/*********************************************************************** * 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" #include "util.h" #include "../contrib/lax_der_parsing.c" #include "../contrib/lax_der_privatekey_parsing.c" #include "modinv32_impl.h" #ifdef SECP256K1_WIDEMUL_INT128 #include "modinv64_impl.h" #endif static int count = 64; static rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_fe *fe) { do { unsigned char b32[32]; rustsecp256k1_v0_5_0_testrand256_test(b32); if (rustsecp256k1_v0_5_0_fe_set_b32(fe, b32)) { break; } } while(1); } void random_field_element_magnitude(rustsecp256k1_v0_5_0_fe *fe) { rustsecp256k1_v0_5_0_fe zero; int n = rustsecp256k1_v0_5_0_testrand_int(9); rustsecp256k1_v0_5_0_fe_normalize(fe); if (n == 0) { return; } rustsecp256k1_v0_5_0_fe_clear(&zero); rustsecp256k1_v0_5_0_fe_negate(&zero, &zero, 0); rustsecp256k1_v0_5_0_fe_mul_int(&zero, n - 1); rustsecp256k1_v0_5_0_fe_add(fe, &zero); #ifdef VERIFY CHECK(fe->magnitude == n); #endif } void random_group_element_test(rustsecp256k1_v0_5_0_ge *ge) { rustsecp256k1_v0_5_0_fe fe; do { random_field_element_test(&fe); if (rustsecp256k1_v0_5_0_ge_set_xo_var(ge, &fe, rustsecp256k1_v0_5_0_testrand_bits(1))) { rustsecp256k1_v0_5_0_fe_normalize(&ge->y); break; } } while(1); ge->infinity = 0; } void random_group_element_jacobian_test(rustsecp256k1_v0_5_0_gej *gej, const rustsecp256k1_v0_5_0_ge *ge) { rustsecp256k1_v0_5_0_fe z2, z3; do { random_field_element_test(&gej->z); if (!rustsecp256k1_v0_5_0_fe_is_zero(&gej->z)) { break; } } while(1); rustsecp256k1_v0_5_0_fe_sqr(&z2, &gej->z); rustsecp256k1_v0_5_0_fe_mul(&z3, &z2, &gej->z); rustsecp256k1_v0_5_0_fe_mul(&gej->x, &ge->x, &z2); rustsecp256k1_v0_5_0_fe_mul(&gej->y, &ge->y, &z3); gej->infinity = ge->infinity; } void random_gej_test(rustsecp256k1_v0_5_0_gej *gej) { rustsecp256k1_v0_5_0_ge ge; random_group_element_test(&ge); random_group_element_jacobian_test(gej, &ge); } void random_scalar_order_test(rustsecp256k1_v0_5_0_scalar *num) { do { unsigned char b32[32]; int overflow = 0; rustsecp256k1_v0_5_0_testrand256_test(b32); rustsecp256k1_v0_5_0_scalar_set_b32(num, b32, &overflow); if (overflow || rustsecp256k1_v0_5_0_scalar_is_zero(num)) { continue; } break; } while(1); } void random_scalar_order(rustsecp256k1_v0_5_0_scalar *num) { do { unsigned char b32[32]; int overflow = 0; rustsecp256k1_v0_5_0_testrand256(b32); rustsecp256k1_v0_5_0_scalar_set_b32(num, b32, &overflow); if (overflow || rustsecp256k1_v0_5_0_scalar_is_zero(num)) { continue; } break; } while(1); } void random_scalar_order_b32(unsigned char *b32) { rustsecp256k1_v0_5_0_scalar num; random_scalar_order(&num); rustsecp256k1_v0_5_0_scalar_get_b32(b32, &num); } void run_context_tests(int use_prealloc) { rustsecp256k1_v0_5_0_pubkey pubkey; rustsecp256k1_v0_5_0_pubkey zero_pubkey; rustsecp256k1_v0_5_0_ecdsa_signature sig; unsigned char ctmp[32]; int32_t ecount; int32_t ecount2; rustsecp256k1_v0_5_0_context *none; rustsecp256k1_v0_5_0_context *sign; rustsecp256k1_v0_5_0_context *vrfy; rustsecp256k1_v0_5_0_context *both; rustsecp256k1_v0_5_0_context *sttc; void *none_prealloc = NULL; void *sign_prealloc = NULL; void *vrfy_prealloc = NULL; void *both_prealloc = NULL; void *sttc_prealloc = NULL; rustsecp256k1_v0_5_0_gej pubj; rustsecp256k1_v0_5_0_ge pub; rustsecp256k1_v0_5_0_scalar msg, key, nonce; rustsecp256k1_v0_5_0_scalar sigr, sigs; if (use_prealloc) { none_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_NONE)); sign_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); vrfy_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); both_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); sttc_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_clone_size(rustsecp256k1_v0_5_0_context_no_precomp)); CHECK(none_prealloc != NULL); CHECK(sign_prealloc != NULL); CHECK(vrfy_prealloc != NULL); CHECK(both_prealloc != NULL); CHECK(sttc_prealloc != NULL); none = rustsecp256k1_v0_5_0_context_preallocated_create(none_prealloc, SECP256K1_CONTEXT_NONE); sign = rustsecp256k1_v0_5_0_context_preallocated_create(sign_prealloc, SECP256K1_CONTEXT_SIGN); vrfy = rustsecp256k1_v0_5_0_context_preallocated_create(vrfy_prealloc, SECP256K1_CONTEXT_VERIFY); both = rustsecp256k1_v0_5_0_context_preallocated_create(both_prealloc, SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); sttc = rustsecp256k1_v0_5_0_context_preallocated_clone(rustsecp256k1_v0_5_0_context_no_precomp, sttc_prealloc); } else { none = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_NONE); sign = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_SIGN); vrfy = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_VERIFY); both = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); sttc = rustsecp256k1_v0_5_0_context_clone(rustsecp256k1_v0_5_0_context_no_precomp); } memset(&zero_pubkey, 0, sizeof(zero_pubkey)); ecount = 0; ecount2 = 10; rustsecp256k1_v0_5_0_context_set_illegal_callback(sttc, counting_illegal_callback_fn, &ecount); rustsecp256k1_v0_5_0_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2); /* set error callback (to a function that still aborts in case malloc() fails in rustsecp256k1_v0_5_0_context_clone() below) */ rustsecp256k1_v0_5_0_context_set_error_callback(sign, rustsecp256k1_v0_5_0_default_illegal_callback_fn, NULL); CHECK(sign->error_callback.fn != vrfy->error_callback.fn); CHECK(sign->error_callback.fn == rustsecp256k1_v0_5_0_default_illegal_callback_fn); /* check if sizes for cloning are consistent */ CHECK(rustsecp256k1_v0_5_0_context_preallocated_clone_size(none) == rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(rustsecp256k1_v0_5_0_context_preallocated_clone_size(sign) == rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(rustsecp256k1_v0_5_0_context_preallocated_clone_size(vrfy) == rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(rustsecp256k1_v0_5_0_context_preallocated_clone_size(both) == rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(rustsecp256k1_v0_5_0_context_preallocated_clone_size(sttc) >= sizeof(rustsecp256k1_v0_5_0_context)); /*** clone and destroy all of them to make sure cloning was complete ***/ { rustsecp256k1_v0_5_0_context *ctx_tmp; if (use_prealloc) { /* clone into a non-preallocated context and then again into a new preallocated one. */ ctx_tmp = none; none = rustsecp256k1_v0_5_0_context_clone(none); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(none_prealloc); none_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(none_prealloc != NULL); ctx_tmp = none; none = rustsecp256k1_v0_5_0_context_preallocated_clone(none, none_prealloc); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = sign; sign = rustsecp256k1_v0_5_0_context_clone(sign); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(sign_prealloc); sign_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(sign_prealloc != NULL); ctx_tmp = sign; sign = rustsecp256k1_v0_5_0_context_preallocated_clone(sign, sign_prealloc); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = vrfy; vrfy = rustsecp256k1_v0_5_0_context_clone(vrfy); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(vrfy_prealloc); vrfy_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(vrfy_prealloc != NULL); ctx_tmp = vrfy; vrfy = rustsecp256k1_v0_5_0_context_preallocated_clone(vrfy, vrfy_prealloc); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = both; both = rustsecp256k1_v0_5_0_context_clone(both); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(both_prealloc); both_prealloc = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(both_prealloc != NULL); ctx_tmp = both; both = rustsecp256k1_v0_5_0_context_preallocated_clone(both, both_prealloc); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(prealloc_tmp != NULL); ctx_tmp = none; none = rustsecp256k1_v0_5_0_context_preallocated_clone(none, prealloc_tmp); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = none; none = rustsecp256k1_v0_5_0_context_clone(none); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(prealloc_tmp != NULL); ctx_tmp = sign; sign = rustsecp256k1_v0_5_0_context_preallocated_clone(sign, prealloc_tmp); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = sign; sign = rustsecp256k1_v0_5_0_context_clone(sign); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); ctx_tmp = vrfy; vrfy = rustsecp256k1_v0_5_0_context_preallocated_clone(vrfy, prealloc_tmp); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = vrfy; vrfy = rustsecp256k1_v0_5_0_context_clone(vrfy); rustsecp256k1_v0_5_0_context_preallocated_destroy(ctx_tmp); free(prealloc_tmp); prealloc_tmp = malloc(rustsecp256k1_v0_5_0_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); ctx_tmp = both; both = rustsecp256k1_v0_5_0_context_preallocated_clone(both, prealloc_tmp); rustsecp256k1_v0_5_0_context_destroy(ctx_tmp); ctx_tmp = both; both = rustsecp256k1_v0_5_0_context_clone(both); rustsecp256k1_v0_5_0_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 == rustsecp256k1_v0_5_0_default_illegal_callback_fn); /* And that it resets back to default. */ rustsecp256k1_v0_5_0_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); rustsecp256k1_v0_5_0_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key); rustsecp256k1_v0_5_0_ge_set_gej(&pub, &pubj); /* Verify context-type checking illegal-argument errors. */ memset(ctmp, 1, 32); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(sttc, &pubkey, ctmp) == 0); CHECK(ecount == 1); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(sign, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(sttc, &sig, ctmp, ctmp, NULL, NULL) == 0); CHECK(ecount == 2); VG_UNDEF(&sig, sizeof(sig)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1); VG_CHECK(&sig, sizeof(sig)); CHECK(ecount2 == 10); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 1); CHECK(ecount2 == 10); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(sttc, &sig, ctmp, &pubkey) == 1); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 1); CHECK(ecount2 == 10); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(sttc, &pubkey, ctmp) == 1); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 1); CHECK(ecount2 == 10); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(sttc, &pubkey) == 1); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(sign, &pubkey) == 1); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(sign, NULL) == 0); CHECK(ecount2 == 11); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(sttc, &zero_pubkey) == 0); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(sttc, &pubkey, ctmp) == 1); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_context_randomize(sttc, ctmp) == 1); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_context_randomize(sttc, NULL) == 1); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_context_randomize(sign, ctmp) == 1); CHECK(ecount2 == 11); CHECK(rustsecp256k1_v0_5_0_context_randomize(sign, NULL) == 1); CHECK(ecount2 == 11); rustsecp256k1_v0_5_0_context_set_illegal_callback(sttc, NULL, NULL); rustsecp256k1_v0_5_0_context_set_illegal_callback(sign, NULL, NULL); /* obtain a working nonce */ do { random_scalar_order_test(&nonce); } while(!rustsecp256k1_v0_5_0_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); /* try signing */ CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); /* try verifying */ CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); /* cleanup */ if (use_prealloc) { rustsecp256k1_v0_5_0_context_preallocated_destroy(none); rustsecp256k1_v0_5_0_context_preallocated_destroy(sign); rustsecp256k1_v0_5_0_context_preallocated_destroy(vrfy); rustsecp256k1_v0_5_0_context_preallocated_destroy(both); rustsecp256k1_v0_5_0_context_preallocated_destroy(sttc); free(none_prealloc); free(sign_prealloc); free(vrfy_prealloc); free(both_prealloc); free(sttc_prealloc); } else { rustsecp256k1_v0_5_0_context_destroy(none); rustsecp256k1_v0_5_0_context_destroy(sign); rustsecp256k1_v0_5_0_context_destroy(vrfy); rustsecp256k1_v0_5_0_context_destroy(both); rustsecp256k1_v0_5_0_context_destroy(sttc); } /* Defined as no-op. */ rustsecp256k1_v0_5_0_context_destroy(NULL); rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_context *none = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_NONE); rustsecp256k1_v0_5_0_scratch_space *scratch; rustsecp256k1_v0_5_0_scratch_space local_scratch; /* Test public API */ rustsecp256k1_v0_5_0_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount); rustsecp256k1_v0_5_0_context_set_error_callback(none, counting_illegal_callback_fn, &ecount); scratch = rustsecp256k1_v0_5_0_scratch_space_create(none, 1000); CHECK(scratch != NULL); CHECK(ecount == 0); /* Test internal API */ CHECK(rustsecp256k1_v0_5_0_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); CHECK(rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_scratch_checkpoint(&none->error_callback, scratch); CHECK(rustsecp256k1_v0_5_0_scratch_alloc(&none->error_callback, scratch, 500) != NULL); CHECK(rustsecp256k1_v0_5_0_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_scratch_alloc(&none->error_callback, scratch, 501) == NULL); CHECK(rustsecp256k1_v0_5_0_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); CHECK(rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); CHECK(scratch->alloc_size == 0); CHECK(rustsecp256k1_v0_5_0_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); CHECK(rustsecp256k1_v0_5_0_scratch_alloc(&none->error_callback, scratch, 500) != NULL); CHECK(scratch->alloc_size != 0); /* try to apply a bad checkpoint */ checkpoint_2 = rustsecp256k1_v0_5_0_scratch_checkpoint(&none->error_callback, scratch); rustsecp256k1_v0_5_0_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); CHECK(ecount == 0); rustsecp256k1_v0_5_0_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */ CHECK(ecount == 1); rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scratch_space_destroy(none, scratch); memset(&local_scratch, 0, sizeof(local_scratch)); scratch = &local_scratch; CHECK(!rustsecp256k1_v0_5_0_scratch_max_allocation(&none->error_callback, scratch, 0)); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_scratch_alloc(&none->error_callback, scratch, 500) == NULL); CHECK(ecount == 4); rustsecp256k1_v0_5_0_scratch_space_destroy(none, scratch); CHECK(ecount == 5); /* Test that large integers do not wrap around in a bad way */ scratch = rustsecp256k1_v0_5_0_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 || !rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_scratch_alloc(&none->error_callback, scratch, SIZE_MAX) == NULL); rustsecp256k1_v0_5_0_scratch_space_destroy(none, scratch); /* cleanup */ rustsecp256k1_v0_5_0_scratch_space_destroy(none, NULL); /* no-op */ rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ctz32_var_debruijn(b32[i] << shift) == shift); CHECK(rustsecp256k1_v0_5_0_ctz32_var(b32[i] << shift) == shift); } } for (i = 0; i < sizeof(b64) / sizeof(b64[0]); ++i) { for (shift = 0; shift < 64; ++shift) { CHECK(rustsecp256k1_v0_5_0_ctz64_var_debruijn(b64[i] << shift) == shift); CHECK(rustsecp256k1_v0_5_0_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]; rustsecp256k1_v0_5_0_sha256 hasher; rustsecp256k1_v0_5_0_sha256_initialize(&hasher); rustsecp256k1_v0_5_0_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); rustsecp256k1_v0_5_0_sha256_finalize(&hasher, out); CHECK(rustsecp256k1_v0_5_0_memcmp_var(out, outputs[i], 32) == 0); if (strlen(inputs[i]) > 0) { int split = rustsecp256k1_v0_5_0_testrand_int(strlen(inputs[i])); rustsecp256k1_v0_5_0_sha256_initialize(&hasher); rustsecp256k1_v0_5_0_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); rustsecp256k1_v0_5_0_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); rustsecp256k1_v0_5_0_sha256_finalize(&hasher, out); CHECK(rustsecp256k1_v0_5_0_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++) { rustsecp256k1_v0_5_0_hmac_sha256 hasher; unsigned char out[32]; rustsecp256k1_v0_5_0_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); rustsecp256k1_v0_5_0_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); rustsecp256k1_v0_5_0_hmac_sha256_finalize(&hasher, out); CHECK(rustsecp256k1_v0_5_0_memcmp_var(out, outputs[i], 32) == 0); if (strlen(inputs[i]) > 0) { int split = rustsecp256k1_v0_5_0_testrand_int(strlen(inputs[i])); rustsecp256k1_v0_5_0_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); rustsecp256k1_v0_5_0_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); rustsecp256k1_v0_5_0_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); rustsecp256k1_v0_5_0_hmac_sha256_finalize(&hasher, out); CHECK(rustsecp256k1_v0_5_0_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} }; rustsecp256k1_v0_5_0_rfc6979_hmac_sha256 rng; unsigned char out[32]; int i; rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_initialize(&rng, key1, 64); for (i = 0; i < 3; i++) { rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_generate(&rng, out, 32); CHECK(rustsecp256k1_v0_5_0_memcmp_var(out, out1[i], 32) == 0); } rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_finalize(&rng); rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_initialize(&rng, key1, 65); for (i = 0; i < 3; i++) { rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_generate(&rng, out, 32); CHECK(rustsecp256k1_v0_5_0_memcmp_var(out, out1[i], 32) != 0); } rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_finalize(&rng); rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_initialize(&rng, key2, 64); for (i = 0; i < 3; i++) { rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_generate(&rng, out, 32); CHECK(rustsecp256k1_v0_5_0_memcmp_var(out, out2[i], 32) == 0); } rustsecp256k1_v0_5_0_rfc6979_hmac_sha256_finalize(&rng); } void run_tagged_sha256_tests(void) { int ecount = 0; rustsecp256k1_v0_5_0_context *none = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_NONE); unsigned char tag[32] = { 0 }; unsigned char msg[32] = { 0 }; unsigned char hash32[32]; unsigned char hash_expected[32] = { 0x04, 0x7A, 0x5E, 0x17, 0xB5, 0x86, 0x47, 0xC1, 0x3C, 0xC6, 0xEB, 0xC0, 0xAA, 0x58, 0x3B, 0x62, 0xFB, 0x16, 0x43, 0x32, 0x68, 0x77, 0x40, 0x6C, 0xE2, 0x76, 0x55, 0x9A, 0x3B, 0xDE, 0x55, 0xB3 }; rustsecp256k1_v0_5_0_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount); /* API test */ CHECK(rustsecp256k1_v0_5_0_tagged_sha256(none, hash32, tag, sizeof(tag), msg, sizeof(msg)) == 1); CHECK(rustsecp256k1_v0_5_0_tagged_sha256(none, NULL, tag, sizeof(tag), msg, sizeof(msg)) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_tagged_sha256(none, hash32, NULL, 0, msg, sizeof(msg)) == 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_tagged_sha256(none, hash32, tag, sizeof(tag), NULL, 0) == 0); CHECK(ecount == 3); /* Static test vector */ memcpy(tag, "tag", 3); memcpy(msg, "msg", 3); CHECK(rustsecp256k1_v0_5_0_tagged_sha256(none, hash32, tag, 3, msg, 3) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(hash32, hash_expected, sizeof(hash32)) == 0); rustsecp256k1_v0_5_0_context_destroy(none); } /***** 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 ? rustsecp256k1_v0_5_0_testrand32() : rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_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]); } } } /***** MODINV TESTS *****/ /* Compute the modular inverse of (odd) x mod 2^64. */ uint64_t modinv2p64(uint64_t x) { /* If w = 1/x mod 2^(2^L), then w*(2 - w*x) = 1/x mod 2^(2^(L+1)). See * Hacker's Delight second edition, Henry S. Warren, Jr., pages 245-247 for * why. Start with L=0, for which it is true for every odd x that * 1/x=1 mod 2. Iterating 6 times gives us 1/x mod 2^64. */ int l; uint64_t w = 1; CHECK(x & 1); for (l = 0; l < 6; ++l) w *= (2 - w*x); return w; } /* compute out = (a*b) mod m; if b=NULL, treat b=1. * * Out is a 512-bit number (represented as 32 uint16_t's in LE order). The other * arguments are 256-bit numbers (represented as 16 uint16_t's in LE order). */ void mulmod256(uint16_t* out, const uint16_t* a, const uint16_t* b, const uint16_t* m) { uint16_t mul[32]; uint64_t c = 0; int i, j; int m_bitlen = 0; int mul_bitlen = 0; if (b != NULL) { /* Compute the product of a and b, and put it in mul. */ for (i = 0; i < 32; ++i) { for (j = i <= 15 ? 0 : i - 15; j <= i && j <= 15; j++) { c += (uint64_t)a[j] * b[i - j]; } mul[i] = c & 0xFFFF; c >>= 16; } CHECK(c == 0); /* compute the highest set bit in mul */ for (i = 511; i >= 0; --i) { if ((mul[i >> 4] >> (i & 15)) & 1) { mul_bitlen = i; break; } } } else { /* if b==NULL, set mul=a. */ memcpy(mul, a, 32); memset(mul + 16, 0, 32); /* compute the highest set bit in mul */ for (i = 255; i >= 0; --i) { if ((mul[i >> 4] >> (i & 15)) & 1) { mul_bitlen = i; break; } } } /* Compute the highest set bit in m. */ for (i = 255; i >= 0; --i) { if ((m[i >> 4] >> (i & 15)) & 1) { m_bitlen = i; break; } } /* Try do mul -= m<= 0; --i) { uint16_t mul2[32]; int64_t cs; /* Compute mul2 = mul - m<= 0 && bitpos < 256) { sub |= ((m[bitpos >> 4] >> (bitpos & 15)) & 1) << p; } } /* Add mul[j]-sub to accumulator, and shift bottom 16 bits out to mul2[j]. */ cs += mul[j]; cs -= sub; mul2[j] = (cs & 0xFFFF); cs >>= 16; } /* If remainder of subtraction is 0, set mul = mul2. */ if (cs == 0) { memcpy(mul, mul2, sizeof(mul)); } } /* Sanity check: test that all limbs higher than m's highest are zero */ for (i = (m_bitlen >> 4) + 1; i < 32; ++i) { CHECK(mul[i] == 0); } memcpy(out, mul, 32); } /* Convert a 256-bit number represented as 16 uint16_t's to signed30 notation. */ void uint16_to_signed30(rustsecp256k1_v0_5_0_modinv32_signed30* out, const uint16_t* in) { int i; memset(out->v, 0, sizeof(out->v)); for (i = 0; i < 256; ++i) { out->v[i / 30] |= (int32_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 30); } } /* Convert a 256-bit number in signed30 notation to a representation as 16 uint16_t's. */ void signed30_to_uint16(uint16_t* out, const rustsecp256k1_v0_5_0_modinv32_signed30* in) { int i; memset(out, 0, 32); for (i = 0; i < 256; ++i) { out[i >> 4] |= (((in->v[i / 30]) >> (i % 30)) & 1) << (i & 15); } } /* Randomly mutate the sign of limbs in signed30 representation, without changing the value. */ void mutate_sign_signed30(rustsecp256k1_v0_5_0_modinv32_signed30* x) { int i; for (i = 0; i < 16; ++i) { int pos = rustsecp256k1_v0_5_0_testrand_bits(3); if (x->v[pos] > 0 && x->v[pos + 1] <= 0x3fffffff) { x->v[pos] -= 0x40000000; x->v[pos + 1] += 1; } else if (x->v[pos] < 0 && x->v[pos + 1] >= 0x3fffffff) { x->v[pos] += 0x40000000; x->v[pos + 1] -= 1; } } } /* Test rustsecp256k1_v0_5_0_modinv32{_var}, using inputs in 16-bit limb format, and returning inverse. */ void test_modinv32_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) { uint16_t tmp[16]; rustsecp256k1_v0_5_0_modinv32_signed30 x; rustsecp256k1_v0_5_0_modinv32_modinfo m; int i, vartime, nonzero; uint16_to_signed30(&x, in); nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4] | x.v[5] | x.v[6] | x.v[7] | x.v[8]) != 0; uint16_to_signed30(&m.modulus, mod); mutate_sign_signed30(&m.modulus); /* compute 1/modulus mod 2^30 */ m.modulus_inv30 = modinv2p64(m.modulus.v[0]) & 0x3fffffff; CHECK(((m.modulus_inv30 * m.modulus.v[0]) & 0x3fffffff) == 1); for (vartime = 0; vartime < 2; ++vartime) { /* compute inverse */ (vartime ? rustsecp256k1_v0_5_0_modinv32_var : rustsecp256k1_v0_5_0_modinv32)(&x, &m); /* produce output */ signed30_to_uint16(out, &x); /* check if the inverse times the input is 1 (mod m), unless x is 0. */ mulmod256(tmp, out, in, mod); CHECK(tmp[0] == nonzero); for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0); /* invert again */ (vartime ? rustsecp256k1_v0_5_0_modinv32_var : rustsecp256k1_v0_5_0_modinv32)(&x, &m); /* check if the result is equal to the input */ signed30_to_uint16(tmp, &x); for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]); } } #ifdef SECP256K1_WIDEMUL_INT128 /* Convert a 256-bit number represented as 16 uint16_t's to signed62 notation. */ void uint16_to_signed62(rustsecp256k1_v0_5_0_modinv64_signed62* out, const uint16_t* in) { int i; memset(out->v, 0, sizeof(out->v)); for (i = 0; i < 256; ++i) { out->v[i / 62] |= (int64_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 62); } } /* Convert a 256-bit number in signed62 notation to a representation as 16 uint16_t's. */ void signed62_to_uint16(uint16_t* out, const rustsecp256k1_v0_5_0_modinv64_signed62* in) { int i; memset(out, 0, 32); for (i = 0; i < 256; ++i) { out[i >> 4] |= (((in->v[i / 62]) >> (i % 62)) & 1) << (i & 15); } } /* Randomly mutate the sign of limbs in signed62 representation, without changing the value. */ void mutate_sign_signed62(rustsecp256k1_v0_5_0_modinv64_signed62* x) { static const int64_t M62 = (int64_t)(UINT64_MAX >> 2); int i; for (i = 0; i < 8; ++i) { int pos = rustsecp256k1_v0_5_0_testrand_bits(2); if (x->v[pos] > 0 && x->v[pos + 1] <= M62) { x->v[pos] -= (M62 + 1); x->v[pos + 1] += 1; } else if (x->v[pos] < 0 && x->v[pos + 1] >= -M62) { x->v[pos] += (M62 + 1); x->v[pos + 1] -= 1; } } } /* Test rustsecp256k1_v0_5_0_modinv64{_var}, using inputs in 16-bit limb format, and returning inverse. */ void test_modinv64_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) { static const int64_t M62 = (int64_t)(UINT64_MAX >> 2); uint16_t tmp[16]; rustsecp256k1_v0_5_0_modinv64_signed62 x; rustsecp256k1_v0_5_0_modinv64_modinfo m; int i, vartime, nonzero; uint16_to_signed62(&x, in); nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4]) != 0; uint16_to_signed62(&m.modulus, mod); mutate_sign_signed62(&m.modulus); /* compute 1/modulus mod 2^62 */ m.modulus_inv62 = modinv2p64(m.modulus.v[0]) & M62; CHECK(((m.modulus_inv62 * m.modulus.v[0]) & M62) == 1); for (vartime = 0; vartime < 2; ++vartime) { /* compute inverse */ (vartime ? rustsecp256k1_v0_5_0_modinv64_var : rustsecp256k1_v0_5_0_modinv64)(&x, &m); /* produce output */ signed62_to_uint16(out, &x); /* check if the inverse times the input is 1 (mod m), unless x is 0. */ mulmod256(tmp, out, in, mod); CHECK(tmp[0] == nonzero); for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0); /* invert again */ (vartime ? rustsecp256k1_v0_5_0_modinv64_var : rustsecp256k1_v0_5_0_modinv64)(&x, &m); /* check if the result is equal to the input */ signed62_to_uint16(tmp, &x); for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]); } } #endif /* test if a and b are coprime */ int coprime(const uint16_t* a, const uint16_t* b) { uint16_t x[16], y[16], t[16]; int i; int iszero; memcpy(x, a, 32); memcpy(y, b, 32); /* simple gcd loop: while x!=0, (x,y)=(y%x,x) */ while (1) { iszero = 1; for (i = 0; i < 16; ++i) { if (x[i] != 0) { iszero = 0; break; } } if (iszero) break; mulmod256(t, y, NULL, x); memcpy(y, x, 32); memcpy(x, t, 32); } /* return whether y=1 */ if (y[0] != 1) return 0; for (i = 1; i < 16; ++i) { if (y[i] != 0) return 0; } return 1; } void run_modinv_tests(void) { /* Fixed test cases. Each tuple is (input, modulus, output), each as 16x16 bits in LE order. */ static const uint16_t CASES[][3][16] = { /* Test cases triggering edge cases in divsteps */ /* Test case known to need 713 divsteps */ {{0x1513, 0x5389, 0x54e9, 0x2798, 0x1957, 0x66a0, 0x8057, 0x3477, 0x7784, 0x1052, 0x326a, 0x9331, 0x6506, 0xa95c, 0x91f3, 0xfb5e}, {0x2bdd, 0x8df4, 0xcc61, 0x481f, 0xdae5, 0x5ca7, 0xf43b, 0x7d54, 0x13d6, 0x469b, 0x2294, 0x20f4, 0xb2a4, 0xa2d1, 0x3ff1, 0xfd4b}, {0xffd8, 0xd9a0, 0x456e, 0x81bb, 0xbabd, 0x6cea, 0x6dbd, 0x73ab, 0xbb94, 0x3d3c, 0xdf08, 0x31c4, 0x3e32, 0xc179, 0x2486, 0xb86b}}, /* Test case known to need 589 divsteps, reaching delta=-140 and delta=141. */ {{0x3fb1, 0x903b, 0x4eb7, 0x4813, 0xd863, 0x26bf, 0xd89f, 0xa8a9, 0x02fe, 0x57c6, 0x554a, 0x4eab, 0x165e, 0x3d61, 0xee1e, 0x456c}, {0x9295, 0x823b, 0x5c1f, 0x5386, 0x48e0, 0x02ff, 0x4c2a, 0xa2da, 0xe58f, 0x967c, 0xc97e, 0x3f5a, 0x69fb, 0x52d9, 0x0a86, 0xb4a3}, {0x3d30, 0xb893, 0xa809, 0xa7a8, 0x26f5, 0x5b42, 0x55be, 0xf4d0, 0x12c2, 0x7e6a, 0xe41a, 0x90c7, 0xebfa, 0xf920, 0x304e, 0x1419}}, /* Test case known to need 650 divsteps, and doing 65 consecutive (f,g/2) steps. */ {{0x8583, 0x5058, 0xbeae, 0xeb69, 0x48bc, 0x52bb, 0x6a9d, 0xcc94, 0x2a21, 0x87d5, 0x5b0d, 0x42f6, 0x5b8a, 0x2214, 0xe9d6, 0xa040}, {0x7531, 0x27cb, 0x7e53, 0xb739, 0x6a5f, 0x83f5, 0xa45c, 0xcb1d, 0x8a87, 0x1c9c, 0x51d7, 0x851c, 0xb9d8, 0x1fbe, 0xc241, 0xd4a3}, {0xcdb4, 0x275c, 0x7d22, 0xa906, 0x0173, 0xc054, 0x7fdf, 0x5005, 0x7fb8, 0x9059, 0xdf51, 0x99df, 0x2654, 0x8f6e, 0x070f, 0xb347}}, /* example needing 713 divsteps; delta=-2..3 */ {{0xe2e9, 0xee91, 0x4345, 0xe5ad, 0xf3ec, 0x8f42, 0x0364, 0xd5c9, 0xff49, 0xbef5, 0x4544, 0x4c7c, 0xae4b, 0xfd9d, 0xb35b, 0xda9d}, {0x36e7, 0x8cca, 0x2ed0, 0x47b3, 0xaca4, 0xb374, 0x7d2a, 0x0772, 0x6bdb, 0xe0a7, 0x900b, 0xfe10, 0x788c, 0x6f22, 0xd909, 0xf298}, {0xd8c6, 0xba39, 0x13ed, 0x198c, 0x16c8, 0xb837, 0xa5f2, 0x9797, 0x0113, 0x882a, 0x15b5, 0x324c, 0xabee, 0xe465, 0x8170, 0x85ac}}, /* example needing 713 divsteps; delta=-2..3 */ {{0xd5b7, 0x2966, 0x040e, 0xf59a, 0x0387, 0xd96d, 0xbfbc, 0xd850, 0x2d96, 0x872a, 0xad81, 0xc03c, 0xbb39, 0xb7fa, 0xd904, 0xef78}, {0x6279, 0x4314, 0xfdd3, 0x1568, 0x0982, 0x4d13, 0x625f, 0x010c, 0x22b1, 0x0cc3, 0xf22d, 0x5710, 0x1109, 0x5751, 0x7714, 0xfcf2}, {0xdb13, 0x5817, 0x232e, 0xe456, 0xbbbc, 0x6fbe, 0x4572, 0xa358, 0xc76d, 0x928e, 0x0162, 0x5314, 0x8325, 0x5683, 0xe21b, 0xda88}}, /* example needing 713 divsteps; delta=-2..3 */ {{0xa06f, 0x71ee, 0x3bac, 0x9ebb, 0xdeaa, 0x09ed, 0x1cf7, 0x9ec9, 0x7158, 0x8b72, 0x5d53, 0x5479, 0x5c75, 0xbb66, 0x9125, 0xeccc}, {0x2941, 0xd46c, 0x3cd4, 0x4a9d, 0x5c4a, 0x256b, 0xbd6c, 0x9b8e, 0x8fe0, 0x8a14, 0xffe8, 0x2496, 0x618d, 0xa9d7, 0x5018, 0xfb29}, {0x437c, 0xbd60, 0x7590, 0x94bb, 0x0095, 0xd35e, 0xd4fe, 0xd6da, 0x0d4e, 0x5342, 0x4cd2, 0x169b, 0x661c, 0x1380, 0xed2d, 0x85c1}}, /* example reaching delta=-64..65; 661 divsteps */ {{0xfde4, 0x68d6, 0x6c48, 0x7f77, 0x1c78, 0x96de, 0x2fd9, 0xa6c2, 0xbbb5, 0xd319, 0x69cf, 0xd4b3, 0xa321, 0xcda0, 0x172e, 0xe530}, {0xd9e3, 0x0f60, 0x3d86, 0xeeab, 0x25ee, 0x9582, 0x2d50, 0xfe16, 0xd4e2, 0xe3ba, 0x94e2, 0x9833, 0x6c5e, 0x8982, 0x13b6, 0xe598}, {0xe675, 0xf55a, 0x10f6, 0xabde, 0x5113, 0xecaa, 0x61ae, 0xad9f, 0x0c27, 0xef33, 0x62e5, 0x211d, 0x08fa, 0xa78d, 0xc675, 0x8bae}}, /* example reaching delta=-64..65; 661 divsteps */ {{0x21bf, 0x52d5, 0x8fd4, 0xaa18, 0x156a, 0x7247, 0xebb8, 0x5717, 0x4eb5, 0x1421, 0xb58f, 0x3b0b, 0x5dff, 0xe533, 0xb369, 0xd28a}, {0x9f6b, 0xe463, 0x2563, 0xc74d, 0x6d81, 0x636a, 0x8fc8, 0x7a94, 0x9429, 0x1585, 0xf35e, 0x7ff5, 0xb64f, 0x9720, 0xba74, 0xe108}, {0xa5ab, 0xea7b, 0xfe5e, 0x8a85, 0x13be, 0x7934, 0xe8a0, 0xa187, 0x86b5, 0xe477, 0xb9a4, 0x75d7, 0x538f, 0xdd70, 0xc781, 0xb67d}}, /* example reaching delta=-64..65; 661 divsteps */ {{0xa41a, 0x3e8d, 0xf1f5, 0x9493, 0x868c, 0x5103, 0x2725, 0x3ceb, 0x6032, 0x3624, 0xdc6b, 0x9120, 0xbf4c, 0x8821, 0x91ad, 0xb31a}, {0x5c0b, 0xdda5, 0x20f8, 0x32a1, 0xaf73, 0x6ec5, 0x4779, 0x43d6, 0xd454, 0x9573, 0xbf84, 0x5a58, 0xe04e, 0x307e, 0xd1d5, 0xe230}, {0xda15, 0xbcd6, 0x7180, 0xabd3, 0x04e6, 0x6986, 0xc0d7, 0x90bb, 0x3a4d, 0x7c95, 0xaaab, 0x9ab3, 0xda34, 0xa7f6, 0x9636, 0x6273}}, /* example doing 123 consecutive (f,g/2) steps; 615 divsteps */ {{0xb4d6, 0xb38f, 0x00aa, 0xebda, 0xd4c2, 0x70b8, 0x9dad, 0x58ee, 0x68f8, 0x48d3, 0xb5ff, 0xf422, 0x9e46, 0x2437, 0x18d0, 0xd9cc}, {0x5c83, 0xfed7, 0x97f5, 0x3f07, 0xcaad, 0x95b1, 0xb4a4, 0xb005, 0x23af, 0xdd27, 0x6c0d, 0x932c, 0xe2b2, 0xe3ae, 0xfb96, 0xdf67}, {0x3105, 0x0127, 0xfd48, 0x039b, 0x35f1, 0xbc6f, 0x6c0a, 0xb572, 0xe4df, 0xebad, 0x8edc, 0xb89d, 0x9555, 0x4c26, 0x1fef, 0x997c}}, /* example doing 123 consecutive (f,g/2) steps; 614 divsteps */ {{0x5138, 0xd474, 0x385f, 0xc964, 0x00f2, 0x6df7, 0x862d, 0xb185, 0xb264, 0xe9e1, 0x466c, 0xf39e, 0xafaf, 0x5f41, 0x47e2, 0xc89d}, {0x8607, 0x9c81, 0x46a2, 0x7dcc, 0xcb0c, 0x9325, 0xe149, 0x2bde, 0x6632, 0x2869, 0xa261, 0xb163, 0xccee, 0x22ae, 0x91e0, 0xcfd5}, {0x831c, 0xda22, 0xb080, 0xba7a, 0x26e2, 0x54b0, 0x073b, 0x5ea0, 0xed4b, 0xcb3d, 0xbba1, 0xbec8, 0xf2ad, 0xae0d, 0x349b, 0x17d1}}, /* example doing 123 consecutive (f,g/2) steps; 614 divsteps */ {{0xe9a5, 0xb4ad, 0xd995, 0x9953, 0xcdff, 0x50d7, 0xf715, 0x9dc7, 0x3e28, 0x15a9, 0x95a3, 0x8554, 0x5b5e, 0xad1d, 0x6d57, 0x3d50}, {0x3ad9, 0xbd60, 0x5cc7, 0x6b91, 0xadeb, 0x71f6, 0x7cc4, 0xa58a, 0x2cce, 0xf17c, 0x38c9, 0x97ed, 0x65fb, 0x3fa6, 0xa6bc, 0xeb24}, {0xf96c, 0x1963, 0x8151, 0xa0cc, 0x299b, 0xf277, 0x001a, 0x16bb, 0xfd2e, 0x532d, 0x0410, 0xe117, 0x6b00, 0x44ec, 0xca6a, 0x1745}}, /* example doing 446 (f,g/2) steps; 523 divsteps */ {{0x3758, 0xa56c, 0xe41e, 0x4e47, 0x0975, 0xa82b, 0x107c, 0x89cf, 0x2093, 0x5a0c, 0xda37, 0xe007, 0x6074, 0x4f68, 0x2f5a, 0xbb8a}, {0x4beb, 0xa40f, 0x2c42, 0xd9d6, 0x97e8, 0xca7c, 0xd395, 0x894f, 0x1f50, 0x8067, 0xa233, 0xb850, 0x1746, 0x1706, 0xbcda, 0xdf32}, {0x762a, 0xceda, 0x4c45, 0x1ca0, 0x8c37, 0xd8c5, 0xef57, 0x7a2c, 0x6e98, 0xe38a, 0xc50e, 0x2ca9, 0xcb85, 0x24d5, 0xc29c, 0x61f6}}, /* example doing 446 (f,g/2) steps; 523 divsteps */ {{0x6f38, 0x74ad, 0x7332, 0x4073, 0x6521, 0xb876, 0xa370, 0xa6bd, 0xcea5, 0xbd06, 0x969f, 0x77c6, 0x1e69, 0x7c49, 0x7d51, 0xb6e7}, {0x3f27, 0x4be4, 0xd81e, 0x1396, 0xb21f, 0x92aa, 0x6dc3, 0x6283, 0x6ada, 0x3ca2, 0xc1e5, 0x8b9b, 0xd705, 0x5598, 0x8ba1, 0xe087}, {0x6a22, 0xe834, 0xbc8d, 0xcee9, 0x42fc, 0xfc77, 0x9c45, 0x1ca8, 0xeb66, 0xed74, 0xaaf9, 0xe75f, 0xfe77, 0x46d2, 0x179b, 0xbf3e}}, /* example doing 336 (f,(f+g)/2) steps; 693 divsteps */ {{0x7ea7, 0x444e, 0x84ea, 0xc447, 0x7c1f, 0xab97, 0x3de6, 0x5878, 0x4e8b, 0xc017, 0x03e0, 0xdc40, 0xbbd0, 0x74ce, 0x0169, 0x7ab5}, {0x4023, 0x154f, 0xfbe4, 0x8195, 0xfda0, 0xef54, 0x9e9a, 0xc703, 0x2803, 0xf760, 0x6302, 0xed5b, 0x7157, 0x6456, 0xdd7d, 0xf14b}, {0xb6fb, 0xe3b3, 0x0733, 0xa77e, 0x44c5, 0x3003, 0xc937, 0xdd4d, 0x5355, 0x14e9, 0x184e, 0xcefe, 0xe6b5, 0xf2e0, 0x0a28, 0x5b74}}, /* example doing 336 (f,(f+g)/2) steps; 687 divsteps */ {{0xa893, 0xb5f4, 0x1ede, 0xa316, 0x242c, 0xbdcc, 0xb017, 0x0836, 0x3a37, 0x27fb, 0xfb85, 0x251e, 0xa189, 0xb15d, 0xa4b8, 0xc24c}, {0xb0b7, 0x57ba, 0xbb6d, 0x9177, 0xc896, 0xc7f2, 0x43b4, 0x85a6, 0xe6c4, 0xe50e, 0x3109, 0x7ca5, 0xd73d, 0x13ff, 0x0c3d, 0xcd62}, {0x48ca, 0xdb34, 0xe347, 0x2cef, 0x4466, 0x10fb, 0x7ee1, 0x6344, 0x4308, 0x966d, 0xd4d1, 0xb099, 0x994f, 0xd025, 0x2187, 0x5866}}, /* example doing 267 (g,(g-f)/2) steps; 678 divsteps */ {{0x0775, 0x1754, 0x01f6, 0xdf37, 0xc0be, 0x8197, 0x072f, 0x6cf5, 0x8b36, 0x8069, 0x5590, 0xb92d, 0x6084, 0x47a4, 0x23fe, 0xddd5}, {0x8e1b, 0xda37, 0x27d9, 0x312e, 0x3a2f, 0xef6d, 0xd9eb, 0x8153, 0xdcba, 0x9fa3, 0x9f80, 0xead5, 0x134d, 0x2ebb, 0x5ec0, 0xe032}, {0x1cb6, 0x5a61, 0x1bed, 0x77d6, 0xd5d1, 0x7498, 0xef33, 0x2dd2, 0x1089, 0xedbd, 0x6958, 0x16ae, 0x336c, 0x45e6, 0x4361, 0xbadc}}, /* example doing 267 (g,(g-f)/2) steps; 676 divsteps */ {{0x0207, 0xf948, 0xc430, 0xf36b, 0xf0a7, 0x5d36, 0x751f, 0x132c, 0x6f25, 0xa630, 0xca1f, 0xc967, 0xaf9c, 0x34e7, 0xa38f, 0xbe9f}, {0x5fb9, 0x7321, 0x6561, 0x5fed, 0x54ec, 0x9c3a, 0xee0e, 0x6717, 0x49af, 0xb896, 0xf4f5, 0x451c, 0x722a, 0xf116, 0x64a9, 0xcf0b}, {0xf4d7, 0xdb47, 0xfef2, 0x4806, 0x4cb8, 0x18c7, 0xd9a7, 0x4951, 0x14d8, 0x5c3a, 0xd22d, 0xd7b2, 0x750c, 0x3de7, 0x8b4a, 0x19aa}}, /* Test cases triggering edge cases in divsteps variant starting with delta=1/2 */ /* example needing 590 divsteps; delta=-5/2..7/2 */ {{0x9118, 0xb640, 0x53d7, 0x30ab, 0x2a23, 0xd907, 0x9323, 0x5b3a, 0xb6d4, 0x538a, 0x7637, 0xfe97, 0xfd05, 0x3cc0, 0x453a, 0xfb7e}, {0x6983, 0x4f75, 0x4ad1, 0x48ad, 0xb2d9, 0x521d, 0x3dbc, 0x9cc0, 0x4b60, 0x0ac6, 0xd3be, 0x0fb6, 0xd305, 0x3895, 0x2da5, 0xfdf8}, {0xcec1, 0x33ac, 0xa801, 0x8194, 0xe36c, 0x65ef, 0x103b, 0xca54, 0xfa9b, 0xb41d, 0x9b52, 0xb6f7, 0xa611, 0x84aa, 0x3493, 0xbf54}}, /* example needing 590 divsteps; delta=-3/2..5/2 */ {{0xb5f2, 0x42d0, 0x35e8, 0x8ca0, 0x4b62, 0x6e1d, 0xbdf3, 0x890e, 0x8c82, 0x23d8, 0xc79a, 0xc8e8, 0x789e, 0x353d, 0x9766, 0xea9d}, {0x6fa1, 0xacba, 0x4b7a, 0x5de1, 0x95d0, 0xc845, 0xebbf, 0x6f5a, 0x30cf, 0x52db, 0x69b7, 0xe278, 0x4b15, 0x8411, 0x2ab2, 0xf3e7}, {0xf12c, 0x9d6d, 0x95fa, 0x1878, 0x9f13, 0x4fb5, 0x3c8b, 0xa451, 0x7182, 0xc4b6, 0x7e2a, 0x7bb7, 0x6e0e, 0x5b68, 0xde55, 0x9927}}, /* example needing 590 divsteps; delta=-3/2..5/2 */ {{0x229c, 0x4ef8, 0x1e93, 0xe5dc, 0xcde5, 0x6d62, 0x263b, 0xad11, 0xced0, 0x88ff, 0xae8e, 0x3183, 0x11d2, 0xa50b, 0x350d, 0xeb40}, {0x3157, 0xe2ea, 0x8a02, 0x0aa3, 0x5ae1, 0xb26c, 0xea27, 0x6805, 0x87e2, 0x9461, 0x37c1, 0x2f8d, 0x85d2, 0x77a8, 0xf805, 0xeec9}, {0x6f4e, 0x2748, 0xf7e5, 0xd8d3, 0xabe2, 0x7270, 0xc4e0, 0xedc7, 0xf196, 0x78ca, 0x9139, 0xd8af, 0x72c6, 0xaf2f, 0x85d2, 0x6cd3}}, /* example needing 590 divsteps; delta=-5/2..7/2 */ {{0xdce8, 0xf1fe, 0x6708, 0x021e, 0xf1ca, 0xd609, 0x5443, 0x85ce, 0x7a05, 0x8f9c, 0x90c3, 0x52e7, 0x8e1d, 0x97b8, 0xc0bf, 0xf2a1}, {0xbd3d, 0xed11, 0x1625, 0xb4c5, 0x844c, 0xa413, 0x2569, 0xb9ba, 0xcd35, 0xff84, 0xcd6e, 0x7f0b, 0x7d5d, 0x10df, 0x3efe, 0xfbe5}, {0xa9dd, 0xafef, 0xb1b7, 0x4c8d, 0x50e4, 0xafbf, 0x2d5a, 0xb27c, 0x0653, 0x66b6, 0x5d36, 0x4694, 0x7e35, 0xc47c, 0x857f, 0x32c5}}, /* example needing 590 divsteps; delta=-3/2..5/2 */ {{0x7902, 0xc9f8, 0x926b, 0xaaeb, 0x90f8, 0x1c89, 0xcce3, 0x96b7, 0x28b2, 0x87a2, 0x136d, 0x695a, 0xa8df, 0x9061, 0x9e31, 0xee82}, {0xd3a9, 0x3c02, 0x818c, 0x6b81, 0x34b3, 0xebbb, 0xe2c8, 0x7712, 0xbfd6, 0x8248, 0xa6f4, 0xba6f, 0x03bb, 0xfb54, 0x7575, 0xfe89}, {0x8246, 0x0d63, 0x478e, 0xf946, 0xf393, 0x0451, 0x08c2, 0x5919, 0x5fd6, 0x4c61, 0xbeb7, 0x9a15, 0x30e1, 0x55fc, 0x6a01, 0x3724}}, /* example reaching delta=-127/2..129/2; 571 divsteps */ {{0x3eff, 0x926a, 0x77f5, 0x1fff, 0x1a5b, 0xf3ef, 0xf64b, 0x8681, 0xf800, 0xf9bc, 0x761d, 0xe268, 0x62b0, 0xa032, 0xba9c, 0xbe56}, {0xb8f9, 0x00e7, 0x47b7, 0xdffc, 0xfd9d, 0x5abb, 0xa19b, 0x1868, 0x31fd, 0x3b29, 0x3674, 0x5449, 0xf54d, 0x1d19, 0x6ac7, 0xff6f}, {0xf1d7, 0x3551, 0x5682, 0x9adf, 0xe8aa, 0x19a5, 0x8340, 0x71db, 0xb7ab, 0x4cfd, 0xf661, 0x632c, 0xc27e, 0xd3c6, 0xdf42, 0xd306}}, /* example reaching delta=-127/2..129/2; 571 divsteps */ {{0x0000, 0x0000, 0x0000, 0x0000, 0x3aff, 0x2ed7, 0xf2e0, 0xabc7, 0x8aee, 0x166e, 0x7ed0, 0x9ac7, 0x714a, 0xb9c5, 0x4d58, 0xad6c}, {0x9cf9, 0x47e2, 0xa421, 0xb277, 0xffc2, 0x2747, 0x6486, 0x94c1, 0x1d99, 0xd49b, 0x1096, 0x991a, 0xe986, 0xae02, 0xe89b, 0xea36}, {0x1fb4, 0x98d8, 0x19b7, 0x80e9, 0xcdac, 0xaa5a, 0xf1e6, 0x0074, 0xe393, 0xed8b, 0x8d5c, 0xe17d, 0x81b3, 0xc16d, 0x54d3, 0x9be3}}, /* example reaching delta=-127/2..129/2; 571 divsteps */ {{0xd047, 0x7e36, 0x3157, 0x7ab6, 0xb4d9, 0x8dae, 0x7534, 0x4f5d, 0x489e, 0xa8ab, 0x8a3d, 0xd52c, 0x62af, 0xa032, 0xba9c, 0xbe56}, {0xb1f1, 0x737f, 0x5964, 0x5afb, 0x3712, 0x8ef9, 0x19f7, 0x9669, 0x664d, 0x03ad, 0xc352, 0xf7a5, 0xf545, 0x1d19, 0x6ac7, 0xff6f}, {0xa834, 0x5256, 0x27bc, 0x33bd, 0xba11, 0x5a7b, 0x791e, 0xe6c0, 0x9ac4, 0x9370, 0x1130, 0x28b4, 0x2b2e, 0x231b, 0x082a, 0x796e}}, /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ {{0x6ab1, 0x6ea0, 0x1a99, 0xe0c2, 0xdd45, 0x645d, 0x8dbc, 0x466a, 0xfa64, 0x4289, 0xd3f7, 0xfc8f, 0x2894, 0xe3c5, 0xa008, 0xcc14}, {0xc75f, 0xc083, 0x4cc2, 0x64f2, 0x2aff, 0x4c12, 0x8461, 0xc4ae, 0xbbfa, 0xb336, 0xe4b2, 0x3ac5, 0x2c22, 0xf56c, 0x5381, 0xe943}, {0xcd80, 0x760d, 0x4395, 0xb3a6, 0xd497, 0xf583, 0x82bd, 0x1daa, 0xbe92, 0x2613, 0xfdfb, 0x869b, 0x0425, 0xa333, 0x7056, 0xc9c5}}, /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ {{0x71d4, 0x64df, 0xec4f, 0x74d8, 0x7e0c, 0x40d3, 0x7073, 0x4cc8, 0x2a2a, 0xb1ff, 0x8518, 0x6513, 0xb0ea, 0x640a, 0x62d9, 0xd5f4}, {0xdc75, 0xd937, 0x3b13, 0x1d36, 0xdf83, 0xd034, 0x1c1c, 0x4332, 0x4cc3, 0xeeec, 0x7d94, 0x6771, 0x3384, 0x74b0, 0x947d, 0xf2c4}, {0x0a82, 0x37a4, 0x12d5, 0xec97, 0x972c, 0xe6bf, 0xc348, 0xa0a9, 0xc50c, 0xdc7c, 0xae30, 0x19d1, 0x0fca, 0x35e1, 0xd6f6, 0x81ee}}, /* example doing 123 consecutive (f,g/2) steps; 554 divsteps */ {{0xa6b1, 0xabc5, 0x5bbc, 0x7f65, 0xdd32, 0xaa73, 0xf5a3, 0x1982, 0xced4, 0xe949, 0x0fd6, 0x2bc4, 0x2bd7, 0xe3c5, 0xa008, 0xcc14}, {0x4b5f, 0x8f96, 0xa375, 0xfbcf, 0x1c7d, 0xf1ec, 0x03f5, 0xb35d, 0xb999, 0xdb1f, 0xc9a1, 0xb4c7, 0x1dd5, 0xf56c, 0x5381, 0xe943}, {0xaa3d, 0x38b9, 0xf17d, 0xeed9, 0x9988, 0x69ee, 0xeb88, 0x1495, 0x203f, 0x18c8, 0x82b7, 0xdcb2, 0x34a7, 0x6b00, 0x6998, 0x589a}}, /* example doing 453 (f,g/2) steps; 514 divsteps */ {{0xa478, 0xe60d, 0x3244, 0x60e6, 0xada3, 0xfe50, 0xb6b1, 0x2eae, 0xd0ef, 0xa7b1, 0xef63, 0x05c0, 0xe213, 0x443e, 0x4427, 0x2448}, {0x258f, 0xf9ef, 0xe02b, 0x92dd, 0xd7f3, 0x252b, 0xa503, 0x9089, 0xedff, 0x96c1, 0xfe3a, 0x3a39, 0x198a, 0x981d, 0x0627, 0xedb7}, {0x595a, 0x45be, 0x8fb0, 0x2265, 0xc210, 0x02b8, 0xdce9, 0xe241, 0xcab6, 0xbf0d, 0x0049, 0x8d9a, 0x2f51, 0xae54, 0x5785, 0xb411}}, /* example doing 453 (f,g/2) steps; 514 divsteps */ {{0x48f0, 0x7db3, 0xdafe, 0x1c92, 0x5912, 0xe11a, 0xab52, 0xede1, 0x3182, 0x8980, 0x5d2b, 0x9b5b, 0x8718, 0xda27, 0x1683, 0x1de2}, {0x168f, 0x6f36, 0xce7a, 0xf435, 0x19d4, 0xda5e, 0x2351, 0x9af5, 0xb003, 0x0ef5, 0x3b4c, 0xecec, 0xa9f0, 0x78e1, 0xdfef, 0xe823}, {0x5f55, 0xfdcc, 0xb233, 0x2914, 0x84f0, 0x97d1, 0x9cf4, 0x2159, 0xbf56, 0xb79c, 0x17a3, 0x7cef, 0xd5de, 0x34f0, 0x5311, 0x4c54}}, /* example doing 510 (f,(f+g)/2) steps; 512 divsteps */ {{0x2789, 0x2e04, 0x6e0e, 0xb6cd, 0xe4de, 0x4dbf, 0x228d, 0x7877, 0xc335, 0x806b, 0x38cd, 0x8049, 0xa73b, 0xcfa2, 0x82f7, 0x9e19}, {0xc08d, 0xb99d, 0xb8f3, 0x663d, 0xbbb3, 0x1284, 0x1485, 0x1d49, 0xc98f, 0x9e78, 0x1588, 0x11e3, 0xd91a, 0xa2c7, 0xfff1, 0xc7b9}, {0x1e1f, 0x411d, 0x7c49, 0x0d03, 0xe789, 0x2f8e, 0x5d55, 0xa95e, 0x826e, 0x8de5, 0x52a0, 0x1abc, 0x4cd7, 0xd13a, 0x4395, 0x63e1}}, /* example doing 510 (f,(f+g)/2) steps; 512 divsteps */ {{0xd5a1, 0xf786, 0x555c, 0xb14b, 0x44ae, 0x535f, 0x4a49, 0xffc3, 0xf497, 0x70d1, 0x57c8, 0xa933, 0xc85a, 0x1910, 0x75bf, 0x960b}, {0xfe53, 0x5058, 0x496d, 0xfdff, 0x6fb8, 0x4100, 0x92bd, 0xe0c4, 0xda89, 0xe0a4, 0x841b, 0x43d4, 0xa388, 0x957f, 0x99ca, 0x9abf}, {0xe530, 0x05bc, 0xfeec, 0xfc7e, 0xbcd3, 0x1239, 0x54cb, 0x7042, 0xbccb, 0x139e, 0x9076, 0x0203, 0x6068, 0x90c7, 0x1ddf, 0x488d}}, /* example doing 228 (g,(g-f)/2) steps; 538 divsteps */ {{0x9488, 0xe54b, 0x0e43, 0x81d2, 0x06e7, 0x4b66, 0x36d0, 0x53d6, 0x2b68, 0x22ec, 0x3fa9, 0xc1a7, 0x9ad2, 0xa596, 0xb3ac, 0xdf42}, {0xe31f, 0x0b28, 0x5f3b, 0xc1ff, 0x344c, 0xbf5f, 0xd2ec, 0x2936, 0x9995, 0xdeb2, 0xae6c, 0x2852, 0xa2c6, 0xb306, 0x8120, 0xe305}, {0xa56e, 0xfb98, 0x1537, 0x4d85, 0x619e, 0x866c, 0x3cd4, 0x779a, 0xdd66, 0xa80d, 0xdc2f, 0xcae4, 0xc74c, 0x5175, 0xa65d, 0x605e}}, /* example doing 228 (g,(g-f)/2) steps; 537 divsteps */ {{0x8cd5, 0x376d, 0xd01b, 0x7176, 0x19ef, 0xcf09, 0x8403, 0x5e52, 0x83c1, 0x44de, 0xb91e, 0xb33d, 0xe15c, 0x51e7, 0xbad8, 0x6359}, {0x3b75, 0xf812, 0x5f9e, 0xa04e, 0x92d3, 0x226e, 0x540e, 0x7c9a, 0x31c6, 0x46d2, 0x0b7b, 0xdb4a, 0xe662, 0x4950, 0x0265, 0xf76f}, {0x09ed, 0x692f, 0xe8f1, 0x3482, 0xab54, 0x36b4, 0x8442, 0x6ae9, 0x4329, 0x6505, 0x183b, 0x1c1d, 0x482d, 0x7d63, 0xb44f, 0xcc09}}, /* Test cases with the group order as modulus. */ /* Test case with the group order as modulus, needing 635 divsteps. */ {{0x95ed, 0x6c01, 0xd113, 0x5ff1, 0xd7d0, 0x29cc, 0x5817, 0x6120, 0xca8e, 0xaad1, 0x25ae, 0x8e84, 0x9af6, 0x30bf, 0xf0ed, 0x1686}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x1631, 0xbf4a, 0x286a, 0x2716, 0x469f, 0x2ac8, 0x1312, 0xe9bc, 0x04f4, 0x304b, 0x9931, 0x113b, 0xd932, 0xc8f4, 0x0d0d, 0x01a1}}, /* example with group size as modulus needing 631 divsteps */ {{0x85ed, 0xc284, 0x9608, 0x3c56, 0x19b6, 0xbb5b, 0x2850, 0xdab7, 0xa7f5, 0xe9ab, 0x06a4, 0x5bbb, 0x1135, 0xa186, 0xc424, 0xc68b}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x8479, 0x450a, 0x8fa3, 0xde05, 0xb2f5, 0x7793, 0x7269, 0xbabb, 0xc3b3, 0xd49b, 0x3377, 0x03c6, 0xe694, 0xc760, 0xd3cb, 0x2811}}, /* example with group size as modulus needing 565 divsteps starting at delta=1/2 */ {{0x8432, 0x5ceb, 0xa847, 0x6f1e, 0x51dd, 0x535a, 0x6ddc, 0x70ce, 0x6e70, 0xc1f6, 0x18f2, 0x2a7e, 0xc8e7, 0x39f8, 0x7e96, 0xebbf}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x257e, 0x449f, 0x689f, 0x89aa, 0x3989, 0xb661, 0x376c, 0x1e32, 0x654c, 0xee2e, 0xf4e2, 0x33c8, 0x3f2f, 0x9716, 0x6046, 0xcaa3}}, /* Test case with the group size as modulus, needing 981 divsteps with broken eta handling. */ {{0xfeb9, 0xb877, 0xee41, 0x7fa3, 0x87da, 0x94c4, 0x9d04, 0xc5ae, 0x5708, 0x0994, 0xfc79, 0x0916, 0xbf32, 0x3ad8, 0xe11c, 0x5ca2}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0f12, 0x075e, 0xce1c, 0x6f92, 0xc80f, 0xca92, 0x9a04, 0x6126, 0x4b6c, 0x57d6, 0xca31, 0x97f3, 0x1f99, 0xf4fd, 0xda4d, 0x42ce}}, /* Test case with the group size as modulus, input = 0. */ {{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, /* Test case with the group size as modulus, input = 1. */ {{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, /* Test case with the group size as modulus, input = 2. */ {{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x20a1, 0x681b, 0x2f46, 0xdfe9, 0x501d, 0x57a4, 0x6e73, 0x5d57, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}}, /* Test case with the group size as modulus, input = group - 1. */ {{0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}}, /* Test cases with the field size as modulus. */ /* Test case with the field size as modulus, needing 637 divsteps. */ {{0x9ec3, 0x1919, 0xca84, 0x7c11, 0xf996, 0x06f3, 0x5408, 0x6688, 0x1320, 0xdb8a, 0x632a, 0x0dcb, 0x8a84, 0x6bee, 0x9c95, 0xe34e}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x18e5, 0x19b6, 0xdf92, 0x1aaa, 0x09fb, 0x8a3f, 0x52b0, 0x8701, 0xac0c, 0x2582, 0xda44, 0x9bcc, 0x6828, 0x1c53, 0xbd8f, 0xbd2c}}, /* example with field size as modulus needing 637 divsteps */ {{0xaec3, 0xa7cf, 0x2f2d, 0x0693, 0x5ad5, 0xa8ff, 0x7ec7, 0x30ff, 0x0c8b, 0xc242, 0xcab2, 0x063a, 0xf86e, 0x6057, 0x9cbd, 0xf6d8}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0310, 0x579d, 0xcb38, 0x9030, 0x3ded, 0x9bb9, 0x1234, 0x63ce, 0x0c63, 0x8e3d, 0xacfe, 0x3c20, 0xdc85, 0xf859, 0x919e, 0x1d45}}, /* example with field size as modulus needing 564 divsteps starting at delta=1/2 */ {{0x63ae, 0x8d10, 0x0071, 0xdb5c, 0xb454, 0x78d1, 0x744a, 0x5f8e, 0xe4d8, 0x87b1, 0x8e62, 0x9590, 0xcede, 0xa070, 0x36b4, 0x7f6f}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0xfdc8, 0xe8d5, 0xbe15, 0x9f86, 0xa5fe, 0xf18e, 0xa7ff, 0xd291, 0xf4c2, 0x9c87, 0xf150, 0x073e, 0x69b8, 0xf7c4, 0xee4b, 0xc7e6}}, /* Test case with the field size as modulus, needing 935 divsteps with broken eta handling. */ {{0x1b37, 0xbdc3, 0x8bcd, 0x25e3, 0x1eae, 0x567d, 0x30b6, 0xf0d8, 0x9277, 0x0cf8, 0x9c2e, 0xecd7, 0x631d, 0xe38f, 0xd4f8, 0x5c93}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x1622, 0xe05b, 0xe880, 0x7de9, 0x3e45, 0xb682, 0xee6c, 0x67ed, 0xa179, 0x15db, 0x6b0d, 0xa656, 0x7ccb, 0x8ef7, 0xa2ff, 0xe279}}, /* Test case with the field size as modulus, input = 0. */ {{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, /* Test case with the field size as modulus, input = 1. */ {{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}}, /* Test case with the field size as modulus, input = 2. */ {{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0xfe18, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}}, /* Test case with the field size as modulus, input = field - 1. */ {{0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}, {0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}}, /* Selected from a large number of random inputs to reach small/large * d/e values in various configurations. */ {{0x3a08, 0x23e1, 0x4d8c, 0xe606, 0x3263, 0x67af, 0x9bf1, 0x9d70, 0xf5fd, 0x12e4, 0x03c8, 0xb9ca, 0xe847, 0x8c5d, 0x6322, 0xbd30}, {0x8359, 0x59dd, 0x1831, 0x7c1a, 0x1e83, 0xaee1, 0x770d, 0xcea8, 0xfbb1, 0xeed6, 0x10b5, 0xe2c6, 0x36ea, 0xee17, 0xe32c, 0xffff}, {0x1727, 0x0f36, 0x6f85, 0x5d0c, 0xca6c, 0x3072, 0x9628, 0x5842, 0xcb44, 0x7c2b, 0xca4f, 0x62e5, 0x29b1, 0x6ffd, 0x9055, 0xc196}}, {{0x905d, 0x41c8, 0xa2ff, 0x295b, 0x72bb, 0x4679, 0x6d01, 0x2c98, 0xb3e0, 0xc537, 0xa310, 0xe07e, 0xe72f, 0x4999, 0x1148, 0xf65e}, {0x5b41, 0x4239, 0x3c37, 0x5130, 0x30e3, 0xff35, 0xc51f, 0x1a43, 0xdb23, 0x13cf, 0x9f49, 0xf70c, 0x5e70, 0xd411, 0x3005, 0xf8c6}, {0xc30e, 0x68f0, 0x201a, 0xe10c, 0x864a, 0x6243, 0xe946, 0x43ae, 0xf3f1, 0x52dc, 0x1f7f, 0x50d4, 0x2797, 0x064c, 0x5ca4, 0x90e3}}, {{0xf1b5, 0xc6e5, 0xd2c4, 0xff95, 0x27c5, 0x0c92, 0x5d19, 0x7ae5, 0x4fbe, 0x5438, 0x99e1, 0x880d, 0xd892, 0xa05c, 0x6ffd, 0x7eac}, {0x2153, 0xcc9d, 0xfc6c, 0x8358, 0x49a1, 0x01e2, 0xcef0, 0x4969, 0xd69a, 0x8cef, 0xf5b2, 0xfd95, 0xdcc2, 0x71f4, 0x6ae2, 0xceeb}, {0x9b2e, 0xcdc6, 0x0a5c, 0x7317, 0x9084, 0xe228, 0x56cf, 0xd512, 0x628a, 0xce21, 0x3473, 0x4e13, 0x8823, 0x1ed0, 0x34d0, 0xbfa3}}, {{0x5bae, 0x53e5, 0x5f4d, 0x21ca, 0xb875, 0x8ecf, 0x9aa6, 0xbe3c, 0x9f96, 0x7b82, 0x375d, 0x4d3e, 0x491c, 0xb1eb, 0x04c9, 0xb6c8}, {0xfcfd, 0x10b7, 0x73b2, 0xd23b, 0xa357, 0x67da, 0x0d9f, 0x8702, 0xa037, 0xff8e, 0x0e8b, 0x1801, 0x2c5c, 0x4e6e, 0x4558, 0xfff2}, {0xc50f, 0x5654, 0x6713, 0x5ef5, 0xa7ce, 0xa647, 0xc832, 0x69ce, 0x1d5c, 0x4310, 0x0746, 0x5a01, 0x96ea, 0xde4b, 0xa88b, 0x5543}}, {{0xdc7f, 0x5e8c, 0x89d1, 0xb077, 0xd521, 0xcf90, 0x32fa, 0x5737, 0x839e, 0x1464, 0x007c, 0x09c6, 0x9371, 0xe8ea, 0xc1cb, 0x75c4}, {0xe3a3, 0x107f, 0xa82a, 0xa375, 0x4578, 0x60f4, 0x75c9, 0x5ee4, 0x3fd7, 0x2736, 0x2871, 0xd3d2, 0x5f1d, 0x1abb, 0xa764, 0xffff}, {0x45c6, 0x1f2e, 0xb14c, 0x84d7, 0x7bb7, 0x5a04, 0x0504, 0x3f33, 0x5cc1, 0xb07a, 0x6a6c, 0x786f, 0x647f, 0xe1d7, 0x78a2, 0x4cf4}}, {{0xc006, 0x356f, 0x8cd2, 0x967b, 0xb49e, 0x2d4e, 0x14bf, 0x4bcb, 0xddab, 0xd3f9, 0xa068, 0x2c1c, 0xd242, 0xa56d, 0xf2c7, 0x5f97}, {0x465b, 0xb745, 0x0e0d, 0x69a9, 0x987d, 0xcb37, 0xf637, 0xb311, 0xc4d6, 0x2ddb, 0xf68f, 0x2af9, 0x959d, 0x3f53, 0x98f2, 0xf640}, {0xc0f2, 0x6bfb, 0xf5c3, 0x91c1, 0x6b05, 0x0825, 0x5ca0, 0x7df7, 0x9d55, 0x6d9e, 0xfe94, 0x2ad9, 0xd9f0, 0xe68b, 0xa72b, 0xd1b2}}, {{0x2279, 0x61ba, 0x5bc6, 0x136b, 0xf544, 0x717c, 0xafda, 0x02bd, 0x79af, 0x1fad, 0xea09, 0x81bb, 0x932b, 0x32c9, 0xdf1d, 0xe576}, {0x8215, 0x7817, 0xca82, 0x43b0, 0x9b06, 0xea65, 0x1291, 0x0621, 0x0089, 0x46fe, 0xc5a6, 0xddd7, 0x8065, 0xc6a0, 0x214b, 0xfc64}, {0x04bf, 0x6f2a, 0x86b2, 0x841a, 0x4a95, 0xc632, 0x97b7, 0x5821, 0x2b18, 0x1bb0, 0x3e97, 0x935e, 0xcc7d, 0x066b, 0xd513, 0xc251}}, {{0x76e8, 0x5bc2, 0x3eaa, 0x04fc, 0x9974, 0x92c1, 0x7c15, 0xfa89, 0x1151, 0x36ee, 0x48b2, 0x049c, 0x5f16, 0xcee4, 0x925b, 0xe98e}, {0x913f, 0x0a2d, 0xa185, 0x9fea, 0xda5a, 0x4025, 0x40d7, 0x7cfa, 0x88ca, 0xbbe8, 0xb265, 0xb7e4, 0x6cb1, 0xed64, 0xc6f9, 0xffb5}, {0x6ab1, 0x1a86, 0x5009, 0x152b, 0x1cc4, 0xe2c8, 0x960b, 0x19d0, 0x3554, 0xc562, 0xd013, 0xcf91, 0x10e1, 0x7933, 0xe195, 0xcf49}}, {{0x9cb5, 0xd2d7, 0xc6ed, 0xa818, 0xb495, 0x06ee, 0x0f4a, 0x06e3, 0x4c5a, 0x80ce, 0xd49a, 0x4cd7, 0x7487, 0x92af, 0xe516, 0x676c}, {0xd6e9, 0x6b85, 0x619a, 0xb52c, 0x20a0, 0x2f79, 0x3545, 0x1edd, 0x5a6f, 0x8082, 0x9b80, 0xf8f8, 0xc78a, 0xd0a3, 0xadf4, 0xffff}, {0x01c2, 0x2118, 0xef5e, 0xa877, 0x046a, 0xd2c2, 0x2ad5, 0x951c, 0x8900, 0xa5c9, 0x8d0f, 0x6b61, 0x55d3, 0xd572, 0x48de, 0x9219}}, {{0x5114, 0x0644, 0x23dd, 0x01d3, 0xc101, 0xa659, 0xea17, 0x640f, 0xf767, 0x2644, 0x9cec, 0xd8ba, 0xd6da, 0x9156, 0x8aeb, 0x875a}, {0xc1bf, 0xdae9, 0xe96b, 0xce77, 0xf7a1, 0x3e99, 0x5c2e, 0x973b, 0xd048, 0x5bd0, 0x4e8a, 0xcb85, 0xce39, 0x37f5, 0x815d, 0xffff}, {0x48cc, 0x35b6, 0x26d4, 0x2ea6, 0x50d6, 0xa2f9, 0x64b6, 0x03bf, 0xd00c, 0xe057, 0x3343, 0xfb79, 0x3ce5, 0xf717, 0xc5af, 0xe185}}, {{0x13ff, 0x6c76, 0x2077, 0x16e0, 0xd5ca, 0xf2ad, 0x8dba, 0x8f49, 0x7887, 0x16f9, 0xb646, 0xfc87, 0xfa31, 0x5096, 0xf08c, 0x3fbe}, {0x8139, 0x6fd7, 0xf6df, 0xa7bf, 0x6699, 0x5361, 0x6f65, 0x13c8, 0xf4d1, 0xe28f, 0xc545, 0x0a8c, 0x5274, 0xb0a6, 0xffff, 0xffff}, {0x22ca, 0x0cd6, 0xc1b5, 0xb064, 0x44a7, 0x297b, 0x495f, 0x34ac, 0xfa95, 0xec62, 0xf08d, 0x621c, 0x66a6, 0xba94, 0x84c6, 0x8ee0}}, {{0xaa30, 0x312e, 0x439c, 0x4e88, 0x2e2f, 0x32dc, 0xb880, 0xa28e, 0xf795, 0xc910, 0xb406, 0x8dd7, 0xb187, 0xa5a5, 0x38f1, 0xe49e}, {0xfb19, 0xf64a, 0xba6a, 0x8ec2, 0x7255, 0xce89, 0x2cf9, 0x9cba, 0xe1fe, 0x50da, 0x1705, 0xac52, 0xe3d4, 0x4269, 0x0648, 0xfd77}, {0xb4c8, 0x6e8a, 0x2b5f, 0x4c2d, 0x5a67, 0xa7bb, 0x7d6d, 0x5569, 0xa0ea, 0x244a, 0xc0f2, 0xf73d, 0x58cf, 0xac7f, 0xd32b, 0x3018}}, {{0xc953, 0x1ae1, 0xae46, 0x8709, 0x19c2, 0xa986, 0x9abe, 0x1611, 0x0395, 0xd5ab, 0xf0f6, 0xb5b0, 0x5b2b, 0x0317, 0x80ba, 0x376d}, {0xfe77, 0xbc03, 0xac2f, 0x9d00, 0xa175, 0x293d, 0x3b56, 0x0e3a, 0x0a9c, 0xf40c, 0x690e, 0x1508, 0x95d4, 0xddc4, 0xe805, 0xffff}, {0xb1ce, 0x0929, 0xa5fe, 0x4b50, 0x9d5d, 0x8187, 0x2557, 0x4376, 0x11ba, 0xdcef, 0xc1f3, 0xd531, 0x1824, 0x93f6, 0xd81f, 0x8f83}}, {{0xb8d2, 0xb900, 0x4a0c, 0x7188, 0xa5bf, 0x1b0b, 0x2ae5, 0xa35b, 0x98e0, 0x610c, 0x86db, 0x2487, 0xa267, 0x002c, 0xebb6, 0xc5f4}, {0x9cdd, 0x1c1b, 0x2f06, 0x43d1, 0xce47, 0xc334, 0x6e60, 0xc016, 0x989e, 0x0ab2, 0x0cac, 0x1196, 0xe2d9, 0x2e04, 0xc62b, 0xffff}, {0xdc36, 0x1f05, 0x6aa9, 0x7a20, 0x944f, 0x2fd3, 0xa553, 0xdb4f, 0xbd5c, 0x3a75, 0x25d4, 0xe20e, 0xa387, 0x1410, 0xdbb1, 0x1b60}}, {{0x76b3, 0x2207, 0x4930, 0x5dd7, 0x65a0, 0xd55c, 0xb443, 0x53b7, 0x5c22, 0x818a, 0xb2e7, 0x9de8, 0x9985, 0xed45, 0x33b1, 0x53e8}, {0x7913, 0x44e1, 0xf15b, 0x5edd, 0x34f3, 0x4eba, 0x0758, 0x7104, 0x32d9, 0x28f3, 0x4401, 0x85c5, 0xb695, 0xb899, 0xc0f2, 0xffff}, {0x7f43, 0xd202, 0x24c9, 0x69f3, 0x74dc, 0x1a69, 0xeaee, 0x5405, 0x1755, 0x4bb8, 0x04e3, 0x2fd2, 0xada8, 0x39eb, 0x5b4d, 0x96ca}}, {{0x807b, 0x7112, 0xc088, 0xdafd, 0x02fa, 0x9d95, 0x5e42, 0xc033, 0xde0a, 0xeecf, 0x8e90, 0x8da1, 0xb17e, 0x9a5b, 0x4c6d, 0x1914}, {0x4871, 0xd1cb, 0x47d7, 0x327f, 0x09ec, 0x97bb, 0x2fae, 0xd346, 0x6b78, 0x3707, 0xfeb2, 0xa6ab, 0x13df, 0x76b0, 0x8fb9, 0xffb3}, {0x179e, 0xb63b, 0x4784, 0x231e, 0x9f42, 0x7f1a, 0xa3fb, 0xdd8c, 0xd1eb, 0xb4c9, 0x8ca7, 0x018c, 0xf691, 0x576c, 0xa7d6, 0xce27}}, {{0x5f45, 0x7c64, 0x083d, 0xedd5, 0x08a0, 0x0c64, 0x6c6f, 0xec3c, 0xe2fb, 0x352c, 0x9303, 0x75e4, 0xb4e0, 0x8b09, 0xaca4, 0x7025}, {0x1025, 0xb482, 0xfed5, 0xa678, 0x8966, 0x9359, 0x5329, 0x98bb, 0x85b2, 0x73ba, 0x9982, 0x6fdc, 0xf190, 0xbe8c, 0xdc5c, 0xfd93}, {0x83a2, 0x87a4, 0xa680, 0x52a1, 0x1ba1, 0x8848, 0x5db7, 0x9744, 0x409c, 0x0745, 0x0e1e, 0x1cfc, 0x00cd, 0xf573, 0x2071, 0xccaa}}, {{0xf61f, 0x63d4, 0x536c, 0x9eb9, 0x5ddd, 0xbb11, 0x9014, 0xe904, 0xfe01, 0x6b45, 0x1858, 0xcb5b, 0x4c38, 0x43e1, 0x381d, 0x7f94}, {0xf61f, 0x63d4, 0xd810, 0x7ca3, 0x8a04, 0x4b83, 0x11fc, 0xdf94, 0x4169, 0xbd05, 0x608e, 0x7151, 0x4fbf, 0xb31a, 0x38a7, 0xa29b}, {0xe621, 0xdfa5, 0x3d06, 0x1d03, 0x81e6, 0x00da, 0x53a6, 0x965e, 0x93e5, 0x2164, 0x5b61, 0x59b8, 0xa629, 0x8d73, 0x699a, 0x6111}}, {{0x4cc3, 0xd29e, 0xf4a3, 0x3428, 0x2048, 0xeec9, 0x5f50, 0x99a4, 0x6de9, 0x05f2, 0x5aa9, 0x5fd2, 0x98b4, 0x1adc, 0x225f, 0x777f}, {0xe649, 0x37da, 0x5ba6, 0x5765, 0x3f4a, 0x8a1c, 0x2e79, 0xf550, 0x1a54, 0xcd1e, 0x7218, 0x3c3c, 0x6311, 0xfe28, 0x95fb, 0xed97}, {0xe9b6, 0x0c47, 0x3f0e, 0x849b, 0x11f8, 0xe599, 0x5e4d, 0xd618, 0xa06d, 0x33a0, 0x9a3e, 0x44db, 0xded8, 0x10f0, 0x94d2, 0x81fb}}, {{0x2e59, 0x7025, 0xd413, 0x455a, 0x1ce3, 0xbd45, 0x7263, 0x27f7, 0x23e3, 0x518e, 0xbe06, 0xc8c4, 0xe332, 0x4276, 0x68b4, 0xb166}, {0x596f, 0x0cf6, 0xc8ec, 0x787b, 0x04c1, 0x473c, 0xd2b8, 0x8d54, 0x9cdf, 0x77f2, 0xd3f3, 0x6735, 0x0638, 0xf80e, 0x9467, 0xc6aa}, {0xc7e7, 0x1822, 0xb62a, 0xec0d, 0x89cd, 0x7846, 0xbfa2, 0x35d5, 0xfa38, 0x870f, 0x494b, 0x1697, 0x8b17, 0xf904, 0x10b6, 0x9822}}, {{0x6d5b, 0x1d4f, 0x0aaf, 0x807b, 0x35fb, 0x7ee8, 0x00c6, 0x059a, 0xddf0, 0x1fb1, 0xc38a, 0xd78e, 0x2aa4, 0x79e7, 0xad28, 0xc3f1}, {0xe3bb, 0x174e, 0xe0a8, 0x74b6, 0xbd5b, 0x35f6, 0x6d23, 0x6328, 0xc11f, 0x83e1, 0xf928, 0xa918, 0x838e, 0xbf43, 0xe243, 0xfffb}, {0x9cf2, 0x6b8b, 0x3476, 0x9d06, 0xdcf2, 0xdb8a, 0x89cd, 0x4857, 0x75c2, 0xabb8, 0x490b, 0xc9bd, 0x890e, 0xe36e, 0xd552, 0xfffa}}, {{0x2f09, 0x9d62, 0xa9fc, 0xf090, 0xd6d1, 0x9d1d, 0x1828, 0xe413, 0xc92b, 0x3d5a, 0x1373, 0x368c, 0xbaf2, 0x2158, 0x71eb, 0x08a3}, {0x2f09, 0x1d62, 0x4630, 0x0de1, 0x06dc, 0xf7f1, 0xc161, 0x1e92, 0x7495, 0x97e4, 0x94b6, 0xa39e, 0x4f1b, 0x18f8, 0x7bd4, 0x0c4c}, {0xeb3d, 0x723d, 0x0907, 0x525b, 0x463a, 0x49a8, 0xc6b8, 0xce7f, 0x740c, 0x0d7d, 0xa83b, 0x457f, 0xae8e, 0xc6af, 0xd331, 0x0475}}, {{0x6abd, 0xc7af, 0x3e4e, 0x95fd, 0x8fc4, 0xee25, 0x1f9c, 0x0afe, 0x291d, 0xcde0, 0x48f4, 0xb2e8, 0xf7af, 0x8f8d, 0x0bd6, 0x078d}, {0x4037, 0xbf0e, 0x2081, 0xf363, 0x13b2, 0x381e, 0xfb6e, 0x818e, 0x27e4, 0x5662, 0x18b0, 0x0cd2, 0x81f5, 0x9415, 0x0d6c, 0xf9fb}, {0xd205, 0x0981, 0x0498, 0x1f08, 0xdb93, 0x1732, 0x0579, 0x1424, 0xad95, 0x642f, 0x050c, 0x1d6d, 0xfc95, 0xfc4a, 0xd41b, 0x3521}}, {{0xf23a, 0x4633, 0xaef4, 0x1a92, 0x3c8b, 0x1f09, 0x30f3, 0x4c56, 0x2a2f, 0x4f62, 0xf5e4, 0x8329, 0x63cc, 0xb593, 0xec6a, 0xc428}, {0x93a7, 0xfcf6, 0x606d, 0xd4b2, 0x2aad, 0x28b4, 0xc65b, 0x8998, 0x4e08, 0xd178, 0x0900, 0xc82b, 0x7470, 0xa342, 0x7c0f, 0xffff}, {0x315f, 0xf304, 0xeb7b, 0xe5c3, 0x1451, 0x6311, 0x8f37, 0x93a8, 0x4a38, 0xa6c6, 0xe393, 0x1087, 0x6301, 0xd673, 0x4ec4, 0xffff}}, {{0x892e, 0xeed0, 0x1165, 0xcbc1, 0x5545, 0xa280, 0x7243, 0x10c9, 0x9536, 0x36af, 0xb3fc, 0x2d7c, 0xe8a5, 0x09d6, 0xe1d4, 0xe85d}, {0xae09, 0xc28a, 0xd777, 0xbd80, 0x23d6, 0xf980, 0xeb7c, 0x4e0e, 0xf7dc, 0x6475, 0xf10a, 0x2d33, 0x5dfd, 0x797a, 0x7f1c, 0xf71a}, {0x4064, 0x8717, 0xd091, 0x80b0, 0x4527, 0x8442, 0xac8b, 0x9614, 0xc633, 0x35f5, 0x7714, 0x2e83, 0x4aaa, 0xd2e4, 0x1acd, 0x0562}}, {{0xdb64, 0x0937, 0x308b, 0x53b0, 0x00e8, 0xc77f, 0x2f30, 0x37f7, 0x79ce, 0xeb7f, 0xde81, 0x9286, 0xafda, 0x0e62, 0xae00, 0x0067}, {0x2cc7, 0xd362, 0xb161, 0x0557, 0x4ff2, 0xb9c8, 0x06fe, 0x5f2b, 0xde33, 0x0190, 0x28c6, 0xb886, 0xee2b, 0x5a4e, 0x3289, 0x0185}, {0x4215, 0x923e, 0xf34f, 0xb362, 0x88f8, 0xceec, 0xafdd, 0x7f42, 0x0c57, 0x56b2, 0xa366, 0x6a08, 0x0826, 0xfb8f, 0x1b03, 0x0163}}, {{0xa4ba, 0x8408, 0x810a, 0xdeba, 0x47a3, 0x853a, 0xeb64, 0x2f74, 0x3039, 0x038c, 0x7fbb, 0x498e, 0xd1e9, 0x46fb, 0x5691, 0x32a4}, {0xd749, 0xb49d, 0x20b7, 0x2af6, 0xd34a, 0xd2da, 0x0a10, 0xf781, 0x58c9, 0x171f, 0x3cb6, 0x6337, 0x88cd, 0xcf1e, 0xb246, 0x7351}, {0xf729, 0xcf0a, 0x96ea, 0x032c, 0x4a8f, 0x42fe, 0xbac8, 0xec65, 0x1510, 0x0d75, 0x4c17, 0x8d29, 0xa03f, 0x8b7e, 0x2c49, 0x0000}}, {{0x0fa4, 0x8e1c, 0x3788, 0xba3c, 0x8d52, 0xd89d, 0x12c8, 0xeced, 0x9fe6, 0x9b88, 0xecf3, 0xe3c8, 0xac48, 0x76ed, 0xf23e, 0xda79}, {0x1103, 0x227c, 0x5b00, 0x3fcf, 0xc5d0, 0x2d28, 0x8020, 0x4d1c, 0xc6b9, 0x67f9, 0x6f39, 0x989a, 0xda53, 0x3847, 0xd416, 0xe0d0}, {0xdd8e, 0xcf31, 0x3710, 0x7e44, 0xa511, 0x933c, 0x0cc3, 0x5145, 0xf632, 0x5e1d, 0x038f, 0x5ce7, 0x7265, 0xda9d, 0xded6, 0x08f8}}, {{0xe2c8, 0x91d5, 0xa5f5, 0x735f, 0x6b58, 0x56dc, 0xb39d, 0x5c4a, 0x57d0, 0xa1c2, 0xd92f, 0x9ad4, 0xf7c4, 0x51dd, 0xaf5c, 0x0096}, {0x1739, 0x7207, 0x7505, 0xbf35, 0x42de, 0x0a29, 0xa962, 0xdedf, 0x53e8, 0x12bf, 0xcde7, 0xd8e2, 0x8d4d, 0x2c4b, 0xb1b1, 0x0628}, {0x992d, 0xe3a7, 0xb422, 0xc198, 0x23ab, 0xa6ef, 0xb45d, 0x50da, 0xa738, 0x014a, 0x2310, 0x85fb, 0x5fe8, 0x1b18, 0x1774, 0x03a7}}, {{0x1f16, 0x2b09, 0x0236, 0xee90, 0xccf9, 0x9775, 0x8130, 0x4c91, 0x9091, 0x310b, 0x6dc4, 0x86f6, 0xc2e8, 0xef60, 0xfc0e, 0xf3a4}, {0x9f49, 0xac15, 0x02af, 0x110f, 0xc59d, 0x5677, 0xa1a9, 0x38d5, 0x914f, 0xa909, 0x3a3a, 0x4a39, 0x3703, 0xea30, 0x73da, 0xffad}, {0x15ed, 0xdd16, 0x83c7, 0x270a, 0x862f, 0xd8ad, 0xcaa1, 0x5f41, 0x99a9, 0x3fc8, 0x7bb2, 0x360a, 0xb06d, 0xfadc, 0x1b36, 0xffa8}}, {{0xc4e0, 0xb8fd, 0x5106, 0xe169, 0x754c, 0xa58c, 0xc413, 0x8224, 0x5483, 0x63ec, 0xd477, 0x8473, 0x4778, 0x9281, 0x0000, 0x0000}, {0x85e1, 0xff54, 0xb200, 0xe413, 0xf4f4, 0x4c0f, 0xfcec, 0xc183, 0x60d3, 0x1b0c, 0x3834, 0x601c, 0x943c, 0xbe6e, 0x0002, 0x0000}, {0xf4f8, 0xfd5e, 0x61ef, 0xece8, 0x9199, 0xe5c4, 0x05a6, 0xe6c3, 0xc4ae, 0x8b28, 0x66b1, 0x8a95, 0x9ece, 0x8f4a, 0x0001, 0x0000}}, {{0xeae9, 0xa1b4, 0xc6d8, 0x2411, 0x2b5a, 0x1dd0, 0x2dc9, 0xb57b, 0x5ccd, 0x4957, 0xaf59, 0xa04b, 0x5f42, 0xab7c, 0x2826, 0x526f}, {0xf407, 0x165a, 0xb724, 0x2f12, 0x2ea1, 0x470b, 0x4464, 0xbd35, 0x606f, 0xd73e, 0x50d3, 0x8a7f, 0x8029, 0x7ffc, 0xbe31, 0x6cfb}, {0x8171, 0x1f4c, 0xced2, 0x9c99, 0x6d7e, 0x5a0f, 0xfefb, 0x59e3, 0xa0c8, 0xabd9, 0xc4c5, 0x57d3, 0xbfa3, 0x4f11, 0x96a2, 0x5a7d}}, {{0xe068, 0x4cc0, 0x8bcd, 0xc903, 0x9e52, 0xb3e1, 0xd745, 0x0995, 0xdd8f, 0xf14b, 0xd2ac, 0xd65a, 0xda1d, 0xa742, 0xbac5, 0x474c}, {0x7481, 0xf2ad, 0x9757, 0x2d82, 0xb683, 0xb16b, 0x0002, 0x7b60, 0x8f0c, 0x2594, 0x8f64, 0x3b7a, 0x3552, 0x8d9d, 0xb9d7, 0x67eb}, {0xcaab, 0xb9a1, 0xf966, 0xe311, 0x5b34, 0x0fa0, 0x6abc, 0x8134, 0xab3d, 0x90f6, 0x1984, 0x9232, 0xec17, 0x74e5, 0x2ceb, 0x434e}}, {{0x0fb1, 0x7a55, 0x1a5c, 0x53eb, 0xd7b3, 0x7a01, 0xca32, 0x31f6, 0x3b74, 0x679e, 0x1501, 0x6c57, 0xdb20, 0x8b7c, 0xd7d0, 0x8097}, {0xb127, 0xb20c, 0xe3a2, 0x96f3, 0xe0d8, 0xd50c, 0x14b4, 0x0b40, 0x6eeb, 0xa258, 0x99db, 0x3c8c, 0x0f51, 0x4198, 0x3887, 0xffd0}, {0x0273, 0x9f8c, 0x9669, 0xbbba, 0x1c49, 0x767c, 0xc2af, 0x59f0, 0x1366, 0xd397, 0x63ac, 0x6fe8, 0x1a9a, 0x1259, 0x01d0, 0x0016}}, {{0x7876, 0x2a35, 0xa24a, 0x433e, 0x5501, 0x573c, 0xd76d, 0xcb82, 0x1334, 0xb4a6, 0xf290, 0xc797, 0xeae9, 0x2b83, 0x1e2b, 0x8b14}, {0x3885, 0x8aef, 0x9dea, 0x2b8c, 0xdd7c, 0xd7cd, 0xb0cc, 0x05ee, 0x361b, 0x3800, 0xb0d4, 0x4c23, 0xbd3f, 0x5180, 0x9783, 0xff80}, {0xab36, 0x3104, 0xdae8, 0x0704, 0x4a28, 0x6714, 0x824b, 0x0051, 0x8134, 0x1f6a, 0x712d, 0x1f03, 0x03b2, 0xecac, 0x377d, 0xfef9}} }; int i, j, ok; /* Test known inputs/outputs */ for (i = 0; (size_t)i < sizeof(CASES) / sizeof(CASES[0]); ++i) { uint16_t out[16]; test_modinv32_uint16(out, CASES[i][0], CASES[i][1]); for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]); #ifdef SECP256K1_WIDEMUL_INT128 test_modinv64_uint16(out, CASES[i][0], CASES[i][1]); for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]); #endif } for (i = 0; i < 100 * count; ++i) { /* 256-bit numbers in 16-uint16_t's notation */ static const uint16_t ZERO[16] = {0}; uint16_t xd[16]; /* the number (in range [0,2^256)) to be inverted */ uint16_t md[16]; /* the modulus (odd, in range [3,2^256)) */ uint16_t id[16]; /* the inverse of xd mod md */ /* generate random xd and md, so that md is odd, md>1, xd 256) { now = 256 - i; } rustsecp256k1_v0_5_0_scalar_set_int(&t, rustsecp256k1_v0_5_0_scalar_get_bits_var(&s, 256 - now - i, now)); for (j = 0; j < now; j++) { rustsecp256k1_v0_5_0_scalar_add(&n, &n, &n); } rustsecp256k1_v0_5_0_scalar_add(&n, &n, &t); i += now; } CHECK(rustsecp256k1_v0_5_0_scalar_eq(&n, &s)); } { /* test rustsecp256k1_v0_5_0_scalar_shr_int */ rustsecp256k1_v0_5_0_scalar r; int i; random_scalar_order_test(&r); for (i = 0; i < 100; ++i) { int low; int shift = 1 + rustsecp256k1_v0_5_0_testrand_int(15); int expected = r.d[0] % (1 << shift); low = rustsecp256k1_v0_5_0_scalar_shr_int(&r, shift); CHECK(expected == low); } } { /* Test commutativity of add. */ rustsecp256k1_v0_5_0_scalar r1, r2; rustsecp256k1_v0_5_0_scalar_add(&r1, &s1, &s2); rustsecp256k1_v0_5_0_scalar_add(&r2, &s2, &s1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } { rustsecp256k1_v0_5_0_scalar r1, r2; rustsecp256k1_v0_5_0_scalar b; int i; /* Test add_bit. */ int bit = rustsecp256k1_v0_5_0_testrand_bits(8); rustsecp256k1_v0_5_0_scalar_set_int(&b, 1); CHECK(rustsecp256k1_v0_5_0_scalar_is_one(&b)); for (i = 0; i < bit; i++) { rustsecp256k1_v0_5_0_scalar_add(&b, &b, &b); } r1 = s1; r2 = s1; if (!rustsecp256k1_v0_5_0_scalar_add(&r1, &r1, &b)) { /* No overflow happened. */ rustsecp256k1_v0_5_0_scalar_cadd_bit(&r2, bit, 1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); /* cadd is a noop when flag is zero */ rustsecp256k1_v0_5_0_scalar_cadd_bit(&r2, bit, 0); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } } { /* Test commutativity of mul. */ rustsecp256k1_v0_5_0_scalar r1, r2; rustsecp256k1_v0_5_0_scalar_mul(&r1, &s1, &s2); rustsecp256k1_v0_5_0_scalar_mul(&r2, &s2, &s1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } { /* Test associativity of add. */ rustsecp256k1_v0_5_0_scalar r1, r2; rustsecp256k1_v0_5_0_scalar_add(&r1, &s1, &s2); rustsecp256k1_v0_5_0_scalar_add(&r1, &r1, &s); rustsecp256k1_v0_5_0_scalar_add(&r2, &s2, &s); rustsecp256k1_v0_5_0_scalar_add(&r2, &s1, &r2); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } { /* Test associativity of mul. */ rustsecp256k1_v0_5_0_scalar r1, r2; rustsecp256k1_v0_5_0_scalar_mul(&r1, &s1, &s2); rustsecp256k1_v0_5_0_scalar_mul(&r1, &r1, &s); rustsecp256k1_v0_5_0_scalar_mul(&r2, &s2, &s); rustsecp256k1_v0_5_0_scalar_mul(&r2, &s1, &r2); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } { /* Test distributitivity of mul over add. */ rustsecp256k1_v0_5_0_scalar r1, r2, t; rustsecp256k1_v0_5_0_scalar_add(&r1, &s1, &s2); rustsecp256k1_v0_5_0_scalar_mul(&r1, &r1, &s); rustsecp256k1_v0_5_0_scalar_mul(&r2, &s1, &s); rustsecp256k1_v0_5_0_scalar_mul(&t, &s2, &s); rustsecp256k1_v0_5_0_scalar_add(&r2, &r2, &t); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &r2)); } { /* Test multiplicative identity. */ rustsecp256k1_v0_5_0_scalar r1, v1; rustsecp256k1_v0_5_0_scalar_set_int(&v1,1); rustsecp256k1_v0_5_0_scalar_mul(&r1, &s1, &v1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &s1)); } { /* Test additive identity. */ rustsecp256k1_v0_5_0_scalar r1, v0; rustsecp256k1_v0_5_0_scalar_set_int(&v0,0); rustsecp256k1_v0_5_0_scalar_add(&r1, &s1, &v0); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &s1)); } { /* Test zero product property. */ rustsecp256k1_v0_5_0_scalar r1, v0; rustsecp256k1_v0_5_0_scalar_set_int(&v0,0); rustsecp256k1_v0_5_0_scalar_mul(&r1, &s1, &v0); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &v0)); } } void run_scalar_set_b32_seckey_tests(void) { unsigned char b32[32]; rustsecp256k1_v0_5_0_scalar s1; rustsecp256k1_v0_5_0_scalar s2; /* Usually set_b32 and set_b32_seckey give the same result */ random_scalar_order_b32(b32); rustsecp256k1_v0_5_0_scalar_set_b32(&s1, b32, NULL); CHECK(rustsecp256k1_v0_5_0_scalar_set_b32_seckey(&s2, b32) == 1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&s1, &s2) == 1); memset(b32, 0, sizeof(b32)); CHECK(rustsecp256k1_v0_5_0_scalar_set_b32_seckey(&s2, b32) == 0); memset(b32, 0xFF, sizeof(b32)); CHECK(rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_scalar s, o; rustsecp256k1_v0_5_0_scalar_set_int(&s, 1); CHECK(rustsecp256k1_v0_5_0_scalar_is_one(&s)); rustsecp256k1_v0_5_0_scalar_negate(&o, &s); rustsecp256k1_v0_5_0_scalar_add(&o, &o, &s); CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&o)); rustsecp256k1_v0_5_0_scalar_negate(&o, &o); CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&o)); } { /* Does check_overflow check catch all ones? */ static const rustsecp256k1_v0_5_0_scalar overflowed = SECP256K1_SCALAR_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); CHECK(rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_scalar x; rustsecp256k1_v0_5_0_scalar y; rustsecp256k1_v0_5_0_scalar z; rustsecp256k1_v0_5_0_scalar zz; rustsecp256k1_v0_5_0_scalar one; rustsecp256k1_v0_5_0_scalar r1; rustsecp256k1_v0_5_0_scalar r2; rustsecp256k1_v0_5_0_scalar zzv; 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}} }; rustsecp256k1_v0_5_0_scalar_set_int(&one, 1); for (i = 0; i < 33; i++) { rustsecp256k1_v0_5_0_scalar_set_b32(&x, chal[i][0], &overflow); CHECK(!overflow); rustsecp256k1_v0_5_0_scalar_set_b32(&y, chal[i][1], &overflow); CHECK(!overflow); rustsecp256k1_v0_5_0_scalar_set_b32(&r1, res[i][0], &overflow); CHECK(!overflow); rustsecp256k1_v0_5_0_scalar_set_b32(&r2, res[i][1], &overflow); CHECK(!overflow); rustsecp256k1_v0_5_0_scalar_mul(&z, &x, &y); CHECK(!rustsecp256k1_v0_5_0_scalar_check_overflow(&z)); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&r1, &z)); if (!rustsecp256k1_v0_5_0_scalar_is_zero(&y)) { rustsecp256k1_v0_5_0_scalar_inverse(&zz, &y); CHECK(!rustsecp256k1_v0_5_0_scalar_check_overflow(&zz)); rustsecp256k1_v0_5_0_scalar_inverse_var(&zzv, &y); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&zzv, &zz)); rustsecp256k1_v0_5_0_scalar_mul(&z, &z, &zz); CHECK(!rustsecp256k1_v0_5_0_scalar_check_overflow(&z)); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&x, &z)); rustsecp256k1_v0_5_0_scalar_mul(&zz, &zz, &y); CHECK(!rustsecp256k1_v0_5_0_scalar_check_overflow(&zz)); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&one, &zz)); } } } } /***** FIELD TESTS *****/ void random_fe(rustsecp256k1_v0_5_0_fe *x) { unsigned char bin[32]; do { rustsecp256k1_v0_5_0_testrand256(bin); if (rustsecp256k1_v0_5_0_fe_set_b32(x, bin)) { return; } } while(1); } void random_fe_test(rustsecp256k1_v0_5_0_fe *x) { unsigned char bin[32]; do { rustsecp256k1_v0_5_0_testrand256_test(bin); if (rustsecp256k1_v0_5_0_fe_set_b32(x, bin)) { return; } } while(1); } void random_fe_non_zero(rustsecp256k1_v0_5_0_fe *nz) { int tries = 10; while (--tries >= 0) { random_fe(nz); rustsecp256k1_v0_5_0_fe_normalize(nz); if (!rustsecp256k1_v0_5_0_fe_is_zero(nz)) { break; } } /* Infinitesimal probability of spurious failure here */ CHECK(tries >= 0); } void random_fe_non_square(rustsecp256k1_v0_5_0_fe *ns) { rustsecp256k1_v0_5_0_fe r; random_fe_non_zero(ns); if (rustsecp256k1_v0_5_0_fe_sqrt(&r, ns)) { rustsecp256k1_v0_5_0_fe_negate(ns, ns, 1); } } int check_fe_equal(const rustsecp256k1_v0_5_0_fe *a, const rustsecp256k1_v0_5_0_fe *b) { rustsecp256k1_v0_5_0_fe an = *a; rustsecp256k1_v0_5_0_fe bn = *b; rustsecp256k1_v0_5_0_fe_normalize_weak(&an); rustsecp256k1_v0_5_0_fe_normalize_var(&bn); return rustsecp256k1_v0_5_0_fe_equal_var(&an, &bn); } 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 rustsecp256k1_v0_5_0_fe_storage fes = SECP256K1_FE_STORAGE_CONST( 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL ); static const rustsecp256k1_v0_5_0_fe fe = SECP256K1_FE_CONST( 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL ); rustsecp256k1_v0_5_0_fe fe2; unsigned char b322[32]; rustsecp256k1_v0_5_0_fe_storage fes2; /* Check conversions to fe. */ CHECK(rustsecp256k1_v0_5_0_fe_set_b32(&fe2, b32)); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&fe, &fe2)); rustsecp256k1_v0_5_0_fe_from_storage(&fe2, &fes); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&fe, &fe2)); /* Check conversion from fe. */ rustsecp256k1_v0_5_0_fe_get_b32(b322, &fe); CHECK(rustsecp256k1_v0_5_0_memcmp_var(b322, b32, 32) == 0); rustsecp256k1_v0_5_0_fe_to_storage(&fes2, &fe); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&fes2, &fes, sizeof(fes)) == 0); } /* Returns true if two field elements have the same representation. */ int fe_identical(const rustsecp256k1_v0_5_0_fe *a, const rustsecp256k1_v0_5_0_fe *b) { int ret = 1; #ifdef VERIFY ret &= (a->magnitude == b->magnitude); ret &= (a->normalized == b->normalized); #endif /* Compare the struct member that holds the limbs. */ ret &= (rustsecp256k1_v0_5_0_memcmp_var(a->n, b->n, sizeof(a->n)) == 0); return ret; } void run_field_misc(void) { rustsecp256k1_v0_5_0_fe x; rustsecp256k1_v0_5_0_fe y; rustsecp256k1_v0_5_0_fe z; rustsecp256k1_v0_5_0_fe q; rustsecp256k1_v0_5_0_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5); int i, j; for (i = 0; i < 5*count; i++) { rustsecp256k1_v0_5_0_fe_storage xs, ys, zs; random_fe(&x); random_fe_non_zero(&y); /* Test the fe equality and comparison operations. */ CHECK(rustsecp256k1_v0_5_0_fe_cmp_var(&x, &x) == 0); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&x, &x)); z = x; rustsecp256k1_v0_5_0_fe_add(&z,&y); /* Test fe conditional move; z is not normalized here. */ q = x; rustsecp256k1_v0_5_0_fe_cmov(&x, &z, 0); #ifdef VERIFY CHECK(x.normalized && x.magnitude == 1); #endif rustsecp256k1_v0_5_0_fe_cmov(&x, &x, 1); CHECK(!fe_identical(&x, &z)); CHECK(fe_identical(&x, &q)); rustsecp256k1_v0_5_0_fe_cmov(&q, &z, 1); #ifdef VERIFY CHECK(!q.normalized && q.magnitude == z.magnitude); #endif CHECK(fe_identical(&q, &z)); rustsecp256k1_v0_5_0_fe_normalize_var(&x); rustsecp256k1_v0_5_0_fe_normalize_var(&z); CHECK(!rustsecp256k1_v0_5_0_fe_equal_var(&x, &z)); rustsecp256k1_v0_5_0_fe_normalize_var(&q); rustsecp256k1_v0_5_0_fe_cmov(&q, &z, (i&1)); #ifdef VERIFY CHECK(q.normalized && q.magnitude == 1); #endif for (j = 0; j < 6; j++) { rustsecp256k1_v0_5_0_fe_negate(&z, &z, j+1); rustsecp256k1_v0_5_0_fe_normalize_var(&q); rustsecp256k1_v0_5_0_fe_cmov(&q, &z, (j&1)); #ifdef VERIFY CHECK((q.normalized != (j&1)) && q.magnitude == ((j&1) ? z.magnitude : 1)); #endif } rustsecp256k1_v0_5_0_fe_normalize_var(&z); /* Test storage conversion and conditional moves. */ rustsecp256k1_v0_5_0_fe_to_storage(&xs, &x); rustsecp256k1_v0_5_0_fe_to_storage(&ys, &y); rustsecp256k1_v0_5_0_fe_to_storage(&zs, &z); rustsecp256k1_v0_5_0_fe_storage_cmov(&zs, &xs, 0); rustsecp256k1_v0_5_0_fe_storage_cmov(&zs, &zs, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&xs, &zs, sizeof(xs)) != 0); rustsecp256k1_v0_5_0_fe_storage_cmov(&ys, &xs, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&xs, &ys, sizeof(xs)) == 0); rustsecp256k1_v0_5_0_fe_from_storage(&x, &xs); rustsecp256k1_v0_5_0_fe_from_storage(&y, &ys); rustsecp256k1_v0_5_0_fe_from_storage(&z, &zs); /* Test that mul_int, mul, and add agree. */ rustsecp256k1_v0_5_0_fe_add(&y, &x); rustsecp256k1_v0_5_0_fe_add(&y, &x); z = x; rustsecp256k1_v0_5_0_fe_mul_int(&z, 3); CHECK(check_fe_equal(&y, &z)); rustsecp256k1_v0_5_0_fe_add(&y, &x); rustsecp256k1_v0_5_0_fe_add(&z, &x); CHECK(check_fe_equal(&z, &y)); z = x; rustsecp256k1_v0_5_0_fe_mul_int(&z, 5); rustsecp256k1_v0_5_0_fe_mul(&q, &x, &fe5); CHECK(check_fe_equal(&z, &q)); rustsecp256k1_v0_5_0_fe_negate(&x, &x, 1); rustsecp256k1_v0_5_0_fe_add(&z, &x); rustsecp256k1_v0_5_0_fe_add(&q, &x); CHECK(check_fe_equal(&y, &z)); CHECK(check_fe_equal(&q, &y)); } } void test_fe_mul(const rustsecp256k1_v0_5_0_fe* a, const rustsecp256k1_v0_5_0_fe* b, int use_sqr) { rustsecp256k1_v0_5_0_fe c, an, bn; /* Variables in BE 32-byte format. */ unsigned char a32[32], b32[32], c32[32]; /* Variables in LE 16x uint16_t format. */ uint16_t a16[16], b16[16], c16[16]; /* Field modulus in LE 16x uint16_t format. */ static const uint16_t m16[16] = { 0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, }; uint16_t t16[32]; int i; /* Compute C = A * B in fe format. */ c = *a; if (use_sqr) { rustsecp256k1_v0_5_0_fe_sqr(&c, &c); } else { rustsecp256k1_v0_5_0_fe_mul(&c, &c, b); } /* Convert A, B, C into LE 16x uint16_t format. */ an = *a; bn = *b; rustsecp256k1_v0_5_0_fe_normalize_var(&c); rustsecp256k1_v0_5_0_fe_normalize_var(&an); rustsecp256k1_v0_5_0_fe_normalize_var(&bn); rustsecp256k1_v0_5_0_fe_get_b32(a32, &an); rustsecp256k1_v0_5_0_fe_get_b32(b32, &bn); rustsecp256k1_v0_5_0_fe_get_b32(c32, &c); for (i = 0; i < 16; ++i) { a16[i] = a32[31 - 2*i] + ((uint16_t)a32[30 - 2*i] << 8); b16[i] = b32[31 - 2*i] + ((uint16_t)b32[30 - 2*i] << 8); c16[i] = c32[31 - 2*i] + ((uint16_t)c32[30 - 2*i] << 8); } /* Compute T = A * B in LE 16x uint16_t format. */ mulmod256(t16, a16, b16, m16); /* Compare */ CHECK(rustsecp256k1_v0_5_0_memcmp_var(t16, c16, 32) == 0); } void run_fe_mul(void) { int i; for (i = 0; i < 100 * count; ++i) { rustsecp256k1_v0_5_0_fe a, b, c, d; random_fe(&a); random_field_element_magnitude(&a); random_fe(&b); random_field_element_magnitude(&b); random_fe_test(&c); random_field_element_magnitude(&c); random_fe_test(&d); random_field_element_magnitude(&d); test_fe_mul(&a, &a, 1); test_fe_mul(&c, &c, 1); test_fe_mul(&a, &b, 0); test_fe_mul(&a, &c, 0); test_fe_mul(&c, &b, 0); test_fe_mul(&c, &d, 0); } } void run_sqr(void) { rustsecp256k1_v0_5_0_fe x, s; { int i; rustsecp256k1_v0_5_0_fe_set_int(&x, 1); rustsecp256k1_v0_5_0_fe_negate(&x, &x, 1); for (i = 1; i <= 512; ++i) { rustsecp256k1_v0_5_0_fe_mul_int(&x, 2); rustsecp256k1_v0_5_0_fe_normalize(&x); rustsecp256k1_v0_5_0_fe_sqr(&s, &x); } } } void test_sqrt(const rustsecp256k1_v0_5_0_fe *a, const rustsecp256k1_v0_5_0_fe *k) { rustsecp256k1_v0_5_0_fe r1, r2; int v = rustsecp256k1_v0_5_0_fe_sqrt(&r1, a); CHECK((v == 0) == (k == NULL)); if (k != NULL) { /* Check that the returned root is +/- the given known answer */ rustsecp256k1_v0_5_0_fe_negate(&r2, &r1, 1); rustsecp256k1_v0_5_0_fe_add(&r1, k); rustsecp256k1_v0_5_0_fe_add(&r2, k); rustsecp256k1_v0_5_0_fe_normalize(&r1); rustsecp256k1_v0_5_0_fe_normalize(&r2); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&r1) || rustsecp256k1_v0_5_0_fe_is_zero(&r2)); } } void run_sqrt(void) { rustsecp256k1_v0_5_0_fe ns, x, s, t; int i; /* Check sqrt(0) is 0 */ rustsecp256k1_v0_5_0_fe_set_int(&x, 0); rustsecp256k1_v0_5_0_fe_sqr(&s, &x); test_sqrt(&s, &x); /* Check sqrt of small squares (and their negatives) */ for (i = 1; i <= 100; i++) { rustsecp256k1_v0_5_0_fe_set_int(&x, i); rustsecp256k1_v0_5_0_fe_sqr(&s, &x); test_sqrt(&s, &x); rustsecp256k1_v0_5_0_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); rustsecp256k1_v0_5_0_fe_sqr(&s, &x); test_sqrt(&s, &x); rustsecp256k1_v0_5_0_fe_negate(&t, &s, 1); test_sqrt(&t, NULL); rustsecp256k1_v0_5_0_fe_mul(&t, &s, &ns); test_sqrt(&t, NULL); } } } /***** FIELD/SCALAR INVERSE TESTS *****/ static const rustsecp256k1_v0_5_0_scalar scalar_minus_one = SECP256K1_SCALAR_CONST( 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xBAAEDCE6, 0xAF48A03B, 0xBFD25E8C, 0xD0364140 ); static const rustsecp256k1_v0_5_0_fe fe_minus_one = SECP256K1_FE_CONST( 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFC2E ); /* These tests test the following identities: * * for x==0: 1/x == 0 * for x!=0: x*(1/x) == 1 * for x!=0 and x!=1: 1/(1/x - 1) + 1 == -1/(x-1) */ void test_inverse_scalar(rustsecp256k1_v0_5_0_scalar* out, const rustsecp256k1_v0_5_0_scalar* x, int var) { rustsecp256k1_v0_5_0_scalar l, r, t; (var ? rustsecp256k1_v0_5_0_scalar_inverse_var : rustsecp256k1_v0_5_0_scalar_inverse)(&l, x); /* l = 1/x */ if (out) *out = l; if (rustsecp256k1_v0_5_0_scalar_is_zero(x)) { CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&l)); return; } rustsecp256k1_v0_5_0_scalar_mul(&t, x, &l); /* t = x*(1/x) */ CHECK(rustsecp256k1_v0_5_0_scalar_is_one(&t)); /* x*(1/x) == 1 */ rustsecp256k1_v0_5_0_scalar_add(&r, x, &scalar_minus_one); /* r = x-1 */ if (rustsecp256k1_v0_5_0_scalar_is_zero(&r)) return; (var ? rustsecp256k1_v0_5_0_scalar_inverse_var : rustsecp256k1_v0_5_0_scalar_inverse)(&r, &r); /* r = 1/(x-1) */ rustsecp256k1_v0_5_0_scalar_add(&l, &scalar_minus_one, &l); /* l = 1/x-1 */ (var ? rustsecp256k1_v0_5_0_scalar_inverse_var : rustsecp256k1_v0_5_0_scalar_inverse)(&l, &l); /* l = 1/(1/x-1) */ rustsecp256k1_v0_5_0_scalar_add(&l, &l, &rustsecp256k1_v0_5_0_scalar_one); /* l = 1/(1/x-1)+1 */ rustsecp256k1_v0_5_0_scalar_add(&l, &r, &l); /* l = 1/(1/x-1)+1 + 1/(x-1) */ CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&l)); /* l == 0 */ } void test_inverse_field(rustsecp256k1_v0_5_0_fe* out, const rustsecp256k1_v0_5_0_fe* x, int var) { rustsecp256k1_v0_5_0_fe l, r, t; (var ? rustsecp256k1_v0_5_0_fe_inv_var : rustsecp256k1_v0_5_0_fe_inv)(&l, x) ; /* l = 1/x */ if (out) *out = l; t = *x; /* t = x */ if (rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&t)) { CHECK(rustsecp256k1_v0_5_0_fe_normalizes_to_zero(&l)); return; } rustsecp256k1_v0_5_0_fe_mul(&t, x, &l); /* t = x*(1/x) */ rustsecp256k1_v0_5_0_fe_add(&t, &fe_minus_one); /* t = x*(1/x)-1 */ CHECK(rustsecp256k1_v0_5_0_fe_normalizes_to_zero(&t)); /* x*(1/x)-1 == 0 */ r = *x; /* r = x */ rustsecp256k1_v0_5_0_fe_add(&r, &fe_minus_one); /* r = x-1 */ if (rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&r)) return; (var ? rustsecp256k1_v0_5_0_fe_inv_var : rustsecp256k1_v0_5_0_fe_inv)(&r, &r); /* r = 1/(x-1) */ rustsecp256k1_v0_5_0_fe_add(&l, &fe_minus_one); /* l = 1/x-1 */ (var ? rustsecp256k1_v0_5_0_fe_inv_var : rustsecp256k1_v0_5_0_fe_inv)(&l, &l); /* l = 1/(1/x-1) */ rustsecp256k1_v0_5_0_fe_add(&l, &rustsecp256k1_v0_5_0_fe_one); /* l = 1/(1/x-1)+1 */ rustsecp256k1_v0_5_0_fe_add(&l, &r); /* l = 1/(1/x-1)+1 + 1/(x-1) */ CHECK(rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&l)); /* l == 0 */ } void run_inverse_tests(void) { /* Fixed test cases for field inverses: pairs of (x, 1/x) mod p. */ static const rustsecp256k1_v0_5_0_fe fe_cases[][2] = { /* 0 */ {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}, /* 1 */ {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1)}, /* -1 */ {SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e), SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e)}, /* 2 */ {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2), SECP256K1_FE_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7ffffe18)}, /* 2**128 */ {SECP256K1_FE_CONST(0, 0, 0, 1, 0, 0, 0, 0), SECP256K1_FE_CONST(0xbcb223fe, 0xdc24a059, 0xd838091d, 0xd2253530, 0xffffffff, 0xffffffff, 0xffffffff, 0x434dd931)}, /* Input known to need 637 divsteps */ {SECP256K1_FE_CONST(0xe34e9c95, 0x6bee8a84, 0x0dcb632a, 0xdb8a1320, 0x66885408, 0x06f3f996, 0x7c11ca84, 0x19199ec3), SECP256K1_FE_CONST(0xbd2cbd8f, 0x1c536828, 0x9bccda44, 0x2582ac0c, 0x870152b0, 0x8a3f09fb, 0x1aaadf92, 0x19b618e5)}, /* Input known to need 567 divsteps starting with delta=1/2. */ {SECP256K1_FE_CONST(0xf6bc3ba3, 0x636451c4, 0x3e46357d, 0x2c21d619, 0x0988e234, 0x15985661, 0x6672982b, 0xa7549bfc), SECP256K1_FE_CONST(0xb024fdc7, 0x5547451e, 0x426c585f, 0xbd481425, 0x73df6b75, 0xeef6d9d0, 0x389d87d4, 0xfbb440ba)}, /* Input known to need 566 divsteps starting with delta=1/2. */ {SECP256K1_FE_CONST(0xb595d81b, 0x2e3c1e2f, 0x482dbc65, 0xe4865af7, 0x9a0a50aa, 0x29f9e618, 0x6f87d7a5, 0x8d1063ae), SECP256K1_FE_CONST(0xc983337c, 0x5d5c74e1, 0x49918330, 0x0b53afb5, 0xa0428a0b, 0xce6eef86, 0x059bd8ef, 0xe5b908de)}, /* Set of 10 inputs accessing all 128 entries in the modinv32 divsteps_var table */ {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0xe0ff1f80, 0x1f000000, 0x00000000, 0x00000000, 0xfeff0100, 0x00000000), SECP256K1_FE_CONST(0x9faf9316, 0x77e5049d, 0x0b5e7a1b, 0xef70b893, 0x18c9e30c, 0x045e7fd7, 0x29eddf8c, 0xd62e9e3d)}, {SECP256K1_FE_CONST(0x621a538d, 0x511b2780, 0x35688252, 0x53f889a4, 0x6317c3ac, 0x32ba0a46, 0x6277c0d1, 0xccd31192), SECP256K1_FE_CONST(0x38513b0c, 0x5eba856f, 0xe29e882e, 0x9b394d8c, 0x34bda011, 0xeaa66943, 0x6a841a4c, 0x6ae8bcff)}, {SECP256K1_FE_CONST(0x00000200, 0xf0ffff1f, 0x00000000, 0x0000e0ff, 0xffffffff, 0xfffcffff, 0xffffffff, 0xffff0100), SECP256K1_FE_CONST(0x5da42a52, 0x3640de9e, 0x13e64343, 0x0c7591b7, 0x6c1e3519, 0xf048c5b6, 0x0484217c, 0xedbf8b2f)}, {SECP256K1_FE_CONST(0xd1343ef9, 0x4b952621, 0x7c52a2ee, 0x4ea1281b, 0x4ab46410, 0x9f26998d, 0xa686a8ff, 0x9f2103e8), SECP256K1_FE_CONST(0x84044385, 0x9a4619bf, 0x74e35b6d, 0xa47e0c46, 0x6b7fb47d, 0x9ffab128, 0xb0775aa3, 0xcb318bd1)}, {SECP256K1_FE_CONST(0xb27235d2, 0xc56a52be, 0x210db37a, 0xd50d23a4, 0xbe621bdd, 0x5df22c6a, 0xe926ba62, 0xd2e4e440), SECP256K1_FE_CONST(0x67a26e54, 0x483a9d3c, 0xa568469e, 0xd258ab3d, 0xb9ec9981, 0xdca9b1bd, 0x8d2775fe, 0x53ae429b)}, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00e0ffff, 0xffffff83, 0xffffffff, 0x3f00f00f, 0x000000e0, 0xffffffff), SECP256K1_FE_CONST(0x310e10f8, 0x23bbfab0, 0xac94907d, 0x076c9a45, 0x8d357d7f, 0xc763bcee, 0x00d0e615, 0x5a6acef6)}, {SECP256K1_FE_CONST(0xfeff0300, 0x001c0000, 0xf80700c0, 0x0ff0ffff, 0xffffffff, 0x0fffffff, 0xffff0100, 0x7f0000fe), SECP256K1_FE_CONST(0x28e2fdb4, 0x0709168b, 0x86f598b0, 0x3453a370, 0x530cf21f, 0x32f978d5, 0x1d527a71, 0x59269b0c)}, {SECP256K1_FE_CONST(0xc2591afa, 0x7bb98ef7, 0x090bb273, 0x85c14f87, 0xbb0b28e0, 0x54d3c453, 0x85c66753, 0xd5574d2f), SECP256K1_FE_CONST(0xfdca70a2, 0x70ce627c, 0x95e66fae, 0x848a6dbb, 0x07ffb15c, 0x5f63a058, 0xba4140ed, 0x6113b503)}, {SECP256K1_FE_CONST(0xf5475db3, 0xedc7b5a3, 0x411c047e, 0xeaeb452f, 0xc625828e, 0x1cf5ad27, 0x8eec1060, 0xc7d3e690), SECP256K1_FE_CONST(0x5eb756c0, 0xf963f4b9, 0xdc6a215e, 0xec8cc2d8, 0x2e9dec01, 0xde5eb88d, 0x6aba7164, 0xaecb2c5a)}, {SECP256K1_FE_CONST(0x00000000, 0x00f8ffff, 0xffffffff, 0x01000000, 0xe0ff1f00, 0x00000000, 0xffffff7f, 0x00000000), SECP256K1_FE_CONST(0xe0d2e3d8, 0x49b6157d, 0xe54e88c2, 0x1a7f02ca, 0x7dd28167, 0xf1125d81, 0x7bfa444e, 0xbe110037)}, /* Selection of randomly generated inputs that reach high/low d/e values in various configurations. */ {SECP256K1_FE_CONST(0x13cc08a4, 0xd8c41f0f, 0x179c3e67, 0x54c46c67, 0xc4109221, 0x09ab3b13, 0xe24d9be1, 0xffffe950), SECP256K1_FE_CONST(0xb80c8006, 0xd16abaa7, 0xcabd71e5, 0xcf6714f4, 0x966dd3d0, 0x64767a2d, 0xe92c4441, 0x51008cd1)}, {SECP256K1_FE_CONST(0xaa6db990, 0x95efbca1, 0x3cc6ff71, 0x0602e24a, 0xf49ff938, 0x99fffc16, 0x46f40993, 0xc6e72057), SECP256K1_FE_CONST(0xd5d3dd69, 0xb0c195e5, 0x285f1d49, 0xe639e48c, 0x9223f8a9, 0xca1d731d, 0x9ca482f9, 0xa5b93e06)}, {SECP256K1_FE_CONST(0x1c680eac, 0xaeabffd8, 0x9bdc4aee, 0x1781e3de, 0xa3b08108, 0x0015f2e0, 0x94449e1b, 0x2f67a058), SECP256K1_FE_CONST(0x7f083f8d, 0x31254f29, 0x6510f475, 0x245c373d, 0xc5622590, 0x4b323393, 0x32ed1719, 0xc127444b)}, {SECP256K1_FE_CONST(0x147d44b3, 0x012d83f8, 0xc160d386, 0x1a44a870, 0x9ba6be96, 0x8b962707, 0x267cbc1a, 0xb65b2f0a), SECP256K1_FE_CONST(0x555554ff, 0x170aef1e, 0x50a43002, 0xe51fbd36, 0xafadb458, 0x7a8aded1, 0x0ca6cd33, 0x6ed9087c)}, {SECP256K1_FE_CONST(0x12423796, 0x22f0fe61, 0xf9ca017c, 0x5384d107, 0xa1fbf3b2, 0x3b018013, 0x916a3c37, 0x4000b98c), SECP256K1_FE_CONST(0x20257700, 0x08668f94, 0x1177e306, 0x136c01f5, 0x8ed1fbd2, 0x95ec4589, 0xae38edb9, 0xfd19b6d7)}, {SECP256K1_FE_CONST(0xdcf2d030, 0x9ab42cb4, 0x93ffa181, 0xdcd23619, 0x39699b52, 0x08909a20, 0xb5a17695, 0x3a9dcf21), SECP256K1_FE_CONST(0x1f701dea, 0xe211fb1f, 0x4f37180d, 0x63a0f51c, 0x29fe1e40, 0xa40b6142, 0x2e7b12eb, 0x982b06b6)}, {SECP256K1_FE_CONST(0x79a851f6, 0xa6314ed3, 0xb35a55e6, 0xca1c7d7f, 0xe32369ea, 0xf902432e, 0x375308c5, 0xdfd5b600), SECP256K1_FE_CONST(0xcaae00c5, 0xe6b43851, 0x9dabb737, 0x38cba42c, 0xa02c8549, 0x7895dcbf, 0xbd183d71, 0xafe4476a)}, {SECP256K1_FE_CONST(0xede78fdd, 0xcfc92bf1, 0x4fec6c6c, 0xdb8d37e2, 0xfb66bc7b, 0x28701870, 0x7fa27c9a, 0x307196ec), SECP256K1_FE_CONST(0x68193a6c, 0x9a8b87a7, 0x2a760c64, 0x13e473f6, 0x23ae7bed, 0x1de05422, 0x88865427, 0xa3418265)}, {SECP256K1_FE_CONST(0xa40b2079, 0xb8f88e89, 0xa7617997, 0x89baf5ae, 0x174df343, 0x75138eae, 0x2711595d, 0x3fc3e66c), SECP256K1_FE_CONST(0x9f99c6a5, 0x6d685267, 0xd4b87c37, 0x9d9c4576, 0x358c692b, 0x6bbae0ed, 0x3389c93d, 0x7fdd2655)}, {SECP256K1_FE_CONST(0x7c74c6b6, 0xe98d9151, 0x72645cf1, 0x7f06e321, 0xcefee074, 0x15b2113a, 0x10a9be07, 0x08a45696), SECP256K1_FE_CONST(0x8c919a88, 0x898bc1e0, 0x77f26f97, 0x12e655b7, 0x9ba0ac40, 0xe15bb19e, 0x8364cc3b, 0xe227a8ee)}, {SECP256K1_FE_CONST(0x109ba1ce, 0xdafa6d4a, 0xa1cec2b2, 0xeb1069f4, 0xb7a79e5b, 0xec6eb99b, 0xaec5f643, 0xee0e723e), SECP256K1_FE_CONST(0x93d13eb8, 0x4bb0bcf9, 0xe64f5a71, 0xdbe9f359, 0x7191401c, 0x6f057a4a, 0xa407fe1b, 0x7ecb65cc)}, {SECP256K1_FE_CONST(0x3db076cd, 0xec74a5c9, 0xf61dd138, 0x90e23e06, 0xeeedd2d0, 0x74cbc4e0, 0x3dbe1e91, 0xded36a78), SECP256K1_FE_CONST(0x3f07f966, 0x8e2a1e09, 0x706c71df, 0x02b5e9d5, 0xcb92ddbf, 0xcdd53010, 0x16545564, 0xe660b107)}, {SECP256K1_FE_CONST(0xe31c73ed, 0xb4c4b82c, 0x02ae35f7, 0x4cdec153, 0x98b522fd, 0xf7d2460c, 0x6bf7c0f8, 0x4cf67b0d), SECP256K1_FE_CONST(0x4b8f1faf, 0x94e8b070, 0x19af0ff6, 0xa319cd31, 0xdf0a7ffb, 0xefaba629, 0x59c50666, 0x1fe5b843)}, {SECP256K1_FE_CONST(0x4c8b0e6e, 0x83392ab6, 0xc0e3e9f1, 0xbbd85497, 0x16698897, 0xf552d50d, 0x79652ddb, 0x12f99870), SECP256K1_FE_CONST(0x56d5101f, 0xd23b7949, 0x17dc38d6, 0xf24022ef, 0xcf18e70a, 0x5cc34424, 0x438544c3, 0x62da4bca)}, {SECP256K1_FE_CONST(0xb0e040e2, 0x40cc35da, 0x7dd5c611, 0x7fccb178, 0x28888137, 0xbc930358, 0xea2cbc90, 0x775417dc), SECP256K1_FE_CONST(0xca37f0d4, 0x016dd7c8, 0xab3ae576, 0x96e08d69, 0x68ed9155, 0xa9b44270, 0x900ae35d, 0x7c7800cd)}, {SECP256K1_FE_CONST(0x8a32ea49, 0x7fbb0bae, 0x69724a9d, 0x8e2105b2, 0xbdf69178, 0x862577ef, 0x35055590, 0x667ddaef), SECP256K1_FE_CONST(0xd02d7ead, 0xc5e190f0, 0x559c9d72, 0xdaef1ffc, 0x64f9f425, 0xf43645ea, 0x7341e08d, 0x11768e96)}, {SECP256K1_FE_CONST(0xa3592d98, 0x9abe289d, 0x579ebea6, 0xbb0857a8, 0xe242ab73, 0x85f9a2ce, 0xb6998f0f, 0xbfffbfc6), SECP256K1_FE_CONST(0x093c1533, 0x32032efa, 0x6aa46070, 0x0039599e, 0x589c35f4, 0xff525430, 0x7fe3777a, 0x44b43ddc)}, {SECP256K1_FE_CONST(0x647178a3, 0x229e607b, 0xcc98521a, 0xcce3fdd9, 0x1e1bc9c9, 0x97fb7c6a, 0x61b961e0, 0x99b10709), SECP256K1_FE_CONST(0x98217c13, 0xd51ddf78, 0x96310e77, 0xdaebd908, 0x602ca683, 0xcb46d07a, 0xa1fcf17e, 0xc8e2feb3)}, {SECP256K1_FE_CONST(0x7334627c, 0x73f98968, 0x99464b4b, 0xf5964958, 0x1b95870d, 0xc658227e, 0x5e3235d8, 0xdcab5787), SECP256K1_FE_CONST(0x000006fd, 0xc7e9dd94, 0x40ae367a, 0xe51d495c, 0x07603b9b, 0x2d088418, 0x6cc5c74c, 0x98514307)}, {SECP256K1_FE_CONST(0x82e83876, 0x96c28938, 0xa50dd1c5, 0x605c3ad1, 0xc048637d, 0x7a50825f, 0x335ed01a, 0x00005760), SECP256K1_FE_CONST(0xb0393f9f, 0x9f2aa55e, 0xf5607e2e, 0x5287d961, 0x60b3e704, 0xf3e16e80, 0xb4f9a3ea, 0xfec7f02d)}, {SECP256K1_FE_CONST(0xc97b6cec, 0x3ee6b8dc, 0x98d24b58, 0x3c1970a1, 0xfe06297a, 0xae813529, 0xe76bb6bd, 0x771ae51d), SECP256K1_FE_CONST(0x0507c702, 0xd407d097, 0x47ddeb06, 0xf6625419, 0x79f48f79, 0x7bf80d0b, 0xfc34b364, 0x253a5db1)}, {SECP256K1_FE_CONST(0xd559af63, 0x77ea9bc4, 0x3cf1ad14, 0x5c7a4bbb, 0x10e7d18b, 0x7ce0dfac, 0x380bb19d, 0x0bb99bd3), SECP256K1_FE_CONST(0x00196119, 0xb9b00d92, 0x34edfdb5, 0xbbdc42fc, 0xd2daa33a, 0x163356ca, 0xaa8754c8, 0xb0ec8b0b)}, {SECP256K1_FE_CONST(0x8ddfa3dc, 0x52918da0, 0x640519dc, 0x0af8512a, 0xca2d33b2, 0xbde52514, 0xda9c0afc, 0xcb29fce4), SECP256K1_FE_CONST(0xb3e4878d, 0x5cb69148, 0xcd54388b, 0xc23acce0, 0x62518ba8, 0xf09def92, 0x7b31e6aa, 0x6ba35b02)}, {SECP256K1_FE_CONST(0xf8207492, 0xe3049f0a, 0x65285f2b, 0x0bfff996, 0x00ca112e, 0xc05da837, 0x546d41f9, 0x5194fb91), SECP256K1_FE_CONST(0x7b7ee50b, 0xa8ed4bbd, 0xf6469930, 0x81419a5c, 0x071441c7, 0x290d046e, 0x3b82ea41, 0x611c5f95)}, {SECP256K1_FE_CONST(0x050f7c80, 0x5bcd3c6b, 0x823cb724, 0x5ce74db7, 0xa4e39f5c, 0xbd8828d7, 0xfd4d3e07, 0x3ec2926a), SECP256K1_FE_CONST(0x000d6730, 0xb0171314, 0x4764053d, 0xee157117, 0x48fd61da, 0xdea0b9db, 0x1d5e91c6, 0xbdc3f59e)}, {SECP256K1_FE_CONST(0x3e3ea8eb, 0x05d760cf, 0x23009263, 0xb3cb3ac9, 0x088f6f0d, 0x3fc182a3, 0xbd57087c, 0xe67c62f9), SECP256K1_FE_CONST(0xbe988716, 0xa29c1bf6, 0x4456aed6, 0xab1e4720, 0x49929305, 0x51043bf4, 0xebd833dd, 0xdd511e8b)}, {SECP256K1_FE_CONST(0x6964d2a9, 0xa7fa6501, 0xa5959249, 0x142f4029, 0xea0c1b5f, 0x2f487ef6, 0x301ac80a, 0x768be5cd), SECP256K1_FE_CONST(0x3918ffe4, 0x07492543, 0xed24d0b7, 0x3df95f8f, 0xaffd7cb4, 0x0de2191c, 0x9ec2f2ad, 0x2c0cb3c6)}, {SECP256K1_FE_CONST(0x37c93520, 0xf6ddca57, 0x2b42fd5e, 0xb5c7e4de, 0x11b5b81c, 0xb95e91f3, 0x95c4d156, 0x39877ccb), SECP256K1_FE_CONST(0x9a94b9b5, 0x57eb71ee, 0x4c975b8b, 0xac5262a8, 0x077b0595, 0xe12a6b1f, 0xd728edef, 0x1a6bf956)} }; /* Fixed test cases for scalar inverses: pairs of (x, 1/x) mod n. */ static const rustsecp256k1_v0_5_0_scalar scalar_cases[][2] = { /* 0 */ {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0)}, /* 1 */ {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1), SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1)}, /* -1 */ {SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140), SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140)}, /* 2 */ {SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 2), SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x5d576e73, 0x57a4501d, 0xdfe92f46, 0x681b20a1)}, /* 2**128 */ {SECP256K1_SCALAR_CONST(0, 0, 0, 1, 0, 0, 0, 0), SECP256K1_SCALAR_CONST(0x50a51ac8, 0x34b9ec24, 0x4b0dff66, 0x5588b13e, 0x9984d5b3, 0xcf80ef0f, 0xd6a23766, 0xa3ee9f22)}, /* Input known to need 635 divsteps */ {SECP256K1_SCALAR_CONST(0xcb9f1d35, 0xdd4416c2, 0xcd71bf3f, 0x6365da66, 0x3c9b3376, 0x8feb7ae9, 0x32a5ef60, 0x19199ec3), SECP256K1_SCALAR_CONST(0x1d7c7bba, 0xf1893d53, 0xb834bd09, 0x36b411dc, 0x42c2e42f, 0xec72c428, 0x5e189791, 0x8e9bc708)}, /* Input known to need 566 divsteps starting with delta=1/2. */ {SECP256K1_SCALAR_CONST(0x7e3c993d, 0xa4272488, 0xbc015b49, 0x2db54174, 0xd382083a, 0xebe6db35, 0x80f82eff, 0xcd132c72), SECP256K1_SCALAR_CONST(0x086f34a0, 0x3e631f76, 0x77418f28, 0xcc84ac95, 0x6304439d, 0x365db268, 0x312c6ded, 0xd0b934f8)}, /* Input known to need 565 divsteps starting with delta=1/2. */ {SECP256K1_SCALAR_CONST(0xbad7e587, 0x3f307859, 0x60d93147, 0x8a18491e, 0xb38a9fd5, 0x254350d3, 0x4b1f0e4b, 0x7dd6edc4), SECP256K1_SCALAR_CONST(0x89f2df26, 0x39e2b041, 0xf19bd876, 0xd039c8ac, 0xc2223add, 0x29c4943e, 0x6632d908, 0x515f467b)}, /* Selection of randomly generated inputs that reach low/high d/e values in various configurations. */ {SECP256K1_SCALAR_CONST(0x1950d757, 0xb37a5809, 0x435059bb, 0x0bb8997e, 0x07e1e3c8, 0x5e5d7d2c, 0x6a0ed8e3, 0xdbde180e), SECP256K1_SCALAR_CONST(0xbf72af9b, 0x750309e2, 0x8dda230b, 0xfe432b93, 0x7e25e475, 0x4388251e, 0x633d894b, 0x3bcb6f8c)}, {SECP256K1_SCALAR_CONST(0x9bccf4e7, 0xc5a515e3, 0x50637aa9, 0xbb65a13f, 0x391749a1, 0x62de7d4e, 0xf6d7eabb, 0x3cd10ce0), SECP256K1_SCALAR_CONST(0xaf2d5623, 0xb6385a33, 0xcd0365be, 0x5e92a70d, 0x7f09179c, 0x3baaf30f, 0x8f9cc83b, 0x20092f67)}, {SECP256K1_SCALAR_CONST(0x73a57111, 0xb242952a, 0x5c5dee59, 0xf3be2ace, 0xa30a7659, 0xa46e5f47, 0xd21267b1, 0x39e642c9), SECP256K1_SCALAR_CONST(0xa711df07, 0xcbcf13ef, 0xd61cc6be, 0xbcd058ce, 0xb02cf157, 0x272d4a18, 0x86d0feb3, 0xcd5fa004)}, {SECP256K1_SCALAR_CONST(0x04884963, 0xce0580b1, 0xba547030, 0x3c691db3, 0x9cd2c84f, 0x24c7cebd, 0x97ebfdba, 0x3e785ec2), SECP256K1_SCALAR_CONST(0xaaaaaf14, 0xd7c99ba7, 0x517ce2c1, 0x78a28b4c, 0x3769a851, 0xe5c5a03d, 0x4cc28f33, 0x0ec4dc5d)}, {SECP256K1_SCALAR_CONST(0x1679ed49, 0x21f537b1, 0x815cb8ae, 0x9efc511c, 0x5b9fa037, 0x0b0f275e, 0x6c985281, 0x6c4a9905), SECP256K1_SCALAR_CONST(0xb14ac3d5, 0x62b52999, 0xef34ead1, 0xffca4998, 0x0294341a, 0x1f8172aa, 0xea1624f9, 0x302eea62)}, {SECP256K1_SCALAR_CONST(0x626b37c0, 0xf0057c35, 0xee982f83, 0x452a1fd3, 0xea826506, 0x48b08a9d, 0x1d2c4799, 0x4ad5f6ec), SECP256K1_SCALAR_CONST(0xe38643b7, 0x567bfc2f, 0x5d2f1c15, 0xe327239c, 0x07112443, 0x69509283, 0xfd98e77a, 0xdb71c1e8)}, {SECP256K1_SCALAR_CONST(0x1850a3a7, 0x759efc56, 0x54f287b2, 0x14d1234b, 0xe263bbc9, 0xcf4d8927, 0xd5f85f27, 0x965bd816), SECP256K1_SCALAR_CONST(0x3b071831, 0xcac9619a, 0xcceb0596, 0xf614d63b, 0x95d0db2f, 0xc6a00901, 0x8eaa2621, 0xabfa0009)}, {SECP256K1_SCALAR_CONST(0x94ae5d06, 0xa27dc400, 0x487d72be, 0xaa51ebed, 0xe475b5c0, 0xea675ffc, 0xf4df627a, 0xdca4222f), SECP256K1_SCALAR_CONST(0x01b412ed, 0xd7830956, 0x1532537e, 0xe5e3dc99, 0x8fd3930a, 0x54f8d067, 0x32ef5760, 0x594438a5)}, {SECP256K1_SCALAR_CONST(0x1f24278a, 0xb5bfe374, 0xa328dbbc, 0xebe35f48, 0x6620e009, 0xd58bb1b4, 0xb5a6bf84, 0x8815f63a), SECP256K1_SCALAR_CONST(0xfe928416, 0xca5ba2d3, 0xfde513da, 0x903a60c7, 0x9e58ad8a, 0x8783bee4, 0x083a3843, 0xa608c914)}, {SECP256K1_SCALAR_CONST(0xdc107d58, 0x274f6330, 0x67dba8bc, 0x26093111, 0x5201dfb8, 0x968ce3f5, 0xf34d1bd4, 0xf2146504), SECP256K1_SCALAR_CONST(0x660cfa90, 0x13c3d93e, 0x7023b1e5, 0xedd09e71, 0x6d9c9d10, 0x7a3d2cdb, 0xdd08edc3, 0xaa78fcfb)}, {SECP256K1_SCALAR_CONST(0x7cd1e905, 0xc6f02776, 0x2f551cc7, 0x5da61cff, 0x7da05389, 0x1119d5a4, 0x631c7442, 0x894fd4f7), SECP256K1_SCALAR_CONST(0xff20862a, 0x9d3b1a37, 0x1628803b, 0x3004ccae, 0xaa23282a, 0xa89a1109, 0xd94ece5e, 0x181bdc46)}, {SECP256K1_SCALAR_CONST(0x5b9dade8, 0x23d26c58, 0xcd12d818, 0x25b8ae97, 0x3dea04af, 0xf482c96b, 0xa062f254, 0x9e453640), SECP256K1_SCALAR_CONST(0x50c38800, 0x15fa53f4, 0xbe1e5392, 0x5c9b120a, 0x262c22c7, 0x18fa0816, 0x5f2baab4, 0x8cb5db46)}, {SECP256K1_SCALAR_CONST(0x11cdaeda, 0x969c464b, 0xef1f4ab0, 0x5b01d22e, 0x656fd098, 0x882bea84, 0x65cdbe7a, 0x0c19ff03), SECP256K1_SCALAR_CONST(0x1968d0fa, 0xac46f103, 0xb55f1f72, 0xb3820bed, 0xec6b359a, 0x4b1ae0ad, 0x7e38e1fb, 0x295ccdfb)}, {SECP256K1_SCALAR_CONST(0x2c351aa1, 0x26e91589, 0x194f8a1e, 0x06561f66, 0x0cb97b7f, 0x10914454, 0x134d1c03, 0x157266b4), SECP256K1_SCALAR_CONST(0xbe49ada6, 0x92bd8711, 0x41b176c4, 0xa478ba95, 0x14883434, 0x9d1cd6f3, 0xcc4b847d, 0x22af80f5)}, {SECP256K1_SCALAR_CONST(0x6ba07c6e, 0x13a60edb, 0x6247f5c3, 0x84b5fa56, 0x76fe3ec5, 0x80426395, 0xf65ec2ae, 0x623ba730), SECP256K1_SCALAR_CONST(0x25ac23f7, 0x418cd747, 0x98376f9d, 0x4a11c7bf, 0x24c8ebfe, 0x4c8a8655, 0x345f4f52, 0x1c515595)}, {SECP256K1_SCALAR_CONST(0x9397a712, 0x8abb6951, 0x2d4a3d54, 0x703b1c2a, 0x0661dca8, 0xd75c9b31, 0xaed4d24b, 0xd2ab2948), SECP256K1_SCALAR_CONST(0xc52e8bef, 0xd55ce3eb, 0x1c897739, 0xeb9fb606, 0x36b9cd57, 0x18c51cc2, 0x6a87489e, 0xffd0dcf3)}, {SECP256K1_SCALAR_CONST(0xe6a808cc, 0xeb437888, 0xe97798df, 0x4e224e44, 0x7e3b380a, 0x207c1653, 0x889f3212, 0xc6738b6f), SECP256K1_SCALAR_CONST(0x31f9ae13, 0xd1e08b20, 0x757a2e5e, 0x5243a0eb, 0x8ae35f73, 0x19bb6122, 0xb910f26b, 0xda70aa55)}, {SECP256K1_SCALAR_CONST(0xd0320548, 0xab0effe7, 0xa70779e0, 0x61a347a6, 0xb8c1e010, 0x9d5281f8, 0x2ee588a6, 0x80000000), SECP256K1_SCALAR_CONST(0x1541897e, 0x78195c90, 0x7583dd9e, 0x728b6100, 0xbce8bc6d, 0x7a53b471, 0x5dcd9e45, 0x4425fcaf)}, {SECP256K1_SCALAR_CONST(0x93d623f1, 0xd45b50b0, 0x796e9186, 0x9eac9407, 0xd30edc20, 0xef6304cf, 0x250494e7, 0xba503de9), SECP256K1_SCALAR_CONST(0x7026d638, 0x1178b548, 0x92043952, 0x3c7fb47c, 0xcd3ea236, 0x31d82b01, 0x612fc387, 0x80b9b957)}, {SECP256K1_SCALAR_CONST(0xf860ab39, 0x55f5d412, 0xa4d73bcc, 0x3b48bd90, 0xc248ffd3, 0x13ca10be, 0x8fba84cc, 0xdd28d6a3), SECP256K1_SCALAR_CONST(0x5c32fc70, 0xe0b15d67, 0x76694700, 0xfe62be4d, 0xeacdb229, 0x7a4433d9, 0x52155cd0, 0x7649ab59)}, {SECP256K1_SCALAR_CONST(0x4e41311c, 0x0800af58, 0x7a690a8e, 0xe175c9ba, 0x6981ab73, 0xac532ea8, 0x5c1f5e63, 0x6ac1f189), SECP256K1_SCALAR_CONST(0xfffffff9, 0xd075982c, 0x7fbd3825, 0xc05038a2, 0x4533b91f, 0x94ec5f45, 0xb280b28f, 0x842324dc)}, {SECP256K1_SCALAR_CONST(0x48e473bf, 0x3555eade, 0xad5d7089, 0x2424c4e4, 0x0a99397c, 0x2dc796d8, 0xb7a43a69, 0xd0364141), SECP256K1_SCALAR_CONST(0x634976b2, 0xa0e47895, 0x1ec38593, 0x266d6fd0, 0x6f602644, 0x9bb762f1, 0x7180c704, 0xe23a4daa)}, {SECP256K1_SCALAR_CONST(0xbe83878d, 0x3292fc54, 0x26e71c62, 0x556ccedc, 0x7cbb8810, 0x4032a720, 0x34ead589, 0xe4d6bd13), SECP256K1_SCALAR_CONST(0x6cd150ad, 0x25e59d0f, 0x74cbae3d, 0x6377534a, 0x1e6562e8, 0xb71b9d18, 0xe1e5d712, 0x8480abb3)}, {SECP256K1_SCALAR_CONST(0xcdddf2e5, 0xefc15f88, 0xc9ee06de, 0x8a846ca9, 0x28561581, 0x68daa5fb, 0xd1cf3451, 0xeb1782d0), SECP256K1_SCALAR_CONST(0xffffffd9, 0xed8d2af4, 0x993c865a, 0x23e9681a, 0x3ca3a3dc, 0xe6d5a46e, 0xbd86bd87, 0x61b55c70)}, {SECP256K1_SCALAR_CONST(0xb6a18f1f, 0x04872df9, 0x08165ec4, 0x319ca19c, 0x6c0359ab, 0x1f7118fb, 0xc2ef8082, 0xca8b7785), SECP256K1_SCALAR_CONST(0xff55b19b, 0x0f1ac78c, 0x0f0c88c2, 0x2358d5ad, 0x5f455e4e, 0x3330b72f, 0x274dc153, 0xffbf272b)}, {SECP256K1_SCALAR_CONST(0xea4898e5, 0x30eba3e8, 0xcf0e5c3d, 0x06ec6844, 0x01e26fb6, 0x75636225, 0xc5d08f4c, 0x1decafa0), SECP256K1_SCALAR_CONST(0xe5a014a8, 0xe3c4ec1e, 0xea4f9b32, 0xcfc7b386, 0x00630806, 0x12c08d02, 0x6407ccc2, 0xb067d90e)}, {SECP256K1_SCALAR_CONST(0x70e9aea9, 0x7e933af0, 0x8a23bfab, 0x23e4b772, 0xff951863, 0x5ffcf47d, 0x6bebc918, 0x2ca58265), SECP256K1_SCALAR_CONST(0xf4e00006, 0x81bc6441, 0x4eb6ec02, 0xc194a859, 0x80ad7c48, 0xba4e9afb, 0x8b6bdbe0, 0x989d8f77)}, {SECP256K1_SCALAR_CONST(0x3c56c774, 0x46efe6f0, 0xe93618b8, 0xf9b5a846, 0xd247df61, 0x83b1e215, 0x06dc8bcc, 0xeefc1bf5), SECP256K1_SCALAR_CONST(0xfff8937a, 0x2cd9586b, 0x43c25e57, 0xd1cefa7a, 0x9fb91ed3, 0x95b6533d, 0x8ad0de5b, 0xafb93f00)}, {SECP256K1_SCALAR_CONST(0xfb5c2772, 0x5cb30e83, 0xe38264df, 0xe4e3ebf3, 0x392aa92e, 0xa68756a1, 0x51279ac5, 0xb50711a8), SECP256K1_SCALAR_CONST(0x000013af, 0x1105bfe7, 0xa6bbd7fb, 0x3d638f99, 0x3b266b02, 0x072fb8bc, 0x39251130, 0x2e0fd0ea)} }; int i, var, testrand; unsigned char b32[32]; rustsecp256k1_v0_5_0_fe x_fe; rustsecp256k1_v0_5_0_scalar x_scalar; memset(b32, 0, sizeof(b32)); /* Test fixed test cases through test_inverse_{scalar,field}, both ways. */ for (i = 0; (size_t)i < sizeof(fe_cases)/sizeof(fe_cases[0]); ++i) { for (var = 0; var <= 1; ++var) { test_inverse_field(&x_fe, &fe_cases[i][0], var); check_fe_equal(&x_fe, &fe_cases[i][1]); test_inverse_field(&x_fe, &fe_cases[i][1], var); check_fe_equal(&x_fe, &fe_cases[i][0]); } } for (i = 0; (size_t)i < sizeof(scalar_cases)/sizeof(scalar_cases[0]); ++i) { for (var = 0; var <= 1; ++var) { test_inverse_scalar(&x_scalar, &scalar_cases[i][0], var); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&x_scalar, &scalar_cases[i][1])); test_inverse_scalar(&x_scalar, &scalar_cases[i][1], var); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&x_scalar, &scalar_cases[i][0])); } } /* Test inputs 0..999 and their respective negations. */ for (i = 0; i < 1000; ++i) { b32[31] = i & 0xff; b32[30] = (i >> 8) & 0xff; rustsecp256k1_v0_5_0_scalar_set_b32(&x_scalar, b32, NULL); rustsecp256k1_v0_5_0_fe_set_b32(&x_fe, b32); for (var = 0; var <= 1; ++var) { test_inverse_scalar(NULL, &x_scalar, var); test_inverse_field(NULL, &x_fe, var); } rustsecp256k1_v0_5_0_scalar_negate(&x_scalar, &x_scalar); rustsecp256k1_v0_5_0_fe_negate(&x_fe, &x_fe, 1); for (var = 0; var <= 1; ++var) { test_inverse_scalar(NULL, &x_scalar, var); test_inverse_field(NULL, &x_fe, var); } } /* test 128*count random inputs; half with testrand256_test, half with testrand256 */ for (testrand = 0; testrand <= 1; ++testrand) { for (i = 0; i < 64 * count; ++i) { (testrand ? rustsecp256k1_v0_5_0_testrand256_test : rustsecp256k1_v0_5_0_testrand256)(b32); rustsecp256k1_v0_5_0_scalar_set_b32(&x_scalar, b32, NULL); rustsecp256k1_v0_5_0_fe_set_b32(&x_fe, b32); for (var = 0; var <= 1; ++var) { test_inverse_scalar(NULL, &x_scalar, var); test_inverse_field(NULL, &x_fe, var); } } } } /***** GROUP TESTS *****/ void ge_equals_ge(const rustsecp256k1_v0_5_0_ge *a, const rustsecp256k1_v0_5_0_ge *b) { CHECK(a->infinity == b->infinity); if (a->infinity) { return; } CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&a->x, &b->x)); CHECK(rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_gej *a, const rustsecp256k1_v0_5_0_gej *b) { rustsecp256k1_v0_5_0_gej a2; rustsecp256k1_v0_5_0_gej b2; int ret = 1; ret &= a->infinity == b->infinity; if (ret && !a->infinity) { a2 = *a; b2 = *b; rustsecp256k1_v0_5_0_fe_normalize(&a2.x); rustsecp256k1_v0_5_0_fe_normalize(&a2.y); rustsecp256k1_v0_5_0_fe_normalize(&a2.z); rustsecp256k1_v0_5_0_fe_normalize(&b2.x); rustsecp256k1_v0_5_0_fe_normalize(&b2.y); rustsecp256k1_v0_5_0_fe_normalize(&b2.z); ret &= rustsecp256k1_v0_5_0_fe_cmp_var(&a2.x, &b2.x) == 0; ret &= rustsecp256k1_v0_5_0_fe_cmp_var(&a2.y, &b2.y) == 0; ret &= rustsecp256k1_v0_5_0_fe_cmp_var(&a2.z, &b2.z) == 0; } return ret; } void ge_equals_gej(const rustsecp256k1_v0_5_0_ge *a, const rustsecp256k1_v0_5_0_gej *b) { rustsecp256k1_v0_5_0_fe z2s; rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_fe_sqr(&z2s, &b->z); rustsecp256k1_v0_5_0_fe_mul(&u1, &a->x, &z2s); u2 = b->x; rustsecp256k1_v0_5_0_fe_normalize_weak(&u2); rustsecp256k1_v0_5_0_fe_mul(&s1, &a->y, &z2s); rustsecp256k1_v0_5_0_fe_mul(&s1, &s1, &b->z); s2 = b->y; rustsecp256k1_v0_5_0_fe_normalize_weak(&s2); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&u1, &u2)); CHECK(rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_ge *ge = (rustsecp256k1_v0_5_0_ge *)checked_malloc(&ctx->error_callback, sizeof(rustsecp256k1_v0_5_0_ge) * (1 + 4 * runs)); rustsecp256k1_v0_5_0_gej *gej = (rustsecp256k1_v0_5_0_gej *)checked_malloc(&ctx->error_callback, sizeof(rustsecp256k1_v0_5_0_gej) * (1 + 4 * runs)); rustsecp256k1_v0_5_0_fe zf; rustsecp256k1_v0_5_0_fe zfi2, zfi3; rustsecp256k1_v0_5_0_gej_set_infinity(&gej[0]); rustsecp256k1_v0_5_0_ge_clear(&ge[0]); rustsecp256k1_v0_5_0_ge_set_gej_var(&ge[0], &gej[0]); for (i = 0; i < runs; i++) { int j; rustsecp256k1_v0_5_0_ge g; random_group_element_test(&g); if (i >= runs - 2) { rustsecp256k1_v0_5_0_ge_mul_lambda(&g, &ge[1]); } if (i >= runs - 1) { rustsecp256k1_v0_5_0_ge_mul_lambda(&g, &g); } ge[1 + 4 * i] = g; ge[2 + 4 * i] = g; rustsecp256k1_v0_5_0_ge_neg(&ge[3 + 4 * i], &g); rustsecp256k1_v0_5_0_ge_neg(&ge[4 + 4 * i], &g); rustsecp256k1_v0_5_0_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]); random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_fe_is_zero(&zf)); random_field_element_magnitude(&zf); rustsecp256k1_v0_5_0_fe_inv_var(&zfi3, &zf); rustsecp256k1_v0_5_0_fe_sqr(&zfi2, &zfi3); rustsecp256k1_v0_5_0_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). */ rustsecp256k1_v0_5_0_gej refj, resj; rustsecp256k1_v0_5_0_ge ref; rustsecp256k1_v0_5_0_fe zr; rustsecp256k1_v0_5_0_gej_add_var(&refj, &gej[i1], &gej[i2], rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i1]) ? NULL : &zr); /* Check Z ratio. */ if (!rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i1]) && !rustsecp256k1_v0_5_0_gej_is_infinity(&refj)) { rustsecp256k1_v0_5_0_fe zrz; rustsecp256k1_v0_5_0_fe_mul(&zrz, &zr, &gej[i1].z); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&zrz, &refj.z)); } rustsecp256k1_v0_5_0_ge_set_gej_var(&ref, &refj); /* Test gej + ge with Z ratio result (var). */ rustsecp256k1_v0_5_0_gej_add_ge_var(&resj, &gej[i1], &ge[i2], rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i1]) ? NULL : &zr); ge_equals_gej(&ref, &resj); if (!rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i1]) && !rustsecp256k1_v0_5_0_gej_is_infinity(&resj)) { rustsecp256k1_v0_5_0_fe zrz; rustsecp256k1_v0_5_0_fe_mul(&zrz, &zr, &gej[i1].z); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&zrz, &resj.z)); } /* Test gej + ge (var, with additional Z factor). */ { rustsecp256k1_v0_5_0_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */ rustsecp256k1_v0_5_0_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2); rustsecp256k1_v0_5_0_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3); random_field_element_magnitude(&ge2_zfi.x); random_field_element_magnitude(&ge2_zfi.y); rustsecp256k1_v0_5_0_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf); ge_equals_gej(&ref, &resj); } /* Test gej + ge (const). */ if (i2 != 0) { /* rustsecp256k1_v0_5_0_gej_add_ge does not support its second argument being infinity. */ rustsecp256k1_v0_5_0_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)) { rustsecp256k1_v0_5_0_fe zr2; /* Normal doubling with Z ratio result. */ rustsecp256k1_v0_5_0_gej_double_var(&resj, &gej[i1], &zr2); ge_equals_gej(&ref, &resj); /* Check Z ratio. */ rustsecp256k1_v0_5_0_fe_mul(&zr2, &zr2, &gej[i1].z); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&zr2, &resj.z)); /* Normal doubling. */ rustsecp256k1_v0_5_0_gej_double_var(&resj, &gej[i2], NULL); ge_equals_gej(&ref, &resj); /* Constant-time doubling. */ rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ge_is_infinity(&ref)); } /* Test adding infinity. */ if (i1 == 0) { CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&ge[i1])); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i1])); ge_equals_gej(&ref, &gej[i2]); } if (i2 == 0) { CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&ge[i2])); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&gej[i2])); ge_equals_gej(&ref, &gej[i1]); } } } /* Test adding all points together in random order equals infinity. */ { rustsecp256k1_v0_5_0_gej sum = SECP256K1_GEJ_CONST_INFINITY; rustsecp256k1_v0_5_0_gej *gej_shuffled = (rustsecp256k1_v0_5_0_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(rustsecp256k1_v0_5_0_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 + rustsecp256k1_v0_5_0_testrand_int(4 * runs + 1 - i); if (swap != i) { rustsecp256k1_v0_5_0_gej t = gej_shuffled[i]; gej_shuffled[i] = gej_shuffled[swap]; gej_shuffled[swap] = t; } } for (i = 0; i < 4 * runs + 1; i++) { rustsecp256k1_v0_5_0_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL); } CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&sum)); free(gej_shuffled); } /* Test batch gej -> ge conversion without known z ratios. */ { rustsecp256k1_v0_5_0_ge *ge_set_all = (rustsecp256k1_v0_5_0_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(rustsecp256k1_v0_5_0_ge)); rustsecp256k1_v0_5_0_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1); for (i = 0; i < 4 * runs + 1; i++) { rustsecp256k1_v0_5_0_fe s; random_fe_non_zero(&s); rustsecp256k1_v0_5_0_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++) { int odd; random_group_element_test(&ge[i]); odd = rustsecp256k1_v0_5_0_fe_is_odd(&ge[i].x); CHECK(odd == 0 || odd == 1); /* randomly set half the points to infinity */ if (odd == i % 2) { rustsecp256k1_v0_5_0_ge_set_infinity(&ge[i]); } rustsecp256k1_v0_5_0_gej_set_ge(&gej[i], &ge[i]); } /* batch convert */ rustsecp256k1_v0_5_0_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]); } /* Test batch gej -> ge conversion with all infinities. */ for (i = 0; i < 4 * runs + 1; i++) { rustsecp256k1_v0_5_0_gej_set_infinity(&gej[i]); } /* batch convert */ rustsecp256k1_v0_5_0_ge_set_all_gej_var(ge, gej, 4 * runs + 1); /* check result */ for (i = 0; i < 4 * runs + 1; i++) { CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&ge[i])); } free(ge); free(gej); } void test_intialized_inf(void) { rustsecp256k1_v0_5_0_ge p; rustsecp256k1_v0_5_0_gej pj, npj, infj1, infj2, infj3; rustsecp256k1_v0_5_0_fe zinv; /* Test that adding P+(-P) results in a fully initialized infinity*/ random_group_element_test(&p); rustsecp256k1_v0_5_0_gej_set_ge(&pj, &p); rustsecp256k1_v0_5_0_gej_neg(&npj, &pj); rustsecp256k1_v0_5_0_gej_add_var(&infj1, &pj, &npj, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&infj1)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj1.x)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj1.y)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj1.z)); rustsecp256k1_v0_5_0_gej_add_ge_var(&infj2, &npj, &p, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&infj2)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj2.x)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj2.y)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj2.z)); rustsecp256k1_v0_5_0_fe_set_int(&zinv, 1); rustsecp256k1_v0_5_0_gej_add_zinv_var(&infj3, &npj, &p, &zinv); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&infj3)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj3.x)); CHECK(rustsecp256k1_v0_5_0_fe_is_zero(&infj3.y)); CHECK(rustsecp256k1_v0_5_0_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() */ rustsecp256k1_v0_5_0_gej aj = SECP256K1_GEJ_CONST( 0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30, 0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb, 0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8, 0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d ); rustsecp256k1_v0_5_0_gej bj = SECP256K1_GEJ_CONST( 0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86, 0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7, 0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57, 0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2 ); rustsecp256k1_v0_5_0_gej sumj = SECP256K1_GEJ_CONST( 0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027, 0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a, 0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08, 0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe ); rustsecp256k1_v0_5_0_ge b; rustsecp256k1_v0_5_0_gej resj; rustsecp256k1_v0_5_0_ge res; rustsecp256k1_v0_5_0_ge_set_gej(&b, &bj); rustsecp256k1_v0_5_0_gej_add_var(&resj, &aj, &bj, NULL); rustsecp256k1_v0_5_0_ge_set_gej(&res, &resj); ge_equals_gej(&res, &sumj); rustsecp256k1_v0_5_0_gej_add_ge(&resj, &aj, &b); rustsecp256k1_v0_5_0_ge_set_gej(&res, &resj); ge_equals_gej(&res, &sumj); rustsecp256k1_v0_5_0_gej_add_ge_var(&resj, &aj, &b, NULL); rustsecp256k1_v0_5_0_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_gej_cmov(const rustsecp256k1_v0_5_0_gej *a, const rustsecp256k1_v0_5_0_gej *b) { rustsecp256k1_v0_5_0_gej t = *a; rustsecp256k1_v0_5_0_gej_cmov(&t, b, 0); CHECK(gej_xyz_equals_gej(&t, a)); rustsecp256k1_v0_5_0_gej_cmov(&t, b, 1); CHECK(gej_xyz_equals_gej(&t, b)); } void run_gej(void) { int i; rustsecp256k1_v0_5_0_gej a, b; /* Tests for rustsecp256k1_v0_5_0_gej_cmov */ for (i = 0; i < count; i++) { rustsecp256k1_v0_5_0_gej_set_infinity(&a); rustsecp256k1_v0_5_0_gej_set_infinity(&b); test_gej_cmov(&a, &b); random_gej_test(&a); test_gej_cmov(&a, &b); test_gej_cmov(&b, &a); b = a; test_gej_cmov(&a, &b); random_gej_test(&b); test_gej_cmov(&a, &b); test_gej_cmov(&b, &a); } } void test_ec_combine(void) { rustsecp256k1_v0_5_0_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); rustsecp256k1_v0_5_0_pubkey data[6]; const rustsecp256k1_v0_5_0_pubkey* d[6]; rustsecp256k1_v0_5_0_pubkey sd; rustsecp256k1_v0_5_0_pubkey sd2; rustsecp256k1_v0_5_0_gej Qj; rustsecp256k1_v0_5_0_ge Q; int i; for (i = 1; i <= 6; i++) { rustsecp256k1_v0_5_0_scalar s; random_scalar_order_test(&s); rustsecp256k1_v0_5_0_scalar_add(&sum, &sum, &s); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s); rustsecp256k1_v0_5_0_ge_set_gej(&Q, &Qj); rustsecp256k1_v0_5_0_pubkey_save(&data[i - 1], &Q); d[i - 1] = &data[i - 1]; rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum); rustsecp256k1_v0_5_0_ge_set_gej(&Q, &Qj); rustsecp256k1_v0_5_0_pubkey_save(&sd, &Q); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &sd2, d, i) == 1); CHECK(rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_fe* x) { /* The input itself, normalized. */ rustsecp256k1_v0_5_0_fe fex = *x; /* Results of set_xo_var(..., 0), set_xo_var(..., 1). */ rustsecp256k1_v0_5_0_ge ge_even, ge_odd; /* Return values of the above calls. */ int res_even, res_odd; rustsecp256k1_v0_5_0_fe_normalize_var(&fex); res_even = rustsecp256k1_v0_5_0_ge_set_xo_var(&ge_even, &fex, 0); res_odd = rustsecp256k1_v0_5_0_ge_set_xo_var(&ge_odd, &fex, 1); CHECK(res_even == res_odd); if (res_even) { rustsecp256k1_v0_5_0_fe_normalize_var(&ge_odd.x); rustsecp256k1_v0_5_0_fe_normalize_var(&ge_even.x); rustsecp256k1_v0_5_0_fe_normalize_var(&ge_odd.y); rustsecp256k1_v0_5_0_fe_normalize_var(&ge_even.y); /* No infinity allowed. */ CHECK(!ge_even.infinity); CHECK(!ge_odd.infinity); /* Check that the x coordinates check out. */ CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&ge_even.x, x)); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&ge_odd.x, x)); /* Check odd/even Y in ge_odd, ge_even. */ CHECK(rustsecp256k1_v0_5_0_fe_is_odd(&ge_odd.y)); CHECK(!rustsecp256k1_v0_5_0_fe_is_odd(&ge_even.y)); } } void run_group_decompress(void) { int i; for (i = 0; i < count * 4; i++) { rustsecp256k1_v0_5_0_fe fe; random_fe_test(&fe); test_group_decompress(&fe); } } /***** ECMULT TESTS *****/ void test_pre_g_table(const rustsecp256k1_v0_5_0_ge_storage * pre_g, size_t n) { /* Tests the pre_g / pre_g_128 tables for consistency. * For independent verification we take a "geometric" approach to verification. * We check that every entry is on-curve. * We check that for consecutive entries p and q, that p + gg - q = 0 by checking * (1) p, gg, and -q are colinear. * (2) p, gg, and -q are all distinct. * where gg is twice the generator, where the generator is the first table entry. * * Checking the table's generators are correct is done in run_ecmult_pre_g. */ rustsecp256k1_v0_5_0_gej g2; rustsecp256k1_v0_5_0_ge p, q, gg; rustsecp256k1_v0_5_0_fe dpx, dpy, dqx, dqy; size_t i; CHECK(0 < n); rustsecp256k1_v0_5_0_ge_from_storage(&p, &pre_g[0]); CHECK(rustsecp256k1_v0_5_0_ge_is_valid_var(&p)); rustsecp256k1_v0_5_0_gej_set_ge(&g2, &p); rustsecp256k1_v0_5_0_gej_double_var(&g2, &g2, NULL); rustsecp256k1_v0_5_0_ge_set_gej_var(&gg, &g2); for (i = 1; i < n; ++i) { rustsecp256k1_v0_5_0_fe_negate(&dpx, &p.x, 1); rustsecp256k1_v0_5_0_fe_add(&dpx, &gg.x); rustsecp256k1_v0_5_0_fe_normalize_weak(&dpx); rustsecp256k1_v0_5_0_fe_negate(&dpy, &p.y, 1); rustsecp256k1_v0_5_0_fe_add(&dpy, &gg.y); rustsecp256k1_v0_5_0_fe_normalize_weak(&dpy); /* Check that p is not equal to gg */ CHECK(!rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&dpx) || !rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&dpy)); rustsecp256k1_v0_5_0_ge_from_storage(&q, &pre_g[i]); CHECK(rustsecp256k1_v0_5_0_ge_is_valid_var(&q)); rustsecp256k1_v0_5_0_fe_negate(&dqx, &q.x, 1); rustsecp256k1_v0_5_0_fe_add(&dqx, &gg.x); rustsecp256k1_v0_5_0_fe_normalize_weak(&dqx); dqy = q.y; rustsecp256k1_v0_5_0_fe_add(&dqy, &gg.y); rustsecp256k1_v0_5_0_fe_normalize_weak(&dqy); /* Check that -q is not equal to gg */ CHECK(!rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&dqx) || !rustsecp256k1_v0_5_0_fe_normalizes_to_zero_var(&dqy)); /* Check that -q is not equal to p */ CHECK(!rustsecp256k1_v0_5_0_fe_equal_var(&dpx, &dqx) || !rustsecp256k1_v0_5_0_fe_equal_var(&dpy, &dqy)); /* Check that p, -q and gg are colinear */ rustsecp256k1_v0_5_0_fe_mul(&dpx, &dpx, &dqy); rustsecp256k1_v0_5_0_fe_mul(&dpy, &dpy, &dqx); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&dpx, &dpy)); p = q; } } void run_ecmult_pre_g(void) { rustsecp256k1_v0_5_0_ge_storage gs; rustsecp256k1_v0_5_0_gej gj; rustsecp256k1_v0_5_0_ge g; size_t i; /* Check that the pre_g and pre_g_128 tables are consistent. */ test_pre_g_table(rustsecp256k1_v0_5_0_pre_g, ECMULT_TABLE_SIZE(WINDOW_G)); test_pre_g_table(rustsecp256k1_v0_5_0_pre_g_128, ECMULT_TABLE_SIZE(WINDOW_G)); /* Check the first entry from the pre_g table. */ rustsecp256k1_v0_5_0_ge_to_storage(&gs, &rustsecp256k1_v0_5_0_ge_const_g); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&gs, &rustsecp256k1_v0_5_0_pre_g[0], sizeof(gs)) == 0); /* Check the first entry from the pre_g_128 table. */ rustsecp256k1_v0_5_0_gej_set_ge(&gj, &rustsecp256k1_v0_5_0_ge_const_g); for (i = 0; i < 128; ++i) { rustsecp256k1_v0_5_0_gej_double_var(&gj, &gj, NULL); } rustsecp256k1_v0_5_0_ge_set_gej(&g, &gj); rustsecp256k1_v0_5_0_ge_to_storage(&gs, &g); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&gs, &rustsecp256k1_v0_5_0_pre_g_128[0], sizeof(gs)) == 0); } void run_ecmult_chain(void) { /* random starting point A (on the curve) */ rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scalar xn = SECP256K1_SCALAR_CONST( 0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c, 0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407 ); rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337); static const rustsecp256k1_v0_5_0_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113); /* accumulators with the resulting coefficients to A and G */ rustsecp256k1_v0_5_0_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); rustsecp256k1_v0_5_0_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); /* actual points */ rustsecp256k1_v0_5_0_gej x; rustsecp256k1_v0_5_0_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; */ rustsecp256k1_v0_5_0_ecmult(&x, &x, &xn, &gn); /* also compute ae and ge: the actual accumulated factors for A and G */ /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */ rustsecp256k1_v0_5_0_scalar_mul(&ae, &ae, &xn); rustsecp256k1_v0_5_0_scalar_mul(&ge, &ge, &xn); rustsecp256k1_v0_5_0_scalar_add(&ge, &ge, &gn); /* modify xn and gn */ rustsecp256k1_v0_5_0_scalar_mul(&xn, &xn, &xf); rustsecp256k1_v0_5_0_scalar_mul(&gn, &gn, &gf); /* verify */ if (i == 19999) { /* expected result after 19999 iterations */ rustsecp256k1_v0_5_0_gej rp = SECP256K1_GEJ_CONST( 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE, 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830, 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D, 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88 ); rustsecp256k1_v0_5_0_gej_neg(&rp, &rp); rustsecp256k1_v0_5_0_gej_add_var(&rp, &rp, &x, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&rp)); } } /* redo the computation, but directly with the resulting ae and ge coefficients: */ rustsecp256k1_v0_5_0_ecmult(&x2, &a, &ae, &ge); rustsecp256k1_v0_5_0_gej_neg(&x2, &x2); rustsecp256k1_v0_5_0_gej_add_var(&x2, &x2, &x, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&x2)); } void test_point_times_order(const rustsecp256k1_v0_5_0_gej *point) { /* X * (point + G) + (order-X) * (pointer + G) = 0 */ rustsecp256k1_v0_5_0_scalar x; rustsecp256k1_v0_5_0_scalar nx; rustsecp256k1_v0_5_0_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); rustsecp256k1_v0_5_0_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); rustsecp256k1_v0_5_0_gej res1, res2; rustsecp256k1_v0_5_0_ge res3; unsigned char pub[65]; size_t psize = 65; random_scalar_order_test(&x); rustsecp256k1_v0_5_0_scalar_negate(&nx, &x); rustsecp256k1_v0_5_0_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */ rustsecp256k1_v0_5_0_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */ rustsecp256k1_v0_5_0_gej_add_var(&res1, &res1, &res2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&res1)); rustsecp256k1_v0_5_0_ge_set_gej(&res3, &res1); CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&res3)); CHECK(rustsecp256k1_v0_5_0_ge_is_valid_var(&res3) == 0); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0); psize = 65; CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0); /* check zero/one edge cases */ rustsecp256k1_v0_5_0_ecmult(&res1, point, &zero, &zero); rustsecp256k1_v0_5_0_ge_set_gej(&res3, &res1); CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&res3)); rustsecp256k1_v0_5_0_ecmult(&res1, point, &one, &zero); rustsecp256k1_v0_5_0_ge_set_gej(&res3, &res1); ge_equals_gej(&res3, point); rustsecp256k1_v0_5_0_ecmult(&res1, point, &zero, &one); rustsecp256k1_v0_5_0_ge_set_gej(&res3, &res1); ge_equals_ge(&res3, &rustsecp256k1_v0_5_0_ge_const_g); } /* These scalars reach large (in absolute value) outputs when fed to rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_scalar* target, int mode) { /* Mode: 0=ecmult_gen, 1=ecmult, 2=ecmult_const */ rustsecp256k1_v0_5_0_scalar n1, n2; rustsecp256k1_v0_5_0_ge p; rustsecp256k1_v0_5_0_gej pj, p1j, p2j, ptj; static const rustsecp256k1_v0_5_0_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); rustsecp256k1_v0_5_0_scalar_add(&n2, &n1, target); rustsecp256k1_v0_5_0_scalar_negate(&n2, &n2); /* Generate a random input point. */ if (mode != 0) { random_group_element_test(&p); rustsecp256k1_v0_5_0_gej_set_ge(&pj, &p); } /* EC multiplications */ if (mode == 0) { rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &p1j, &n1); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &p2j, &n2); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &ptj, target); } else if (mode == 1) { rustsecp256k1_v0_5_0_ecmult(&p1j, &pj, &n1, &zero); rustsecp256k1_v0_5_0_ecmult(&p2j, &pj, &n2, &zero); rustsecp256k1_v0_5_0_ecmult(&ptj, &pj, target, &zero); } else { rustsecp256k1_v0_5_0_ecmult_const(&p1j, &p, &n1, 256); rustsecp256k1_v0_5_0_ecmult_const(&p2j, &p, &n2, 256); rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_gej_add_var(&ptj, &ptj, &p1j, NULL); rustsecp256k1_v0_5_0_gej_add_var(&ptj, &ptj, &p2j, NULL); CHECK(rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2); static const rustsecp256k1_v0_5_0_fe xr = SECP256K1_FE_CONST( 0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C, 0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45 ); for (i = 0; i < 500; i++) { rustsecp256k1_v0_5_0_ge p; if (rustsecp256k1_v0_5_0_ge_set_xo_var(&p, &x, 1)) { rustsecp256k1_v0_5_0_gej j; CHECK(rustsecp256k1_v0_5_0_ge_is_valid_var(&p)); rustsecp256k1_v0_5_0_gej_set_ge(&j, &p); test_point_times_order(&j); } rustsecp256k1_v0_5_0_fe_sqr(&x, &x); } rustsecp256k1_v0_5_0_fe_normalize_var(&x); CHECK(rustsecp256k1_v0_5_0_fe_equal_var(&x, &xr)); } void ecmult_const_random_mult(void) { /* random starting point A (on the curve) */ rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scalar xn = SECP256K1_SCALAR_CONST( 0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327, 0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b ); /* expected xn * A (from sage) */ rustsecp256k1_v0_5_0_ge expected_b = SECP256K1_GE_CONST( 0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd, 0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786, 0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f, 0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956 ); rustsecp256k1_v0_5_0_gej b; rustsecp256k1_v0_5_0_ecmult_const(&b, &a, &xn, 256); CHECK(rustsecp256k1_v0_5_0_ge_is_valid_var(&a)); ge_equals_gej(&expected_b, &b); } void ecmult_const_commutativity(void) { rustsecp256k1_v0_5_0_scalar a; rustsecp256k1_v0_5_0_scalar b; rustsecp256k1_v0_5_0_gej res1; rustsecp256k1_v0_5_0_gej res2; rustsecp256k1_v0_5_0_ge mid1; rustsecp256k1_v0_5_0_ge mid2; random_scalar_order_test(&a); random_scalar_order_test(&b); rustsecp256k1_v0_5_0_ecmult_const(&res1, &rustsecp256k1_v0_5_0_ge_const_g, &a, 256); rustsecp256k1_v0_5_0_ecmult_const(&res2, &rustsecp256k1_v0_5_0_ge_const_g, &b, 256); rustsecp256k1_v0_5_0_ge_set_gej(&mid1, &res1); rustsecp256k1_v0_5_0_ge_set_gej(&mid2, &res2); rustsecp256k1_v0_5_0_ecmult_const(&res1, &mid1, &b, 256); rustsecp256k1_v0_5_0_ecmult_const(&res2, &mid2, &a, 256); rustsecp256k1_v0_5_0_ge_set_gej(&mid1, &res1); rustsecp256k1_v0_5_0_ge_set_gej(&mid2, &res2); ge_equals_ge(&mid1, &mid2); } void ecmult_const_mult_zero_one(void) { rustsecp256k1_v0_5_0_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); rustsecp256k1_v0_5_0_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); rustsecp256k1_v0_5_0_scalar negone; rustsecp256k1_v0_5_0_gej res1; rustsecp256k1_v0_5_0_ge res2; rustsecp256k1_v0_5_0_ge point; rustsecp256k1_v0_5_0_scalar_negate(&negone, &one); random_group_element_test(&point); rustsecp256k1_v0_5_0_ecmult_const(&res1, &point, &zero, 3); rustsecp256k1_v0_5_0_ge_set_gej(&res2, &res1); CHECK(rustsecp256k1_v0_5_0_ge_is_infinity(&res2)); rustsecp256k1_v0_5_0_ecmult_const(&res1, &point, &one, 2); rustsecp256k1_v0_5_0_ge_set_gej(&res2, &res1); ge_equals_ge(&res2, &point); rustsecp256k1_v0_5_0_ecmult_const(&res1, &point, &negone, 256); rustsecp256k1_v0_5_0_gej_neg(&res1, &res1); rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_scalar scalar = SECP256K1_SCALAR_CONST( 0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d, 0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b ); const rustsecp256k1_v0_5_0_gej expected_point = SECP256K1_GEJ_CONST( 0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd, 0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f, 0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196, 0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435 ); rustsecp256k1_v0_5_0_gej point; rustsecp256k1_v0_5_0_ge res; int i; rustsecp256k1_v0_5_0_gej_set_ge(&point, &rustsecp256k1_v0_5_0_ge_const_g); for (i = 0; i < 100; ++i) { rustsecp256k1_v0_5_0_ge tmp; rustsecp256k1_v0_5_0_ge_set_gej(&tmp, &point); rustsecp256k1_v0_5_0_ecmult_const(&point, &tmp, &scalar, 256); } rustsecp256k1_v0_5_0_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 { rustsecp256k1_v0_5_0_scalar *sc; rustsecp256k1_v0_5_0_ge *pt; } ecmult_multi_data; static int ecmult_multi_callback(rustsecp256k1_v0_5_0_scalar *sc, rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_scalar *sc, rustsecp256k1_v0_5_0_ge *pt, size_t idx, void *cbdata) { (void)sc; (void)pt; (void)idx; (void)cbdata; return 0; } void test_ecmult_multi(rustsecp256k1_v0_5_0_scratch *scratch, rustsecp256k1_v0_5_0_ecmult_multi_func ecmult_multi) { int ncount; rustsecp256k1_v0_5_0_scalar szero; rustsecp256k1_v0_5_0_scalar sc[32]; rustsecp256k1_v0_5_0_ge pt[32]; rustsecp256k1_v0_5_0_gej r; rustsecp256k1_v0_5_0_gej r2; ecmult_multi_data data; data.sc = sc; data.pt = pt; rustsecp256k1_v0_5_0_scalar_set_int(&szero, 0); /* No points to multiply */ CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, NULL, ecmult_multi_callback, &data, 0)); /* Check 1- and 2-point multiplies against ecmult */ for (ncount = 0; ncount < count; ncount++) { rustsecp256k1_v0_5_0_ge ptg; rustsecp256k1_v0_5_0_gej ptgj; random_scalar_order(&sc[0]); random_scalar_order(&sc[1]); random_group_element_test(&ptg); rustsecp256k1_v0_5_0_gej_set_ge(&ptgj, &ptg); pt[0] = ptg; pt[1] = rustsecp256k1_v0_5_0_ge_const_g; /* only G scalar */ rustsecp256k1_v0_5_0_ecmult(&r2, &ptgj, &szero, &sc[0]); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); /* 1-point */ rustsecp256k1_v0_5_0_ecmult(&r2, &ptgj, &sc[0], &szero); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 1)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); /* Try to multiply 1 point, but callback returns false */ CHECK(!ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1)); /* 2-point */ rustsecp256k1_v0_5_0_ecmult(&r2, &ptgj, &sc[0], &sc[1]); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 2)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); /* 2-point with G scalar */ rustsecp256k1_v0_5_0_ecmult(&r2, &ptgj, &sc[0], &sc[1]); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); } /* Check infinite outputs of various forms */ for (ncount = 0; ncount < count; ncount++) { rustsecp256k1_v0_5_0_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]); rustsecp256k1_v0_5_0_ge_set_infinity(&pt[i]); } CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); } for (j = 0; j < 3; j++) { for (i = 0; i < 32; i++) { random_group_element_test(&ptg); pt[i] = ptg; rustsecp256k1_v0_5_0_scalar_set_int(&sc[i], 0); } CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(rustsecp256k1_v0_5_0_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]); rustsecp256k1_v0_5_0_scalar_negate(&sc[2*i + 1], &sc[2*i]); pt[2 * i] = ptg; pt[2 * i + 1] = ptg; } CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_ge_neg(&pt[2*i+1], &pt[2*i]); } CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); } random_group_element_test(&ptg); rustsecp256k1_v0_5_0_scalar_set_int(&sc[0], 0); pt[0] = ptg; for (i = 1; i < 32; i++) { pt[i] = ptg; random_scalar_order(&sc[i]); rustsecp256k1_v0_5_0_scalar_add(&sc[0], &sc[0], &sc[i]); rustsecp256k1_v0_5_0_scalar_negate(&sc[i], &sc[i]); } CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 32)); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); } /* Check random points, constant scalar */ for (ncount = 0; ncount < count; ncount++) { size_t i; rustsecp256k1_v0_5_0_gej_set_infinity(&r); random_scalar_order(&sc[0]); for (i = 0; i < 20; i++) { rustsecp256k1_v0_5_0_ge ptg; sc[i] = sc[0]; random_group_element_test(&ptg); pt[i] = ptg; rustsecp256k1_v0_5_0_gej_add_ge_var(&r, &r, &pt[i], NULL); } rustsecp256k1_v0_5_0_ecmult(&r2, &r, &sc[0], &szero); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); } /* Check random scalars, constant point */ for (ncount = 0; ncount < count; ncount++) { size_t i; rustsecp256k1_v0_5_0_ge ptg; rustsecp256k1_v0_5_0_gej p0j; rustsecp256k1_v0_5_0_scalar rs; rustsecp256k1_v0_5_0_scalar_set_int(&rs, 0); random_group_element_test(&ptg); for (i = 0; i < 20; i++) { random_scalar_order(&sc[i]); pt[i] = ptg; rustsecp256k1_v0_5_0_scalar_add(&rs, &rs, &sc[i]); } rustsecp256k1_v0_5_0_gej_set_ge(&p0j, &pt[0]); rustsecp256k1_v0_5_0_ecmult(&r2, &p0j, &rs, &szero); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); rustsecp256k1_v0_5_0_gej_neg(&r2, &r2); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_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]); } rustsecp256k1_v0_5_0_scalar_clear(&sc[0]); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); rustsecp256k1_v0_5_0_scalar_clear(&sc[1]); rustsecp256k1_v0_5_0_scalar_clear(&sc[2]); rustsecp256k1_v0_5_0_scalar_clear(&sc[3]); rustsecp256k1_v0_5_0_scalar_clear(&sc[4]); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 6)); CHECK(ecmult_multi(&ctx->error_callback, scratch, &r, &szero, ecmult_multi_callback, &data, 5)); CHECK(rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_ge ptg; rustsecp256k1_v0_5_0_gej ptgj; random_group_element_test(&ptg); rustsecp256k1_v0_5_0_gej_set_ge(&ptgj, &ptg); for(t0i = 0; t0i < TOP; t0i++) { for(t1i = 0; t1i < TOP; t1i++) { rustsecp256k1_v0_5_0_gej t0p, t1p; rustsecp256k1_v0_5_0_scalar t0, t1; rustsecp256k1_v0_5_0_scalar_set_int(&t0, (t0i + 1) / 2); rustsecp256k1_v0_5_0_scalar_cond_negate(&t0, t0i & 1); rustsecp256k1_v0_5_0_scalar_set_int(&t1, (t1i + 1) / 2); rustsecp256k1_v0_5_0_scalar_cond_negate(&t1, t1i & 1); rustsecp256k1_v0_5_0_ecmult(&t0p, &ptgj, &t0, &szero); rustsecp256k1_v0_5_0_ecmult(&t1p, &ptgj, &t1, &szero); for(s0i = 0; s0i < TOP; s0i++) { for(s1i = 0; s1i < TOP; s1i++) { rustsecp256k1_v0_5_0_scalar tmp1, tmp2; rustsecp256k1_v0_5_0_gej expected, actual; rustsecp256k1_v0_5_0_ge_set_gej(&pt[0], &t0p); rustsecp256k1_v0_5_0_ge_set_gej(&pt[1], &t1p); rustsecp256k1_v0_5_0_scalar_set_int(&sc[0], (s0i + 1) / 2); rustsecp256k1_v0_5_0_scalar_cond_negate(&sc[0], s0i & 1); rustsecp256k1_v0_5_0_scalar_set_int(&sc[1], (s1i + 1) / 2); rustsecp256k1_v0_5_0_scalar_cond_negate(&sc[1], s1i & 1); rustsecp256k1_v0_5_0_scalar_mul(&tmp1, &t0, &sc[0]); rustsecp256k1_v0_5_0_scalar_mul(&tmp2, &t1, &sc[1]); rustsecp256k1_v0_5_0_scalar_add(&tmp1, &tmp1, &tmp2); rustsecp256k1_v0_5_0_ecmult(&expected, &ptgj, &tmp1, &szero); CHECK(ecmult_multi(&ctx->error_callback, scratch, &actual, &szero, ecmult_multi_callback, &data, 2)); rustsecp256k1_v0_5_0_gej_neg(&expected, &expected); rustsecp256k1_v0_5_0_gej_add_var(&actual, &actual, &expected, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&actual)); } } } } } } int test_ecmult_multi_random(rustsecp256k1_v0_5_0_scratch *scratch) { /* Large random test for ecmult_multi_* functions which exercises: * - Few or many inputs (0 up to 128, roughly exponentially distributed). * - Few or many 0*P or a*INF inputs (roughly uniformly distributed). * - Including or excluding an nonzero a*G term (or such a term at all). * - Final expected result equal to infinity or not (roughly 50%). * - ecmult_multi_var, ecmult_strauss_single_batch, ecmult_pippenger_single_batch */ /* These 4 variables define the eventual input to the ecmult_multi function. * g_scalar is the G scalar fed to it (or NULL, possibly, if g_scalar=0), and * scalars[0..filled-1] and gejs[0..filled-1] are the scalars and points * which form its normal inputs. */ int filled = 0; rustsecp256k1_v0_5_0_scalar g_scalar = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); rustsecp256k1_v0_5_0_scalar scalars[128]; rustsecp256k1_v0_5_0_gej gejs[128]; /* The expected result, and the computed result. */ rustsecp256k1_v0_5_0_gej expected, computed; /* Temporaries. */ rustsecp256k1_v0_5_0_scalar sc_tmp; rustsecp256k1_v0_5_0_ge ge_tmp; /* Variables needed for the actual input to ecmult_multi. */ rustsecp256k1_v0_5_0_ge ges[128]; ecmult_multi_data data; int i; /* Which multiplication function to use */ int fn = rustsecp256k1_v0_5_0_testrand_int(3); rustsecp256k1_v0_5_0_ecmult_multi_func ecmult_multi = fn == 0 ? rustsecp256k1_v0_5_0_ecmult_multi_var : fn == 1 ? rustsecp256k1_v0_5_0_ecmult_strauss_batch_single : rustsecp256k1_v0_5_0_ecmult_pippenger_batch_single; /* Simulate exponentially distributed num. */ int num_bits = 2 + rustsecp256k1_v0_5_0_testrand_int(6); /* Number of (scalar, point) inputs (excluding g). */ int num = rustsecp256k1_v0_5_0_testrand_int((1 << num_bits) + 1); /* Number of those which are nonzero. */ int num_nonzero = rustsecp256k1_v0_5_0_testrand_int(num + 1); /* Whether we're aiming to create an input with nonzero expected result. */ int nonzero_result = rustsecp256k1_v0_5_0_testrand_bits(1); /* Whether we will provide nonzero g multiplicand. In some cases our hand * is forced here based on num_nonzero and nonzero_result. */ int g_nonzero = num_nonzero == 0 ? nonzero_result : num_nonzero == 1 && !nonzero_result ? 1 : (int)rustsecp256k1_v0_5_0_testrand_bits(1); /* Which g_scalar pointer to pass into ecmult_multi(). */ const rustsecp256k1_v0_5_0_scalar* g_scalar_ptr = (g_nonzero || rustsecp256k1_v0_5_0_testrand_bits(1)) ? &g_scalar : NULL; /* How many EC multiplications were performed in this function. */ int mults = 0; /* How many randomization steps to apply to the input list. */ int rands = (int)rustsecp256k1_v0_5_0_testrand_bits(3); if (rands > num_nonzero) rands = num_nonzero; rustsecp256k1_v0_5_0_gej_set_infinity(&expected); rustsecp256k1_v0_5_0_gej_set_infinity(&gejs[0]); rustsecp256k1_v0_5_0_scalar_set_int(&scalars[0], 0); if (g_nonzero) { /* If g_nonzero, set g_scalar to nonzero value r. */ random_scalar_order_test(&g_scalar); if (!nonzero_result) { /* If expected=0 is desired, add a (a*r, -(1/a)*g) term to compensate. */ CHECK(num_nonzero > filled); random_scalar_order_test(&sc_tmp); rustsecp256k1_v0_5_0_scalar_mul(&scalars[filled], &sc_tmp, &g_scalar); rustsecp256k1_v0_5_0_scalar_inverse_var(&sc_tmp, &sc_tmp); rustsecp256k1_v0_5_0_scalar_negate(&sc_tmp, &sc_tmp); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &gejs[filled], &sc_tmp); ++filled; ++mults; } } if (nonzero_result && filled < num_nonzero) { /* If a nonzero result is desired, and there is space, add a random nonzero term. */ random_scalar_order_test(&scalars[filled]); random_group_element_test(&ge_tmp); rustsecp256k1_v0_5_0_gej_set_ge(&gejs[filled], &ge_tmp); ++filled; } if (nonzero_result) { /* Compute the expected result using normal ecmult. */ CHECK(filled <= 1); rustsecp256k1_v0_5_0_ecmult(&expected, &gejs[0], &scalars[0], &g_scalar); mults += filled + g_nonzero; } /* At this point we have expected = scalar_g*G + sum(scalars[i]*gejs[i] for i=0..filled-1). */ CHECK(filled <= 1 + !nonzero_result); CHECK(filled <= num_nonzero); /* Add entries to scalars,gejs so that there are num of them. All the added entries * either have scalar=0 or point=infinity, so these do not change the expected result. */ while (filled < num) { if (rustsecp256k1_v0_5_0_testrand_bits(1)) { rustsecp256k1_v0_5_0_gej_set_infinity(&gejs[filled]); random_scalar_order_test(&scalars[filled]); } else { rustsecp256k1_v0_5_0_scalar_set_int(&scalars[filled], 0); random_group_element_test(&ge_tmp); rustsecp256k1_v0_5_0_gej_set_ge(&gejs[filled], &ge_tmp); } ++filled; } /* Now perform cheapish transformations on gejs and scalars, for indices * 0..num_nonzero-1, which do not change the expected result, but may * convert some of them to be both non-0-scalar and non-infinity-point. */ for (i = 0; i < rands; ++i) { int j; rustsecp256k1_v0_5_0_scalar v, iv; /* Shuffle the entries. */ for (j = 0; j < num_nonzero; ++j) { int k = rustsecp256k1_v0_5_0_testrand_int(num_nonzero - j); if (k != 0) { rustsecp256k1_v0_5_0_gej gej = gejs[j]; rustsecp256k1_v0_5_0_scalar sc = scalars[j]; gejs[j] = gejs[j + k]; scalars[j] = scalars[j + k]; gejs[j + k] = gej; scalars[j + k] = sc; } } /* Perturb all consecutive pairs of inputs: * a*P + b*Q -> (a+b)*P + b*(Q-P). */ for (j = 0; j + 1 < num_nonzero; j += 2) { rustsecp256k1_v0_5_0_gej gej; rustsecp256k1_v0_5_0_scalar_add(&scalars[j], &scalars[j], &scalars[j+1]); rustsecp256k1_v0_5_0_gej_neg(&gej, &gejs[j]); rustsecp256k1_v0_5_0_gej_add_var(&gejs[j+1], &gejs[j+1], &gej, NULL); } /* Transform the last input: a*P -> (v*a) * ((1/v)*P). */ CHECK(num_nonzero >= 1); random_scalar_order_test(&v); rustsecp256k1_v0_5_0_scalar_inverse(&iv, &v); rustsecp256k1_v0_5_0_scalar_mul(&scalars[num_nonzero - 1], &scalars[num_nonzero - 1], &v); rustsecp256k1_v0_5_0_ecmult(&gejs[num_nonzero - 1], &gejs[num_nonzero - 1], &iv, NULL); ++mults; } /* Shuffle all entries (0..num-1). */ for (i = 0; i < num; ++i) { int j = rustsecp256k1_v0_5_0_testrand_int(num - i); if (j != 0) { rustsecp256k1_v0_5_0_gej gej = gejs[i]; rustsecp256k1_v0_5_0_scalar sc = scalars[i]; gejs[i] = gejs[i + j]; scalars[i] = scalars[i + j]; gejs[i + j] = gej; scalars[i + j] = sc; } } /* Compute affine versions of all inputs. */ rustsecp256k1_v0_5_0_ge_set_all_gej_var(ges, gejs, filled); /* Invoke ecmult_multi code. */ data.sc = scalars; data.pt = ges; CHECK(ecmult_multi(&ctx->error_callback, scratch, &computed, g_scalar_ptr, ecmult_multi_callback, &data, filled)); mults += num_nonzero + g_nonzero; /* Compare with expected result. */ rustsecp256k1_v0_5_0_gej_neg(&computed, &computed); rustsecp256k1_v0_5_0_gej_add_var(&computed, &computed, &expected, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&computed)); return mults; } void test_ecmult_multi_batch_single(rustsecp256k1_v0_5_0_ecmult_multi_func ecmult_multi) { rustsecp256k1_v0_5_0_scalar szero; rustsecp256k1_v0_5_0_scalar sc; rustsecp256k1_v0_5_0_ge pt; rustsecp256k1_v0_5_0_gej r; ecmult_multi_data data; rustsecp256k1_v0_5_0_scratch *scratch_empty; random_group_element_test(&pt); random_scalar_order(&sc); data.sc = ≻ data.pt = &pt; rustsecp256k1_v0_5_0_scalar_set_int(&szero, 0); /* Try to multiply 1 point, but scratch space is empty.*/ scratch_empty = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, 0); CHECK(!ecmult_multi(&ctx->error_callback, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1)); rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch_empty); } void test_rustsecp256k1_v0_5_0_pippenger_bucket_window_inv(void) { int i; CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_pippenger_bucket_window(rustsecp256k1_v0_5_0_pippenger_bucket_window_inv(i)) == i); if (i != PIPPENGER_MAX_BUCKET_WINDOW) { CHECK(rustsecp256k1_v0_5_0_pippenger_bucket_window(rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_testrand_bits(8); size_t max_size = rustsecp256k1_v0_5_0_pippenger_scratch_size(rustsecp256k1_v0_5_0_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12); rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, scratch_size); CHECK(scratch != NULL); checkpoint = rustsecp256k1_v0_5_0_scratch_checkpoint(&ctx->error_callback, scratch); n_points_supported = rustsecp256k1_v0_5_0_pippenger_max_points(&ctx->error_callback, scratch); if (n_points_supported == 0) { rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch); continue; } bucket_window = rustsecp256k1_v0_5_0_pippenger_bucket_window(n_points_supported); /* allocate `total_alloc` bytes over `PIPPENGER_SCRATCH_OBJECTS` many allocations */ total_alloc = rustsecp256k1_v0_5_0_pippenger_scratch_size(n_points_supported, bucket_window); for (i = 0; i < PIPPENGER_SCRATCH_OBJECTS - 1; i++) { CHECK(rustsecp256k1_v0_5_0_scratch_alloc(&ctx->error_callback, scratch, 1)); total_alloc--; } CHECK(rustsecp256k1_v0_5_0_scratch_alloc(&ctx->error_callback, scratch, total_alloc)); rustsecp256k1_v0_5_0_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0); max_n_batch_points = 1; n = 0; CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_scalar scG; rustsecp256k1_v0_5_0_scalar szero; rustsecp256k1_v0_5_0_scalar *sc = (rustsecp256k1_v0_5_0_scalar *)checked_malloc(&ctx->error_callback, sizeof(rustsecp256k1_v0_5_0_scalar) * n_points); rustsecp256k1_v0_5_0_ge *pt = (rustsecp256k1_v0_5_0_ge *)checked_malloc(&ctx->error_callback, sizeof(rustsecp256k1_v0_5_0_ge) * n_points); rustsecp256k1_v0_5_0_gej r; rustsecp256k1_v0_5_0_gej r2; ecmult_multi_data data; int i; rustsecp256k1_v0_5_0_scratch *scratch; rustsecp256k1_v0_5_0_gej_set_infinity(&r2); rustsecp256k1_v0_5_0_scalar_set_int(&szero, 0); /* Get random scalars and group elements and compute result */ random_scalar_order(&scG); rustsecp256k1_v0_5_0_ecmult(&r2, &r2, &szero, &scG); for(i = 0; i < n_points; i++) { rustsecp256k1_v0_5_0_ge ptg; rustsecp256k1_v0_5_0_gej ptgj; random_group_element_test(&ptg); rustsecp256k1_v0_5_0_gej_set_ge(&ptgj, &ptg); pt[i] = ptg; random_scalar_order(&sc[i]); rustsecp256k1_v0_5_0_ecmult(&ptgj, &ptgj, &sc[i], NULL); rustsecp256k1_v0_5_0_gej_add_var(&r2, &r2, &ptgj, NULL); } data.sc = sc; data.pt = pt; rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, 0); CHECK(rustsecp256k1_v0_5_0_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, rustsecp256k1_v0_5_0_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); CHECK(rustsecp256k1_v0_5_0_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch); for(i = 1; i <= n_points; i++) { if (i > ECMULT_PIPPENGER_THRESHOLD) { int bucket_window = rustsecp256k1_v0_5_0_pippenger_bucket_window(i); size_t scratch_size = rustsecp256k1_v0_5_0_pippenger_scratch_size(i, bucket_window); scratch = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); } else { size_t scratch_size = rustsecp256k1_v0_5_0_strauss_scratch_size(i); scratch = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); } CHECK(rustsecp256k1_v0_5_0_ecmult_multi_var(&ctx->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); rustsecp256k1_v0_5_0_gej_add_var(&r, &r, &r2, NULL); CHECK(rustsecp256k1_v0_5_0_gej_is_infinity(&r)); rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch); } free(sc); free(pt); } void run_ecmult_multi_tests(void) { rustsecp256k1_v0_5_0_scratch *scratch; int64_t todo = (int64_t)320 * count; test_rustsecp256k1_v0_5_0_pippenger_bucket_window_inv(); test_ecmult_multi_pippenger_max_points(); scratch = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, 819200); test_ecmult_multi(scratch, rustsecp256k1_v0_5_0_ecmult_multi_var); test_ecmult_multi(NULL, rustsecp256k1_v0_5_0_ecmult_multi_var); test_ecmult_multi(scratch, rustsecp256k1_v0_5_0_ecmult_pippenger_batch_single); test_ecmult_multi_batch_single(rustsecp256k1_v0_5_0_ecmult_pippenger_batch_single); test_ecmult_multi(scratch, rustsecp256k1_v0_5_0_ecmult_strauss_batch_single); test_ecmult_multi_batch_single(rustsecp256k1_v0_5_0_ecmult_strauss_batch_single); while (todo > 0) { todo -= test_ecmult_multi_random(scratch); } rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch); /* Run test_ecmult_multi with space for exactly one point */ scratch = rustsecp256k1_v0_5_0_scratch_create(&ctx->error_callback, rustsecp256k1_v0_5_0_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); test_ecmult_multi(scratch, rustsecp256k1_v0_5_0_ecmult_multi_var); rustsecp256k1_v0_5_0_scratch_destroy(&ctx->error_callback, scratch); test_ecmult_multi_batch_size_helper(); test_ecmult_multi_batching(); } void test_wnaf(const rustsecp256k1_v0_5_0_scalar *number, int w) { rustsecp256k1_v0_5_0_scalar x, two, t; int wnaf[256]; int zeroes = -1; int i; int bits; rustsecp256k1_v0_5_0_scalar_set_int(&x, 0); rustsecp256k1_v0_5_0_scalar_set_int(&two, 2); bits = rustsecp256k1_v0_5_0_ecmult_wnaf(wnaf, 256, number, w); CHECK(bits <= 256); for (i = bits-1; i >= 0; i--) { int v = wnaf[i]; rustsecp256k1_v0_5_0_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) { rustsecp256k1_v0_5_0_scalar_set_int(&t, v); } else { rustsecp256k1_v0_5_0_scalar_set_int(&t, -v); rustsecp256k1_v0_5_0_scalar_negate(&t, &t); } rustsecp256k1_v0_5_0_scalar_add(&x, &x, &t); } CHECK(rustsecp256k1_v0_5_0_scalar_eq(&x, number)); /* check that wnaf represents number */ } void test_constant_wnaf_negate(const rustsecp256k1_v0_5_0_scalar *number) { rustsecp256k1_v0_5_0_scalar neg1 = *number; rustsecp256k1_v0_5_0_scalar neg2 = *number; int sign1 = 1; int sign2 = 1; if (!rustsecp256k1_v0_5_0_scalar_get_bits(&neg1, 0, 1)) { rustsecp256k1_v0_5_0_scalar_negate(&neg1, &neg1); sign1 = -1; } sign2 = rustsecp256k1_v0_5_0_scalar_cond_negate(&neg2, rustsecp256k1_v0_5_0_scalar_is_even(&neg2)); CHECK(sign1 == sign2); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&neg1, &neg2)); } void test_constant_wnaf(const rustsecp256k1_v0_5_0_scalar *number, int w) { rustsecp256k1_v0_5_0_scalar x, shift; int wnaf[256] = {0}; int i; int skew; int bits = 256; rustsecp256k1_v0_5_0_scalar num = *number; rustsecp256k1_v0_5_0_scalar scalar_skew; rustsecp256k1_v0_5_0_scalar_set_int(&x, 0); rustsecp256k1_v0_5_0_scalar_set_int(&shift, 1 << w); for (i = 0; i < 16; ++i) { rustsecp256k1_v0_5_0_scalar_shr_int(&num, 8); } bits = 128; skew = rustsecp256k1_v0_5_0_wnaf_const(wnaf, &num, w, bits); for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) { rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scalar_mul(&x, &x, &shift); if (v >= 0) { rustsecp256k1_v0_5_0_scalar_set_int(&t, v); } else { rustsecp256k1_v0_5_0_scalar_set_int(&t, -v); rustsecp256k1_v0_5_0_scalar_negate(&t, &t); } rustsecp256k1_v0_5_0_scalar_add(&x, &x, &t); } /* Skew num because when encoding numbers as odd we use an offset */ rustsecp256k1_v0_5_0_scalar_set_int(&scalar_skew, skew); rustsecp256k1_v0_5_0_scalar_add(&num, &num, &scalar_skew); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&x, &num)); } void test_fixed_wnaf(const rustsecp256k1_v0_5_0_scalar *number, int w) { rustsecp256k1_v0_5_0_scalar x, shift; int wnaf[256] = {0}; int i; int skew; rustsecp256k1_v0_5_0_scalar num = *number; rustsecp256k1_v0_5_0_scalar_set_int(&x, 0); rustsecp256k1_v0_5_0_scalar_set_int(&shift, 1 << w); for (i = 0; i < 16; ++i) { rustsecp256k1_v0_5_0_scalar_shr_int(&num, 8); } skew = rustsecp256k1_v0_5_0_wnaf_fixed(wnaf, &num, w); for (i = WNAF_SIZE(w)-1; i >= 0; --i) { rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scalar_mul(&x, &x, &shift); if (v >= 0) { rustsecp256k1_v0_5_0_scalar_set_int(&t, v); } else { rustsecp256k1_v0_5_0_scalar_set_int(&t, -v); rustsecp256k1_v0_5_0_scalar_negate(&t, &t); } rustsecp256k1_v0_5_0_scalar_add(&x, &x, &t); } /* If skew is 1 then add 1 to num */ rustsecp256k1_v0_5_0_scalar_cadd_bit(&num, 0, skew == 1); CHECK(rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_scalar num; rustsecp256k1_v0_5_0_scalar_set_int(&num, 0); skew = rustsecp256k1_v0_5_0_wnaf_fixed(wnaf, &num, w); for (i = WNAF_SIZE(w)-1; i >= 0; --i) { int v = wnaf[i]; CHECK(v == 0); } CHECK(skew == 0); rustsecp256k1_v0_5_0_scalar_set_int(&num, 1); skew = rustsecp256k1_v0_5_0_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 }; rustsecp256k1_v0_5_0_scalar_set_int(&num, 0xffffffff); skew = rustsecp256k1_v0_5_0_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 }; rustsecp256k1_v0_5_0_scalar_set_int(&num, 0xeeeeeeee); skew = rustsecp256k1_v0_5_0_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 }; rustsecp256k1_v0_5_0_scalar_set_int(&num, 0x01010101); skew = rustsecp256k1_v0_5_0_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 }; rustsecp256k1_v0_5_0_scalar_set_int(&num, 0x01ef1ef1); skew = rustsecp256k1_v0_5_0_wnaf_fixed(wnaf, &num, w); test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); CHECK(skew == 0); } } void run_wnaf(void) { int i; rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_scalar_one; rustsecp256k1_v0_5_0_scalar_negate(&n, &n); test_constant_wnaf(&n, 4); /* Test -2, which may not lead to overflows in wnaf_const */ rustsecp256k1_v0_5_0_scalar_add(&n, &rustsecp256k1_v0_5_0_scalar_one, &rustsecp256k1_v0_5_0_scalar_one); rustsecp256k1_v0_5_0_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 */ rustsecp256k1_v0_5_0_scalar_inverse(&n, &n); test_constant_wnaf(&n, 4); rustsecp256k1_v0_5_0_scalar_add(&n, &n, &rustsecp256k1_v0_5_0_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)); } rustsecp256k1_v0_5_0_scalar_set_int(&n, 0); CHECK(rustsecp256k1_v0_5_0_scalar_cond_negate(&n, 1) == -1); CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&n)); CHECK(rustsecp256k1_v0_5_0_scalar_cond_negate(&n, 0) == 1); CHECK(rustsecp256k1_v0_5_0_scalar_is_zero(&n)); } static int test_ecmult_accumulate_cb(rustsecp256k1_v0_5_0_scalar* sc, rustsecp256k1_v0_5_0_ge* pt, size_t idx, void* data) { const rustsecp256k1_v0_5_0_scalar* indata = (const rustsecp256k1_v0_5_0_scalar*)data; *sc = *indata; *pt = rustsecp256k1_v0_5_0_ge_const_g; CHECK(idx == 0); return 1; } void test_ecmult_accumulate(rustsecp256k1_v0_5_0_sha256* acc, const rustsecp256k1_v0_5_0_scalar* x, rustsecp256k1_v0_5_0_scratch* scratch) { /* Compute x*G in 6 different ways, serialize it uncompressed, and feed it into acc. */ rustsecp256k1_v0_5_0_gej rj1, rj2, rj3, rj4, rj5, rj6, gj, infj; rustsecp256k1_v0_5_0_ge r; const rustsecp256k1_v0_5_0_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); unsigned char bytes[65]; size_t size = 65; rustsecp256k1_v0_5_0_gej_set_ge(&gj, &rustsecp256k1_v0_5_0_ge_const_g); rustsecp256k1_v0_5_0_gej_set_infinity(&infj); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &rj1, x); rustsecp256k1_v0_5_0_ecmult(&rj2, &gj, x, &zero); rustsecp256k1_v0_5_0_ecmult(&rj3, &infj, &zero, x); rustsecp256k1_v0_5_0_ecmult_multi_var(NULL, scratch, &rj4, x, NULL, NULL, 0); rustsecp256k1_v0_5_0_ecmult_multi_var(NULL, scratch, &rj5, &zero, test_ecmult_accumulate_cb, (void*)x, 1); rustsecp256k1_v0_5_0_ecmult_const(&rj6, &rustsecp256k1_v0_5_0_ge_const_g, x, 256); rustsecp256k1_v0_5_0_ge_set_gej_var(&r, &rj1); ge_equals_gej(&r, &rj2); ge_equals_gej(&r, &rj3); ge_equals_gej(&r, &rj4); ge_equals_gej(&r, &rj5); ge_equals_gej(&r, &rj6); if (rustsecp256k1_v0_5_0_ge_is_infinity(&r)) { /* Store infinity as 0x00 */ const unsigned char zerobyte[1] = {0}; rustsecp256k1_v0_5_0_sha256_write(acc, zerobyte, 1); } else { /* Store other points using their uncompressed serialization. */ rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&r, bytes, &size, 0); CHECK(size == 65); rustsecp256k1_v0_5_0_sha256_write(acc, bytes, size); } } void test_ecmult_constants(void) { /* Test ecmult_gen for: * - For i in 0..36: * - Key i * - Key -i * - For i in 0..255: * - For j in 1..255 (only odd values): * - Key (j*2^i) mod order */ rustsecp256k1_v0_5_0_scalar x; rustsecp256k1_v0_5_0_sha256 acc; unsigned char b32[32]; int i, j; rustsecp256k1_v0_5_0_scratch_space *scratch = rustsecp256k1_v0_5_0_scratch_space_create(ctx, 65536); /* Expected hash of all the computed points; created with an independent * implementation. */ static const unsigned char expected32[32] = { 0xe4, 0x71, 0x1b, 0x4d, 0x14, 0x1e, 0x68, 0x48, 0xb7, 0xaf, 0x47, 0x2b, 0x4c, 0xd2, 0x04, 0x14, 0x3a, 0x75, 0x87, 0x60, 0x1a, 0xf9, 0x63, 0x60, 0xd0, 0xcb, 0x1f, 0xaa, 0x85, 0x9a, 0xb7, 0xb4 }; rustsecp256k1_v0_5_0_sha256_initialize(&acc); for (i = 0; i <= 36; ++i) { rustsecp256k1_v0_5_0_scalar_set_int(&x, i); test_ecmult_accumulate(&acc, &x, scratch); rustsecp256k1_v0_5_0_scalar_negate(&x, &x); test_ecmult_accumulate(&acc, &x, scratch); }; for (i = 0; i < 256; ++i) { for (j = 1; j < 256; j += 2) { int k; rustsecp256k1_v0_5_0_scalar_set_int(&x, j); for (k = 0; k < i; ++k) rustsecp256k1_v0_5_0_scalar_add(&x, &x, &x); test_ecmult_accumulate(&acc, &x, scratch); } } rustsecp256k1_v0_5_0_sha256_finalize(&acc, b32); CHECK(rustsecp256k1_v0_5_0_memcmp_var(b32, expected32, 32) == 0); rustsecp256k1_v0_5_0_scratch_space_destroy(ctx, scratch); } 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. */ rustsecp256k1_v0_5_0_scalar key; rustsecp256k1_v0_5_0_scalar b; unsigned char seed32[32]; rustsecp256k1_v0_5_0_gej pgej; rustsecp256k1_v0_5_0_gej pgej2; rustsecp256k1_v0_5_0_gej i; rustsecp256k1_v0_5_0_ge pge; random_scalar_order_test(&key); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key); rustsecp256k1_v0_5_0_testrand256(seed32); b = ctx->ecmult_gen_ctx.blind; i = ctx->ecmult_gen_ctx.initial; rustsecp256k1_v0_5_0_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32); CHECK(!rustsecp256k1_v0_5_0_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind)); rustsecp256k1_v0_5_0_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)); rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_scalar b; rustsecp256k1_v0_5_0_gej initial; rustsecp256k1_v0_5_0_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0); b = ctx->ecmult_gen_ctx.blind; initial = ctx->ecmult_gen_ctx.initial; rustsecp256k1_v0_5_0_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0); CHECK(rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_scalar* full) { rustsecp256k1_v0_5_0_scalar s, s1, slam; const unsigned char zero[32] = {0}; unsigned char tmp[32]; rustsecp256k1_v0_5_0_scalar_split_lambda(&s1, &slam, full); /* check slam*lambda + s1 == full */ rustsecp256k1_v0_5_0_scalar_mul(&s, &rustsecp256k1_v0_5_0_const_lambda, &slam); rustsecp256k1_v0_5_0_scalar_add(&s, &s, &s1); CHECK(rustsecp256k1_v0_5_0_scalar_eq(&s, full)); /* check that both are <= 128 bits in size */ if (rustsecp256k1_v0_5_0_scalar_is_high(&s1)) { rustsecp256k1_v0_5_0_scalar_negate(&s1, &s1); } if (rustsecp256k1_v0_5_0_scalar_is_high(&slam)) { rustsecp256k1_v0_5_0_scalar_negate(&slam, &slam); } rustsecp256k1_v0_5_0_scalar_get_b32(tmp, &s1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zero, tmp, 16) == 0); rustsecp256k1_v0_5_0_scalar_get_b32(tmp, &slam); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zero, tmp, 16) == 0); } void run_endomorphism_tests(void) { unsigned i; static rustsecp256k1_v0_5_0_scalar s; test_scalar_split(&rustsecp256k1_v0_5_0_scalar_zero); test_scalar_split(&rustsecp256k1_v0_5_0_scalar_one); rustsecp256k1_v0_5_0_scalar_negate(&s,&rustsecp256k1_v0_5_0_scalar_one); test_scalar_split(&s); test_scalar_split(&rustsecp256k1_v0_5_0_const_lambda); rustsecp256k1_v0_5_0_scalar_add(&s, &rustsecp256k1_v0_5_0_const_lambda, &rustsecp256k1_v0_5_0_scalar_one); test_scalar_split(&s); for (i = 0; i < 100U * count; ++i) { rustsecp256k1_v0_5_0_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]; rustsecp256k1_v0_5_0_pubkey pubkey; rustsecp256k1_v0_5_0_ge ge; size_t pubkeyclen; int32_t ecount; ecount = 0; rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); outl = 65; VG_UNDEF(pubkeyo, 65); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1); VG_CHECK(pubkeyo, outl); CHECK(outl == 33); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_pubkey_load(ctx, &ge, &pubkey) == 1); memset(&pubkey, 0, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); rustsecp256k1_v0_5_0_pubkey_save(&pubkey, &ge); VG_CHECK(&pubkey, sizeof(pubkey)); outl = 65; VG_UNDEF(pubkeyo, 65); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); VG_CHECK(pubkeyo, outl); CHECK(outl == 65); CHECK(pubkeyo[0] == 4); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 1); } } } rustsecp256k1_v0_5_0_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]; rustsecp256k1_v0_5_0_ge ge; rustsecp256k1_v0_5_0_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); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_pubkey_load(ctx, &ge, &pubkey) == 0); CHECK(ecount == 1); /* Valid parse. */ memset(&pubkey, 0, sizeof(pubkey)); ecount = 0; VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(rustsecp256k1_v0_5_0_context_no_precomp, &pubkey, pubkeyc, 65) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(ecount == 0); VG_UNDEF(&ge, sizeof(ge)); CHECK(rustsecp256k1_v0_5_0_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(&rustsecp256k1_v0_5_0_ge_const_g, &ge); CHECK(ecount == 0); /* rustsecp256k1_v0_5_0_ec_pubkey_serialize illegal args. */ ecount = 0; len = 65; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); CHECK(ecount == 1); CHECK(len == 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); CHECK(ecount == 2); len = 65; VG_UNDEF(sout, 65); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0); VG_CHECK(sout, 65); CHECK(ecount == 3); CHECK(len == 0); len = 65; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0); CHECK(ecount == 4); CHECK(len == 0); len = 65; VG_UNDEF(sout, 65); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); CHECK(ecount == 1); /* Does the illegal arg callback actually change the behavior? */ rustsecp256k1_v0_5_0_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); CHECK(ecount == 1); CHECK(ecount2 == 10); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_pubkey)] = {0x00}; unsigned char ctmp[33]; unsigned char ctmp2[33]; rustsecp256k1_v0_5_0_pubkey pubkey; rustsecp256k1_v0_5_0_pubkey pubkey2; rustsecp256k1_v0_5_0_pubkey pubkey_one; rustsecp256k1_v0_5_0_pubkey pubkey_negone; const rustsecp256k1_v0_5_0_pubkey *pubkeys[3]; size_t len; int32_t ecount; /* Group order is too large, reject. */ CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, orderc) == 0); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, orderc) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); /* Maximum value is too large, reject. */ memset(ctmp, 255, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); /* Zero is too small, reject. */ memset(ctmp, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); /* One must be accepted. */ ctmp[31] = 0x01; CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 1); memset(&pubkey, 0, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) > 0); pubkey_one = pubkey; /* Group order + 1 is too large, reject. */ memcpy(ctmp, orderc, 32); ctmp[31] = 0x42; CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 0); memset(&pubkey, 1, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); /* -1 must be accepted. */ ctmp[31] = 0x40; CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 1); memset(&pubkey, 0, sizeof(pubkey)); VG_UNDEF(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); VG_CHECK(&pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) > 0); pubkey_negone = pubkey; /* Tweak of zero leaves the value unchanged. */ memset(ctmp2, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40); memcpy(&pubkey2, &pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Multiply tweak of zero zeroizes the output. */ CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zeros, ctmp, 32) == 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp2) == 1); CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 0); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zeros, ctmp, 32) == 0); memcpy(ctmp, orderc, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp, orderc) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zeros, ctmp, 32) == 0); memcpy(ctmp, orderc, 32); ctmp[31] = 0x40; CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, ctmp, orderc) == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); /* If the resulting key in rustsecp256k1_v0_5_0_ec_seckey_tweak_add and * rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(zeros, ctmp2, 32) == 0); ctmp2[31] = 1; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1); ctmp2[31] = 2; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); ctmp2[31] = 1; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Tweak mul * 2 = 1+1. */ CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); ctmp2[31] = 2; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); /* Test argument errors. */ ecount = 0; rustsecp256k1_v0_5_0_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); CHECK(ecount == 0); /* Zeroize pubkey on parse error. */ memset(&pubkey, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0); memcpy(&pubkey, &pubkey2, sizeof(pubkey)); memset(&pubkey2, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey2, zeros, sizeof(pubkey2)) == 0); /* Plain argument errors. */ ecount = 0; CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, ctmp) == 1); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, NULL) == 0); CHECK(ecount == 1); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 4; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 4; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, ctmp, NULL) == 0); CHECK(ecount == 2); ecount = 0; memset(ctmp2, 0, 32); ctmp2[31] = 1; CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, NULL, ctmp2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, ctmp, NULL) == 0); CHECK(ecount == 2); ecount = 0; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, NULL, ctmp) == 0); CHECK(ecount == 1); memset(&pubkey, 1, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, NULL) == 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); /* rustsecp256k1_v0_5_0_ec_pubkey_combine tests. */ ecount = 0; pubkeys[0] = &pubkey_one; VG_UNDEF(&pubkeys[0], sizeof(rustsecp256k1_v0_5_0_pubkey *)); VG_UNDEF(&pubkeys[1], sizeof(rustsecp256k1_v0_5_0_pubkey *)); VG_UNDEF(&pubkeys[2], sizeof(rustsecp256k1_v0_5_0_pubkey *)); memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); CHECK(ecount == 2); memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); CHECK(ecount == 3); pubkeys[0] = &pubkey_negone; memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) > 0); CHECK(ecount == 3); len = 33; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(ctmp, ctmp2, 33) == 0); /* Result is infinity. */ pubkeys[0] = &pubkey_one; pubkeys[1] = &pubkey_negone; memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) == 0); CHECK(ecount == 3); /* Passes through infinity but comes out one. */ pubkeys[2] = &pubkey_one; memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) > 0); CHECK(ecount == 3); len = 33; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(ctmp, ctmp2, 33) == 0); /* Adds to two. */ pubkeys[1] = &pubkey_one; memset(&pubkey, 255, sizeof(rustsecp256k1_v0_5_0_pubkey)); VG_UNDEF(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1); VG_CHECK(&pubkey, sizeof(rustsecp256k1_v0_5_0_pubkey)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, zeros, sizeof(rustsecp256k1_v0_5_0_pubkey)) > 0); CHECK(ecount == 3); rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_negate(ctx, seckey) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(seckey, seckey_tmp, 32) != 0); CHECK(rustsecp256k1_v0_5_0_ec_seckey_negate(ctx, seckey) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(seckey, seckey_tmp, 32) == 0); /* Check that privkey alias gives same result */ CHECK(rustsecp256k1_v0_5_0_ec_seckey_negate(ctx, seckey) == 1); CHECK(rustsecp256k1_v0_5_0_ec_privkey_negate(ctx, seckey_tmp) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(seckey, seckey_tmp, 32) == 0); /* Negating all 0s fails */ memset(seckey, 0, 32); memset(seckey_tmp, 0, 32); CHECK(rustsecp256k1_v0_5_0_ec_seckey_negate(ctx, seckey) == 0); /* Check that seckey is not modified */ CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ec_seckey_negate(ctx, seckey) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(seckey, seckey_tmp, 32) == 0); } void random_sign(rustsecp256k1_v0_5_0_scalar *sigr, rustsecp256k1_v0_5_0_scalar *sigs, const rustsecp256k1_v0_5_0_scalar *key, const rustsecp256k1_v0_5_0_scalar *msg, int *recid) { rustsecp256k1_v0_5_0_scalar nonce; do { random_scalar_order_test(&nonce); } while(!rustsecp256k1_v0_5_0_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid)); } void test_ecdsa_sign_verify(void) { rustsecp256k1_v0_5_0_gej pubj; rustsecp256k1_v0_5_0_ge pub; rustsecp256k1_v0_5_0_scalar one; rustsecp256k1_v0_5_0_scalar msg, key; rustsecp256k1_v0_5_0_scalar sigr, sigs; int getrec; int recid; random_scalar_order_test(&msg); random_scalar_order_test(&key); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key); rustsecp256k1_v0_5_0_ge_set_gej(&pub, &pubj); getrec = rustsecp256k1_v0_5_0_testrand_bits(1); /* The specific way in which this conditional is written sidesteps a potential bug in clang. See the commit messages of the commit that introduced this comment for details. */ if (getrec) { random_sign(&sigr, &sigs, &key, &msg, &recid); CHECK(recid >= 0 && recid < 4); } else { random_sign(&sigr, &sigs, &key, &msg, NULL); } CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg)); rustsecp256k1_v0_5_0_scalar_set_int(&one, 1); rustsecp256k1_v0_5_0_scalar_add(&msg, &msg, &one); CHECK(!rustsecp256k1_v0_5_0_ecdsa_sig_verify(&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 rustsecp256k1_v0_5_0_ecdsa_signature *sig) { static const unsigned char res[sizeof(rustsecp256k1_v0_5_0_ecdsa_signature)] = {0}; return rustsecp256k1_v0_5_0_memcmp_var(sig, res, sizeof(rustsecp256k1_v0_5_0_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]; rustsecp256k1_v0_5_0_ecdsa_signature signature[6]; rustsecp256k1_v0_5_0_scalar r, s; unsigned char sig[74]; size_t siglen = 74; unsigned char pubkeyc[65]; size_t pubkeyclen = 65; rustsecp256k1_v0_5_0_pubkey pubkey; rustsecp256k1_v0_5_0_pubkey pubkey_tmp; unsigned char seckey[300]; size_t seckeylen = 300; /* Generate a random key and message. */ { rustsecp256k1_v0_5_0_scalar msg, key; random_scalar_order_test(&msg); random_scalar_order_test(&key); rustsecp256k1_v0_5_0_scalar_get_b32(privkey, &key); rustsecp256k1_v0_5_0_scalar_get_b32(message, &msg); } /* Construct and verify corresponding public key. */ CHECK(rustsecp256k1_v0_5_0_ec_seckey_verify(ctx, privkey) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, privkey) == 1); /* Verify exporting and importing public key. */ CHECK(rustsecp256k1_v0_5_0_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, rustsecp256k1_v0_5_0_testrand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED)); memset(&pubkey, 0, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1); /* Verify negation changes the key and changes it back */ memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey)); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0); /* Verify private key import and export. */ CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, rustsecp256k1_v0_5_0_testrand_bits(1) == 1)); CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(privkey, privkey2, 32) == 0); /* Optionally tweak the keys using addition. */ if (rustsecp256k1_v0_5_0_testrand_int(3) == 0) { int ret1; int ret2; int ret3; unsigned char rnd[32]; unsigned char privkey_tmp[32]; rustsecp256k1_v0_5_0_pubkey pubkey2; rustsecp256k1_v0_5_0_testrand256_test(rnd); memcpy(privkey_tmp, privkey, 32); ret1 = rustsecp256k1_v0_5_0_ec_seckey_tweak_add(ctx, privkey, rnd); ret2 = rustsecp256k1_v0_5_0_ec_pubkey_tweak_add(ctx, &pubkey, rnd); /* Check that privkey alias gives same result */ ret3 = rustsecp256k1_v0_5_0_ec_privkey_tweak_add(ctx, privkey_tmp, rnd); CHECK(ret1 == ret2); CHECK(ret2 == ret3); if (ret1 == 0) { return; } CHECK(rustsecp256k1_v0_5_0_memcmp_var(privkey, privkey_tmp, 32) == 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); } /* Optionally tweak the keys using multiplication. */ if (rustsecp256k1_v0_5_0_testrand_int(3) == 0) { int ret1; int ret2; int ret3; unsigned char rnd[32]; unsigned char privkey_tmp[32]; rustsecp256k1_v0_5_0_pubkey pubkey2; rustsecp256k1_v0_5_0_testrand256_test(rnd); memcpy(privkey_tmp, privkey, 32); ret1 = rustsecp256k1_v0_5_0_ec_seckey_tweak_mul(ctx, privkey, rnd); ret2 = rustsecp256k1_v0_5_0_ec_pubkey_tweak_mul(ctx, &pubkey, rnd); /* Check that privkey alias gives same result */ ret3 = rustsecp256k1_v0_5_0_ec_privkey_tweak_mul(ctx, privkey_tmp, rnd); CHECK(ret1 == ret2); CHECK(ret2 == ret3); if (ret1 == 0) { return; } CHECK(rustsecp256k1_v0_5_0_memcmp_var(privkey, privkey_tmp, 32) == 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0); } /* Sign. */ CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1); extra[31] = 1; CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1); extra[31] = 0; extra[0] = 1; CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[0], &signature[4], sizeof(signature[0])) == 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[0], &signature[1], sizeof(signature[0])) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[0], &signature[2], sizeof(signature[0])) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[0], &signature[3], sizeof(signature[0])) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[1], &signature[2], sizeof(signature[0])) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[1], &signature[3], sizeof(signature[0])) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[2], &signature[3], sizeof(signature[0])) != 0); /* Verify. */ CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1); /* Test lower-S form, malleate, verify and fail, test again, malleate again */ CHECK(!rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, NULL, &signature[0])); rustsecp256k1_v0_5_0_ecdsa_signature_load(ctx, &r, &s, &signature[0]); rustsecp256k1_v0_5_0_scalar_negate(&s, &s); rustsecp256k1_v0_5_0_ecdsa_signature_save(&signature[5], &r, &s); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); CHECK(!rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(!rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); rustsecp256k1_v0_5_0_scalar_negate(&s, &s); rustsecp256k1_v0_5_0_ecdsa_signature_save(&signature[5], &r, &s); CHECK(!rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, NULL, &signature[5])); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&signature[5], &signature[0], 64) == 0); /* Serialize/parse DER and verify again */ CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); memset(&signature[0], 0, sizeof(signature[0])); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); /* Serialize/destroy/parse DER and verify again. */ siglen = 74; CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); sig[rustsecp256k1_v0_5_0_testrand_int(siglen)] += 1 + rustsecp256k1_v0_5_0_testrand_int(255); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 || rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0); } void test_random_pubkeys(void) { rustsecp256k1_v0_5_0_ge elem; rustsecp256k1_v0_5_0_ge elem2; unsigned char in[65]; /* Generate some randomly sized pubkeys. */ size_t len = rustsecp256k1_v0_5_0_testrand_bits(2) == 0 ? 65 : 33; if (rustsecp256k1_v0_5_0_testrand_bits(2) == 0) { len = rustsecp256k1_v0_5_0_testrand_bits(6); } if (len == 65) { in[0] = rustsecp256k1_v0_5_0_testrand_bits(1) ? 4 : (rustsecp256k1_v0_5_0_testrand_bits(1) ? 6 : 7); } else { in[0] = rustsecp256k1_v0_5_0_testrand_bits(1) ? 2 : 3; } if (rustsecp256k1_v0_5_0_testrand_bits(3) == 0) { in[0] = rustsecp256k1_v0_5_0_testrand_bits(8); } if (len > 1) { rustsecp256k1_v0_5_0_testrand256(&in[1]); } if (len > 33) { rustsecp256k1_v0_5_0_testrand256(&in[33]); } if (rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&elem, out, &size, len == 33)); CHECK(size == len); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&elem, in, &size, 0)); CHECK(size == 65); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&elem2, in, size)); ge_equals_ge(&elem,&elem2); /* Check that the X9.62 hybrid type is checked. */ in[0] = rustsecp256k1_v0_5_0_testrand_bits(1) ? 6 : 7; res = rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_eckey_pubkey_serialize(&elem, out, &size, 0)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&in[1], &out[1], 64) == 0); } } } void run_pubkey_comparison(void) { unsigned char pk1_ser[33] = { 0x02, 0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11, 0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23 }; const unsigned char pk2_ser[33] = { 0x02, 0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d, 0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c }; rustsecp256k1_v0_5_0_pubkey pk1; rustsecp256k1_v0_5_0_pubkey pk2; int32_t ecount = 0; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pk1, pk1_ser, sizeof(pk1_ser)) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pk2, pk2_ser, sizeof(pk2_ser)) == 1); rustsecp256k1_v0_5_0_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, NULL, &pk2) < 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk1, NULL) > 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk1, &pk2) < 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk2, &pk1) > 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk1, &pk1) == 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk2, &pk2) == 0); CHECK(ecount == 2); { rustsecp256k1_v0_5_0_pubkey pk_tmp; memset(&pk_tmp, 0, sizeof(pk_tmp)); /* illegal pubkey */ CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk_tmp, &pk2) < 0); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk_tmp, &pk_tmp) == 0); CHECK(ecount == 5); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk2, &pk_tmp) > 0); CHECK(ecount == 6); } rustsecp256k1_v0_5_0_context_set_illegal_callback(ctx, NULL, NULL); /* Make pk2 the same as pk1 but with 3 rather than 2. Note that in * an uncompressed encoding, these would have the opposite ordering */ pk1_ser[0] = 3; CHECK(rustsecp256k1_v0_5_0_ec_pubkey_parse(ctx, &pk2, pk1_ser, sizeof(pk1_ser)) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk1, &pk2) < 0); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_cmp(ctx, &pk2, &pk1) > 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}; int ret = 0; rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_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; parsed_der = rustsecp256k1_v0_5_0_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen); if (parsed_der) { ret |= (!rustsecp256k1_v0_5_0_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0; valid_der = (rustsecp256k1_v0_5_0_memcmp_var(compact_der, zeroes, 32) != 0) && (rustsecp256k1_v0_5_0_memcmp_var(compact_der + 32, zeroes, 32) != 0); } if (valid_der) { ret |= (!rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1; roundtrips_der = (len_der == siglen) && rustsecp256k1_v0_5_0_memcmp_var(roundtrip_der, sig, siglen) == 0; } parsed_der_lax = rustsecp256k1_v0_5_0_ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen); if (parsed_der_lax) { ret |= (!rustsecp256k1_v0_5_0_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10; valid_der_lax = (rustsecp256k1_v0_5_0_memcmp_var(compact_der_lax, zeroes, 32) != 0) && (rustsecp256k1_v0_5_0_memcmp_var(compact_der_lax + 32, zeroes, 32) != 0); } if (valid_der_lax) { ret |= (!rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11; roundtrips_der_lax = (len_der_lax == siglen) && rustsecp256k1_v0_5_0_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) || (rustsecp256k1_v0_5_0_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; } 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 = rustsecp256k1_v0_5_0_testrand_bits(3); if (action < 1 && *len > 3) { /* Delete a byte. */ pos = rustsecp256k1_v0_5_0_testrand_int(*len); memmove(sig + pos, sig + pos + 1, *len - pos - 1); (*len)--; return; } else if (action < 2 && *len < 2048) { /* Insert a byte. */ pos = rustsecp256k1_v0_5_0_testrand_int(1 + *len); memmove(sig + pos + 1, sig + pos, *len - pos); sig[pos] = rustsecp256k1_v0_5_0_testrand_bits(8); (*len)++; return; } else if (action < 4) { /* Modify a byte. */ sig[rustsecp256k1_v0_5_0_testrand_int(*len)] += 1 + rustsecp256k1_v0_5_0_testrand_int(255); return; } else { /* action < 8 */ /* Modify a bit. */ sig[rustsecp256k1_v0_5_0_testrand_int(*len)] ^= 1 << rustsecp256k1_v0_5_0_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 = rustsecp256k1_v0_5_0_testrand_bits(2) == 0; *certainly_der = der; *certainly_not_der = 0; indet = der ? 0 : rustsecp256k1_v0_5_0_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 : (rustsecp256k1_v0_5_0_testrand_bits(3) != 0); /* The length of the number in bytes (the first byte of which will always be nonzero) */ nlen[n] = nlow[n] ? rustsecp256k1_v0_5_0_testrand_int(33) : 32 + rustsecp256k1_v0_5_0_testrand_int(200) * rustsecp256k1_v0_5_0_testrand_bits(3) / 8; CHECK(nlen[n] <= 232); /* The top bit of the number. */ nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : rustsecp256k1_v0_5_0_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 + rustsecp256k1_v0_5_0_testrand_bits(7) : 1 + rustsecp256k1_v0_5_0_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] ? rustsecp256k1_v0_5_0_testrand_int(3) : rustsecp256k1_v0_5_0_testrand_int(300 - nlen[n]) * rustsecp256k1_v0_5_0_testrand_bits(3) / 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 = rustsecp256k1_v0_5_0_testrand_int(127 - nlenlen[n]) * rustsecp256k1_v0_5_0_testrand_bits(4) * rustsecp256k1_v0_5_0_testrand_bits(4) / 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 : rustsecp256k1_v0_5_0_testrand_int(980 - tlen) * rustsecp256k1_v0_5_0_testrand_bits(3) / 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 : rustsecp256k1_v0_5_0_testrand_int(990 - tlen) * rustsecp256k1_v0_5_0_testrand_bits(3) / 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 = rustsecp256k1_v0_5_0_testrand_int(127 - tlenlen) * rustsecp256k1_v0_5_0_testrand_bits(4) * rustsecp256k1_v0_5_0_testrand_bits(4) / 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 */ rustsecp256k1_v0_5_0_testrand_bytes_test(sig + *len, nlen[n]); *len += nlen[n]; nlen[n] = 0; } /* Generate random garbage inside tuple. */ rustsecp256k1_v0_5_0_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. */ rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_ecdsa_signature sig; /* Test the case where ECDSA recomputes a point that is infinity. */ { rustsecp256k1_v0_5_0_gej keyj; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 1); rustsecp256k1_v0_5_0_scalar_negate(&ss, &ss); rustsecp256k1_v0_5_0_scalar_inverse(&ss, &ss); rustsecp256k1_v0_5_0_scalar_set_int(&sr, 1); rustsecp256k1_v0_5_0_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr); rustsecp256k1_v0_5_0_ge_set_gej(&key, &keyj); msg = ss; CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&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 }; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 1); rustsecp256k1_v0_5_0_scalar_set_int(&msg, 0); rustsecp256k1_v0_5_0_scalar_set_int(&sr, 0); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key, pubkey_mods_zero, 33)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify( &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 }; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 0); rustsecp256k1_v0_5_0_scalar_set_int(&msg, 0); rustsecp256k1_v0_5_0_scalar_set_int(&sr, 1); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&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 }; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_ge key2; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 2); rustsecp256k1_v0_5_0_scalar_set_int(&msg, 0); rustsecp256k1_v0_5_0_scalar_set_int(&sr, 2); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key2, pubkey2, 33)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); rustsecp256k1_v0_5_0_scalar_negate(&ss, &ss); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); rustsecp256k1_v0_5_0_scalar_set_int(&ss, 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&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 }; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_ge key2; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 1); rustsecp256k1_v0_5_0_scalar_set_int(&msg, 1); rustsecp256k1_v0_5_0_scalar_set_b32(&sr, csr, NULL); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key2, pubkey2, 33)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); rustsecp256k1_v0_5_0_scalar_negate(&ss, &ss); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1); rustsecp256k1_v0_5_0_scalar_set_int(&ss, 2); rustsecp256k1_v0_5_0_scalar_inverse_var(&ss, &ss); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&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 }; rustsecp256k1_v0_5_0_ge key; rustsecp256k1_v0_5_0_scalar msg; rustsecp256k1_v0_5_0_scalar sr, ss; rustsecp256k1_v0_5_0_scalar_set_int(&ss, 1); rustsecp256k1_v0_5_0_scalar_set_int(&msg, 1); rustsecp256k1_v0_5_0_scalar_negate(&msg, &msg); rustsecp256k1_v0_5_0_scalar_set_b32(&sr, csr, NULL); CHECK(rustsecp256k1_v0_5_0_eckey_pubkey_parse(&key, pubkey, 33)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); rustsecp256k1_v0_5_0_scalar_negate(&ss, &ss); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1); rustsecp256k1_v0_5_0_scalar_set_int(&ss, 3); rustsecp256k1_v0_5_0_scalar_inverse_var(&ss, &ss); CHECK(rustsecp256k1_v0_5_0_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0); } /* Signature where s would be zero. */ { rustsecp256k1_v0_5_0_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; rustsecp256k1_v0_5_0_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0); msg[31] = 0xaa; CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1); CHECK(ecount == 0); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1); CHECK(rustsecp256k1_v0_5_0_ec_pubkey_create(ctx, &pubkey, key) == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0); CHECK(ecount == 4); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0); CHECK(ecount == 5); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &sig, msg, NULL) == 0); CHECK(ecount == 6); CHECK(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1); CHECK(ecount == 6); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0); CHECK(ecount == 8); siglen = 72; CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0); CHECK(ecount == 9); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0); CHECK(ecount == 10); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0); CHECK(ecount == 11); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1); CHECK(ecount == 11); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0); CHECK(ecount == 12); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0); CHECK(ecount == 13); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0); CHECK(ecount == 13); ecount = 0; CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_normalize(ctx, NULL, NULL) == 0); CHECK(ecount == 1); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0); CHECK(ecount == 2); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1); CHECK(ecount == 3); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0); CHECK(ecount == 4); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0); CHECK(ecount == 5); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1); CHECK(ecount == 5); memset(signature, 255, 64); CHECK(rustsecp256k1_v0_5_0_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0); CHECK(ecount == 5); rustsecp256k1_v0_5_0_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]; rustsecp256k1_v0_5_0_ecdsa_signature sig2; rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1); CHECK(!is_empty_signature(&sig)); CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1); CHECK(!is_empty_signature(&sig2)); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&sig, &sig2, sizeof(sig)) == 0); /* The default nonce function is deterministic. */ CHECK(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); CHECK(rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); rustsecp256k1_v0_5_0_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); for (j = 0; j < i; j++) { CHECK(!rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); CHECK(!is_empty_signature(&sig2)); rustsecp256k1_v0_5_0_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); for (j = 0; j < i; j++) { CHECK(!rustsecp256k1_v0_5_0_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(rustsecp256k1_v0_5_0_memcmp_var(nonce, nonce2, 32) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(nonce, nonce3, 32) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(nonce, nonce4, 32) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(nonce2, nonce3, 32) != 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(nonce2, nonce4, 32) != 0); CHECK(rustsecp256k1_v0_5_0_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_MODULE_ECDH # include "modules/ecdh/tests_impl.h" #endif #ifdef ENABLE_MODULE_RECOVERY # include "modules/recovery/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_rustsecp256k1_v0_5_0_memczero_test(void) { unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; unsigned char buf2[sizeof(buf1)]; /* rustsecp256k1_v0_5_0_memczero(..., ..., 0) is a noop. */ memcpy(buf2, buf1, sizeof(buf1)); rustsecp256k1_v0_5_0_memczero(buf1, sizeof(buf1), 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); /* rustsecp256k1_v0_5_0_memczero(..., ..., 1) zeros the buffer. */ memset(buf2, 0, sizeof(buf2)); rustsecp256k1_v0_5_0_memczero(buf1, sizeof(buf1) , 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(buf1, buf2, sizeof(buf1)) == 0); } void int_cmov_test(void) { int r = INT_MAX; int a = 0; rustsecp256k1_v0_5_0_int_cmov(&r, &a, 0); CHECK(r == INT_MAX); r = 0; a = INT_MAX; rustsecp256k1_v0_5_0_int_cmov(&r, &a, 1); CHECK(r == INT_MAX); a = 0; rustsecp256k1_v0_5_0_int_cmov(&r, &a, 1); CHECK(r == 0); a = 1; rustsecp256k1_v0_5_0_int_cmov(&r, &a, 1); CHECK(r == 1); r = 1; a = 0; rustsecp256k1_v0_5_0_int_cmov(&r, &a, 0); CHECK(r == 1); } void fe_cmov_test(void) { static const rustsecp256k1_v0_5_0_fe zero = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const rustsecp256k1_v0_5_0_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const rustsecp256k1_v0_5_0_fe max = SECP256K1_FE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); rustsecp256k1_v0_5_0_fe r = max; rustsecp256k1_v0_5_0_fe a = zero; rustsecp256k1_v0_5_0_fe_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; rustsecp256k1_v0_5_0_fe_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; rustsecp256k1_v0_5_0_fe_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; rustsecp256k1_v0_5_0_fe_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; rustsecp256k1_v0_5_0_fe_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); } void fe_storage_cmov_test(void) { static const rustsecp256k1_v0_5_0_fe_storage zero = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const rustsecp256k1_v0_5_0_fe_storage one = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const rustsecp256k1_v0_5_0_fe_storage max = SECP256K1_FE_STORAGE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); rustsecp256k1_v0_5_0_fe_storage r = max; rustsecp256k1_v0_5_0_fe_storage a = zero; rustsecp256k1_v0_5_0_fe_storage_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; rustsecp256k1_v0_5_0_fe_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; rustsecp256k1_v0_5_0_fe_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; rustsecp256k1_v0_5_0_fe_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; rustsecp256k1_v0_5_0_fe_storage_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); } void scalar_cmov_test(void) { static const rustsecp256k1_v0_5_0_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); static const rustsecp256k1_v0_5_0_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const rustsecp256k1_v0_5_0_scalar max = SECP256K1_SCALAR_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); rustsecp256k1_v0_5_0_scalar r = max; rustsecp256k1_v0_5_0_scalar a = zero; rustsecp256k1_v0_5_0_scalar_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; rustsecp256k1_v0_5_0_scalar_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; rustsecp256k1_v0_5_0_scalar_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; rustsecp256k1_v0_5_0_scalar_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; rustsecp256k1_v0_5_0_scalar_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); } void ge_storage_cmov_test(void) { static const rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_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 rustsecp256k1_v0_5_0_ge_storage max = SECP256K1_GE_STORAGE_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL ); rustsecp256k1_v0_5_0_ge_storage r = max; rustsecp256k1_v0_5_0_ge_storage a = zero; rustsecp256k1_v0_5_0_ge_storage_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); r = zero; a = max; rustsecp256k1_v0_5_0_ge_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &max, sizeof(r)) == 0); a = zero; rustsecp256k1_v0_5_0_ge_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &zero, sizeof(r)) == 0); a = one; rustsecp256k1_v0_5_0_ge_storage_cmov(&r, &a, 1); CHECK(rustsecp256k1_v0_5_0_memcmp_var(&r, &one, sizeof(r)) == 0); r = one; a = zero; rustsecp256k1_v0_5_0_ge_storage_cmov(&r, &a, 0); CHECK(rustsecp256k1_v0_5_0_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 && strlen(env) > 0) { 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 */ rustsecp256k1_v0_5_0_testrand_init(argc > 2 ? argv[2] : NULL); /* initialize */ run_context_tests(0); run_context_tests(1); run_scratch_tests(); ctx = rustsecp256k1_v0_5_0_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); if (rustsecp256k1_v0_5_0_testrand_bits(1)) { unsigned char rand32[32]; rustsecp256k1_v0_5_0_testrand256(rand32); CHECK(rustsecp256k1_v0_5_0_context_randomize(ctx, rustsecp256k1_v0_5_0_testrand_bits(1) ? rand32 : NULL)); } run_rand_bits(); run_rand_int(); run_ctz_tests(); run_modinv_tests(); run_inverse_tests(); run_sha256_tests(); run_hmac_sha256_tests(); run_rfc6979_hmac_sha256_tests(); run_tagged_sha256_tests(); /* scalar tests */ run_scalar_tests(); /* field tests */ run_field_misc(); run_field_convert(); run_fe_mul(); run_sqr(); run_sqrt(); /* group tests */ run_ge(); run_gej(); run_group_decompress(); /* ecmult tests */ run_ecmult_pre_g(); 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_pubkey_comparison(); run_random_pubkeys(); run_ecdsa_der_parse(); run_ecdsa_sign_verify(); run_ecdsa_end_to_end(); run_ecdsa_edge_cases(); #ifdef ENABLE_MODULE_RECOVERY /* ECDSA pubkey recovery tests */ run_recovery_tests(); #endif #ifdef ENABLE_MODULE_EXTRAKEYS run_extrakeys_tests(); #endif #ifdef ENABLE_MODULE_SCHNORRSIG run_schnorrsig_tests(); #endif /* util tests */ run_rustsecp256k1_v0_5_0_memczero_test(); run_cmov_tests(); rustsecp256k1_v0_5_0_testrand_finish(); /* shutdown */ rustsecp256k1_v0_5_0_context_destroy(ctx); printf("no problems found\n"); return 0; }