/********************************************************************** * 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 #include #include #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]; int i; secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 32, msg1, 32); 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); 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_mul(&x, a, ai); secp256k1_fe_set_int(&one, 1); 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 char *c64 = "0001020304050607111213141516171822232425262728293334353637383940"; 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]; char c642[64]; secp256k1_fe_storage_t fes2; /* Check conversions to fe. */ CHECK(secp256k1_fe_set_b32(&fe2, b32)); CHECK(secp256k1_fe_equal_var(&fe, &fe2)); CHECK(secp256k1_fe_set_hex(&fe2, c64)); 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_get_hex(c642, &fe); CHECK(memcmp(c642, c64, 64) == 0); secp256k1_fe_to_storage(&fes2, &fe); CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0); } void run_field_misc(void) { const unsigned char f32_5[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, 0x05, }; secp256k1_fe_t x; secp256k1_fe_t y; secp256k1_fe_t z; secp256k1_fe_t q; secp256k1_fe_t fe5; int i; CHECK(secp256k1_fe_set_b32(&fe5, f32_5)); 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_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; } } secp256k1_gej_set_infinity(&sum); 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) { secp256k1_gej_t a; secp256k1_gej_t x; secp256k1_gej_t x2; secp256k1_fe_t ax; secp256k1_fe_t ay; secp256k1_scalar_t xn; secp256k1_scalar_t gn; secp256k1_scalar_t xf; secp256k1_scalar_t gf; secp256k1_scalar_t ae; secp256k1_scalar_t ge; int i; /* two random initial factors xn and gn */ static const unsigned char xni[32] = { 0x84, 0xcc, 0x54, 0x52, 0xf7, 0xfd, 0xe1, 0xed, 0xb4, 0xd3, 0x8a, 0x8c, 0xe9, 0xb1, 0xb8, 0x4c, 0xce, 0xf3, 0x1f, 0x14, 0x6e, 0x56, 0x9b, 0xe9, 0x70, 0x5d, 0x35, 0x7a, 0x42, 0x98, 0x54, 0x07 }; static const unsigned char gni[32] = { 0xa1, 0xe5, 0x8d, 0x22, 0x55, 0x3d, 0xcd, 0x42, 0xb2, 0x39, 0x80, 0x62, 0x5d, 0x4c, 0x57, 0xa9, 0x6e, 0x93, 0x23, 0xd4, 0x2b, 0x31, 0x52, 0xe5, 0xca, 0x2c, 0x39, 0x90, 0xed, 0xc7, 0xc9, 0xde }; /* two small multipliers to be applied to xn and gn in every iteration: */ static const unsigned char xfi[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0x13,0x37}; static const unsigned char gfi[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0x71,0x13}; char res[131]; char res2[131]; /* random starting point A (on the curve) */ VERIFY_CHECK(secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004")); VERIFY_CHECK(secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f")); secp256k1_gej_set_xy(&a, &ax, &ay); secp256k1_scalar_set_b32(&xn, xni, NULL); secp256k1_scalar_set_b32(&gn, gni, NULL); secp256k1_scalar_set_b32(&xf, xfi, NULL); secp256k1_scalar_set_b32(&gf, gfi, NULL); /* accumulators with the resulting coefficients to A and G */ secp256k1_scalar_set_int(&ae, 1); secp256k1_scalar_set_int(&ge, 0); /* 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) { secp256k1_gej_get_hex(res, &x); CHECK(memcmp(res, "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)", 131) == 0); } } /* redo the computation, but directly with the resulting ae and ge coefficients: */ secp256k1_ecmult(&x2, &a, &ae, &ge); secp256k1_gej_get_hex(res, &x); secp256k1_gej_get_hex(res2, &x2); CHECK(memcmp(res, res2, 131) == 0); } 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; char c[64]; secp256k1_fe_t x; VERIFY_CHECK(secp256k1_fe_set_hex(&x, "0000000000000000000000000000000000000000000000000000000000000002")); 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_get_hex(c, &x); CHECK(memcmp(c, "7603CB59B0EF6C63FE6084792A0C378CDB3233A80F8A9A09A877DEAD31B38C45", 64) == 0); } 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 privkey[32]; unsigned char message[32]; unsigned char privkey2[32]; unsigned char csignature[64]; unsigned char signature[72]; unsigned char pubkey[65]; unsigned char recpubkey[65]; unsigned char seckey[300]; int signaturelen = 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); /* Verify. */ CHECK(secp256k1_ecdsa_verify(message, signature, signaturelen, 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 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. */ { 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; 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, NULL) == 0); CHECK(siglen == 0); /* Zero key results in signature failure. */ memset(key, 0, 32); CHECK(secp256k1_ecdsa_sign(msg, sig, &siglen, key, NULL, NULL) == 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, NULL) == 0); CHECK(siglen == 0); CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, nonce_function_test_fail, NULL, &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, NULL) == 1); CHECK(siglen > 0); CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, nonce_function_rfc6979, NULL) == 1); CHECK(siglen > 0); CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0)); CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, nonce_function_test_retry, NULL, &recid) == 1); CHECK(!is_empty_compact_signature(sig)); CHECK(secp256k1_ecdsa_sign_compact(msg, sig2, key, nonce_function_rfc6979, NULL, &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, NULL) == 1); CHECK(siglen > 0); CHECK(secp256k1_ecdsa_sign(msg, sig2, &siglen2, key, NULL, NULL) == 1); CHECK(siglen2 > 0); CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0)); CHECK(secp256k1_ecdsa_sign_compact(msg, sig, key, NULL, NULL, &recid) == 1); CHECK(!is_empty_compact_signature(sig)); CHECK(secp256k1_ecdsa_sign_compact(msg, sig2, key, NULL, NULL, &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, NULL) == 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, NULL) == 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) { uint64_t seed; /* find iteration count */ if (argc > 1) { count = strtol(argv[1], NULL, 0); } /* find random seed */ if (argc > 2) { sscanf(argv[2], "%" I64uFORMAT, (unsigned long long*)&seed); } else { FILE *frand = fopen("/dev/urandom", "r"); if (!frand || !fread(&seed, sizeof(seed), 1, frand)) { seed = time(NULL) * 1337; } fclose(frand); } secp256k1_rand_seed(seed); printf("test count = %i\n", count); printf("random seed = %" I64uFORMAT "\n", (unsigned long long)seed); /* 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 printf("random run = %llu\n", (unsigned long long)secp256k1_rand32() + ((unsigned long long)secp256k1_rand32() << 32)); /* shutdown */ secp256k1_stop(); /* shutting down twice shouldn't cause any double frees. */ secp256k1_stop(); return 0; }