diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c index 35d3c9854..c7f1d7700 100644 --- a/src/secp256k1/src/tests.c +++ b/src/secp256k1/src/tests.c @@ -1,5714 +1,5735 @@ /*********************************************************************** * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #if defined HAVE_CONFIG_H #include "libsecp256k1-config.h" #endif #include #include #include #include #include "secp256k1.c" #include "include/secp256k1.h" #include "include/secp256k1_preallocated.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" # if OPENSSL_VERSION_NUMBER < 0x10100000L void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;} # endif #endif #include "contrib/lax_der_parsing.c" #include "contrib/lax_der_privatekey_parsing.c" static int count = 64; static secp256k1_context *ctx = NULL; 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 random_field_element_test(secp256k1_fe *fe) { do { unsigned char b32[32]; secp256k1_testrand256_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_testrand_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); #ifdef VERIFY CHECK(fe->magnitude == n); #endif } 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_testrand_bits(1))) { secp256k1_fe_normalize(&ge->y); break; } } while(1); ge->infinity = 0; } 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_testrand256_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_testrand256(b32); secp256k1_scalar_set_b32(num, b32, &overflow); if (overflow || secp256k1_scalar_is_zero(num)) { continue; } break; } while(1); } void random_scalar_order_b32(unsigned char *b32) { secp256k1_scalar num; random_scalar_order(&num); secp256k1_scalar_get_b32(b32, &num); } void run_context_tests(int use_prealloc) { secp256k1_pubkey pubkey; secp256k1_pubkey zero_pubkey; secp256k1_ecdsa_signature sig; unsigned char ctmp[32]; int32_t ecount; int32_t ecount2; secp256k1_context *none; secp256k1_context *sign; secp256k1_context *vrfy; secp256k1_context *both; void *none_prealloc = NULL; void *sign_prealloc = NULL; void *vrfy_prealloc = NULL; void *both_prealloc = NULL; secp256k1_gej pubj; secp256k1_ge pub; secp256k1_scalar msg, key, nonce; secp256k1_scalar sigr, sigs; if (use_prealloc) { none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(none_prealloc != NULL); CHECK(sign_prealloc != NULL); CHECK(vrfy_prealloc != NULL); CHECK(both_prealloc != NULL); none = secp256k1_context_preallocated_create(none_prealloc, SECP256K1_CONTEXT_NONE); sign = secp256k1_context_preallocated_create(sign_prealloc, SECP256K1_CONTEXT_SIGN); vrfy = secp256k1_context_preallocated_create(vrfy_prealloc, SECP256K1_CONTEXT_VERIFY); both = secp256k1_context_preallocated_create(both_prealloc, SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); } else { none = secp256k1_context_create(SECP256K1_CONTEXT_NONE); sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY); both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); } memset(&zero_pubkey, 0, sizeof(zero_pubkey)); ecount = 0; ecount2 = 10; secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount); secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2); /* set error callback (to a function that still aborts in case malloc() fails in secp256k1_context_clone() below) */ secp256k1_context_set_error_callback(sign, secp256k1_default_illegal_callback_fn, NULL); CHECK(sign->error_callback.fn != vrfy->error_callback.fn); CHECK(sign->error_callback.fn == secp256k1_default_illegal_callback_fn); /* check if sizes for cloning are consistent */ CHECK(secp256k1_context_preallocated_clone_size(none) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(secp256k1_context_preallocated_clone_size(sign) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(secp256k1_context_preallocated_clone_size(vrfy) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(secp256k1_context_preallocated_clone_size(both) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); /*** clone and destroy all of them to make sure cloning was complete ***/ { secp256k1_context *ctx_tmp; if (use_prealloc) { /* clone into a non-preallocated context and then again into a new preallocated one. */ ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp); free(none_prealloc); none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(none_prealloc != NULL); ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, none_prealloc); secp256k1_context_destroy(ctx_tmp); ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp); free(sign_prealloc); sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(sign_prealloc != NULL); ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, sign_prealloc); secp256k1_context_destroy(ctx_tmp); ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp); free(vrfy_prealloc); vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(vrfy_prealloc != NULL); ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, vrfy_prealloc); secp256k1_context_destroy(ctx_tmp); ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp); free(both_prealloc); both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(both_prealloc != NULL); ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, both_prealloc); secp256k1_context_destroy(ctx_tmp); } else { /* clone into a preallocated context and then again into a new non-preallocated one. */ void *prealloc_tmp; prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(prealloc_tmp != NULL); ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(prealloc_tmp != NULL); ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); } } /* Verify that the error callback makes it across the clone. */ CHECK(sign->error_callback.fn != vrfy->error_callback.fn); CHECK(sign->error_callback.fn == secp256k1_default_illegal_callback_fn); /* And that it resets back to default. */ secp256k1_context_set_error_callback(sign, NULL, NULL); CHECK(vrfy->error_callback.fn == sign->error_callback.fn); /*** 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); /* Verify context-type checking illegal-argument errors. */ memset(ctmp, 1, 32); CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0); CHECK(ecount == 1); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0); CHECK(ecount == 2); VG_UNDEF(&sig, sizeof(sig)); CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1); VG_CHECK(&sig, sizeof(sig)); CHECK(ecount2 == 10); CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0); CHECK(ecount2 == 11); CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1); CHECK(ecount == 2); CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0); CHECK(ecount2 == 12); CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1); CHECK(ecount == 2); CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0); CHECK(ecount2 == 13); CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1); CHECK(ecount == 2); CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1); CHECK(ecount == 2); CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0); CHECK(ecount2 == 14); CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0); CHECK(ecount == 3); CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1); CHECK(ecount == 3); CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1); CHECK(ecount == 3); CHECK(secp256k1_context_randomize(vrfy, NULL) == 1); CHECK(ecount == 3); CHECK(secp256k1_context_randomize(sign, ctmp) == 1); CHECK(ecount2 == 14); CHECK(secp256k1_context_randomize(sign, NULL) == 1); CHECK(ecount2 == 14); secp256k1_context_set_illegal_callback(vrfy, NULL, NULL); secp256k1_context_set_illegal_callback(sign, NULL, NULL); /* 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 */ if (use_prealloc) { secp256k1_context_preallocated_destroy(none); secp256k1_context_preallocated_destroy(sign); secp256k1_context_preallocated_destroy(vrfy); secp256k1_context_preallocated_destroy(both); free(none_prealloc); free(sign_prealloc); free(vrfy_prealloc); free(both_prealloc); } else { secp256k1_context_destroy(none); secp256k1_context_destroy(sign); secp256k1_context_destroy(vrfy); secp256k1_context_destroy(both); } /* Defined as no-op. */ secp256k1_context_destroy(NULL); secp256k1_context_preallocated_destroy(NULL); } void run_scratch_tests(void) { const size_t adj_alloc = ((500 + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT; int32_t ecount = 0; size_t checkpoint; size_t checkpoint_2; secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE); secp256k1_scratch_space *scratch; secp256k1_scratch_space local_scratch; /* Test public API */ secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount); secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount); scratch = secp256k1_scratch_space_create(none, 1000); CHECK(scratch != NULL); CHECK(ecount == 0); /* Test internal API */ CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1)); CHECK(scratch->alloc_size == 0); CHECK(scratch->alloc_size % ALIGNMENT == 0); /* Allocating 500 bytes succeeds */ checkpoint = secp256k1_scratch_checkpoint(&none->error_callback, scratch); CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); CHECK(scratch->alloc_size != 0); CHECK(scratch->alloc_size % ALIGNMENT == 0); /* Allocating another 501 bytes fails */ CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 501) == NULL); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); CHECK(scratch->alloc_size != 0); CHECK(scratch->alloc_size % ALIGNMENT == 0); /* ...but it succeeds once we apply the checkpoint to undo it */ secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); CHECK(scratch->alloc_size == 0); CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL); CHECK(scratch->alloc_size != 0); /* try to apply a bad checkpoint */ checkpoint_2 = secp256k1_scratch_checkpoint(&none->error_callback, scratch); secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); CHECK(ecount == 0); secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */ CHECK(ecount == 1); secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, (size_t) -1); /* this is just wildly invalid */ CHECK(ecount == 2); /* try to use badly initialized scratch space */ secp256k1_scratch_space_destroy(none, scratch); memset(&local_scratch, 0, sizeof(local_scratch)); scratch = &local_scratch; CHECK(!secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0)); CHECK(ecount == 3); CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) == NULL); CHECK(ecount == 4); secp256k1_scratch_space_destroy(none, scratch); CHECK(ecount == 5); /* Test that large integers do not wrap around in a bad way */ scratch = secp256k1_scratch_space_create(none, 1000); /* Try max allocation with a large number of objects. Only makes sense if * ALIGNMENT is greater than 1 because otherwise the objects take no extra * space. */ CHECK(ALIGNMENT <= 1 || !secp256k1_scratch_max_allocation(&none->error_callback, scratch, (SIZE_MAX / (ALIGNMENT - 1)) + 1)); /* Try allocating SIZE_MAX to test wrap around which only happens if * ALIGNMENT > 1, otherwise it returns NULL anyway because the scratch * space is too small. */ CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, SIZE_MAX) == NULL); secp256k1_scratch_space_destroy(none, scratch); /* cleanup */ secp256k1_scratch_space_destroy(none, NULL); /* no-op */ secp256k1_context_destroy(none); } +void run_ctz_tests(void) { + static const uint32_t b32[] = {1, 0xffffffff, 0x5e56968f, 0xe0d63129}; + static const uint64_t b64[] = {1, 0xffffffffffffffff, 0xbcd02462139b3fc3, 0x98b5f80c769693ef}; + int shift; + unsigned i; + for (i = 0; i < sizeof(b32) / sizeof(b32[0]); ++i) { + for (shift = 0; shift < 32; ++shift) { + CHECK(secp256k1_ctz32_var_debruijn(b32[i] << shift) == shift); + CHECK(secp256k1_ctz32_var(b32[i] << shift) == shift); + } + } + for (i = 0; i < sizeof(b64) / sizeof(b64[0]); ++i) { + for (shift = 0; shift < 64; ++shift) { + CHECK(secp256k1_ctz64_var_debruijn(b64[i] << shift) == shift); + CHECK(secp256k1_ctz64_var(b64[i] << shift) == shift); + } + } +} + /***** 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 hasher; secp256k1_sha256_initialize(&hasher); secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); secp256k1_sha256_finalize(&hasher, out); CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0); if (strlen(inputs[i]) > 0) { int split = secp256k1_testrand_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(secp256k1_memcmp_var(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 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(secp256k1_memcmp_var(out, outputs[i], 32) == 0); if (strlen(inputs[i]) > 0) { int split = secp256k1_testrand_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(secp256k1_memcmp_var(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 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(secp256k1_memcmp_var(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(secp256k1_memcmp_var(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(secp256k1_memcmp_var(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_testrand32() : secp256k1_testrand_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_testrand_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_testrand_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) { int i; secp256k1_scalar s; secp256k1_num n1; secp256k1_num n2; secp256k1_num n1p2, n2p1, n1m2, n2m1; random_num_order_test(&n1); /* n1 = R1 */ if (secp256k1_testrand_bits(1)) { random_num_negate(&n1); } random_num_order_test(&n2); /* n2 = R2 */ if (secp256k1_testrand_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)); /* check is_one */ secp256k1_scalar_set_int(&s, 1); secp256k1_scalar_get_num(&n1, &s); CHECK(secp256k1_num_is_one(&n1)); /* check that 2^n + 1 is never 1 */ secp256k1_scalar_get_num(&n2, &s); for (i = 0; i < 250; ++i) { secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */ secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */ CHECK(!secp256k1_num_is_one(&n1p2)); } } void test_num_mod(void) { int i; secp256k1_scalar s; secp256k1_num order, n; /* check that 0 mod anything is 0 */ random_scalar_order_test(&s); secp256k1_scalar_get_num(&order, &s); secp256k1_scalar_set_int(&s, 0); secp256k1_scalar_get_num(&n, &s); secp256k1_num_mod(&n, &order); CHECK(secp256k1_num_is_zero(&n)); /* check that anything mod 1 is 0 */ secp256k1_scalar_set_int(&s, 1); secp256k1_scalar_get_num(&order, &s); secp256k1_scalar_get_num(&n, &s); secp256k1_num_mod(&n, &order); CHECK(secp256k1_num_is_zero(&n)); /* check that increasing the number past 2^256 does not break this */ random_scalar_order_test(&s); secp256k1_scalar_get_num(&n, &s); /* multiply by 2^8, which'll test this case with high probability */ for (i = 0; i < 8; ++i) { secp256k1_num_add(&n, &n, &n); } secp256k1_num_mod(&n, &order); CHECK(secp256k1_num_is_zero(&n)); } void test_num_jacobi(void) { secp256k1_scalar sqr; secp256k1_scalar small; secp256k1_scalar five; /* five is not a quadratic residue */ secp256k1_num order, n; int i; /* squares mod 5 are 1, 4 */ const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 }; /* check some small values with 5 as the order */ secp256k1_scalar_set_int(&five, 5); secp256k1_scalar_get_num(&order, &five); for (i = 0; i < 10; ++i) { secp256k1_scalar_set_int(&small, i); secp256k1_scalar_get_num(&n, &small); CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]); } /** test large values with 5 as group order */ secp256k1_scalar_get_num(&order, &five); /* we first need a scalar which is not a multiple of 5 */ do { secp256k1_num fiven; random_scalar_order_test(&sqr); secp256k1_scalar_get_num(&fiven, &five); secp256k1_scalar_get_num(&n, &sqr); secp256k1_num_mod(&n, &fiven); } while (secp256k1_num_is_zero(&n)); /* next force it to be a residue. 2 is a nonresidue mod 5 so we can * just multiply by two, i.e. add the number to itself */ if (secp256k1_num_jacobi(&n, &order) == -1) { secp256k1_num_add(&n, &n, &n); } /* test residue */ CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* test nonresidue */ secp256k1_num_add(&n, &n, &n); CHECK(secp256k1_num_jacobi(&n, &order) == -1); /** test with secp group order as order */ secp256k1_scalar_order_get_num(&order); random_scalar_order_test(&sqr); secp256k1_scalar_sqr(&sqr, &sqr); /* test residue */ secp256k1_scalar_get_num(&n, &sqr); CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* test nonresidue */ secp256k1_scalar_mul(&sqr, &sqr, &five); secp256k1_scalar_get_num(&n, &sqr); CHECK(secp256k1_num_jacobi(&n, &order) == -1); /* test multiple of the order*/ CHECK(secp256k1_num_jacobi(&order, &order) == 0); /* check one less than the order */ secp256k1_scalar_set_int(&small, 1); secp256k1_scalar_get_num(&n, &small); secp256k1_num_sub(&n, &order, &n); CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */ } void run_num_smalltests(void) { int i; for (i = 0; i < 100*count; i++) { test_num_negate(); test_num_add_sub(); test_num_mod(); test_num_jacobi(); } } #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_testrand_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 multiplying 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_testrand_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_testrand_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)); #ifndef USE_NUM_NONE secp256k1_scalar_get_num(&invnum, &inv); CHECK(secp256k1_num_is_one(&invnum)); #endif } } { /* 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_testrand_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_set_b32_seckey_tests(void) { unsigned char b32[32]; secp256k1_scalar s1; secp256k1_scalar s2; /* Usually set_b32 and set_b32_seckey give the same result */ random_scalar_order_b32(b32); secp256k1_scalar_set_b32(&s1, b32, NULL); CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 1); CHECK(secp256k1_scalar_eq(&s1, &s2) == 1); memset(b32, 0, sizeof(b32)); CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); memset(b32, 0xFF, sizeof(b32)); CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); } void run_scalar_tests(void) { int i; for (i = 0; i < 128 * count; i++) { scalar_test(); } for (i = 0; i < count; i++) { run_scalar_set_b32_seckey_tests(); } { /* (-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 { /* Test secp256k1_scalar_set_b32 boundary conditions */ secp256k1_num order; secp256k1_scalar scalar; unsigned char bin[32]; unsigned char bin_tmp[32]; int overflow = 0; /* 2^256-1 - order */ static const secp256k1_scalar all_ones_minus_order = SECP256K1_SCALAR_CONST( 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000001UL, 0x45512319UL, 0x50B75FC4UL, 0x402DA173UL, 0x2FC9BEBEUL ); /* A scalar set to 0s should be 0. */ memset(bin, 0, 32); secp256k1_scalar_set_b32(&scalar, bin, &overflow); CHECK(overflow == 0); CHECK(secp256k1_scalar_is_zero(&scalar)); /* A scalar with value of the curve order should be 0. */ secp256k1_scalar_order_get_num(&order); secp256k1_num_get_bin(bin, 32, &order); secp256k1_scalar_set_b32(&scalar, bin, &overflow); CHECK(overflow == 1); CHECK(secp256k1_scalar_is_zero(&scalar)); /* A scalar with value of the curve order minus one should not overflow. */ bin[31] -= 1; secp256k1_scalar_set_b32(&scalar, bin, &overflow); CHECK(overflow == 0); secp256k1_scalar_get_b32(bin_tmp, &scalar); CHECK(secp256k1_memcmp_var(bin, bin_tmp, 32) == 0); /* A scalar set to all 1s should overflow. */ memset(bin, 0xFF, 32); secp256k1_scalar_set_b32(&scalar, bin, &overflow); CHECK(overflow == 1); CHECK(secp256k1_scalar_eq(&scalar, &all_ones_minus_order)); } #endif { /* Does check_overflow check catch all ones? */ static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); CHECK(secp256k1_scalar_check_overflow(&overflowed)); } { /* Static test vectors. * These were reduced from ~10^12 random vectors based on comparison-decision * and edge-case coverage on 32-bit and 64-bit implementations. * The responses were generated with Sage 5.9. */ secp256k1_scalar x; secp256k1_scalar y; secp256k1_scalar z; secp256k1_scalar zz; secp256k1_scalar one; secp256k1_scalar r1; secp256k1_scalar r2; #if defined(USE_SCALAR_INV_NUM) secp256k1_scalar zzv; #endif int overflow; unsigned char chal[33][2][32] = { {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff}, {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}}, {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}}, {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00}, {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}}, {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff, 0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00, 0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}}, {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0}, {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 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, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f}, {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff, 0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}}, {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff}, {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}}, {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff, 0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f, 0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}}, {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00}, {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}}, {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}}, {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80}, {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00}, {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80, 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}}, {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff, 0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 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, 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, 0x40}}, {{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, 0x00}}, {{0x7f, 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}, {0x7f, 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, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}}, {{0x7f, 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}, {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, 0x02}}, {{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}, {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}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00, 0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff}, {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}}, {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00}, {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f, 0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}}, {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80, 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}}, {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00, 0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f, 0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}}, {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83, 0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0}, {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, 0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}}, {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}, {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}} }; unsigned char res[33][2][32] = { {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9, 0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1, 0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6, 0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35}, {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d, 0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c, 0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49, 0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}}, {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22, 0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c, 0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f, 0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8}, {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77, 0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4, 0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59, 0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}}, {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef, 0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab, 0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55, 0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c}, {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96, 0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f, 0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12, 0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}}, {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c, 0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf, 0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9, 0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48}, {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42, 0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5, 0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c, 0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}}, {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb, 0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74, 0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6, 0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63}, {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3, 0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99, 0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58, 0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}}, {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b, 0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7, 0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f, 0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0}, {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d, 0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d, 0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9, 0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}}, {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7, 0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70, 0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06, 0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e}, {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9, 0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79, 0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e, 0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}}, {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb, 0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5, 0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a, 0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe}, {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48, 0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e, 0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc, 0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}}, {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b, 0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0, 0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53, 0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8}, {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c, 0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01, 0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f, 0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}}, {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7, 0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c, 0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92, 0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30}, {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62, 0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e, 0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb, 0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}}, {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25, 0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d, 0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0, 0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13}, {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60, 0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00, 0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4, 0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}}, {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31, 0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4, 0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88, 0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa}, {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57, 0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38, 0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51, 0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}}, {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c, 0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f, 0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2, 0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4}, {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01, 0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4, 0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86, 0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}}, {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5, 0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51, 0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3, 0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62}, {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c, 0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91, 0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c, 0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}}, {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e, 0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56, 0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58, 0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4}, {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41, 0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7, 0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92, 0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}}, {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec, 0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19, 0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3, 0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4}, {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87, 0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a, 0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92, 0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}}, {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64, 0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3, 0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f, 0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33}, {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c, 0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d, 0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea, 0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}}, {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7, 0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a, 0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae, 0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe}, {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc, 0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39, 0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14, 0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}}, {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23, 0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d, 0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2, 0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16}, {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c, 0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84, 0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0, 0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}}, {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb, 0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94, 0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b, 0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e}, {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54, 0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00, 0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb, 0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}}, {{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}, {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}}, {{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}, {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}}, {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}, {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0, 0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b, 0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94, 0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8}, {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26, 0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d, 0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a, 0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}}, {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, 0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd}, {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, {{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}, {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}}, {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39, 0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea, 0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf, 0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae}, {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b, 0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb, 0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6, 0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}}, {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a, 0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f, 0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9, 0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56}, {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93, 0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07, 0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71, 0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}}, {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87, 0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9, 0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55, 0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73}, {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d, 0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86, 0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb, 0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}}, {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2, 0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7, 0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41, 0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7}, {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06, 0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04, 0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08, 0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}}, {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2, 0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b, 0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40, 0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68}, {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e, 0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a, 0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b, 0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}}, {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67, 0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f, 0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a, 0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51}, {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2, 0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38, 0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34, 0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}}, {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}, {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}} }; secp256k1_scalar_set_int(&one, 1); for (i = 0; i < 33; i++) { secp256k1_scalar_set_b32(&x, chal[i][0], &overflow); CHECK(!overflow); secp256k1_scalar_set_b32(&y, chal[i][1], &overflow); CHECK(!overflow); secp256k1_scalar_set_b32(&r1, res[i][0], &overflow); CHECK(!overflow); secp256k1_scalar_set_b32(&r2, res[i][1], &overflow); CHECK(!overflow); secp256k1_scalar_mul(&z, &x, &y); CHECK(!secp256k1_scalar_check_overflow(&z)); CHECK(secp256k1_scalar_eq(&r1, &z)); if (!secp256k1_scalar_is_zero(&y)) { secp256k1_scalar_inverse(&zz, &y); CHECK(!secp256k1_scalar_check_overflow(&zz)); #if defined(USE_SCALAR_INV_NUM) secp256k1_scalar_inverse_var(&zzv, &y); CHECK(secp256k1_scalar_eq(&zzv, &zz)); #endif secp256k1_scalar_mul(&z, &z, &zz); CHECK(!secp256k1_scalar_check_overflow(&z)); CHECK(secp256k1_scalar_eq(&x, &z)); secp256k1_scalar_mul(&zz, &zz, &y); CHECK(!secp256k1_scalar_check_overflow(&zz)); CHECK(secp256k1_scalar_eq(&one, &zz)); } secp256k1_scalar_mul(&z, &x, &x); CHECK(!secp256k1_scalar_check_overflow(&z)); secp256k1_scalar_sqr(&zz, &x); CHECK(!secp256k1_scalar_check_overflow(&zz)); CHECK(secp256k1_scalar_eq(&zz, &z)); CHECK(secp256k1_scalar_eq(&r2, &zz)); } } } /***** FIELD TESTS *****/ void random_fe(secp256k1_fe *x) { unsigned char bin[32]; do { secp256k1_testrand256(bin); if (secp256k1_fe_set_b32(x, bin)) { return; } } while(1); } void random_fe_test(secp256k1_fe *x) { unsigned char bin[32]; do { secp256k1_testrand256_test(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(&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(secp256k1_memcmp_var(b322, b32, 32) == 0); secp256k1_fe_to_storage(&fes2, &fe); CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0); } int fe_secp256k1_memcmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { secp256k1_fe t = *b; #ifdef VERIFY t.magnitude = a->magnitude; t.normalized = a->normalized; #endif return secp256k1_memcmp_var(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); #ifdef VERIFY CHECK(x.normalized && x.magnitude == 1); #endif secp256k1_fe_cmov(&x, &x, 1); CHECK(fe_secp256k1_memcmp_var(&x, &z) != 0); CHECK(fe_secp256k1_memcmp_var(&x, &q) == 0); secp256k1_fe_cmov(&q, &z, 1); #ifdef VERIFY CHECK(!q.normalized && q.magnitude == z.magnitude); #endif CHECK(fe_secp256k1_memcmp_var(&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)); #ifdef VERIFY CHECK(q.normalized && q.magnitude == 1); #endif 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)); #ifdef VERIFY CHECK((q.normalized != (j&1)) && q.magnitude == ((j&1) ? z.magnitude : 1)); #endif } 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(secp256k1_memcmp_var(&xs, &zs, sizeof(xs)) != 0); secp256k1_fe_storage_cmov(&ys, &xs, 1); CHECK(secp256k1_memcmp_var(&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_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(&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; int runs = 6; /* 25 points are used: * - infinity * - for each of four random points p1 p2 p3 p4, we add the point, its * negation, and then those two again but with randomized Z coordinate. * - The same is then done for lambda*p1 and lambda^2*p1. */ secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs)); secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (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); if (i >= runs - 2) { secp256k1_ge_mul_lambda(&g, &ge[1]); } if (i >= runs - 1) { secp256k1_ge_mul_lambda(&g, &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); } } /* 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); /* Constant-time doubling. */ secp256k1_gej_double(&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 sum = SECP256K1_GEJ_CONST_INFINITY; secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (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_testrand_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 without known z ratios. */ { secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge)); secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1); 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_all[i], &gej[i]); } free(ge_set_all); } /* Test batch gej -> ge conversion with many infinities. */ for (i = 0; i < 4 * runs + 1; i++) { random_group_element_test(&ge[i]); /* randomly set half the points to infinity */ if(secp256k1_fe_is_odd(&ge[i].x)) { secp256k1_ge_set_infinity(&ge[i]); } secp256k1_gej_set_ge(&gej[i], &ge[i]); } /* batch invert */ secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1); /* check result */ for (i = 0; i < 4 * runs + 1; i++) { ge_equals_gej(&ge[i], &gej[i]); } free(ge); free(gej); } void test_intialized_inf(void) { secp256k1_ge p; secp256k1_gej pj, npj, infj1, infj2, infj3; secp256k1_fe zinv; /* Test that adding P+(-P) results in a fully initalized infinity*/ random_group_element_test(&p); secp256k1_gej_set_ge(&pj, &p); secp256k1_gej_neg(&npj, &pj); secp256k1_gej_add_var(&infj1, &pj, &npj, NULL); CHECK(secp256k1_gej_is_infinity(&infj1)); CHECK(secp256k1_fe_is_zero(&infj1.x)); CHECK(secp256k1_fe_is_zero(&infj1.y)); CHECK(secp256k1_fe_is_zero(&infj1.z)); secp256k1_gej_add_ge_var(&infj2, &npj, &p, NULL); CHECK(secp256k1_gej_is_infinity(&infj2)); CHECK(secp256k1_fe_is_zero(&infj2.x)); CHECK(secp256k1_fe_is_zero(&infj2.y)); CHECK(secp256k1_fe_is_zero(&infj2.z)); secp256k1_fe_set_int(&zinv, 1); secp256k1_gej_add_zinv_var(&infj3, &npj, &p, &zinv); CHECK(secp256k1_gej_is_infinity(&infj3)); CHECK(secp256k1_fe_is_zero(&infj3.x)); CHECK(secp256k1_fe_is_zero(&infj3.y)); CHECK(secp256k1_fe_is_zero(&infj3.z)); } 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-core/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(); test_intialized_inf(); } 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(secp256k1_memcmp_var(&sd, &sd2, sizeof(sd)) == 0); } } void run_ec_combine(void) { int i; for (i = 0; i < count * 8; i++) { test_ec_combine(); } } void test_group_decompress(const secp256k1_fe* x) { /* The input itself, normalized. */ secp256k1_fe fex = *x; secp256k1_fe fez; /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */ secp256k1_ge ge_quad, ge_even, ge_odd; secp256k1_gej gej_quad; /* Return values of the above calls. */ int res_quad, res_even, res_odd; secp256k1_fe_normalize_var(&fex); res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex); res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0); res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1); CHECK(res_quad == res_even); CHECK(res_quad == res_odd); if (res_quad) { secp256k1_fe_normalize_var(&ge_quad.x); secp256k1_fe_normalize_var(&ge_odd.x); secp256k1_fe_normalize_var(&ge_even.x); secp256k1_fe_normalize_var(&ge_quad.y); secp256k1_fe_normalize_var(&ge_odd.y); secp256k1_fe_normalize_var(&ge_even.y); /* No infinity allowed. */ CHECK(!ge_quad.infinity); CHECK(!ge_even.infinity); CHECK(!ge_odd.infinity); /* Check that the x coordinates check out. */ CHECK(secp256k1_fe_equal_var(&ge_quad.x, x)); CHECK(secp256k1_fe_equal_var(&ge_even.x, x)); CHECK(secp256k1_fe_equal_var(&ge_odd.x, x)); /* Check that the Y coordinate result in ge_quad is a square. */ CHECK(secp256k1_fe_is_quad_var(&ge_quad.y)); /* Check odd/even Y in ge_odd, ge_even. */ CHECK(secp256k1_fe_is_odd(&ge_odd.y)); CHECK(!secp256k1_fe_is_odd(&ge_even.y)); /* Check secp256k1_gej_has_quad_y_var. */ secp256k1_gej_set_ge(&gej_quad, &ge_quad); CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); do { random_fe_test(&fez); } while (secp256k1_fe_is_zero(&fez)); secp256k1_gej_rescale(&gej_quad, &fez); CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); secp256k1_gej_neg(&gej_quad, &gej_quad); CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); do { random_fe_test(&fez); } while (secp256k1_fe_is_zero(&fez)); secp256k1_gej_rescale(&gej_quad, &fez); CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); secp256k1_gej_neg(&gej_quad, &gej_quad); CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); } } void run_group_decompress(void) { int i; for (i = 0; i < count * 4; i++) { secp256k1_fe fe; random_fe_test(&fe); test_group_decompress(&fe); } } /***** 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)); 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); } /* These scalars reach large (in absolute value) outputs when fed to secp256k1_scalar_split_lambda. * * They are computed as: * - For a in [-2, -1, 0, 1, 2]: * - For b in [-3, -1, 1, 3]: * - Output (a*LAMBDA + (ORDER+b)/2) % ORDER */ static const secp256k1_scalar scalars_near_split_bounds[20] = { SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fc), SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fd), SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fe), SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6ff), SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632d), SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632e), SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632f), SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf76330), SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b209f), SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a0), SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a1), SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a2), SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede11), SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede12), SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede13), SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede14), SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a42), SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a43), SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a44), SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a45) }; void test_ecmult_target(const secp256k1_scalar* target, int mode) { /* Mode: 0=ecmult_gen, 1=ecmult, 2=ecmult_const */ secp256k1_scalar n1, n2; secp256k1_ge p; secp256k1_gej pj, p1j, p2j, ptj; static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); /* Generate random n1,n2 such that n1+n2 = -target. */ random_scalar_order_test(&n1); secp256k1_scalar_add(&n2, &n1, target); secp256k1_scalar_negate(&n2, &n2); /* Generate a random input point. */ if (mode != 0) { random_group_element_test(&p); secp256k1_gej_set_ge(&pj, &p); } /* EC multiplications */ if (mode == 0) { secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &p1j, &n1); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &p2j, &n2); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &ptj, target); } else if (mode == 1) { secp256k1_ecmult(&ctx->ecmult_ctx, &p1j, &pj, &n1, &zero); secp256k1_ecmult(&ctx->ecmult_ctx, &p2j, &pj, &n2, &zero); secp256k1_ecmult(&ctx->ecmult_ctx, &ptj, &pj, target, &zero); } else { secp256k1_ecmult_const(&p1j, &p, &n1, 256); secp256k1_ecmult_const(&p2j, &p, &n2, 256); secp256k1_ecmult_const(&ptj, &p, target, 256); } /* Add them all up: n1*P + n2*P + target*P = (n1+n2+target)*P = (n1+n1-n1-n2)*P = 0. */ secp256k1_gej_add_var(&ptj, &ptj, &p1j, NULL); secp256k1_gej_add_var(&ptj, &ptj, &p2j, NULL); CHECK(secp256k1_gej_is_infinity(&ptj)); } void run_ecmult_near_split_bound(void) { int i; unsigned j; for (i = 0; i < 4*count; ++i) { for (j = 0; j < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++j) { test_ecmult_target(&scalars_near_split_bounds[j], 0); test_ecmult_target(&scalars_near_split_bounds[j], 1); test_ecmult_target(&scalars_near_split_bounds[j], 2); } } } 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); 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, 256); 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, 256); secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256); secp256k1_ge_set_gej(&mid1, &res1); secp256k1_ge_set_gej(&mid2, &res2); secp256k1_ecmult_const(&res1, &mid1, &b, 256); secp256k1_ecmult_const(&res2, &mid2, &a, 256); 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, 3); secp256k1_ge_set_gej(&res2, &res1); CHECK(secp256k1_ge_is_infinity(&res2)); secp256k1_ecmult_const(&res1, &point, &one, 2); secp256k1_ge_set_gej(&res2, &res1); ge_equals_ge(&res2, &point); secp256k1_ecmult_const(&res1, &point, &negone, 256); 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, 256); } 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(); } typedef struct { secp256k1_scalar *sc; secp256k1_ge *pt; } ecmult_multi_data; static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { ecmult_multi_data *data = (ecmult_multi_data*) cbdata; *sc = data->sc[idx]; *pt = data->pt[idx]; return 1; } static int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { (void)sc; (void)pt; (void)idx; (void)cbdata; return 0; } void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) { int ncount; secp256k1_scalar szero; secp256k1_scalar sc[32]; secp256k1_ge pt[32]; secp256k1_gej r; secp256k1_gej r2; ecmult_multi_data data; data.sc = sc; data.pt = pt; secp256k1_scalar_set_int(&szero, 0); /* No points to multiply */ CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0)); /* Check 1- and 2-point multiplies against ecmult */ for (ncount = 0; ncount < count; ncount++) { secp256k1_ge ptg; secp256k1_gej ptgj; random_scalar_order(&sc[0]); random_scalar_order(&sc[1]); random_group_element_test(&ptg); secp256k1_gej_set_ge(&ptgj, &ptg); pt[0] = ptg; pt[1] = secp256k1_ge_const_g; /* only G scalar */ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); /* 1-point */ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); /* Try to multiply 1 point, but callback returns false */ CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1)); /* 2-point */ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); /* 2-point with G scalar */ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); } /* Check infinite outputs of various forms */ for (ncount = 0; ncount < count; ncount++) { secp256k1_ge ptg; size_t i, j; size_t sizes[] = { 2, 10, 32 }; for (j = 0; j < 3; j++) { for (i = 0; i < 32; i++) { random_scalar_order(&sc[i]); secp256k1_ge_set_infinity(&pt[i]); } CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(secp256k1_gej_is_infinity(&r)); } for (j = 0; j < 3; j++) { for (i = 0; i < 32; i++) { random_group_element_test(&ptg); pt[i] = ptg; secp256k1_scalar_set_int(&sc[i], 0); } CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(secp256k1_gej_is_infinity(&r)); } for (j = 0; j < 3; j++) { random_group_element_test(&ptg); for (i = 0; i < 16; i++) { random_scalar_order(&sc[2*i]); secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]); pt[2 * i] = ptg; pt[2 * i + 1] = ptg; } CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(secp256k1_gej_is_infinity(&r)); random_scalar_order(&sc[0]); for (i = 0; i < 16; i++) { random_group_element_test(&ptg); sc[2*i] = sc[0]; sc[2*i+1] = sc[0]; pt[2 * i] = ptg; secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]); } CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(secp256k1_gej_is_infinity(&r)); } random_group_element_test(&ptg); secp256k1_scalar_set_int(&sc[0], 0); pt[0] = ptg; for (i = 1; i < 32; i++) { pt[i] = ptg; random_scalar_order(&sc[i]); secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]); secp256k1_scalar_negate(&sc[i], &sc[i]); } CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32)); CHECK(secp256k1_gej_is_infinity(&r)); } /* Check random points, constant scalar */ for (ncount = 0; ncount < count; ncount++) { size_t i; secp256k1_gej_set_infinity(&r); random_scalar_order(&sc[0]); for (i = 0; i < 20; i++) { secp256k1_ge ptg; sc[i] = sc[0]; random_group_element_test(&ptg); pt[i] = ptg; secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL); } secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); } /* Check random scalars, constant point */ for (ncount = 0; ncount < count; ncount++) { size_t i; secp256k1_ge ptg; secp256k1_gej p0j; secp256k1_scalar rs; secp256k1_scalar_set_int(&rs, 0); random_group_element_test(&ptg); for (i = 0; i < 20; i++) { random_scalar_order(&sc[i]); pt[i] = ptg; secp256k1_scalar_add(&rs, &rs, &sc[i]); } secp256k1_gej_set_ge(&p0j, &pt[0]); secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); secp256k1_gej_neg(&r2, &r2); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); } /* Sanity check that zero scalars don't cause problems */ for (ncount = 0; ncount < 20; ncount++) { random_scalar_order(&sc[ncount]); random_group_element_test(&pt[ncount]); } secp256k1_scalar_clear(&sc[0]); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); secp256k1_scalar_clear(&sc[1]); secp256k1_scalar_clear(&sc[2]); secp256k1_scalar_clear(&sc[3]); secp256k1_scalar_clear(&sc[4]); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6)); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5)); CHECK(secp256k1_gej_is_infinity(&r)); /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */ { const size_t TOP = 8; size_t s0i, s1i; size_t t0i, t1i; secp256k1_ge ptg; secp256k1_gej ptgj; random_group_element_test(&ptg); secp256k1_gej_set_ge(&ptgj, &ptg); for(t0i = 0; t0i < TOP; t0i++) { for(t1i = 0; t1i < TOP; t1i++) { secp256k1_gej t0p, t1p; secp256k1_scalar t0, t1; secp256k1_scalar_set_int(&t0, (t0i + 1) / 2); secp256k1_scalar_cond_negate(&t0, t0i & 1); secp256k1_scalar_set_int(&t1, (t1i + 1) / 2); secp256k1_scalar_cond_negate(&t1, t1i & 1); secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero); secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero); for(s0i = 0; s0i < TOP; s0i++) { for(s1i = 0; s1i < TOP; s1i++) { secp256k1_scalar tmp1, tmp2; secp256k1_gej expected, actual; secp256k1_ge_set_gej(&pt[0], &t0p); secp256k1_ge_set_gej(&pt[1], &t1p); secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2); secp256k1_scalar_cond_negate(&sc[0], s0i & 1); secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2); secp256k1_scalar_cond_negate(&sc[1], s1i & 1); secp256k1_scalar_mul(&tmp1, &t0, &sc[0]); secp256k1_scalar_mul(&tmp2, &t1, &sc[1]); secp256k1_scalar_add(&tmp1, &tmp1, &tmp2); secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero); CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2)); secp256k1_gej_neg(&expected, &expected); secp256k1_gej_add_var(&actual, &actual, &expected, NULL); CHECK(secp256k1_gej_is_infinity(&actual)); } } } } } } void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) { secp256k1_scalar szero; secp256k1_scalar sc; secp256k1_ge pt; secp256k1_gej r; ecmult_multi_data data; secp256k1_scratch *scratch_empty; random_group_element_test(&pt); random_scalar_order(&sc); data.sc = ≻ data.pt = &pt; secp256k1_scalar_set_int(&szero, 0); /* Try to multiply 1 point, but scratch space is empty.*/ scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0); CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1)); secp256k1_scratch_destroy(&ctx->error_callback, scratch_empty); } void test_secp256k1_pippenger_bucket_window_inv(void) { int i; CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0); for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) { /* Bucket_window of 8 is not used with endo */ if (i == 8) { continue; } CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i); if (i != PIPPENGER_MAX_BUCKET_WINDOW) { CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i); } } } /** * Probabilistically test the function returning the maximum number of possible points * for a given scratch space. */ void test_ecmult_multi_pippenger_max_points(void) { size_t scratch_size = secp256k1_testrand_int(256); size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12); secp256k1_scratch *scratch; size_t n_points_supported; int bucket_window = 0; for(; scratch_size < max_size; scratch_size+=256) { size_t i; size_t total_alloc; size_t checkpoint; scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size); CHECK(scratch != NULL); checkpoint = secp256k1_scratch_checkpoint(&ctx->error_callback, scratch); n_points_supported = secp256k1_pippenger_max_points(&ctx->error_callback, scratch); if (n_points_supported == 0) { secp256k1_scratch_destroy(&ctx->error_callback, scratch); continue; } bucket_window = secp256k1_pippenger_bucket_window(n_points_supported); /* allocate `total_alloc` bytes over `PIPPENGER_SCRATCH_OBJECTS` many allocations */ total_alloc = secp256k1_pippenger_scratch_size(n_points_supported, bucket_window); for (i = 0; i < PIPPENGER_SCRATCH_OBJECTS - 1; i++) { CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 1)); total_alloc--; } CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, total_alloc)); secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint); secp256k1_scratch_destroy(&ctx->error_callback, scratch); } CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW); } void test_ecmult_multi_batch_size_helper(void) { size_t n_batches, n_batch_points, max_n_batch_points, n; max_n_batch_points = 0; n = 1; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0); max_n_batch_points = 1; n = 0; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == 0); CHECK(n_batch_points == 0); max_n_batch_points = 2; n = 5; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == 3); CHECK(n_batch_points == 2); max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; n = ECMULT_MAX_POINTS_PER_BATCH; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == 1); CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH); max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1; n = ECMULT_MAX_POINTS_PER_BATCH + 1; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == 2); CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1); max_n_batch_points = 1; n = SIZE_MAX; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == SIZE_MAX); CHECK(n_batch_points == 1); max_n_batch_points = 2; n = SIZE_MAX; CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); CHECK(n_batches == SIZE_MAX/2 + 1); CHECK(n_batch_points == 2); } /** * Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to * 1 <= i <= num points. */ void test_ecmult_multi_batching(void) { static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD; secp256k1_scalar scG; secp256k1_scalar szero; secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_scalar) * n_points); secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * n_points); secp256k1_gej r; secp256k1_gej r2; ecmult_multi_data data; int i; secp256k1_scratch *scratch; secp256k1_gej_set_infinity(&r2); secp256k1_scalar_set_int(&szero, 0); /* Get random scalars and group elements and compute result */ random_scalar_order(&scG); secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG); for(i = 0; i < n_points; i++) { secp256k1_ge ptg; secp256k1_gej ptgj; random_group_element_test(&ptg); secp256k1_gej_set_ge(&ptgj, &ptg); pt[i] = ptg; random_scalar_order(&sc[i]); secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL); secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL); } data.sc = sc; data.pt = pt; secp256k1_gej_neg(&r2, &r2); /* Test with empty scratch space. It should compute the correct result using * ecmult_mult_simple algorithm which doesn't require a scratch space. */ scratch = secp256k1_scratch_create(&ctx->error_callback, 0); CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); secp256k1_scratch_destroy(&ctx->error_callback, scratch); /* Test with space for 1 point in pippenger. That's not enough because * ecmult_multi selects strauss which requires more memory. It should * therefore select the simple algorithm. */ scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); secp256k1_scratch_destroy(&ctx->error_callback, scratch); for(i = 1; i <= n_points; i++) { if (i > ECMULT_PIPPENGER_THRESHOLD) { int bucket_window = secp256k1_pippenger_bucket_window(i); size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window); scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); } else { size_t scratch_size = secp256k1_strauss_scratch_size(i); scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); } CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); secp256k1_gej_add_var(&r, &r, &r2, NULL); CHECK(secp256k1_gej_is_infinity(&r)); secp256k1_scratch_destroy(&ctx->error_callback, scratch); } free(sc); free(pt); } void run_ecmult_multi_tests(void) { secp256k1_scratch *scratch; test_secp256k1_pippenger_bucket_window_inv(); test_ecmult_multi_pippenger_max_points(); scratch = secp256k1_scratch_create(&ctx->error_callback, 819200); test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); test_ecmult_multi(NULL, secp256k1_ecmult_multi_var); test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single); test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single); test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single); test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single); secp256k1_scratch_destroy(&ctx->error_callback, scratch); /* Run test_ecmult_multi with space for exactly one point */ scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); secp256k1_scratch_destroy(&ctx->error_callback, scratch); test_ecmult_multi_batch_size_helper(); test_ecmult_multi_batching(); } 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; int skew; int bits = 256; secp256k1_scalar num = *number; secp256k1_scalar scalar_skew; secp256k1_scalar_set_int(&x, 0); secp256k1_scalar_set_int(&shift, 1 << w); for (i = 0; i < 16; ++i) { secp256k1_scalar_shr_int(&num, 8); } bits = 128; skew = secp256k1_wnaf_const(wnaf, &num, w, bits); for (i = WNAF_SIZE_BITS(bits, 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); } /* Skew num because when encoding numbers as odd we use an offset */ secp256k1_scalar_set_int(&scalar_skew, 1 << (skew == 2)); secp256k1_scalar_add(&num, &num, &scalar_skew); CHECK(secp256k1_scalar_eq(&x, &num)); } void test_fixed_wnaf(const secp256k1_scalar *number, int w) { secp256k1_scalar x, shift; int wnaf[256] = {0}; int i; int skew; secp256k1_scalar num = *number; secp256k1_scalar_set_int(&x, 0); secp256k1_scalar_set_int(&shift, 1 << w); for (i = 0; i < 16; ++i) { secp256k1_scalar_shr_int(&num, 8); } skew = secp256k1_wnaf_fixed(wnaf, &num, w); for (i = WNAF_SIZE(w)-1; i >= 0; --i) { secp256k1_scalar t; int v = wnaf[i]; CHECK(v == 0 || 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); } /* If skew is 1 then add 1 to num */ secp256k1_scalar_cadd_bit(&num, 0, skew == 1); CHECK(secp256k1_scalar_eq(&x, &num)); } /* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the * rest is 0.*/ void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) { int i; for (i = WNAF_SIZE(w)-1; i >= 8; --i) { CHECK(wnaf[i] == 0); } for (i = 7; i >= 0; --i) { CHECK(wnaf[i] == wnaf_expected[i]); } } void test_fixed_wnaf_small(void) { int w = 4; int wnaf[256] = {0}; int i; int skew; secp256k1_scalar num; secp256k1_scalar_set_int(&num, 0); skew = secp256k1_wnaf_fixed(wnaf, &num, w); for (i = WNAF_SIZE(w)-1; i >= 0; --i) { int v = wnaf[i]; CHECK(v == 0); } CHECK(skew == 0); secp256k1_scalar_set_int(&num, 1); skew = secp256k1_wnaf_fixed(wnaf, &num, w); for (i = WNAF_SIZE(w)-1; i >= 1; --i) { int v = wnaf[i]; CHECK(v == 0); } CHECK(wnaf[0] == 1); CHECK(skew == 0); { int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf }; secp256k1_scalar_set_int(&num, 0xffffffff); skew = secp256k1_wnaf_fixed(wnaf, &num, w); test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); CHECK(skew == 0); } { int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf }; secp256k1_scalar_set_int(&num, 0xeeeeeeee); skew = secp256k1_wnaf_fixed(wnaf, &num, w); test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); CHECK(skew == 1); } { int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 }; secp256k1_scalar_set_int(&num, 0x01010101); skew = secp256k1_wnaf_fixed(wnaf, &num, w); test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); CHECK(skew == 0); } { int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 }; secp256k1_scalar_set_int(&num, 0x01ef1ef1); skew = secp256k1_wnaf_fixed(wnaf, &num, w); test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); CHECK(skew == 0); } } void run_wnaf(void) { int i; secp256k1_scalar n = {{0}}; test_constant_wnaf(&n, 4); /* 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); /* Test -1, because it's a special case in wnaf_const */ n = secp256k1_scalar_one; secp256k1_scalar_negate(&n, &n); test_constant_wnaf(&n, 4); /* Test -2, which may not lead to overflows in wnaf_const */ secp256k1_scalar_add(&n, &secp256k1_scalar_one, &secp256k1_scalar_one); secp256k1_scalar_negate(&n, &n); test_constant_wnaf(&n, 4); /* Test (1/2) - 1 = 1/-2 and 1/2 = (1/-2) + 1 as corner cases of negation handling in wnaf_const */ secp256k1_scalar_inverse(&n, &n); test_constant_wnaf(&n, 4); secp256k1_scalar_add(&n, &n, &secp256k1_scalar_one); test_constant_wnaf(&n, 4); /* Test 0 for fixed wnaf */ test_fixed_wnaf_small(); /* 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)); test_fixed_wnaf(&n, 4 + (i % 10)); } secp256k1_scalar_set_int(&n, 0); CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1); CHECK(secp256k1_scalar_is_zero(&n)); CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1); CHECK(secp256k1_scalar_is_zero(&n)); } 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 affine 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_testrand256(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(); } } /***** ENDOMORPHISH TESTS *****/ void test_scalar_split(const secp256k1_scalar* full) { secp256k1_scalar s, s1, slam; const unsigned char zero[32] = {0}; unsigned char tmp[32]; secp256k1_scalar_split_lambda(&s1, &slam, full); /* check slam*lambda + s1 == full */ secp256k1_scalar_mul(&s, &secp256k1_const_lambda, &slam); secp256k1_scalar_add(&s, &s, &s1); CHECK(secp256k1_scalar_eq(&s, 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(secp256k1_memcmp_var(zero, tmp, 16) == 0); secp256k1_scalar_get_b32(tmp, &slam); CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0); } void run_endomorphism_tests(void) { unsigned i; static secp256k1_scalar s; test_scalar_split(&secp256k1_scalar_zero); test_scalar_split(&secp256k1_scalar_one); secp256k1_scalar_negate(&s,&secp256k1_scalar_one); test_scalar_split(&s); test_scalar_split(&secp256k1_const_lambda); secp256k1_scalar_add(&s, &secp256k1_const_lambda, &secp256k1_scalar_one); test_scalar_split(&s); for (i = 0; i < 100U * count; ++i) { secp256k1_scalar full; random_scalar_order_test(&full); test_scalar_split(&full); } for (i = 0; i < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++i) { test_scalar_split(&scalars_near_split_bounds[i]); } } 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(secp256k1_memcmp_var(&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, SECP256K1_EC_UNCOMPRESSED) == 1); VG_CHECK(pubkeyo, outl); CHECK(outl == 65); CHECK(pubkeyo[0] == 4); CHECK(secp256k1_memcmp_var(&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 sout[65]; unsigned char shortkey[2]; secp256k1_ge ge; secp256k1_pubkey pubkey; size_t len; 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); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 1); /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */ CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0); CHECK(ecount == 2); /* NULL input string. Illegal arg and zeroize output. */ memset(&pubkey, 0xfe, sizeof(pubkey)); ecount = 0; VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 1); CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 2); /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */ memset(&pubkey, 0xfe, sizeof(pubkey)); ecount = 0; VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 1); /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */ memset(&pubkey, 0xfe, sizeof(pubkey)); ecount = 0; VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 1); /* Valid parse. */ memset(&pubkey, 0, sizeof(pubkey)); ecount = 0; VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1); CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); VG_UNDEF(&ge, sizeof(ge)); CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1); VG_CHECK(&ge.x, sizeof(ge.x)); VG_CHECK(&ge.y, sizeof(ge.y)); VG_CHECK(&ge.infinity, sizeof(ge.infinity)); ge_equals_ge(&secp256k1_ge_const_g, &ge); CHECK(ecount == 0); /* secp256k1_ec_pubkey_serialize illegal args. */ ecount = 0; len = 65; CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); CHECK(ecount == 1); CHECK(len == 0); CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); CHECK(ecount == 2); len = 65; VG_UNDEF(sout, 65); CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0); VG_CHECK(sout, 65); CHECK(ecount == 3); CHECK(len == 0); len = 65; CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0); CHECK(ecount == 4); CHECK(len == 0); len = 65; VG_UNDEF(sout, 65); CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); VG_CHECK(sout, 65); CHECK(ecount == 4); CHECK(len == 65); /* Multiple illegal args. Should still set arg error only once. */ ecount = 0; ecount2 = 11; CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); CHECK(ecount == 1); /* Does the illegal arg callback actually change the behavior? */ secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2); CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); CHECK(ecount == 1); CHECK(ecount2 == 10); secp256k1_context_set_illegal_callback(ctx, NULL, NULL); /* Try a bunch of prefabbed points with all possible encodings. */ for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) { ec_pubkey_parse_pointtest(valid[i], 1, 1); } for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) { ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0); } for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) { ec_pubkey_parse_pointtest(invalid[i], 0, 0); } } void run_eckey_edge_case_test(void) { const unsigned char orderc[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 }; const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00}; unsigned char ctmp[33]; unsigned char ctmp2[33]; secp256k1_pubkey pubkey; secp256k1_pubkey pubkey2; secp256k1_pubkey pubkey_one; secp256k1_pubkey pubkey_negone; const secp256k1_pubkey *pubkeys[3]; size_t len; int32_t ecount; /* Group order is too large, reject. */ CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); /* Maximum value is too large, reject. */ memset(ctmp, 255, 32); CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); /* Zero is too small, reject. */ memset(ctmp, 0, 32); CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); /* One must be accepted. */ ctmp[31] = 0x01; CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); memset(&pubkey, 0, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); pubkey_one = pubkey; /* Group order + 1 is too large, reject. */ memcpy(ctmp, orderc, 32); ctmp[31] = 0x42; CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); /* -1 must be accepted. */ ctmp[31] = 0x40; CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); memset(&pubkey, 0, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); pubkey_negone = pubkey; /* Tweak of zero leaves the value unchanged. */ memset(ctmp2, 0, 32); CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 1); CHECK(secp256k1_memcmp_var(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40); memcpy(&pubkey2, &pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Multiply tweak of zero zeroizes the output. */ CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing seckey, the seckey is zeroized. */ memcpy(ctmp, orderc, 32); memset(ctmp2, 0, 32); ctmp2[31] = 0x01; CHECK(secp256k1_ec_seckey_verify(ctx, ctmp2) == 1); CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); memcpy(ctmp, orderc, 32); CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing tweak, the seckey is zeroized. */ memcpy(ctmp, orderc, 32); ctmp[31] = 0x40; CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, orderc) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); memcpy(ctmp, orderc, 32); ctmp[31] = 0x40; CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, orderc) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0); memcpy(ctmp, orderc, 32); ctmp[31] = 0x40; /* If pubkey_tweak_add or pubkey_tweak_mul are called with an overflowing tweak, the pubkey is zeroized. */ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); /* If the resulting key in secp256k1_ec_seckey_tweak_add and * secp256k1_ec_pubkey_tweak_add is 0 the functions fail and in the latter * case the pubkey is zeroized. */ memcpy(ctmp, orderc, 32); ctmp[31] = 0x40; memset(ctmp2, 0, 32); ctmp2[31] = 1; CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 0); CHECK(secp256k1_memcmp_var(zeros, ctmp2, 32) == 0); ctmp2[31] = 1; CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); /* Tweak computation wraps and results in a key of 1. */ ctmp2[31] = 2; CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 1); CHECK(secp256k1_memcmp_var(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1); ctmp2[31] = 2; CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); ctmp2[31] = 1; CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1); CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Tweak mul * 2 = 1+1. */ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); ctmp2[31] = 2; CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1); CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Test argument errors. */ ecount = 0; secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); CHECK(ecount == 0); /* Zeroize pubkey on parse error. */ memset(&pubkey, 0, 32); CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); CHECK(ecount == 1); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); memset(&pubkey2, 0, 32); CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0); CHECK(ecount == 2); CHECK(secp256k1_memcmp_var(&pubkey2, zeros, sizeof(pubkey2)) == 0); /* Plain argument errors. */ ecount = 0; CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); CHECK(ecount == 0); CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0); CHECK(ecount == 1); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 4; CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 4; CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); CHECK(secp256k1_ec_seckey_tweak_add(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 1; CHECK(secp256k1_ec_seckey_tweak_mul(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, NULL) == 0); CHECK(ecount == 2); ecount = 0; CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0); CHECK(ecount == 1); memset(&pubkey, 1, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); /* secp256k1_ec_pubkey_combine tests. */ ecount = 0; pubkeys[0] = &pubkey_one; VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *)); VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *)); VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *)); memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); CHECK(ecount == 1); CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); CHECK(ecount == 2); memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); CHECK(ecount == 3); pubkeys[0] = &pubkey_negone; memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); CHECK(ecount == 3); len = 33; CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1); CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0); /* Result is infinity. */ pubkeys[0] = &pubkey_one; pubkeys[1] = &pubkey_negone; memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); CHECK(ecount == 3); /* Passes through infinity but comes out one. */ pubkeys[2] = &pubkey_one; memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); CHECK(ecount == 3); len = 33; CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1); CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0); /* Adds to two. */ pubkeys[1] = &pubkey_one; memset(&pubkey, 255, sizeof(secp256k1_pubkey)); VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1); VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); CHECK(ecount == 3); secp256k1_context_set_illegal_callback(ctx, NULL, NULL); } void run_eckey_negate_test(void) { unsigned char seckey[32]; unsigned char seckey_tmp[32]; random_scalar_order_b32(seckey); memcpy(seckey_tmp, seckey, 32); /* Verify negation changes the key and changes it back */ CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) != 0); CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); /* Check that privkey alias gives same result */ CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); CHECK(secp256k1_ec_privkey_negate(ctx, seckey_tmp) == 1); CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); /* Negating all 0s fails */ memset(seckey, 0, 32); memset(seckey_tmp, 0, 32); CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0); /* Check that seckey is not modified */ CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); /* Negating an overflowing seckey fails and the seckey is zeroed. In this * test, the seckey has 16 random bytes to ensure that ec_seckey_negate * doesn't just set seckey to a constant value in case of failure. */ random_scalar_order_b32(seckey); memset(seckey, 0xFF, 16); memset(seckey_tmp, 0, 32); CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0); CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0); } void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) { secp256k1_scalar nonce; do { random_scalar_order_test(&nonce); } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid)); } void test_ecdsa_sign_verify(void) { secp256k1_gej pubj; secp256k1_ge pub; secp256k1_scalar one; secp256k1_scalar msg, key; secp256k1_scalar sigr, sigs; int getrec; /* Initialize recid to suppress a false positive -Wconditional-uninitialized in clang. VG_UNDEF ensures that valgrind will still treat the variable as uninitialized. */ int recid = -1; VG_UNDEF(&recid, sizeof(recid)); random_scalar_order_test(&msg); random_scalar_order_test(&key); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key); secp256k1_ge_set_gej(&pub, &pubj); getrec = secp256k1_testrand_bits(1); random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL); if (getrec) { CHECK(recid >= 0 && recid < 4); } CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg)); secp256k1_scalar_set_int(&one, 1); secp256k1_scalar_add(&msg, &msg, &one); CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &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, const unsigned char *algo16, void *data, unsigned int counter) { (void)msg32; (void)key32; (void)algo16; memcpy(nonce32, data, 32); return (counter == 0); } static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { /* 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, algo16, data, counter - 1); } static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { /* 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 deterministic 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, algo16, data, counter - 5); } int is_empty_signature(const secp256k1_ecdsa_signature *sig) { static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0}; return secp256k1_memcmp_var(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0; } void test_ecdsa_end_to_end(void) { unsigned char extra[32] = {0x00}; unsigned char privkey[32]; unsigned char message[32]; unsigned char privkey2[32]; secp256k1_ecdsa_signature signature[6]; secp256k1_scalar r, s; unsigned char sig[74]; size_t siglen = 74; unsigned char pubkeyc[65]; size_t pubkeyclen = 65; secp256k1_pubkey pubkey; secp256k1_pubkey pubkey_tmp; unsigned char seckey[300]; size_t seckeylen = 300; /* Generate a random key and message. */ { secp256k1_scalar 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(ctx, privkey) == 1); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1); /* Verify exporting and importing public key. */ CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_testrand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED)); memset(&pubkey, 0, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1); /* Verify negation changes the key and changes it back */ memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey)); CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0); CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0); /* Verify private key import and export. */ CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_testrand_bits(1) == 1)); CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1); CHECK(secp256k1_memcmp_var(privkey, privkey2, 32) == 0); /* Optionally tweak the keys using addition. */ if (secp256k1_testrand_int(3) == 0) { int ret1; int ret2; int ret3; unsigned char rnd[32]; unsigned char privkey_tmp[32]; secp256k1_pubkey pubkey2; secp256k1_testrand256_test(rnd); memcpy(privkey_tmp, privkey, 32); ret1 = secp256k1_ec_seckey_tweak_add(ctx, privkey, rnd); ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd); /* Check that privkey alias gives same result */ ret3 = secp256k1_ec_privkey_tweak_add(ctx, privkey_tmp, rnd); CHECK(ret1 == ret2); CHECK(ret2 == ret3); if (ret1 == 0) { return; } CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); } /* Optionally tweak the keys using multiplication. */ if (secp256k1_testrand_int(3) == 0) { int ret1; int ret2; int ret3; unsigned char rnd[32]; unsigned char privkey_tmp[32]; secp256k1_pubkey pubkey2; secp256k1_testrand256_test(rnd); memcpy(privkey_tmp, privkey, 32); ret1 = secp256k1_ec_seckey_tweak_mul(ctx, privkey, rnd); ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd); /* Check that privkey alias gives same result */ ret3 = secp256k1_ec_privkey_tweak_mul(ctx, privkey_tmp, rnd); CHECK(ret1 == ret2); CHECK(ret2 == ret3); if (ret1 == 0) { return; } CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); } /* Sign. */ CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1); CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1); CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1); extra[31] = 1; CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1); extra[31] = 0; extra[0] = 1; CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1); CHECK(secp256k1_memcmp_var(&signature[0], &signature[4], sizeof(signature[0])) == 0); CHECK(secp256k1_memcmp_var(&signature[0], &signature[1], sizeof(signature[0])) != 0); CHECK(secp256k1_memcmp_var(&signature[0], &signature[2], sizeof(signature[0])) != 0); CHECK(secp256k1_memcmp_var(&signature[0], &signature[3], sizeof(signature[0])) != 0); CHECK(secp256k1_memcmp_var(&signature[1], &signature[2], sizeof(signature[0])) != 0); CHECK(secp256k1_memcmp_var(&signature[1], &signature[3], sizeof(signature[0])) != 0); CHECK(secp256k1_memcmp_var(&signature[2], &signature[3], sizeof(signature[0])) != 0); /* Verify. */ CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1); CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1); CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1); /* Test lower-S form, malleate, verify and fail, test again, malleate again */ CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0])); secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]); secp256k1_scalar_negate(&s, &s); secp256k1_ecdsa_signature_save(&signature[5], &r, &s); CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0); CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); secp256k1_scalar_negate(&s, &s); secp256k1_ecdsa_signature_save(&signature[5], &r, &s); CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); CHECK(secp256k1_memcmp_var(&signature[5], &signature[0], 64) == 0); /* Serialize/parse DER and verify again */ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); memset(&signature[0], 0, sizeof(signature[0])); CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1); CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); /* Serialize/destroy/parse DER and verify again. */ siglen = 74; CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); sig[secp256k1_testrand_int(siglen)] += 1 + secp256k1_testrand_int(255); CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 || secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0); } void test_random_pubkeys(void) { secp256k1_ge elem; secp256k1_ge elem2; unsigned char in[65]; /* Generate some randomly sized pubkeys. */ size_t len = secp256k1_testrand_bits(2) == 0 ? 65 : 33; if (secp256k1_testrand_bits(2) == 0) { len = secp256k1_testrand_bits(6); } if (len == 65) { in[0] = secp256k1_testrand_bits(1) ? 4 : (secp256k1_testrand_bits(1) ? 6 : 7); } else { in[0] = secp256k1_testrand_bits(1) ? 2 : 3; } if (secp256k1_testrand_bits(3) == 0) { in[0] = secp256k1_testrand_bits(8); } if (len > 1) { secp256k1_testrand256(&in[1]); } if (len > 33) { secp256k1_testrand256(&in[33]); } if (secp256k1_eckey_pubkey_parse(&elem, in, len)) { unsigned char out[65]; unsigned char firstb; int res; size_t 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(secp256k1_memcmp_var(&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] = secp256k1_testrand_bits(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(secp256k1_memcmp_var(&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(); } } int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) { static const unsigned char zeroes[32] = {0}; #ifdef ENABLE_OPENSSL_TESTS static const unsigned char max_scalar[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 }; #endif int ret = 0; secp256k1_ecdsa_signature sig_der; unsigned char roundtrip_der[2048]; unsigned char compact_der[64]; size_t len_der = 2048; int parsed_der = 0, valid_der = 0, roundtrips_der = 0; secp256k1_ecdsa_signature sig_der_lax; unsigned char roundtrip_der_lax[2048]; unsigned char compact_der_lax[64]; size_t len_der_lax = 2048; int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0; #ifdef ENABLE_OPENSSL_TESTS ECDSA_SIG *sig_openssl; const BIGNUM *r = NULL, *s = NULL; const unsigned char *sigptr; unsigned char roundtrip_openssl[2048]; int len_openssl = 2048; int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0; #endif parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen); if (parsed_der) { ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0; valid_der = (secp256k1_memcmp_var(compact_der, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der + 32, zeroes, 32) != 0); } if (valid_der) { ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1; roundtrips_der = (len_der == siglen) && secp256k1_memcmp_var(roundtrip_der, sig, siglen) == 0; } parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen); if (parsed_der_lax) { ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10; valid_der_lax = (secp256k1_memcmp_var(compact_der_lax, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der_lax + 32, zeroes, 32) != 0); } if (valid_der_lax) { ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11; roundtrips_der_lax = (len_der_lax == siglen) && secp256k1_memcmp_var(roundtrip_der_lax, sig, siglen) == 0; } if (certainly_der) { ret |= (!parsed_der) << 2; } if (certainly_not_der) { ret |= (parsed_der) << 17; } if (valid_der) { ret |= (!roundtrips_der) << 3; } if (valid_der) { ret |= (!roundtrips_der_lax) << 12; ret |= (len_der != len_der_lax) << 13; ret |= ((len_der != len_der_lax) || (secp256k1_memcmp_var(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14; } ret |= (roundtrips_der != roundtrips_der_lax) << 15; if (parsed_der) { ret |= (!parsed_der_lax) << 16; } #ifdef ENABLE_OPENSSL_TESTS sig_openssl = ECDSA_SIG_new(); sigptr = sig; parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL); if (parsed_openssl) { ECDSA_SIG_get0(sig_openssl, &r, &s); valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256; if (valid_openssl) { unsigned char tmp[32] = {0}; BN_bn2bin(r, tmp + 32 - BN_num_bytes(r)); valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0; } if (valid_openssl) { unsigned char tmp[32] = {0}; BN_bn2bin(s, tmp + 32 - BN_num_bytes(s)); valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0; } } len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL); if (len_openssl <= 2048) { unsigned char *ptr = roundtrip_openssl; CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl); roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (secp256k1_memcmp_var(roundtrip_openssl, sig, siglen) == 0); } else { len_openssl = 0; } ECDSA_SIG_free(sig_openssl); ret |= (parsed_der && !parsed_openssl) << 4; ret |= (valid_der && !valid_openssl) << 5; ret |= (roundtrips_openssl && !parsed_der) << 6; ret |= (roundtrips_der != roundtrips_openssl) << 7; if (roundtrips_openssl) { ret |= (len_der != (size_t)len_openssl) << 8; ret |= ((len_der != (size_t)len_openssl) || (secp256k1_memcmp_var(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9; } #endif return ret; } static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) { size_t i; for (i = 0; i < ptrlen; i++) { int shift = ptrlen - 1 - i; if (shift >= 4) { ptr[i] = 0; } else { ptr[i] = (val >> shift) & 0xFF; } } } static void damage_array(unsigned char *sig, size_t *len) { int pos; int action = secp256k1_testrand_bits(3); if (action < 1 && *len > 3) { /* Delete a byte. */ pos = secp256k1_testrand_int(*len); memmove(sig + pos, sig + pos + 1, *len - pos - 1); (*len)--; return; } else if (action < 2 && *len < 2048) { /* Insert a byte. */ pos = secp256k1_testrand_int(1 + *len); memmove(sig + pos + 1, sig + pos, *len - pos); sig[pos] = secp256k1_testrand_bits(8); (*len)++; return; } else if (action < 4) { /* Modify a byte. */ sig[secp256k1_testrand_int(*len)] += 1 + secp256k1_testrand_int(255); return; } else { /* action < 8 */ /* Modify a bit. */ sig[secp256k1_testrand_int(*len)] ^= 1 << secp256k1_testrand_bits(3); return; } } static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) { int der; int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2]; size_t tlen, elen, glen; int indet; int n; *len = 0; der = secp256k1_testrand_bits(2) == 0; *certainly_der = der; *certainly_not_der = 0; indet = der ? 0 : secp256k1_testrand_int(10) == 0; for (n = 0; n < 2; n++) { /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */ nlow[n] = der ? 1 : (secp256k1_testrand_bits(3) != 0); /* The length of the number in bytes (the first byte of which will always be nonzero) */ nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_int(8) / 8; CHECK(nlen[n] <= 232); /* The top bit of the number. */ nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_testrand_bits(1)); /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */ nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_testrand_bits(7) : 1 + secp256k1_testrand_int(127)); /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */ nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_int(8) / 8); if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) { *certainly_not_der = 1; } CHECK(nlen[n] + nzlen[n] <= 300); /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */ nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2); if (!der) { /* nlenlen[n] max 127 bytes */ int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256; nlenlen[n] += add; if (add != 0) { *certainly_not_der = 1; } } CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427); } /* The total length of the data to go, so far */ tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1]; CHECK(tlen <= 856); /* The length of the garbage inside the tuple. */ elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_int(8) / 8; if (elen != 0) { *certainly_not_der = 1; } tlen += elen; CHECK(tlen <= 980); /* The length of the garbage after the end of the tuple. */ glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_int(8) / 8; if (glen != 0) { *certainly_not_der = 1; } CHECK(tlen + glen <= 990); /* Write the tuple header. */ sig[(*len)++] = 0x30; if (indet) { /* Indeterminate length */ sig[(*len)++] = 0x80; *certainly_not_der = 1; } else { int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2); if (!der) { int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256; tlenlen += add; if (add != 0) { *certainly_not_der = 1; } } if (tlenlen == 0) { /* Short length notation */ sig[(*len)++] = tlen; } else { /* Long length notation */ sig[(*len)++] = 128 + tlenlen; assign_big_endian(sig + *len, tlenlen, tlen); *len += tlenlen; } tlen += tlenlen; } tlen += 2; CHECK(tlen + glen <= 1119); for (n = 0; n < 2; n++) { /* Write the integer header. */ sig[(*len)++] = 0x02; if (nlenlen[n] == 0) { /* Short length notation */ sig[(*len)++] = nlen[n] + nzlen[n]; } else { /* Long length notation. */ sig[(*len)++] = 128 + nlenlen[n]; assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]); *len += nlenlen[n]; } /* Write zero padding */ while (nzlen[n] > 0) { sig[(*len)++] = 0x00; nzlen[n]--; } if (nlen[n] == 32 && !nlow[n]) { /* Special extra 16 0xFF bytes in "high" 32-byte numbers */ int i; for (i = 0; i < 16; i++) { sig[(*len)++] = 0xFF; } nlen[n] -= 16; } /* Write first byte of number */ if (nlen[n] > 0) { sig[(*len)++] = nhbyte[n]; nlen[n]--; } /* Generate remaining random bytes of number */ secp256k1_testrand_bytes_test(sig + *len, nlen[n]); *len += nlen[n]; nlen[n] = 0; } /* Generate random garbage inside tuple. */ secp256k1_testrand_bytes_test(sig + *len, elen); *len += elen; /* Generate end-of-contents bytes. */ if (indet) { sig[(*len)++] = 0; sig[(*len)++] = 0; tlen += 2; } CHECK(tlen + glen <= 1121); /* Generate random garbage outside tuple. */ secp256k1_testrand_bytes_test(sig + *len, glen); *len += glen; tlen += glen; CHECK(tlen <= 1121); CHECK(tlen == *len); } void run_ecdsa_der_parse(void) { int i,j; for (i = 0; i < 200 * count; i++) { unsigned char buffer[2048]; size_t buflen = 0; int certainly_der = 0; int certainly_not_der = 0; random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der); CHECK(buflen <= 2048); for (j = 0; j < 16; j++) { int ret = 0; if (j > 0) { damage_array(buffer, &buflen); /* We don't know anything anymore about the DERness of the result */ certainly_der = 0; certainly_not_der = 0; } ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der); if (ret != 0) { size_t k; fprintf(stderr, "Failure %x on ", ret); for (k = 0; k < buflen; k++) { fprintf(stderr, "%02x ", buffer[k]); } fprintf(stderr, "\n"); } CHECK(ret == 0); } } } /* Tests several edge cases. */ void test_ecdsa_edge_cases(void) { int t; secp256k1_ecdsa_signature sig; /* Test the case where ECDSA recomputes a point that is infinity. */ { secp256k1_gej keyj; secp256k1_ge key; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 1); secp256k1_scalar_negate(&ss, &ss); secp256k1_scalar_inverse(&ss, &ss); secp256k1_scalar_set_int(&sr, 1); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr); secp256k1_ge_set_gej(&key, &keyj); msg = ss; CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); } /* Verify signature with r of zero fails. */ { const unsigned char pubkey_mods_zero[33] = { 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 }; secp256k1_ge key; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 1); secp256k1_scalar_set_int(&msg, 0); secp256k1_scalar_set_int(&sr, 0); CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); } /* Verify signature with s of zero fails. */ { const unsigned char pubkey[33] = { 0x02, 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 }; secp256k1_ge key; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 0); secp256k1_scalar_set_int(&msg, 0); secp256k1_scalar_set_int(&sr, 1); CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); } /* Verify signature with message 0 passes. */ { const unsigned char pubkey[33] = { 0x02, 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, 0x02 }; const unsigned char pubkey2[33] = { 0x02, 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, 0x43 }; secp256k1_ge key; secp256k1_ge key2; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 2); secp256k1_scalar_set_int(&msg, 0); secp256k1_scalar_set_int(&sr, 2); CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); secp256k1_scalar_negate(&ss, &ss); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); secp256k1_scalar_set_int(&ss, 1); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0); } /* Verify signature with message 1 passes. */ { const unsigned char pubkey[33] = { 0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22, 0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05, 0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c, 0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76, 0x25 }; const unsigned char pubkey2[33] = { 0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40, 0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae, 0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f, 0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10, 0x62 }; const unsigned char csr[32] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb }; secp256k1_ge key; secp256k1_ge key2; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 1); secp256k1_scalar_set_int(&msg, 1); secp256k1_scalar_set_b32(&sr, csr, NULL); CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); secp256k1_scalar_negate(&ss, &ss); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); secp256k1_scalar_set_int(&ss, 2); secp256k1_scalar_inverse_var(&ss, &ss); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0); } /* Verify signature with message -1 passes. */ { const unsigned char pubkey[33] = { 0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0, 0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52, 0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27, 0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20, 0xf1 }; const unsigned char csr[32] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee }; secp256k1_ge key; secp256k1_scalar msg; secp256k1_scalar sr, ss; secp256k1_scalar_set_int(&ss, 1); secp256k1_scalar_set_int(&msg, 1); secp256k1_scalar_negate(&msg, &msg); secp256k1_scalar_set_b32(&sr, csr, NULL); CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); secp256k1_scalar_negate(&ss, &ss); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); secp256k1_scalar_set_int(&ss, 3); secp256k1_scalar_inverse_var(&ss, &ss); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); } /* Signature where s would be zero. */ { secp256k1_pubkey pubkey; size_t siglen; int32_t ecount; unsigned char signature[72]; static 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, }; ecount = 0; secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0); msg[31] = 0xaa; CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1); CHECK(ecount == 0); CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 1); CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 2); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 3); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1); CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0); CHECK(ecount == 4); CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0); CHECK(ecount == 5); CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0); CHECK(ecount == 6); CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1); CHECK(ecount == 6); CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0); CHECK(ecount == 7); /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */ CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0); CHECK(ecount == 8); siglen = 72; CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0); CHECK(ecount == 9); CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0); CHECK(ecount == 10); CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0); CHECK(ecount == 11); CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1); CHECK(ecount == 11); CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0); CHECK(ecount == 12); CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0); CHECK(ecount == 13); CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1); CHECK(ecount == 13); siglen = 10; /* Too little room for a signature does not fail via ARGCHECK. */ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0); CHECK(ecount == 13); ecount = 0; CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0); CHECK(ecount == 1); CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0); CHECK(ecount == 2); CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0); CHECK(ecount == 3); CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1); CHECK(ecount == 3); CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0); CHECK(ecount == 4); CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0); CHECK(ecount == 5); CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1); CHECK(ecount == 5); memset(signature, 255, 64); CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0); CHECK(ecount == 5); secp256k1_context_set_illegal_callback(ctx, NULL, NULL); } /* Nonce function corner cases. */ for (t = 0; t < 2; t++) { static const unsigned char zero[32] = {0x00}; int i; unsigned char key[32]; unsigned char msg[32]; secp256k1_ecdsa_signature sig2; secp256k1_scalar sr[512], ss; const unsigned char *extra; extra = t == 0 ? NULL : zero; memset(msg, 0, 32); msg[31] = 1; /* High key results in signature failure. */ memset(key, 0xFF, 32); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0); CHECK(is_empty_signature(&sig)); /* Zero key results in signature failure. */ memset(key, 0, 32); CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0); CHECK(is_empty_signature(&sig)); /* Nonce function failure results in signature failure. */ key[31] = 1; CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0); CHECK(is_empty_signature(&sig)); /* The retry loop successfully makes its way to the first good value. */ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1); CHECK(!is_empty_signature(&sig)); CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1); CHECK(!is_empty_signature(&sig2)); CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0); /* The default nonce function is deterministic. */ CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0); /* The default nonce function changes output with different messages. */ for(i = 0; i < 256; i++) { int j; msg[0] = i; CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); for (j = 0; j < i; j++) { CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); } } msg[0] = 0; msg[31] = 2; /* The default nonce function changes output with different keys. */ for(i = 256; i < 512; i++) { int j; key[0] = i - 256; CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); for (j = 0; j < i; j++) { CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); } } key[0] = 0; } { /* Check that optional nonce arguments do not have equivalent effect. */ const unsigned char zeros[32] = {0}; unsigned char nonce[32]; unsigned char nonce2[32]; unsigned char nonce3[32]; unsigned char nonce4[32]; VG_UNDEF(nonce,32); VG_UNDEF(nonce2,32); VG_UNDEF(nonce3,32); VG_UNDEF(nonce4,32); CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1); VG_CHECK(nonce,32); CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1); VG_CHECK(nonce2,32); CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1); VG_CHECK(nonce3,32); CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1); VG_CHECK(nonce4,32); CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); CHECK(secp256k1_memcmp_var(nonce, nonce3, 32) != 0); CHECK(secp256k1_memcmp_var(nonce, nonce4, 32) != 0); CHECK(secp256k1_memcmp_var(nonce2, nonce3, 32) != 0); CHECK(secp256k1_memcmp_var(nonce2, nonce4, 32) != 0); CHECK(secp256k1_memcmp_var(nonce3, nonce4, 32) != 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, }; size_t outlen = 300; CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0)); outlen = 300; CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1)); } } void run_ecdsa_edge_cases(void) { test_ecdsa_edge_cases(); } #ifdef ENABLE_OPENSSL_TESTS EC_KEY *get_openssl_key(const unsigned char *key32) { unsigned char privkey[300]; size_t privkeylen; const unsigned char* pbegin = privkey; int compr = secp256k1_testrand_bits(1); EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1); CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, 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 qj; secp256k1_ge q; secp256k1_scalar sigr, sigs; secp256k1_scalar one; secp256k1_scalar msg2; secp256k1_scalar key, msg; EC_KEY *ec_key; unsigned int sigsize = 80; size_t secp_sigsize = 80; unsigned char message[32]; unsigned char signature[80]; unsigned char key32[32]; secp256k1_testrand256_test(message); secp256k1_scalar_set_b32(&msg, message, NULL); random_scalar_order_test(&key); secp256k1_scalar_get_b32(key32, &key); secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key); secp256k1_ge_set_gej(&q, &qj); ec_key = get_openssl_key(key32); CHECK(ec_key != NULL); CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key)); CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize)); CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg)); secp256k1_scalar_set_int(&one, 1); secp256k1_scalar_add(&msg2, &msg, &one); CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2)); random_sign(&sigr, &sigs, &key, &msg, NULL); CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs)); 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 #ifdef ENABLE_MODULE_ECDH # include "modules/ecdh/tests_impl.h" #endif #ifdef ENABLE_MODULE_MULTISET # include "modules/multiset/tests_impl.h" #endif #ifdef ENABLE_MODULE_RECOVERY # include "modules/recovery/tests_impl.h" #endif #ifdef ENABLE_MODULE_SCHNORR # include "modules/schnorr/tests_impl.h" #endif #ifdef ENABLE_MODULE_EXTRAKEYS # include "modules/extrakeys/tests_impl.h" #endif #ifdef ENABLE_MODULE_SCHNORRSIG # include "modules/schnorrsig/tests_impl.h" #endif void run_secp256k1_memczero_test(void) { unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; unsigned char buf2[sizeof(buf1)]; /* secp256k1_memczero(..., ..., 0) is a noop. */ memcpy(buf2, buf1, sizeof(buf1)); secp256k1_memczero(buf1, sizeof(buf1), 0); CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); /* secp256k1_memczero(..., ..., 1) zeros the buffer. */ memset(buf2, 0, sizeof(buf2)); secp256k1_memczero(buf1, sizeof(buf1) , 1); CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); } void int_cmov_test(void) { int r = INT_MAX; int a = 0; secp256k1_int_cmov(&r, &a, 0); CHECK(r == INT_MAX); r = 0; a = INT_MAX; secp256k1_int_cmov(&r, &a, 1); CHECK(r == INT_MAX); a = 0; secp256k1_int_cmov(&r, &a, 1); CHECK(r == 0); a = 1; secp256k1_int_cmov(&r, &a, 1); CHECK(r == 1); r = 1; a = 0; secp256k1_int_cmov(&r, &a, 0); CHECK(r == 1); } void fe_cmov_test(void) { static const secp256k1_fe zero = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_fe max = SECP256K1_FE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); secp256k1_fe r = max; secp256k1_fe a = zero; secp256k1_fe_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; secp256k1_fe_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; secp256k1_fe_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; secp256k1_fe_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; secp256k1_fe_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); } void fe_storage_cmov_test(void) { static const secp256k1_fe_storage zero = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const secp256k1_fe_storage one = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_fe_storage max = SECP256K1_FE_STORAGE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); secp256k1_fe_storage r = max; secp256k1_fe_storage a = zero; secp256k1_fe_storage_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; secp256k1_fe_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; secp256k1_fe_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; secp256k1_fe_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; secp256k1_fe_storage_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); } void scalar_cmov_test(void) { static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_scalar max = SECP256K1_SCALAR_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); secp256k1_scalar r = max; secp256k1_scalar a = zero; secp256k1_scalar_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; secp256k1_scalar_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; secp256k1_scalar_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; secp256k1_scalar_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; secp256k1_scalar_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); } void ge_storage_cmov_test(void) { static const secp256k1_ge_storage zero = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); static const secp256k1_ge_storage one = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_ge_storage max = SECP256K1_GE_STORAGE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); secp256k1_ge_storage r = max; secp256k1_ge_storage a = zero; secp256k1_ge_storage_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; secp256k1_ge_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; secp256k1_ge_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; secp256k1_ge_storage_cmov(&r, &a, 1); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; secp256k1_ge_storage_cmov(&r, &a, 0); CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0); } void run_cmov_tests(void) { int_cmov_test(); fe_cmov_test(); fe_storage_cmov_test(); scalar_cmov_test(); ge_storage_cmov_test(); } int main(int argc, char **argv) { /* Disable buffering for stdout to improve reliability of getting * diagnostic information. Happens right at the start of main because * setbuf must be used before any other operation on the stream. */ setbuf(stdout, NULL); /* Also disable buffering for stderr because it's not guaranteed that it's * unbuffered on all systems. */ setbuf(stderr, NULL); /* find iteration count */ if (argc > 1) { count = strtol(argv[1], NULL, 0); } else { const char* env = getenv("SECP256K1_TEST_ITERS"); if (env) { count = strtol(env, NULL, 0); } } if (count <= 0) { fputs("An iteration count of 0 or less is not allowed.\n", stderr); return EXIT_FAILURE; } printf("test count = %i\n", count); /* find random seed */ secp256k1_testrand_init(argc > 2 ? argv[2] : NULL); /* initialize */ run_context_tests(0); run_context_tests(1); run_scratch_tests(); ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); if (secp256k1_testrand_bits(1)) { unsigned char rand32[32]; secp256k1_testrand256(rand32); CHECK(secp256k1_context_randomize(ctx, secp256k1_testrand_bits(1) ? rand32 : NULL)); } run_rand_bits(); run_rand_int(); + run_ctz_tests(); + 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_misc(); run_field_convert(); run_sqr(); run_sqrt(); /* group tests */ run_ge(); run_group_decompress(); /* ecmult tests */ run_wnaf(); run_point_times_order(); run_ecmult_near_split_bound(); run_ecmult_chain(); run_ecmult_constants(); run_ecmult_gen_blind(); run_ecmult_const_tests(); run_ecmult_multi_tests(); run_ec_combine(); /* endomorphism tests */ run_endomorphism_tests(); /* EC point parser test */ run_ec_pubkey_parse_test(); /* EC key edge cases */ run_eckey_edge_case_test(); /* EC key arithmetic test */ run_eckey_negate_test(); #ifdef ENABLE_MODULE_ECDH /* ecdh tests */ run_ecdh_tests(); #endif /* ecdsa tests */ run_random_pubkeys(); run_ecdsa_der_parse(); run_ecdsa_sign_verify(); run_ecdsa_end_to_end(); run_ecdsa_edge_cases(); #ifdef ENABLE_OPENSSL_TESTS run_ecdsa_openssl(); #endif #ifdef ENABLE_MODULE_MULTISET run_multiset_tests(); #endif #ifdef ENABLE_MODULE_RECOVERY /* ECDSA pubkey recovery tests */ run_recovery_tests(); #endif #ifdef ENABLE_MODULE_SCHNORR /* Schnorr signature tests */ run_schnorr_tests(); #endif #ifdef ENABLE_MODULE_EXTRAKEYS run_extrakeys_tests(); #endif #ifdef ENABLE_MODULE_SCHNORRSIG run_schnorrsig_tests(); #endif /* util tests */ run_secp256k1_memczero_test(); run_cmov_tests(); secp256k1_testrand_finish(); /* shutdown */ secp256k1_context_destroy(ctx); printf("no problems found\n"); return 0; } diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h index b7e457c48..f78846836 100644 --- a/src/secp256k1/src/util.h +++ b/src/secp256k1/src/util.h @@ -1,279 +1,344 @@ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_UTIL_H #define SECP256K1_UTIL_H #if defined HAVE_CONFIG_H #include "libsecp256k1-config.h" #endif #include #include #include #include typedef struct { void (*fn)(const char *text, void* data); const void* data; } secp256k1_callback; static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) { cb->fn(text, (void*)cb->data); } #ifdef DETERMINISTIC #define TEST_FAILURE(msg) do { \ fprintf(stderr, "%s\n", msg); \ abort(); \ } while(0); #else #define TEST_FAILURE(msg) do { \ fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ abort(); \ } while(0) #endif #if SECP256K1_GNUC_PREREQ(3, 0) #define EXPECT(x,c) __builtin_expect((x),(c)) #else #define EXPECT(x,c) (x) #endif #ifdef DETERMINISTIC #define CHECK(cond) do { \ if (EXPECT(!(cond), 0)) { \ TEST_FAILURE("test condition failed"); \ } \ } while(0) #else #define CHECK(cond) do { \ if (EXPECT(!(cond), 0)) { \ TEST_FAILURE("test condition failed: " #cond); \ } \ } while(0) #endif /* Like assert(), but when VERIFY is defined, and side-effect safe. */ #if defined(COVERAGE) #define VERIFY_CHECK(check) #define VERIFY_SETUP(stmt) #elif defined(VERIFY) #define VERIFY_CHECK CHECK #define VERIFY_SETUP(stmt) do { stmt; } while(0) #else #define VERIFY_CHECK(cond) do { (void)(cond); } while(0) #define VERIFY_SETUP(stmt) #endif /* Define `VG_UNDEF` and `VG_CHECK` when VALGRIND is defined */ #if !defined(VG_CHECK) # if defined(VALGRIND) # include # 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 /* Like `VG_CHECK` but on VERIFY only */ #if defined(VERIFY) #define VG_CHECK_VERIFY(x,y) VG_CHECK((x), (y)) #else #define VG_CHECK_VERIFY(x,y) #endif static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) { void *ret = malloc(size); if (ret == NULL) { secp256k1_callback_call(cb, "Out of memory"); } return ret; } static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) { void *ret = realloc(ptr, size); if (ret == NULL) { secp256k1_callback_call(cb, "Out of memory"); } return ret; } #if defined(__BIGGEST_ALIGNMENT__) #define ALIGNMENT __BIGGEST_ALIGNMENT__ #else /* Using 16 bytes alignment because common architectures never have alignment * requirements above 8 for any of the types we care about. In addition we * leave some room because currently we don't care about a few bytes. */ #define ALIGNMENT 16 #endif #define ROUND_TO_ALIGN(size) ((((size) + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT) /* Assume there is a contiguous memory object with bounds [base, base + max_size) * of which the memory range [base, *prealloc_ptr) is already allocated for usage, * where *prealloc_ptr is an aligned pointer. In that setting, this functions * reserves the subobject [*prealloc_ptr, *prealloc_ptr + alloc_size) of * alloc_size bytes by increasing *prealloc_ptr accordingly, taking into account * alignment requirements. * * The function returns an aligned pointer to the newly allocated subobject. * * This is useful for manual memory management: if we're simply given a block * [base, base + max_size), the caller can use this function to allocate memory * in this block and keep track of the current allocation state with *prealloc_ptr. * * It is VERIFY_CHECKed that there is enough space left in the memory object and * *prealloc_ptr is aligned relative to base. */ static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_size, void* base, size_t max_size) { size_t aligned_alloc_size = ROUND_TO_ALIGN(alloc_size); void* ret; VERIFY_CHECK(prealloc_ptr != NULL); VERIFY_CHECK(*prealloc_ptr != NULL); VERIFY_CHECK(base != NULL); VERIFY_CHECK((unsigned char*)*prealloc_ptr >= (unsigned char*)base); VERIFY_CHECK(((unsigned char*)*prealloc_ptr - (unsigned char*)base) % ALIGNMENT == 0); VERIFY_CHECK((unsigned char*)*prealloc_ptr - (unsigned char*)base + aligned_alloc_size <= max_size); ret = *prealloc_ptr; *prealloc_ptr = (unsigned char*)*prealloc_ptr + aligned_alloc_size; return ret; } /* Macro for restrict, when available and not in a VERIFY build. */ #if defined(SECP256K1_BUILD) && defined(VERIFY) # define SECP256K1_RESTRICT #else # if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) # if SECP256K1_GNUC_PREREQ(3,0) # define SECP256K1_RESTRICT __restrict__ # elif (defined(_MSC_VER) && _MSC_VER >= 1400) # define SECP256K1_RESTRICT __restrict # else # define SECP256K1_RESTRICT # endif # else # define SECP256K1_RESTRICT restrict # endif #endif #if defined(_WIN32) # define I64FORMAT "I64d" # define I64uFORMAT "I64u" #else # define I64FORMAT "lld" # define I64uFORMAT "llu" #endif #if defined(__GNUC__) # define SECP256K1_GNUC_EXT __extension__ #else # define SECP256K1_GNUC_EXT #endif /* If SECP256K1_{LITTLE,BIG}_ENDIAN is not explicitly provided, infer from various other system macros. */ #if !defined(SECP256K1_LITTLE_ENDIAN) && !defined(SECP256K1_BIG_ENDIAN) /* Inspired by https://github.com/rofl0r/endianness.h/blob/9853923246b065a3b52d2c43835f3819a62c7199/endianness.h#L52L73 */ # if (defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__) || \ defined(_X86_) || defined(__x86_64__) || defined(__i386__) || \ defined(__i486__) || defined(__i586__) || defined(__i686__) || \ defined(__MIPSEL) || defined(_MIPSEL) || defined(MIPSEL) || \ defined(__ARMEL__) || defined(__AARCH64EL__) || \ (defined(__LITTLE_ENDIAN__) && __LITTLE_ENDIAN__ == 1) || \ (defined(_LITTLE_ENDIAN) && _LITTLE_ENDIAN == 1) || \ defined(_M_IX86) || defined(_M_AMD64) || defined(_M_ARM) /* MSVC */ # define SECP256K1_LITTLE_ENDIAN # endif # if (defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__) && __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__) || \ defined(__MIPSEB) || defined(_MIPSEB) || defined(MIPSEB) || \ defined(__MICROBLAZEEB__) || defined(__ARMEB__) || defined(__AARCH64EB__) || \ (defined(__BIG_ENDIAN__) && __BIG_ENDIAN__ == 1) || \ (defined(_BIG_ENDIAN) && _BIG_ENDIAN == 1) # define SECP256K1_BIG_ENDIAN # endif #endif #if defined(SECP256K1_LITTLE_ENDIAN) == defined(SECP256K1_BIG_ENDIAN) # error Please make sure that either SECP256K1_LITTLE_ENDIAN or SECP256K1_BIG_ENDIAN is set, see src/util.h. #endif /* Zero memory if flag == 1. Flag must be 0 or 1. Constant time. */ static SECP256K1_INLINE void secp256k1_memczero(void *s, size_t len, int flag) { unsigned char *p = (unsigned char *)s; /* Access flag with a volatile-qualified lvalue. This prevents clang from figuring out (after inlining) that flag can take only be 0 or 1, which leads to variable time code. */ volatile int vflag = flag; unsigned char mask = -(unsigned char) vflag; while (len) { *p &= ~mask; p++; len--; } } /** Semantics like memcmp. Variable-time. * * We use this to avoid possible compiler bugs with memcmp, e.g. * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=95189 */ static SECP256K1_INLINE int secp256k1_memcmp_var(const void *s1, const void *s2, size_t n) { const unsigned char *p1 = s1, *p2 = s2; size_t i; for (i = 0; i < n; i++) { int diff = p1[i] - p2[i]; if (diff != 0) { return diff; } } return 0; } /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized and non-negative.*/ static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag) { unsigned int mask0, mask1, r_masked, a_masked; /* Access flag with a volatile-qualified lvalue. This prevents clang from figuring out (after inlining) that flag can take only be 0 or 1, which leads to variable time code. */ volatile int vflag = flag; /* Casting a negative int to unsigned and back to int is implementation defined behavior */ VERIFY_CHECK(*r >= 0 && *a >= 0); mask0 = (unsigned int)vflag + ~0u; mask1 = ~mask0; r_masked = ((unsigned int)*r & mask0); a_masked = ((unsigned int)*a & mask1); *r = (int)(r_masked | a_masked); } /* If USE_FORCE_WIDEMUL_{INT128,INT64} is set, use that wide multiplication implementation. * Otherwise use the presence of __SIZEOF_INT128__ to decide. */ #if defined(USE_FORCE_WIDEMUL_INT128) # define SECP256K1_WIDEMUL_INT128 1 #elif defined(USE_FORCE_WIDEMUL_INT64) # define SECP256K1_WIDEMUL_INT64 1 #elif defined(UINT128_MAX) || defined(__SIZEOF_INT128__) # define SECP256K1_WIDEMUL_INT128 1 #else # define SECP256K1_WIDEMUL_INT64 1 #endif #if defined(SECP256K1_WIDEMUL_INT128) # if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__) SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; SECP256K1_GNUC_EXT typedef __int128 int128_t; #define UINT128_MAX ((uint128_t)(-1)) #define INT128_MAX ((int128_t)(UINT128_MAX >> 1)) #define INT128_MIN (-INT128_MAX - 1) /* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals. */ # endif #endif +#ifndef __has_builtin +#define __has_builtin(x) 0 +#endif + +/* Determine the number of trailing zero bits in a (non-zero) 32-bit x. + * This function is only intended to be used as fallback for + * secp256k1_ctz32_var, but permits it to be tested separately. */ +static SECP256K1_INLINE int secp256k1_ctz32_var_debruijn(uint32_t x) { + static const uint8_t debruijn[32] = { + 0x00, 0x01, 0x02, 0x18, 0x03, 0x13, 0x06, 0x19, 0x16, 0x04, 0x14, 0x0A, + 0x10, 0x07, 0x0C, 0x1A, 0x1F, 0x17, 0x12, 0x05, 0x15, 0x09, 0x0F, 0x0B, + 0x1E, 0x11, 0x08, 0x0E, 0x1D, 0x0D, 0x1C, 0x1B + }; + return debruijn[((x & -x) * 0x04D7651F) >> 27]; +} + +/* Determine the number of trailing zero bits in a (non-zero) 64-bit x. + * This function is only intended to be used as fallback for + * secp256k1_ctz64_var, but permits it to be tested separately. */ +static SECP256K1_INLINE int secp256k1_ctz64_var_debruijn(uint64_t x) { + static const uint8_t debruijn[64] = { + 0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28, + 62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11, + 63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10, + 51, 25, 36, 32, 60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12 + }; + return debruijn[((x & -x) * 0x022FDD63CC95386D) >> 58]; +} + +/* Determine the number of trailing zero bits in a (non-zero) 32-bit x. */ +static SECP256K1_INLINE int secp256k1_ctz32_var(uint32_t x) { + VERIFY_CHECK(x != 0); +#if (__has_builtin(__builtin_ctz) || SECP256K1_GNUC_PREREQ(3,4)) + /* If the unsigned type is sufficient to represent the largest uint32_t, consider __builtin_ctz. */ + if (((unsigned)UINT32_MAX) == UINT32_MAX) { + return __builtin_ctz(x); + } +#endif +#if (__has_builtin(__builtin_ctzl) || SECP256K1_GNUC_PREREQ(3,4)) + /* Otherwise consider __builtin_ctzl (the unsigned long type is always at least 32 bits). */ + return __builtin_ctzl(x); +#else + /* If no suitable CTZ builtin is available, use a (variable time) software emulation. */ + return secp256k1_ctz32_var_debruijn(x); +#endif +} + +/* Determine the number of trailing zero bits in a (non-zero) 64-bit x. */ +static SECP256K1_INLINE int secp256k1_ctz64_var(uint64_t x) { + VERIFY_CHECK(x != 0); +#if (__has_builtin(__builtin_ctzl) || SECP256K1_GNUC_PREREQ(3,4)) + /* If the unsigned long type is sufficient to represent the largest uint64_t, consider __builtin_ctzl. */ + if (((unsigned long)UINT64_MAX) == UINT64_MAX) { + return __builtin_ctzl(x); + } +#endif +#if (__has_builtin(__builtin_ctzll) || SECP256K1_GNUC_PREREQ(3,4)) + /* Otherwise consider __builtin_ctzll (the unsigned long long type is always at least 64 bits). */ + return __builtin_ctzll(x); +#else + /* If no suitable CTZ builtin is available, use a (variable time) software emulation. */ + return secp256k1_ctz64_var_debruijn(x); +#endif +} + #endif /* SECP256K1_UTIL_H */