diff options
Diffstat (limited to 'src/secp256k1')
55 files changed, 10917 insertions, 0 deletions
diff --git a/src/secp256k1/.gitignore b/src/secp256k1/.gitignore new file mode 100644 index 0000000000..b9f7d243ec --- /dev/null +++ b/src/secp256k1/.gitignore @@ -0,0 +1,36 @@ +bench_inv +bench_sign +bench_verify +bench_recover +tests +*.exe +*.so +*.a +!.gitignore + +Makefile +configure +.libs/ +Makefile.in +aclocal.m4 +autom4te.cache/ +config.log +config.status +*.tar.gz +*.la +libtool +.deps/ +.dirstamp +build-aux/ +*.lo +*.o +*~ +src/libsecp256k1-config.h +src/libsecp256k1-config.h.in +m4/libtool.m4 +m4/ltoptions.m4 +m4/ltsugar.m4 +m4/ltversion.m4 +m4/lt~obsolete.m4 +src/stamp-h1 +libsecp256k1.pc diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml new file mode 100644 index 0000000000..40f8dae23f --- /dev/null +++ b/src/secp256k1/.travis.yml @@ -0,0 +1,32 @@ +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 diff --git a/src/secp256k1/COPYING b/src/secp256k1/COPYING new file mode 100644 index 0000000000..4522a5990e --- /dev/null +++ b/src/secp256k1/COPYING @@ -0,0 +1,19 @@ +Copyright (c) 2013 Pieter Wuille + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am new file mode 100644 index 0000000000..cc15338b7e --- /dev/null +++ b/src/secp256k1/Makefile.am @@ -0,0 +1,77 @@ +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 diff --git a/src/secp256k1/README.md b/src/secp256k1/README.md new file mode 100644 index 0000000000..6095db4220 --- /dev/null +++ b/src/secp256k1/README.md @@ -0,0 +1,61 @@ +libsecp256k1 +============ + +[](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 diff --git a/src/secp256k1/TODO b/src/secp256k1/TODO new file mode 100644 index 0000000000..a300e1c5eb --- /dev/null +++ b/src/secp256k1/TODO @@ -0,0 +1,3 @@ +* Unit tests for fieldelem/groupelem, including ones intended to + trigger fieldelem's boundary cases. +* Complete constant-time operations for signing/keygen diff --git a/src/secp256k1/autogen.sh b/src/secp256k1/autogen.sh new file mode 100755 index 0000000000..65286b9353 --- /dev/null +++ b/src/secp256k1/autogen.sh @@ -0,0 +1,3 @@ +#!/bin/sh +set -e +autoreconf -if --warnings=all diff --git a/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4 new file mode 100644 index 0000000000..4a398d6c93 --- /dev/null +++ b/src/secp256k1/build-aux/m4/bitcoin_secp.m4 @@ -0,0 +1,61 @@ +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 +]) diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac new file mode 100644 index 0000000000..3dc1829516 --- /dev/null +++ b/src/secp256k1/configure.ac @@ -0,0 +1,330 @@ +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 diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h new file mode 100644 index 0000000000..a6e39d13db --- /dev/null +++ b/src/secp256k1/include/secp256k1.h @@ -0,0 +1,295 @@ +#ifndef _SECP256K1_ +# define _SECP256K1_ + +# ifdef __cplusplus +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(unsigned int flags); + +/** Free all memory associated with this library. After this, no + * functions can be called anymore, except secp256k1_start() + */ +void secp256k1_stop(void); + +/** Verify an ECDSA signature. + * Returns: 1: correct signature + * 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. + */ +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: 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 *msg32, + unsigned char *sig, + int *siglen, + const unsigned char *seckey, + 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: 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 *msg32, + unsigned char *sig64, + const unsigned char *seckey, + 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 successfully recovered (which guarantees a correct signature). + * 0: otherwise. + * 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 (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. + */ +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 +) 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 (cannot be NULL) + */ +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 + */ +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 (cannot be NULL) + * Out: pubkey: pointer to a 33-byte (if compressed) or 65-byte (if uncompressed) + * area to store the public key (cannot be NULL) + * pubkeylen: pointer to int that will be updated to contains the pubkey's + * length (cannot be NULL) + * Returns: 1: secret was valid, public key stores + * 0: secret was invalid, try again. + * Requires starting using SECP256K1_START_SIGN. + */ +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); + +/** 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); + +/** 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); + +/** 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); + +/** 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 +} +# endif + +#endif diff --git a/src/secp256k1/libsecp256k1.pc.in b/src/secp256k1/libsecp256k1.pc.in new file mode 100644 index 0000000000..1c72dd0003 --- /dev/null +++ b/src/secp256k1/libsecp256k1.pc.in @@ -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 + diff --git a/src/secp256k1/obj/.gitignore b/src/secp256k1/obj/.gitignore new file mode 100644 index 0000000000..e69de29bb2 --- /dev/null +++ b/src/secp256k1/obj/.gitignore diff --git a/src/secp256k1/src/bench.h b/src/secp256k1/src/bench.h new file mode 100644 index 0000000000..0559b3e853 --- /dev/null +++ b/src/secp256k1/src/bench.h @@ -0,0 +1,56 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c new file mode 100644 index 0000000000..a960549b94 --- /dev/null +++ b/src/secp256k1/src/bench_internal.c @@ -0,0 +1,318 @@ +/********************************************************************** + * 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; +} diff --git a/src/secp256k1/src/bench_recover.c b/src/secp256k1/src/bench_recover.c new file mode 100644 index 0000000000..6991cc9d6c --- /dev/null +++ b/src/secp256k1/src/bench_recover.c @@ -0,0 +1,49 @@ +/********************************************************************** + * 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; +} diff --git a/src/secp256k1/src/bench_sign.c b/src/secp256k1/src/bench_sign.c new file mode 100644 index 0000000000..c5b6829a84 --- /dev/null +++ b/src/secp256k1/src/bench_sign.c @@ -0,0 +1,48 @@ +/********************************************************************** + * 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; +} diff --git a/src/secp256k1/src/bench_verify.c b/src/secp256k1/src/bench_verify.c new file mode 100644 index 0000000000..c279305a0d --- /dev/null +++ b/src/secp256k1/src/bench_verify.c @@ -0,0 +1,55 @@ +/********************************************************************** + * 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; +} diff --git a/src/secp256k1/src/ecdsa.h b/src/secp256k1/src/ecdsa.h new file mode 100644 index 0000000000..c195e7afcb --- /dev/null +++ b/src/secp256k1/src/ecdsa.h @@ -0,0 +1,23 @@ +/********************************************************************** + * 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 "scalar.h" +#include "group.h" + +typedef struct { + secp256k1_scalar_t r, s; +} secp256k1_ecdsa_sig_t; + +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 diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h new file mode 100644 index 0000000000..1a77649390 --- /dev/null +++ b/src/secp256k1/src/ecdsa_impl.h @@ -0,0 +1,231 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/eckey.h b/src/secp256k1/src/eckey.h new file mode 100644 index 0000000000..6de5dc0a59 --- /dev/null +++ b/src/secp256k1/src/eckey.h @@ -0,0 +1,24 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/eckey_impl.h b/src/secp256k1/src/eckey_impl.h new file mode 100644 index 0000000000..3e06d05b47 --- /dev/null +++ b/src/secp256k1/src/eckey_impl.h @@ -0,0 +1,190 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h new file mode 100644 index 0000000000..15a7100a4a --- /dev/null +++ b/src/secp256k1/src/ecmult.h @@ -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_ +#define _SECP256K1_ECMULT_ + +#include "num.h" +#include "group.h" + +static void secp256k1_ecmult_start(void); +static void secp256k1_ecmult_stop(void); + +/** Double multiply: R = na*A + ng*G */ +static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng); + +#endif diff --git a/src/secp256k1/src/ecmult_gen.h b/src/secp256k1/src/ecmult_gen.h new file mode 100644 index 0000000000..42f822f9ce --- /dev/null +++ b/src/secp256k1/src/ecmult_gen.h @@ -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 diff --git a/src/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h new file mode 100644 index 0000000000..849452c7a1 --- /dev/null +++ b/src/secp256k1/src/ecmult_gen_impl.h @@ -0,0 +1,126 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h new file mode 100644 index 0000000000..ece0b0a459 --- /dev/null +++ b/src/secp256k1/src/ecmult_impl.h @@ -0,0 +1,288 @@ +/********************************************************************** + * 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 = checked_malloc(sizeof(secp256k1_gej_t) * table_size); + secp256k1_ge_t *prea = 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 diff --git a/src/secp256k1/src/field.h b/src/secp256k1/src/field.h new file mode 100644 index 0000000000..9e6d7d3c04 --- /dev/null +++ b/src/secp256k1/src/field.h @@ -0,0 +1,116 @@ +/********************************************************************** + * 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_ + +/** Field element module. + * + * Field elements can be represented in several ways, but code accessing + * it (and implementations) need to take certain properaties into account: + * - Each field element can be normalized or not. + * - Each field element has a magnitude, which represents how far away + * its representation is away from normalization. Normalized elements + * always have a magnitude of 1, but a magnitude of 1 doesn't imply + * normality. + */ + +#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" +#else +#error "Please select field implementation" +#endif + +/** Normalize a field element. */ +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. */ +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. */ +static int secp256k1_fe_is_zero(const secp256k1_fe_t *a); + +/** Check the "oddness" of a field element. Requires the input to be normalized. */ +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 */ +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. 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 */ +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. */ +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. */ +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. */ +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). */ +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). */ +static void secp256k1_fe_sqr(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). */ +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. */ +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 the storage type. */ +static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t*); + +/** 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 diff --git a/src/secp256k1/src/field_10x26.h b/src/secp256k1/src/field_10x26.h new file mode 100644 index 0000000000..44bce6525d --- /dev/null +++ b/src/secp256k1/src/field_10x26.h @@ -0,0 +1,47 @@ +/********************************************************************** + * 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_ + +#include <stdint.h> + +typedef struct { + /* X = sum(i=0..9, elem[i]*2^26) mod n */ + uint32_t n[10]; +#ifdef VERIFY + int magnitude; + int normalized; +#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 diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h new file mode 100644 index 0000000000..0afbb18a4a --- /dev/null +++ b/src/secp256k1/src/field_10x26_impl.h @@ -0,0 +1,1111 @@ +/********************************************************************** + * 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_ + +#include <stdio.h> +#include <string.h> +#include "util.h" +#include "num.h" +#include "field.h" + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe_t *a) { + const uint32_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + r &= (d[0] <= 0x3FFFFFFUL * m); + r &= (d[1] <= 0x3FFFFFFUL * m); + r &= (d[2] <= 0x3FFFFFFUL * m); + r &= (d[3] <= 0x3FFFFFFUL * m); + r &= (d[4] <= 0x3FFFFFFUL * m); + r &= (d[5] <= 0x3FFFFFFUL * m); + r &= (d[6] <= 0x3FFFFFFUL * m); + r &= (d[7] <= 0x3FFFFFFUL * m); + r &= (d[8] <= 0x3FFFFFFUL * m); + r &= (d[9] <= 0x03FFFFFUL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 32); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[9] == 0x03FFFFFUL)) { + uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2]; + if (mid == 0x3FFFFFFUL) { + r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL); + } + } + } + VERIFY_CHECK(r == 1); +} +#else +static void secp256k1_fe_verify(const secp256k1_fe_t *a) { + (void)a; +} +#endif + +static void secp256k1_fe_normalize(secp256k1_fe_t *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + if (x) { + t0 += 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint32_t z0, z1; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) { + uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9; + uint32_t z0, z1; + uint32_t x; + + t0 = r->n[0]; + t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + x = t9 >> 22; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0x3FFFFFFUL; + z1 = z0 ^ 0x3D0UL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) + return 0; + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + t4 = r->n[4]; + t5 = r->n[5]; + t6 = r->n[6]; + t7 = r->n[7]; + t8 = r->n[8]; + + t9 &= 0x03FFFFFUL; + t1 += (x << 6); + + t1 += (t0 >> 26); t0 = z0; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_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; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) { + const uint32_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_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<10; 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 = 9; i >= 0; i--) { + if (a->n[i] > b->n[i]) return 1; + if (a->n[i] < b->n[i]) return -1; + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) { + int i; + 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 (i=0; i<32; i++) { + int j; + for (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; + } + } + if (r->n[9] == 0x3FFFFFUL && (r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL && (r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL) { + 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<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; + } +} + +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] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4]; + r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5]; + r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6]; + r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7]; + r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8]; + r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; + r->n[5] *= a; + r->n[6] *= a; + r->n[7] *= a; + r->n[8] *= a; + r->n[9] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_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]; + r->n[5] += a->n[5]; + r->n[6] += a->n[6]; + r->n[7] += a->n[7]; + r->n[8] += a->n[8]; + r->n[9] += a->n[9]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + VERIFY_BITS(b[0], 30); + VERIFY_BITS(b[1], 30); + VERIFY_BITS(b[2], 30); + VERIFY_BITS(b[3], 30); + VERIFY_BITS(b[4], 30); + VERIFY_BITS(b[5], 30); + VERIFY_BITS(b[6], 30); + VERIFY_BITS(b[7], 30); + VERIFY_BITS(b[8], 30); + VERIFY_BITS(b[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)a[0] * b[9] + + (uint64_t)a[1] * b[8] + + (uint64_t)a[2] * b[7] + + (uint64_t)a[3] * b[6] + + (uint64_t)a[4] * b[5] + + (uint64_t)a[5] * b[4] + + (uint64_t)a[6] * b[3] + + (uint64_t)a[7] * b[2] + + (uint64_t)a[8] * b[1] + + (uint64_t)a[9] * b[0]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * b[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)a[1] * b[9] + + (uint64_t)a[2] * b[8] + + (uint64_t)a[3] * b[7] + + (uint64_t)a[4] * b[6] + + (uint64_t)a[5] * b[5] + + (uint64_t)a[6] * b[4] + + (uint64_t)a[7] * b[3] + + (uint64_t)a[8] * b[2] + + (uint64_t)a[9] * b[1]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)a[0] * b[1] + + (uint64_t)a[1] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)a[2] * b[9] + + (uint64_t)a[3] * b[8] + + (uint64_t)a[4] * b[7] + + (uint64_t)a[5] * b[6] + + (uint64_t)a[6] * b[5] + + (uint64_t)a[7] * b[4] + + (uint64_t)a[8] * b[3] + + (uint64_t)a[9] * b[2]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)a[0] * b[2] + + (uint64_t)a[1] * b[1] + + (uint64_t)a[2] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)a[3] * b[9] + + (uint64_t)a[4] * b[8] + + (uint64_t)a[5] * b[7] + + (uint64_t)a[6] * b[6] + + (uint64_t)a[7] * b[5] + + (uint64_t)a[8] * b[4] + + (uint64_t)a[9] * b[3]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[3] + + (uint64_t)a[1] * b[2] + + (uint64_t)a[2] * b[1] + + (uint64_t)a[3] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)a[4] * b[9] + + (uint64_t)a[5] * b[8] + + (uint64_t)a[6] * b[7] + + (uint64_t)a[7] * b[6] + + (uint64_t)a[8] * b[5] + + (uint64_t)a[9] * b[4]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[4] + + (uint64_t)a[1] * b[3] + + (uint64_t)a[2] * b[2] + + (uint64_t)a[3] * b[1] + + (uint64_t)a[4] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[5] * b[9] + + (uint64_t)a[6] * b[8] + + (uint64_t)a[7] * b[7] + + (uint64_t)a[8] * b[6] + + (uint64_t)a[9] * b[5]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[5] + + (uint64_t)a[1] * b[4] + + (uint64_t)a[2] * b[3] + + (uint64_t)a[3] * b[2] + + (uint64_t)a[4] * b[1] + + (uint64_t)a[5] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[6] * b[9] + + (uint64_t)a[7] * b[8] + + (uint64_t)a[8] * b[7] + + (uint64_t)a[9] * b[6]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[6] + + (uint64_t)a[1] * b[5] + + (uint64_t)a[2] * b[4] + + (uint64_t)a[3] * b[3] + + (uint64_t)a[4] * b[2] + + (uint64_t)a[5] * b[1] + + (uint64_t)a[6] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[7] * b[9] + + (uint64_t)a[8] * b[8] + + (uint64_t)a[9] * b[7]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[7] + + (uint64_t)a[1] * b[6] + + (uint64_t)a[2] * b[5] + + (uint64_t)a[3] * b[4] + + (uint64_t)a[4] * b[3] + + (uint64_t)a[5] * b[2] + + (uint64_t)a[6] * b[1] + + (uint64_t)a[7] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[8] * b[9] + + (uint64_t)a[9] * b[8]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[8] + + (uint64_t)a[1] * b[7] + + (uint64_t)a[2] * b[6] + + (uint64_t)a[3] * b[5] + + (uint64_t)a[4] * b[4] + + (uint64_t)a[5] * b[3] + + (uint64_t)a[6] * b[2] + + (uint64_t)a[7] * b[1] + + (uint64_t)a[8] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * b[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)(a[0]*2) * a[9] + + (uint64_t)(a[1]*2) * a[8] + + (uint64_t)(a[2]*2) * a[7] + + (uint64_t)(a[3]*2) * a[6] + + (uint64_t)(a[4]*2) * a[5]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * a[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)(a[1]*2) * a[9] + + (uint64_t)(a[2]*2) * a[8] + + (uint64_t)(a[3]*2) * a[7] + + (uint64_t)(a[4]*2) * a[6] + + (uint64_t)a[5] * a[5]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)(a[0]*2) * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)(a[2]*2) * a[9] + + (uint64_t)(a[3]*2) * a[8] + + (uint64_t)(a[4]*2) * a[7] + + (uint64_t)(a[5]*2) * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[2] + + (uint64_t)a[1] * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)(a[3]*2) * a[9] + + (uint64_t)(a[4]*2) * a[8] + + (uint64_t)(a[5]*2) * a[7] + + (uint64_t)a[6] * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[3] + + (uint64_t)(a[1]*2) * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)(a[4]*2) * a[9] + + (uint64_t)(a[5]*2) * a[8] + + (uint64_t)(a[6]*2) * a[7]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[4] + + (uint64_t)(a[1]*2) * a[3] + + (uint64_t)a[2] * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[5]*2) * a[9] + + (uint64_t)(a[6]*2) * a[8] + + (uint64_t)a[7] * a[7]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[5] + + (uint64_t)(a[1]*2) * a[4] + + (uint64_t)(a[2]*2) * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[6]*2) * a[9] + + (uint64_t)(a[7]*2) * a[8]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[6] + + (uint64_t)(a[1]*2) * a[5] + + (uint64_t)(a[2]*2) * a[4] + + (uint64_t)a[3] * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[7]*2) * a[9] + + (uint64_t)a[8] * a[8]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[7] + + (uint64_t)(a[1]*2) * a[6] + + (uint64_t)(a[2]*2) * a[5] + + (uint64_t)(a[3]*2) * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[8]*2) * a[9]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[8] + + (uint64_t)(a[1]*2) * a[7] + + (uint64_t)(a[2]*2) * a[6] + + (uint64_t)(a[3]*2) * a[5] + + (uint64_t)a[4] * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * a[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + + +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) { + uint32_t mask0, mask1; + mask0 = flag + ~((uint32_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); + r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1); + r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1); + r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 26; + r->n[1] = a->n[1] >> 6 | a->n[2] << 20; + r->n[2] = a->n[2] >> 12 | a->n[3] << 14; + r->n[3] = a->n[3] >> 18 | a->n[4] << 8; + r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28; + r->n[5] = a->n[6] >> 4 | a->n[7] << 22; + r->n[6] = a->n[7] >> 10 | a->n[8] << 16; + r->n[7] = a->n[8] >> 16 | a->n[9] << 10; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) { + r->n[0] = a->n[0] & 0x3FFFFFFUL; + r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL); + r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL); + r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL); + r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL); + r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL; + r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL); + r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL); + r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL); + r->n[9] = a->n[7] >> 10; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; +#endif +} + +#endif diff --git a/src/secp256k1/src/field_5x52.h b/src/secp256k1/src/field_5x52.h new file mode 100644 index 0000000000..4513d36f49 --- /dev/null +++ b/src/secp256k1/src/field_5x52.h @@ -0,0 +1,47 @@ +/********************************************************************** + * 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_ + +#include <stdint.h> + +typedef struct { + /* X = sum(i=0..4, elem[i]*2^52) mod n */ + uint64_t n[5]; +#ifdef VERIFY + int magnitude; + int normalized; +#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 diff --git a/src/secp256k1/src/field_5x52_asm_impl.h b/src/secp256k1/src/field_5x52_asm_impl.h new file mode 100644 index 0000000000..98cc004bf0 --- /dev/null +++ b/src/secp256k1/src/field_5x52_asm_impl.h @@ -0,0 +1,502 @@ +/********************************************************************** + * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or 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 diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h new file mode 100644 index 0000000000..2f9c8704a8 --- /dev/null +++ b/src/secp256k1/src/field_5x52_impl.h @@ -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_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 diff --git a/src/secp256k1/src/field_5x52_int128_impl.h b/src/secp256k1/src/field_5x52_int128_impl.h new file mode 100644 index 0000000000..9280bb5ea2 --- /dev/null +++ b/src/secp256k1/src/field_5x52_int128_impl.h @@ -0,0 +1,277 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h new file mode 100644 index 0000000000..047914cf28 --- /dev/null +++ b/src/secp256k1/src/field_impl.h @@ -0,0 +1,214 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h new file mode 100644 index 0000000000..d1e5834909 --- /dev/null +++ b/src/secp256k1/src/group.h @@ -0,0 +1,118 @@ +/********************************************************************** + * 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_ + +#include "num.h" +#include "field.h" + +/** A group element of the secp256k1 curve, in affine coordinates. */ +typedef struct { + secp256k1_fe_t x; + secp256k1_fe_t y; + 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 z; + int infinity; /* whether this represents the point at infinity */ +} secp256k1_gej_t; + +#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0} +#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} + +typedef struct { + secp256k1_fe_storage_t x; + secp256k1_fe_storage_t y; +} secp256k1_ge_storage_t; + +#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 */ +static void secp256k1_ge_set_infinity(secp256k1_ge_t *r); + +/** Set a group element equal to the point with given X and Y coordinates */ +static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y); + +/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness + * for Y. Return value indicates whether the result is valid. */ +static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a); + +/** Check whether a group element is valid (i.e., on the curve). */ +static int secp256k1_ge_is_valid_var(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 */ +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. */ +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. */ +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. */ +static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_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) */ +static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a); + +/** Set r equal to the double of 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. */ +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 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); + +/** 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. */ +static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a); +#endif + +/** 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 diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h new file mode 100644 index 0000000000..8d8c359c5a --- /dev/null +++ b/src/secp256k1/src/group_impl.h @@ -0,0 +1,430 @@ +/********************************************************************** + * 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 = checked_malloc(sizeof(secp256k1_fe_t) * len); + for (i = 0; i < len; i++) { + if (!a[i].infinity) { + az[count++] = a[i].z; + } + } + + azi = 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 diff --git a/src/secp256k1/src/hash.h b/src/secp256k1/src/hash.h new file mode 100644 index 0000000000..843423d7f7 --- /dev/null +++ b/src/secp256k1/src/hash.h @@ -0,0 +1,41 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or 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 diff --git a/src/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h new file mode 100644 index 0000000000..60fdbf7718 --- /dev/null +++ b/src/secp256k1/src/hash_impl.h @@ -0,0 +1,286 @@ +/********************************************************************** + * 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); + memset(rng->k, 0x00, 32); + + 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) { + 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); + + 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) { + 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) { + 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 diff --git a/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java new file mode 100644 index 0000000000..90a498eaa2 --- /dev/null +++ b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java @@ -0,0 +1,60 @@ +package org.bitcoin; + +import java.nio.ByteBuffer; +import java.nio.ByteOrder; + +import com.google.common.base.Preconditions; + + +/** + * This class holds native methods to handle ECDSA verification. + * You can find an example library that can be used for this at + * https://github.com/sipa/secp256k1 + */ +public class NativeSecp256k1 { + public static final boolean enabled; + static { + boolean isEnabled = true; + try { + System.loadLibrary("javasecp256k1"); + } catch (UnsatisfiedLinkError e) { + isEnabled = false; + } + enabled = isEnabled; + } + + private static ThreadLocal<ByteBuffer> nativeECDSABuffer = new ThreadLocal<ByteBuffer>(); + /** + * Verifies the given secp256k1 signature in native code. + * Calling when enabled == false is undefined (probably library not loaded) + * + * @param data The data which was signed, must be exactly 32 bytes + * @param signature The signature + * @param pub The public key which did the signing + */ + public static boolean verify(byte[] data, byte[] signature, byte[] pub) { + Preconditions.checkArgument(data.length == 32 && signature.length <= 520 && pub.length <= 520); + + ByteBuffer byteBuff = nativeECDSABuffer.get(); + if (byteBuff == null) { + byteBuff = ByteBuffer.allocateDirect(32 + 8 + 520 + 520); + byteBuff.order(ByteOrder.nativeOrder()); + nativeECDSABuffer.set(byteBuff); + } + byteBuff.rewind(); + byteBuff.put(data); + byteBuff.putInt(signature.length); + byteBuff.putInt(pub.length); + byteBuff.put(signature); + byteBuff.put(pub); + return secp256k1_ecdsa_verify(byteBuff) == 1; + } + + /** + * @param byteBuff signature format is byte[32] data, + * native-endian int signatureLength, native-endian int pubkeyLength, + * byte[signatureLength] signature, byte[pubkeyLength] pub + * @returns 1 for valid signature, anything else for invalid + */ + private static native int secp256k1_ecdsa_verify(ByteBuffer byteBuff); +} diff --git a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c new file mode 100644 index 0000000000..bb4cd70728 --- /dev/null +++ b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c @@ -0,0 +1,23 @@ +#include "org_bitcoin_NativeSecp256k1.h" +#include "include/secp256k1.h" + +JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify + (JNIEnv* env, jclass classObject, jobject byteBufferObject) +{ + unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject); + int sigLen = *((int*)(data + 32)); + int pubLen = *((int*)(data + 32 + 4)); + + return secp256k1_ecdsa_verify(data, 32, data+32+8, sigLen, data+32+8+sigLen, pubLen); +} + +static void __javasecp256k1_attach(void) __attribute__((constructor)); +static void __javasecp256k1_detach(void) __attribute__((destructor)); + +static void __javasecp256k1_attach(void) { + secp256k1_start(SECP256K1_START_VERIFY); +} + +static void __javasecp256k1_detach(void) { + secp256k1_stop(); +} diff --git a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h new file mode 100644 index 0000000000..d7fb004fa8 --- /dev/null +++ b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h @@ -0,0 +1,21 @@ +/* DO NOT EDIT THIS FILE - it is machine generated */ +#include <jni.h> +/* Header for class org_bitcoin_NativeSecp256k1 */ + +#ifndef _Included_org_bitcoin_NativeSecp256k1 +#define _Included_org_bitcoin_NativeSecp256k1 +#ifdef __cplusplus +extern "C" { +#endif +/* + * Class: org_bitcoin_NativeSecp256k1 + * Method: secp256k1_ecdsa_verify + * Signature: (Ljava/nio/ByteBuffer;)I + */ +JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify + (JNIEnv *, jclass, jobject); + +#ifdef __cplusplus +} +#endif +#endif diff --git a/src/secp256k1/src/num.h b/src/secp256k1/src/num.h new file mode 100644 index 0000000000..339b6bb6ec --- /dev/null +++ b/src/secp256k1/src/num.h @@ -0,0 +1,68 @@ +/********************************************************************** + * 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" +#else +#error "Please select num implementation" +#endif + +/** Copy a number. */ +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. */ +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. */ +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. */ +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. */ +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. */ +static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b); + +/** Subtract two (signed) numbers. */ +static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b); + +/** Multiply two (signed) numbers. */ +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. */ +static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m); + +/** 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. */ +static int secp256k1_num_is_zero(const secp256k1_num_t *a); + +/** Check whether a number is strictly negative. */ +static int secp256k1_num_is_neg(const secp256k1_num_t *a); + +/** Change a number's sign. */ +static void secp256k1_num_negate(secp256k1_num_t *r); + +#endif + +#endif diff --git a/src/secp256k1/src/num_gmp.h b/src/secp256k1/src/num_gmp.h new file mode 100644 index 0000000000..baa1f2bf2e --- /dev/null +++ b/src/secp256k1/src/num_gmp.h @@ -0,0 +1,20 @@ +/********************************************************************** + * 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_ + +#include <gmp.h> + +#define NUM_LIMBS ((256+GMP_NUMB_BITS-1)/GMP_NUMB_BITS) + +typedef struct { + mp_limb_t data[2*NUM_LIMBS]; + int neg; + int limbs; +} secp256k1_num_t; + +#endif diff --git a/src/secp256k1/src/num_gmp_impl.h b/src/secp256k1/src/num_gmp_impl.h new file mode 100644 index 0000000000..3e4b92d329 --- /dev/null +++ b/src/secp256k1/src/num_gmp_impl.h @@ -0,0 +1,237 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/num_impl.h b/src/secp256k1/src/num_impl.h new file mode 100644 index 0000000000..0b0e3a072a --- /dev/null +++ b/src/secp256k1/src/num_impl.h @@ -0,0 +1,24 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h new file mode 100644 index 0000000000..f5d09f8d47 --- /dev/null +++ b/src/secp256k1/src/scalar.h @@ -0,0 +1,93 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/scalar_4x64.h b/src/secp256k1/src/scalar_4x64.h new file mode 100644 index 0000000000..82899aa7b0 --- /dev/null +++ b/src/secp256k1/src/scalar_4x64.h @@ -0,0 +1,19 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or 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 diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h new file mode 100644 index 0000000000..ff365292f8 --- /dev/null +++ b/src/secp256k1/src/scalar_4x64_impl.h @@ -0,0 +1,920 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/scalar_8x32.h b/src/secp256k1/src/scalar_8x32.h new file mode 100644 index 0000000000..f17017e24e --- /dev/null +++ b/src/secp256k1/src/scalar_8x32.h @@ -0,0 +1,19 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or 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 diff --git a/src/secp256k1/src/scalar_8x32_impl.h b/src/secp256k1/src/scalar_8x32_impl.h new file mode 100644 index 0000000000..22b31d4112 --- /dev/null +++ b/src/secp256k1/src/scalar_8x32_impl.h @@ -0,0 +1,681 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h new file mode 100644 index 0000000000..3acbe264ae --- /dev/null +++ b/src/secp256k1/src/scalar_impl.h @@ -0,0 +1,289 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c new file mode 100644 index 0000000000..8c4eca4b62 --- /dev/null +++ b/src/secp256k1/src/secp256k1.c @@ -0,0 +1,372 @@ +/********************************************************************** + * 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.* + **********************************************************************/ + +#define SECP256K1_BUILD (1) + +#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_ecmult_gen_stop(); +} + +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_scalar_t m; + int ret = -3; + DEBUG_CHECK(secp256k1_ecmult_consts != NULL); + DEBUG_CHECK(msg32 != NULL); + DEBUG_CHECK(sig != NULL); + DEBUG_CHECK(pubkey != NULL); + + 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; + } + } else { + ret = -2; + } + } else { + ret = -1; + } + + return ret; +} + +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, 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_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(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_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)) { + ret = secp256k1_eckey_pubkey_serialize(&q, pubkey, pubkeylen, compressed); + } + } + } + return ret; +} + +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_ec_pubkey_verify(const unsigned char *pubkey, int pubkeylen) { + secp256k1_ge_t q; + DEBUG_CHECK(pubkey != NULL); + + return secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen); +} + +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_scalar_clear(&sec); + secp256k1_ge_set_gej(&p, &pj); + ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, compressed); + } + if (!ret) { + *pubkeylen = 0; + } + return ret; +} + +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) { + 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) { + int oldlen = pubkeylen; + ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33); + VERIFY_CHECK(pubkeylen == oldlen); + } + } + + return ret; +} + +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_scalar_get_b32(seckey, &sec); + } + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&factor); + return ret; +} + +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) { + ret = secp256k1_eckey_pubkey_tweak_mul(&p, &factor); + } + if (ret) { + int oldlen = pubkeylen; + ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33); + VERIFY_CHECK(pubkeylen == oldlen); + } + } + + return ret; +} + +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_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; +} diff --git a/src/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h new file mode 100644 index 0000000000..041bb92c47 --- /dev/null +++ b/src/secp256k1/src/testrand.h @@ -0,0 +1,28 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h new file mode 100644 index 0000000000..21c69f1c51 --- /dev/null +++ b/src/secp256k1/src/testrand_impl.h @@ -0,0 +1,60 @@ +/********************************************************************** + * 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 diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c new file mode 100644 index 0000000000..f7f1acac64 --- /dev/null +++ b/src/secp256k1/src/tests.c @@ -0,0 +1,1880 @@ +/********************************************************************** + * 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.* + **********************************************************************/ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include <stdio.h> +#include <stdlib.h> + +#include <time.h> + +#include "secp256k1.c" +#include "testrand_impl.h" + +#ifdef ENABLE_OPENSSL_TESTS +#include "openssl/bn.h" +#include "openssl/ec.h" +#include "openssl/ecdsa.h" +#include "openssl/obj_mac.h" +#endif + +static int count = 64; + +void random_field_element_test(secp256k1_fe_t *fe) { + do { + unsigned char b32[32]; + secp256k1_rand256_test(b32); + if (secp256k1_fe_set_b32(fe, b32)) { + break; + } + } while(1); +} + +void random_field_element_magnitude(secp256k1_fe_t *fe) { + secp256k1_fe_t zero; + int n = secp256k1_rand32() % 9; + secp256k1_fe_normalize(fe); + if (n == 0) { + return; + } + secp256k1_fe_clear(&zero); + secp256k1_fe_negate(&zero, &zero, 0); + secp256k1_fe_mul_int(&zero, n - 1); + secp256k1_fe_add(fe, &zero); +#ifdef VERIFY + CHECK(fe->magnitude == n); +#endif +} + +void random_group_element_test(secp256k1_ge_t *ge) { + secp256k1_fe_t fe; + do { + random_field_element_test(&fe); + if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand32() & 1)) + break; + } while(1); +} + +void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge_t *ge) { + secp256k1_fe_t z2, z3; + do { + random_field_element_test(&gej->z); + if (!secp256k1_fe_is_zero(&gej->z)) { + break; + } + } while(1); + secp256k1_fe_sqr(&z2, &gej->z); + secp256k1_fe_mul(&z3, &z2, &gej->z); + secp256k1_fe_mul(&gej->x, &ge->x, &z2); + secp256k1_fe_mul(&gej->y, &ge->y, &z3); + gej->infinity = ge->infinity; +} + +void random_scalar_order_test(secp256k1_scalar_t *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_rand256_test(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) + continue; + break; + } while(1); +} + +void random_scalar_order(secp256k1_scalar_t *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_rand256(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) + continue; + break; + } while(1); +} + +/***** HASH TESTS *****/ + +void run_sha256_tests(void) { + static const char *inputs[8] = { + "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe", + "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq", + "For this sample, this 63-byte string will be used as input data", + "This is exactly 64 bytes long, not counting the terminating byte" + }; + static const unsigned char outputs[8][32] = { + {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}, + {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad}, + {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50}, + {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d}, + {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30}, + {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1}, + {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42}, + {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8} + }; + int i; + for (i = 0; i < 8; i++) { + unsigned char out[32]; + secp256k1_sha256_t hasher; + secp256k1_sha256_initialize(&hasher); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + secp256k1_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + if (strlen(inputs[i]) > 0) { + int split = secp256k1_rand32() % strlen(inputs[i]); + secp256k1_sha256_initialize(&hasher); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + secp256k1_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + } + } +} + +void run_hmac_sha256_tests(void) { + static const char *keys[6] = { + "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b", + "\x4a\x65\x66\x65", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa" + }; + static const char *inputs[6] = { + "\x48\x69\x20\x54\x68\x65\x72\x65", + "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f", + "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd", + "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd", + "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74", + "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e" + }; + static const unsigned char outputs[6][32] = { + {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7}, + {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43}, + {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe}, + {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b}, + {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54}, + {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2} + }; + int i; + for (i = 0; i < 6; i++) { + secp256k1_hmac_sha256_t hasher; + unsigned char out[32]; + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + if (strlen(inputs[i]) > 0) { + int split = secp256k1_rand32() % strlen(inputs[i]); + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + } + } +} + +void run_rfc6979_hmac_sha256_tests(void) { + static const unsigned char key1[32] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00}; + static const unsigned char msg1[32] = {0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a}; + static const unsigned char out1[3][32] = { + {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb}, + {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a}, + {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e} + }; + + static const unsigned char key2[32] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}; + static const unsigned char msg2[32] = {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}; + static const unsigned char out2[3][32] = { + {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95}, + {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9}, + {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94} + }; + + secp256k1_rfc6979_hmac_sha256_t rng; + unsigned char out[32]; + unsigned char zero[1] = {0}; + int i; + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 32, msg1, 32, NULL, 1); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out1[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 32, msg1, 32, zero, 1); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out1[i], 32) != 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 32, msg2, 32, zero, 0); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out2[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); +} + +/***** NUM TESTS *****/ + +#ifndef USE_NUM_NONE +void random_num_negate(secp256k1_num_t *num) { + if (secp256k1_rand32() & 1) + secp256k1_num_negate(num); +} + +void random_num_order_test(secp256k1_num_t *num) { + secp256k1_scalar_t sc; + random_scalar_order_test(&sc); + secp256k1_scalar_get_num(num, &sc); +} + +void random_num_order(secp256k1_num_t *num) { + secp256k1_scalar_t sc; + random_scalar_order(&sc); + secp256k1_scalar_get_num(num, &sc); +} + +void test_num_negate(void) { + secp256k1_num_t n1; + secp256k1_num_t n2; + random_num_order_test(&n1); /* n1 = R */ + random_num_negate(&n1); + secp256k1_num_copy(&n2, &n1); /* n2 = R */ + secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */ + CHECK(secp256k1_num_is_zero(&n1)); + secp256k1_num_copy(&n1, &n2); /* n1 = R */ + secp256k1_num_negate(&n1); /* n1 = -R */ + CHECK(!secp256k1_num_is_zero(&n1)); + secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */ + CHECK(secp256k1_num_is_zero(&n1)); + secp256k1_num_copy(&n1, &n2); /* n1 = R */ + secp256k1_num_negate(&n1); /* n1 = -R */ + CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2)); + secp256k1_num_negate(&n1); /* n1 = R */ + CHECK(secp256k1_num_eq(&n1, &n2)); +} + +void test_num_add_sub(void) { + secp256k1_num_t n1; + secp256k1_num_t n2; + secp256k1_num_t n1p2, n2p1, n1m2, n2m1; + int r = secp256k1_rand32(); + random_num_order_test(&n1); /* n1 = R1 */ + if (r & 1) { + random_num_negate(&n1); + } + random_num_order_test(&n2); /* n2 = R2 */ + if (r & 2) { + random_num_negate(&n2); + } + secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */ + secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */ + secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */ + secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */ + CHECK(secp256k1_num_eq(&n1p2, &n2p1)); + CHECK(!secp256k1_num_eq(&n1p2, &n1m2)); + secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */ + CHECK(secp256k1_num_eq(&n2m1, &n1m2)); + CHECK(!secp256k1_num_eq(&n2m1, &n1)); + secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */ + CHECK(secp256k1_num_eq(&n2m1, &n1)); + CHECK(!secp256k1_num_eq(&n2p1, &n1)); + secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */ + CHECK(secp256k1_num_eq(&n2p1, &n1)); +} + +void run_num_smalltests(void) { + int i; + for (i = 0; i < 100*count; i++) { + test_num_negate(); + test_num_add_sub(); + } +} +#endif + +/***** SCALAR TESTS *****/ + +void scalar_test(void) { + secp256k1_scalar_t s; + secp256k1_scalar_t s1; + secp256k1_scalar_t s2; +#ifndef USE_NUM_NONE + secp256k1_num_t snum, s1num, s2num; + secp256k1_num_t order, half_order; +#endif + unsigned char c[32]; + + /* Set 's' to a random scalar, with value 'snum'. */ + random_scalar_order_test(&s); + + /* Set 's1' to a random scalar, with value 's1num'. */ + random_scalar_order_test(&s1); + + /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */ + random_scalar_order_test(&s2); + secp256k1_scalar_get_b32(c, &s2); + +#ifndef USE_NUM_NONE + secp256k1_scalar_get_num(&snum, &s); + secp256k1_scalar_get_num(&s1num, &s1); + secp256k1_scalar_get_num(&s2num, &s2); + + secp256k1_scalar_order_get_num(&order); + half_order = order; + secp256k1_num_shift(&half_order, 1); +#endif + + { + int i; + /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar_t n; + secp256k1_scalar_set_int(&n, 0); + for (i = 0; i < 256; i += 4) { + secp256k1_scalar_t t; + int j; + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4)); + for (j = 0; j < 4; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + + { + /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar_t n; + int i = 0; + secp256k1_scalar_set_int(&n, 0); + while (i < 256) { + secp256k1_scalar_t t; + int j; + int now = (secp256k1_rand32() % 15) + 1; + if (now + i > 256) { + now = 256 - i; + } + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now)); + for (j = 0; j < now; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + i += now; + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + +#ifndef USE_NUM_NONE + { + /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */ + secp256k1_num_t rnum; + secp256k1_num_t r2num; + secp256k1_scalar_t r; + secp256k1_num_add(&rnum, &snum, &s2num); + secp256k1_num_mod(&rnum, &order); + secp256k1_scalar_add(&r, &s, &s2); + secp256k1_scalar_get_num(&r2num, &r); + CHECK(secp256k1_num_eq(&rnum, &r2num)); + } + + { + /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */ + secp256k1_scalar_t r; + secp256k1_num_t r2num; + secp256k1_num_t rnum; + secp256k1_num_mul(&rnum, &snum, &s2num); + secp256k1_num_mod(&rnum, &order); + secp256k1_scalar_mul(&r, &s, &s2); + secp256k1_scalar_get_num(&r2num, &r); + CHECK(secp256k1_num_eq(&rnum, &r2num)); + /* The result can only be zero if at least one of the factors was zero. */ + CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2))); + /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */ + CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2))); + CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s))); + } + + { + secp256k1_scalar_t neg; + secp256k1_num_t negnum; + secp256k1_num_t negnum2; + /* Check that comparison with zero matches comparison with zero on the number. */ + CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s)); + /* Check that comparison with the half order is equal to testing for high scalar. */ + CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0)); + secp256k1_scalar_negate(&neg, &s); + secp256k1_num_sub(&negnum, &order, &snum); + secp256k1_num_mod(&negnum, &order); + /* Check that comparison with the half order is equal to testing for high scalar after negation. */ + CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0)); + /* Negating should change the high property, unless the value was already zero. */ + CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s)); + secp256k1_scalar_get_num(&negnum2, &neg); + /* Negating a scalar should be equal to (order - n) mod order on the number. */ + CHECK(secp256k1_num_eq(&negnum, &negnum2)); + secp256k1_scalar_add(&neg, &neg, &s); + /* Adding a number to its negation should result in zero. */ + CHECK(secp256k1_scalar_is_zero(&neg)); + secp256k1_scalar_negate(&neg, &neg); + /* Negating zero should still result in zero. */ + CHECK(secp256k1_scalar_is_zero(&neg)); + } + + { + /* Test secp256k1_scalar_mul_shift_var. */ + secp256k1_scalar_t r; + secp256k1_num_t one; + secp256k1_num_t rnum; + secp256k1_num_t rnum2; + unsigned char cone[1] = {0x01}; + unsigned int shift = 256 + (secp256k1_rand32() % 257); + secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift); + secp256k1_num_mul(&rnum, &s1num, &s2num); + secp256k1_num_shift(&rnum, shift - 1); + secp256k1_num_set_bin(&one, cone, 1); + secp256k1_num_add(&rnum, &rnum, &one); + secp256k1_num_shift(&rnum, 1); + secp256k1_scalar_get_num(&rnum2, &r); + CHECK(secp256k1_num_eq(&rnum, &rnum2)); + } +#endif + + { + /* Test that scalar inverses are equal to the inverse of their number modulo the order. */ + if (!secp256k1_scalar_is_zero(&s)) { + secp256k1_scalar_t inv; +#ifndef USE_NUM_NONE + secp256k1_num_t invnum; + secp256k1_num_t invnum2; +#endif + secp256k1_scalar_inverse(&inv, &s); +#ifndef USE_NUM_NONE + secp256k1_num_mod_inverse(&invnum, &snum, &order); + secp256k1_scalar_get_num(&invnum2, &inv); + CHECK(secp256k1_num_eq(&invnum, &invnum2)); +#endif + secp256k1_scalar_mul(&inv, &inv, &s); + /* Multiplying a scalar with its inverse must result in one. */ + CHECK(secp256k1_scalar_is_one(&inv)); + secp256k1_scalar_inverse(&inv, &inv); + /* Inverting one must result in one. */ + CHECK(secp256k1_scalar_is_one(&inv)); + } + } + + { + /* Test commutativity of add. */ + secp256k1_scalar_t r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + secp256k1_scalar_t r1, r2; + secp256k1_scalar_t b; + int i; + /* Test add_bit. */ + int bit = secp256k1_rand32() % 256; + secp256k1_scalar_set_int(&b, 1); + CHECK(secp256k1_scalar_is_one(&b)); + for (i = 0; i < bit; i++) { + secp256k1_scalar_add(&b, &b, &b); + } + r1 = s1; + r2 = s1; + if (!secp256k1_scalar_add(&r1, &r1, &b)) { + /* No overflow happened. */ + secp256k1_scalar_add_bit(&r2, bit); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + } + + { + /* Test commutativity of mul. */ + secp256k1_scalar_t r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of add. */ + secp256k1_scalar_t r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r1, &r1, &s); + secp256k1_scalar_add(&r2, &s2, &s); + secp256k1_scalar_add(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of mul. */ + secp256k1_scalar_t r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s2, &s); + secp256k1_scalar_mul(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test distributitivity of mul over add. */ + secp256k1_scalar_t r1, r2, t; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s1, &s); + secp256k1_scalar_mul(&t, &s2, &s); + secp256k1_scalar_add(&r2, &r2, &t); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test square. */ + secp256k1_scalar_t r1, r2; + secp256k1_scalar_sqr(&r1, &s1); + secp256k1_scalar_mul(&r2, &s1, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test multiplicative identity. */ + secp256k1_scalar_t r1, v1; + secp256k1_scalar_set_int(&v1,1); + secp256k1_scalar_mul(&r1, &s1, &v1); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test additive identity. */ + secp256k1_scalar_t r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_add(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test zero product property. */ + secp256k1_scalar_t r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_mul(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &v0)); + } + +} + +void run_scalar_tests(void) { + int i; + for (i = 0; i < 128 * count; i++) { + scalar_test(); + } + + { + /* (-1)+1 should be zero. */ + secp256k1_scalar_t s, o; + secp256k1_scalar_set_int(&s, 1); + CHECK(secp256k1_scalar_is_one(&s)); + secp256k1_scalar_negate(&o, &s); + secp256k1_scalar_add(&o, &o, &s); + CHECK(secp256k1_scalar_is_zero(&o)); + secp256k1_scalar_negate(&o, &o); + CHECK(secp256k1_scalar_is_zero(&o)); + } + +#ifndef USE_NUM_NONE + { + /* A scalar with value of the curve order should be 0. */ + secp256k1_num_t order; + secp256k1_scalar_t zero; + unsigned char bin[32]; + int overflow = 0; + secp256k1_scalar_order_get_num(&order); + secp256k1_num_get_bin(bin, 32, &order); + secp256k1_scalar_set_b32(&zero, bin, &overflow); + CHECK(overflow == 1); + CHECK(secp256k1_scalar_is_zero(&zero)); + } +#endif +} + +/***** FIELD TESTS *****/ + +void random_fe(secp256k1_fe_t *x) { + unsigned char bin[32]; + do { + secp256k1_rand256(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +void random_fe_non_zero(secp256k1_fe_t *nz) { + int tries = 10; + while (--tries >= 0) { + random_fe(nz); + secp256k1_fe_normalize(nz); + if (!secp256k1_fe_is_zero(nz)) + break; + } + /* Infinitesimal probability of spurious failure here */ + CHECK(tries >= 0); +} + +void random_fe_non_square(secp256k1_fe_t *ns) { + secp256k1_fe_t r; + random_fe_non_zero(ns); + if (secp256k1_fe_sqrt_var(&r, ns)) { + secp256k1_fe_negate(ns, ns, 1); + } +} + +int check_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) { + secp256k1_fe_t an = *a; + secp256k1_fe_t bn = *b; + secp256k1_fe_normalize_weak(&an); + secp256k1_fe_normalize_var(&bn); + return secp256k1_fe_equal_var(&an, &bn); +} + +int check_fe_inverse(const secp256k1_fe_t *a, const secp256k1_fe_t *ai) { + secp256k1_fe_t x; + secp256k1_fe_t one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_fe_mul(&x, a, ai); + return check_fe_equal(&x, &one); +} + +void run_field_convert(void) { + static const unsigned char b32[32] = { + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, + 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40 + }; + static const secp256k1_fe_storage_t fes = SECP256K1_FE_STORAGE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + static const secp256k1_fe_t fe = SECP256K1_FE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + secp256k1_fe_t fe2; + unsigned char b322[32]; + secp256k1_fe_storage_t fes2; + /* Check conversions to fe. */ + CHECK(secp256k1_fe_set_b32(&fe2, b32)); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + secp256k1_fe_from_storage(&fe2, &fes); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + /* Check conversion from fe. */ + secp256k1_fe_get_b32(b322, &fe); + CHECK(memcmp(b322, b32, 32) == 0); + secp256k1_fe_to_storage(&fes2, &fe); + CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0); +} + +void run_field_misc(void) { + secp256k1_fe_t x; + secp256k1_fe_t y; + secp256k1_fe_t z; + secp256k1_fe_t q; + secp256k1_fe_t fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5); + int i; + for (i = 0; i < 5*count; i++) { + secp256k1_fe_storage_t xs, ys, zs; + random_fe(&x); + random_fe_non_zero(&y); + /* Test the fe equality and comparison operations. */ + CHECK(secp256k1_fe_cmp_var(&x, &x) == 0); + CHECK(secp256k1_fe_equal_var(&x, &x)); + z = x; + secp256k1_fe_add(&z,&y); + secp256k1_fe_normalize(&z); + /* Test storage conversion and conditional moves. */ + secp256k1_fe_to_storage(&xs, &x); + secp256k1_fe_to_storage(&ys, &y); + secp256k1_fe_to_storage(&zs, &z); + secp256k1_fe_storage_cmov(&zs, &xs, 0); + CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0); + secp256k1_fe_storage_cmov(&ys, &xs, 1); + CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0); + secp256k1_fe_from_storage(&x, &xs); + secp256k1_fe_from_storage(&y, &ys); + secp256k1_fe_from_storage(&z, &zs); + /* Test that mul_int, mul, and add agree. */ + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&y, &x); + z = x; + secp256k1_fe_mul_int(&z, 3); + CHECK(check_fe_equal(&y, &z)); + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&z, &x); + CHECK(check_fe_equal(&z, &y)); + z = x; + secp256k1_fe_mul_int(&z, 5); + secp256k1_fe_mul(&q, &x, &fe5); + CHECK(check_fe_equal(&z, &q)); + secp256k1_fe_negate(&x, &x, 1); + secp256k1_fe_add(&z, &x); + secp256k1_fe_add(&q, &x); + CHECK(check_fe_equal(&y, &z)); + CHECK(check_fe_equal(&q, &y)); + } +} + +void run_field_inv(void) { + secp256k1_fe_t x, xi, xii; + int i; + for (i = 0; i < 10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_var(void) { + secp256k1_fe_t x, xi, xii; + int i; + for (i = 0; i < 10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv_var(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv_var(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_all_var(void) { + secp256k1_fe_t x[16], xi[16], xii[16]; + int i; + /* Check it's safe to call for 0 elements */ + secp256k1_fe_inv_all_var(0, xi, x); + for (i = 0; i < count; i++) { + size_t j; + size_t len = (secp256k1_rand32() & 15) + 1; + for (j = 0; j < len; j++) + random_fe_non_zero(&x[j]); + secp256k1_fe_inv_all_var(len, xi, x); + for (j = 0; j < len; j++) + CHECK(check_fe_inverse(&x[j], &xi[j])); + secp256k1_fe_inv_all_var(len, xii, xi); + for (j = 0; j < len; j++) + CHECK(check_fe_equal(&x[j], &xii[j])); + } +} + +void run_sqr(void) { + secp256k1_fe_t x, s; + + { + int i; + secp256k1_fe_set_int(&x, 1); + secp256k1_fe_negate(&x, &x, 1); + + for (i = 1; i <= 512; ++i) { + secp256k1_fe_mul_int(&x, 2); + secp256k1_fe_normalize(&x); + secp256k1_fe_sqr(&s, &x); + } + } +} + +void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) { + secp256k1_fe_t r1, r2; + int v = secp256k1_fe_sqrt_var(&r1, a); + CHECK((v == 0) == (k == NULL)); + + if (k != NULL) { + /* Check that the returned root is +/- the given known answer */ + secp256k1_fe_negate(&r2, &r1, 1); + secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k); + secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2); + CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2)); + } +} + +void run_sqrt(void) { + secp256k1_fe_t ns, x, s, t; + int i; + + /* Check sqrt(0) is 0 */ + secp256k1_fe_set_int(&x, 0); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + + /* Check sqrt of small squares (and their negatives) */ + for (i = 1; i <= 100; i++) { + secp256k1_fe_set_int(&x, i); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + } + + /* Consistency checks for large random values */ + for (i = 0; i < 10; i++) { + int j; + random_fe_non_square(&ns); + for (j = 0; j < count; j++) { + random_fe(&x); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + secp256k1_fe_mul(&t, &s, &ns); + test_sqrt(&t, NULL); + } + } +} + +/***** GROUP TESTS *****/ + +void ge_equals_ge(const secp256k1_ge_t *a, const secp256k1_ge_t *b) { + CHECK(a->infinity == b->infinity); + if (a->infinity) + return; + CHECK(secp256k1_fe_equal_var(&a->x, &b->x)); + CHECK(secp256k1_fe_equal_var(&b->y, &b->y)); +} + +void ge_equals_gej(const secp256k1_ge_t *a, const secp256k1_gej_t *b) { + secp256k1_fe_t z2s; + secp256k1_fe_t u1, u2, s1, s2; + CHECK(a->infinity == b->infinity); + if (a->infinity) + return; + /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */ + secp256k1_fe_sqr(&z2s, &b->z); + secp256k1_fe_mul(&u1, &a->x, &z2s); + u2 = b->x; secp256k1_fe_normalize_weak(&u2); + secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z); + s2 = b->y; secp256k1_fe_normalize_weak(&s2); + CHECK(secp256k1_fe_equal_var(&u1, &u2)); + CHECK(secp256k1_fe_equal_var(&s1, &s2)); +} + +void test_ge(void) { + int i, i1; + int runs = 4; + /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4). + * The second in each pair of identical points uses a random Z coordinate in the Jacobian form. + * All magnitudes are randomized. + * All 17*17 combinations of points are added to eachother, using all applicable methods. + */ + secp256k1_ge_t *ge = malloc(sizeof(secp256k1_ge_t) * (1 + 4 * runs)); + secp256k1_gej_t *gej = malloc(sizeof(secp256k1_gej_t) * (1 + 4 * runs)); + secp256k1_gej_set_infinity(&gej[0]); + secp256k1_ge_clear(&ge[0]); + secp256k1_ge_set_gej_var(&ge[0], &gej[0]); + for (i = 0; i < runs; i++) { + int j; + secp256k1_ge_t g; + random_group_element_test(&g); + ge[1 + 4 * i] = g; + ge[2 + 4 * i] = g; + secp256k1_ge_neg(&ge[3 + 4 * i], &g); + secp256k1_ge_neg(&ge[4 + 4 * i], &g); + secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]); + random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]); + secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]); + random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]); + for (j = 0; j < 4; j++) { + random_field_element_magnitude(&ge[1 + j + 4 * i].x); + random_field_element_magnitude(&ge[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].x); + random_field_element_magnitude(&gej[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].z); + } + } + + for (i1 = 0; i1 < 1 + 4 * runs; i1++) { + int i2; + for (i2 = 0; i2 < 1 + 4 * runs; i2++) { + /* Compute reference result using gej + gej (var). */ + secp256k1_gej_t refj, resj; + secp256k1_ge_t ref; + secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2]); + secp256k1_ge_set_gej_var(&ref, &refj); + + /* Test gej + ge (var). */ + secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2]); + ge_equals_gej(&ref, &resj); + + /* Test gej + ge (const). */ + if (i2 != 0) { + /* secp256k1_gej_add_ge does not support its second argument being infinity. */ + secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]); + ge_equals_gej(&ref, &resj); + } + + /* Test doubling (var). */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) { + /* Normal doubling. */ + secp256k1_gej_double_var(&resj, &gej[i1]); + ge_equals_gej(&ref, &resj); + secp256k1_gej_double_var(&resj, &gej[i2]); + ge_equals_gej(&ref, &resj); + } + + /* Test adding opposites. */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) { + CHECK(secp256k1_ge_is_infinity(&ref)); + } + + /* Test adding infinity. */ + if (i1 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i1])); + CHECK(secp256k1_gej_is_infinity(&gej[i1])); + ge_equals_gej(&ref, &gej[i2]); + } + if (i2 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i2])); + CHECK(secp256k1_gej_is_infinity(&gej[i2])); + ge_equals_gej(&ref, &gej[i1]); + } + } + } + + /* Test adding all points together in random order equals infinity. */ + { + secp256k1_gej_t sum = SECP256K1_GEJ_CONST_INFINITY; + secp256k1_gej_t *gej_shuffled = malloc((4 * runs + 1) * sizeof(secp256k1_gej_t)); + for (i = 0; i < 4 * runs + 1; i++) { + gej_shuffled[i] = gej[i]; + } + for (i = 0; i < 4 * runs + 1; i++) { + int swap = i + secp256k1_rand32() % (4 * runs + 1 - i); + if (swap != i) { + secp256k1_gej_t t = gej_shuffled[i]; + gej_shuffled[i] = gej_shuffled[swap]; + gej_shuffled[swap] = t; + } + } + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i]); + } + CHECK(secp256k1_gej_is_infinity(&sum)); + free(gej_shuffled); + } + + /* Test batch gej -> ge conversion. */ + { + secp256k1_ge_t *ge_set_all = malloc((4 * runs + 1) * sizeof(secp256k1_ge_t)); + secp256k1_ge_set_all_gej_var(4 * runs + 1, ge_set_all, gej); + for (i = 0; i < 4 * runs + 1; i++) { + ge_equals_gej(&ge_set_all[i], &gej[i]); + } + free(ge_set_all); + } + + free(ge); + free(gej); +} + +void run_ge(void) { + int i; + for (i = 0; i < count * 32; i++) { + test_ge(); + } +} + +/***** ECMULT TESTS *****/ + +void run_ecmult_chain(void) { + /* random starting point A (on the curve) */ + secp256k1_gej_t a = SECP256K1_GEJ_CONST( + 0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3, + 0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004, + 0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f, + 0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f + ); + /* two random initial factors xn and gn */ + secp256k1_scalar_t xn = SECP256K1_SCALAR_CONST( + 0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c, + 0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407 + ); + secp256k1_scalar_t gn = SECP256K1_SCALAR_CONST( + 0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9, + 0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de + ); + /* two small multipliers to be applied to xn and gn in every iteration: */ + static const secp256k1_scalar_t xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337); + static const secp256k1_scalar_t gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113); + /* accumulators with the resulting coefficients to A and G */ + secp256k1_scalar_t ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_scalar_t ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + /* actual points */ + secp256k1_gej_t x = a; + secp256k1_gej_t x2; + int i; + + /* the point being computed */ + x = a; + for (i = 0; i < 200*count; i++) { + /* in each iteration, compute X = xn*X + gn*G; */ + secp256k1_ecmult(&x, &x, &xn, &gn); + /* also compute ae and ge: the actual accumulated factors for A and G */ + /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */ + secp256k1_scalar_mul(&ae, &ae, &xn); + secp256k1_scalar_mul(&ge, &ge, &xn); + secp256k1_scalar_add(&ge, &ge, &gn); + /* modify xn and gn */ + secp256k1_scalar_mul(&xn, &xn, &xf); + secp256k1_scalar_mul(&gn, &gn, &gf); + + /* verify */ + if (i == 19999) { + /* expected result after 19999 iterations */ + secp256k1_gej_t rp = SECP256K1_GEJ_CONST( + 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE, + 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830, + 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D, + 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88 + ); + + secp256k1_gej_neg(&rp, &rp); + secp256k1_gej_add_var(&rp, &rp, &x); + CHECK(secp256k1_gej_is_infinity(&rp)); + } + } + /* redo the computation, but directly with the resulting ae and ge coefficients: */ + secp256k1_ecmult(&x2, &a, &ae, &ge); + secp256k1_gej_neg(&x2, &x2); + secp256k1_gej_add_var(&x2, &x2, &x); + CHECK(secp256k1_gej_is_infinity(&x2)); +} + +void test_point_times_order(const secp256k1_gej_t *point) { + /* X * (point + G) + (order-X) * (pointer + G) = 0 */ + secp256k1_scalar_t x; + secp256k1_scalar_t nx; + secp256k1_gej_t res1, res2; + secp256k1_ge_t res3; + unsigned char pub[65]; + int psize = 65; + random_scalar_order_test(&x); + secp256k1_scalar_negate(&nx, &x); + secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */ + secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */ + secp256k1_gej_add_var(&res1, &res1, &res2); + CHECK(secp256k1_gej_is_infinity(&res1)); + CHECK(secp256k1_gej_is_valid_var(&res1) == 0); + secp256k1_ge_set_gej(&res3, &res1); + CHECK(secp256k1_ge_is_infinity(&res3)); + CHECK(secp256k1_ge_is_valid_var(&res3) == 0); + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0); + psize = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0); +} + +void run_point_times_order(void) { + int i; + secp256k1_fe_t x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2); + static const secp256k1_fe_t xr = SECP256K1_FE_CONST( + 0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C, + 0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45 + ); + for (i = 0; i < 500; i++) { + secp256k1_ge_t p; + if (secp256k1_ge_set_xo_var(&p, &x, 1)) { + secp256k1_gej_t j; + CHECK(secp256k1_ge_is_valid_var(&p)); + secp256k1_gej_set_ge(&j, &p); + CHECK(secp256k1_gej_is_valid_var(&j)); + test_point_times_order(&j); + } + secp256k1_fe_sqr(&x, &x); + } + secp256k1_fe_normalize_var(&x); + CHECK(secp256k1_fe_equal_var(&x, &xr)); +} + +void test_wnaf(const secp256k1_scalar_t *number, int w) { + secp256k1_scalar_t x, two, t; + int wnaf[256]; + int zeroes = -1; + int i; + int bits; + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&two, 2); + bits = secp256k1_ecmult_wnaf(wnaf, number, w); + CHECK(bits <= 256); + for (i = bits-1; i >= 0; i--) { + int v = wnaf[i]; + secp256k1_scalar_mul(&x, &x, &two); + if (v) { + CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */ + zeroes=0; + CHECK((v & 1) == 1); /* check non-zero elements are odd */ + CHECK(v <= (1 << (w-1)) - 1); /* check range below */ + CHECK(v >= -(1 << (w-1)) - 1); /* check range above */ + } else { + CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */ + zeroes++; + } + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */ +} + +void run_wnaf(void) { + int i; + secp256k1_scalar_t n; + for (i = 0; i < count; i++) { + random_scalar_order(&n); + if (i % 1) + secp256k1_scalar_negate(&n, &n); + test_wnaf(&n, 4+(i%10)); + } +} + +void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *key, const secp256k1_scalar_t *msg, int *recid) { + secp256k1_scalar_t nonce; + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(sig, key, msg, &nonce, recid)); +} + +void test_ecdsa_sign_verify(void) { + secp256k1_gej_t pubj; + secp256k1_ge_t pub; + secp256k1_scalar_t one; + secp256k1_scalar_t msg, key; + secp256k1_ecdsa_sig_t sig; + int recid; + int getrec; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&pubj, &key); + secp256k1_ge_set_gej(&pub, &pubj); + getrec = secp256k1_rand32()&1; + random_sign(&sig, &key, &msg, getrec?&recid:NULL); + if (getrec) CHECK(recid >= 0 && recid < 4); + CHECK(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg)); + secp256k1_scalar_set_int(&one, 1); + secp256k1_scalar_add(&msg, &msg, &one); + CHECK(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg)); +} + +void run_ecdsa_sign_verify(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_ecdsa_sign_verify(); + } +} + +/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */ +static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) { + (void)msg32; + (void)key32; + memcpy(nonce32, data, 32); + return (counter == 0); +} + +static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) { + /* Dummy nonce generator that has a fatal error on the first counter value. */ + if (counter == 0) return 0; + return nonce_function_rfc6979(nonce32, msg32, key32, counter - 1, data); +} + +static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) { + /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */ + if (counter < 3) { + memset(nonce32, counter==0 ? 0 : 255, 32); + if (counter == 2) nonce32[31]--; + return 1; + } + if (counter < 5) { + static const unsigned char order[] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41 + }; + memcpy(nonce32, order, 32); + if (counter == 4) nonce32[31]++; + return 1; + } + /* Retry rate of 6979 is negligible esp. as we only call this in determinstic tests. */ + /* If someone does fine a case where it retries for secp256k1, we'd like to know. */ + if (counter > 5) return 0; + return nonce_function_rfc6979(nonce32, msg32, key32, counter - 5, data); +} + +int is_empty_compact_signature(const unsigned char *sig64) { + static const unsigned char res[64] = {0}; + return memcmp(sig64, res, 64) == 0; +} + +void test_ecdsa_end_to_end(void) { + unsigned char extra[32] = {0x00}; + unsigned char privkey[32]; + unsigned char message[32]; + unsigned char privkey2[32]; + unsigned char csignature[64]; + unsigned char signature[72]; + unsigned char signature2[72]; + unsigned char signature3[72]; + unsigned char signature4[72]; + unsigned char pubkey[65]; + unsigned char recpubkey[65]; + unsigned char seckey[300]; + int signaturelen = 72; + int signaturelen2 = 72; + int signaturelen3 = 72; + int signaturelen4 = 72; + int recid = 0; + int recpubkeylen = 0; + int pubkeylen = 65; + int seckeylen = 300; + + /* Generate a random key and message. */ + { + secp256k1_scalar_t msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(privkey, &key); + secp256k1_scalar_get_b32(message, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, (secp256k1_rand32() & 3) != 0) == 1); + if (secp256k1_rand32() & 1) { + CHECK(secp256k1_ec_pubkey_decompress(pubkey, &pubkeylen)); + } + CHECK(secp256k1_ec_pubkey_verify(pubkey, pubkeylen)); + + /* Verify private key import and export. */ + CHECK(secp256k1_ec_privkey_export(privkey, seckey, &seckeylen, secp256k1_rand32() % 2) == 1); + CHECK(secp256k1_ec_privkey_import(privkey2, seckey, seckeylen) == 1); + CHECK(memcmp(privkey, privkey2, 32) == 0); + + /* Optionally tweak the keys using addition. */ + if (secp256k1_rand32() % 3 == 0) { + int ret1; + int ret2; + unsigned char rnd[32]; + unsigned char pubkey2[65]; + int pubkeylen2 = 65; + secp256k1_rand256_test(rnd); + ret1 = secp256k1_ec_privkey_tweak_add(privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_add(pubkey, pubkeylen, rnd); + CHECK(ret1 == ret2); + if (ret1 == 0) return; + CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1); + CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0); + } + + /* Optionally tweak the keys using multiplication. */ + if (secp256k1_rand32() % 3 == 0) { + int ret1; + int ret2; + unsigned char rnd[32]; + unsigned char pubkey2[65]; + int pubkeylen2 = 65; + secp256k1_rand256_test(rnd); + ret1 = secp256k1_ec_privkey_tweak_mul(privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_mul(pubkey, pubkeylen, rnd); + CHECK(ret1 == ret2); + if (ret1 == 0) return; + CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1); + CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0); + } + + /* Sign. */ + CHECK(secp256k1_ecdsa_sign(message, signature, &signaturelen, privkey, NULL, NULL) == 1); + CHECK(signaturelen > 0); + CHECK(secp256k1_ecdsa_sign(message, signature2, &signaturelen2, privkey, NULL, extra) == 1); + CHECK(signaturelen2 > 0); + extra[31] = 1; + CHECK(secp256k1_ecdsa_sign(message, signature3, &signaturelen3, privkey, NULL, extra) == 1); + CHECK(signaturelen3 > 0); + extra[31] = 0; + extra[0] = 1; + CHECK(secp256k1_ecdsa_sign(message, signature4, &signaturelen4, privkey, NULL, extra) == 1); + CHECK(signaturelen3 > 0); + CHECK((signaturelen != signaturelen2) || (memcmp(signature, signature2, signaturelen) != 0)); + CHECK((signaturelen != signaturelen3) || (memcmp(signature, signature3, signaturelen) != 0)); + CHECK((signaturelen3 != signaturelen2) || (memcmp(signature3, signature2, signaturelen3) != 0)); + CHECK((signaturelen4 != signaturelen3) || (memcmp(signature4, signature3, signaturelen4) != 0)); + CHECK((signaturelen4 != signaturelen2) || (memcmp(signature4, signature2, signaturelen4) != 0)); + CHECK((signaturelen4 != signaturelen) || (memcmp(signature4, signature, signaturelen4) != 0)); + /* Verify. */ + CHECK(secp256k1_ecdsa_verify(message, signature, signaturelen, pubkey, pubkeylen) == 1); + CHECK(secp256k1_ecdsa_verify(message, signature2, signaturelen2, pubkey, pubkeylen) == 1); + CHECK(secp256k1_ecdsa_verify(message, signature3, signaturelen3, pubkey, pubkeylen) == 1); + CHECK(secp256k1_ecdsa_verify(message, signature4, signaturelen4, pubkey, pubkeylen) == 1); + /* Destroy signature and verify again. */ + signature[signaturelen - 1 - secp256k1_rand32() % 20] += 1 + (secp256k1_rand32() % 255); + CHECK(secp256k1_ecdsa_verify(message, signature, signaturelen, pubkey, pubkeylen) != 1); + + /* Compact sign. */ + CHECK(secp256k1_ecdsa_sign_compact(message, csignature, privkey, NULL, NULL, &recid) == 1); + CHECK(!is_empty_compact_signature(csignature)); + /* Recover. */ + CHECK(secp256k1_ecdsa_recover_compact(message, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) == 1); + CHECK(recpubkeylen == pubkeylen); + CHECK(memcmp(pubkey, recpubkey, pubkeylen) == 0); + /* Destroy signature and verify again. */ + csignature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255); + CHECK(secp256k1_ecdsa_recover_compact(message, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) != 1 || + memcmp(pubkey, recpubkey, pubkeylen) != 0); + CHECK(recpubkeylen == pubkeylen); + +} + +void test_random_pubkeys(void) { + secp256k1_ge_t elem; + secp256k1_ge_t elem2; + unsigned char in[65]; + /* Generate some randomly sized pubkeys. */ + uint32_t r = secp256k1_rand32(); + int len = (r & 3) == 0 ? 65 : 33; + r>>=2; + if ((r & 3) == 0) len = (r & 252) >> 3; + r>>=8; + if (len == 65) { + in[0] = (r & 2) ? 4 : (r & 1? 6 : 7); + } else { + in[0] = (r & 1) ? 2 : 3; + } + r>>=2; + if ((r & 7) == 0) in[0] = (r & 2040) >> 3; + r>>=11; + if (len > 1) secp256k1_rand256(&in[1]); + if (len > 33) secp256k1_rand256(&in[33]); + if (secp256k1_eckey_pubkey_parse(&elem, in, len)) { + unsigned char out[65]; + unsigned char firstb; + int res; + int size = len; + firstb = in[0]; + /* If the pubkey can be parsed, it should round-trip... */ + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33)); + CHECK(size == len); + CHECK(memcmp(&in[1], &out[1], len-1) == 0); + /* ... except for the type of hybrid inputs. */ + if ((in[0] != 6) && (in[0] != 7)) CHECK(in[0] == out[0]); + size = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0)); + CHECK(size == 65); + CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size)); + ge_equals_ge(&elem,&elem2); + /* Check that the X9.62 hybrid type is checked. */ + in[0] = (r & 1) ? 6 : 7; + res = secp256k1_eckey_pubkey_parse(&elem2, in, size); + if (firstb == 2 || firstb == 3) { + if (in[0] == firstb + 4) CHECK(res); + else CHECK(!res); + } + if (res) { + ge_equals_ge(&elem,&elem2); + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0)); + CHECK(memcmp(&in[1], &out[1], 64) == 0); + } + } +} + +void run_random_pubkeys(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_random_pubkeys(); + } +} + +void run_ecdsa_end_to_end(void) { + int i; + for (i = 0; i < 64*count; i++) { + test_ecdsa_end_to_end(); + } +} + +/* Tests several edge cases. */ +void test_ecdsa_edge_cases(void) { + const unsigned char msg32[32] = { + 'T', 'h', 'i', 's', ' ', 'i', 's', ' ', + 'a', ' ', 'v', 'e', 'r', 'y', ' ', 's', + 'e', 'c', 'r', 'e', 't', ' ', 'm', 'e', + 's', 's', 'a', 'g', 'e', '.', '.', '.' + }; + const unsigned char sig64[64] = { + /* Generated by signing the above message with nonce 'This is the nonce we will use...' + * and secret key 0 (which is not valid), resulting in recid 0. */ + 0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8, + 0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96, + 0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63, + 0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32, + 0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E, + 0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD, + 0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86, + 0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57 + }; + unsigned char pubkey[65]; + int t; + int pubkeylen = 65; + /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */ + const unsigned char sigb64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + unsigned char pubkeyb[33]; + int pubkeyblen = 33; + int recid; + + CHECK(!secp256k1_ecdsa_recover_compact(msg32, sig64, pubkey, &pubkeylen, 0, 0)); + CHECK(secp256k1_ecdsa_recover_compact(msg32, sig64, pubkey, &pubkeylen, 0, 1)); + CHECK(!secp256k1_ecdsa_recover_compact(msg32, sig64, pubkey, &pubkeylen, 0, 2)); + CHECK(!secp256k1_ecdsa_recover_compact(msg32, sig64, pubkey, &pubkeylen, 0, 3)); + + for (recid = 0; recid < 4; recid++) { + int i; + int recid2; + /* (4,4) encoded in DER. */ + unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04}; + unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01}; + unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00}; + unsigned char sigbderalt1[39] = { + 0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt2[39] = { + 0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + unsigned char sigbderalt3[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt4[40] = { + 0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + /* (order + r,4) encoded in DER. */ + unsigned char sigbderlong[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, + 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, + 0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04 + }; + CHECK(secp256k1_ecdsa_recover_compact(msg32, sigb64, pubkeyb, &pubkeyblen, 1, recid)); + CHECK(secp256k1_ecdsa_verify(msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 1); + for (recid2 = 0; recid2 < 4; recid2++) { + unsigned char pubkey2b[33]; + int pubkey2blen = 33; + CHECK(secp256k1_ecdsa_recover_compact(msg32, sigb64, pubkey2b, &pubkey2blen, 1, recid2)); + /* Verifying with (order + r,4) should always fail. */ + CHECK(secp256k1_ecdsa_verify(msg32, sigbderlong, sizeof(sigbderlong), pubkey2b, pubkey2blen) != 1); + } + /* DER parsing tests. */ + /* Zero length r/s. */ + CHECK(secp256k1_ecdsa_verify(msg32, sigcder_zr, sizeof(sigcder_zr), pubkeyb, pubkeyblen) == -2); + CHECK(secp256k1_ecdsa_verify(msg32, sigcder_zs, sizeof(sigcder_zs), pubkeyb, pubkeyblen) == -2); + /* Leading zeros. */ + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt1, sizeof(sigbderalt1), pubkeyb, pubkeyblen) == 1); + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt2, sizeof(sigbderalt2), pubkeyb, pubkeyblen) == 1); + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == 1); + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == 1); + sigbderalt3[4] = 1; + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == -2); + sigbderalt4[7] = 1; + CHECK(secp256k1_ecdsa_verify(msg32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == -2); + /* Damage signature. */ + sigbder[7]++; + CHECK(secp256k1_ecdsa_verify(msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 0); + sigbder[7]--; + CHECK(secp256k1_ecdsa_verify(msg32, sigbder, 6, pubkeyb, pubkeyblen) == -2); + CHECK(secp256k1_ecdsa_verify(msg32, sigbder, sizeof(sigbder)-1, pubkeyb, pubkeyblen) == -2); + for(i = 0; i < 8; i++) { + int c; + unsigned char orig = sigbder[i]; + /*Try every single-byte change.*/ + for (c = 0; c < 256; c++) { + if (c == orig ) continue; + sigbder[i] = c; + CHECK(secp256k1_ecdsa_verify(msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == + (i==4 || i==7) ? 0 : -2 ); + } + sigbder[i] = orig; + } + } + + /* Test the case where ECDSA recomputes a point that is infinity. */ + { + secp256k1_gej_t keyj; + secp256k1_ge_t key; + secp256k1_scalar_t msg; + secp256k1_ecdsa_sig_t sig; + secp256k1_scalar_set_int(&sig.s, 1); + secp256k1_scalar_negate(&sig.s, &sig.s); + secp256k1_scalar_inverse(&sig.s, &sig.s); + secp256k1_scalar_set_int(&sig.r, 1); + secp256k1_ecmult_gen(&keyj, &sig.r); + secp256k1_ge_set_gej(&key, &keyj); + msg = sig.s; + CHECK(secp256k1_ecdsa_sig_verify(&sig, &key, &msg) == 0); + } + + /* Test r/s equal to zero */ + { + /* (1,1) encoded in DER. */ + unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01}; + unsigned char sigc64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + unsigned char pubkeyc[65]; + int pubkeyclen = 65; + CHECK(secp256k1_ecdsa_recover_compact(msg32, sigc64, pubkeyc, &pubkeyclen, 0, 0) == 1); + CHECK(secp256k1_ecdsa_verify(msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 1); + sigcder[4] = 0; + sigc64[31] = 0; + CHECK(secp256k1_ecdsa_recover_compact(msg32, sigc64, pubkeyb, &pubkeyblen, 1, 0) == 0); + CHECK(secp256k1_ecdsa_verify(msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 0); + sigcder[4] = 1; + sigcder[7] = 0; + sigc64[31] = 1; + sigc64[63] = 0; + CHECK(secp256k1_ecdsa_recover_compact(msg32, sigc64, pubkeyb, &pubkeyblen, 1, 0) == 0); + CHECK(secp256k1_ecdsa_verify(msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 0); + } + + /*Signature where s would be zero.*/ + { + const unsigned char nonce[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + static const unsigned char nonce2[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40 + }; + const unsigned char key[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + unsigned char msg[32] = { + 0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53, + 0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7, + 0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62, + 0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9, + }; + unsigned char sig[72]; + int siglen = 72; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, precomputed_nonce_function, nonce) == 0); + CHECK(siglen == 0); + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, precomputed_nonce_function, nonce2) == 0); + CHECK(siglen == 0); + msg[31] = 0xaa; + siglen = 72; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, precomputed_nonce_function, nonce) == 1); + CHECK(siglen > 0); + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, precomputed_nonce_function, nonce2) == 1); + CHECK(siglen > 0); + siglen = 10; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, precomputed_nonce_function, nonce) != 1); + CHECK(siglen == 0); + } + + /* Nonce function corner cases. */ + for (t = 0; t < 2; t++) { + static const unsigned char zero[32] = {0x00}; + int i; + unsigned char key[32]; + unsigned char msg[32]; + unsigned char sig[72]; + unsigned char sig2[72]; + secp256k1_ecdsa_sig_t s[512]; + int siglen = 72; + int siglen2 = 72; + int recid2; + const unsigned char *extra; + extra = t == 0 ? NULL : zero; + memset(msg, 0, 32); + msg[31] = 1; + /* High key results in signature failure. */ + memset(key, 0xFF, 32); + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, NULL, extra) == 0); + CHECK(siglen == 0); + /* Zero key results in signature failure. */ + memset(key, 0, 32); + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, NULL, extra) == 0); + CHECK(siglen == 0); + /* Nonce function failure results in signature failure. */ + key[31] = 1; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, nonce_function_test_fail, extra) == 0); + CHECK(siglen == 0); + CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, nonce_function_test_fail, extra, &recid) == 0); + CHECK(is_empty_compact_signature(sig)); + /* The retry loop successfully makes its way to the first good value. */ + siglen = 72; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, nonce_function_test_retry, extra) == 1); + CHECK(siglen > 0); + CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, nonce_function_rfc6979, extra) == 1); + CHECK(siglen > 0); + CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0)); + CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, nonce_function_test_retry, extra, &recid) == 1); + CHECK(!is_empty_compact_signature(sig)); + CHECK(secp256k1_ecdsa_sign_compact(msg, sig2, key, nonce_function_rfc6979, extra, &recid2) == 1); + CHECK(!is_empty_compact_signature(sig2)); + CHECK((recid == recid2) && (memcmp(sig, sig2, 64) == 0)); + /* The default nonce function is determinstic. */ + siglen = 72; + siglen2 = 72; + CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, NULL, extra) == 1); + CHECK(siglen > 0); + CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, NULL, extra) == 1); + CHECK(siglen2 > 0); + CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0)); + CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, NULL, extra, &recid) == 1); + CHECK(!is_empty_compact_signature(sig)); + CHECK(secp256k1_ecdsa_sign_compact(msg, sig2, key, NULL, extra, &recid2) == 1); + CHECK(!is_empty_compact_signature(sig)); + CHECK((recid == recid2) && (memcmp(sig, sig2, 64) == 0)); + /* The default nonce function changes output with different messages. */ + for(i = 0; i < 256; i++) { + int j; + siglen2 = 72; + msg[0] = i; + CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, NULL, extra) == 1); + CHECK(!is_empty_compact_signature(sig)); + CHECK(secp256k1_ecdsa_sig_parse(&s[i], sig2, siglen2)); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&s[i].r, &s[j].r)); + } + } + msg[0] = 0; + msg[31] = 2; + /* The default nonce function changes output with different keys. */ + for(i = 256; i < 512; i++) { + int j; + siglen2 = 72; + key[0] = i - 256; + CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, NULL, extra) == 1); + CHECK(secp256k1_ecdsa_sig_parse(&s[i], sig2, siglen2)); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&s[i].r, &s[j].r)); + } + } + key[0] = 0; + } + + /* Privkey export where pubkey is the point at infinity. */ + { + unsigned char privkey[300]; + unsigned char seckey[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41, + }; + int outlen = 300; + CHECK(!secp256k1_ec_privkey_export(seckey, privkey, &outlen, 0)); + CHECK(!secp256k1_ec_privkey_export(seckey, privkey, &outlen, 1)); + } +} + +void run_ecdsa_edge_cases(void) { + test_ecdsa_edge_cases(); +} + +#ifdef ENABLE_OPENSSL_TESTS +EC_KEY *get_openssl_key(const secp256k1_scalar_t *key) { + unsigned char privkey[300]; + int privkeylen; + const unsigned char* pbegin = privkey; + int compr = secp256k1_rand32() & 1; + EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1); + CHECK(secp256k1_eckey_privkey_serialize(privkey, &privkeylen, key, compr)); + CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen)); + CHECK(EC_KEY_check_key(ec_key)); + return ec_key; +} + +void test_ecdsa_openssl(void) { + secp256k1_gej_t qj; + secp256k1_ge_t q; + secp256k1_ecdsa_sig_t sig; + secp256k1_scalar_t one; + secp256k1_scalar_t msg2; + secp256k1_scalar_t key, msg; + EC_KEY *ec_key; + unsigned int sigsize = 80; + int secp_sigsize = 80; + unsigned char message[32]; + unsigned char signature[80]; + secp256k1_rand256_test(message); + secp256k1_scalar_set_b32(&msg, message, NULL); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&qj, &key); + secp256k1_ge_set_gej(&q, &qj); + ec_key = get_openssl_key(&key); + CHECK(ec_key); + CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key)); + CHECK(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize)); + CHECK(secp256k1_ecdsa_sig_verify(&sig, &q, &msg)); + secp256k1_scalar_set_int(&one, 1); + secp256k1_scalar_add(&msg2, &msg, &one); + CHECK(!secp256k1_ecdsa_sig_verify(&sig, &q, &msg2)); + + random_sign(&sig, &key, &msg, NULL); + CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sig)); + CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1); + + EC_KEY_free(ec_key); +} + +void run_ecdsa_openssl(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_ecdsa_openssl(); + } +} +#endif + +int main(int argc, char **argv) { + unsigned char seed16[16] = {0}; + unsigned char run32[32] = {0}; + /* find iteration count */ + if (argc > 1) { + count = strtol(argv[1], NULL, 0); + } + + /* find random seed */ + if (argc > 2) { + int pos = 0; + const char* ch = argv[2]; + while (pos < 16 && ch[0] != 0 && ch[1] != 0) { + unsigned short sh; + if (sscanf(ch, "%2hx", &sh)) { + seed16[pos] = sh; + } else { + break; + } + ch += 2; + pos++; + } + } else { + FILE *frand = fopen("/dev/urandom", "r"); + if (!frand || !fread(&seed16, sizeof(seed16), 1, frand)) { + uint64_t t = time(NULL) * (uint64_t)1337; + seed16[0] ^= t; + seed16[1] ^= t >> 8; + seed16[2] ^= t >> 16; + seed16[3] ^= t >> 24; + seed16[4] ^= t >> 32; + seed16[5] ^= t >> 40; + seed16[6] ^= t >> 48; + seed16[7] ^= t >> 56; + } + fclose(frand); + } + secp256k1_rand_seed(seed16); + + printf("test count = %i\n", count); + printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]); + + /* initialize */ + secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY); + + /* initializing a second time shouldn't cause any harm or memory leaks. */ + secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY); + + run_sha256_tests(); + run_hmac_sha256_tests(); + run_rfc6979_hmac_sha256_tests(); + +#ifndef USE_NUM_NONE + /* num tests */ + run_num_smalltests(); +#endif + + /* scalar tests */ + run_scalar_tests(); + + /* field tests */ + run_field_inv(); + run_field_inv_var(); + run_field_inv_all_var(); + run_field_misc(); + run_field_convert(); + run_sqr(); + run_sqrt(); + + /* group tests */ + run_ge(); + + /* ecmult tests */ + run_wnaf(); + run_point_times_order(); + run_ecmult_chain(); + + /* ecdsa tests */ + run_random_pubkeys(); + run_ecdsa_sign_verify(); + run_ecdsa_end_to_end(); + run_ecdsa_edge_cases(); +#ifdef ENABLE_OPENSSL_TESTS + run_ecdsa_openssl(); +#endif + + secp256k1_rand256(run32); + printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]); + + /* shutdown */ + secp256k1_stop(); + + /* shutting down twice shouldn't cause any double frees. */ + secp256k1_stop(); + return 0; +} diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h new file mode 100644 index 0000000000..ae98639f7c --- /dev/null +++ b/src/secp256k1/src/util.h @@ -0,0 +1,104 @@ +/********************************************************************** + * 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_ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include <stdlib.h> +#include <stdint.h> +#include <stdio.h> + +#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 + +#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 |