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126 KiB

/**********************************************************************
* Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "secp256k1.c"
#include "include/secp256k1.h"
#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
#include "contrib/lax_der_parsing.h"
#if !defined(VG_CHECK)
# if defined(VALGRIND)
# include <valgrind/memcheck.h>
# define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
# define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
# else
# define VG_UNDEF(x,y)
# define VG_CHECK(x,y)
# endif
#endif
static int count = 64;
static secp256k1_context *ctx = NULL;
void random_field_element_test(secp256k1_fe *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 *fe) {
secp256k1_fe zero;
int n = secp256k1_rand_int(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);
VERIFY_CHECK(fe->magnitude == n);
}
void random_group_element_test(secp256k1_ge *ge) {
secp256k1_fe fe;
do {
random_field_element_test(&fe);
if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
secp256k1_fe_normalize(&ge->y);
break;
}
} while(1);
}
void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
secp256k1_fe 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 *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 *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);
}
void run_context_tests(void) {
secp256k1_context *none = secp256k1_context_create(0);
secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
secp256k1_gej pubj;
secp256k1_ge pub;
secp256k1_scalar msg, key, nonce;
secp256k1_scalar sigr, sigs;
/*** clone and destroy all of them to make sure cloning was complete ***/
{
secp256k1_context *ctx_tmp;
ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_destroy(ctx_tmp);
ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
}
/*** attempt to use them ***/
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
secp256k1_ge_set_gej(&pub, &pubj);
/* obtain a working nonce */
do {
random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try signing */
CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try verifying */
CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
/* cleanup */
secp256k1_context_destroy(none);
secp256k1_context_destroy(sign);
secp256k1_context_destroy(vrfy);
secp256k1_context_destroy(both);
}
/***** 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_rand_int(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_rand_int(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[65] = {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, 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, 0};
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[64] = {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, 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];
int i;
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
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, 65);
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, 64);
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);
}
/***** RANDOM TESTS *****/
void test_rand_bits(int rand32, int bits) {
/* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
* get a false negative chance below once in a billion */
static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
/* We try multiplying the results with various odd numbers, which shouldn't
* influence the uniform distribution modulo a power of 2. */
static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
/* We only select up to 6 bits from the output to analyse */
unsigned int usebits = bits > 6 ? 6 : bits;
unsigned int maxshift = bits - usebits;
/* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
number, track all observed outcomes, one per bit in a uint64_t. */
uint64_t x[6][27] = {{0}};
unsigned int i, shift, m;
/* Multiply the output of all rand calls with the odd number m, which
should not change the uniformity of its distribution. */
for (i = 0; i < rounds[usebits]; i++) {
uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
CHECK((((uint64_t)r) >> bits) == 0);
for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
uint32_t rm = r * mults[m];
for (shift = 0; shift <= maxshift; shift++) {
x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
}
}
}
for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
for (shift = 0; shift <= maxshift; shift++) {
/* Test that the lower usebits bits of x[shift] are 1 */
CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
}
}
}
/* Subrange must be a whole divisor of range, and at most 64 */
void test_rand_int(uint32_t range, uint32_t subrange) {
/* (1-1/subrange)^rounds < 1/10^9 */
int rounds = (subrange * 2073) / 100;
int i;
uint64_t x = 0;
CHECK((range % subrange) == 0);
for (i = 0; i < rounds; i++) {
uint32_t r = secp256k1_rand_int(range);
CHECK(r < range);
r = r % subrange;
x |= (((uint64_t)1) << r);
}
/* Test that the lower subrange bits of x are 1. */
CHECK(((~x) << (64 - subrange)) == 0);
}
void run_rand_bits(void) {
size_t b;
test_rand_bits(1, 32);
for (b = 1; b <= 32; b++) {
test_rand_bits(0, b);
}
}
void run_rand_int(void) {
static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
unsigned int m, s;
for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
test_rand_int(ms[m] * ss[s], ss[s]);
}
}
}
/***** NUM TESTS *****/
#ifndef USE_NUM_NONE
void random_num_negate(secp256k1_num *num) {
if (secp256k1_rand_bits(1)) {
secp256k1_num_negate(num);
}
}
void random_num_order_test(secp256k1_num *num) {
secp256k1_scalar sc;
random_scalar_order_test(&sc);
secp256k1_scalar_get_num(num, &sc);
}
void random_num_order(secp256k1_num *num) {
secp256k1_scalar sc;
random_scalar_order(&sc);
secp256k1_scalar_get_num(num, &sc);
}
void test_num_negate(void) {
secp256k1_num n1;
secp256k1_num n2;
random_num_order_test(&n1); /* n1 = R */
random_num_negate(&n1);
secp256k1_num_copy(&n2, &n1); /* n2 = R */
secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */
CHECK(secp256k1_num_is_zero(&n1));
secp256k1_num_copy(&n1, &n2); /* n1 = R */
secp256k1_num_negate(&n1); /* n1 = -R */
CHECK(!secp256k1_num_is_zero(&n1));
secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */
CHECK(secp256k1_num_is_zero(&n1));
secp256k1_num_copy(&n1, &n2); /* n1 = R */
secp256k1_num_negate(&n1); /* n1 = -R */
CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
secp256k1_num_negate(&n1); /* n1 = R */
CHECK(secp256k1_num_eq(&n1, &n2));
}
void test_num_add_sub(void) {
secp256k1_num n1;
secp256k1_num n2;
secp256k1_num n1p2, n2p1, n1m2, n2m1;
random_num_order_test(&n1); /* n1 = R1 */
if (secp256k1_rand_bits(1)) {
random_num_negate(&n1);
}
random_num_order_test(&n2); /* n2 = R2 */
if (secp256k1_rand_bits(1)) {
random_num_negate(&n2);
}
secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */
CHECK(secp256k1_num_eq(&n1p2, &n2p1));
CHECK(!secp256k1_num_eq(&n1p2, &n1m2));
secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */
CHECK(secp256k1_num_eq(&n2m1, &n1m2));
CHECK(!secp256k1_num_eq(&n2m1, &n1));
secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */
CHECK(secp256k1_num_eq(&n2m1, &n1));
CHECK(!secp256k1_num_eq(&n2p1, &n1));
secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
CHECK(secp256k1_num_eq(&n2p1, &n1));
}
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 s;
secp256k1_scalar s1;
secp256k1_scalar s2;
#ifndef USE_NUM_NONE
secp256k1_num snum, s1num, s2num;
secp256k1_num order, half_order;
#endif
unsigned char c[32];
/* Set 's' to a random scalar, with value 'snum'. */
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 n;
secp256k1_scalar_set_int(&n, 0);
for (i = 0; i < 256; i += 4) {
secp256k1_scalar 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 n;
int i = 0;
secp256k1_scalar_set_int(&n, 0);
while (i < 256) {
secp256k1_scalar t;
int j;
int now = secp256k1_rand_int(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 rnum;
secp256k1_num r2num;
secp256k1_scalar r;
secp256k1_num_add(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_add(&r, &s, &s2);
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
}
{
/* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
secp256k1_scalar r;
secp256k1_num r2num;
secp256k1_num rnum;
secp256k1_num_mul(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_mul(&r, &s, &s2);
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
/* The result can only be zero if at least one of the factors was zero. */
CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
/* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
}
{
secp256k1_scalar neg;
secp256k1_num negnum;
secp256k1_num negnum2;
/* Check that comparison with zero matches comparison with zero on the number. */
CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
/* Check that comparison with the half order is equal to testing for high scalar. */
CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
secp256k1_scalar_negate(&neg, &s);
secp256k1_num_sub(&negnum, &order, &snum);
secp256k1_num_mod(&negnum, &order);
/* Check that comparison with the half order is equal to testing for high scalar after negation. */
CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
/* Negating should change the high property, unless the value was already zero. */
CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
secp256k1_scalar_get_num(&negnum2, &neg);
/* Negating a scalar should be equal to (order - n) mod order on the number. */
CHECK(secp256k1_num_eq(&negnum, &negnum2));
secp256k1_scalar_add(&neg, &neg, &s);
/* Adding a number to its negation should result in zero. */
CHECK(secp256k1_scalar_is_zero(&neg));
secp256k1_scalar_negate(&neg, &neg);
/* Negating zero should still result in zero. */
CHECK(secp256k1_scalar_is_zero(&neg));
}
{
/* Test secp256k1_scalar_mul_shift_var. */
secp256k1_scalar r;
secp256k1_num one;
secp256k1_num rnum;
secp256k1_num rnum2;
unsigned char cone[1] = {0x01};
unsigned int shift = 256 + secp256k1_rand_int(257);
secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
secp256k1_num_mul(&rnum, &s1num, &s2num);
secp256k1_num_shift(&rnum, shift - 1);
secp256k1_num_set_bin(&one, cone, 1);
secp256k1_num_add(&rnum, &rnum, &one);
secp256k1_num_shift(&rnum, 1);
secp256k1_scalar_get_num(&rnum2, &r);
CHECK(secp256k1_num_eq(&rnum, &rnum2));
}
{
/* test secp256k1_scalar_shr_int */
secp256k1_scalar r;
int i;
random_scalar_order_test(&r);
for (i = 0; i < 100; ++i) {
int low;
int shift = 1 + secp256k1_rand_int(15);
int expected = r.d[0] % (1 << shift);
low = secp256k1_scalar_shr_int(&r, shift);
CHECK(expected == low);
}
}
#endif
{
/* Test that scalar inverses are equal to the inverse of their number modulo the order. */
if (!secp256k1_scalar_is_zero(&s)) {
secp256k1_scalar inv;
#ifndef USE_NUM_NONE
secp256k1_num invnum;
secp256k1_num invnum2;
#endif
secp256k1_scalar_inverse(&inv, &s);
#ifndef USE_NUM_NONE
secp256k1_num_mod_inverse(&invnum, &snum, &order);
secp256k1_scalar_get_num(&invnum2, &inv);
CHECK(secp256k1_num_eq(&invnum, &invnum2));
#endif
secp256k1_scalar_mul(&inv, &inv, &s);
/* Multiplying a scalar with its inverse must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
secp256k1_scalar_inverse(&inv, &inv);
/* Inverting one must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
}
}
{
/* Test commutativity of add. */
secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
secp256k1_scalar r1, r2;
secp256k1_scalar b;
int i;
/* Test add_bit. */
int bit = secp256k1_rand_bits(8);
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_cadd_bit(&r2, bit, 1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
/* cadd is a noop when flag is zero */
secp256k1_scalar_cadd_bit(&r2, bit, 0);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
{
/* Test commutativity of mul. */
secp256k1_scalar 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 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 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 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 r1, r2;
secp256k1_scalar_sqr(&r1, &s1);
secp256k1_scalar_mul(&r2, &s1, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test multiplicative identity. */
secp256k1_scalar r1, v1;
secp256k1_scalar_set_int(&v1,1);
secp256k1_scalar_mul(&r1, &s1, &v1);
CHECK(secp256k1_scalar_eq(&r1, &s1));
}
{
/* Test additive identity. */
secp256k1_scalar 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 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 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 order;
secp256k1_scalar 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 *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 *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 *ns) {
secp256k1_fe 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 *a, const secp256k1_fe *b) {
secp256k1_fe an = *a;
secp256k1_fe 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 *a, const secp256k1_fe *ai) {
secp256k1_fe x;
secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_fe_mul(&x, a, ai);
return check_fe_equal(&x, &one);
}
void run_field_convert(void) {
static const unsigned char b32[32] = {
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
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 fes = SECP256K1_FE_STORAGE_CONST(
0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
);
static const secp256k1_fe fe = SECP256K1_FE_CONST(
0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
);
secp256k1_fe fe2;
unsigned char b322[32];
secp256k1_fe_storage 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);
}
int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
secp256k1_fe t = *b;
#ifdef VERIFY
t.magnitude = a->magnitude;
t.normalized = a->normalized;
#endif
return memcmp(a, &t, sizeof(secp256k1_fe));
}
void run_field_misc(void) {
secp256k1_fe x;
secp256k1_fe y;
secp256k1_fe z;
secp256k1_fe q;
secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
int i, j;
for (i = 0; i < 5*count; i++) {
secp256k1_fe_storage 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);
/* Test fe conditional move; z is not normalized here. */
q = x;
secp256k1_fe_cmov(&x, &z, 0);
VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
secp256k1_fe_cmov(&x, &x, 1);
CHECK(fe_memcmp(&x, &z) != 0);
CHECK(fe_memcmp(&x, &q) == 0);
secp256k1_fe_cmov(&q, &z, 1);
VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
CHECK(fe_memcmp(&q, &z) == 0);
secp256k1_fe_normalize_var(&x);
secp256k1_fe_normalize_var(&z);
CHECK(!secp256k1_fe_equal_var(&x, &z));
secp256k1_fe_normalize_var(&q);
secp256k1_fe_cmov(&q, &z, (i&1));
VERIFY_CHECK(q.normalized && q.magnitude == 1);
for (j = 0; j < 6; j++) {
secp256k1_fe_negate(&z, &z, j+1);
secp256k1_fe_normalize_var(&q);
secp256k1_fe_cmov(&q, &z, (j&1));
VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
}
secp256k1_fe_normalize_var(&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);
secp256k1_fe_storage_cmov(&zs, &zs, 1);
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 x, xi, xii;
int i;
for (i = 0; i < 10*count; i++) {
random_fe_non_zero(&x);
secp256k1_fe_inv(&xi, &x);
CHECK(check_fe_inverse(&x, &xi));
secp256k1_fe_inv(&xii, &xi);
CHECK(check_fe_equal(&x, &xii));
}
}
void run_field_inv_var(void) {
secp256k1_fe x, xi, xii;
int i;
for (i = 0; i < 10*count; i++) {
random_fe_non_zero(&x);
secp256k1_fe_inv_var(&xi, &x);
CHECK(check_fe_inverse(&x, &xi));
secp256k1_fe_inv_var(&xii, &xi);
CHECK(check_fe_equal(&x, &xii));
}
}
void run_field_inv_all_var(void) {
secp256k1_fe x[16], xi[16], xii[16];
int i;
/* Check it's safe to call for 0 elements */
secp256k1_fe_inv_all_var(0, xi, x);
for (i = 0; i < count; i++) {
size_t j;
size_t len = secp256k1_rand_int(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 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 *a, const secp256k1_fe *k) {
secp256k1_fe 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 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 *a, const secp256k1_ge *b) {
CHECK(a->infinity == b->infinity);
if (a->infinity) {
return;
}
CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
}
/* This compares jacobian points including their Z, not just their geometric meaning. */
int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
secp256k1_gej a2;
secp256k1_gej b2;
int ret = 1;
ret &= a->infinity == b->infinity;
if (ret && !a->infinity) {
a2 = *a;
b2 = *b;
secp256k1_fe_normalize(&a2.x);
secp256k1_fe_normalize(&a2.y);
secp256k1_fe_normalize(&a2.z);
secp256k1_fe_normalize(&b2.x);
secp256k1_fe_normalize(&b2.y);
secp256k1_fe_normalize(&b2.z);
ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
}
return ret;
}
void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
secp256k1_fe z2s;
secp256k1_fe 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;
#ifdef USE_ENDOMORPHISM
int runs = 6;
#else
int runs = 4;
#endif
/* 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.
*
* When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
*/
secp256k1_ge *ge = (secp256k1_ge *)malloc(sizeof(secp256k1_ge) * (1 + 4 * runs));
secp256k1_gej *gej = (secp256k1_gej *)malloc(sizeof(secp256k1_gej) * (1 + 4 * runs));
secp256k1_fe *zinv = (secp256k1_fe *)malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
secp256k1_fe zf;
secp256k1_fe zfi2, zfi3;
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 g;
random_group_element_test(&g);
#ifdef USE_ENDOMORPHISM
if (i >= runs - 2) {
secp256k1_ge_mul_lambda(&g, &ge[1]);
}
if (i >= runs - 1) {
secp256k1_ge_mul_lambda(&g, &g);
}
#endif
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);
}
}
/* Compute z inverses. */
{
secp256k1_fe *zs = malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
for (i = 0; i < 4 * runs + 1; i++) {
if (i == 0) {
/* The point at infinity does not have a meaningful z inverse. Any should do. */
do {
random_field_element_test(&zs[i]);
} while(secp256k1_fe_is_zero(&zs[i]));
} else {
zs[i] = gej[i].z;
}
}
secp256k1_fe_inv_all_var(4 * runs + 1, zinv, zs);
free(zs);
}
/* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
do {
random_field_element_test(&zf);
} while(secp256k1_fe_is_zero(&zf));
random_field_element_magnitude(&zf);
secp256k1_fe_inv_var(&zfi3, &zf);
secp256k1_fe_sqr(&zfi2, &zfi3);
secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
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 refj, resj;
secp256k1_ge ref;
secp256k1_fe zr;
secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
/* Check Z ratio. */
if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
}
secp256k1_ge_set_gej_var(&ref, &refj);
/* Test gej + ge with Z ratio result (var). */
secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
ge_equals_gej(&ref, &resj);
if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
}
/* Test gej + ge (var, with additional Z factor). */
{
secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
random_field_element_magnitude(&ge2_zfi.x);
random_field_element_magnitude(&ge2_zfi.y);
secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
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)) {
secp256k1_fe zr2;
/* Normal doubling with Z ratio result. */
secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
ge_equals_gej(&ref, &resj);
/* Check Z ratio. */
secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
/* Normal doubling. */
secp256k1_gej_double_var(&resj, &gej[i2], NULL);
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 sum = SECP256K1_GEJ_CONST_INFINITY;
secp256k1_gej *gej_shuffled = (secp256k1_gej *)malloc((4 * runs + 1) * sizeof(secp256k1_gej));
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_rand_int(4 * runs + 1 - i);
if (swap != i) {
secp256k1_gej 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], NULL);
}
CHECK(secp256k1_gej_is_infinity(&sum));
free(gej_shuffled);
}
/* Test batch gej -> ge conversion with and without known z ratios. */
{
secp256k1_fe *zr = (secp256k1_fe *)malloc((4 * runs + 1) * sizeof(secp256k1_fe));
secp256k1_ge *ge_set_table = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
secp256k1_ge *ge_set_all = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
for (i = 0; i < 4 * runs + 1; i++) {
/* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
if (i < 4 * runs) {
secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
}
}
secp256k1_ge_set_table_gej_var(4 * runs + 1, ge_set_table, gej, zr);
secp256k1_ge_set_all_gej_var(4 * runs + 1, ge_set_all, gej, &ctx->error_callback);
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_fe s;
random_fe_non_zero(&s);
secp256k1_gej_rescale(&gej[i], &s);
ge_equals_gej(&ge_set_table[i], &gej[i]);
ge_equals_gej(&ge_set_all[i], &gej[i]);
}
free(ge_set_table);
free(ge_set_all);
free(zr);
}
free(ge);
free(gej);
free(zinv);
}
void test_add_neg_y_diff_x(void) {
/* The point of this test is to check that we can add two points
* whose y-coordinates are negatives of each other but whose x
* coordinates differ. If the x-coordinates were the same, these
* points would be negatives of each other and their sum is
* infinity. This is cool because it "covers up" any degeneracy
* in the addition algorithm that would cause the xy coordinates
* of the sum to be wrong (since infinity has no xy coordinates).
* HOWEVER, if the x-coordinates are different, infinity is the
* wrong answer, and such degeneracies are exposed. This is the
* root of https://github.com/bitcoin/secp256k1/issues/257 which
* this test is a regression test for.
*
* These points were generated in sage as
* # secp256k1 params
* F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
* C = EllipticCurve ([F (0), F (7)])
* G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
* N = FiniteField(G.order())
*
* # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
* x = polygen(N)
* lam = (1 - x^3).roots()[1][0]
*
* # random "bad pair"
* P = C.random_element()
* Q = -int(lam) * P
* print " P: %x %x" % P.xy()
* print " Q: %x %x" % Q.xy()
* print "P + Q: %x %x" % (P + Q).xy()
*/
secp256k1_gej aj = SECP256K1_GEJ_CONST(
0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
);
secp256k1_gej bj = SECP256K1_GEJ_CONST(
0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
);
secp256k1_gej sumj = SECP256K1_GEJ_CONST(
0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
);
secp256k1_ge b;
secp256k1_gej resj;
secp256k1_ge res;
secp256k1_ge_set_gej(&b, &bj);
secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
secp256k1_gej_add_ge(&resj, &aj, &b);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
secp256k1_ge_set_gej(&res, &resj);
ge_equals_gej(&res, &sumj);
}
void run_ge(void) {
int i;
for (i = 0; i < count * 32; i++) {
test_ge();
}
test_add_neg_y_diff_x();
}
void test_ec_combine(void) {
secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_pubkey data[6];
const secp256k1_pubkey* d[6];
secp256k1_pubkey sd;
secp256k1_pubkey sd2;
secp256k1_gej Qj;
secp256k1_ge Q;
int i;
for (i = 1; i <= 6; i++) {
secp256k1_scalar s;
random_scalar_order_test(&s);
secp256k1_scalar_add(&sum, &sum, &s);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&data[i - 1], &Q);
d[i - 1] = &data[i - 1];
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&sd, &Q);
CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
}
}
void run_ec_combine(void) {
int i;
for (i = 0; i < count * 8; i++) {
test_ec_combine();
}
}
/***** ECMULT TESTS *****/
void run_ecmult_chain(void) {
/* random starting point A (on the curve) */
secp256k1_gej 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 xn = SECP256K1_SCALAR_CONST(
0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
);
secp256k1_scalar 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 xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
/* accumulators with the resulting coefficients to A and G */
secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
/* actual points */
secp256k1_gej x;
secp256k1_gej 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(&ctx->ecmult_ctx, &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 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, NULL);
CHECK(secp256k1_gej_is_infinity(&rp));
}
}
/* redo the computation, but directly with the resulting ae and ge coefficients: */
secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
secp256k1_gej_neg(&x2, &x2);
secp256k1_gej_add_var(&x2, &x2, &x, NULL);
CHECK(secp256k1_gej_is_infinity(&x2));
}
void test_point_times_order(const secp256k1_gej *point) {
/* X * (point + G) + (order-X) * (pointer + G) = 0 */
secp256k1_scalar x;
secp256k1_scalar nx;
secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_gej res1, res2;
secp256k1_ge res3;
unsigned char pub[65];
size_t psize = 65;
random_scalar_order_test(&x);
secp256k1_scalar_negate(&nx, &x);
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
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);
/* check zero/one edge cases */
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
secp256k1_ge_set_gej(&res3, &res1);
ge_equals_gej(&res3, point);
secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
secp256k1_ge_set_gej(&res3, &res1);
ge_equals_ge(&res3, &secp256k1_ge_const_g);
}
void run_point_times_order(void) {
int i;
secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
static const secp256k1_fe xr = SECP256K1_FE_CONST(
0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
);
for (i = 0; i < 500; i++) {
secp256k1_ge p;
if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
secp256k1_gej 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 ecmult_const_random_mult(void) {
/* random starting point A (on the curve) */
secp256k1_ge a = SECP256K1_GE_CONST(
0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
);
/* random initial factor xn */
secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
);
/* expected xn * A (from sage) */
secp256k1_ge expected_b = SECP256K1_GE_CONST(
0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
);
secp256k1_gej b;
secp256k1_ecmult_const(&b, &a, &xn);
CHECK(secp256k1_ge_is_valid_var(&a));
ge_equals_gej(&expected_b, &b);
}
void ecmult_const_commutativity(void) {
secp256k1_scalar a;
secp256k1_scalar b;
secp256k1_gej res1;
secp256k1_gej res2;
secp256k1_ge mid1;
secp256k1_ge mid2;
random_scalar_order_test(&a);
random_scalar_order_test(&b);
secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
secp256k1_ecmult_const(&res1, &mid1, &b);
secp256k1_ecmult_const(&res2, &mid2, &a);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
ge_equals_ge(&mid1, &mid2);
}
void ecmult_const_mult_zero_one(void) {
secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_scalar negone;
secp256k1_gej res1;
secp256k1_ge res2;
secp256k1_ge point;
secp256k1_scalar_negate(&negone, &one);
random_group_element_test(&point);
secp256k1_ecmult_const(&res1, &point, &zero);
secp256k1_ge_set_gej(&res2, &res1);
CHECK(secp256k1_ge_is_infinity(&res2));
secp256k1_ecmult_const(&res1, &point, &one);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
secp256k1_ecmult_const(&res1, &point, &negone);
secp256k1_gej_neg(&res1, &res1);
secp256k1_ge_set_gej(&res2, &res1);
ge_equals_ge(&res2, &point);
}
void ecmult_const_chain_multiply(void) {
/* Check known result (randomly generated test problem from sage) */
const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
);
const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
);
secp256k1_gej point;
secp256k1_ge res;
int i;
secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
for (i = 0; i < 100; ++i) {
secp256k1_ge tmp;
secp256k1_ge_set_gej(&tmp, &point);
secp256k1_ecmult_const(&point, &tmp, &scalar);
}
secp256k1_ge_set_gej(&res, &point);
ge_equals_gej(&res, &expected_point);
}
void run_ecmult_const_tests(void) {
ecmult_const_mult_zero_one();
ecmult_const_random_mult();
ecmult_const_commutativity();
ecmult_const_chain_multiply();
}
void test_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar 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, 256, 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 test_constant_wnaf_negate(const secp256k1_scalar *number) {
secp256k1_scalar neg1 = *number;
secp256k1_scalar neg2 = *number;
int sign1 = 1;
int sign2 = 1;
if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
secp256k1_scalar_negate(&neg1, &neg1);
sign1 = -1;
}
sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
CHECK(sign1 == sign2);
CHECK(secp256k1_scalar_eq(&neg1, &neg2));
}
void test_constant_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar x, shift;
int wnaf[256] = {0};
int i;
#ifdef USE_ENDOMORPHISM
int skew;
#endif
secp256k1_scalar num = *number;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&shift, 1 << w);
/* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
#ifdef USE_ENDOMORPHISM
for (i = 0; i < 16; ++i) {
secp256k1_scalar_shr_int(&num, 8);
}
skew = secp256k1_wnaf_const(wnaf, num, w);
#else
secp256k1_wnaf_const(wnaf, num, w);
#endif
for (i = WNAF_SIZE(w); i >= 0; --i) {
secp256k1_scalar t;
int v = wnaf[i];
CHECK(v != 0); /* check nonzero */
CHECK(v & 1); /* check parity */
CHECK(v > -(1 << w)); /* check range above */
CHECK(v < (1 << w)); /* check range below */
secp256k1_scalar_mul(&x, &x, &shift);
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);
}
#ifdef USE_ENDOMORPHISM
/* Skew num because when encoding 128-bit numbers as odd we use an offset */
secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
#endif
CHECK(secp256k1_scalar_eq(&x, &num));
}
void run_wnaf(void) {
int i;
secp256k1_scalar n = {{0}};
/* Sanity check: 1 and 2 are the smallest odd and even numbers and should
* have easier-to-diagnose failure modes */
n.d[0] = 1;
test_constant_wnaf(&n, 4);
n.d[0] = 2;
test_constant_wnaf(&n, 4);
/* Random tests */
for (i = 0; i < count; i++) {
random_scalar_order(&n);
test_wnaf(&n, 4+(i%10));
test_constant_wnaf_negate(&n);
test_constant_wnaf(&n, 4 + (i % 10));
}
}
void test_ecmult_constants(void) {
/* Test ecmult_gen() for [0..36) and [order-36..0). */
secp256k1_scalar x;
secp256k1_gej r;
secp256k1_ge ng;
int i;
int j;
secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
for (i = 0; i < 36; i++ ) {
secp256k1_scalar_set_int(&x, i);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
for (j = 0; j < i; j++) {
if (j == i - 1) {
ge_equals_gej(&secp256k1_ge_const_g, &r);
}
secp256k1_gej_add_ge(&r, &r, &ng);
}
CHECK(secp256k1_gej_is_infinity(&r));
}
for (i = 1; i <= 36; i++ ) {
secp256k1_scalar_set_int(&x, i);
secp256k1_scalar_negate(&x, &x);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
for (j = 0; j < i; j++) {
if (j == i - 1) {
ge_equals_gej(&ng, &r);
}
secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
}
CHECK(secp256k1_gej_is_infinity(&r));
}
}
void run_ecmult_constants(void) {
test_ecmult_constants();
}
void test_ecmult_gen_blind(void) {
/* Test ecmult_gen() blinding and confirm that the blinding changes, the affline points match, and the z's don't match. */
secp256k1_scalar key;
secp256k1_scalar b;
unsigned char seed32[32];
secp256k1_gej pgej;
secp256k1_gej pgej2;
secp256k1_gej i;
secp256k1_ge pge;
random_scalar_order_test(&key);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
secp256k1_rand256(seed32);
b = ctx->ecmult_gen_ctx.blind;
i = ctx->ecmult_gen_ctx.initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
secp256k1_ge_set_gej(&pge, &pgej);
ge_equals_gej(&pge, &pgej2);
}
void test_ecmult_gen_blind_reset(void) {
/* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
secp256k1_scalar b;
secp256k1_gej initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
b = ctx->ecmult_gen_ctx.blind;
initial = ctx->ecmult_gen_ctx.initial;
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
}
void run_ecmult_gen_blind(void) {
int i;
test_ecmult_gen_blind_reset();
for (i = 0; i < 10; i++) {
test_ecmult_gen_blind();
}
}
#ifdef USE_ENDOMORPHISM
/***** ENDOMORPHISH TESTS *****/
void test_scalar_split(void) {
secp256k1_scalar full;
secp256k1_scalar s1, slam;
const unsigned char zero[32] = {0};
unsigned char tmp[32];
random_scalar_order_test(&full);
secp256k1_scalar_split_lambda(&s1, &slam, &full);
/* check that both are <= 128 bits in size */
if (secp256k1_scalar_is_high(&s1)) {
secp256k1_scalar_negate(&s1, &s1);
}
if (secp256k1_scalar_is_high(&slam)) {
secp256k1_scalar_negate(&slam, &slam);
}
secp256k1_scalar_get_b32(tmp, &s1);
CHECK(memcmp(zero, tmp, 16) == 0);
secp256k1_scalar_get_b32(tmp, &slam);
CHECK(memcmp(zero, tmp, 16) == 0);
}
void run_endomorphism_tests(void) {
test_scalar_split();
}
#endif
static void counting_illegal_callback_fn(const char* str, void* data) {
/* Dummy callback function that just counts. */
int32_t *p;
(void)str;
p = data;
(*p)++;
}
static void uncounting_illegal_callback_fn(const char* str, void* data) {
/* Dummy callback function that just counts (backwards). */
int32_t *p;
(void)str;
p = data;
(*p)--;
}
void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
unsigned char pubkeyc[65];
secp256k1_pubkey pubkey;
secp256k1_ge ge;
size_t pubkeyclen;
int32_t ecount;
ecount = 0;
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
/* Smaller sizes are tested exhaustively elsewhere. */
int32_t i;
memcpy(&pubkeyc[1], input, 64);
VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
for (i = 0; i < 256; i++) {
/* Try all type bytes. */
int xpass;
int ypass;
int ysign;
pubkeyc[0] = i;
/* What sign does this point have? */
ysign = (input[63] & 1) + 2;
/* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
/* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
if (xpass || ypass) {
/* These cases must parse. */
unsigned char pubkeyo[65];
size_t outl;
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
ecount = 0;
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
VG_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
VG_UNDEF(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
VG_CHECK(pubkeyo, outl);
CHECK(outl == 33);
CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
if (ypass) {
/* This test isn't always done because we decode with alternative signs, so the y won't match. */
CHECK(pubkeyo[0] == ysign);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
memset(&pubkey, 0, sizeof(pubkey));
VG_UNDEF(&pubkey, sizeof(pubkey));
secp256k1_pubkey_save(&pubkey, &ge);
VG_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
VG_UNDEF(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, 0) == 1);
VG_CHECK(pubkeyo, outl);
CHECK(outl == 65);
CHECK(pubkeyo[0] == 4);
CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
}
CHECK(ecount == 0);
} else {
/* These cases must fail to parse. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
}
}
secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
}
void run_ec_pubkey_parse_test(void) {
#define SECP256K1_EC_PARSE_TEST_NVALID (12)
const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
{
/* Point with leading and trailing zeros in x and y serialization. */
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
},
{
/* Point with x equal to a 3rd root of unity.*/
0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Point with largest x. (1/2) */
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, 0x2c,
0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
},
{
/* Point with largest x. (2/2) */
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, 0x2c,
0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
},
{
/* Point with smallest x. (1/2) */
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,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Point with smallest x. (2/2) */
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,
0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
},
{
/* Point with largest y. (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
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, 0x2e,
},
{
/* Point with largest y. (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
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, 0x2e,
},
{
/* Point with largest y. (3/3) */
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
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, 0x2e,
},
{
/* Point with smallest y. (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
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,
},
{
/* Point with smallest y. (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
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,
},
{
/* Point with smallest y. (3/3) */
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
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
}
};
#define SECP256K1_EC_PARSE_TEST_NXVALID (4)
const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
{
/* Valid if y overflow ignored (y = 1 mod p). (1/3) */
0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
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, 0x30,
},
{
/* Valid if y overflow ignored (y = 1 mod p). (2/3) */
0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
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, 0x30,
},
{
/* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
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, 0x30,
},
{
/* x on curve, y is from y^2 = x^3 + 8. */
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, 0x03
}
};
#define SECP256K1_EC_PARSE_TEST_NINVALID (7)
const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
{
/* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
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,
},
{
/* Valid if x overflow ignored (x = 1 mod p). */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
},
{
/* Valid if x overflow ignored (x = 1 mod p). */
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
},
{
/* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
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, 0x2e,
0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
},
{
/* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
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, 0x2e,
0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
},
{
/* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
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,
0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
},
{
/* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
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,
0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
}
};
const unsigned char pubkeyc[66] = {
/* Serialization of G. */
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, 0x00
};
unsigned char shortkey[2];
secp256k1_ge ge;
secp256k1_pubkey pubkey;
int32_t i;
int32_t ecount;
int32_t ecount2;
ecount = 0;
/* Nothing should be reading this far into pubkeyc. */
VG_UNDEF(&pubkeyc[65], 1);
secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
/* Zero length claimed, fail, zeroize, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(shortkey, 2);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
/* Length one claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 256 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
shortkey[0] = i;
VG_UNDEF(&shortkey[1], 1);
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
/* Length two claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 65536 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
shortkey[0] = i & 255;
shortkey[1] = i >> 8;
VG_UNDEF(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
VG_CHECK(&pubkey, sizeof(pubkey));
CHECK(ecount == 0);
CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
CHECK(ecount == 1);
}
memset(&pubkey, 0xfe, sizeof(pubkey));
ecount = 0;
VG_UNDEF(&pubkey, sizeof(pubkey));
/* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0)