64bit scalar explicitly requested but __int128 support not available])
fi
;;
32bit)
;;
*)
AC_MSG_ERROR([invalid scalar implementation selected])
;;
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
case $set_asm in
x86_64)
AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations])
;;
no)
;;
*)
AC_MSG_ERROR([invalid assembly optimizations])
;;
esac
# select field implementation
case $set_field in
64bit)
AC_DEFINE(USE_FIELD_5X52, 1, [Define this symbol to use the FIELD_5X52 implementation])
;;
32bit)
AC_DEFINE(USE_FIELD_10X26, 1, [Define this symbol to use the FIELD_10X26 implementation])
;;
*)
AC_MSG_ERROR([invalid field implementation])
;;
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
#select scalar implementation
case $set_scalar in
64bit)
AC_DEFINE(USE_SCALAR_4X64, 1, [Define this symbol to use the 4x64 scalar implementation])
;;
32bit)
AC_DEFINE(USE_SCALAR_8X32, 1, [Define this symbol to use the 8x32 scalar implementation])
;;
*)
AC_MSG_ERROR([invalid scalar implementation])
;;
esac
if test x"$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
fi
fi
if test x"$set_bignum" = x"gmp"; then
SECP_LIBS="$SECP_LIBS $GMP_LIBS"
SECP_INCLUDES="$SECP_INCLUDES $GMP_CPPFLAGS"
fi
if test x"$use_endomorphism" = x"yes"; then
AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
fi
AC_C_BIGENDIAN()
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: $use_endomorphism])
AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
AC_CONFIG_FILES([Makefile libsecp256k1.pc])
AC_SUBST(SECP_INCLUDES)
AC_SUBST(SECP_LIBS)
AC_SUBST(SECP_TEST_LIBS)
AC_SUBST(SECP_TEST_INCLUDES)
AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
dnl make sure nothing new is exported so that we don't break the cache
PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"
unset PKG_CONFIG_PATH
PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP"
AC_OUTPUT

278
crypto/secp256k1/secp256k1/include/secp256k1.h
View File

@ -5,12 +5,52 @@
extern "C" {
# endif
# if !defined(SECP256K1_GNUC_PREREQ)
# if defined(__GNUC__)&&defined(__GNUC_MINOR__)
# define SECP256K1_GNUC_PREREQ(_maj,_min) \
((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
# else
# define SECP256K1_GNUC_PREREQ(_maj,_min) 0
# endif
# endif
# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
# if SECP256K1_GNUC_PREREQ(2,7)
# define SECP256K1_INLINE __inline__
# elif (defined(_MSC_VER))
# define SECP256K1_INLINE __inline
# else
# define SECP256K1_INLINE
# endif
# else
# define SECP256K1_INLINE inline
# endif
/**Warning attributes
* NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
* some paranoid null checks. */
# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
# define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
# else
# define SECP256K1_WARN_UNUSED_RESULT
# endif
# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
# define SECP256K1_ARG_NONNULL(_x) __attribute__ ((__nonnull__(_x)))
# else
# define SECP256K1_ARG_NONNULL(_x)
# endif
/** Flags to pass to secp256k1_start. */
# define SECP256K1_START_VERIFY (1 << 0)
# define SECP256K1_START_SIGN (1 << 1)
/** Initialize the library. This may take some time (10-100 ms).
* You need to call this before calling any other function.
* It cannot run in parallel with any other functions, but once
* secp256k1_start() returns, all other functions are thread-safe.
*/
void secp256k1_start(void);
void secp256k1_start(unsigned int flags);
/** Free all memory associated with this library. After this, no
* functions can be called anymore, except secp256k1_start()
@ -22,97 +62,231 @@ void secp256k1_stop(void);
* 0: incorrect signature
* -1: invalid public key
* -2: invalid signature
* In: msg32: the 32-byte message hash being verified (cannot be NULL)
* sig: the signature being verified (cannot be NULL)
* siglen: the length of the signature
* pubkey: the public key to verify with (cannot be NULL)
* pubkeylen: the length of pubkey
* Requires starting using SECP256K1_START_VERIFY.
*/
int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen,
const unsigned char *sig, int siglen,
const unsigned char *pubkey, int pubkeylen);
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
const unsigned char *msg32,
const unsigned char *sig,
int siglen,
const unsigned char *pubkey,
int pubkeylen
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
/** A pointer to a function to deterministically generate a nonce.
* Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
* In: msg32: the 32-byte message hash being verified (will not be NULL)
* key32: pointer to a 32-byte secret key (will not be NULL)
* attempt: how many iterations we have tried to find a nonce.
* This will almost always be 0, but different attempt values
* are required to result in a different nonce.
* data: Arbitrary data pointer that is passed through.
* Out: nonce32: pointer to a 32-byte array to be filled by the function.
* Except for test cases, this function should compute some cryptographic hash of
* the message, the key and the attempt.
*/
typedef int (*secp256k1_nonce_function_t)(
unsigned char *nonce32,
const unsigned char *msg32,
const unsigned char *key32,
unsigned int attempt,
const void *data
);
/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
* If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
* extra entropy.
*/
extern const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979;
/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
extern const secp256k1_nonce_function_t secp256k1_nonce_function_default;
/** Create an ECDSA signature.
* Returns: 1: signature created
* 0: nonce invalid, try another one
* In: msg: the message being signed
* msglen: the length of the message being signed
* seckey: pointer to a 32-byte secret key (assumed to be valid)
* nonce: pointer to a 32-byte nonce (generated with a cryptographic PRNG)
* Out: sig: pointer to a 72-byte array where the signature will be placed.
* siglen: pointer to an int, which will be updated to the signature length (<=72).
* 0: the nonce generation function failed, the private key was invalid, or there is not
* enough space in the signature (as indicated by siglen).
* 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)
* Out: sig: pointer to an array where the signature will be placed (cannot be NULL)
* In/Out: siglen: pointer to an int with the length of sig, which will be updated
* to contain the actual signature length (<=72). If 0 is returned, this will be
* set to zero.
* Requires starting using SECP256K1_START_SIGN.
*
* The sig always has an s value in the lower half of the range (From 0x1
* to 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
* inclusive), unlike many other implementations.
* With ECDSA a third-party can can forge a second distinct signature
* of the same message given a single initial signature without knowing
* the key by setting s to its additive inverse mod-order, 'flipping' the
* sign of the random point R which is not included in the signature.
* Since the forgery is of the same message this isn't universally
* problematic, but in systems where message malleability or uniqueness
* of signatures is important this can cause issues. This forgery can be
* blocked by all verifiers forcing signers to use a canonical form. The
* lower-S form reduces the size of signatures slightly on average when
* variable length encodings (such as DER) are used and is cheap to
* verify, making it a good choice. Security of always using lower-S is
* assured because anyone can trivially modify a signature after the
* fact to enforce this property. Adjusting it inside the signing
* function avoids the need to re-serialize or have curve specific
* constants outside of the library. By always using a canonical form
* even in applications where it isn't needed it becomes possible to
* impose a requirement later if a need is discovered.
* No other forms of ECDSA malleability are known and none seem likely,
* but there is no formal proof that ECDSA, even with this additional
* restriction, is free of other malleability. Commonly used serialization
* schemes will also accept various non-unique encodings, so care should
* be taken when this property is required for an application.
*/
int secp256k1_ecdsa_sign(const unsigned char *msg, int msglen,
unsigned char *sig, int *siglen,
int secp256k1_ecdsa_sign(
const unsigned char *msg32,
unsigned char *sig,
int *siglen,
const unsigned char *seckey,
const unsigned char *nonce);
secp256k1_nonce_function_t noncefp,
const void *ndata
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
/** Create a compact ECDSA signature (64 byte + recovery id).
* Returns: 1: signature created
* 0: nonce invalid, try another one
* In: msg: the message being signed
* msglen: the length of the message being signed
* seckey: pointer to a 32-byte secret key (assumed to be valid)
* nonce: pointer to a 32-byte nonce (generated with a cryptographic PRNG)
* Out: sig: pointer to a 64-byte array where the signature will be placed.
* recid: pointer to an int, which will be updated to contain the recovery id.
* 0: the nonce generation function failed, or the secret key was invalid.
* 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)
* Out: sig: pointer to a 64-byte array where the signature will be placed (cannot be NULL)
* In case 0 is returned, the returned signature length will be zero.
* recid: pointer to an int, which will be updated to contain the recovery id (can be NULL)
* Requires starting using SECP256K1_START_SIGN.
*/
int secp256k1_ecdsa_sign_compact(const unsigned char *msg, int msglen,
int secp256k1_ecdsa_sign_compact(
const unsigned char *msg32,
unsigned char *sig64,
const unsigned char *seckey,
const unsigned char *nonce,
int *recid);
secp256k1_nonce_function_t noncefp,
const void *ndata,
int *recid
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
/** Recover an ECDSA public key from a compact signature.
* Returns: 1: public key succesfully recovered (which guarantees a correct signature).
* Returns: 1: public key successfully recovered (which guarantees a correct signature).
* 0: otherwise.
* In: msg: the message assumed to be signed
* msglen: the length of the message
* sig64: signature as 64 byte array
* In: msg32: the 32-byte message hash assumed to be signed (cannot be NULL)
* sig64: signature as 64 byte array (cannot be NULL)
* compressed: whether to recover a compressed or uncompressed pubkey
* recid: the recovery id (as returned by ecdsa_sign_compact)
* Out: pubkey: pointer to a 33 or 65 byte array to put the pubkey.
* pubkeylen: pointer to an int that will contain the pubkey length.
* recid: the recovery id (0-3, as returned by ecdsa_sign_compact)
* Out: pubkey: pointer to a 33 or 65 byte array to put the pubkey (cannot be NULL)
* pubkeylen: pointer to an int that will contain the pubkey length (cannot be NULL)
* Requires starting using SECP256K1_START_VERIFY.
*/
int secp256k1_ecdsa_recover_compact(const unsigned char *msg, int msglen,
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover_compact(
const unsigned char *msg32,
const unsigned char *sig64,
unsigned char *pubkey, int *pubkeylen,
int compressed, int recid);
unsigned char *pubkey,
int *pubkeylen,
int compressed,
int recid
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
/** Verify an ECDSA secret key.
* Returns: 1: secret key is valid
* 0: secret key is invalid
* In: seckey: pointer to a 32-byte secret key
* In: seckey: pointer to a 32-byte secret key (cannot be NULL)
*/
int secp256k1_ecdsa_seckey_verify(const unsigned char *seckey);
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(const unsigned char *seckey) SECP256K1_ARG_NONNULL(1);
/** Just validate a public key.
* Returns: 1: valid public key
* 0: invalid public key
* In: pubkey: pointer to a 33-byte or 65-byte public key (cannot be NULL).
* pubkeylen: length of pubkey
*/
int secp256k1_ecdsa_pubkey_verify(const unsigned char *pubkey, int pubkeylen);
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_verify(const unsigned char *pubkey, int pubkeylen) SECP256K1_ARG_NONNULL(1);
/** Compute the public key for a secret key.
* In: compressed: whether the computed public key should be compressed
* seckey: pointer to a 32-byte private key.
* seckey: pointer to a 32-byte private key (cannot be NULL)
* Out: pubkey: pointer to a 33-byte (if compressed) or 65-byte (if uncompressed)
* area to store the public key.
* area to store the public key (cannot be NULL)
* pubkeylen: pointer to int that will be updated to contains the pubkey's
* length.
* length (cannot be NULL)
* Returns: 1: secret was valid, public key stores
* 0: secret was invalid, try again.
* Requires starting using SECP256K1_START_SIGN.
*/
int secp256k1_ecdsa_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed);
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
unsigned char *pubkey,
int *pubkeylen,
const unsigned char *seckey,
int compressed
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
int secp256k1_ecdsa_pubkey_decompress(unsigned char *pubkey, int *pubkeylen);
/** Decompress a public key.
* In/Out: pubkey: pointer to a 65-byte array to put the decompressed public key.
It must contain a 33-byte or 65-byte public key already (cannot be NULL)
* pubkeylen: pointer to the size of the public key pointed to by pubkey (cannot be NULL)
It will be updated to reflect the new size.
* Returns: 0 if the passed public key was invalid, 1 otherwise. If 1 is returned, the
pubkey is replaced with its decompressed version.
*/
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_decompress(
unsigned char *pubkey,
int *pubkeylen
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
int secp256k1_ecdsa_privkey_export(const unsigned char *seckey,
unsigned char *privkey, int *privkeylen,
int compressed);
/** Export a private key in DER format. */
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_export(
const unsigned char *seckey,
unsigned char *privkey,
int *privkeylen,
int compressed
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
int secp256k1_ecdsa_privkey_import(unsigned char *seckey,
const unsigned char *privkey, int privkeylen);
/** Import a private key in DER format. */
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_import(
unsigned char *seckey,
const unsigned char *privkey,
int privkeylen
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
int secp256k1_ecdsa_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak);
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak);
int secp256k1_ecdsa_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak);
int secp256k1_ecdsa_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak);
/** Tweak a private key by adding tweak to it. */
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
unsigned char *seckey,
const unsigned char *tweak
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
/** Tweak a public key by adding tweak times the generator to it.
* Requires starting with SECP256K1_START_VERIFY.
*/
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
unsigned char *pubkey,
int pubkeylen,
const unsigned char *tweak
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
/** Tweak a private key by multiplying it with tweak. */
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
unsigned char *seckey,
const unsigned char *tweak
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
/** Tweak a public key by multiplying it with tweak.
* Requires starting with SECP256K1_START_VERIFY.
*/
SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
unsigned char *pubkey,
int pubkeylen,
const unsigned char *tweak
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
# ifdef __cplusplus
}

13
crypto/secp256k1/secp256k1/libsecp256k1.pc.in Normal file
View File

@ -0,0 +1,13 @@
prefix=@prefix@
exec_prefix=@exec_prefix@
libdir=@libdir@
includedir=@includedir@
Name: libsecp256k1
Description: Optimized C library for EC operations on curve secp256k1
URL: https://github.com/bitcoin/secp256k1
Version: @PACKAGE_VERSION@
Cflags: -I${includedir}
Libs.private: @SECP_LIBS@
Libs: -L${libdir} -lsecp256k1

0
crypto/secp256k1/secp256k1/obj/.gitignore vendored Normal file
View File

64
crypto/secp256k1/secp256k1/src/bench.c
View File

@ -1,64 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#include <stdio.h>
#include "impl/num.h"
#include "impl/field.h"
#include "impl/group.h"
#include "impl/ecmult.h"
#include "impl/ecdsa.h"
#include "impl/util.h"
void random_num_order(secp256k1_num_t *num) {
do {
unsigned char b32[32];
secp256k1_rand256(b32);
secp256k1_num_set_bin(num, b32, 32);
if (secp256k1_num_is_zero(num))
continue;
if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0)
continue;
break;
} while(1);
}
int main() {
secp256k1_fe_start();
secp256k1_ge_start();
secp256k1_ecmult_start();
secp256k1_fe_t x;
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t r, s, m;
secp256k1_num_init(&r);
secp256k1_num_init(&s);
secp256k1_num_init(&m);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
secp256k1_fe_set_hex(&x, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64);
int cnt = 0;
int good = 0;
for (int i=0; i<1000000; i++) {
random_num_order(&r);
random_num_order(&s);
random_num_order(&m);
secp256k1_ecdsa_sig_set_rs(&sig, &r, &s);
secp256k1_ge_t pubkey; secp256k1_ge_set_xo(&pubkey, &x, 1);
if (secp256k1_ge_is_valid(&pubkey)) {
cnt++;
good += secp256k1_ecdsa_sig_verify(&sig, &pubkey, &m);
}
}
printf("%i/%i\n", good, cnt);
secp256k1_num_free(&r);
secp256k1_num_free(&s);
secp256k1_num_free(&m);
secp256k1_ecdsa_sig_free(&sig);
secp256k1_ecmult_stop();
secp256k1_ge_stop();
secp256k1_fe_stop();
return 0;
}

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_BENCH_H_
#define _SECP256K1_BENCH_H_
#include <stdio.h>
#include <math.h>
#include "sys/time.h"
static double gettimedouble(void) {
struct timeval tv;
gettimeofday(&tv, NULL);
return tv.tv_usec * 0.000001 + tv.tv_sec;
}
void print_number(double x) {
double y = x;
int c = 0;
if (y < 0.0) y = -y;
while (y < 100.0) {
y *= 10.0;
c++;
}
printf("%.*f", c, x);
}
void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) {
int i;
double min = HUGE_VAL;
double sum = 0.0;
double max = 0.0;
for (i = 0; i < count; i++) {
double begin, total;
if (setup) setup(data);
begin = gettimedouble();
benchmark(data);
total = gettimedouble() - begin;
if (teardown) teardown(data);
if (total < min) min = total;
if (total > max) max = total;
sum += total;
}
printf("%s: min ", name);
print_number(min * 1000000.0 / iter);
printf("us / avg ");
print_number((sum / count) * 1000000.0 / iter);
printf("us / avg ");
print_number(max * 1000000.0 / iter);
printf("us\n");
}
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#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"
#include "ecmult_impl.h"
#include "bench.h"
typedef struct {
secp256k1_scalar_t scalar_x, scalar_y;
secp256k1_fe_t fe_x, fe_y;
secp256k1_ge_t ge_x, ge_y;
secp256k1_gej_t gej_x, gej_y;
unsigned char data[32];
int wnaf[256];
} bench_inv_t;
void bench_setup(void* arg) {
bench_inv_t *data = (bench_inv_t*)arg;
static const unsigned char init_x[32] = {
0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13,
0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35,
0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59,
0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83
};
static const unsigned char init_y[32] = {
0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83,
0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5,
0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9,
0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3
};
secp256k1_scalar_set_b32(&data->scalar_x, init_x, NULL);
secp256k1_scalar_set_b32(&data->scalar_y, init_y, NULL);
secp256k1_fe_set_b32(&data->fe_x, init_x);
secp256k1_fe_set_b32(&data->fe_y, init_y);
CHECK(secp256k1_ge_set_xo_var(&data->ge_x, &data->fe_x, 0));
CHECK(secp256k1_ge_set_xo_var(&data->ge_y, &data->fe_y, 1));
secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
memcpy(data->data, init_x, 32);
}
void bench_scalar_add(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_scalar_negate(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_scalar_negate(&data->scalar_x, &data->scalar_x);
}
}
void bench_scalar_sqr(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_scalar_sqr(&data->scalar_x, &data->scalar_x);
}
}
void bench_scalar_mul(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_scalar_mul(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
#ifdef USE_ENDOMORPHISM
void bench_scalar_split(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_scalar_t l, r;
secp256k1_scalar_split_lambda_var(&l, &r, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
#endif
void bench_scalar_inverse(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000; i++) {
secp256k1_scalar_inverse(&data->scalar_x, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_scalar_inverse_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000; i++) {
secp256k1_scalar_inverse_var(&data->scalar_x, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_field_normalize(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_fe_normalize(&data->fe_x);
}
}
void bench_field_normalize_weak(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_fe_normalize_weak(&data->fe_x);
}
}
void bench_field_mul(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_fe_mul(&data->fe_x, &data->fe_x, &data->fe_y);
}
}
void bench_field_sqr(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_fe_sqr(&data->fe_x, &data->fe_x);
}
}
void bench_field_inverse(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_inv(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_field_inverse_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_inv_var(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_field_sqrt_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_sqrt_var(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_group_double_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_double_var(&data->gej_x, &data->gej_x);
}
}
void bench_group_add_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y);
}
}
void bench_group_add_affine(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_ge(&data->gej_x, &data->gej_x, &data->ge_y);
}
}
void bench_group_add_affine_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y);
}
}
void bench_ecmult_wnaf(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_ecmult_wnaf(data->wnaf, &data->scalar_x, WINDOW_A);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_sha256_t sha;
for (i = 0; i < 20000; i++) {
secp256k1_sha256_initialize(&sha);
secp256k1_sha256_write(&sha, data->data, 32);
secp256k1_sha256_finalize(&sha, data->data);
}
}
void bench_hmac_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_hmac_sha256_t hmac;
for (i = 0; i < 20000; i++) {
secp256k1_hmac_sha256_initialize(&hmac, data->data, 32);
secp256k1_hmac_sha256_write(&hmac, data->data, 32);
secp256k1_hmac_sha256_finalize(&hmac, data->data);
}
}
void bench_rfc6979_hmac_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_rfc6979_hmac_sha256_t rng;
for (i = 0; i < 20000; i++) {
secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 32, data->data, 32, NULL, 0);
secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
}
}
int have_flag(int argc, char** argv, char *flag) {
char** argm = argv + argc;
argv++;
if (argv == argm) {
return 1;
}
while (argv != NULL && argv != argm) {
if (strcmp(*argv, flag) == 0) return 1;
argv++;
}
return 0;
}
int main(int argc, char **argv) {
bench_inv_t data;
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, 200000);
#ifdef USE_ENDOMORPHISM
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, 20000);
#endif
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, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, 2000000);
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, 2000000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt_var", bench_field_sqrt_var, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
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, 200000);
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, 200000);
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, 200000);
if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
return 0;
}

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/**********************************************************************
* 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.*
**********************************************************************/
#include "include/secp256k1.h"
#include "util.h"
#include "bench.h"
typedef struct {
unsigned char msg[32];
unsigned char sig[64];
} bench_recover_t;
void bench_recover(void* arg) {
int i;
bench_recover_t *data = (bench_recover_t*)arg;
unsigned char pubkey[33];
for (i = 0; i < 20000; i++) {
int j;
int pubkeylen = 33;
CHECK(secp256k1_ecdsa_recover_compact(data->msg, data->sig, pubkey, &pubkeylen, 1, i % 2));
for (j = 0; j < 32; j++) {
data->sig[j + 32] = data->msg[j]; /* Move former message to S. */
data->msg[j] = data->sig[j]; /* Move former R to message. */
data->sig[j] = pubkey[j + 1]; /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
}
}
}
void bench_recover_setup(void* arg) {
int i;
bench_recover_t *data = (bench_recover_t*)arg;
for (i = 0; i < 32; i++) data->msg[i] = 1 + i;
for (i = 0; i < 64; i++) data->sig[i] = 65 + i;
}
int main(void) {
bench_recover_t data;
secp256k1_start(SECP256K1_START_VERIFY);
run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, 20000);
secp256k1_stop();
return 0;
}

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/**********************************************************************
* 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.*
**********************************************************************/
#include "include/secp256k1.h"
#include "util.h"
#include "bench.h"
typedef struct {
unsigned char msg[32];
unsigned char key[32];
} bench_sign_t;
static void bench_sign_setup(void* arg) {
int i;
bench_sign_t *data = (bench_sign_t*)arg;
for (i = 0; i < 32; i++) data->msg[i] = i + 1;
for (i = 0; i < 32; i++) data->key[i] = i + 65;
}
static void bench_sign(void* arg) {
int i;
bench_sign_t *data = (bench_sign_t*)arg;
unsigned char sig[64];
for (i = 0; i < 20000; i++) {
int j;
int recid = 0;
CHECK(secp256k1_ecdsa_sign_compact(data->msg, sig, data->key, NULL, NULL, &recid));
for (j = 0; j < 32; j++) {
data->msg[j] = sig[j]; /* Move former R to message. */
data->key[j] = sig[j + 32]; /* Move former S to key. */
}
}
}
int main(void) {
bench_sign_t data;
secp256k1_start(SECP256K1_START_SIGN);
run_benchmark("ecdsa_sign", bench_sign, bench_sign_setup, NULL, &data, 10, 20000);
secp256k1_stop();
return 0;
}

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/**********************************************************************
* 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.*
**********************************************************************/
#include <stdio.h>
#include <string.h>
#include "include/secp256k1.h"
#include "util.h"
#include "bench.h"
typedef struct {
unsigned char msg[32];
unsigned char key[32];
unsigned char sig[72];
int siglen;
unsigned char pubkey[33];
int pubkeylen;
} benchmark_verify_t;
static void benchmark_verify(void* arg) {
int i;
benchmark_verify_t* data = (benchmark_verify_t*)arg;
for (i = 0; i < 20000; i++) {
data->sig[data->siglen - 1] ^= (i & 0xFF);
data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
CHECK(secp256k1_ecdsa_verify(data->msg, data->sig, data->siglen, data->pubkey, data->pubkeylen) == (i == 0));
data->sig[data->siglen - 1] ^= (i & 0xFF);
data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
}
}
int main(void) {
int i;
benchmark_verify_t data;
secp256k1_start(SECP256K1_START_VERIFY | SECP256K1_START_SIGN);
for (i = 0; i < 32; i++) data.msg[i] = 1 + i;
for (i = 0; i < 32; i++) data.key[i] = 33 + i;
data.siglen = 72;
secp256k1_ecdsa_sign(data.msg, data.sig, &data.siglen, data.key, NULL, NULL);
data.pubkeylen = 33;
CHECK(secp256k1_ec_pubkey_create(data.pubkey, &data.pubkeylen, data.key, 1));
run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, 20000);
secp256k1_stop();
return 0;
}

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECDSA_
#define _SECP256K1_ECDSA_
#include "num.h"
#include "scalar.h"
#include "group.h"
typedef struct {
secp256k1_num_t r, s;
secp256k1_scalar_t r, s;
} secp256k1_ecdsa_sig_t;
void static secp256k1_ecdsa_sig_init(secp256k1_ecdsa_sig_t *r);
void static secp256k1_ecdsa_sig_free(secp256k1_ecdsa_sig_t *r);
int static secp256k1_ecdsa_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size);
void static secp256k1_ecdsa_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed);
int static secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size);
int static secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a);
int static secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_num_t *message);
int static secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_num_t *seckey, const secp256k1_num_t *message, const secp256k1_num_t *nonce, int *recid);
int static secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_num_t *message, int recid);
void static secp256k1_ecdsa_sig_set_rs(secp256k1_ecdsa_sig_t *sig, const secp256k1_num_t *r, const secp256k1_num_t *s);
int static secp256k1_ecdsa_privkey_parse(secp256k1_num_t *key, const unsigned char *privkey, int privkeylen);
int static secp256k1_ecdsa_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_num_t *key, int compressed);
static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size);
static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a);
static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message);
static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid);
static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid);
#endif

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/**********************************************************************
* 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_ECDSA_IMPL_H_
#define _SECP256K1_ECDSA_IMPL_H_
#include "scalar.h"
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecmult_gen.h"
#include "ecdsa.h"
/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
* sage: for t in xrange(1023, -1, -1):
* .. p = 2**256 - 2**32 - t
* .. if p.is_prime():
* .. print '%x'%p
* .. break
* 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
* 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
*/
static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
);
/** Difference between field and order, values 'p' and 'n' values defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
* sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
* '14551231950b75fc4402da1722fc9baee'
*/
static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
);
static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
unsigned char ra[32] = {0}, sa[32] = {0};
const unsigned char *rp;
const unsigned char *sp;
int lenr;
int lens;
int overflow;
if (sig[0] != 0x30) {
return 0;
}
lenr = sig[3];
if (5+lenr >= size) {
return 0;
}
lens = sig[lenr+5];
if (sig[1] != lenr+lens+4) {
return 0;
}
if (lenr+lens+6 > size) {
return 0;
}
if (sig[2] != 0x02) {
return 0;
}
if (lenr == 0) {
return 0;
}
if (sig[lenr+4] != 0x02) {
return 0;
}
if (lens == 0) {
return 0;
}
sp = sig + 6 + lenr;
while (lens > 0 && sp[0] == 0) {
lens--;
sp++;
}
if (lens > 32) {
return 0;
}
rp = sig + 4;
while (lenr > 0 && rp[0] == 0) {
lenr--;
rp++;
}
if (lenr > 32) {
return 0;
}
memcpy(ra + 32 - lenr, rp, lenr);
memcpy(sa + 32 - lens, sp, lens);
overflow = 0;
secp256k1_scalar_set_b32(&r->r, ra, &overflow);
if (overflow) {
return 0;
}
secp256k1_scalar_set_b32(&r->s, sa, &overflow);
if (overflow) {
return 0;
}
return 1;
}
static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a) {
unsigned char r[33] = {0}, s[33] = {0};
unsigned char *rp = r, *sp = s;
int lenR = 33, lenS = 33;
secp256k1_scalar_get_b32(&r[1], &a->r);
secp256k1_scalar_get_b32(&s[1], &a->s);
while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
if (*size < 6+lenS+lenR) {
return 0;
}
*size = 6 + lenS + lenR;
sig[0] = 0x30;
sig[1] = 4 + lenS + lenR;
sig[2] = 0x02;
sig[3] = lenR;
memcpy(sig+4, rp, lenR);
sig[4+lenR] = 0x02;
sig[5+lenR] = lenS;
memcpy(sig+lenR+6, sp, lenS);
return 1;
}
static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message) {
unsigned char c[32];
secp256k1_scalar_t sn, u1, u2;
secp256k1_fe_t xr;
secp256k1_gej_t pubkeyj;
secp256k1_gej_t pr;
if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
return 0;
}
secp256k1_scalar_inverse_var(&sn, &sig->s);
secp256k1_scalar_mul(&u1, &sn, message);
secp256k1_scalar_mul(&u2, &sn, &sig->r);
secp256k1_gej_set_ge(&pubkeyj, pubkey);
secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
if (secp256k1_gej_is_infinity(&pr)) {
return 0;
}
secp256k1_scalar_get_b32(c, &sig->r);
secp256k1_fe_set_b32(&xr, c);
/** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
* in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
* compute the remainder modulo n, and compare it to xr. However:
*
* xr == X(pr) mod n
* <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
* [Since 2 * n > p, h can only be 0 or 1]
* <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
* [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
* <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
* [Multiplying both sides of the equations by pr.z^2 mod p]
* <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
*
* Thus, we can avoid the inversion, but we have to check both cases separately.
* secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
*/
if (secp256k1_gej_eq_x_var(&xr, &pr)) {
/* xr.x == xr * xr.z^2 mod p, so the signature is valid. */
return 1;
}
if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
/* xr + p >= n, so we can skip testing the second case. */
return 0;
}
secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
if (secp256k1_gej_eq_x_var(&xr, &pr)) {
/* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
return 1;
}
return 0;
}
static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid) {
unsigned char brx[32];
secp256k1_fe_t fx;
secp256k1_ge_t x;
secp256k1_gej_t xj;
secp256k1_scalar_t rn, u1, u2;
secp256k1_gej_t qj;
if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
return 0;
}
secp256k1_scalar_get_b32(brx, &sig->r);
VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
if (recid & 2) {
if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
return 0;
}
secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
}
if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
return 0;
}
secp256k1_gej_set_ge(&xj, &x);
secp256k1_scalar_inverse_var(&rn, &sig->r);
secp256k1_scalar_mul(&u1, &rn, message);
secp256k1_scalar_negate(&u1, &u1);
secp256k1_scalar_mul(&u2, &rn, &sig->s);
secp256k1_ecmult(&qj, &xj, &u2, &u1);
secp256k1_ge_set_gej_var(pubkey, &qj);
return !secp256k1_gej_is_infinity(&qj);
}
static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid) {
unsigned char b[32];
secp256k1_gej_t rp;
secp256k1_ge_t r;
secp256k1_scalar_t n;
int overflow = 0;
secp256k1_ecmult_gen(&rp, nonce);
secp256k1_ge_set_gej(&r, &rp);
secp256k1_fe_normalize(&r.x);
secp256k1_fe_normalize(&r.y);
secp256k1_fe_get_b32(b, &r.x);
secp256k1_scalar_set_b32(&sig->r, b, &overflow);
if (secp256k1_scalar_is_zero(&sig->r)) {
/* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature. */
secp256k1_gej_clear(&rp);
secp256k1_ge_clear(&r);
return 0;
}
if (recid) {
*recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
}
secp256k1_scalar_mul(&n, &sig->r, seckey);
secp256k1_scalar_add(&n, &n, message);
secp256k1_scalar_inverse(&sig->s, nonce);
secp256k1_scalar_mul(&sig->s, &sig->s, &n);
secp256k1_scalar_clear(&n);
secp256k1_gej_clear(&rp);
secp256k1_ge_clear(&r);
if (secp256k1_scalar_is_zero(&sig->s)) {
return 0;
}
if (secp256k1_scalar_is_high(&sig->s)) {
secp256k1_scalar_negate(&sig->s, &sig->s);
if (recid) {
*recid ^= 1;
}
}
return 1;
}
#endif

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/**********************************************************************
* 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_ECKEY_
#define _SECP256K1_ECKEY_
#include "group.h"
#include "scalar.h"
static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size);
static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed);
static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen);
static int secp256k1_eckey_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed);
static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
#endif

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/**********************************************************************
* 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_ECKEY_IMPL_H_
#define _SECP256K1_ECKEY_IMPL_H_
#include "eckey.h"
#include "scalar.h"
#include "field.h"
#include "group.h"
#include "ecmult_gen.h"
static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size) {
if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
secp256k1_fe_t x;
return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == 0x03);
} else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
secp256k1_fe_t x, y;
if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
return 0;
}
secp256k1_ge_set_xy(elem, &x, &y);
if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07)) {
return 0;
}
return secp256k1_ge_is_valid_var(elem);
} else {
return 0;
}
}
static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed) {
if (secp256k1_ge_is_infinity(elem)) {
return 0;
}
secp256k1_fe_normalize_var(&elem->x);
secp256k1_fe_normalize_var(&elem->y);
secp256k1_fe_get_b32(&pub[1], &elem->x);
if (compressed) {
*size = 33;
pub[0] = 0x02 | (secp256k1_fe_is_odd(&elem->y) ? 0x01 : 0x00);
} else {
*size = 65;
pub[0] = 0x04;
secp256k1_fe_get_b32(&pub[33], &elem->y);
}
return 1;
}
static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen) {
unsigned char c[32] = {0};
const unsigned char *end = privkey + privkeylen;
int lenb = 0;
int len = 0;
int overflow = 0;
/* sequence header */
if (end < privkey+1 || *privkey != 0x30) {
return 0;
}
privkey++;
/* sequence length constructor */
if (end < privkey+1 || !(*privkey & 0x80)) {
return 0;
}
lenb = *privkey & ~0x80; privkey++;
if (lenb < 1 || lenb > 2) {
return 0;
}
if (end < privkey+lenb) {
return 0;
}
/* sequence length */
len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
privkey += lenb;
if (end < privkey+len) {
return 0;
}
/* sequence element 0: version number (=1) */
if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
return 0;
}
privkey += 3;
/* sequence element 1: octet string, up to 32 bytes */
if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
return 0;
}
memcpy(c + 32 - privkey[1], privkey + 2, privkey[1]);
secp256k1_scalar_set_b32(key, c, &overflow);
memset(c, 0, 32);
return !overflow;
}
static int secp256k1_eckey_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed) {
secp256k1_gej_t rp;
secp256k1_ge_t r;
int pubkeylen = 0;
secp256k1_ecmult_gen(&rp, key);
secp256k1_ge_set_gej(&r, &rp);
if (compressed) {
static const unsigned char begin[] = {
0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_scalar_get_b32(ptr, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 1)) {
return 0;
}
ptr += pubkeylen;
*privkeylen = ptr - privkey;
} else {
static const unsigned char begin[] = {
0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_scalar_get_b32(ptr, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 0)) {
return 0;
}
ptr += pubkeylen;
*privkeylen = ptr - privkey;
}
return 1;
}
static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
secp256k1_scalar_add(key, key, tweak);
if (secp256k1_scalar_is_zero(key)) {
return 0;
}
return 1;
}
static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
secp256k1_gej_t pt;
secp256k1_scalar_t one;
secp256k1_gej_set_ge(&pt, key);
secp256k1_scalar_set_int(&one, 1);
secp256k1_ecmult(&pt, &pt, &one, tweak);
if (secp256k1_gej_is_infinity(&pt)) {
return 0;
}
secp256k1_ge_set_gej(key, &pt);
return 1;
}
static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
if (secp256k1_scalar_is_zero(tweak)) {
return 0;
}
secp256k1_scalar_mul(key, key, tweak);
return 1;
}
static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
secp256k1_scalar_t zero;
secp256k1_gej_t pt;
if (secp256k1_scalar_is_zero(tweak)) {
return 0;
}
secp256k1_scalar_set_int(&zero, 0);
secp256k1_gej_set_ge(&pt, key);
secp256k1_ecmult(&pt, &pt, tweak, &zero);
secp256k1_ge_set_gej(key, &pt);
return 1;
}
#endif

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@ -1,6 +1,8 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_
#define _SECP256K1_ECMULT_
@ -11,9 +13,7 @@
static void secp256k1_ecmult_start(void);
static void secp256k1_ecmult_stop(void);
/** Multiply with the generator: R = a*G */
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *a);
/** Double multiply: R = na*A + ng*G */
static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng);
static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng);
#endif

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@ -0,0 +1,19 @@
/**********************************************************************
* 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_ECMULT_GEN_
#define _SECP256K1_ECMULT_GEN_
#include "scalar.h"
#include "group.h"
static void secp256k1_ecmult_gen_start(void);
static void secp256k1_ecmult_gen_stop(void);
/** Multiply with the generator: R = a*G */
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *a);
#endif

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/**********************************************************************
* 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_ECMULT_GEN_IMPL_H_
#define _SECP256K1_ECMULT_GEN_IMPL_H_
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"
typedef struct {
/* For accelerating the computation of a*G:
* To harden against timing attacks, use the following mechanism:
* * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
* * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
* * U_i = U * 2^i (for i=0..62)
* * U_i = U * (1-2^63) (for i=63)
* where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
* For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
* precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
* None of the resulting prec group elements have a known scalar, and neither do any of
* the intermediate sums while computing a*G.
*/
secp256k1_ge_storage_t prec[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
} secp256k1_ecmult_gen_consts_t;
static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
static void secp256k1_ecmult_gen_start(void) {
secp256k1_ge_t prec[1024];
secp256k1_gej_t gj;
secp256k1_gej_t nums_gej;
secp256k1_ecmult_gen_consts_t *ret;
int i, j;
if (secp256k1_ecmult_gen_consts != NULL) {
return;
}
/* Allocate the precomputation table. */
ret = (secp256k1_ecmult_gen_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_gen_consts_t));
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
{
static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
secp256k1_fe_t nums_x;
secp256k1_ge_t nums_ge;
VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
secp256k1_gej_set_ge(&nums_gej, &nums_ge);
/* Add G to make the bits in x uniformly distributed. */
secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g);
}
/* compute prec. */
{
secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
secp256k1_gej_t gbase;
secp256k1_gej_t numsbase;
gbase = gj; /* 16^j * G */
numsbase = nums_gej; /* 2^j * nums. */
for (j = 0; j < 64; j++) {
/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
precj[j*16] = numsbase;
for (i = 1; i < 16; i++) {
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
}
/* Multiply gbase by 16. */
for (i = 0; i < 4; i++) {
secp256k1_gej_double_var(&gbase, &gbase);
}
/* Multiply numbase by 2. */
secp256k1_gej_double_var(&numsbase, &numsbase);
if (j == 62) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
}
}
secp256k1_ge_set_all_gej_var(1024, prec, precj);
}
for (j = 0; j < 64; j++) {
for (i = 0; i < 16; i++) {
secp256k1_ge_to_storage(&ret->prec[j][i], &prec[j*16 + i]);
}
}
/* Set the global pointer to the precomputation table. */
secp256k1_ecmult_gen_consts = ret;
}
static void secp256k1_ecmult_gen_stop(void) {
secp256k1_ecmult_gen_consts_t *c;
if (secp256k1_ecmult_gen_consts == NULL) {
return;
}
c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
secp256k1_ecmult_gen_consts = NULL;
free(c);
}
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
secp256k1_ge_t add;
secp256k1_ge_storage_t adds;
int bits;
int i, j;
secp256k1_gej_set_infinity(r);
add.infinity = 0;
for (j = 0; j < 64; j++) {
bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
for (i = 0; i < 16; i++) {
secp256k1_ge_storage_cmov(&adds, &c->prec[j][i], i == bits);
}
secp256k1_ge_from_storage(&add, &adds);
secp256k1_gej_add_ge(r, r, &add);
}
bits = 0;
secp256k1_ge_clear(&add);
}
#endif

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@ -0,0 +1,302 @@
/**********************************************************************
* 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_ECMULT_IMPL_H_
#define _SECP256K1_ECMULT_IMPL_H_
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
/* optimal for 128-bit and 256-bit exponents. */
#define WINDOW_A 5
/** larger numbers may result in slightly better performance, at the cost of
exponentially larger precomputed tables. */
#ifdef USE_ENDOMORPHISM
/** Two tables for window size 15: 1.375 MiB. */
#define WINDOW_G 15
#else
/** One table for window size 16: 1.375 MiB. */
#define WINDOW_G 16
#endif
/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
* pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
* 2^(w-2) entries.
*
* There are two versions of this function:
* - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
* fast to precompute, but slower to use in later additions.
* - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
* (much) slower to precompute, but a bit faster to use in later additions.
* To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
* G is constant, so it only needs to be done once in advance.
*/
static void secp256k1_ecmult_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
secp256k1_gej_t d;
int i;
pre[0] = *a;
secp256k1_gej_double_var(&d, &pre[0]);
for (i = 1; i < (1 << (w-2)); i++) {
secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]);
}
}
static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t *pre, const secp256k1_gej_t *a, int w) {
secp256k1_gej_t d;
int i;
const int table_size = 1 << (w-2);
secp256k1_gej_t *prej = (secp256k1_gej_t *)checked_malloc(sizeof(secp256k1_gej_t) * table_size);
secp256k1_ge_t *prea = (secp256k1_ge_t *)checked_malloc(sizeof(secp256k1_ge_t) * table_size);
prej[0] = *a;
secp256k1_gej_double_var(&d, a);
for (i = 1; i < table_size; i++) {
secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]);
}
secp256k1_ge_set_all_gej_var(table_size, prea, prej);
for (i = 0; i < table_size; i++) {
secp256k1_ge_to_storage(&pre[i], &prea[i]);
}
free(prej);
free(prea);
}
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
*(r) = (pre)[((n)-1)/2]; \
} else { \
secp256k1_gej_neg((r), &(pre)[(-(n)-1)/2]); \
} \
} while(0)
#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
} else { \
secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
secp256k1_ge_neg((r), (r)); \
} \
} while(0)
typedef struct {
/* For accelerating the computation of a*P + b*G: */
secp256k1_ge_storage_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of the generator */
#ifdef USE_ENDOMORPHISM
secp256k1_ge_storage_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of 2^128*generator */
#endif
} secp256k1_ecmult_consts_t;
static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
static void secp256k1_ecmult_start(void) {
secp256k1_gej_t gj;
secp256k1_ecmult_consts_t *ret;
if (secp256k1_ecmult_consts != NULL) {
return;
}
/* Allocate the precomputation table. */
ret = (secp256k1_ecmult_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_consts_t));
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* precompute the tables with odd multiples */
secp256k1_ecmult_table_precomp_ge_storage_var(ret->pre_g, &gj, WINDOW_G);
#ifdef USE_ENDOMORPHISM
{
secp256k1_gej_t g_128j;
int i;
/* calculate 2^128*generator */
g_128j = gj;
for (i = 0; i < 128; i++) {
secp256k1_gej_double_var(&g_128j, &g_128j);
}
secp256k1_ecmult_table_precomp_ge_storage_var(ret->pre_g_128, &g_128j, WINDOW_G);
}
#endif
/* Set the global pointer to the precomputation table. */
secp256k1_ecmult_consts = ret;
}
static void secp256k1_ecmult_stop(void) {
secp256k1_ecmult_consts_t *c;
if (secp256k1_ecmult_consts == NULL) {
return;
}
c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts;
secp256k1_ecmult_consts = NULL;
free(c);
}
/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
* with the following guarantees:
* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
* - the number of set values in wnaf is returned. This number is at most 256, and at most one more
* - than the number of bits in the (absolute value) of the input.
*/
static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_scalar_t *a, int w) {
secp256k1_scalar_t s = *a;
int set_bits = 0;
int bit = 0;
int sign = 1;
if (secp256k1_scalar_get_bits(&s, 255, 1)) {
secp256k1_scalar_negate(&s, &s);
sign = -1;
}
while (bit < 256) {
int now;
int word;
if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
bit++;
continue;
}
while (set_bits < bit) {
wnaf[set_bits++] = 0;
}
now = w;
if (bit + now > 256) {
now = 256 - bit;
}
word = secp256k1_scalar_get_bits_var(&s, bit, now);
if (word & (1 << (w-1))) {
secp256k1_scalar_add_bit(&s, bit + w);
wnaf[set_bits++] = sign * (word - (1 << w));
} else {
wnaf[set_bits++] = sign * word;
}
bit += now;
}
return set_bits;
}
static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
secp256k1_gej_t tmpj;
secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ge_t tmpa;
const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
#ifdef USE_ENDOMORPHISM
secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_scalar_t na_1, na_lam;
/* Splitted G factors. */
secp256k1_scalar_t ng_1, ng_128;
int wnaf_na_1[130];
int wnaf_na_lam[130];
int bits_na_1;
int bits_na_lam;
int wnaf_ng_1[129];
int bits_ng_1;
int wnaf_ng_128[129];
int bits_ng_128;
#else
int wnaf_na[256];
int bits_na;
int wnaf_ng[257];
int bits_ng;
#endif
int i;
int bits;
#ifdef USE_ENDOMORPHISM
/* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
secp256k1_scalar_split_lambda_var(&na_1, &na_lam, na);
/* build wnaf representation for na_1 and na_lam. */
bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
VERIFY_CHECK(bits_na_1 <= 130);
VERIFY_CHECK(bits_na_lam <= 130);
bits = bits_na_1;
if (bits_na_lam > bits) {
bits = bits_na_lam;
}
#else
/* build wnaf representation for na. */
bits_na = secp256k1_ecmult_wnaf(wnaf_na, na, WINDOW_A);
bits = bits_na;
#endif
/* calculate odd multiples of a */
secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A);
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
/* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
/* Build wnaf representation for ng_1 and ng_128 */
bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G);
bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
if (bits_ng_1 > bits) {
bits = bits_ng_1;
}
if (bits_ng_128 > bits) {
bits = bits_ng_128;
}
#else
bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, ng, WINDOW_G);
if (bits_ng > bits) {
bits = bits_ng;
}
#endif
secp256k1_gej_set_infinity(r);
for (i = bits-1; i >= 0; i--) {
int n;
secp256k1_gej_double_var(r, r);
#ifdef USE_ENDOMORPHISM
if (i < bits_na_1 && (n = wnaf_na_1[i])) {
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
secp256k1_gej_add_var(r, r, &tmpj);
}
if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
secp256k1_gej_add_var(r, r, &tmpj);
}
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g, n, WINDOW_G);
secp256k1_gej_add_ge_var(r, r, &tmpa);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g_128, n, WINDOW_G);
secp256k1_gej_add_ge_var(r, r, &tmpa);
}
#else
if (i < bits_na && (n = wnaf_na[i])) {
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
secp256k1_gej_add_var(r, r, &tmpj);
}
if (i < bits_ng && (n = wnaf_ng[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, c->pre_g, n, WINDOW_G);
secp256k1_gej_add_ge_var(r, r, &tmpa);
}
#endif
}
}
#endif

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@ -1,6 +1,8 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_
#define _SECP256K1_FIELD_
@ -16,86 +18,99 @@
* normality.
*/
#if defined(USE_FIELD_GMP)
#include "field_gmp.h"
#elif defined(USE_FIELD_10X26)
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_FIELD_10X26)
#include "field_10x26.h"
#elif defined(USE_FIELD_5X52)
#include "field_5x52.h"
#elif defined(USE_FIELD_5X64)
#include "field_5x64.h"
#else
#error "Please select field implementation"
#endif
typedef struct {
secp256k1_num_t p;
} secp256k1_fe_consts_t;
static const secp256k1_fe_consts_t *secp256k1_fe_consts = NULL;
/** Initialize field element precomputation data. */
void static secp256k1_fe_start(void);
/** Unload field element precomputation data. */
void static secp256k1_fe_stop(void);
/** Normalize a field element. */
void static secp256k1_fe_normalize(secp256k1_fe_t *r);
static void secp256k1_fe_normalize(secp256k1_fe_t *r);
/** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r);
/** Normalize a field element, without constant-time guarantee. */
static void secp256k1_fe_normalize_var(secp256k1_fe_t *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_t *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_t *r);
/** Set a field element equal to a small integer. Resulting field element is normalized. */
void static secp256k1_fe_set_int(secp256k1_fe_t *r, int a);
static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a);
/** Verify whether a field element is zero. Requires the input to be normalized. */
int static secp256k1_fe_is_zero(const secp256k1_fe_t *a);
static int secp256k1_fe_is_zero(const secp256k1_fe_t *a);
/** Check the "oddness" of a field element. Requires the input to be normalized. */
int static secp256k1_fe_is_odd(const secp256k1_fe_t *a);
static int secp256k1_fe_is_odd(const secp256k1_fe_t *a);
/** Compare two field elements. Requires magnitude-1 inputs. */
static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
/** Compare two field elements. Requires both inputs to be normalized */
int static secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
/** Set a field element equal to 32-byte big endian value. Resulting field element is normalized. */
void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a);
/** Set a field element equal to 32-byte big endian value. If succesful, the resulting field element is normalized. */
static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a);
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a);
static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a);
/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
* as an argument. The magnitude of the output is one higher. */
void static secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m);
static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m);
/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
* small integer. */
void static secp256k1_fe_mul_int(secp256k1_fe_t *r, int a);
static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a);
/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
void static secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a);
static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a);
/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
void static secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t *b);
static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b);
/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a);
static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a);
/** Sets a field element to be the (modular) square root of another. Requires the inputs' magnitude to
* be at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
void static secp256k1_fe_sqrt(secp256k1_fe_t *r, const secp256k1_fe_t *a);
/** Sets a field element to be the (modular) square root (if any exist) of another. Requires the
* input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be
* normalized). Return value indicates whether a square root was found. */
static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *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). */
void static secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a);
static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a);
/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
void static secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *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(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a);
/** Convert a field element to a hexadecimal string. */
void static secp256k1_fe_get_hex(char *r, int *rlen, const secp256k1_fe_t *a);
/** Convert a field element to the storage type. */
static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t*);
/** Convert a hexadecimal string to a field element. */
void static secp256k1_fe_set_hex(secp256k1_fe_t *r, const char *a, int alen);
/** Convert a field element back from the storage type. */
static void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t*);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag);
#endif

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crypto/secp256k1/secp256k1/src/field_10x26.h
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@ -1,6 +1,8 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
@ -8,7 +10,7 @@
#include <stdint.h>
typedef struct {
// X = sum(i=0..9, elem[i]*2^26) mod n
/* X = sum(i=0..9, elem[i]*2^26) mod n */
uint32_t n[10];
#ifdef VERIFY
int magnitude;
@ -16,4 +18,30 @@ typedef struct {
#endif
} secp256k1_fe_t;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) & 0x3FFFFFFUL, \
((d0) >> 26) | ((d1) & 0xFFFFFUL) << 6, \
((d1) >> 20) | ((d2) & 0x3FFFUL) << 12, \
((d2) >> 14) | ((d3) & 0xFFUL) << 18, \
((d3) >> 8) | ((d4) & 0x3) << 24, \
((d4) >> 2) & 0x3FFFFFFUL, \
((d4) >> 28) | ((d5) & 0x3FFFFFUL) << 4, \
((d5) >> 22) | ((d6) & 0xFFFF) << 10, \
((d6) >> 16) | ((d7) & 0x3FF) << 16, \
((d7) >> 10) \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
typedef struct {
uint32_t n[8];
} secp256k1_fe_storage_t;
#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
#endif

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36
crypto/secp256k1/secp256k1/src/field_5x52.h
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@ -1,6 +1,8 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
@ -8,7 +10,7 @@
#include <stdint.h>
typedef struct {
// X = sum(i=0..4, elem[i]*2^52) mod n
/* X = sum(i=0..4, elem[i]*2^52) mod n */
uint64_t n[5];
#ifdef VERIFY
int magnitude;
@ -16,4 +18,30 @@ typedef struct {
#endif
} secp256k1_fe_t;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) | ((uint64_t)(d1) & 0xFFFFFUL) << 32, \
((d1) >> 20) | ((uint64_t)(d2)) << 12 | ((uint64_t)(d3) & 0xFFUL) << 44, \
((d3) >> 8) | ((uint64_t)(d4) & 0xFFFFFFFUL) << 24, \
((d4) >> 28) | ((uint64_t)(d5)) << 4 | ((uint64_t)(d6) & 0xFFFFUL) << 36, \
((d6) >> 16) | ((uint64_t)(d7)) << 16 \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
typedef struct {
uint64_t n[4];
} secp256k1_fe_storage_t;
#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
(d0) | ((uint64_t)(d1)) << 32, \
(d2) | ((uint64_t)(d3)) << 32, \
(d4) | ((uint64_t)(d5)) << 32, \
(d6) | ((uint64_t)(d7)) << 32 \
}}
#endif

463
crypto/secp256k1/secp256k1/src/field_5x52_asm.asm
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@ -1,463 +0,0 @@
;; Added by Diederik Huys, March 2013
;;
;; Provided public procedures:
;; secp256k1_fe_mul_inner
;; secp256k1_fe_sqr_inner
;;
;; Needed tools: YASM (http://yasm.tortall.net)
;;
;;
BITS 64
;; Procedure ExSetMult
;; Register Layout:
;; INPUT: rdi = a->n
;; rsi = b->n
;; rdx = r->a
;;
;; INTERNAL: rdx:rax = multiplication accumulator
;; r9:r8 = c
;; r10-r13 = t0-t3
;; r14 = b.n[0] / t4
;; r15 = b.n[1] / t5
;; rbx = b.n[2] / t6
;; rcx = b.n[3] / t7
;; rbp = Constant 0FFFFFFFFFFFFFh / t8
;; rsi = b.n / b.n[4] / t9
GLOBAL secp256k1_fe_mul_inner
ALIGN 32
secp256k1_fe_mul_inner:
push rbp
push rbx
push r12
push r13
push r14
push r15
push rdx
mov r14,[rsi+8*0] ; preload b.n[0]. This will be the case until
; b.n[0] is no longer needed, then we reassign
; r14 to t4
;; c=a.n[0] * b.n[0]
mov rax,[rdi+0*8] ; load a.n[0]
mov rbp,0FFFFFFFFFFFFFh
mul r14 ; rdx:rax=a.n[0]*b.n[0]
mov r15,[rsi+1*8]
mov r10,rbp ; load modulus into target register for t0
mov r8,rax
and r10,rax ; only need lower qword of c
shrd r8,rdx,52
xor r9,r9 ; c < 2^64, so we ditch the HO part
;; c+=a.n[0] * b.n[1] + a.n[1] * b.n[0]
mov rax,[rdi+0*8]
mul r15
add r8,rax
adc r9,rdx
mov rax,[rdi+1*8]
mul r14
mov r11,rbp
mov rbx,[rsi+2*8]
add r8,rax
adc r9,rdx
and r11,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[0 1 2] * b.n[2 1 0]
mov rax,[rdi+0*8]
mul rbx
add r8,rax
adc r9,rdx
mov rax,[rdi+1*8]
mul r15
add r8,rax
adc r9,rdx
mov rax,[rdi+2*8]
mul r14
mov r12,rbp
mov rcx,[rsi+3*8]
add r8,rax
adc r9,rdx
and r12,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[0 1 2 3] * b.n[3 2 1 0]
mov rax,[rdi+0*8]
mul rcx
add r8,rax
adc r9,rdx
mov rax,[rdi+1*8]
mul rbx
add r8,rax
adc r9,rdx
mov rax,[rdi+2*8]
mul r15
add r8,rax
adc r9,rdx
mov rax,[rdi+3*8]
mul r14
mov r13,rbp
mov rsi,[rsi+4*8] ; load b.n[4] and destroy pointer
add r8,rax
adc r9,rdx
and r13,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[0 1 2 3 4] * b.n[4 3 2 1 0]
mov rax,[rdi+0*8]
mul rsi
add r8,rax
adc r9,rdx
mov rax,[rdi+1*8]
mul rcx
add r8,rax
adc r9,rdx
mov rax,[rdi+2*8]
mul rbx
add r8,rax
adc r9,rdx
mov rax,[rdi+3*8]
mul r15
add r8,rax
adc r9,rdx
mov rax,[rdi+4*8]
mul r14
mov r14,rbp ; load modulus into t4 and destroy a.n[0]
add r8,rax
adc r9,rdx
and r14,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[1 2 3 4] * b.n[4 3 2 1]
mov rax,[rdi+1*8]
mul rsi
add r8,rax
adc r9,rdx
mov rax,[rdi+2*8]
mul rcx
add r8,rax
adc r9,rdx
mov rax,[rdi+3*8]
mul rbx
add r8,rax
adc r9,rdx
mov rax,[rdi+4*8]
mul r15
mov r15,rbp
add r8,rax
adc r9,rdx
and r15,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[2 3 4] * b.n[4 3 2]
mov rax,[rdi+2*8]
mul rsi
add r8,rax
adc r9,rdx
mov rax,[rdi+3*8]
mul rcx
add r8,rax
adc r9,rdx
mov rax,[rdi+4*8]
mul rbx
mov rbx,rbp
add r8,rax
adc r9,rdx
and rbx,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[3 4] * b.n[4 3]
mov rax,[rdi+3*8]
mul rsi
add r8,rax
adc r9,rdx
mov rax,[rdi+4*8]
mul rcx
mov rcx,rbp
add r8,rax
adc r9,rdx
and rcx,r8
shrd r8,r9,52
xor r9,r9
;; c+=a.n[4] * b.n[4]
mov rax,[rdi+4*8]
mul rsi
;; mov rbp,rbp ; modulus already there!
add r8,rax
adc r9,rdx
and rbp,r8
shrd r8,r9,52
xor r9,r9
mov rsi,r8 ; load c into t9 and destroy b.n[4]
;; *******************************************************
common_exit_norm:
mov rdi,01000003D10h ; load constant
mov rax,r15 ; get t5
mul rdi
add rax,r10 ; +t0
adc rdx,0
mov r10,0FFFFFFFFFFFFFh ; modulus. Sadly, we ran out of registers!
mov r8,rax ; +c
and r10,rax
shrd r8,rdx,52
xor r9,r9
mov rax,rbx ; get t6
mul rdi
add rax,r11 ; +t1
adc rdx,0
mov r11,0FFFFFFFFFFFFFh ; modulus
add r8,rax ; +c
adc r9,rdx
and r11,r8
shrd r8,r9,52
xor r9,r9
mov rax,rcx ; get t7
mul rdi
add rax,r12 ; +t2
adc rdx,0
pop rbx ; retrieve pointer to this.n
mov r12,0FFFFFFFFFFFFFh ; modulus
add r8,rax ; +c
adc r9,rdx
and r12,r8
mov [rbx+2*8],r12 ; mov into this.n[2]
shrd r8,r9,52
xor r9,r9
mov rax,rbp ; get t8
mul rdi
add rax,r13 ; +t3
adc rdx,0
mov r13,0FFFFFFFFFFFFFh ; modulus
add r8,rax ; +c
adc r9,rdx
and r13,r8
mov [rbx+3*8],r13 ; -> this.n[3]
shrd r8,r9,52
xor r9,r9
mov rax,rsi ; get t9
mul rdi
add rax,r14 ; +t4
adc rdx,0
mov r14,0FFFFFFFFFFFFh ; !!!
add r8,rax ; +c
adc r9,rdx
and r14,r8
mov [rbx+4*8],r14 ; -> this.n[4]
shrd r8,r9,48 ; !!!
xor r9,r9
mov rax,01000003D1h
mul r8
add rax,r10
adc rdx,0
mov r10,0FFFFFFFFFFFFFh ; modulus
mov r8,rax
and rax,r10
shrd r8,rdx,52
mov [rbx+0*8],rax ; -> this.n[0]
add r8,r11
mov [rbx+1*8],r8 ; -> this.n[1]
pop r15
pop r14
pop r13
pop r12
pop rbx
pop rbp
ret
;; PROC ExSetSquare
;; Register Layout:
;; INPUT: rdi = a.n
;; rsi = this.a
;; INTERNAL: rdx:rax = multiplication accumulator
;; r9:r8 = c
;; r10-r13 = t0-t3
;; r14 = a.n[0] / t4
;; r15 = a.n[1] / t5
;; rbx = a.n[2] / t6
;; rcx = a.n[3] / t7
;; rbp = 0FFFFFFFFFFFFFh / t8
;; rsi = a.n[4] / t9
GLOBAL secp256k1_fe_sqr_inner
ALIGN 32
secp256k1_fe_sqr_inner:
push rbp
push rbx
push r12
push r13
push r14
push r15
push rsi
mov rbp,0FFFFFFFFFFFFFh
;; c=a.n[0] * a.n[0]
mov r14,[rdi+0*8] ; r14=a.n[0]
mov r10,rbp ; modulus
mov rax,r14
mul rax
mov r15,[rdi+1*8] ; a.n[1]
add r14,r14 ; r14=2*a.n[0]
mov r8,rax
and r10,rax ; only need lower qword
shrd r8,rdx,52
xor r9,r9
;; c+=2*a.n[0] * a.n[1]
mov rax,r14 ; r14=2*a.n[0]
mul r15
mov rbx,[rdi+2*8] ; rbx=a.n[2]
mov r11,rbp ; modulus
add r8,rax
adc r9,rdx
and r11,r8
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[0]*a.n[2]+a.n[1]*a.n[1]
mov rax,r14
mul rbx
add r8,rax
adc r9,rdx
mov rax,r15
mov r12,rbp ; modulus
mul rax
mov rcx,[rdi+3*8] ; rcx=a.n[3]
add r15,r15 ; r15=a.n[1]*2
add r8,rax
adc r9,rdx
and r12,r8 ; only need lower dword
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[0]*a.n[3]+2*a.n[1]*a.n[2]
mov rax,r14
mul rcx
add r8,rax
adc r9,rdx
mov rax,r15 ; rax=2*a.n[1]
mov r13,rbp ; modulus
mul rbx
mov rsi,[rdi+4*8] ; rsi=a.n[4]
add r8,rax
adc r9,rdx
and r13,r8
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[0]*a.n[4]+2*a.n[1]*a.n[3]+a.n[2]*a.n[2]
mov rax,r14 ; last time we need 2*a.n[0]
mul rsi
add r8,rax
adc r9,rdx
mov rax,r15
mul rcx
mov r14,rbp ; modulus
add r8,rax
adc r9,rdx
mov rax,rbx
mul rax
add rbx,rbx ; rcx=2*a.n[2]
add r8,rax
adc r9,rdx
and r14,r8
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[1]*a.n[4]+2*a.n[2]*a.n[3]
mov rax,r15 ; last time we need 2*a.n[1]
mul rsi
add r8,rax
adc r9,rdx
mov rax,rbx
mul rcx
mov r15,rbp ; modulus
add r8,rax
adc r9,rdx
and r15,r8
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[2]*a.n[4]+a.n[3]*a.n[3]
mov rax,rbx ; last time we need 2*a.n[2]
mul rsi
add r8,rax
adc r9,rdx
mov rax,rcx ; a.n[3]
mul rax
mov rbx,rbp ; modulus
add r8,rax
adc r9,rdx
and rbx,r8 ; only need lower dword
lea rax,[2*rcx]
shrd r8,r9,52
xor r9,r9
;; c+=2*a.n[3]*a.n[4]
mul rsi
mov rcx,rbp ; modulus
add r8,rax
adc r9,rdx
and rcx,r8 ; only need lower dword
shrd r8,r9,52
xor r9,r9
;; c+=a.n[4]*a.n[4]
mov rax,rsi
mul rax
;; mov rbp,rbp ; modulus is already there!
add r8,rax
adc r9,rdx
and rbp,r8
shrd r8,r9,52
xor r9,r9
mov rsi,r8
;; *******************************************************
jmp common_exit_norm
end

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crypto/secp256k1/secp256k1/src/field_5x52_asm_impl.h Normal file
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@ -0,0 +1,502 @@
/**********************************************************************
* 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.*
**********************************************************************/
/**
* Changelog:
* - March 2013, Diederik Huys: original version
* - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm
* - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly
*/
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
/**
* Registers: rdx:rax = multiplication accumulator
* r9:r8 = c
* r15:rcx = d
* r10-r14 = a0-a4
* rbx = b
* rdi = r
* rsi = a / t?
*/
uint64_t tmp1, tmp2, tmp3;
__asm__ __volatile__(
"movq 0(%%rsi),%%r10\n"
"movq 8(%%rsi),%%r11\n"
"movq 16(%%rsi),%%r12\n"
"movq 24(%%rsi),%%r13\n"
"movq 32(%%rsi),%%r14\n"
/* d += a3 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r13\n"
"movq %%rax,%%rcx\n"
"movq %%rdx,%%r15\n"
/* d += a2 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d = a0 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c = a4 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r14\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += (c & M) * R */
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* t3 (tmp1) = d & M */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
"movq %%rsi,%q1\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* d += a4 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a0 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += c * R */
"movq %%r8,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* t4 = d & M (%%rsi) */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* tx = t4 >> 48 (tmp3) */
"movq %%rsi,%%rax\n"
"shrq $48,%%rax\n"
"movq %%rax,%q3\n"
/* t4 &= (M >> 4) (tmp2) */
"movq $0xffffffffffff,%%rax\n"
"andq %%rax,%%rsi\n"
"movq %%rsi,%q2\n"
/* c = a0 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r10\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += a4 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* u0 = d & M (%%rsi) */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* u0 = (u0 << 4) | tx (%%rsi) */
"shlq $4,%%rsi\n"
"movq %q3,%%rax\n"
"orq %%rax,%%rsi\n"
/* c += u0 * (R >> 4) */
"movq $0x1000003d1,%%rax\n"
"mulq %%rsi\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[0] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,0(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a1 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a0 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a4 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c += (d & M) * R */
"movq %%rcx,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* r[1] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,8(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a2 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a1 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a0 * b2 (last use of %%r10 = a0) */
"movq 16(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */
"movq %q2,%%rsi\n"
"movq %q1,%%r10\n"
/* d += a4 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c += (d & M) * R */
"movq %%rcx,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 (%%rcx only) */
"shrdq $52,%%r15,%%rcx\n"
/* r[2] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,16(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += t3 */
"addq %%r10,%%r8\n"
/* c += d * R */
"movq %%rcx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[3] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,24(%%rdi)\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* c += t4 (%%r8 only) */
"addq %%rsi,%%r8\n"
/* r[4] = c */
"movq %%r8,32(%%rdi)\n"
: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
: "b"(b), "D"(r)
: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
);
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
/**
* Registers: rdx:rax = multiplication accumulator
* r9:r8 = c
* rcx:rbx = d
* r10-r14 = a0-a4
* r15 = M (0xfffffffffffff)
* rdi = r
* rsi = a / t?
*/
uint64_t tmp1, tmp2, tmp3;
__asm__ __volatile__(
"movq 0(%%rsi),%%r10\n"
"movq 8(%%rsi),%%r11\n"
"movq 16(%%rsi),%%r12\n"
"movq 24(%%rsi),%%r13\n"
"movq 32(%%rsi),%%r14\n"
"movq $0xfffffffffffff,%%r15\n"
/* d = (a0*2) * a3 */
"leaq (%%r10,%%r10,1),%%rax\n"
"mulq %%r13\n"
"movq %%rax,%%rbx\n"
"movq %%rdx,%%rcx\n"
/* d += (a1*2) * a2 */
"leaq (%%r11,%%r11,1),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c = a4 * a4 */
"movq %%r14,%%rax\n"
"mulq %%r14\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += (c & M) * R */
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* t3 (tmp1) = d & M */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
"movq %%rsi,%q1\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* a4 *= 2 */
"addq %%r14,%%r14\n"
/* d += a0 * a4 */
"movq %%r10,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d+= (a1*2) * a3 */
"leaq (%%r11,%%r11,1),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += a2 * a2 */
"movq %%r12,%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += c * R */
"movq %%r8,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* t4 = d & M (%%rsi) */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* tx = t4 >> 48 (tmp3) */
"movq %%rsi,%%rax\n"
"shrq $48,%%rax\n"
"movq %%rax,%q3\n"
/* t4 &= (M >> 4) (tmp2) */
"movq $0xffffffffffff,%%rax\n"
"andq %%rax,%%rsi\n"
"movq %%rsi,%q2\n"
/* c = a0 * a0 */
"movq %%r10,%%rax\n"
"mulq %%r10\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += a1 * a4 */
"movq %%r11,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += (a2*2) * a3 */
"leaq (%%r12,%%r12,1),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* u0 = d & M (%%rsi) */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* u0 = (u0 << 4) | tx (%%rsi) */
"shlq $4,%%rsi\n"
"movq %q3,%%rax\n"
"orq %%rax,%%rsi\n"
/* c += u0 * (R >> 4) */
"movq $0x1000003d1,%%rax\n"
"mulq %%rsi\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[0] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,0(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* a0 *= 2 */
"addq %%r10,%%r10\n"
/* c += a0 * a1 */
"movq %%r10,%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a2 * a4 */
"movq %%r12,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += a3 * a3 */
"movq %%r13,%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c += (d & M) * R */
"movq %%rbx,%%rax\n"
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* r[1] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,8(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a0 * a2 (last use of %%r10) */
"movq %%r10,%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */
"movq %q2,%%rsi\n"
"movq %q1,%%r10\n"
/* c += a1 * a1 */
"movq %%r11,%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a3 * a4 */
"movq %%r13,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c += (d & M) * R */
"movq %%rbx,%%rax\n"
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 (%%rbx only) */
"shrdq $52,%%rcx,%%rbx\n"
/* r[2] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,16(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += t3 */
"addq %%r10,%%r8\n"
/* c += d * R */
"movq %%rbx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[3] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,24(%%rdi)\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* c += t4 (%%r8 only) */
"addq %%rsi,%%r8\n"
/* r[4] = c */
"movq %%r8,32(%%rdi)\n"
: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
: "D"(r)
: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
);
}
#endif

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crypto/secp256k1/secp256k1/src/field_5x52_impl.h Normal file
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@ -0,0 +1,439 @@
/**********************************************************************
* 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_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include <string.h>
#include "util.h"
#include "num.h"
#include "field.h"
#if defined(USE_ASM_X86_64)
#include "field_5x52_asm_impl.h"
#else
#include "field_5x52_int128_impl.h"
#endif
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
* represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
* each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
* is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
* accept any input with magnitude at most M, and have different rules for propagating magnitude to their
* output.
*/
#ifdef VERIFY
static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
const uint64_t *d = a->n;
int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
/* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
r &= (a->magnitude >= 0);
r &= (a->magnitude <= 2048);
if (a->normalized) {
r &= (a->magnitude <= 1);
if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
r &= (d[0] < 0xFFFFEFFFFFC2FULL);
}
}
VERIFY_CHECK(r == 1);
}
#else
static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
(void)a;
}
#endif
static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
/* Apply the final reduction (for constant-time behaviour, we do it always) */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
if (x) {
t0 += 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
}
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
uint64_t z0, z1;
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
uint64_t t0, t1, t2, t3, t4;
uint64_t z0, z1;
uint64_t x;
t0 = r->n[0];
t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
x = t4 >> 48;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
z0 = t0 & 0xFFFFFFFFFFFFFULL;
z1 = z0 ^ 0x1000003D0ULL;
/* Fast return path should catch the majority of cases */
if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
return 0;
}
t1 = r->n[1];
t2 = r->n[2];
t3 = r->n[3];
t4 &= 0x0FFFFFFFFFFFFULL;
t1 += (t0 >> 52); t0 = z0;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
const uint64_t *t = a->n;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
}
SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return a->n[0] & 1;
}
SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
int i;
#ifdef VERIFY
a->magnitude = 0;
a->normalized = 1;
#endif
for (i=0; i<5; i++) {
a->n[i] = 0;
}
}
static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
int i;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
VERIFY_CHECK(b->normalized);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
#endif
for (i = 4; i >= 0; i--) {
if (a->n[i] > b->n[i]) {
return 1;
}
if (a->n[i] < b->n[i]) {
return -1;
}
}
return 0;
}
static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
int i;
r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
for (i=0; i<32; i++) {
int j;
for (j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
}
}
if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
return 0;
}
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
return 1;
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
int i;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
for (i=0; i<32; i++) {
int j;
int c = 0;
for (j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
}
r[31-i] = c;
}
}
SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= m);
secp256k1_fe_verify(a);
#endif
r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
#ifdef VERIFY
r->magnitude = m + 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
r->n[0] *= a;
r->n[1] *= a;
r->n[2] *= a;
r->n[3] *= a;
r->n[4] *= a;
#ifdef VERIFY
r->magnitude *= a;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
secp256k1_fe_verify(a);
#endif
r->n[0] += a->n[0];
r->n[1] += a->n[1];
r->n[2] += a->n[2];
r->n[3] += a->n[3];
r->n[4] += a->n[4];
#ifdef VERIFY
r->magnitude += a->magnitude;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
VERIFY_CHECK(b->magnitude <= 8);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
VERIFY_CHECK(r != b);
#endif
secp256k1_fe_mul_inner(r->n, a->n, b->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
secp256k1_fe_verify(a);
#endif
secp256k1_fe_sqr_inner(r->n, a->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag) {
uint64_t mask0, mask1;
mask0 = flag + ~((uint64_t)0);
mask1 = ~mask0;
r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
}
static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
#endif
r->n[0] = a->n[0] | a->n[1] << 52;
r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
}
static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) {
r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
r->n[4] = a->n[3] >> 16;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
#endif

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/**********************************************************************
* 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_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
#include <stdint.h>
#ifdef VERIFY
#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
#else
#define VERIFY_BITS(x, n) do { } while(0)
#endif
SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
uint128_t c, d;
uint64_t t3, t4, tx, u0;
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
VERIFY_BITS(a[0], 56);
VERIFY_BITS(a[1], 56);
VERIFY_BITS(a[2], 56);
VERIFY_BITS(a[3], 56);
VERIFY_BITS(a[4], 52);
VERIFY_BITS(b[0], 56);
VERIFY_BITS(b[1], 56);
VERIFY_BITS(b[2], 56);
VERIFY_BITS(b[3], 56);
VERIFY_BITS(b[4], 52);
VERIFY_CHECK(r != b);
/* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
* px is a shorthand for sum(a[i]*b[x-i], i=0..x).
* Note that [x 0 0 0 0 0] = [x*R].
*/
d = (uint128_t)a0 * b[3]
+ (uint128_t)a1 * b[2]
+ (uint128_t)a2 * b[1]
+ (uint128_t)a3 * b[0];
VERIFY_BITS(d, 114);
/* [d 0 0 0] = [p3 0 0 0] */
c = (uint128_t)a4 * b[4];
VERIFY_BITS(c, 112);
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (c & M) * R; c >>= 52;
VERIFY_BITS(d, 115);
VERIFY_BITS(c, 60);
/* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
t3 = d & M; d >>= 52;
VERIFY_BITS(t3, 52);
VERIFY_BITS(d, 63);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (uint128_t)a0 * b[4]
+ (uint128_t)a1 * b[3]
+ (uint128_t)a2 * b[2]
+ (uint128_t)a3 * b[1]
+ (uint128_t)a4 * b[0];
VERIFY_BITS(d, 115);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
d += c * R;
VERIFY_BITS(d, 116);
/* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
t4 = d & M; d >>= 52;
VERIFY_BITS(t4, 52);
VERIFY_BITS(d, 64);
/* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
tx = (t4 >> 48); t4 &= (M >> 4);
VERIFY_BITS(tx, 4);
VERIFY_BITS(t4, 48);
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
c = (uint128_t)a0 * b[0];
VERIFY_BITS(c, 112);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
d += (uint128_t)a1 * b[4]
+ (uint128_t)a2 * b[3]
+ (uint128_t)a3 * b[2]
+ (uint128_t)a4 * b[1];
VERIFY_BITS(d, 115);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = d & M; d >>= 52;
VERIFY_BITS(u0, 52);
VERIFY_BITS(d, 63);
/* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
/* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = (u0 << 4) | tx;
VERIFY_BITS(u0, 56);
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)u0 * (R >> 4);
VERIFY_BITS(c, 115);
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
r[0] = c & M; c >>= 52;
VERIFY_BITS(r[0], 52);
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)a0 * b[1]
+ (uint128_t)a1 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (uint128_t)a2 * b[4]
+ (uint128_t)a3 * b[3]
+ (uint128_t)a4 * b[2];
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
r[1] = c & M; c >>= 52;
VERIFY_BITS(r[1], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (uint128_t)a0 * b[2]
+ (uint128_t)a1 * b[1]
+ (uint128_t)a2 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (uint128_t)a3 * b[4]
+ (uint128_t)a4 * b[3];
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[2] = c & M; c >>= 52;
VERIFY_BITS(r[2], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += d * R + t3;;
VERIFY_BITS(c, 100);
/* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[3] = c & M; c >>= 52;
VERIFY_BITS(r[3], 52);
VERIFY_BITS(c, 48);
/* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += t4;
VERIFY_BITS(c, 49);
/* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[4] = c;
VERIFY_BITS(r[4], 49);
/* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
uint128_t c, d;
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
int64_t t3, t4, tx, u0;
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
VERIFY_BITS(a[0], 56);
VERIFY_BITS(a[1], 56);
VERIFY_BITS(a[2], 56);
VERIFY_BITS(a[3], 56);
VERIFY_BITS(a[4], 52);
/** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
* px is a shorthand for sum(a[i]*a[x-i], i=0..x).
* Note that [x 0 0 0 0 0] = [x*R].
*/
d = (uint128_t)(a0*2) * a3
+ (uint128_t)(a1*2) * a2;
VERIFY_BITS(d, 114);
/* [d 0 0 0] = [p3 0 0 0] */
c = (uint128_t)a4 * a4;
VERIFY_BITS(c, 112);
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (c & M) * R; c >>= 52;
VERIFY_BITS(d, 115);
VERIFY_BITS(c, 60);
/* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
t3 = d & M; d >>= 52;
VERIFY_BITS(t3, 52);
VERIFY_BITS(d, 63);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
a4 *= 2;
d += (uint128_t)a0 * a4
+ (uint128_t)(a1*2) * a3
+ (uint128_t)a2 * a2;
VERIFY_BITS(d, 115);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
d += c * R;
VERIFY_BITS(d, 116);
/* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
t4 = d & M; d >>= 52;
VERIFY_BITS(t4, 52);
VERIFY_BITS(d, 64);
/* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
tx = (t4 >> 48); t4 &= (M >> 4);
VERIFY_BITS(tx, 4);
VERIFY_BITS(t4, 48);
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
c = (uint128_t)a0 * a0;
VERIFY_BITS(c, 112);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
d += (uint128_t)a1 * a4
+ (uint128_t)(a2*2) * a3;
VERIFY_BITS(d, 114);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = d & M; d >>= 52;
VERIFY_BITS(u0, 52);
VERIFY_BITS(d, 62);
/* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
/* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = (u0 << 4) | tx;
VERIFY_BITS(u0, 56);
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)u0 * (R >> 4);
VERIFY_BITS(c, 113);
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
r[0] = c & M; c >>= 52;
VERIFY_BITS(r[0], 52);
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
a0 *= 2;
c += (uint128_t)a0 * a1;
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (uint128_t)a2 * a4
+ (uint128_t)a3 * a3;
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
r[1] = c & M; c >>= 52;
VERIFY_BITS(r[1], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (uint128_t)a0 * a2
+ (uint128_t)a1 * a1;
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (uint128_t)a3 * a4;
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[2] = c & M; c >>= 52;
VERIFY_BITS(r[2], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += d * R + t3;;
VERIFY_BITS(c, 100);
/* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[3] = c & M; c >>= 52;
VERIFY_BITS(r[3], 52);
VERIFY_BITS(c, 48);
/* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += t4;
VERIFY_BITS(c, 49);
/* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[4] = c;
VERIFY_BITS(r[4], 49);
/* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
}
#endif

19
crypto/secp256k1/secp256k1/src/field_5x64.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
#include <stdint.h>
typedef struct {
// X = sum(i=0..4, elem[i]*2^64) mod n
uint64_t n[5];
#ifdef VERIFY
int reduced; // n[4] == 0
int normalized; // reduced and X < 2^256 - 0x100003D1
#endif
} secp256k1_fe_t;
#endif

332
crypto/secp256k1/secp256k1/src/field_5x64_asm.asm
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;; Added by Diederik Huys, March 2013
;;
;; Provided public procedures:
;; secp256k1_fe_mul_inner
;; secp256k1_fe_sqr_inner
;;
;; Needed tools: YASM (http://yasm.tortall.net)
;;
;;
BITS 64
COMP_LIMB EQU 000000001000003D1h
;; Procedure ExSetMult
;; Register Layout:
;; INPUT: rdi = a->n
;; rsi = b->n
;; rdx = r->a
;;
;; INTERNAL: rdx:rax = multiplication accumulator
;; r8-r10 = c0-c2
;; r11-r15 = b.n[0]-b.n[4] / r3 - r7
;; rbx = r0
;; rcx = r1
;; rbp = r2
;;
GLOBAL secp256k1_fe_mul_inner
ALIGN 32
secp256k1_fe_mul_inner:
push rbp
push rbx
push r12
push r13
push r14
push r15
push rdx
mov r11,[rsi+8*0] ; preload b.n[0]
;; step 1: mul_c2
mov rax,[rdi+0*8] ; load a.n[0]
mul r11 ; rdx:rax=a.n[0]*b.n[0]
mov r12,[rsi+1*8] ; preload b.n[1]
mov rbx,rax ; retire LO qword (r[0])
mov r8,rdx ; save overflow
xor r9,r9 ; overflow HO qwords
xor r10,r10
;; c+=a.n[0] * b.n[1] + a.n[1] * b.n[0]
mov rax,[rdi+0*8]
mul r12
mov r13,[rsi+2*8] ; preload b.n[2]
add r8,rax ; still the same :-)
adc r9,rdx ;
adc r10,0 ; mmm...
mov rax,[rdi+1*8]
mul r11
add r8,rax
adc r9,rdx
adc r10,0
mov rcx,r8 ; retire r[1]
xor r8,r8
;; c+=a.n[0 1 2] * b.n[2 1 0]
mov rax,[rdi+0*8]
mul r13
mov r14,[rsi+3*8] ; preload b.n[3]
add r9,rax
adc r10,rdx
adc r8,0
mov rax,[rdi+1*8]
mul r12
add r9,rax
adc r10,rdx
adc r8,0
mov rax,[rdi+2*8]
mul r11
add r9,rax
adc r10,rdx
adc r8,0
mov rbp,r9 ; retire r[2]
xor r9,r9
;; c+=a.n[0 1 2 3] * b.n[3 2 1 0]
mov rax,[rdi+0*8]
mul r14
add r10,rax
adc r8,rdx
adc r9,0
mov rax,[rdi+1*8]
mul r13
add r10,rax
adc r8,rdx
adc r9,0
mov rax,[rdi+2*8]
mul r12
add r10,rax
adc r8,rdx
adc r9,0
mov rax,[rdi+3*8]
mul r11
add r10,rax
adc r8,rdx
adc r9,0
mov r11,r10 ; retire r[3]
xor r10,r10
;; c+=a.n[1 2 3] * b.n[3 2 1]
mov rax,[rdi+1*8]
mul r14
add r8,rax
adc r9,rdx
adc r10,0
mov rax,[rdi+2*8]
mul r13
add r8,rax
adc r9,rdx
adc r10,0
mov rax,[rdi+3*8]
mul r12
add r8,rax
adc r9,rdx
adc r10,0
mov r12,r8 ; retire r[4]
xor r8,r8
;; c+=a.n[2 3] * b.n[3 2]
mov rax,[rdi+2*8]
mul r14
add r9,rax ; still the same :-)
adc r10,rdx ;
adc r8,0 ; mmm...
mov rax,[rdi+3*8]
mul r13
add r9,rax
adc r10,rdx
adc r8,0
mov r13,r9 ; retire r[5]
xor r9,r9
;; c+=a.n[3] * b.n[3]
mov rax,[rdi+3*8]
mul r14
add r10,rax
adc r8,rdx
mov r14,r10
mov r15,r8
;; *******************************************************
common_exit_norm:
mov rdi,COMP_LIMB
mov rax,r12
mul rdi
add rax,rbx
adc rcx,rdx
pop rbx
mov [rbx],rax
mov rax,r13 ; get r5
mul rdi
add rax,rcx ; +r1
adc rbp,rdx
mov [rbx+1*8],rax
mov rax,r14 ; get r6
mul rdi
add rax,rbp ; +r2
adc r11,rdx
mov [rbx+2*8],rax
mov rax,r15 ; get r7
mul rdi
add rax,r11 ; +r3
adc rdx,0
mov [rbx+3*8],rax
mov [rbx+4*8],rdx
pop r15
pop r14
pop r13
pop r12
pop rbx
pop rbp
ret
;; PROC ExSetSquare
;; Register Layout:
;; INPUT: rdi = a.n
;; rsi = this.a
;; INTERNAL: rdx:rax = multiplication accumulator
;; r8-r10 = c
;; r11-r15 = a.n[0]-a.n[4] / r3-r7
;; rbx = r0
;; rcx = r1
;; rbp = r2
GLOBAL secp256k1_fe_sqr_inner
ALIGN 32
secp256k1_fe_sqr_inner:
push rbp
push rbx
push r12
push r13
push r14
push r15
push rsi
mov r11,[rdi+8*0] ; preload a.n[0]
;; step 1: mul_c2
mov rax,r11 ; load a.n[0]
mul rax ; rdx:rax=a.n[0]²
mov r12,[rdi+1*8] ; preload a.n[1]
mov rbx,rax ; retire LO qword (r[0])
mov r8,rdx ; save overflow
xor r9,r9 ; overflow HO qwords
xor r10,r10
;; c+=2*a.n[0] * a.n[1]
mov rax,r11 ; load a.n[0]
mul r12 ; rdx:rax=a.n[0] * a.n[1]
mov r13,[rdi+2*8] ; preload a.n[2]
add rax,rax ; rdx:rax*=2
adc rdx,rdx
adc r10,0
add r8,rax ; still the same :-)
adc r9,rdx
adc r10,0 ; mmm...
mov rcx,r8 ; retire r[1]
xor r8,r8
;; c+=2*a.n[0]*a.n[2]+a.n[1]*a.n[1]
mov rax,r11 ; load a.n[0]
mul r13 ; * a.n[2]
mov r14,[rdi+3*8] ; preload a.n[3]
add rax,rax ; rdx:rax*=2
adc rdx,rdx
adc r8,0
add r9,rax
adc r10,rdx
adc r8,0
mov rax,r12
mul rax
add r9,rax
adc r10,rdx
adc r8,0
mov rbp,r9
xor r9,r9
;; c+=2*a.n[0]*a.n[3]+2*a.n[1]*a.n[2]
mov rax,r11 ; load a.n[0]
mul r14 ; * a.n[3]
add rax,rax ; rdx:rax*=2
adc rdx,rdx
adc r9,0
add r10,rax
adc r8,rdx
adc r9,0
mov rax,r12 ; load a.n[1]
mul r13 ; * a.n[2]
add rax,rax
adc rdx,rdx
adc r9,0
add r10,rax
adc r8,rdx
adc r9,0
mov r11,r10
xor r10,r10
;; c+=2*a.n[1]*a.n[3]+a.n[2]*a.n[2]
mov rax,r12 ; load a.n[1]
mul r14 ; * a.n[3]
add rax,rax ; rdx:rax*=2
adc rdx,rdx
adc r10,0
add r8,rax
adc r9,rdx
adc r10,0
mov rax,r13
mul rax
add r8,rax
adc r9,rdx
adc r10,0
mov r12,r8
xor r8,r8
;; c+=2*a.n[2]*a.n[3]
mov rax,r13 ; load a.n[2]
mul r14 ; * a.n[3]
add rax,rax ; rdx:rax*=2
adc rdx,rdx
adc r8,0
add r9,rax
adc r10,rdx
adc r8,0
mov r13,r9
xor r9,r9
;; c+=a.n[3]²
mov rax,r14
mul rax
add r10,rax
adc r8,rdx
mov r14,r10
mov r15,r8
jmp common_exit_norm
end

16
crypto/secp256k1/secp256k1/src/field_gmp.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
#include <gmp.h>
#define FIELD_LIMBS ((256 + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS)
typedef struct {
mp_limb_t n[FIELD_LIMBS+1];
} secp256k1_fe_t;
#endif

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crypto/secp256k1/secp256k1/src/field_impl.h Normal file
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/**********************************************************************
* 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_FIELD_IMPL_H_
#define _SECP256K1_FIELD_IMPL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include "util.h"
#if defined(USE_FIELD_10X26)
#include "field_10x26_impl.h"
#elif defined(USE_FIELD_5X52)
#include "field_5x52_impl.h"
#else
#error "Please select field implementation"
#endif
SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
secp256k1_fe_t na;
secp256k1_fe_negate(&na, a, 1);
secp256k1_fe_add(&na, b);
return secp256k1_fe_normalizes_to_zero_var(&na);
}
static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_t x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
int j;
/** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
* { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
* 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
secp256k1_fe_sqr(&x2, a);
secp256k1_fe_mul(&x2, &x2, a);
secp256k1_fe_sqr(&x3, &x2);
secp256k1_fe_mul(&x3, &x3, a);
x6 = x3;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x6, &x6);
}
secp256k1_fe_mul(&x6, &x6, &x3);
x9 = x6;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x9, &x9);
}
secp256k1_fe_mul(&x9, &x9, &x3);
x11 = x9;
for (j=0; j<2; j++) {
secp256k1_fe_sqr(&x11, &x11);
}
secp256k1_fe_mul(&x11, &x11, &x2);
x22 = x11;
for (j=0; j<11; j++) {
secp256k1_fe_sqr(&x22, &x22);
}
secp256k1_fe_mul(&x22, &x22, &x11);
x44 = x22;
for (j=0; j<22; j++) {
secp256k1_fe_sqr(&x44, &x44);
}
secp256k1_fe_mul(&x44, &x44, &x22);
x88 = x44;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x88, &x88);
}
secp256k1_fe_mul(&x88, &x88, &x44);
x176 = x88;
for (j=0; j<88; j++) {
secp256k1_fe_sqr(&x176, &x176);
}
secp256k1_fe_mul(&x176, &x176, &x88);
x220 = x176;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x220, &x220);
}
secp256k1_fe_mul(&x220, &x220, &x44);
x223 = x220;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x223, &x223);
}
secp256k1_fe_mul(&x223, &x223, &x3);
/* The final result is then assembled using a sliding window over the blocks. */
t1 = x223;
for (j=0; j<23; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x22);
for (j=0; j<6; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x2);
secp256k1_fe_sqr(&t1, &t1);
secp256k1_fe_sqr(r, &t1);
/* Check that a square root was actually calculated */
secp256k1_fe_sqr(&t1, r);
return secp256k1_fe_equal_var(&t1, a);
}
static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_t 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_t *r, const secp256k1_fe_t *a) {
#if defined(USE_FIELD_INV_BUILTIN)
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
secp256k1_num_t n, 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
};
unsigned char b[32];
secp256k1_fe_t 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);
VERIFY_CHECK(secp256k1_fe_set_b32(r, b));
#else
#error "Please select field inverse implementation"
#endif
}
static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_t 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) {
int j = i--;
secp256k1_fe_mul(&r[j], &r[i], &u);
secp256k1_fe_mul(&u, &u, &a[j]);
}
r[0] = u;
}
#endif

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@ -1,6 +1,8 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_GROUP_
#define _SECP256K1_GROUP_
@ -12,97 +14,105 @@
typedef struct {
secp256k1_fe_t x;
secp256k1_fe_t y;
int infinity; // whether this represents the point at infinity
int infinity; /* whether this represents the point at infinity */
} secp256k1_ge_t;
#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
/** A group element of the secp256k1 curve, in jacobian coordinates. */
typedef struct {
secp256k1_fe_t x; // actual X: x/z^2
secp256k1_fe_t y; // actual Y: y/z^3
secp256k1_fe_t x; /* actual X: x/z^2 */
secp256k1_fe_t y; /* actual Y: y/z^3 */
secp256k1_fe_t z;
int infinity; // whether this represents the point at infinity
int infinity; /* whether this represents the point at infinity */
} secp256k1_gej_t;
/** Global constants related to the group */
#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
typedef struct {
secp256k1_num_t order; // the order of the curve (= order of its generator)
secp256k1_num_t half_order; // half the order of the curve (= order of its generator)
secp256k1_ge_t g; // the generator point
secp256k1_fe_storage_t x;
secp256k1_fe_storage_t y;
} secp256k1_ge_storage_t;
// constants related to secp256k1's efficiently computable endomorphism
secp256k1_fe_t beta;
secp256k1_num_t lambda, a1b2, b1, a2;
} secp256k1_ge_consts_t;
static const secp256k1_ge_consts_t *secp256k1_ge_consts = NULL;
/** Initialize the group module. */
void static secp256k1_ge_start(void);
/** De-initialize the group module. */
void static secp256k1_ge_stop(void);
#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
/** Set a group element equal to the point at infinity */
void static secp256k1_ge_set_infinity(secp256k1_ge_t *r);
static void secp256k1_ge_set_infinity(secp256k1_ge_t *r);
/** Set a group element equal to the point with given X and Y coordinates */
void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
/** Set a group element (jacobian) equal to the point with given X coordinate, and given oddness for Y.
The result is not guaranteed to be valid. */
void static secp256k1_ge_set_xo(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd);
/** 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_t *r, const secp256k1_fe_t *x, int odd);
/** Check whether a group element is the point at infinity. */
int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
/** Check whether a group element is valid (i.e., on the curve). */
int static secp256k1_ge_is_valid(const secp256k1_ge_t *a);
static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a);
void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a);
static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
/** Set a group element equal to another which is given in jacobian coordinates */
void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a);
/** Set a group element (jacobian) equal to the point at infinity. */
void static secp256k1_gej_set_infinity(secp256k1_gej_t *r);
static void secp256k1_gej_set_infinity(secp256k1_gej_t *r);
/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
/** Get the X coordinate of a group element (jacobian). */
void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a);
/** Compare the X coordinate of a group element (jacobian). */
static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a);
/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
/** Check whether a group element is the point at infinity. */
int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
/** Set r equal to the double of a. */
void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a);
static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a);
/** Set r equal to the sum of a and b. */
void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
/** Set r equal to the sum of a and b (with b given in jacobian coordinates). This is more efficient
than secp256k1_gej_add. */
void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a);
/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
guarantee, and b is allowed to be infinity. */
static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
#ifdef USE_ENDOMORPHISM
/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
#endif
/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (given that a is
not more than 256 bits). */
void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a);
/** Clear a secp256k1_gej_t to prevent leaking sensitive information. */
static void secp256k1_gej_clear(secp256k1_gej_t *r);
/** Clear a secp256k1_ge_t to prevent leaking sensitive information. */
static void secp256k1_ge_clear(secp256k1_ge_t *r);
/** Convert a group element to the storage type. */
static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t*);
/** Convert a group element back from the storage type. */
static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t*);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag);
#endif

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@ -0,0 +1,434 @@
/**********************************************************************
* 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_GROUP_IMPL_H_
#define _SECP256K1_GROUP_IMPL_H_
#include <string.h>
#include "num.h"
#include "field.h"
#include "group.h"
/** Generator for secp256k1, value 'g' defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
*/
static const secp256k1_ge_t secp256k1_ge_const_g = SECP256K1_GE_CONST(
0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
);
static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
r->infinity = 1;
}
static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
}
static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
return a->infinity;
}
static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
*r = *a;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
secp256k1_fe_t z2, z3;
r->infinity = a->infinity;
secp256k1_fe_inv(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
secp256k1_fe_t z2, z3;
r->infinity = a->infinity;
if (a->infinity) {
return;
}
secp256k1_fe_inv_var(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a) {
secp256k1_fe_t *az;
secp256k1_fe_t *azi;
size_t i;
size_t count = 0;
az = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * len);
for (i = 0; i < len; i++) {
if (!a[i].infinity) {
az[count++] = a[i].z;
}
}
azi = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * count);
secp256k1_fe_inv_all_var(count, azi, az);
free(az);
count = 0;
for (i = 0; i < len; i++) {
r[i].infinity = a[i].infinity;
if (!a[i].infinity) {
secp256k1_fe_t zi2, zi3;
secp256k1_fe_t *zi = &azi[count++];
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r[i].x, &a[i].x, &zi2);
secp256k1_fe_mul(&r[i].y, &a[i].y, &zi3);
}
}
free(azi);
}
static void secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
r->infinity = 1;
secp256k1_fe_set_int(&r->x, 0);
secp256k1_fe_set_int(&r->y, 0);
secp256k1_fe_set_int(&r->z, 0);
}
static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
secp256k1_fe_set_int(&r->z, 1);
}
static void secp256k1_gej_clear(secp256k1_gej_t *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
}
static void secp256k1_ge_clear(secp256k1_ge_t *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
}
static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
secp256k1_fe_t x2, x3, c;
r->x = *x;
secp256k1_fe_sqr(&x2, x);
secp256k1_fe_mul(&x3, x, &x2);
r->infinity = 0;
secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&c, &x3);
if (!secp256k1_fe_sqrt_var(&r->y, &c)) {
return 0;
}
secp256k1_fe_normalize_var(&r->y);
if (secp256k1_fe_is_odd(&r->y) != odd) {
secp256k1_fe_negate(&r->y, &r->y, 1);
}
return 1;
}
static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
}
static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a) {
secp256k1_fe_t r, r2;
VERIFY_CHECK(!a->infinity);
secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
r2 = a->x; secp256k1_fe_normalize_weak(&r2);
return secp256k1_fe_equal_var(&r, &r2);
}
static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
r->z = a->z;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
return a->infinity;
}
static int secp256k1_gej_is_valid_var(const secp256k1_gej_t *a) {
secp256k1_fe_t y2, x3, z2, z6;
if (a->infinity) {
return 0;
}
/** y^2 = x^3 + 7
* (Y/Z^3)^2 = (X/Z^2)^3 + 7
* Y^2 / Z^6 = X^3 / Z^6 + 7
* Y^2 = X^3 + 7*Z^6
*/
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
secp256k1_fe_mul_int(&z6, 7);
secp256k1_fe_add(&x3, &z6);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a) {
secp256k1_fe_t y2, x3, c;
if (a->infinity) {
return 0;
}
/* y^2 = x^3 + 7 */
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&x3, &c);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
/* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate */
secp256k1_fe_t t1,t2,t3,t4;
/** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
* Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
* y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
*/
r->infinity = a->infinity;
if (r->infinity) {
return;
}
secp256k1_fe_mul(&r->z, &a->z, &a->y);
secp256k1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */
secp256k1_fe_sqr(&t1, &a->x);
secp256k1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */
secp256k1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */
secp256k1_fe_sqr(&t3, &a->y);
secp256k1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */
secp256k1_fe_sqr(&t4, &t3);
secp256k1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */
secp256k1_fe_mul(&t3, &t3, &a->x); /* T3 = 2*X*Y^2 (1) */
r->x = t3;
secp256k1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */
secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
secp256k1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */
secp256k1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */
secp256k1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */
secp256k1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */
secp256k1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
secp256k1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */
secp256k1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
}
static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
/* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
secp256k1_fe_t z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
*r = *b;
return;
}
if (b->infinity) {
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z22, &b->z);
secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_mul(&u1, &a->x, &z22);
secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
/* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
secp256k1_fe_t z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
r->infinity = b->infinity;
r->x = b->x;
r->y = b->y;
secp256k1_fe_set_int(&r->z, 1);
return;
}
if (b->infinity) {
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z12, &a->z);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
/* Operations: 7 mul, 5 sqr, 5 normalize, 19 mul_int/add/negate */
secp256k1_fe_t zz, u1, u2, s1, s2, z, t, m, n, q, rr;
int infinity;
VERIFY_CHECK(!b->infinity);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
/** In:
* Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
* In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
* we find as solution for a unified addition/doubling formula:
* lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
* x3 = lambda^2 - (x1 + x2)
* 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
*
* Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
* U1 = X1*Z2^2, U2 = X2*Z1^2
* S1 = Y1*Z2^3, S2 = Y2*Z1^3
* Z = Z1*Z2
* T = U1+U2
* M = S1+S2
* Q = T*M^2
* R = T^2-U1*U2
* X3 = 4*(R^2-Q)
* Y3 = 4*(R*(3*Q-2*R^2)-M^4)
* Z3 = 2*M*Z
* (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
*/
secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */
secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z2^2 (1) */
secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
z = a->z; /* z = Z = Z1*Z2 (8) */
t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
secp256k1_fe_sqr(&n, &m); /* n = M^2 (1) */
secp256k1_fe_mul(&q, &n, &t); /* q = Q = T*M^2 (1) */
secp256k1_fe_sqr(&n, &n); /* n = M^4 (1) */
secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
secp256k1_fe_mul(&t, &u1, &u2); secp256k1_fe_negate(&t, &t, 1); /* t = -U1*U2 (2) */
secp256k1_fe_add(&rr, &t); /* rr = R = T^2-U1*U2 (3) */
secp256k1_fe_sqr(&t, &rr); /* t = R^2 (1) */
secp256k1_fe_mul(&r->z, &m, &z); /* r->z = M*Z (1) */
infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); /* r->z = Z3 = 2*M*Z (2) */
r->x = t; /* r->x = R^2 (1) */
secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */
secp256k1_fe_add(&r->x, &q); /* r->x = R^2-Q (3) */
secp256k1_fe_normalize(&r->x);
secp256k1_fe_mul_int(&q, 3); /* q = -3*Q (6) */
secp256k1_fe_mul_int(&t, 2); /* t = 2*R^2 (2) */
secp256k1_fe_add(&t, &q); /* t = 2*R^2-3*Q (8) */
secp256k1_fe_mul(&t, &t, &rr); /* t = R*(2*R^2-3*Q) (1) */
secp256k1_fe_add(&t, &n); /* t = R*(2*R^2-3*Q)+M^4 (2) */
secp256k1_fe_negate(&r->y, &t, 2); /* r->y = R*(3*Q-2*R^2)-M^4 (3) */
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_mul_int(&r->x, 4 * (1 - a->infinity)); /* r->x = X3 = 4*(R^2-Q) */
secp256k1_fe_mul_int(&r->y, 4 * (1 - a->infinity)); /* r->y = Y3 = 4*R*(3*Q-2*R^2)-4*M^4 (4) */
/** In case a->infinity == 1, the above code results in r->x, r->y, and r->z all equal to 0.
* Add b->x to x, b->y to y, and 1 to z in that case.
*/
t = b->x; secp256k1_fe_mul_int(&t, a->infinity);
secp256k1_fe_add(&r->x, &t);
t = b->y; secp256k1_fe_mul_int(&t, a->infinity);
secp256k1_fe_add(&r->y, &t);
secp256k1_fe_set_int(&t, a->infinity);
secp256k1_fe_add(&r->z, &t);
r->infinity = infinity;
}
static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t *a) {
secp256k1_fe_t x, y;
VERIFY_CHECK(!a->infinity);
x = a->x;
secp256k1_fe_normalize(&x);
y = a->y;
secp256k1_fe_normalize(&y);
secp256k1_fe_to_storage(&r->x, &x);
secp256k1_fe_to_storage(&r->y, &y);
}
static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t *a) {
secp256k1_fe_from_storage(&r->x, &a->x);
secp256k1_fe_from_storage(&r->y, &a->y);
r->infinity = 0;
}
static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag) {
secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
}
#ifdef USE_ENDOMORPHISM
static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
static const secp256k1_fe_t beta = SECP256K1_FE_CONST(
0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
);
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, &beta);
}
#endif
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_HASH_
#define _SECP256K1_HASH_
#include <stdlib.h>
#include <stdint.h>
typedef struct {
uint32_t s[32];
uint32_t buf[16]; /* In big endian */
size_t bytes;
} secp256k1_sha256_t;
static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash);
static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t size);
static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32);
typedef struct {
secp256k1_sha256_t inner, outer;
} secp256k1_hmac_sha256_t;
static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t size);
static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size);
static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32);
typedef struct {
unsigned char v[32];
unsigned char k[32];
int retry;
} secp256k1_rfc6979_hmac_sha256_t;
static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen);
static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen);
static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng);
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_HASH_IMPL_H_
#define _SECP256K1_HASH_IMPL_H_
#include "hash.h"
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z))))
#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y))))
#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10))
#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7))
#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3))
#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10))
#define Round(a,b,c,d,e,f,g,h,k,w) do { \
uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \
uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \
(d) += t1; \
(h) = t1 + t2; \
} while(0)
#ifdef WORDS_BIGENDIAN
#define BE32(x) (x)
#else
#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
#endif
static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash) {
hash->s[0] = 0x6a09e667ul;
hash->s[1] = 0xbb67ae85ul;
hash->s[2] = 0x3c6ef372ul;
hash->s[3] = 0xa54ff53aul;
hash->s[4] = 0x510e527ful;
hash->s[5] = 0x9b05688cul;
hash->s[6] = 0x1f83d9abul;
hash->s[7] = 0x5be0cd19ul;
hash->bytes = 0;
}
/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) {
uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0]));
Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1]));
Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2]));
Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3]));
Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4]));
Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5]));
Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6]));
Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7]));
Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8]));
Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9]));
Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10]));
Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11]));
Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12]));
Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13]));
Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14]));
Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15]));
Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0));
Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0));
Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0));
s[0] += a;
s[1] += b;
s[2] += c;
s[3] += d;
s[4] += e;
s[5] += f;
s[6] += g;
s[7] += h;
}
static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t len) {
size_t bufsize = hash->bytes & 0x3F;
hash->bytes += len;
while (bufsize + len >= 64) {
/* Fill the buffer, and process it. */
memcpy(((unsigned char*)hash->buf) + bufsize, data, 64 - bufsize);
data += 64 - bufsize;
len -= 64 - bufsize;
secp256k1_sha256_transform(hash->s, hash->buf);
bufsize = 0;
}
if (len) {
/* Fill the buffer with what remains. */
memcpy(((unsigned char*)hash->buf) + bufsize, data, len);
}
}
static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32) {
static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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};
uint32_t sizedesc[2];
uint32_t out[8];
int i = 0;
sizedesc[0] = BE32(hash->bytes >> 29);
sizedesc[1] = BE32(hash->bytes << 3);
secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8);
for (i = 0; i < 8; i++) {
out[i] = BE32(hash->s[i]);
hash->s[i] = 0;
}
memcpy(out32, (const unsigned char*)out, 32);
}
static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t keylen) {
int n;
unsigned char rkey[64];
if (keylen <= 64) {
memcpy(rkey, key, keylen);
memset(rkey + keylen, 0, 64 - keylen);
} else {
secp256k1_sha256_t sha256;
secp256k1_sha256_initialize(&sha256);
secp256k1_sha256_write(&sha256, key, keylen);
secp256k1_sha256_finalize(&sha256, rkey);
memset(rkey + 32, 0, 32);
}
secp256k1_sha256_initialize(&hash->outer);
for (n = 0; n < 64; n++) {
rkey[n] ^= 0x5c;
}
secp256k1_sha256_write(&hash->outer, rkey, 64);
secp256k1_sha256_initialize(&hash->inner);
for (n = 0; n < 64; n++) {
rkey[n] ^= 0x5c ^ 0x36;
}
secp256k1_sha256_write(&hash->inner, rkey, 64);
memset(rkey, 0, 64);
}
static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size) {
secp256k1_sha256_write(&hash->inner, data, size);
}
static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32) {
unsigned char temp[32];
secp256k1_sha256_finalize(&hash->inner, temp);
secp256k1_sha256_write(&hash->outer, temp, 32);
memset(temp, 0, 32);
secp256k1_sha256_finalize(&hash->outer, out32);
}
static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen) {
secp256k1_hmac_sha256_t hmac;
static const unsigned char zero[1] = {0x00};
static const unsigned char one[1] = {0x01};
memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */
memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
/* RFC6979 3.2.d. */
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, zero, 1);
secp256k1_hmac_sha256_write(&hmac, key, keylen);
secp256k1_hmac_sha256_write(&hmac, msg, msglen);
if (rnd && rndlen) {
/* RFC6979 3.6 "Additional data". */
secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
}
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
/* RFC6979 3.2.f. */
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, one, 1);
secp256k1_hmac_sha256_write(&hmac, key, keylen);
secp256k1_hmac_sha256_write(&hmac, msg, msglen);
if (rnd && rndlen) {
/* RFC6979 3.6 "Additional data". */
secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
}
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
rng->retry = 0;
}
static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen) {
/* RFC6979 3.2.h. */
static const unsigned char zero[1] = {0x00};
if (rng->retry) {
secp256k1_hmac_sha256_t hmac;
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, zero, 1);
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
}
while (outlen > 0) {
secp256k1_hmac_sha256_t hmac;
int now = outlen;
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
if (now > 32) {
now = 32;
}
memcpy(out, rng->v, now);
out += now;
outlen -= now;
}
rng->retry = 1;
}
static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng) {
memset(rng->k, 0, 32);
memset(rng->v, 0, 32);
rng->retry = 0;
}
#undef Round
#undef sigma0
#undef sigma1
#undef Sigma0
#undef Sigma1
#undef Ch
#undef Maj
#undef ReadBE32
#undef WriteBE32
#endif

309
crypto/secp256k1/secp256k1/src/impl/ecdsa.h
View File

@ -1,309 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_ECDSA_IMPL_H_
#define _SECP256K1_ECDSA_IMPL_H_
#include "../num.h"
#include "../field.h"
#include "../group.h"
#include "../ecmult.h"
#include "../ecdsa.h"
void static secp256k1_ecdsa_sig_init(secp256k1_ecdsa_sig_t *r) {
secp256k1_num_init(&r->r);
secp256k1_num_init(&r->s);
}
void static secp256k1_ecdsa_sig_free(secp256k1_ecdsa_sig_t *r) {
secp256k1_num_free(&r->r);
secp256k1_num_free(&r->s);
}
int static secp256k1_ecdsa_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size) {
if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
secp256k1_fe_t x;
secp256k1_fe_set_b32(&x, pub+1);
secp256k1_ge_set_xo(elem, &x, pub[0] == 0x03);
} else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
secp256k1_fe_t x, y;
secp256k1_fe_set_b32(&x, pub+1);
secp256k1_fe_set_b32(&y, pub+33);
secp256k1_ge_set_xy(elem, &x, &y);
if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07))
return 0;
} else {
return 0;
}
return secp256k1_ge_is_valid(elem);
}
int static secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
if (sig[0] != 0x30) return 0;
int lenr = sig[3];
if (5+lenr >= size) return 0;
int lens = sig[lenr+5];
if (sig[1] != lenr+lens+4) return 0;
if (lenr+lens+6 > size) return 0;
if (sig[2] != 0x02) return 0;
if (lenr == 0) return 0;
if (sig[lenr+4] != 0x02) return 0;
if (lens == 0) return 0;
secp256k1_num_set_bin(&r->r, sig+4, lenr);
secp256k1_num_set_bin(&r->s, sig+6+lenr, lens);
return 1;
}
int static secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a) {
int lenR = (secp256k1_num_bits(&a->r) + 7)/8;
if (lenR == 0 || secp256k1_num_get_bit(&a->r, lenR*8-1))
lenR++;
int lenS = (secp256k1_num_bits(&a->s) + 7)/8;
if (lenS == 0 || secp256k1_num_get_bit(&a->s, lenS*8-1))
lenS++;
if (*size < 6+lenS+lenR)
return 0;
*size = 6 + lenS + lenR;
sig[0] = 0x30;
sig[1] = 4 + lenS + lenR;
sig[2] = 0x02;
sig[3] = lenR;
secp256k1_num_get_bin(sig+4, lenR, &a->r);
sig[4+lenR] = 0x02;
sig[5+lenR] = lenS;
secp256k1_num_get_bin(sig+lenR+6, lenS, &a->s);
return 1;
}
int static secp256k1_ecdsa_sig_recompute(secp256k1_num_t *r2, const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_num_t *message) {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
if (secp256k1_num_is_neg(&sig->r) || secp256k1_num_is_neg(&sig->s))
return 0;
if (secp256k1_num_is_zero(&sig->r) || secp256k1_num_is_zero(&sig->s))
return 0;
if (secp256k1_num_cmp(&sig->r, &c->order) >= 0 || secp256k1_num_cmp(&sig->s, &c->order) >= 0)
return 0;
int ret = 0;
secp256k1_num_t sn, u1, u2;
secp256k1_num_init(&sn);
secp256k1_num_init(&u1);
secp256k1_num_init(&u2);
secp256k1_num_mod_inverse(&sn, &sig->s, &c->order);
secp256k1_num_mod_mul(&u1, &sn, message, &c->order);
secp256k1_num_mod_mul(&u2, &sn, &sig->r, &c->order);
secp256k1_gej_t pubkeyj; secp256k1_gej_set_ge(&pubkeyj, pubkey);
secp256k1_gej_t pr; secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
if (!secp256k1_gej_is_infinity(&pr)) {
secp256k1_fe_t xr; secp256k1_gej_get_x(&xr, &pr);
secp256k1_fe_normalize(&xr);
unsigned char xrb[32]; secp256k1_fe_get_b32(xrb, &xr);
secp256k1_num_set_bin(r2, xrb, 32);
secp256k1_num_mod(r2, &c->order);
ret = 1;
}
secp256k1_num_free(&sn);
secp256k1_num_free(&u1);
secp256k1_num_free(&u2);
return ret;
}
int static secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_num_t *message, int recid) {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
if (secp256k1_num_is_neg(&sig->r) || secp256k1_num_is_neg(&sig->s))
return 0;
if (secp256k1_num_is_zero(&sig->r) || secp256k1_num_is_zero(&sig->s))
return 0;
if (secp256k1_num_cmp(&sig->r, &c->order) >= 0 || secp256k1_num_cmp(&sig->s, &c->order) >= 0)
return 0;
secp256k1_num_t rx;
secp256k1_num_init(&rx);
secp256k1_num_copy(&rx, &sig->r);
if (recid & 2) {
secp256k1_num_add(&rx, &rx, &c->order);
if (secp256k1_num_cmp(&rx, &secp256k1_fe_consts->p) >= 0)
return 0;
}
unsigned char brx[32];
secp256k1_num_get_bin(brx, 32, &rx);
secp256k1_num_free(&rx);
secp256k1_fe_t fx;
secp256k1_fe_set_b32(&fx, brx);
secp256k1_ge_t x;
secp256k1_ge_set_xo(&x, &fx, recid & 1);
if (!secp256k1_ge_is_valid(&x))
return 0;
secp256k1_gej_t xj;
secp256k1_gej_set_ge(&xj, &x);
secp256k1_num_t rn, u1, u2;
secp256k1_num_init(&rn);
secp256k1_num_init(&u1);
secp256k1_num_init(&u2);
secp256k1_num_mod_inverse(&rn, &sig->r, &c->order);
secp256k1_num_mod_mul(&u1, &rn, message, &c->order);
secp256k1_num_sub(&u1, &c->order, &u1);
secp256k1_num_mod_mul(&u2, &rn, &sig->s, &c->order);
secp256k1_gej_t qj;
secp256k1_ecmult(&qj, &xj, &u2, &u1);
if (secp256k1_gej_is_infinity(&qj))
return 0;
secp256k1_ge_set_gej(pubkey, &qj);
secp256k1_num_free(&rn);
secp256k1_num_free(&u1);
secp256k1_num_free(&u2);
return 1;
}
int static secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_num_t *message) {
secp256k1_num_t r2;
secp256k1_num_init(&r2);
int ret = 0;
ret = secp256k1_ecdsa_sig_recompute(&r2, sig, pubkey, message) && secp256k1_num_cmp(&sig->r, &r2) == 0;
secp256k1_num_free(&r2);
return ret;
}
int static secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_num_t *seckey, const secp256k1_num_t *message, const secp256k1_num_t *nonce, int *recid) {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
secp256k1_gej_t rp;
secp256k1_ecmult_gen(&rp, nonce);
secp256k1_ge_t r;
secp256k1_ge_set_gej(&r, &rp);
unsigned char b[32];
secp256k1_fe_normalize(&r.x);
secp256k1_fe_normalize(&r.y);
secp256k1_fe_get_b32(b, &r.x);
secp256k1_num_set_bin(&sig->r, b, 32);
if (recid)
*recid = (secp256k1_num_cmp(&sig->r, &c->order) >= 0 ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
secp256k1_num_mod(&sig->r, &c->order);
secp256k1_num_t n;
secp256k1_num_init(&n);
secp256k1_num_mod_mul(&n, &sig->r, seckey, &c->order);
secp256k1_num_add(&n, &n, message);
secp256k1_num_mod(&n, &c->order);
secp256k1_num_mod_inverse(&sig->s, nonce, &c->order);
secp256k1_num_mod_mul(&sig->s, &sig->s, &n, &c->order);
secp256k1_num_free(&n);
if (secp256k1_num_is_zero(&sig->s))
return 0;
if (secp256k1_num_cmp(&sig->s, &c->half_order) > 0) {
secp256k1_num_sub(&sig->s, &c->order, &sig->s);
if (recid)
*recid ^= 1;
}
return 1;
}
void static secp256k1_ecdsa_sig_set_rs(secp256k1_ecdsa_sig_t *sig, const secp256k1_num_t *r, const secp256k1_num_t *s) {
secp256k1_num_copy(&sig->r, r);
secp256k1_num_copy(&sig->s, s);
}
void static secp256k1_ecdsa_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed) {
secp256k1_fe_normalize(&elem->x);
secp256k1_fe_normalize(&elem->y);
secp256k1_fe_get_b32(&pub[1], &elem->x);
if (compressed) {
*size = 33;
pub[0] = 0x02 | (secp256k1_fe_is_odd(&elem->y) ? 0x01 : 0x00);
} else {
*size = 65;
pub[0] = 0x04;
secp256k1_fe_get_b32(&pub[33], &elem->y);
}
}
int static secp256k1_ecdsa_privkey_parse(secp256k1_num_t *key, const unsigned char *privkey, int privkeylen) {
const unsigned char *end = privkey + privkeylen;
// sequence header
if (end < privkey+1 || *privkey != 0x30)
return 0;
privkey++;
// sequence length constructor
int lenb = 0;
if (end < privkey+1 || !(*privkey & 0x80))
return 0;
lenb = *privkey & ~0x80; privkey++;
if (lenb < 1 || lenb > 2)
return 0;
if (end < privkey+lenb)
return 0;
// sequence length
int len = 0;
len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
privkey += lenb;
if (end < privkey+len)
return 0;
// sequence element 0: version number (=1)
if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01)
return 0;
privkey += 3;
// sequence element 1: octet string, up to 32 bytes
if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1])
return 0;
secp256k1_num_set_bin(key, privkey+2, privkey[1]);
return 1;
}
int static secp256k1_ecdsa_privkey_serialize(unsigned char *privkey, int *privkeylen, const secp256k1_num_t *key, int compressed) {
secp256k1_gej_t rp;
secp256k1_ecmult_gen(&rp, key);
secp256k1_ge_t r;
secp256k1_ge_set_gej(&r, &rp);
if (compressed) {
static const unsigned char begin[] = {
0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_num_get_bin(ptr, 32, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
int pubkeylen = 0;
secp256k1_ecdsa_pubkey_serialize(&r, ptr, &pubkeylen, 1); ptr += pubkeylen;
*privkeylen = ptr - privkey;
} else {
static const unsigned char begin[] = {
0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_num_get_bin(ptr, 32, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
int pubkeylen = 0;
secp256k1_ecdsa_pubkey_serialize(&r, ptr, &pubkeylen, 0); ptr += pubkeylen;
*privkeylen = ptr - privkey;
}
return 1;
}
#endif

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crypto/secp256k1/secp256k1/src/impl/ecmult.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_ECMULT_IMPL_H_
#define _SECP256K1_ECMULT_IMPL_H_
#include "../num.h"
#include "../group.h"
#include "../ecmult.h"
// optimal for 128-bit and 256-bit exponents.
#define WINDOW_A 5
// larger numbers may result in slightly better performance, at the cost of
// exponentially larger precomputed tables. WINDOW_G == 14 results in 640 KiB.
#define WINDOW_G 14
/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
* pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
* 2^(w-2) entries.
*
* There are two versions of this function:
* - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
* fast to precompute, but slower to use in later additions.
* - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
* (much) slower to precompute, but a bit faster to use in later additions.
* To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
* G is constant, so it only needs to be done once in advance.
*/
void static secp256k1_ecmult_table_precomp_gej(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
pre[0] = *a;
secp256k1_gej_t d; secp256k1_gej_double(&d, &pre[0]);
for (int i=1; i<(1 << (w-2)); i++)
secp256k1_gej_add(&pre[i], &d, &pre[i-1]);
}
void static secp256k1_ecmult_table_precomp_ge(secp256k1_ge_t *pre, const secp256k1_ge_t *a, int w) {
pre[0] = *a;
secp256k1_gej_t x; secp256k1_gej_set_ge(&x, a);
secp256k1_gej_t d; secp256k1_gej_double(&d, &x);
for (int i=1; i<(1 << (w-2)); i++) {
secp256k1_gej_add_ge(&x, &d, &pre[i-1]);
secp256k1_ge_set_gej(&pre[i], &x);
}
}
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
#define ECMULT_TABLE_GET(r,pre,n,w,neg) do { \
assert(((n) & 1) == 1); \
assert((n) >= -((1 << ((w)-1)) - 1)); \
assert((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) \
*(r) = (pre)[((n)-1)/2]; \
else \
(neg)((r), &(pre)[(-(n)-1)/2]); \
} while(0)
#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_gej_neg)
#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg)
typedef struct {
secp256k1_ge_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; // odd multiples of the generator
secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; // odd multiples of 2^128*generator
secp256k1_ge_t prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
secp256k1_ge_t fin; // -(sum(prec[j][0], j=0..63))
} secp256k1_ecmult_consts_t;
static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
static void secp256k1_ecmult_start(void) {
if (secp256k1_ecmult_consts != NULL)
return;
secp256k1_ecmult_consts_t *ret = (secp256k1_ecmult_consts_t*)malloc(sizeof(secp256k1_ecmult_consts_t));
secp256k1_ecmult_consts = ret;
// get the generator
const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
// calculate 2^128*generator
secp256k1_gej_t g_128j; secp256k1_gej_set_ge(&g_128j, g);
for (int i=0; i<128; i++)
secp256k1_gej_double(&g_128j, &g_128j);
secp256k1_ge_t g_128; secp256k1_ge_set_gej(&g_128, &g_128j);
// precompute the tables with odd multiples
secp256k1_ecmult_table_precomp_ge(ret->pre_g, g, WINDOW_G);
secp256k1_ecmult_table_precomp_ge(ret->pre_g_128, &g_128, WINDOW_G);
// compute prec and fin
secp256k1_gej_t gg; secp256k1_gej_set_ge(&gg, g);
secp256k1_ge_t ad = *g;
secp256k1_gej_t fn; secp256k1_gej_set_infinity(&fn);
for (int j=0; j<64; j++) {
secp256k1_ge_set_gej(&ret->prec[j][0], &gg);
secp256k1_gej_add(&fn, &fn, &gg);
for (int i=1; i<16; i++) {
secp256k1_gej_add_ge(&gg, &gg, &ad);
secp256k1_ge_set_gej(&ret->prec[j][i], &gg);
}
ad = ret->prec[j][15];
}
secp256k1_ge_set_gej(&ret->fin, &fn);
secp256k1_ge_neg(&ret->fin, &ret->fin);
}
static void secp256k1_ecmult_stop(void) {
if (secp256k1_ecmult_consts == NULL)
return;
secp256k1_ecmult_consts_t *c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts;
free(c);
secp256k1_ecmult_consts = NULL;
}
/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
* with the following guarantees:
* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
* - the index of the highest non-zero entry in wnaf (=return value-1) is at most bits, where
* bits is the number of bits necessary to represent the absolute value of the input.
*/
static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_num_t *a, int w) {
int ret = 0;
int zeroes = 0;
secp256k1_num_t x;
secp256k1_num_init(&x);
secp256k1_num_copy(&x, a);
int sign = 1;
if (secp256k1_num_is_neg(&x)) {
sign = -1;
secp256k1_num_negate(&x);
}
while (!secp256k1_num_is_zero(&x)) {
while (!secp256k1_num_is_odd(&x)) {
zeroes++;
secp256k1_num_shift(&x, 1);
}
int word = secp256k1_num_shift(&x, w);
while (zeroes) {
wnaf[ret++] = 0;
zeroes--;
}
if (word & (1 << (w-1))) {
secp256k1_num_inc(&x);
wnaf[ret++] = sign * (word - (1 << w));
} else {
wnaf[ret++] = sign * word;
}
zeroes = w-1;
}
secp256k1_num_free(&x);
return ret;
}
void static secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *gn) {
secp256k1_num_t n;
secp256k1_num_init(&n);
secp256k1_num_copy(&n, gn);
const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
secp256k1_gej_set_ge(r, &c->prec[0][secp256k1_num_shift(&n, 4)]);
for (int j=1; j<64; j++)
secp256k1_gej_add_ge(r, r, &c->prec[j][secp256k1_num_shift(&n, 4)]);
secp256k1_num_free(&n);
secp256k1_gej_add_ge(r, r, &c->fin);
}
void static secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng) {
const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
secp256k1_num_t na_1, na_lam;
secp256k1_num_t ng_1, ng_128;
secp256k1_num_init(&na_1);
secp256k1_num_init(&na_lam);
secp256k1_num_init(&ng_1);
secp256k1_num_init(&ng_128);
// split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit)
secp256k1_gej_split_exp(&na_1, &na_lam, na);
// split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit)
secp256k1_num_split(&ng_1, &ng_128, ng, 128);
// build wnaf representation for na_1, na_lam, ng_1, ng_128
int wnaf_na_1[129]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
int wnaf_na_lam[129]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
int wnaf_ng_1[129]; int bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G);
int wnaf_ng_128[129]; int bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
// calculate a_lam = a*lambda
secp256k1_gej_t a_lam; secp256k1_gej_mul_lambda(&a_lam, a);
// calculate odd multiples of a and a_lam
secp256k1_gej_t pre_a_1[ECMULT_TABLE_SIZE(WINDOW_A)], pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ecmult_table_precomp_gej(pre_a_1, a, WINDOW_A);
secp256k1_ecmult_table_precomp_gej(pre_a_lam, &a_lam, WINDOW_A);
int bits = bits_na_1;
if (bits_na_lam > bits) bits = bits_na_lam;
if (bits_ng_1 > bits) bits = bits_ng_1;
if (bits_ng_128 > bits) bits = bits_ng_128;
secp256k1_gej_set_infinity(r);
secp256k1_gej_t tmpj;
secp256k1_ge_t tmpa;
for (int i=bits-1; i>=0; i--) {
secp256k1_gej_double(r, r);
int n;
if (i < bits_na_1 && (n = wnaf_na_1[i])) {
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_1, n, WINDOW_A);
secp256k1_gej_add(r, r, &tmpj);
}
if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
secp256k1_gej_add(r, r, &tmpj);
}
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
ECMULT_TABLE_GET_GE(&tmpa, c->pre_g, n, WINDOW_G);
secp256k1_gej_add_ge(r, r, &tmpa);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
ECMULT_TABLE_GET_GE(&tmpa, c->pre_g_128, n, WINDOW_G);
secp256k1_gej_add_ge(r, r, &tmpa);
}
}
secp256k1_num_free(&na_1);
secp256k1_num_free(&na_lam);
secp256k1_num_free(&ng_1);
secp256k1_num_free(&ng_128);
}
#endif

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crypto/secp256k1/secp256k1/src/impl/field.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_IMPL_H_
#define _SECP256K1_FIELD_IMPL_H_
#if defined(USE_FIELD_GMP)
#include "field_gmp.h"
#elif defined(USE_FIELD_10X26)
#include "field_10x26.h"
#elif defined(USE_FIELD_5X52)
#include "field_5x52.h"
#elif defined(USE_FIELD_5X64)
#include "field_5x64.h"
#else
#error "Please select field implementation"
#endif
void static secp256k1_fe_get_hex(char *r, int *rlen, const secp256k1_fe_t *a) {
if (*rlen < 65) {
*rlen = 65;
return;
}
*rlen = 65;
unsigned char tmp[32];
secp256k1_fe_t b = *a;
secp256k1_fe_normalize(&b);
secp256k1_fe_get_b32(tmp, &b);
for (int i=0; i<32; i++) {
static const char *c = "0123456789ABCDEF";
r[2*i] = c[(tmp[i] >> 4) & 0xF];
r[2*i+1] = c[(tmp[i]) & 0xF];
}
r[64] = 0x00;
}
void static secp256k1_fe_set_hex(secp256k1_fe_t *r, const char *a, int alen) {
unsigned char tmp[32] = {};
static const int cvt[256] = {0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 1, 2, 3, 4, 5, 6,7,8,9,0,0,0,0,0,0,
0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0};
for (int i=0; i<32; i++) {
if (alen > i*2)
tmp[32 - alen/2 + i] = (cvt[(unsigned char)a[2*i]] << 4) + cvt[(unsigned char)a[2*i+1]];
}
secp256k1_fe_set_b32(r, tmp);
}
void static secp256k1_fe_sqrt(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
// calculate a^p, with p={15,780,1022,1023}
secp256k1_fe_t a2; secp256k1_fe_sqr(&a2, a);
secp256k1_fe_t a3; secp256k1_fe_mul(&a3, &a2, a);
secp256k1_fe_t a6; secp256k1_fe_sqr(&a6, &a3);
secp256k1_fe_t a12; secp256k1_fe_sqr(&a12, &a6);
secp256k1_fe_t a15; secp256k1_fe_mul(&a15, &a12, &a3);
secp256k1_fe_t a30; secp256k1_fe_sqr(&a30, &a15);
secp256k1_fe_t a60; secp256k1_fe_sqr(&a60, &a30);
secp256k1_fe_t a120; secp256k1_fe_sqr(&a120, &a60);
secp256k1_fe_t a240; secp256k1_fe_sqr(&a240, &a120);
secp256k1_fe_t a255; secp256k1_fe_mul(&a255, &a240, &a15);
secp256k1_fe_t a510; secp256k1_fe_sqr(&a510, &a255);
secp256k1_fe_t a750; secp256k1_fe_mul(&a750, &a510, &a240);
secp256k1_fe_t a780; secp256k1_fe_mul(&a780, &a750, &a30);
secp256k1_fe_t a1020; secp256k1_fe_sqr(&a1020, &a510);
secp256k1_fe_t a1022; secp256k1_fe_mul(&a1022, &a1020, &a2);
secp256k1_fe_t a1023; secp256k1_fe_mul(&a1023, &a1022, a);
secp256k1_fe_t x = a15;
for (int i=0; i<21; i++) {
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1023);
}
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1022);
for (int i=0; i<2; i++) {
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1023);
}
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(r, &x, &a780);
}
void static secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
// calculate a^p, with p={45,63,1019,1023}
secp256k1_fe_t a2; secp256k1_fe_sqr(&a2, a);
secp256k1_fe_t a3; secp256k1_fe_mul(&a3, &a2, a);
secp256k1_fe_t a4; secp256k1_fe_sqr(&a4, &a2);
secp256k1_fe_t a5; secp256k1_fe_mul(&a5, &a4, a);
secp256k1_fe_t a10; secp256k1_fe_sqr(&a10, &a5);
secp256k1_fe_t a11; secp256k1_fe_mul(&a11, &a10, a);
secp256k1_fe_t a21; secp256k1_fe_mul(&a21, &a11, &a10);
secp256k1_fe_t a42; secp256k1_fe_sqr(&a42, &a21);
secp256k1_fe_t a45; secp256k1_fe_mul(&a45, &a42, &a3);
secp256k1_fe_t a63; secp256k1_fe_mul(&a63, &a42, &a21);
secp256k1_fe_t a126; secp256k1_fe_sqr(&a126, &a63);
secp256k1_fe_t a252; secp256k1_fe_sqr(&a252, &a126);
secp256k1_fe_t a504; secp256k1_fe_sqr(&a504, &a252);
secp256k1_fe_t a1008; secp256k1_fe_sqr(&a1008, &a504);
secp256k1_fe_t a1019; secp256k1_fe_mul(&a1019, &a1008, &a11);
secp256k1_fe_t a1023; secp256k1_fe_mul(&a1023, &a1019, &a4);
secp256k1_fe_t x = a63;
for (int i=0; i<21; i++) {
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1023);
}
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1019);
for (int i=0; i<2; i++) {
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(&x, &x, &a1023);
}
for (int j=0; j<10; j++) secp256k1_fe_sqr(&x, &x);
secp256k1_fe_mul(r, &x, &a45);
}
void static secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#if defined(USE_FIELD_INV_BUILTIN)
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
unsigned char b[32];
secp256k1_fe_t c = *a;
secp256k1_fe_normalize(&c);
secp256k1_fe_get_b32(b, &c);
secp256k1_num_t n;
secp256k1_num_init(&n);
secp256k1_num_set_bin(&n, b, 32);
secp256k1_num_mod_inverse(&n, &n, &secp256k1_fe_consts->p);
secp256k1_num_get_bin(b, 32, &n);
secp256k1_num_free(&n);
secp256k1_fe_set_b32(r, b);
#else
#error "Please select field inverse implementation"
#endif
}
void static secp256k1_fe_start(void) {
static const unsigned char secp256k1_fe_consts_p[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
};
if (secp256k1_fe_consts == NULL) {
secp256k1_fe_inner_start();
secp256k1_fe_consts_t *ret = (secp256k1_fe_consts_t*)malloc(sizeof(secp256k1_fe_consts_t));
secp256k1_num_init(&ret->p);
secp256k1_num_set_bin(&ret->p, secp256k1_fe_consts_p, sizeof(secp256k1_fe_consts_p));
secp256k1_fe_consts = ret;
}
}
void static secp256k1_fe_stop(void) {
if (secp256k1_fe_consts != NULL) {
secp256k1_fe_consts_t *c = (secp256k1_fe_consts_t*)secp256k1_fe_consts;
secp256k1_num_free(&c->p);
free((void*)c);
secp256k1_fe_consts = NULL;
secp256k1_fe_inner_stop();
}
}
#endif

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crypto/secp256k1/secp256k1/src/impl/field_10x26.h
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@ -1,487 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#include <stdio.h>
#include <assert.h>
#include <string.h>
#include "../num.h"
#include "../field.h"
void static secp256k1_fe_inner_start(void) {}
void static secp256k1_fe_inner_stop(void) {}
void static secp256k1_fe_normalize(secp256k1_fe_t *r) {
// fog("normalize in: ", r);
uint32_t c;
c = r->n[0];
uint32_t t0 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[1];
uint32_t t1 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[2];
uint32_t t2 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[3];
uint32_t t3 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[4];
uint32_t t4 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[5];
uint32_t t5 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[6];
uint32_t t6 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[7];
uint32_t t7 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[8];
uint32_t t8 = c & 0x3FFFFFFUL;
c = (c >> 26) + r->n[9];
uint32_t t9 = c & 0x03FFFFFUL;
c >>= 22;
/* r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
fog(" tm1: ", r);
fprintf(stderr, "out c= %08lx\n", (unsigned long)c);*/
// The following code will not modify the t's if c is initially 0.
uint32_t d = c * 0x3D1UL + t0;
t0 = d & 0x3FFFFFFULL;
d = (d >> 26) + t1 + c*0x40;
t1 = d & 0x3FFFFFFULL;
d = (d >> 26) + t2;
t2 = d & 0x3FFFFFFULL;
d = (d >> 26) + t3;
t3 = d & 0x3FFFFFFULL;
d = (d >> 26) + t4;
t4 = d & 0x3FFFFFFULL;
d = (d >> 26) + t5;
t5 = d & 0x3FFFFFFULL;
d = (d >> 26) + t6;
t6 = d & 0x3FFFFFFULL;
d = (d >> 26) + t7;
t7 = d & 0x3FFFFFFULL;
d = (d >> 26) + t8;
t8 = d & 0x3FFFFFFULL;
d = (d >> 26) + t9;
t9 = d & 0x03FFFFFULL;
assert((d >> 22) == 0);
/* r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
fog(" tm2: ", r); */
// Subtract p if result >= p
uint64_t low = ((uint64_t)t1 << 26) | t0;
uint64_t mask = -(int64_t)((t9 < 0x03FFFFFUL) | (t8 < 0x3FFFFFFUL) | (t7 < 0x3FFFFFFUL) | (t6 < 0x3FFFFFFUL) | (t5 < 0x3FFFFFFUL) | (t4 < 0x3FFFFFFUL) | (t3 < 0x3FFFFFFUL) | (t2 < 0x3FFFFFFUL) | (low < 0xFFFFEFFFFFC2FULL));
t9 &= mask;
t8 &= mask;
t7 &= mask;
t6 &= mask;
t5 &= mask;
t4 &= mask;
t3 &= mask;
t2 &= mask;
low -= (~mask & 0xFFFFEFFFFFC2FULL);
// push internal variables back
r->n[0] = low & 0x3FFFFFFUL; r->n[1] = (low >> 26) & 0x3FFFFFFUL; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
/* fog(" out: ", r);*/
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
// TODO: not constant time!
int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return (a->n[0] == 0 && a->n[1] == 0 && a->n[2] == 0 && a->n[3] == 0 && a->n[4] == 0 && a->n[5] == 0 && a->n[6] == 0 && a->n[7] == 0 && a->n[8] == 0 && a->n[9] == 0);
}
int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return a->n[0] & 1;
}
// TODO: not constant time!
int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
#ifdef VERIFY
assert(a->normalized);
assert(b->normalized);
#endif
return (a->n[0] == b->n[0] && a->n[1] == b->n[1] && a->n[2] == b->n[2] && a->n[3] == b->n[3] && a->n[4] == b->n[4] &&
a->n[5] == b->n[5] && a->n[6] == b->n[6] && a->n[7] == b->n[7] && a->n[8] == b->n[8] && a->n[9] == b->n[9]);
}
void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
for (int i=0; i<32; i++) {
for (int j=0; j<4; j++) {
int limb = (8*i+2*j)/26;
int shift = (8*i+2*j)%26;
r->n[limb] |= (uint32_t)((a[31-i] >> (2*j)) & 0x3) << shift;
}
}
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
for (int i=0; i<32; i++) {
int c = 0;
for (int j=0; j<4; j++) {
int limb = (8*i+2*j)/26;
int shift = (8*i+2*j)%26;
c |= ((a->n[limb] >> shift) & 0x3) << (2 * j);
}
r[31-i] = c;
}
}
void static inline secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
#ifdef VERIFY
assert(a->magnitude <= m);
r->magnitude = m + 1;
r->normalized = 0;
#endif
r->n[0] = 0x3FFFC2FUL * (m + 1) - a->n[0];
r->n[1] = 0x3FFFFBFUL * (m + 1) - a->n[1];
r->n[2] = 0x3FFFFFFUL * (m + 1) - a->n[2];
r->n[3] = 0x3FFFFFFUL * (m + 1) - a->n[3];
r->n[4] = 0x3FFFFFFUL * (m + 1) - a->n[4];
r->n[5] = 0x3FFFFFFUL * (m + 1) - a->n[5];
r->n[6] = 0x3FFFFFFUL * (m + 1) - a->n[6];
r->n[7] = 0x3FFFFFFUL * (m + 1) - a->n[7];
r->n[8] = 0x3FFFFFFUL * (m + 1) - a->n[8];
r->n[9] = 0x03FFFFFUL * (m + 1) - a->n[9];
}
void static inline secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
#ifdef VERIFY
r->magnitude *= a;
r->normalized = 0;
#endif
r->n[0] *= a;
r->n[1] *= a;
r->n[2] *= a;
r->n[3] *= a;
r->n[4] *= a;
r->n[5] *= a;
r->n[6] *= a;
r->n[7] *= a;
r->n[8] *= a;
r->n[9] *= a;
}
void static inline secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
r->magnitude += a->magnitude;
r->normalized = 0;
#endif
r->n[0] += a->n[0];
r->n[1] += a->n[1];
r->n[2] += a->n[2];
r->n[3] += a->n[3];
r->n[4] += a->n[4];
r->n[5] += a->n[5];
r->n[6] += a->n[6];
r->n[7] += a->n[7];
r->n[8] += a->n[8];
r->n[9] += a->n[9];
}
void static inline secp256k1_fe_mul_inner(const uint32_t *a, const uint32_t *b, uint32_t *r) {
uint64_t c = (uint64_t)a[0] * b[0];
uint32_t t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[1] +
(uint64_t)a[1] * b[0];
uint32_t t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[2] +
(uint64_t)a[1] * b[1] +
(uint64_t)a[2] * b[0];
uint32_t t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[3] +
(uint64_t)a[1] * b[2] +
(uint64_t)a[2] * b[1] +
(uint64_t)a[3] * b[0];
uint32_t t3 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[4] +
(uint64_t)a[1] * b[3] +
(uint64_t)a[2] * b[2] +
(uint64_t)a[3] * b[1] +
(uint64_t)a[4] * b[0];
uint32_t t4 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[5] +
(uint64_t)a[1] * b[4] +
(uint64_t)a[2] * b[3] +
(uint64_t)a[3] * b[2] +
(uint64_t)a[4] * b[1] +
(uint64_t)a[5] * b[0];
uint32_t t5 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[6] +
(uint64_t)a[1] * b[5] +
(uint64_t)a[2] * b[4] +
(uint64_t)a[3] * b[3] +
(uint64_t)a[4] * b[2] +
(uint64_t)a[5] * b[1] +
(uint64_t)a[6] * b[0];
uint32_t t6 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[7] +
(uint64_t)a[1] * b[6] +
(uint64_t)a[2] * b[5] +
(uint64_t)a[3] * b[4] +
(uint64_t)a[4] * b[3] +
(uint64_t)a[5] * b[2] +
(uint64_t)a[6] * b[1] +
(uint64_t)a[7] * b[0];
uint32_t t7 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[8] +
(uint64_t)a[1] * b[7] +
(uint64_t)a[2] * b[6] +
(uint64_t)a[3] * b[5] +
(uint64_t)a[4] * b[4] +
(uint64_t)a[5] * b[3] +
(uint64_t)a[6] * b[2] +
(uint64_t)a[7] * b[1] +
(uint64_t)a[8] * b[0];
uint32_t t8 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[0] * b[9] +
(uint64_t)a[1] * b[8] +
(uint64_t)a[2] * b[7] +
(uint64_t)a[3] * b[6] +
(uint64_t)a[4] * b[5] +
(uint64_t)a[5] * b[4] +
(uint64_t)a[6] * b[3] +
(uint64_t)a[7] * b[2] +
(uint64_t)a[8] * b[1] +
(uint64_t)a[9] * b[0];
uint32_t t9 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[1] * b[9] +
(uint64_t)a[2] * b[8] +
(uint64_t)a[3] * b[7] +
(uint64_t)a[4] * b[6] +
(uint64_t)a[5] * b[5] +
(uint64_t)a[6] * b[4] +
(uint64_t)a[7] * b[3] +
(uint64_t)a[8] * b[2] +
(uint64_t)a[9] * b[1];
uint32_t t10 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[2] * b[9] +
(uint64_t)a[3] * b[8] +
(uint64_t)a[4] * b[7] +
(uint64_t)a[5] * b[6] +
(uint64_t)a[6] * b[5] +
(uint64_t)a[7] * b[4] +
(uint64_t)a[8] * b[3] +
(uint64_t)a[9] * b[2];
uint32_t t11 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[3] * b[9] +
(uint64_t)a[4] * b[8] +
(uint64_t)a[5] * b[7] +
(uint64_t)a[6] * b[6] +
(uint64_t)a[7] * b[5] +
(uint64_t)a[8] * b[4] +
(uint64_t)a[9] * b[3];
uint32_t t12 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[4] * b[9] +
(uint64_t)a[5] * b[8] +
(uint64_t)a[6] * b[7] +
(uint64_t)a[7] * b[6] +
(uint64_t)a[8] * b[5] +
(uint64_t)a[9] * b[4];
uint32_t t13 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[5] * b[9] +
(uint64_t)a[6] * b[8] +
(uint64_t)a[7] * b[7] +
(uint64_t)a[8] * b[6] +
(uint64_t)a[9] * b[5];
uint32_t t14 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[6] * b[9] +
(uint64_t)a[7] * b[8] +
(uint64_t)a[8] * b[7] +
(uint64_t)a[9] * b[6];
uint32_t t15 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[7] * b[9] +
(uint64_t)a[8] * b[8] +
(uint64_t)a[9] * b[7];
uint32_t t16 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[8] * b[9] +
(uint64_t)a[9] * b[8];
uint32_t t17 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[9] * b[9];
uint32_t t18 = c & 0x3FFFFFFUL; c = c >> 26;
uint32_t t19 = c;
c = t0 + (uint64_t)t10 * 0x3D10UL;
t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t1 + (uint64_t)t10*0x400UL + (uint64_t)t11 * 0x3D10UL;
t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t2 + (uint64_t)t11*0x400UL + (uint64_t)t12 * 0x3D10UL;
t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t3 + (uint64_t)t12*0x400UL + (uint64_t)t13 * 0x3D10UL;
r[3] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t4 + (uint64_t)t13*0x400UL + (uint64_t)t14 * 0x3D10UL;
r[4] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t5 + (uint64_t)t14*0x400UL + (uint64_t)t15 * 0x3D10UL;
r[5] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t6 + (uint64_t)t15*0x400UL + (uint64_t)t16 * 0x3D10UL;
r[6] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t7 + (uint64_t)t16*0x400UL + (uint64_t)t17 * 0x3D10UL;
r[7] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t8 + (uint64_t)t17*0x400UL + (uint64_t)t18 * 0x3D10UL;
r[8] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t9 + (uint64_t)t18*0x400UL + (uint64_t)t19 * 0x1000003D10ULL;
r[9] = c & 0x03FFFFFUL; c = c >> 22;
uint64_t d = t0 + c * 0x3D1UL;
r[0] = d & 0x3FFFFFFUL; d = d >> 26;
d = d + t1 + c*0x40;
r[1] = d & 0x3FFFFFFUL; d = d >> 26;
r[2] = t2 + d;
}
void static inline secp256k1_fe_sqr_inner(const uint32_t *a, uint32_t *r) {
uint64_t c = (uint64_t)a[0] * a[0];
uint32_t t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[1];
uint32_t t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[2] +
(uint64_t)a[1] * a[1];
uint32_t t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[3] +
(uint64_t)(a[1]*2) * a[2];
uint32_t t3 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[4] +
(uint64_t)(a[1]*2) * a[3] +
(uint64_t)a[2] * a[2];
uint32_t t4 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[5] +
(uint64_t)(a[1]*2) * a[4] +
(uint64_t)(a[2]*2) * a[3];
uint32_t t5 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[6] +
(uint64_t)(a[1]*2) * a[5] +
(uint64_t)(a[2]*2) * a[4] +
(uint64_t)a[3] * a[3];
uint32_t t6 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[7] +
(uint64_t)(a[1]*2) * a[6] +
(uint64_t)(a[2]*2) * a[5] +
(uint64_t)(a[3]*2) * a[4];
uint32_t t7 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[8] +
(uint64_t)(a[1]*2) * a[7] +
(uint64_t)(a[2]*2) * a[6] +
(uint64_t)(a[3]*2) * a[5] +
(uint64_t)a[4] * a[4];
uint32_t t8 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[0]*2) * a[9] +
(uint64_t)(a[1]*2) * a[8] +
(uint64_t)(a[2]*2) * a[7] +
(uint64_t)(a[3]*2) * a[6] +
(uint64_t)(a[4]*2) * a[5];
uint32_t t9 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[1]*2) * a[9] +
(uint64_t)(a[2]*2) * a[8] +
(uint64_t)(a[3]*2) * a[7] +
(uint64_t)(a[4]*2) * a[6] +
(uint64_t)a[5] * a[5];
uint32_t t10 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[2]*2) * a[9] +
(uint64_t)(a[3]*2) * a[8] +
(uint64_t)(a[4]*2) * a[7] +
(uint64_t)(a[5]*2) * a[6];
uint32_t t11 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[3]*2) * a[9] +
(uint64_t)(a[4]*2) * a[8] +
(uint64_t)(a[5]*2) * a[7] +
(uint64_t)a[6] * a[6];
uint32_t t12 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[4]*2) * a[9] +
(uint64_t)(a[5]*2) * a[8] +
(uint64_t)(a[6]*2) * a[7];
uint32_t t13 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[5]*2) * a[9] +
(uint64_t)(a[6]*2) * a[8] +
(uint64_t)a[7] * a[7];
uint32_t t14 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[6]*2) * a[9] +
(uint64_t)(a[7]*2) * a[8];
uint32_t t15 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[7]*2) * a[9] +
(uint64_t)a[8] * a[8];
uint32_t t16 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)(a[8]*2) * a[9];
uint32_t t17 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + (uint64_t)a[9] * a[9];
uint32_t t18 = c & 0x3FFFFFFUL; c = c >> 26;
uint32_t t19 = c;
c = t0 + (uint64_t)t10 * 0x3D10UL;
t0 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t1 + (uint64_t)t10*0x400UL + (uint64_t)t11 * 0x3D10UL;
t1 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t2 + (uint64_t)t11*0x400UL + (uint64_t)t12 * 0x3D10UL;
t2 = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t3 + (uint64_t)t12*0x400UL + (uint64_t)t13 * 0x3D10UL;
r[3] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t4 + (uint64_t)t13*0x400UL + (uint64_t)t14 * 0x3D10UL;
r[4] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t5 + (uint64_t)t14*0x400UL + (uint64_t)t15 * 0x3D10UL;
r[5] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t6 + (uint64_t)t15*0x400UL + (uint64_t)t16 * 0x3D10UL;
r[6] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t7 + (uint64_t)t16*0x400UL + (uint64_t)t17 * 0x3D10UL;
r[7] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t8 + (uint64_t)t17*0x400UL + (uint64_t)t18 * 0x3D10UL;
r[8] = c & 0x3FFFFFFUL; c = c >> 26;
c = c + t9 + (uint64_t)t18*0x400UL + (uint64_t)t19 * 0x1000003D10ULL;
r[9] = c & 0x03FFFFFUL; c = c >> 22;
uint64_t d = t0 + c * 0x3D1UL;
r[0] = d & 0x3FFFFFFUL; d = d >> 26;
d = d + t1 + c*0x40;
r[1] = d & 0x3FFFFFFUL; d = d >> 26;
r[2] = t2 + d;
}
void static secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
#ifdef VERIFY
assert(a->magnitude <= 8);
assert(b->magnitude <= 8);
r->magnitude = 1;
r->normalized = 0;
#endif
secp256k1_fe_mul_inner(a->n, b->n, r->n);
}
void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->magnitude <= 8);
r->magnitude = 1;
r->normalized = 0;
#endif
secp256k1_fe_sqr_inner(a->n, r->n);
}
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#include <assert.h>
#include <string.h>
#include "../num.h"
#include "../field.h"
#if defined(USE_FIELD_5X52_ASM)
#include "field_5x52_asm.h"
#elif defined(USE_FIELD_5X52_INT128)
#include "field_5x52_int128.h"
#else
#error "Please select field_5x52 implementation"
#endif
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
* represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
* each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
* is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
* accept any input with magnitude at most M, and have different rules for propagating magnitude to their
* output.
*/
void static secp256k1_fe_inner_start(void) {}
void static secp256k1_fe_inner_stop(void) {}
void static secp256k1_fe_normalize(secp256k1_fe_t *r) {
uint64_t c;
c = r->n[0];
uint64_t t0 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + r->n[1];
uint64_t t1 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + r->n[2];
uint64_t t2 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + r->n[3];
uint64_t t3 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + r->n[4];
uint64_t t4 = c & 0x0FFFFFFFFFFFFULL;
c >>= 48;
// The following code will not modify the t's if c is initially 0.
c = c * 0x1000003D1ULL + t0;
t0 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + t1;
t1 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + t2;
t2 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + t3;
t3 = c & 0xFFFFFFFFFFFFFULL;
c = (c >> 52) + t4;
t4 = c & 0x0FFFFFFFFFFFFULL;
assert((c >> 48) == 0);
// Subtract p if result >= p
uint64_t mask = -(int64_t)((t4 < 0xFFFFFFFFFFFFULL) | (t3 < 0xFFFFFFFFFFFFFULL) | (t2 < 0xFFFFFFFFFFFFFULL) | (t1 < 0xFFFFFFFFFFFFFULL) | (t0 < 0xFFFFEFFFFFC2FULL));
t4 &= mask;
t3 &= mask;
t2 &= mask;
t1 &= mask;
t0 -= (~mask & 0xFFFFEFFFFFC2FULL);
// push internal variables back
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
// TODO: not constant time!
int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return (a->n[0] == 0 && a->n[1] == 0 && a->n[2] == 0 && a->n[3] == 0 && a->n[4] == 0);
}
int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return a->n[0] & 1;
}
// TODO: not constant time!
int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
#ifdef VERIFY
assert(a->normalized);
assert(b->normalized);
#endif
return (a->n[0] == b->n[0] && a->n[1] == b->n[1] && a->n[2] == b->n[2] && a->n[3] == b->n[3] && a->n[4] == b->n[4]);
}
void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
for (int i=0; i<32; i++) {
for (int j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
}
}
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
for (int i=0; i<32; i++) {
int c = 0;
for (int j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
}
r[31-i] = c;
}
}
void static inline secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
#ifdef VERIFY
assert(a->magnitude <= m);
r->magnitude = m + 1;
r->normalized = 0;
#endif
r->n[0] = 0xFFFFEFFFFFC2FULL * (m + 1) - a->n[0];
r->n[1] = 0xFFFFFFFFFFFFFULL * (m + 1) - a->n[1];
r->n[2] = 0xFFFFFFFFFFFFFULL * (m + 1) - a->n[2];
r->n[3] = 0xFFFFFFFFFFFFFULL * (m + 1) - a->n[3];
r->n[4] = 0x0FFFFFFFFFFFFULL * (m + 1) - a->n[4];
}
void static inline secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
#ifdef VERIFY
r->magnitude *= a;
r->normalized = 0;
#endif
r->n[0] *= a;
r->n[1] *= a;
r->n[2] *= a;
r->n[3] *= a;
r->n[4] *= a;
}
void static inline secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
r->magnitude += a->magnitude;
r->normalized = 0;
#endif
r->n[0] += a->n[0];
r->n[1] += a->n[1];
r->n[2] += a->n[2];
r->n[3] += a->n[3];
r->n[4] += a->n[4];
}
void static secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
#ifdef VERIFY
assert(a->magnitude <= 8);
assert(b->magnitude <= 8);
r->magnitude = 1;
r->normalized = 0;
#endif
secp256k1_fe_mul_inner(a->n, b->n, r->n);
}
void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->magnitude <= 8);
r->magnitude = 1;
r->normalized = 0;
#endif
secp256k1_fe_sqr_inner(a->n, r->n);
}
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
void __attribute__ ((sysv_abi)) secp256k1_fe_mul_inner(const uint64_t *a, const uint64_t *b, uint64_t *r);
void __attribute__ ((sysv_abi)) secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t *r);
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
#include <stdint.h>
void static inline secp256k1_fe_mul_inner(const uint64_t *a, const uint64_t *b, uint64_t *r) {
__int128 c = (__int128)a[0] * b[0];
uint64_t t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0FFFFFFFFFFFFFE0
c = c + (__int128)a[0] * b[1] +
(__int128)a[1] * b[0];
uint64_t t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 20000000000000BF
c = c + (__int128)a[0] * b[2] +
(__int128)a[1] * b[1] +
(__int128)a[2] * b[0];
uint64_t t2 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 30000000000001A0
c = c + (__int128)a[0] * b[3] +
(__int128)a[1] * b[2] +
(__int128)a[2] * b[1] +
(__int128)a[3] * b[0];
uint64_t t3 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 4000000000000280
c = c + (__int128)a[0] * b[4] +
(__int128)a[1] * b[3] +
(__int128)a[2] * b[2] +
(__int128)a[3] * b[1] +
(__int128)a[4] * b[0];
uint64_t t4 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 320000000000037E
c = c + (__int128)a[1] * b[4] +
(__int128)a[2] * b[3] +
(__int128)a[3] * b[2] +
(__int128)a[4] * b[1];
uint64_t t5 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 22000000000002BE
c = c + (__int128)a[2] * b[4] +
(__int128)a[3] * b[3] +
(__int128)a[4] * b[2];
uint64_t t6 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 12000000000001DE
c = c + (__int128)a[3] * b[4] +
(__int128)a[4] * b[3];
uint64_t t7 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 02000000000000FE
c = c + (__int128)a[4] * b[4];
uint64_t t8 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 001000000000001E
uint64_t t9 = c;
c = t0 + (__int128)t5 * 0x1000003D10ULL;
t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t1 + (__int128)t6 * 0x1000003D10ULL;
t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t2 + (__int128)t7 * 0x1000003D10ULL;
r[2] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t3 + (__int128)t8 * 0x1000003D10ULL;
r[3] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t4 + (__int128)t9 * 0x1000003D10ULL;
r[4] = c & 0x0FFFFFFFFFFFFULL; c = c >> 48; // c max 000001000003D110
c = t0 + (__int128)c * 0x1000003D1ULL;
r[0] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 1000008
r[1] = t1 + c;
}
void static inline secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t *r) {
__int128 c = (__int128)a[0] * a[0];
uint64_t t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0FFFFFFFFFFFFFE0
c = c + (__int128)(a[0]*2) * a[1];
uint64_t t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 20000000000000BF
c = c + (__int128)(a[0]*2) * a[2] +
(__int128)a[1] * a[1];
uint64_t t2 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 30000000000001A0
c = c + (__int128)(a[0]*2) * a[3] +
(__int128)(a[1]*2) * a[2];
uint64_t t3 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 4000000000000280
c = c + (__int128)(a[0]*2) * a[4] +
(__int128)(a[1]*2) * a[3] +
(__int128)a[2] * a[2];
uint64_t t4 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 320000000000037E
c = c + (__int128)(a[1]*2) * a[4] +
(__int128)(a[2]*2) * a[3];
uint64_t t5 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 22000000000002BE
c = c + (__int128)(a[2]*2) * a[4] +
(__int128)a[3] * a[3];
uint64_t t6 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 12000000000001DE
c = c + (__int128)(a[3]*2) * a[4];
uint64_t t7 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 02000000000000FE
c = c + (__int128)a[4] * a[4];
uint64_t t8 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 001000000000001E
uint64_t t9 = c;
c = t0 + (__int128)t5 * 0x1000003D10ULL;
t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t1 + (__int128)t6 * 0x1000003D10ULL;
t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t2 + (__int128)t7 * 0x1000003D10ULL;
r[2] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t3 + (__int128)t8 * 0x1000003D10ULL;
r[3] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t4 + (__int128)t9 * 0x1000003D10ULL;
r[4] = c & 0x0FFFFFFFFFFFFULL; c = c >> 48; // c max 000001000003D110
c = t0 + (__int128)c * 0x1000003D1ULL;
r[0] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 1000008
r[1] = t1 + c;
}
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#include <assert.h>
#include <string.h>
#include "../num.h"
#include "../field.h"
#include <stdio.h>
#include "field_5x64_asm.h"
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
* represented as 4 uint64_t's in base 2^64, and one overflow uint64_t.
*/
#define FULL_LIMB (0xFFFFFFFFFFFFFFFFULL)
#define LAST_LIMB (0xFFFFFFFEFFFFFC2FULL)
#define COMP_LIMB (0x00000001000003D1ULL)
void static secp256k1_fe_inner_start(void) {}
void static secp256k1_fe_inner_stop(void) {}
void static secp256k1_fe_reduce(secp256k1_fe_t *r) {
unsigned __int128 c = (unsigned __int128)r->n[4] * COMP_LIMB + r->n[0];
uint64_t n0 = c;
c = (c >> 64) + r->n[1];
uint64_t n1 = c;
c = (c >> 64) + r->n[2];
r->n[2] = c;
c = (c >> 64) + r->n[3];
r->n[3] = c;
c = (c >> 64) * COMP_LIMB + n0;
r->n[0] = c;
r->n[1] = n1 + (c >> 64);
assert(r->n[1] >= n1);
r->n[4] = 0;
#ifdef VERIFY
r->reduced = 1;
#endif
}
void static secp256k1_fe_normalize(secp256k1_fe_t *r) {
secp256k1_fe_reduce(r);
// Subtract p if result >= p
uint64_t mask = -(int64_t)((r->n[0] < LAST_LIMB) | (r->n[1] != ~0ULL) | (r->n[2] != ~0ULL) | (r->n[3] != ~0ULL));
r->n[0] -= (~mask & LAST_LIMB);
r->n[1] &= mask;
r->n[2] &= mask;
r->n[3] &= mask;
assert(r->n[4] == 0);
#ifdef VERIFY
r->normalized = 1;
#endif
}
void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
#ifdef VERIFY
r->reduced = 1;
r->normalized = 1;
#endif
}
// TODO: not constant time!
int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return (a->n[0] == 0 && a->n[1] == 0 && a->n[2] == 0 && a->n[3] == 0);
}
int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
return a->n[0] & 1;
}
// TODO: not constant time!
int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
#ifdef VERIFY
assert(a->normalized);
assert(b->normalized);
#endif
return (a->n[0] == b->n[0] && a->n[1] == b->n[1] && a->n[2] == b->n[2] && a->n[3] == b->n[3]);
}
void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
for (int i=0; i<32; i++) {
r->n[i/8] |= (uint64_t)a[31-i] << (i&7)*8;
}
#ifdef VERIFY
r->reduced = 1;
r->normalized = 0;
#endif
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
assert(a->normalized);
#endif
for (int i=0; i<32; i++) {
r[31-i] = a->n[i/8] >> ((i&7)*8);
}
}
void static inline secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *ac, int m) {
secp256k1_fe_t a = *ac;
secp256k1_fe_reduce(&a);
unsigned __int128 c = (unsigned __int128)(~a.n[0]) + LAST_LIMB + 1;
r->n[0] = c;
c = (c >> 64) + (~a.n[1]) + FULL_LIMB;
r->n[1] = c;
c = (c >> 64) + (~a.n[2]) + FULL_LIMB;
r->n[2] = c;
c = (c >> 64) + (~a.n[3]) + FULL_LIMB;
r->n[3] = c;
r->n[4] = 0;
#ifdef VERIFY
r->reduced = 1;
r->normalized = 0;
#endif
}
void static inline secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
#ifdef VERIFY
r->reduced = 0;
r->normalized = 0;
#endif
unsigned __int128 c = (unsigned __int128)r->n[0] * a;
r->n[0] = c;
c = (c >> 64) + (unsigned __int128)r->n[1] * a;
r->n[1] = c;
c = (c >> 64) + (unsigned __int128)r->n[2] * a;
r->n[2] = c;
c = (c >> 64) + (unsigned __int128)r->n[3] * a;
r->n[3] = c;
c = (c >> 64) + (unsigned __int128)r->n[4] * a;
r->n[4] = c;
}
void static inline secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#ifdef VERIFY
r->reduced = 0;
r->normalized = 0;
#endif
unsigned __int128 c = (unsigned __int128)r->n[0] + a->n[0];
r->n[0] = c;
c = (unsigned __int128)r->n[1] + a->n[1] + (c >> 64);
r->n[1] = c;
c = (unsigned __int128)r->n[2] + a->n[2] + (c >> 64);
r->n[2] = c;
c = (unsigned __int128)r->n[3] + a->n[3] + (c >> 64);
r->n[3] = c;
c = (unsigned __int128)r->n[4] + a->n[4] + (c >> 64);
r->n[4] = c;
assert((c >> 64) == 0);
}
#if 0
#define muladd_c3(a,b,c0,c1,c2) { \
unsigned __int128 q1 = ((unsigned __int128)(a)) * (b) + (c0); \
(c0) = q1; \
unsigned __int128 q2 = (q1 >> 64) + (c1) + (((unsigned __int128)(c2)) << 64); \
(c1) = q2; \
(c2) = q2 >> 64; \
}
#define sqradd_c3(a,c0,c1,c2) muladd_c3(a,a,c0,c1,c2)
/*#define muladd_c3(a,b,c0,c1,c2) { \
unsigned __int128 q = (unsigned __int128)(a) * (b) + (c0); \
(c0) = q; \
(c1) += (q >> 64); \
(c2) += ((c1) < (q >> 64))?1:0; \
}*/
#define muladd2_c3(a,b,c0,c1,c2) { \
unsigned __int128 q = (unsigned __int128)(a) * (b); \
uint64_t t1 = (q >> 64); \
uint64_t t0 = q; \
uint64_t t2 = t1+t1; (c2) += (t2<t1)?1:0; \
t1 = t0+t0; t2 += (t1<t0)?1:0; \
(c0) += t1; t2 += ((c0)<t1)?1:0; \
(c1) += t2; (c2) += ((c1)<t2)?1:0; \
}
/*#define muladd2_c3(a,b,c0,c1,c2) { \
muladd_c3(a,b,c0,c1,c2); \
muladd_c3(a,b,c0,c1,c2); \
}*/
#else
#define muladd_c3(a,b,c0,c1,c2) { \
register uint64_t t1, t2; \
asm ("mulq %3" \
: "=a"(t1),"=d"(t2) \
: "a"(a),"m"(b) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c0),"+d"(t2) \
: "a"(t1),"g"(0) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c1),"+r"(c2) \
: "d"(t2),"g"(0) \
: "cc"); \
}
#define sqradd_c3(a,c0,c1,c2) { \
register uint64_t t1, t2; \
asm ("mulq %2" \
: "=a"(t1),"=d"(t2) \
: "a"(a) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c0),"+d"(t2) \
: "a"(t1),"g"(0) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c1),"+r"(c2) \
: "d"(t2),"g"(0) \
: "cc"); \
}
#define muladd2_c3(a,b,c0,c1,c2) { \
register uint64_t t1, t2; \
asm ("mulq %3" \
: "=a"(t1),"=d"(t2) \
: "a"(a),"m"(b) \
: "cc"); \
asm ("addq %0,%0; adcq %2,%1" \
: "+d"(t2),"+r"(c2) \
: "g"(0) \
: "cc"); \
asm ("addq %0,%0; adcq %2,%1" \
: "+a"(t1),"+d"(t2) \
: "g"(0) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c0),"+d"(t2) \
: "a"(t1),"g"(0) \
: "cc"); \
asm ("addq %2,%0; adcq %3,%1" \
: "+r"(c1),"+r"(c2) \
: "d"(t2),"g"(0) \
: "cc"); \
}
#endif
#define mul_c2(a,b,c0,c1) { \
unsigned __int128 q = (unsigned __int128)(a) * (b); \
(c0) = q; \
(c1) = (q >> 64); \
}
void static secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *ac, const secp256k1_fe_t *bc) {
secp256k1_fe_t a = *ac, b = *bc;
secp256k1_fe_reduce(&a);
secp256k1_fe_reduce(&b);
#ifdef USE_FIELD_5X64_ASM
secp256k1_fe_mul_inner((&a)->n,(&b)->n,r->n);
#else
uint64_t c1,c2,c3;
c3=0;
mul_c2(a.n[0], b.n[0], c1, c2);
uint64_t r0 = c1; c1 = 0;
muladd_c3(a.n[0], b.n[1], c2, c3, c1);
muladd_c3(a.n[1], b.n[0], c2, c3, c1);
uint64_t r1 = c2; c2 = 0;
muladd_c3(a.n[2], b.n[0], c3, c1, c2);
muladd_c3(a.n[1], b.n[1], c3, c1, c2);
muladd_c3(a.n[0], b.n[2], c3, c1, c2);
uint64_t r2 = c3; c3 = 0;
muladd_c3(a.n[0], b.n[3], c1, c2, c3);
muladd_c3(a.n[1], b.n[2], c1, c2, c3);
muladd_c3(a.n[2], b.n[1], c1, c2, c3);
muladd_c3(a.n[3], b.n[0], c1, c2, c3);
uint64_t r3 = c1; c1 = 0;
muladd_c3(a.n[3], b.n[1], c2, c3, c1);
muladd_c3(a.n[2], b.n[2], c2, c3, c1);
muladd_c3(a.n[1], b.n[3], c2, c3, c1);
uint64_t r4 = c2; c2 = 0;
muladd_c3(a.n[2], b.n[3], c3, c1, c2);
muladd_c3(a.n[3], b.n[2], c3, c1, c2);
uint64_t r5 = c3; c3 = 0;
muladd_c3(a.n[3], b.n[3], c1, c2, c3);
uint64_t r6 = c1;
uint64_t r7 = c2;
assert(c3 == 0);
unsigned __int128 c = (unsigned __int128)r4 * COMP_LIMB + r0;
r->n[0] = c;
c = (unsigned __int128)r5 * COMP_LIMB + r1 + (c >> 64);
r->n[1] = c;
c = (unsigned __int128)r6 * COMP_LIMB + r2 + (c >> 64);
r->n[2] = c;
c = (unsigned __int128)r7 * COMP_LIMB + r3 + (c >> 64);
r->n[3] = c;
r->n[4] = c >> 64;
#endif
#ifdef VERIFY
r->normalized = 0;
r->reduced = 0;
#endif
secp256k1_fe_reduce(r);
}
/*void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_mul(r, a, a);
}*/
void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *ac) {
secp256k1_fe_t a = *ac;
secp256k1_fe_reduce(&a);
#ifdef USE_FIELD_5X64_ASM
secp256k1_fe_sqr_inner((&a)->n,r->n);
#else
uint64_t c1,c2,c3;
c3=0;
mul_c2(a.n[0], a.n[0], c1, c2);
uint64_t r0 = c1; c1 = 0;
muladd2_c3(a.n[0], a.n[1], c2, c3, c1);
uint64_t r1 = c2; c2 = 0;
muladd2_c3(a.n[2], a.n[0], c3, c1, c2);
sqradd_c3(a.n[1], c3, c1, c2);
uint64_t r2 = c3; c3 = 0;
muladd2_c3(a.n[0], a.n[3], c1, c2, c3);
muladd2_c3(a.n[1], a.n[2], c1, c2, c3);
uint64_t r3 = c1; c1 = 0;
muladd2_c3(a.n[3], a.n[1], c2, c3, c1);
sqradd_c3(a.n[2], c2, c3, c1);
uint64_t r4 = c2; c2 = 0;
muladd2_c3(a.n[2], a.n[3], c3, c1, c2);
uint64_t r5 = c3; c3 = 0;
sqradd_c3(a.n[3], c1, c2, c3);
uint64_t r6 = c1;
uint64_t r7 = c2;
assert(c3 == 0);
unsigned __int128 c = (unsigned __int128)r4 * COMP_LIMB + r0;
r->n[0] = c;
c = (unsigned __int128)r5 * COMP_LIMB + r1 + (c >> 64);
r->n[1] = c;
c = (unsigned __int128)r6 * COMP_LIMB + r2 + (c >> 64);
r->n[2] = c;
c = (unsigned __int128)r7 * COMP_LIMB + r3 + (c >> 64);
r->n[3] = c;
r->n[4] = c >> 64;
#endif
#ifdef VERIFY
r->normalized = 0;
r->reduced = 0;
#endif
secp256k1_fe_reduce(r);
}
#endif

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crypto/secp256k1/secp256k1/src/impl/field_5x64_asm.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
void __attribute__ ((sysv_abi)) secp256k1_fe_mul_inner(const uint64_t *a, const uint64_t *b, uint64_t *r);
void __attribute__ ((sysv_abi)) secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t *r);
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#include <stdio.h>
#include <assert.h>
#include <string.h>
#include "../num.h"
#include "../field.h"
static mp_limb_t secp256k1_field_p[FIELD_LIMBS];
static mp_limb_t secp256k1_field_pc[(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS];
void static secp256k1_fe_inner_start(void) {
for (int i=0; i<(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; i++)
secp256k1_field_pc[i] = 0;
secp256k1_field_pc[0] += 0x3D1UL;
secp256k1_field_pc[32/GMP_NUMB_BITS] += (1UL << (32 % GMP_NUMB_BITS));
for (int i=0; i<FIELD_LIMBS; i++) {
secp256k1_field_p[i] = 0;
}
mpn_sub(secp256k1_field_p, secp256k1_field_p, FIELD_LIMBS, secp256k1_field_pc, (33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS);
}
void static secp256k1_fe_inner_stop(void) {
}
void static secp256k1_fe_normalize(secp256k1_fe_t *r) {
if (r->n[FIELD_LIMBS] != 0) {
#if (GMP_NUMB_BITS >= 40)
mp_limb_t carry = mpn_add_1(r->n, r->n, FIELD_LIMBS, 0x1000003D1ULL * r->n[FIELD_LIMBS]);
mpn_add_1(r->n, r->n, FIELD_LIMBS, 0x1000003D1ULL * carry);
#else
mp_limb_t carry = mpn_add_1(r->n, r->n, FIELD_LIMBS, 0x3D1UL * r->n[FIELD_LIMBS]) +
mpn_add_1(r->n+(32/GMP_NUMB_BITS), r->n+(32/GMP_NUMB_BITS), FIELD_LIMBS-(32/GMP_NUMB_BITS), r->n[FIELD_LIMBS] << (32 % GMP_NUMB_BITS));
mpn_add_1(r->n, r->n, FIELD_LIMBS, 0x3D1UL * carry);
mpn_add_1(r->n+(32/GMP_NUMB_BITS), r->n+(32/GMP_NUMB_BITS), FIELD_LIMBS-(32/GMP_NUMB_BITS), carry << (32%GMP_NUMB_BITS));
#endif
r->n[FIELD_LIMBS] = 0;
}
if (mpn_cmp(r->n, secp256k1_field_p, FIELD_LIMBS) >= 0)
mpn_sub(r->n, r->n, FIELD_LIMBS, secp256k1_field_p, FIELD_LIMBS);
}
void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
r->n[0] = a;
for (int i=1; i<FIELD_LIMBS+1; i++)
r->n[i] = 0;
}
int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
int ret = 1;
for (int i=0; i<FIELD_LIMBS+1; i++)
ret &= (a->n[i] == 0);
return ret;
}
int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
return a->n[0] & 1;
}
int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
int ret = 1;
for (int i=0; i<FIELD_LIMBS+1; i++)
ret &= (a->n[i] == b->n[i]);
return ret;
}
void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
for (int i=0; i<FIELD_LIMBS+1; i++)
r->n[i] = 0;
for (int i=0; i<256; i++) {
int limb = i/GMP_NUMB_BITS;
int shift = i%GMP_NUMB_BITS;
r->n[limb] |= (mp_limb_t)((a[31-i/8] >> (i%8)) & 0x1) << shift;
}
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
for (int i=0; i<32; i++) {
int c = 0;
for (int j=0; j<8; j++) {
int limb = (8*i+j)/GMP_NUMB_BITS;
int shift = (8*i+j)%GMP_NUMB_BITS;
c |= ((a->n[limb] >> shift) & 0x1) << j;
}
r[31-i] = c;
}
}
void static inline secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
*r = *a;
secp256k1_fe_normalize(r);
for (int i=0; i<FIELD_LIMBS; i++)
r->n[i] = ~(r->n[i]);
#if (GMP_NUMB_BITS >= 33)
mpn_sub_1(r->n, r->n, FIELD_LIMBS, 0x1000003D0ULL);
#else
mpn_sub_1(r->n, r->n, FIELD_LIMBS, 0x3D0UL);
mpn_sub_1(r->n+(32/GMP_NUMB_BITS), r->n+(32/GMP_NUMB_BITS), FIELD_LIMBS-(32/GMP_NUMB_BITS), 0x1UL << (32%GMP_NUMB_BITS));
#endif
}
void static inline secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
mpn_mul_1(r->n, r->n, FIELD_LIMBS+1, a);
}
void static inline secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
mpn_add(r->n, r->n, FIELD_LIMBS+1, a->n, FIELD_LIMBS+1);
}
void static secp256k1_fe_reduce(secp256k1_fe_t *r, mp_limb_t *tmp) {
// <A1 A2 A3 A4> <B1 B2 B3 B4>
// B1 B2 B3 B4
// + C * A1 A2 A3 A4
// + A1 A2 A3 A4
#if (GMP_NUMB_BITS >= 33)
mp_limb_t o = mpn_addmul_1(tmp, tmp+FIELD_LIMBS, FIELD_LIMBS, 0x1000003D1ULL);
#else
mp_limb_t o = mpn_addmul_1(tmp, tmp+FIELD_LIMBS, FIELD_LIMBS, 0x3D1UL) +
mpn_addmul_1(tmp+(32/GMP_NUMB_BITS), tmp+FIELD_LIMBS, FIELD_LIMBS-(32/GMP_NUMB_BITS), 0x1UL << (32%GMP_NUMB_BITS));
#endif
mp_limb_t q[1+(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS];
q[(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS] = mpn_mul_1(q, secp256k1_field_pc, (33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS, o);
#if (GMP_NUMB_BITS <= 32)
mp_limb_t o2 = tmp[2*FIELD_LIMBS-(32/GMP_NUMB_BITS)] << (32%GMP_NUMB_BITS);
q[(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS] += mpn_addmul_1(q, secp256k1_field_pc, (33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS, o2);
#endif
r->n[FIELD_LIMBS] = mpn_add(r->n, tmp, FIELD_LIMBS, q, 1+(33+GMP_NUMB_BITS-1)/GMP_NUMB_BITS);
}
void static secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
secp256k1_fe_t ac = *a;
secp256k1_fe_t bc = *b;
secp256k1_fe_normalize(&ac);
secp256k1_fe_normalize(&bc);
mp_limb_t tmp[2*FIELD_LIMBS];
mpn_mul_n(tmp, ac.n, bc.n, FIELD_LIMBS);
secp256k1_fe_reduce(r, tmp);
}
void static secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_t ac = *a;
secp256k1_fe_normalize(&ac);
mp_limb_t tmp[2*FIELD_LIMBS];
mpn_sqr(tmp, ac.n, FIELD_LIMBS);
secp256k1_fe_reduce(r, tmp);
}
#endif

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crypto/secp256k1/secp256k1/src/impl/group.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_GROUP_IMPL_H_
#define _SECP256K1_GROUP_IMPL_H_
#include <string.h>
#include "../num.h"
#include "../field.h"
#include "../group.h"
void static secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
r->infinity = 1;
}
void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
}
int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
return a->infinity;
}
void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_normalize(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a) {
char cx[65]; int lx=65;
char cy[65]; int ly=65;
secp256k1_fe_get_hex(cx, &lx, &a->x);
secp256k1_fe_get_hex(cy, &ly, &a->y);
lx = strlen(cx);
ly = strlen(cy);
int len = lx + ly + 3 + 1;
if (*rlen < len) {
*rlen = len;
return;
}
*rlen = len;
r[0] = '(';
memcpy(r+1, cx, lx);
r[1+lx] = ',';
memcpy(r+2+lx, cy, ly);
r[2+lx+ly] = ')';
r[3+lx+ly] = 0;
}
void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
secp256k1_fe_inv_var(&a->z, &a->z);
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
}
void static secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
r->infinity = 1;
}
void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
secp256k1_fe_set_int(&r->z, 1);
}
void static secp256k1_ge_set_xo(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
r->x = *x;
secp256k1_fe_t x2; secp256k1_fe_sqr(&x2, x);
secp256k1_fe_t x3; secp256k1_fe_mul(&x3, x, &x2);
r->infinity = 0;
secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&c, &x3);
secp256k1_fe_sqrt(&r->y, &c);
secp256k1_fe_normalize(&r->y);
if (secp256k1_fe_is_odd(&r->y) != odd)
secp256k1_fe_negate(&r->y, &r->y, 1);
}
void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
}
void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a) {
secp256k1_fe_t zi2; secp256k1_fe_inv_var(&zi2, &a->z); secp256k1_fe_sqr(&zi2, &zi2);
secp256k1_fe_mul(r, &a->x, &zi2);
}
void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
r->z = a->z;
secp256k1_fe_normalize(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
return a->infinity;
}
int static secp256k1_gej_is_valid(const secp256k1_gej_t *a) {
if (a->infinity)
return 0;
// y^2 = x^3 + 7
// (Y/Z^3)^2 = (X/Z^2)^3 + 7
// Y^2 / Z^6 = X^3 / Z^6 + 7
// Y^2 = X^3 + 7*Z^6
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_t z6; secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
secp256k1_fe_mul_int(&z6, 7);
secp256k1_fe_add(&x3, &z6);
secp256k1_fe_normalize(&y2);
secp256k1_fe_normalize(&x3);
return secp256k1_fe_equal(&y2, &x3);
}
int static secp256k1_ge_is_valid(const secp256k1_ge_t *a) {
if (a->infinity)
return 0;
// y^2 = x^3 + 7
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&x3, &c);
secp256k1_fe_normalize(&y2);
secp256k1_fe_normalize(&x3);
return secp256k1_fe_equal(&y2, &x3);
}
void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
secp256k1_fe_t t5 = a->y;
secp256k1_fe_normalize(&t5);
if (a->infinity || secp256k1_fe_is_zero(&t5)) {
r->infinity = 1;
return;
}
secp256k1_fe_t t1,t2,t3,t4;
secp256k1_fe_mul(&r->z, &t5, &a->z);
secp256k1_fe_mul_int(&r->z, 2); // Z' = 2*Y*Z (2)
secp256k1_fe_sqr(&t1, &a->x);
secp256k1_fe_mul_int(&t1, 3); // T1 = 3*X^2 (3)
secp256k1_fe_sqr(&t2, &t1); // T2 = 9*X^4 (1)
secp256k1_fe_sqr(&t3, &t5);
secp256k1_fe_mul_int(&t3, 2); // T3 = 2*Y^2 (2)
secp256k1_fe_sqr(&t4, &t3);
secp256k1_fe_mul_int(&t4, 2); // T4 = 8*Y^4 (2)
secp256k1_fe_mul(&t3, &a->x, &t3); // T3 = 2*X*Y^2 (1)
r->x = t3;
secp256k1_fe_mul_int(&r->x, 4); // X' = 8*X*Y^2 (4)
secp256k1_fe_negate(&r->x, &r->x, 4); // X' = -8*X*Y^2 (5)
secp256k1_fe_add(&r->x, &t2); // X' = 9*X^4 - 8*X*Y^2 (6)
secp256k1_fe_negate(&t2, &t2, 1); // T2 = -9*X^4 (2)
secp256k1_fe_mul_int(&t3, 6); // T3 = 12*X*Y^2 (6)
secp256k1_fe_add(&t3, &t2); // T3 = 12*X*Y^2 - 9*X^4 (8)
secp256k1_fe_mul(&r->y, &t1, &t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
secp256k1_fe_negate(&t2, &t4, 2); // T2 = -8*Y^4 (3)
secp256k1_fe_add(&r->y, &t2); // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
r->infinity = 0;
}
void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
if (a->infinity) {
*r = *b;
return;
}
if (b->infinity) {
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_t z22; secp256k1_fe_sqr(&z22, &b->z);
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &a->x, &z22);
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_normalize(&u1);
secp256k1_fe_normalize(&u2);
if (secp256k1_fe_equal(&u1, &u2)) {
secp256k1_fe_normalize(&s1);
secp256k1_fe_normalize(&s2);
if (secp256k1_fe_equal(&s1, &s2)) {
secp256k1_gej_double(r, a);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
if (a->infinity) {
r->infinity = b->infinity;
r->x = b->x;
r->y = b->y;
secp256k1_fe_set_int(&r->z, 1);
return;
}
if (b->infinity) {
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1);
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1);
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_normalize(&u1);
secp256k1_fe_normalize(&u2);
if (secp256k1_fe_equal(&u1, &u2)) {
secp256k1_fe_normalize(&s1);
secp256k1_fe_normalize(&s2);
if (secp256k1_fe_equal(&s1, &s2)) {
secp256k1_gej_double(r, a);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a) {
secp256k1_gej_t c = *a;
secp256k1_ge_t t; secp256k1_ge_set_gej(&t, &c);
secp256k1_ge_get_hex(r, rlen, &t);
}
void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
const secp256k1_fe_t *beta = &secp256k1_ge_consts->beta;
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, beta);
}
void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a) {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2;
secp256k1_num_init(&bnc1);
secp256k1_num_init(&bnc2);
secp256k1_num_init(&bnt1);
secp256k1_num_init(&bnt2);
secp256k1_num_init(&bnn2);
secp256k1_num_copy(&bnn2, &c->order);
secp256k1_num_shift(&bnn2, 1);
secp256k1_num_mul(&bnc1, a, &c->a1b2);
secp256k1_num_add(&bnc1, &bnc1, &bnn2);
secp256k1_num_div(&bnc1, &bnc1, &c->order);
secp256k1_num_mul(&bnc2, a, &c->b1);
secp256k1_num_add(&bnc2, &bnc2, &bnn2);
secp256k1_num_div(&bnc2, &bnc2, &c->order);
secp256k1_num_mul(&bnt1, &bnc1, &c->a1b2);
secp256k1_num_mul(&bnt2, &bnc2, &c->a2);
secp256k1_num_add(&bnt1, &bnt1, &bnt2);
secp256k1_num_sub(r1, a, &bnt1);
secp256k1_num_mul(&bnt1, &bnc1, &c->b1);
secp256k1_num_mul(&bnt2, &bnc2, &c->a1b2);
secp256k1_num_sub(r2, &bnt1, &bnt2);
secp256k1_num_free(&bnc1);
secp256k1_num_free(&bnc2);
secp256k1_num_free(&bnt1);
secp256k1_num_free(&bnt2);
secp256k1_num_free(&bnn2);
}
void static secp256k1_ge_start(void) {
static const unsigned char secp256k1_ge_consts_order[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
static const unsigned char secp256k1_ge_consts_g_x[] = {
0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,
0x55,0xA0,0x62,0x95,0xCE,0x87,0x0B,0x07,
0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,
0x59,0xF2,0x81,0x5B,0x16,0xF8,0x17,0x98
};
static const unsigned char secp256k1_ge_consts_g_y[] = {
0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,
0x5D,0xA4,0xFB,0xFC,0x0E,0x11,0x08,0xA8,
0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,
0x9C,0x47,0xD0,0x8F,0xFB,0x10,0xD4,0xB8
};
// properties of secp256k1's efficiently computable endomorphism
static const unsigned char secp256k1_ge_consts_lambda[] = {
0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,
0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,
0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72
};
static const unsigned char secp256k1_ge_consts_beta[] = {
0x7a,0xe9,0x6a,0x2b,0x65,0x7c,0x07,0x10,
0x6e,0x64,0x47,0x9e,0xac,0x34,0x34,0xe9,
0x9c,0xf0,0x49,0x75,0x12,0xf5,0x89,0x95,
0xc1,0x39,0x6c,0x28,0x71,0x95,0x01,0xee
};
static const unsigned char secp256k1_ge_consts_a1b2[] = {
0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15
};
static const unsigned char secp256k1_ge_consts_b1[] = {
0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3
};
static const unsigned char secp256k1_ge_consts_a2[] = {
0x01,
0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,
0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8
};
if (secp256k1_ge_consts == NULL) {
secp256k1_ge_consts_t *ret = (secp256k1_ge_consts_t*)malloc(sizeof(secp256k1_ge_consts_t));
secp256k1_num_init(&ret->order);
secp256k1_num_init(&ret->half_order);
secp256k1_num_init(&ret->lambda);
secp256k1_num_init(&ret->a1b2);
secp256k1_num_init(&ret->a2);
secp256k1_num_init(&ret->b1);
secp256k1_num_set_bin(&ret->order, secp256k1_ge_consts_order, sizeof(secp256k1_ge_consts_order));
secp256k1_num_set_bin(&ret->lambda, secp256k1_ge_consts_lambda, sizeof(secp256k1_ge_consts_lambda));
secp256k1_num_set_bin(&ret->a1b2, secp256k1_ge_consts_a1b2, sizeof(secp256k1_ge_consts_a1b2));
secp256k1_num_set_bin(&ret->a2, secp256k1_ge_consts_a2, sizeof(secp256k1_ge_consts_a2));
secp256k1_num_set_bin(&ret->b1, secp256k1_ge_consts_b1, sizeof(secp256k1_ge_consts_b1));
secp256k1_num_copy(&ret->half_order, &ret->order);
secp256k1_num_shift(&ret->half_order, 1);
secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta);
secp256k1_fe_t g_x, g_y;
secp256k1_fe_set_b32(&g_x, secp256k1_ge_consts_g_x);
secp256k1_fe_set_b32(&g_y, secp256k1_ge_consts_g_y);
secp256k1_ge_set_xy(&ret->g, &g_x, &g_y);
secp256k1_ge_consts = ret;
}
}
void static secp256k1_ge_stop(void) {
if (secp256k1_ge_consts != NULL) {
secp256k1_ge_consts_t *c = (secp256k1_ge_consts_t*)secp256k1_ge_consts;
secp256k1_num_free(&c->order);
secp256k1_num_free(&c->half_order);
secp256k1_num_free(&c->lambda);
secp256k1_num_free(&c->a1b2);
secp256k1_num_free(&c->a2);
secp256k1_num_free(&c->b1);
free((void*)c);
secp256k1_ge_consts = NULL;
}
}
#endif

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crypto/secp256k1/secp256k1/src/impl/num.h
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@ -1,18 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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_
#include "../num.h"
#if defined(USE_NUM_GMP)
#include "num_gmp.h"
#elif defined(USE_NUM_OPENSSL)
#include "num_openssl.h"
#else
#error "Please select num implementation"
#endif
#endif

346
crypto/secp256k1/secp256k1/src/impl/num_gmp.h
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@ -1,346 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 <assert.h>
#include <string.h>
#include <stdlib.h>
#include <gmp.h>
#include "num.h"
#ifdef VERIFY
void static secp256k1_num_sanity(const secp256k1_num_t *a) {
assert(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
}
#else
#define secp256k1_num_sanity(a) do { } while(0)
#endif
void static secp256k1_num_init(secp256k1_num_t *r) {
r->neg = 0;
r->limbs = 1;
r->data[0] = 0;
}
void static secp256k1_num_free(secp256k1_num_t *r) {
}
void static secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
*r = *a;
}
int static secp256k1_num_bits(const secp256k1_num_t *a) {
int ret=(a->limbs-1)*GMP_NUMB_BITS;
mp_limb_t x=a->data[a->limbs-1];
while (x) {
x >>= 1;
ret++;
}
return ret;
}
void static secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
unsigned char tmp[65];
int len = 0;
if (a->limbs>1 || a->data[0] != 0) {
len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
}
int shift = 0;
while (shift < len && tmp[shift] == 0) shift++;
assert(len-shift <= rlen);
memset(r, 0, rlen - len + shift);
if (len > shift)
memcpy(r + rlen - len + shift, tmp + shift, len - shift);
}
void static secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
assert(alen > 0);
assert(alen <= 64);
int len = mpn_set_str(r->data, a, alen, 256);
assert(len <= NUM_LIMBS*2);
r->limbs = len;
r->neg = 0;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
}
void static secp256k1_num_set_int(secp256k1_num_t *r, int a) {
r->limbs = 1;
r->neg = (a < 0);
r->data[0] = (a < 0) ? -a : a;
}
void static secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
r->limbs = a->limbs;
if (c != 0) {
assert(r->limbs < 2*NUM_LIMBS);
r->data[r->limbs++] = c;
}
}
void static secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
assert(c == 0);
r->limbs = a->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
}
void static secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *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);
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;
}
}
void static secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
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
assert(m->limbs <= NUM_LIMBS);
assert(m->data[m->limbs-1] != 0);
mp_limb_t g[NUM_LIMBS+1];
mp_limb_t u[NUM_LIMBS+1];
mp_limb_t v[NUM_LIMBS+1];
for (int i=0; i < m->limbs; i++) {
u[i] = (i < a->limbs) ? a->data[i] : 0;
v[i] = m->data[i];
}
mp_size_t sn = NUM_LIMBS+1;
mp_size_t gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
assert(gn == 1);
assert(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;
}
}
int static secp256k1_num_is_zero(const secp256k1_num_t *a) {
return (a->limbs == 1 && a->data[0] == 0);
}
int static secp256k1_num_is_odd(const secp256k1_num_t *a) {
return a->data[0] & 1;
}
int static secp256k1_num_is_neg(const secp256k1_num_t *a) {
return (a->limbs > 1 || a->data[0] != 0) && a->neg;
}
int static secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
if (a->limbs > b->limbs) return 1;
if (a->limbs < b->limbs) return -1;
return mpn_cmp(a->data, b->data, a->limbs);
}
void static secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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);
}
}
}
void static secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 0);
}
void static secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 1);
}
void static secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
mp_limb_t tmp[2*NUM_LIMBS+1];
assert(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--;
assert(r->limbs <= 2*NUM_LIMBS);
mpn_copyi(r->data, tmp, r->limbs);
r->neg = a->neg ^ b->neg;
}
void static secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
if (b->limbs > a->limbs) {
r->limbs = 1;
r->data[0] = 0;
r->neg = 0;
return;
}
mp_limb_t quo[2*NUM_LIMBS+1];
mp_limb_t rem[2*NUM_LIMBS+1];
mpn_tdiv_qr(quo, rem, 0, a->data, a->limbs, b->data, b->limbs);
mpn_copyi(r->data, quo, a->limbs - b->limbs + 1);
r->limbs = a->limbs - b->limbs + 1;
while (r->limbs > 1 && r->data[r->limbs - 1]==0) r->limbs--;
r->neg = a->neg ^ b->neg;
}
void static secp256k1_num_mod_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, const secp256k1_num_t *m) {
secp256k1_num_mul(r, a, b);
secp256k1_num_mod(r, m);
}
int static secp256k1_num_shift(secp256k1_num_t *r, int bits) {
assert(bits <= GMP_NUMB_BITS);
mp_limb_t ret = mpn_rshift(r->data, r->data, r->limbs, bits);
if (r->limbs>1 && r->data[r->limbs-1]==0) r->limbs--;
ret >>= (GMP_NUMB_BITS - bits);
return ret;
}
int static secp256k1_num_get_bit(const secp256k1_num_t *a, int pos) {
return (a->limbs*GMP_NUMB_BITS > pos) && ((a->data[pos/GMP_NUMB_BITS] >> (pos % GMP_NUMB_BITS)) & 1);
}
void static secp256k1_num_inc(secp256k1_num_t *r) {
mp_limb_t ret = mpn_add_1(r->data, r->data, r->limbs, (mp_limb_t)1);
if (ret) {
assert(r->limbs < 2*NUM_LIMBS);
r->data[r->limbs++] = ret;
}
}
void static secp256k1_num_set_hex(secp256k1_num_t *r, const char *a, int alen) {
static const unsigned char cvt[256] = {
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 1, 2, 3, 4, 5, 6,7,8,9,0,0,0,0,0,0,
0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0
};
unsigned char num[257] = {};
for (int i=0; i<alen; i++) {
num[i] = cvt[a[i]];
}
r->limbs = mpn_set_str(r->data, num, alen, 16);
while (r->limbs > 1 && r->data[r->limbs-1] == 0) r->limbs--;
}
void static secp256k1_num_get_hex(char *r, int rlen, const secp256k1_num_t *a) {
static const unsigned char cvt[16] = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};
unsigned char *tmp = malloc(257);
mp_size_t len = mpn_get_str(tmp, 16, (mp_limb_t*)a->data, a->limbs);
assert(len <= rlen);
for (int i=0; i<len; i++) {
assert(rlen-len+i >= 0);
assert(rlen-len+i < rlen);
assert(tmp[i] >= 0);
assert(tmp[i] < 16);
r[rlen-len+i] = cvt[tmp[i]];
}
for (int i=0; i<rlen-len; i++) {
assert(i >= 0);
assert(i < rlen);
r[i] = cvt[0];
}
free(tmp);
}
void static secp256k1_num_split(secp256k1_num_t *rl, secp256k1_num_t *rh, const secp256k1_num_t *a, int bits) {
assert(bits > 0);
rh->neg = a->neg;
if (bits >= a->limbs * GMP_NUMB_BITS) {
*rl = *a;
rh->limbs = 1;
rh->data[0] = 0;
return;
}
rl->limbs = 0;
rl->neg = a->neg;
int left = bits;
while (left >= GMP_NUMB_BITS) {
rl->data[rl->limbs] = a->data[rl->limbs];
rl->limbs++;
left -= GMP_NUMB_BITS;
}
if (left == 0) {
mpn_copyi(rh->data, a->data + rl->limbs, a->limbs - rl->limbs);
rh->limbs = a->limbs - rl->limbs;
} else {
mpn_rshift(rh->data, a->data + rl->limbs, a->limbs - rl->limbs, left);
rh->limbs = a->limbs - rl->limbs;
while (rh->limbs>1 && rh->data[rh->limbs-1]==0) rh->limbs--;
}
if (left > 0) {
rl->data[rl->limbs] = a->data[rl->limbs] & ((((mp_limb_t)1) << left) - 1);
rl->limbs++;
}
while (rl->limbs>1 && rl->data[rl->limbs-1]==0) rl->limbs--;
}
void static secp256k1_num_negate(secp256k1_num_t *r) {
r->neg ^= 1;
}
#endif

145
crypto/secp256k1/secp256k1/src/impl/num_openssl.h
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@ -1,145 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 <assert.h>
#include <string.h>
#include <stdlib.h>
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include "../num.h"
void static secp256k1_num_init(secp256k1_num_t *r) {
BN_init(&r->bn);
}
void static secp256k1_num_free(secp256k1_num_t *r) {
BN_free(&r->bn);
}
void static secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
BN_copy(&r->bn, &a->bn);
}
void static secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
unsigned int size = BN_num_bytes(&a->bn);
assert(size <= rlen);
memset(r,0,rlen);
BN_bn2bin(&a->bn, r + rlen - size);
}
void static secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
BN_bin2bn(a, alen, &r->bn);
}
void static secp256k1_num_set_int(secp256k1_num_t *r, int a) {
BN_set_word(&r->bn, a < 0 ? -a : a);
BN_set_negative(&r->bn, a < 0);
}
void static secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
BN_CTX *ctx = BN_CTX_new();
BN_mod_inverse(&r->bn, &a->bn, &m->bn, ctx);
BN_CTX_free(ctx);
}
void static secp256k1_num_mod_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, const secp256k1_num_t *m) {
BN_CTX *ctx = BN_CTX_new();
BN_mod_mul(&r->bn, &a->bn, &b->bn, &m->bn, ctx);
BN_CTX_free(ctx);
}
int static secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
return BN_cmp(&a->bn, &b->bn);
}
void static secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
BN_add(&r->bn, &a->bn, &b->bn);
}
void static secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
BN_sub(&r->bn, &a->bn, &b->bn);
}
void static secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
BN_CTX *ctx = BN_CTX_new();
BN_mul(&r->bn, &a->bn, &b->bn, ctx);
BN_CTX_free(ctx);
}
void static secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
BN_CTX *ctx = BN_CTX_new();
BN_div(&r->bn, NULL, &a->bn, &b->bn, ctx);
BN_CTX_free(ctx);
}
void static secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
BN_CTX *ctx = BN_CTX_new();
BN_nnmod(&r->bn, &r->bn, &m->bn, ctx);
BN_CTX_free(ctx);
}
int static secp256k1_num_bits(const secp256k1_num_t *a) {
return BN_num_bits(&a->bn);
}
int static secp256k1_num_shift(secp256k1_num_t *r, int bits) {
int ret = BN_is_zero(&r->bn) ? 0 : r->bn.d[0] & ((1 << bits) - 1);
BN_rshift(&r->bn, &r->bn, bits);
return ret;
}
int static secp256k1_num_is_zero(const secp256k1_num_t *a) {
return BN_is_zero(&a->bn);
}
int static secp256k1_num_is_odd(const secp256k1_num_t *a) {
return BN_is_odd(&a->bn);
}
int static secp256k1_num_is_neg(const secp256k1_num_t *a) {
return BN_is_negative(&a->bn);
}
int static secp256k1_num_get_bit(const secp256k1_num_t *a, int pos) {
return BN_is_bit_set(&a->bn, pos);
}
void static secp256k1_num_inc(secp256k1_num_t *r) {
BN_add_word(&r->bn, 1);
}
void static secp256k1_num_set_hex(secp256k1_num_t *r, const char *a, int alen) {
char *str = (char*)malloc(alen+1);
memcpy(str, a, alen);
str[alen] = 0;
BIGNUM *pbn = &r->bn;
BN_hex2bn(&pbn, str);
free(str);
}
void static secp256k1_num_get_hex(char *r, int rlen, const secp256k1_num_t *a) {
char *str = BN_bn2hex(&a->bn);
int len = strlen(str);
assert(rlen >= len);
for (int i=0; i<rlen-len; i++)
r[i] = '0';
memcpy(r+rlen-len, str, len);
OPENSSL_free(str);
}
void static secp256k1_num_split(secp256k1_num_t *rl, secp256k1_num_t *rh, const secp256k1_num_t *a, int bits) {
BN_copy(&rl->bn, &a->bn);
BN_rshift(&rh->bn, &a->bn, bits);
BN_mask_bits(&rl->bn, bits);
}
void static secp256k1_num_negate(secp256k1_num_t *r) {
BN_set_negative(&r->bn, !BN_is_negative(&r->bn));
}
#endif

45
crypto/secp256k1/secp256k1/src/impl/util.h
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@ -1,45 +0,0 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_UTIL_IMPL_H_
#define _SECP256K1_UTIL_IMPL_H_
#include <stdint.h>
#include <string.h>
#include "../util.h"
static inline uint32_t secp256k1_rand32(void) {
static uint32_t Rz = 11, Rw = 11;
Rz = 36969 * (Rz & 0xFFFF) + (Rz >> 16);
Rw = 18000 * (Rw & 0xFFFF) + (Rw >> 16);
return (Rw << 16) + (Rw >> 16) + Rz;
}
static void secp256k1_rand256(unsigned char *b32) {
for (int i=0; i<8; i++) {
uint32_t r = secp256k1_rand32();
b32[i*4 + 0] = (r >> 0) & 0xFF;
b32[i*4 + 1] = (r >> 8) & 0xFF;
b32[i*4 + 2] = (r >> 16) & 0xFF;
b32[i*4 + 3] = (r >> 24) & 0xFF;
}
}
static void secp256k1_rand256_test(unsigned char *b32) {
int bits=0;
memset(b32, 0, 32);
while (bits < 256) {
uint32_t ent = secp256k1_rand32();
int now = 1 + ((ent % 64)*((ent >> 6) % 32)+16)/31;
uint32_t val = 1 & (ent >> 11);
while (now > 0 && bits < 256) {
b32[bits / 8] |= val << (bits % 8);
now--;
bits++;
}
}
}
#endif

2
crypto/secp256k1/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c
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@ -15,7 +15,7 @@ static void __javasecp256k1_attach(void) __attribute__((constructor));
static void __javasecp256k1_detach(void) __attribute__((destructor));
static void __javasecp256k1_attach(void) {
secp256k1_start();
secp256k1_start(SECP256K1_START_VERIFY);
}
static void __javasecp256k1_detach(void) {

85
crypto/secp256k1/secp256k1/src/num.h
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@ -1,93 +1,68 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_
#define _SECP256K1_NUM_
#ifndef USE_NUM_NONE
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_NUM_GMP)
#include "num_gmp.h"
#elif defined(USE_NUM_OPENSSL)
#include "num_openssl.h"
#else
#error "Please select num implementation"
#endif
/** Initialize a number. */
void static secp256k1_num_init(secp256k1_num_t *r);
/** Free a number. */
void static secp256k1_num_free(secp256k1_num_t *r);
/** Copy a number. */
void static secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a);
static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a);
/** Convert a number's absolute value to a binary big-endian string.
* There must be enough place. */
void static secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a);
static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a);
/** Set a number to the value of a binary big-endian string. */
void static secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen);
/** Set a number equal to a (signed) integer. */
void static secp256k1_num_set_int(secp256k1_num_t *r, int a);
static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen);
/** Compute a modular inverse. The input must be less than the modulus. */
void static secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m);
/** Multiply two numbers modulo another. */
void static secp256k1_num_mod_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, const secp256k1_num_t *m);
static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m);
/** Compare the absolute value of two numbers. */
int static secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b);
static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b);
/** Test whether two number are equal (including sign). */
static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b);
/** Add two (signed) numbers. */
void static secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
/** Subtract two (signed) numbers. */
void static secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
/** Multiply two (signed) numbers. */
void static secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
/** Divide two (signed) numbers. */
void static secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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. */
void static secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m);
static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m);
/** Calculate the number of bits in (the absolute value of) a number. */
int static secp256k1_num_bits(const secp256k1_num_t *a);
/** Right-shift the passed number by bits bits, and return those bits. */
int static secp256k1_num_shift(secp256k1_num_t *r, int bits);
/** Right-shift the passed number by bits bits. */
static void secp256k1_num_shift(secp256k1_num_t *r, int bits);
/** Check whether a number is zero. */
int static secp256k1_num_is_zero(const secp256k1_num_t *a);
/** Check whether a number is odd. */
int static secp256k1_num_is_odd(const secp256k1_num_t *a);
static int secp256k1_num_is_zero(const secp256k1_num_t *a);
/** Check whether a number is strictly negative. */
int static secp256k1_num_is_neg(const secp256k1_num_t *a);
/** Check whether a particular bit is set in a number. */
int static secp256k1_num_get_bit(const secp256k1_num_t *a, int pos);
/** Increase a number by 1. */
void static secp256k1_num_inc(secp256k1_num_t *r);
/** Set a number equal to the value of a hex string (unsigned). */
void static secp256k1_num_set_hex(secp256k1_num_t *r, const char *a, int alen);
/** Convert (the absolute value of) a number to a hexadecimal string. */
void static secp256k1_num_get_hex(char *r, int rlen, const secp256k1_num_t *a);
/** Split a number into a low and high part. */
void static secp256k1_num_split(secp256k1_num_t *rl, secp256k1_num_t *rh, const secp256k1_num_t *a, int bits);
static int secp256k1_num_is_neg(const secp256k1_num_t *a);
/** Change a number's sign. */
void static secp256k1_num_negate(secp256k1_num_t *r);
static void secp256k1_num_negate(secp256k1_num_t *r);
#endif
#endif

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_REPR_
#define _SECP256K1_NUM_REPR_

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/**********************************************************************
* 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_t *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_t *r, const secp256k1_num_t *a) {
*r = *a;
}
static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *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_t *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_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
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_t *r, const secp256k1_num_t *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_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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);
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_is_zero(const secp256k1_num_t *a) {
return (a->limbs == 1 && a->data[0] == 0);
}
static int secp256k1_num_is_neg(const secp256k1_num_t *a) {
return (a->limbs > 1 || a->data[0] != 0) && a->neg;
}
static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *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_t *a, const secp256k1_num_t *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_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 0);
}
static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 1);
}
static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *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_t *r, int bits) {
int i;
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) {
/* 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_t *r) {
r->neg ^= 1;
}
#endif

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/**********************************************************************
* 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

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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef _SECP256K1_NUM_REPR_
#define _SECP256K1_NUM_REPR_
#include <openssl/bn.h>
typedef struct {
BIGNUM bn;
} secp256k1_num_t;
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_
#define _SECP256K1_SCALAR_
#include "num.h"
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_SCALAR_4X64)
#include "scalar_4x64.h"
#elif defined(USE_SCALAR_8X32)
#include "scalar_8x32.h"
#else
#error "Please select scalar implementation"
#endif
/** Clear a scalar to prevent the leak of sensitive data. */
static void secp256k1_scalar_clear(secp256k1_scalar_t *r);
/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
/** Access bits from a scalar. Not constant time. */
static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
/** Set a scalar from a big endian byte array. */
static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *bin, int *overflow);
/** Set a scalar to an unsigned integer. */
static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v);
/** Convert a scalar to a byte array. */
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a);
/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
/** Add a power of two to a scalar. The result is not allowed to overflow. */
static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit);
/** Multiply two scalars (modulo the group order). */
static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
/** Compute the square of a scalar (modulo the group order). */
static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
/** Compute the inverse of a scalar (modulo the group order). */
static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
/** Compute the complement of a scalar (modulo the group order). */
static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
/** Check whether a scalar equals zero. */
static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a);
/** Check whether a scalar equals one. */
static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a);
/** Check whether a scalar is higher than the group order divided by 2. */
static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a);
#ifndef USE_NUM_NONE
/** Convert a scalar to a number. */
static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a);
/** Get the order of the group as a number. */
static void secp256k1_scalar_order_get_num(secp256k1_num_t *r);
#endif
/** Compare two scalars. */
static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
#ifdef USE_ENDOMORPHISM
/** Find r1 and r2 such that r1+r2*2^128 = a. */
static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
#endif
/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift);
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_
#define _SECP256K1_SCALAR_REPR_
#include <stdint.h>
/** A scalar modulo the group order of the secp256k1 curve. */
typedef struct {
uint64_t d[4];
} secp256k1_scalar_t;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
#endif

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/**********************************************************************
* 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_SCALAR_REPR_IMPL_H_
#define _SECP256K1_SCALAR_REPR_IMPL_H_
/* Limbs of the secp256k1 order. */
#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
/* Limbs of 2^256 minus the secp256k1 order. */
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
#define SECP256K1_N_C_2 (1)
/* Limbs of half the secp256k1 order. */
#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
r->d[0] = 0;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
}
SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
r->d[0] = v;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK(count < 32);
VERIFY_CHECK(offset + count <= 256);
if ((offset + count - 1) >> 6 == offset >> 6) {
return secp256k1_scalar_get_bits(a, offset, count);
} else {
VERIFY_CHECK((offset >> 6) + 1 < 4);
return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
}
}
SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
int yes = 0;
int no = 0;
no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
no |= (a->d[2] < SECP256K1_N_2);
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
no |= (a->d[1] < SECP256K1_N_1);
yes |= (a->d[1] > SECP256K1_N_1) & ~no;
yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
return yes;
}
SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsigned int overflow) {
uint128_t t;
VERIFY_CHECK(overflow <= 1);
t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint64_t)r->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
return overflow;
}
static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
int overflow;
uint128_t t = (uint128_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
overflow = t + secp256k1_scalar_check_overflow(r);
VERIFY_CHECK(overflow == 0 || overflow == 1);
secp256k1_scalar_reduce(r, overflow);
return overflow;
}
static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
uint128_t t;
VERIFY_CHECK(bit < 256);
t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
#ifdef VERIFY
VERIFY_CHECK((t >> 64) == 0);
VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
#endif
}
static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56;
r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56;
over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
if (overflow) {
*overflow = over;
}
}
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
}
SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
}
static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
r->d[0] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
r->d[1] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
r->d[2] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
r->d[3] = t & nonzero;
}
SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
}
static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
int yes = 0;
int no = 0;
no |= (a->d[3] < SECP256K1_N_H_3);
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
return yes;
}
/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd(a,b) { \
uint64_t tl, th; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c1 += th; /* overflow is handled on the next line */ \
c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
}
/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
#define muladd_fast(a,b) { \
uint64_t tl, th; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c1 += th; /* never overflows by contract (verified in the next line) */ \
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) ? 1 : 0; /* 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) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c0 += tl2; /* overflow is handled on the next line */ \
th2 += (c0 < tl2) ? 1 : 0; /* 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) ? 1 : 0; /* 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; \
c0 += (a); /* overflow is handled on the next line */ \
over = (c0 < (a)) ? 1 : 0; \
c1 += over; /* overflow is handled on the next line */ \
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
}
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
#define sumadd_fast(a) { \
c0 += (a); /* overflow is handled on the next line */ \
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
VERIFY_CHECK(c2 == 0); \
}
/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */
#define extract(n) { \
(n) = c0; \
c0 = c1; \
c1 = c2; \
c2 = 0; \
}
/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */
#define extract_fast(n) { \
(n) = c0; \
c0 = c1; \
c1 = 0; \
VERIFY_CHECK(c2 == 0); \
}
static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l) {
#ifdef USE_ASM_X86_64
/* Reduce 512 bits into 385. */
uint64_t m0, m1, m2, m3, m4, m5, m6;
uint64_t p0, p1, p2, p3, p4;
uint64_t c;
__asm__ __volatile__(
/* Preload. */
"movq 32(%%rsi), %%r11\n"
"movq 40(%%rsi), %%r12\n"
"movq 48(%%rsi), %%r13\n"
"movq 56(%%rsi), %%r14\n"
/* Initialize r8,r9,r10 */
"movq 0(%%rsi), %%r8\n"
"movq $0, %%r9\n"
"movq $0, %%r10\n"
/* (r8,r9) += n0 * c0 */
"movq %8, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* extract m0 */
"movq %%r8, %q0\n"
"movq $0, %%r8\n"
/* (r9,r10) += l1 */
"addq 8(%%rsi), %%r9\n"
"adcq $0, %%r10\n"
/* (r9,r10,r8) += n1 * c0 */
"movq %8, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += n0 * c1 */
"movq %9, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* extract m1 */
"movq %%r9, %q1\n"
"movq $0, %%r9\n"
/* (r10,r8,r9) += l2 */
"addq 16(%%rsi), %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n2 * c0 */
"movq %8, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n1 * c1 */
"movq %9, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n0 */
"addq %%r11, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* extract m2 */
"movq %%r10, %q2\n"
"movq $0, %%r10\n"
/* (r8,r9,r10) += l3 */
"addq 24(%%rsi), %%r8\n"
"adcq $0, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n3 * c0 */
"movq %8, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n2 * c1 */
"movq %9, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n1 */
"addq %%r12, %%r8\n"
"adcq $0, %%r9\n"
"adcq $0, %%r10\n"
/* extract m3 */
"movq %%r8, %q3\n"
"movq $0, %%r8\n"
/* (r9,r10,r8) += n3 * c1 */
"movq %9, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += n2 */
"addq %%r13, %%r9\n"
"adcq $0, %%r10\n"
"adcq $0, %%r8\n"
/* extract m4 */
"movq %%r9, %q4\n"
/* (r10,r8) += n3 */
"addq %%r14, %%r10\n"
"adcq $0, %%r8\n"
/* extract m5 */
"movq %%r10, %q5\n"
/* extract m6 */
"movq %%r8, %q6\n"
: "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
: "S"(l), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
/* Reduce 385 bits into 258. */
__asm__ __volatile__(
/* Preload */
"movq %q9, %%r11\n"
"movq %q10, %%r12\n"
"movq %q11, %%r13\n"
/* Initialize (r8,r9,r10) */
"movq %q5, %%r8\n"
"movq $0, %%r9\n"
"movq $0, %%r10\n"
/* (r8,r9) += m4 * c0 */
"movq %12, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* extract p0 */
"movq %%r8, %q0\n"
"movq $0, %%r8\n"
/* (r9,r10) += m1 */
"addq %q6, %%r9\n"
"adcq $0, %%r10\n"
/* (r9,r10,r8) += m5 * c0 */
"movq %12, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += m4 * c1 */
"movq %13, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* extract p1 */
"movq %%r9, %q1\n"
"movq $0, %%r9\n"
/* (r10,r8,r9) += m2 */
"addq %q7, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m6 * c0 */
"movq %12, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m5 * c1 */
"movq %13, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m4 */
"addq %%r11, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* extract p2 */
"movq %%r10, %q2\n"
/* (r8,r9) += m3 */
"addq %q8, %%r8\n"
"adcq $0, %%r9\n"
/* (r8,r9) += m6 * c1 */
"movq %13, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* (r8,r9) += m5 */
"addq %%r12, %%r8\n"
"adcq $0, %%r9\n"
/* extract p3 */
"movq %%r8, %q3\n"
/* (r9) += m6 */
"addq %%r13, %%r9\n"
/* extract p4 */
"movq %%r9, %q4\n"
: "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
: "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
/* Reduce 258 bits into 256. */
__asm__ __volatile__(
/* Preload */
"movq %q5, %%r10\n"
/* (rax,rdx) = p4 * c0 */
"movq %7, %%rax\n"
"mulq %%r10\n"
/* (rax,rdx) += p0 */
"addq %q1, %%rax\n"
"adcq $0, %%rdx\n"
/* extract r0 */
"movq %%rax, 0(%q6)\n"
/* Move to (r8,r9) */
"movq %%rdx, %%r8\n"
"movq $0, %%r9\n"
/* (r8,r9) += p1 */
"addq %q2, %%r8\n"
"adcq $0, %%r9\n"
/* (r8,r9) += p4 * c1 */
"movq %8, %%rax\n"
"mulq %%r10\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* Extract r1 */
"movq %%r8, 8(%q6)\n"
"movq $0, %%r8\n"
/* (r9,r8) += p4 */
"addq %%r10, %%r9\n"
"adcq $0, %%r8\n"
/* (r9,r8) += p2 */
"addq %q3, %%r9\n"
"adcq $0, %%r8\n"
/* Extract r2 */
"movq %%r9, 16(%q6)\n"
"movq $0, %%r9\n"
/* (r8,r9) += p3 */
"addq %q4, %%r8\n"
"adcq $0, %%r9\n"
/* Extract r3 */
"movq %%r8, 24(%q6)\n"
/* Extract c */
"movq %%r9, %q0\n"
: "=g"(c)
: "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
#else
uint128_t c;
uint64_t c0, c1, c2;
uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
uint64_t m0, m1, m2, m3, m4, m5;
uint32_t m6;
uint64_t p0, p1, p2, p3;
uint32_t p4;
/* Reduce 512 bits into 385. */
/* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
c0 = l[0]; c1 = 0; c2 = 0;
muladd_fast(n0, SECP256K1_N_C_0);
extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
sumadd(n0);
extract(m2);
sumadd(l[3]);
muladd(n3, SECP256K1_N_C_0);
muladd(n2, SECP256K1_N_C_1);
sumadd(n1);
extract(m3);
muladd(n3, SECP256K1_N_C_1);
sumadd(n2);
extract(m4);
sumadd_fast(n3);
extract_fast(m5);
VERIFY_CHECK(c0 <= 1);
m6 = c0;
/* Reduce 385 bits into 258. */
/* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
c0 = m0; c1 = 0; c2 = 0;
muladd_fast(m4, SECP256K1_N_C_0);
extract_fast(p0);
sumadd_fast(m1);
muladd(m5, SECP256K1_N_C_0);
muladd(m4, SECP256K1_N_C_1);
extract(p1);
sumadd(m2);
muladd(m6, SECP256K1_N_C_0);
muladd(m5, SECP256K1_N_C_1);
sumadd(m4);
extract(p2);
sumadd_fast(m3);
muladd_fast(m6, SECP256K1_N_C_1);
sumadd_fast(m5);
extract_fast(p3);
p4 = c0 + m6;
VERIFY_CHECK(p4 <= 2);
/* Reduce 258 bits into 256. */
/* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p2 + (uint128_t)p4;
r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p3;
r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
#endif
/* Final reduction of r. */
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
}
static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
#ifdef USE_ASM_X86_64
const uint64_t *pb = b->d;
__asm__ __volatile__(
/* Preload */
"movq 0(%%rdi), %%r15\n"
"movq 8(%%rdi), %%rbx\n"
"movq 16(%%rdi), %%rcx\n"
"movq 0(%%rdx), %%r11\n"
"movq 8(%%rdx), %%r12\n"
"movq 16(%%rdx), %%r13\n"
"movq 24(%%rdx), %%r14\n"
/* (rax,rdx) = a0 * b0 */
"movq %%r15, %%rax\n"
"mulq %%r11\n"
/* Extract l0 */
"movq %%rax, 0(%%rsi)\n"
/* (r8,r9,r10) = (rdx) */
"movq %%rdx, %%r8\n"
"xorq %%r9, %%r9\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += a0 * b1 */
"movq %%r15, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a1 * b0 */
"movq %%rbx, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l1 */
"movq %%r8, 8(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += a0 * b2 */
"movq %%r15, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a1 * b1 */
"movq %%rbx, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a2 * b0 */
"movq %%rcx, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l2 */
"movq %%r9, 16(%%rsi)\n"
"xorq %%r9, %%r9\n"
/* (r10,r8,r9) += a0 * b3 */
"movq %%r15, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* Preload a3 */
"movq 24(%%rdi), %%r15\n"
/* (r10,r8,r9) += a1 * b2 */
"movq %%rbx, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += a2 * b1 */
"movq %%rcx, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += a3 * b0 */
"movq %%r15, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* Extract l3 */
"movq %%r10, 24(%%rsi)\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += a1 * b3 */
"movq %%rbx, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a2 * b2 */
"movq %%rcx, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a3 * b1 */
"movq %%r15, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l4 */
"movq %%r8, 32(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += a2 * b3 */
"movq %%rcx, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a3 * b2 */
"movq %%r15, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l5 */
"movq %%r9, 40(%%rsi)\n"
/* (r10,r8) += a3 * b3 */
"movq %%r15, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
/* Extract l6 */
"movq %%r10, 48(%%rsi)\n"
/* Extract l7 */
"movq %%r8, 56(%%rsi)\n"
: "+d"(pb)
: "S"(l), "D"(a->d)
: "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
#else
/* 160 bit accumulator. */
uint64_t c0 = 0, c1 = 0;
uint32_t c2 = 0;
/* l[0..7] = a[0..3] * b[0..3]. */
muladd_fast(a->d[0], b->d[0]);
extract_fast(l[0]);
muladd(a->d[0], b->d[1]);
muladd(a->d[1], b->d[0]);
extract(l[1]);
muladd(a->d[0], b->d[2]);
muladd(a->d[1], b->d[1]);
muladd(a->d[2], b->d[0]);
extract(l[2]);
muladd(a->d[0], b->d[3]);
muladd(a->d[1], b->d[2]);
muladd(a->d[2], b->d[1]);
muladd(a->d[3], b->d[0]);
extract(l[3]);
muladd(a->d[1], b->d[3]);
muladd(a->d[2], b->d[2]);
muladd(a->d[3], b->d[1]);
extract(l[4]);
muladd(a->d[2], b->d[3]);
muladd(a->d[3], b->d[2]);
extract(l[5]);
muladd_fast(a->d[3], b->d[3]);
extract_fast(l[6]);
VERIFY_CHECK(c1 <= 0);
l[7] = c0;
#endif
}
static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *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
static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
uint64_t l[8];
secp256k1_scalar_mul_512(l, a, b);
secp256k1_scalar_reduce_512(r, l);
}
static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *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_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
r1->d[0] = a->d[0];
r1->d[1] = a->d[1];
r1->d[2] = 0;
r1->d[3] = 0;
r2->d[0] = a->d[2];
r2->d[1] = a->d[3];
r2->d[2] = 0;
r2->d[3] = 0;
}
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
}
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
uint64_t l[8];
unsigned int shiftlimbs;
unsigned int shiftlow;
unsigned int shifthigh;
VERIFY_CHECK(shift >= 256);
secp256k1_scalar_mul_512(l, a, b);
shiftlimbs = shift >> 6;
shiftlow = shift & 0x3F;
shifthigh = 64 - shiftlow;
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
if ((l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1) {
secp256k1_scalar_add_bit(r, 0);
}
}
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_
#define _SECP256K1_SCALAR_REPR_
#include <stdint.h>
/** A scalar modulo the group order of the secp256k1 curve. */
typedef struct {
uint32_t d[8];
} secp256k1_scalar_t;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
#endif

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/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
#define _SECP256K1_SCALAR_REPR_IMPL_H_
/* Limbs of the secp256k1 order. */
#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
/* Limbs of 2^256 minus the secp256k1 order. */
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
#define SECP256K1_N_C_2 (~SECP256K1_N_2)
#define SECP256K1_N_C_3 (~SECP256K1_N_3)
#define SECP256K1_N_C_4 (1)
/* Limbs of half the secp256k1 order. */
#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
r->d[0] = 0;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
r->d[4] = 0;
r->d[5] = 0;
r->d[6] = 0;
r->d[7] = 0;
}
SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
r->d[0] = v;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
r->d[4] = 0;
r->d[5] = 0;
r->d[6] = 0;
r->d[7] = 0;
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK(count < 32);
VERIFY_CHECK(offset + count <= 256);
if ((offset + count - 1) >> 5 == offset >> 5) {
return secp256k1_scalar_get_bits(a, offset, count);
} else {
VERIFY_CHECK((offset >> 5) + 1 < 8);
return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
}
}
SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
int yes = 0;
int no = 0;
no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
no |= (a->d[4] < SECP256K1_N_4);
yes |= (a->d[4] > SECP256K1_N_4) & ~no;
no |= (a->d[3] < SECP256K1_N_3) & ~yes;
yes |= (a->d[3] > SECP256K1_N_3) & ~no;
no |= (a->d[2] < SECP256K1_N_2) & ~yes;
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
no |= (a->d[1] < SECP256K1_N_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_1) & ~no;
yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
return yes;
}
SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, uint32_t overflow) {
uint64_t t;
VERIFY_CHECK(overflow <= 1);
t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[5];
r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[6];
r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[7];
r->d[7] = t & 0xFFFFFFFFUL;
return overflow;
}
static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
int overflow;
uint64_t t = (uint64_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[4] + b->d[4];
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[5] + b->d[5];
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[6] + b->d[6];
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[7] + b->d[7];
r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
overflow = t + secp256k1_scalar_check_overflow(r);
VERIFY_CHECK(overflow == 0 || overflow == 1);
secp256k1_scalar_reduce(r, overflow);
return overflow;
}
static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
uint64_t t;
VERIFY_CHECK(bit < 256);
t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
r->d[7] = t & 0xFFFFFFFFULL;
#ifdef VERIFY
VERIFY_CHECK((t >> 32) == 0);
VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
#endif
}
static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
if (overflow) {
*overflow = over;
}
}
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
}
SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
}
static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
r->d[0] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
r->d[1] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
r->d[2] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
r->d[3] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
r->d[4] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
r->d[5] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
r->d[6] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
r->d[7] = t & nonzero;
}
SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
}
static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
int yes = 0;
int no = 0;
no |= (a->d[7] < SECP256K1_N_H_7);
yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
return yes;
}
/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd(a,b) { \
uint32_t tl, th; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c1 += th; /* overflow is handled on the next line */ \
c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
}
/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
#define muladd_fast(a,b) { \
uint32_t tl, th; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c1 += th; /* never overflows by contract (verified in the next line) */ \
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) ? 1 : 0; /* 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) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c0 += tl2; /* overflow is handled on the next line */ \
th2 += (c0 < tl2) ? 1 : 0; /* 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) ? 1 : 0; /* 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; \
c0 += (a); /* overflow is handled on the next line */ \
over = (c0 < (a)) ? 1 : 0; \
c1 += over; /* overflow is handled on the next line */ \
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
}
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
#define sumadd_fast(a) { \
c0 += (a); /* overflow is handled on the next line */ \
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
VERIFY_CHECK(c2 == 0); \
}
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
#define extract(n) { \
(n) = c0; \
c0 = c1; \
c1 = c2; \
c2 = 0; \
}
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
#define extract_fast(n) { \
(n) = c0; \
c0 = c1; \
c1 = 0; \
VERIFY_CHECK(c2 == 0); \
}
static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l) {
uint64_t c;
uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
/* 96 bit accumulator. */
uint32_t c0, c1, c2;
/* Reduce 512 bits into 385. */
/* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
c0 = l[0]; c1 = 0; c2 = 0;
muladd_fast(n0, SECP256K1_N_C_0);
extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
muladd(n0, SECP256K1_N_C_2);
extract(m2);
sumadd(l[3]);
muladd(n3, SECP256K1_N_C_0);
muladd(n2, SECP256K1_N_C_1);
muladd(n1, SECP256K1_N_C_2);
muladd(n0, SECP256K1_N_C_3);
extract(m3);
sumadd(l[4]);
muladd(n4, SECP256K1_N_C_0);
muladd(n3, SECP256K1_N_C_1);
muladd(n2, SECP256K1_N_C_2);
muladd(n1, SECP256K1_N_C_3);
sumadd(n0);
extract(m4);
sumadd(l[5]);
muladd(n5, SECP256K1_N_C_0);
muladd(n4, SECP256K1_N_C_1);
muladd(n3, SECP256K1_N_C_2);
muladd(n2, SECP256K1_N_C_3);
sumadd(n1);
extract(m5);
sumadd(l[6]);
muladd(n6, SECP256K1_N_C_0);
muladd(n5, SECP256K1_N_C_1);
muladd(n4, SECP256K1_N_C_2);
muladd(n3, SECP256K1_N_C_3);
sumadd(n2);
extract(m6);
sumadd(l[7]);
muladd(n7, SECP256K1_N_C_0);
muladd(n6, SECP256K1_N_C_1);
muladd(n5, SECP256K1_N_C_2);
muladd(n4, SECP256K1_N_C_3);
sumadd(n3);
extract(m7);
muladd(n7, SECP256K1_N_C_1);
muladd(n6, SECP256K1_N_C_2);
muladd(n5, SECP256K1_N_C_3);
sumadd(n4);
extract(m8);
muladd(n7, SECP256K1_N_C_2);
muladd(n6, SECP256K1_N_C_3);
sumadd(n5);
extract(m9);
muladd(n7, SECP256K1_N_C_3);
sumadd(n6);
extract(m10);
sumadd_fast(n7);
extract_fast(m11);
VERIFY_CHECK(c0 <= 1);
m12 = c0;
/* Reduce 385 bits into 258. */
/* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
c0 = m0; c1 = 0; c2 = 0;
muladd_fast(m8, SECP256K1_N_C_0);
extract_fast(p0);
sumadd_fast(m1);
muladd(m9, SECP256K1_N_C_0);
muladd(m8, SECP256K1_N_C_1);
extract(p1);
sumadd(m2);
muladd(m10, SECP256K1_N_C_0);
muladd(m9, SECP256K1_N_C_1);
muladd(m8, SECP256K1_N_C_2);
extract(p2);
sumadd(m3);
muladd(m11, SECP256K1_N_C_0);
muladd(m10, SECP256K1_N_C_1);
muladd(m9, SECP256K1_N_C_2);
muladd(m8, SECP256K1_N_C_3);
extract(p3);
sumadd(m4);
muladd(m12, SECP256K1_N_C_0);
muladd(m11, SECP256K1_N_C_1);
muladd(m10, SECP256K1_N_C_2);
muladd(m9, SECP256K1_N_C_3);
sumadd(m8);
extract(p4);
sumadd(m5);
muladd(m12, SECP256K1_N_C_1);
muladd(m11, SECP256K1_N_C_2);
muladd(m10, SECP256K1_N_C_3);
sumadd(m9);
extract(p5);
sumadd(m6);
muladd(m12, SECP256K1_N_C_2);
muladd(m11, SECP256K1_N_C_3);
sumadd(m10);
extract(p6);
sumadd_fast(m7);
muladd_fast(m12, SECP256K1_N_C_3);
sumadd_fast(m11);
extract_fast(p7);
p8 = c0 + m12;
VERIFY_CHECK(p8 <= 2);
/* Reduce 258 bits into 256. */
/* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
c += p4 + (uint64_t)p8;
r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
c += p5;
r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
c += p6;
r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
c += p7;
r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
/* Final reduction of r. */
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
}
static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
/* 96 bit accumulator. */
uint32_t c0 = 0, c1 = 0, c2 = 0;
/* l[0..15] = a[0..7] * b[0..7]. */
muladd_fast(a->d[0], b->d[0]);
extract_fast(l[0]);
muladd(a->d[0], b->d[1]);
muladd(a->d[1], b->d[0]);
extract(l[1]);
muladd(a->d[0], b->d[2]);
muladd(a->d[1], b->d[1]);
muladd(a->d[2], b->d[0]);
extract(l[2]);
muladd(a->d[0], b->d[3]);
muladd(a->d[1], b->d[2]);
muladd(a->d[2], b->d[1]);
muladd(a->d[3], b->d[0]);
extract(l[3]);
muladd(a->d[0], b->d[4]);
muladd(a->d[1], b->d[3]);
muladd(a->d[2], b->d[2]);
muladd(a->d[3], b->d[1]);
muladd(a->d[4], b->d[0]);
extract(l[4]);
muladd(a->d[0], b->d[5]);
muladd(a->d[1], b->d[4]);
muladd(a->d[2], b->d[3]);
muladd(a->d[3], b->d[2]);
muladd(a->d[4], b->d[1]);
muladd(a->d[5], b->d[0]);
extract(l[5]);
muladd(a->d[0], b->d[6]);
muladd(a->d[1], b->d[5]);
muladd(a->d[2], b->d[4]);
muladd(a->d[3], b->d[3]);
muladd(a->d[4], b->d[2]);
muladd(a->d[5], b->d[1]);
muladd(a->d[6], b->d[0]);
extract(l[6]);
muladd(a->d[0], b->d[7]);
muladd(a->d[1], b->d[6]);
muladd(a->d[2], b->d[5]);
muladd(a->d[3], b->d[4]);
muladd(a->d[4], b->d[3]);
muladd(a->d[5], b->d[2]);
muladd(a->d[6], b->d[1]);
muladd(a->d[7], b->d[0]);
extract(l[7]);
muladd(a->d[1], b->d[7]);
muladd(a->d[2], b->d[6]);
muladd(a->d[3], b->d[5]);
muladd(a->d[4], b->d[4]);
muladd(a->d[5], b->d[3]);
muladd(a->d[6], b->d[2]);
muladd(a->d[7], b->d[1]);
extract(l[8]);
muladd(a->d[2], b->d[7]);
muladd(a->d[3], b->d[6]);
muladd(a->d[4], b->d[5]);
muladd(a->d[5], b->d[4]);
muladd(a->d[6], b->d[3]);
muladd(a->d[7], b->d[2]);
extract(l[9]);
muladd(a->d[3], b->d[7]);
muladd(a->d[4], b->d[6]);
muladd(a->d[5], b->d[5]);
muladd(a->d[6], b->d[4]);
muladd(a->d[7], b->d[3]);
extract(l[10]);
muladd(a->d[4], b->d[7]);
muladd(a->d[5], b->d[6]);
muladd(a->d[6], b->d[5]);
muladd(a->d[7], b->d[4]);
extract(l[11]);
muladd(a->d[5], b->d[7]);
muladd(a->d[6], b->d[6]);
muladd(a->d[7], b->d[5]);
extract(l[12]);
muladd(a->d[6], b->d[7]);
muladd(a->d[7], b->d[6]);
extract(l[13]);
muladd_fast(a->d[7], b->d[7]);
extract_fast(l[14]);
VERIFY_CHECK(c1 == 0);
l[15] = c0;
}
static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar_t *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
static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
uint32_t l[16];
secp256k1_scalar_mul_512(l, a, b);
secp256k1_scalar_reduce_512(r, l);
}
static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
uint32_t l[16];
secp256k1_scalar_sqr_512(l, a);
secp256k1_scalar_reduce_512(r, l);
}
#ifdef USE_ENDOMORPHISM
static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
r1->d[0] = a->d[0];
r1->d[1] = a->d[1];
r1->d[2] = a->d[2];
r1->d[3] = a->d[3];
r1->d[4] = 0;
r1->d[5] = 0;
r1->d[6] = 0;
r1->d[7] = 0;
r2->d[0] = a->d[4];
r2->d[1] = a->d[5];
r2->d[2] = a->d[6];
r2->d[3] = a->d[7];
r2->d[4] = 0;
r2->d[5] = 0;
r2->d[6] = 0;
r2->d[7] = 0;
}
#endif
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
}
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
uint32_t l[16];
unsigned int shiftlimbs;
unsigned int shiftlow;
unsigned int shifthigh;
VERIFY_CHECK(shift >= 256);
secp256k1_scalar_mul_512(l, a, b);
shiftlimbs = shift >> 5;
shiftlow = shift & 0x1F;
shifthigh = 32 - shiftlow;
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
if ((l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1) {
secp256k1_scalar_add_bit(r, 0);
}
}
#endif

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@ -0,0 +1,327 @@
/**********************************************************************
* 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.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_IMPL_H_
#define _SECP256K1_SCALAR_IMPL_H_
#include <string.h>
#include "group.h"
#include "scalar.h"
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_SCALAR_4X64)
#include "scalar_4x64_impl.h"
#elif defined(USE_SCALAR_8X32)
#include "scalar_8x32_impl.h"
#else
#error "Please select scalar implementation"
#endif
#ifndef USE_NUM_NONE
static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *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_t *r) {
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
};
secp256k1_num_set_bin(r, order, 32);
}
#endif
static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
secp256k1_scalar_t *t;
int i;
/* First compute x ^ (2^N - 1) for some values of N. */
secp256k1_scalar_t x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
secp256k1_scalar_sqr(&x2, x);
secp256k1_scalar_mul(&x2, &x2, x);
secp256k1_scalar_sqr(&x3, &x2);
secp256k1_scalar_mul(&x3, &x3, x);
secp256k1_scalar_sqr(&x4, &x3);
secp256k1_scalar_mul(&x4, &x4, x);
secp256k1_scalar_sqr(&x6, &x4);
secp256k1_scalar_sqr(&x6, &x6);
secp256k1_scalar_mul(&x6, &x6, &x2);
secp256k1_scalar_sqr(&x7, &x6);
secp256k1_scalar_mul(&x7, &x7, x);
secp256k1_scalar_sqr(&x8, &x7);
secp256k1_scalar_mul(&x8, &x8, x);
secp256k1_scalar_sqr(&x15, &x8);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x15, &x15);
}
secp256k1_scalar_mul(&x15, &x15, &x7);
secp256k1_scalar_sqr(&x30, &x15);
for (i = 0; i < 14; i++) {
secp256k1_scalar_sqr(&x30, &x30);
}
secp256k1_scalar_mul(&x30, &x30, &x15);
secp256k1_scalar_sqr(&x60, &x30);
for (i = 0; i < 29; i++) {
secp256k1_scalar_sqr(&x60, &x60);
}
secp256k1_scalar_mul(&x60, &x60, &x30);
secp256k1_scalar_sqr(&x120, &x60);
for (i = 0; i < 59; i++) {
secp256k1_scalar_sqr(&x120, &x120);
}
secp256k1_scalar_mul(&x120, &x120, &x60);
secp256k1_scalar_sqr(&x127, &x120);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x127, &x127);
}
secp256k1_scalar_mul(&x127, &x127, &x7);
/* Then accumulate the final result (t starts at x127). */
t = &x127;
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
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 < 4; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
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 < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 4; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 8; i++) { /* 000000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
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 */
}
static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
#if defined(USE_SCALAR_INV_BUILTIN)
secp256k1_scalar_inverse(r, x);
#elif defined(USE_SCALAR_INV_NUM)
unsigned char b[32];
secp256k1_num_t n, m;
secp256k1_scalar_get_b32(b, x);
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);
#else
#error "Please select scalar inverse implementation"
#endif
}
#ifdef USE_ENDOMORPHISM
/**
* The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
* lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
* 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
*
* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
* and k2 have a small size.
* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
*
* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
*
* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
*
* g1, g2 are precomputed constants used to replace division with a rounded multiplication
* when decomposing the scalar for an endomorphism-based point multiplication.
*
* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
*
* The derivation is described in the paper "Efficient Software Implementation of Public-Key
* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
* Section 4.3 (here we use a somewhat higher-precision estimate):
* d = a1*b2 - b1*a2
* g1 = round((2^272)*b2/d)
* g2 = round((2^272)*b1/d)
*
* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
*
* The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
*/
static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
secp256k1_scalar_t c1, c2;
static const secp256k1_scalar_t minus_lambda = SECP256K1_SCALAR_CONST(
0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
);
static const secp256k1_scalar_t minus_b1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
);
static const secp256k1_scalar_t minus_b2 = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
);
static const secp256k1_scalar_t g1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
);
static const secp256k1_scalar_t g2 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
);
VERIFY_CHECK(r1 != a);
VERIFY_CHECK(r2 != a);
secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
secp256k1_scalar_mul(&c1, &c1, &minus_b1);
secp256k1_scalar_mul(&c2, &c2, &minus_b2);
secp256k1_scalar_add(r2, &c1, &c2);
secp256k1_scalar_mul(r1, r2, &minus_lambda);
secp256k1_scalar_add(r1, r1, a);
}
#endif
#endif

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@ -1,269 +1,372 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include "impl/num.h"
#include "impl/field.h"
#include "impl/group.h"
#include "impl/ecmult.h"
#include "impl/ecdsa.h"
#define SECP256K1_BUILD (1)
void secp256k1_start(void) {
secp256k1_fe_start();
secp256k1_ge_start();
#include "include/secp256k1.h"
#include "util.h"
#include "num_impl.h"
#include "field_impl.h"
#include "scalar_impl.h"
#include "group_impl.h"
#include "ecmult_impl.h"
#include "ecmult_gen_impl.h"
#include "ecdsa_impl.h"
#include "eckey_impl.h"
#include "hash_impl.h"
void secp256k1_start(unsigned int flags) {
if (flags & SECP256K1_START_SIGN) {
secp256k1_ecmult_gen_start();
}
if (flags & SECP256K1_START_VERIFY) {
secp256k1_ecmult_start();
}
}
void secp256k1_stop(void) {
secp256k1_ecmult_stop();
secp256k1_ge_stop();
secp256k1_fe_stop();
secp256k1_ecmult_gen_stop();
}
int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
int ret = -3;
secp256k1_num_t m;
secp256k1_num_init(&m);
int secp256k1_ecdsa_verify(const unsigned char *msg32, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
secp256k1_ge_t q;
secp256k1_ecdsa_sig_t s;
secp256k1_ecdsa_sig_init(&s);
secp256k1_ge_t q;
secp256k1_num_set_bin(&m, msg, msglen);
secp256k1_scalar_t m;
int ret = -3;
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(msg32 != NULL);
DEBUG_CHECK(sig != NULL);
DEBUG_CHECK(pubkey != NULL);
if (!secp256k1_ecdsa_pubkey_parse(&q, pubkey, pubkeylen)) {
ret = -1;
goto end;
secp256k1_scalar_set_b32(&m, msg32, NULL);
if (secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen)) {
if (secp256k1_ecdsa_sig_parse(&s, sig, siglen)) {
if (secp256k1_ecdsa_sig_verify(&s, &q, &m)) {
/* success is 1, all other values are fail */
ret = 1;
} else {
ret = 0;
}
if (!secp256k1_ecdsa_sig_parse(&s, sig, siglen)) {
} else {
ret = -2;
goto end;
}
if (!secp256k1_ecdsa_sig_verify(&s, &q, &m)) {
ret = 0;
goto end;
} else {
ret = -1;
}
ret = 1;
end:
secp256k1_ecdsa_sig_free(&s);
secp256k1_num_free(&m);
return ret;
}
int secp256k1_ecdsa_sign(const unsigned char *message, int messagelen, unsigned char *signature, int *signaturelen, const unsigned char *seckey, const unsigned char *nonce) {
secp256k1_num_t sec, non, msg;
secp256k1_num_init(&sec);
secp256k1_num_init(&non);
secp256k1_num_init(&msg);
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_set_bin(&non, nonce, 32);
secp256k1_num_set_bin(&msg, message, messagelen);
static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
secp256k1_rfc6979_hmac_sha256_t rng;
unsigned int i;
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key32, 32, msg32, 32, (const unsigned char*)data, data != NULL ? 32 : 0);
for (i = 0; i <= counter; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
return 1;
}
const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
const secp256k1_nonce_function_t secp256k1_nonce_function_default = nonce_function_rfc6979;
int secp256k1_ecdsa_sign(const unsigned char *msg32, unsigned char *signature, int *signaturelen, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata) {
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
int ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, NULL);
if (ret) {
secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig);
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&msg);
secp256k1_num_free(&non);
secp256k1_num_free(&sec);
return ret;
}
int secp256k1_ecdsa_sign_compact(const unsigned char *message, int messagelen, unsigned char *sig64, const unsigned char *seckey, const unsigned char *nonce, int *recid) {
secp256k1_num_t sec, non, msg;
secp256k1_num_init(&sec);
secp256k1_num_init(&non);
secp256k1_num_init(&msg);
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_set_bin(&non, nonce, 32);
secp256k1_num_set_bin(&msg, message, messagelen);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
int ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, recid);
if (ret) {
secp256k1_num_get_bin(sig64, 32, &sig.r);
secp256k1_num_get_bin(sig64 + 32, 32, &sig.s);
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&msg);
secp256k1_num_free(&non);
secp256k1_num_free(&sec);
return ret;
}
int secp256k1_ecdsa_recover_compact(const unsigned char *msg, int msglen, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
secp256k1_scalar_t sec, non, msg;
int ret = 0;
secp256k1_num_t m;
secp256k1_num_init(&m);
int overflow = 0;
unsigned int count = 0;
DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
DEBUG_CHECK(msg32 != NULL);
DEBUG_CHECK(signature != NULL);
DEBUG_CHECK(signaturelen != NULL);
DEBUG_CHECK(seckey != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
/* Fail if the secret key is invalid. */
if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
secp256k1_scalar_set_b32(&msg, msg32, NULL);
while (1) {
unsigned char nonce32[32];
ret = noncefp(nonce32, msg32, seckey, count, noncedata);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&non, nonce32, &overflow);
memset(nonce32, 0, 32);
if (!secp256k1_scalar_is_zero(&non) && !overflow) {
if (secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, NULL)) {
break;
}
}
count++;
}
if (ret) {
ret = secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig);
}
secp256k1_scalar_clear(&msg);
secp256k1_scalar_clear(&non);
secp256k1_scalar_clear(&sec);
}
if (!ret) {
*signaturelen = 0;
}
return ret;
}
int secp256k1_ecdsa_sign_compact(const unsigned char *msg32, unsigned char *sig64, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata, int *recid) {
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
secp256k1_num_set_bin(&sig.r, sig64, 32);
secp256k1_num_set_bin(&sig.s, sig64 + 32, 32);
secp256k1_num_set_bin(&m, msg, msglen);
secp256k1_scalar_t sec, non, msg;
int ret = 0;
int overflow = 0;
unsigned int count = 0;
DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
DEBUG_CHECK(msg32 != NULL);
DEBUG_CHECK(sig64 != NULL);
DEBUG_CHECK(seckey != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
/* Fail if the secret key is invalid. */
if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
secp256k1_scalar_set_b32(&msg, msg32, NULL);
while (1) {
unsigned char nonce32[32];
ret = noncefp(nonce32, msg32, seckey, count, noncedata);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&non, nonce32, &overflow);
memset(nonce32, 0, 32);
if (!secp256k1_scalar_is_zero(&non) && !overflow) {
if (secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, recid)) {
break;
}
}
count++;
}
if (ret) {
secp256k1_scalar_get_b32(sig64, &sig.r);
secp256k1_scalar_get_b32(sig64 + 32, &sig.s);
}
secp256k1_scalar_clear(&msg);
secp256k1_scalar_clear(&non);
secp256k1_scalar_clear(&sec);
}
if (!ret) {
memset(sig64, 0, 64);
}
return ret;
}
int secp256k1_ecdsa_recover_compact(const unsigned char *msg32, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
secp256k1_ge_t q;
secp256k1_ecdsa_sig_t sig;
secp256k1_scalar_t m;
int ret = 0;
int overflow = 0;
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(msg32 != NULL);
DEBUG_CHECK(sig64 != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(pubkeylen != NULL);
DEBUG_CHECK(recid >= 0 && recid <= 3);
secp256k1_scalar_set_b32(&sig.r, sig64, &overflow);
if (!overflow) {
secp256k1_scalar_set_b32(&sig.s, sig64 + 32, &overflow);
if (!overflow) {
secp256k1_scalar_set_b32(&m, msg32, NULL);
if (secp256k1_ecdsa_sig_recover(&sig, &q, &m, recid)) {
secp256k1_ecdsa_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
ret = 1;
ret = secp256k1_eckey_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
}
}
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&m);
return ret;
}
int secp256k1_ecdsa_seckey_verify(const unsigned char *seckey) {
secp256k1_num_t sec;
secp256k1_num_init(&sec);
secp256k1_num_set_bin(&sec, seckey, 32);
int ret = !secp256k1_num_is_zero(&sec) &&
(secp256k1_num_cmp(&sec, &secp256k1_ge_consts->order) < 0);
secp256k1_num_free(&sec);
int secp256k1_ec_seckey_verify(const unsigned char *seckey) {
secp256k1_scalar_t sec;
int ret;
int overflow;
DEBUG_CHECK(seckey != NULL);
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
ret = !secp256k1_scalar_is_zero(&sec) && !overflow;
secp256k1_scalar_clear(&sec);
return ret;
}
int secp256k1_ecdsa_pubkey_verify(const unsigned char *pubkey, int pubkeylen) {
int secp256k1_ec_pubkey_verify(const unsigned char *pubkey, int pubkeylen) {
secp256k1_ge_t q;
return secp256k1_ecdsa_pubkey_parse(&q, pubkey, pubkeylen);
DEBUG_CHECK(pubkey != NULL);
return secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen);
}
int secp256k1_ecdsa_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed) {
secp256k1_num_t sec;
secp256k1_num_init(&sec);
secp256k1_num_set_bin(&sec, seckey, 32);
int secp256k1_ec_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed) {
secp256k1_gej_t pj;
secp256k1_ge_t p;
secp256k1_scalar_t sec;
int overflow;
int ret = 0;
DEBUG_CHECK(secp256k1_ecmult_gen_consts != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(pubkeylen != NULL);
DEBUG_CHECK(seckey != NULL);
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
if (!overflow) {
secp256k1_ecmult_gen(&pj, &sec);
secp256k1_ge_t p;
secp256k1_scalar_clear(&sec);
secp256k1_ge_set_gej(&p, &pj);
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, pubkeylen, compressed);
return 1;
ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, compressed);
}
int secp256k1_ecdsa_pubkey_decompress(unsigned char *pubkey, int *pubkeylen) {
secp256k1_ge_t p;
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, *pubkeylen))
return 0;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, pubkeylen, 0);
return 1;
if (!ret) {
*pubkeylen = 0;
}
int secp256k1_ecdsa_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t term;
secp256k1_num_init(&term);
secp256k1_num_set_bin(&term, tweak, 32);
if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_num_t sec;
secp256k1_num_init(&sec);
if (ret) {
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_add(&sec, &sec, &term);
secp256k1_num_mod(&sec, &secp256k1_ge_consts->order);
if (secp256k1_num_is_zero(&sec))
ret = 0;
}
if (ret)
secp256k1_num_get_bin(seckey, 32, &sec);
secp256k1_num_free(&sec);
secp256k1_num_free(&term);
return ret;
}
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t term;
secp256k1_num_init(&term);
secp256k1_num_set_bin(&term, tweak, 32);
if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
ret = 0;
int secp256k1_ec_pubkey_decompress(unsigned char *pubkey, int *pubkeylen) {
secp256k1_ge_t p;
int ret = 0;
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(pubkeylen != NULL);
if (secp256k1_eckey_pubkey_parse(&p, pubkey, *pubkeylen)) {
ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, 0);
}
return ret;
}
int secp256k1_ec_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
secp256k1_scalar_t term;
secp256k1_scalar_t sec;
int ret = 0;
int overflow = 0;
DEBUG_CHECK(seckey != NULL);
DEBUG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&term, tweak, &overflow);
secp256k1_scalar_set_b32(&sec, seckey, NULL);
ret = secp256k1_eckey_privkey_tweak_add(&sec, &term) && !overflow;
if (ret) {
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen))
ret = 0;
secp256k1_scalar_get_b32(seckey, &sec);
}
secp256k1_scalar_clear(&sec);
secp256k1_scalar_clear(&term);
return ret;
}
int secp256k1_ec_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
secp256k1_ge_t p;
secp256k1_scalar_t term;
int ret = 0;
int overflow = 0;
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&term, tweak, &overflow);
if (!overflow) {
ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
if (ret) {
ret = secp256k1_eckey_pubkey_tweak_add(&p, &term);
}
if (ret) {
secp256k1_gej_t pt;
secp256k1_ecmult_gen(&pt, &term);
secp256k1_gej_add_ge(&pt, &pt, &p);
if (secp256k1_gej_is_infinity(&pt))
ret = 0;
secp256k1_ge_set_gej(&p, &pt);
int oldlen = pubkeylen;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
assert(pubkeylen == oldlen);
ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
VERIFY_CHECK(pubkeylen == oldlen);
}
secp256k1_num_free(&term);
}
return ret;
}
int secp256k1_ecdsa_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t factor;
secp256k1_num_init(&factor);
secp256k1_num_set_bin(&factor, tweak, 32);
if (secp256k1_num_is_zero(&factor))
ret = 0;
if (secp256k1_num_cmp(&factor, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_num_t sec;
secp256k1_num_init(&sec);
int secp256k1_ec_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak) {
secp256k1_scalar_t factor;
secp256k1_scalar_t sec;
int ret = 0;
int overflow = 0;
DEBUG_CHECK(seckey != NULL);
DEBUG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&factor, tweak, &overflow);
secp256k1_scalar_set_b32(&sec, seckey, NULL);
ret = secp256k1_eckey_privkey_tweak_mul(&sec, &factor) && !overflow;
if (ret) {
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_mod_mul(&sec, &sec, &factor, &secp256k1_ge_consts->order);
secp256k1_scalar_get_b32(seckey, &sec);
}
if (ret)
secp256k1_num_get_bin(seckey, 32, &sec);
secp256k1_num_free(&sec);
secp256k1_num_free(&factor);
secp256k1_scalar_clear(&sec);
secp256k1_scalar_clear(&factor);
return ret;
}
int secp256k1_ecdsa_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t factor;
secp256k1_num_init(&factor);
secp256k1_num_set_bin(&factor, tweak, 32);
if (secp256k1_num_is_zero(&factor))
ret = 0;
if (secp256k1_num_cmp(&factor, &secp256k1_ge_consts->order) >= 0)
ret = 0;
int secp256k1_ec_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
secp256k1_ge_t p;
secp256k1_scalar_t factor;
int ret = 0;
int overflow = 0;
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&factor, tweak, &overflow);
if (!overflow) {
ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
if (ret) {
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen))
ret = 0;
ret = secp256k1_eckey_pubkey_tweak_mul(&p, &factor);
}
if (ret) {
secp256k1_num_t zero;
secp256k1_num_init(&zero);
secp256k1_num_set_int(&zero, 0);
secp256k1_gej_t pt;
secp256k1_gej_set_ge(&pt, &p);
secp256k1_ecmult(&pt, &pt, &factor, &zero);
secp256k1_num_free(&zero);
secp256k1_ge_set_gej(&p, &pt);
int oldlen = pubkeylen;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
assert(pubkeylen == oldlen);
ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
VERIFY_CHECK(pubkeylen == oldlen);
}
secp256k1_num_free(&factor);
}
return ret;
}
int secp256k1_ecdsa_privkey_export(const unsigned char *seckey, unsigned char *privkey, int *privkeylen, int compressed) {
secp256k1_num_t key;
secp256k1_num_init(&key);
secp256k1_num_set_bin(&key, seckey, 32);
int ret = secp256k1_ecdsa_privkey_serialize(privkey, privkeylen, &key, compressed);
secp256k1_num_free(&key);
int secp256k1_ec_privkey_export(const unsigned char *seckey, unsigned char *privkey, int *privkeylen, int compressed) {
secp256k1_scalar_t key;
int ret = 0;
DEBUG_CHECK(seckey != NULL);
DEBUG_CHECK(privkey != NULL);
DEBUG_CHECK(privkeylen != NULL);
secp256k1_scalar_set_b32(&key, seckey, NULL);
ret = secp256k1_eckey_privkey_serialize(privkey, privkeylen, &key, compressed);
secp256k1_scalar_clear(&key);
return ret;
}
int secp256k1_ecdsa_privkey_import(unsigned char *seckey, const unsigned char *privkey, int privkeylen) {
secp256k1_num_t key;
secp256k1_num_init(&key);
int ret = secp256k1_ecdsa_privkey_parse(&key, privkey, privkeylen);
if (ret)
secp256k1_num_get_bin(seckey, 32, &key);
secp256k1_num_free(&key);
int secp256k1_ec_privkey_import(unsigned char *seckey, const unsigned char *privkey, int privkeylen) {
secp256k1_scalar_t key;
int ret = 0;
DEBUG_CHECK(seckey != NULL);
DEBUG_CHECK(privkey != NULL);
ret = secp256k1_eckey_privkey_parse(&key, privkey, privkeylen);
if (ret) {
secp256k1_scalar_get_b32(seckey, &key);
}
secp256k1_scalar_clear(&key);
return ret;
}

28
crypto/secp256k1/secp256k1/src/testrand.h Normal file
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/**********************************************************************
* 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_TESTRAND_H_
#define _SECP256K1_TESTRAND_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
/* A non-cryptographic RNG used only for test infrastructure. */
/** Seed the pseudorandom number generator for testing. */
SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
/** Generate a pseudorandom 32-bit number. */
static uint32_t secp256k1_rand32(void);
/** Generate a pseudorandom 32-byte array. */
static void secp256k1_rand256(unsigned char *b32);
/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
static void secp256k1_rand256_test(unsigned char *b32);
#endif

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/**********************************************************************
* 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_TESTRAND_IMPL_H_
#define _SECP256K1_TESTRAND_IMPL_H_
#include <stdint.h>
#include <string.h>
#include "testrand.h"
#include "hash.h"
static secp256k1_rfc6979_hmac_sha256_t secp256k1_test_rng;
static uint32_t secp256k1_test_rng_precomputed[8];
static int secp256k1_test_rng_precomputed_used = 8;
SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, (const unsigned char*)"TestRNG", 7, seed16, 16, NULL, 0);
}
SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
if (secp256k1_test_rng_precomputed_used == 8) {
secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
secp256k1_test_rng_precomputed_used = 0;
}
return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
}
static void secp256k1_rand256(unsigned char *b32) {
secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
}
static void secp256k1_rand256_test(unsigned char *b32) {
int bits=0;
uint64_t ent = 0;
int entleft = 0;
memset(b32, 0, 32);
while (bits < 256) {
int now;
uint32_t val;
if (entleft < 12) {
ent |= ((uint64_t)secp256k1_rand32()) << entleft;
entleft += 32;
}
now = 1 + ((ent % 64)*((ent >> 6) % 32)+16)/31;
val = 1 & (ent >> 11);
ent >>= 12;
entleft -= 12;
while (now > 0 && bits < 256) {
b32[bits / 8] |= val << (bits % 8);
now--;
bits++;
}
}
}
#endif

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crypto/secp256k1/secp256k1/src/tests.c
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crypto/secp256k1/secp256k1/src/util.h
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// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 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 http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_UTIL_H_
#define _SECP256K1_UTIL_H_
/** Generate a pseudorandom 32-bit number. */
static uint32_t secp256k1_rand32(void);
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
/** Generate a pseudorandom 32-byte array. */
static void secp256k1_rand256(unsigned char *b32);
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>
/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
static void secp256k1_rand256_test(unsigned char *b32);
#ifdef DETERMINISTIC
#define TEST_FAILURE(msg) do { \
fprintf(stderr, "%s\n", msg); \
abort(); \
} while(0);
#else
#define TEST_FAILURE(msg) do { \
fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \
abort(); \
} while(0)
#endif
#include "impl/util.h"
#ifdef HAVE_BUILTIN_EXPECT
#define EXPECT(x,c) __builtin_expect((x),(c))
#else
#define EXPECT(x,c) (x)
#endif
#ifdef DETERMINISTIC
#define CHECK(cond) do { \
if (EXPECT(!(cond), 0)) { \
TEST_FAILURE("test condition failed"); \
} \
} while(0)
#else
#define CHECK(cond) do { \
if (EXPECT(!(cond), 0)) { \
TEST_FAILURE("test condition failed: " #cond); \
} \
} while(0)
#endif
/* Like assert(), but safe to use on expressions with side effects. */
#ifndef NDEBUG
#define DEBUG_CHECK CHECK
#else
#define DEBUG_CHECK(cond) do { (void)(cond); } while(0)
#endif
/* Like DEBUG_CHECK(), but when VERIFY is defined instead of NDEBUG not defined. */
#ifdef VERIFY
#define VERIFY_CHECK CHECK
#else
#define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
#endif
static SECP256K1_INLINE void *checked_malloc(size_t size) {
void *ret = malloc(size);
CHECK(ret != NULL);
return ret;
}
/* Macro for restrict, when available and not in a VERIFY build. */
#if defined(SECP256K1_BUILD) && defined(VERIFY)
# define SECP256K1_RESTRICT
#else
# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
# if SECP256K1_GNUC_PREREQ(3,0)
# define SECP256K1_RESTRICT __restrict__
# elif (defined(_MSC_VER) && _MSC_VER >= 1400)
# define SECP256K1_RESTRICT __restrict
# else
# define SECP256K1_RESTRICT
# endif
# else
# define SECP256K1_RESTRICT restrict
# endif
#endif
#if defined(_WIN32)
# define I64FORMAT "I64d"
# define I64uFORMAT "I64u"
#else
# define I64FORMAT "lld"
# define I64uFORMAT "llu"
#endif
#if defined(HAVE___INT128)
# if defined(__GNUC__)
# define SECP256K1_GNUC_EXT __extension__
# else
# define SECP256K1_GNUC_EXT
# endif
SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
#endif
#endif