/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille *
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <stdio.h>
#include <stdlib.h>
+#include <string.h>
+
+#include <time.h>
#include "secp256k1.c"
+#include "include/secp256k1.h"
+#include "include/secp256k1_preallocated.h"
#include "testrand_impl.h"
#ifdef ENABLE_OPENSSL_TESTS
#include "openssl/ec.h"
#include "openssl/ecdsa.h"
#include "openssl/obj_mac.h"
+# if OPENSSL_VERSION_NUMBER < 0x10100000L
+void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;}
+# endif
+#endif
+
+#include "contrib/lax_der_parsing.c"
+#include "contrib/lax_der_privatekey_parsing.c"
+
+#if !defined(VG_CHECK)
+# if defined(VALGRIND)
+# include <valgrind/memcheck.h>
+# define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
+# define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
+# else
+# define VG_UNDEF(x,y)
+# define VG_CHECK(x,y)
+# endif
#endif
static int count = 64;
+static secp256k1_context *ctx = NULL;
-/***** NUM TESTS *****/
+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)++;
+}
-void random_num_negate(secp256k1_num_t *num) {
- if (secp256k1_rand32() & 1)
- secp256k1_num_negate(num);
+static void uncounting_illegal_callback_fn(const char* str, void* data) {
+ /* Dummy callback function that just counts (backwards). */
+ int32_t *p;
+ (void)str;
+ p = data;
+ (*p)--;
}
-void random_field_element_test(secp256k1_fe_t *fe) {
+void random_field_element_test(secp256k1_fe *fe) {
do {
unsigned char b32[32];
secp256k1_rand256_test(b32);
- secp256k1_num_t num;
- secp256k1_num_set_bin(&num, b32, 32);
- if (secp256k1_num_cmp(&num, &secp256k1_fe_consts->p) >= 0)
- continue;
- VERIFY_CHECK(secp256k1_fe_set_b32(fe, b32));
- break;
+ if (secp256k1_fe_set_b32(fe, b32)) {
+ break;
+ }
} while(1);
}
-void random_field_element_magnitude(secp256k1_fe_t *fe) {
+void random_field_element_magnitude(secp256k1_fe *fe) {
+ secp256k1_fe zero;
+ int n = secp256k1_rand_int(9);
secp256k1_fe_normalize(fe);
- int n = secp256k1_rand32() % 4;
- for (int i = 0; i < n; i++) {
- secp256k1_fe_negate(fe, fe, 1 + 2*i);
- secp256k1_fe_negate(fe, fe, 2 + 2*i);
+ if (n == 0) {
+ return;
}
+ secp256k1_fe_clear(&zero);
+ secp256k1_fe_negate(&zero, &zero, 0);
+ secp256k1_fe_mul_int(&zero, n - 1);
+ secp256k1_fe_add(fe, &zero);
+#ifdef VERIFY
+ CHECK(fe->magnitude == n);
+#endif
}
-void random_group_element_test(secp256k1_ge_t *ge) {
- secp256k1_fe_t fe;
+void random_group_element_test(secp256k1_ge *ge) {
+ secp256k1_fe fe;
do {
random_field_element_test(&fe);
- if (secp256k1_ge_set_xo(ge, &fe, secp256k1_rand32() & 1))
+ if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
+ secp256k1_fe_normalize(&ge->y);
break;
+ }
} while(1);
}
-void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge_t *ge) {
+void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
+ secp256k1_fe z2, z3;
do {
random_field_element_test(&gej->z);
if (!secp256k1_fe_is_zero(&gej->z)) {
break;
}
} while(1);
- secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &gej->z);
- secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &z2, &gej->z);
+ secp256k1_fe_sqr(&z2, &gej->z);
+ secp256k1_fe_mul(&z3, &z2, &gej->z);
secp256k1_fe_mul(&gej->x, &ge->x, &z2);
secp256k1_fe_mul(&gej->y, &ge->y, &z3);
gej->infinity = ge->infinity;
}
-void random_num_order_test(secp256k1_num_t *num) {
+void random_scalar_order_test(secp256k1_scalar *num) {
do {
unsigned char b32[32];
+ int overflow = 0;
secp256k1_rand256_test(b32);
- secp256k1_num_set_bin(num, b32, 32);
- if (secp256k1_num_is_zero(num))
- continue;
- if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0)
+ secp256k1_scalar_set_b32(num, b32, &overflow);
+ if (overflow || secp256k1_scalar_is_zero(num)) {
continue;
+ }
break;
} while(1);
}
-void random_scalar_order_test(secp256k1_scalar_t *num) {
+void random_scalar_order(secp256k1_scalar *num) {
do {
unsigned char b32[32];
- secp256k1_rand256_test(b32);
int overflow = 0;
+ secp256k1_rand256(b32);
secp256k1_scalar_set_b32(num, b32, &overflow);
- if (overflow || secp256k1_scalar_is_zero(num))
+ if (overflow || secp256k1_scalar_is_zero(num)) {
continue;
+ }
break;
} while(1);
}
-void random_scalar_order(secp256k1_scalar_t *num) {
+void run_context_tests(int use_prealloc) {
+ secp256k1_pubkey pubkey;
+ secp256k1_pubkey zero_pubkey;
+ secp256k1_ecdsa_signature sig;
+ unsigned char ctmp[32];
+ int32_t ecount;
+ int32_t ecount2;
+ secp256k1_context *none;
+ secp256k1_context *sign;
+ secp256k1_context *vrfy;
+ secp256k1_context *both;
+ void *none_prealloc = NULL;
+ void *sign_prealloc = NULL;
+ void *vrfy_prealloc = NULL;
+ void *both_prealloc = NULL;
+
+ secp256k1_gej pubj;
+ secp256k1_ge pub;
+ secp256k1_scalar msg, key, nonce;
+ secp256k1_scalar sigr, sigs;
+
+ if (use_prealloc) {
+ none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
+ sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN));
+ vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY));
+ both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY));
+ CHECK(none_prealloc != NULL);
+ CHECK(sign_prealloc != NULL);
+ CHECK(vrfy_prealloc != NULL);
+ CHECK(both_prealloc != NULL);
+ none = secp256k1_context_preallocated_create(none_prealloc, SECP256K1_CONTEXT_NONE);
+ sign = secp256k1_context_preallocated_create(sign_prealloc, SECP256K1_CONTEXT_SIGN);
+ vrfy = secp256k1_context_preallocated_create(vrfy_prealloc, SECP256K1_CONTEXT_VERIFY);
+ both = secp256k1_context_preallocated_create(both_prealloc, SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+ } else {
+ none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+ sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+ vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+ both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+ }
+
+ memset(&zero_pubkey, 0, sizeof(zero_pubkey));
+
+ ecount = 0;
+ ecount2 = 10;
+ secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+ secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
+ secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
+ CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
+
+ /* check if sizes for cloning are consistent */
+ CHECK(secp256k1_context_preallocated_clone_size(none) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
+ CHECK(secp256k1_context_preallocated_clone_size(sign) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN));
+ CHECK(secp256k1_context_preallocated_clone_size(vrfy) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY));
+ CHECK(secp256k1_context_preallocated_clone_size(both) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY));
+
+ /*** clone and destroy all of them to make sure cloning was complete ***/
+ {
+ secp256k1_context *ctx_tmp;
+
+ if (use_prealloc) {
+ /* clone into a non-preallocated context and then again into a new preallocated one. */
+ ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(none_prealloc); none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(none_prealloc != NULL);
+ ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, none_prealloc); secp256k1_context_destroy(ctx_tmp);
+
+ ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(sign_prealloc); sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(sign_prealloc != NULL);
+ ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, sign_prealloc); secp256k1_context_destroy(ctx_tmp);
+
+ ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(vrfy_prealloc); vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(vrfy_prealloc != NULL);
+ ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, vrfy_prealloc); secp256k1_context_destroy(ctx_tmp);
+
+ ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(both_prealloc); both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(both_prealloc != NULL);
+ ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, both_prealloc); secp256k1_context_destroy(ctx_tmp);
+ } else {
+ /* clone into a preallocated context and then again into a new non-preallocated one. */
+ void *prealloc_tmp;
+
+ prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(prealloc_tmp != NULL);
+ ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
+ ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(prealloc_tmp);
+
+ prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(prealloc_tmp != NULL);
+ ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
+ ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(prealloc_tmp);
+
+ prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL);
+ ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
+ ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(prealloc_tmp);
+
+ prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL);
+ ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, prealloc_tmp); secp256k1_context_destroy(ctx_tmp);
+ ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp);
+ free(prealloc_tmp);
+ }
+ }
+
+ /* Verify that the error callback makes it across the clone. */
+ CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
+ /* And that it resets back to default. */
+ secp256k1_context_set_error_callback(sign, NULL, NULL);
+ CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
+
+ /*** attempt to use them ***/
+ random_scalar_order_test(&msg);
+ random_scalar_order_test(&key);
+ secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
+ secp256k1_ge_set_gej(&pub, &pubj);
+
+ /* Verify context-type checking illegal-argument errors. */
+ memset(ctmp, 1, 32);
+ CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
+ CHECK(ecount == 1);
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
+ CHECK(ecount == 2);
+ VG_UNDEF(&sig, sizeof(sig));
+ CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
+ VG_CHECK(&sig, sizeof(sig));
+ CHECK(ecount2 == 10);
+ CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
+ CHECK(ecount2 == 11);
+ CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
+ CHECK(ecount2 == 12);
+ CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
+ CHECK(ecount2 == 13);
+ CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0);
+ CHECK(ecount2 == 14);
+ CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_context_randomize(vrfy, NULL) == 1);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_context_randomize(sign, ctmp) == 1);
+ CHECK(ecount2 == 14);
+ CHECK(secp256k1_context_randomize(sign, NULL) == 1);
+ CHECK(ecount2 == 14);
+ secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
+ secp256k1_context_set_illegal_callback(sign, NULL, NULL);
+
+ /* obtain a working nonce */
do {
- unsigned char b32[32];
- secp256k1_rand256(b32);
- int overflow = 0;
- secp256k1_scalar_set_b32(num, b32, &overflow);
- if (overflow || secp256k1_scalar_is_zero(num))
- continue;
- break;
- } while(1);
+ random_scalar_order_test(&nonce);
+ } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+
+ /* try signing */
+ CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+ CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+
+ /* try verifying */
+ CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+ CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+
+ /* cleanup */
+ if (use_prealloc) {
+ secp256k1_context_preallocated_destroy(none);
+ secp256k1_context_preallocated_destroy(sign);
+ secp256k1_context_preallocated_destroy(vrfy);
+ secp256k1_context_preallocated_destroy(both);
+ free(none_prealloc);
+ free(sign_prealloc);
+ free(vrfy_prealloc);
+ free(both_prealloc);
+ } else {
+ secp256k1_context_destroy(none);
+ secp256k1_context_destroy(sign);
+ secp256k1_context_destroy(vrfy);
+ secp256k1_context_destroy(both);
+ }
+ /* Defined as no-op. */
+ secp256k1_context_destroy(NULL);
+ secp256k1_context_preallocated_destroy(NULL);
+
}
-void random_num_order(secp256k1_num_t *num) {
- do {
- unsigned char b32[32];
- secp256k1_rand256(b32);
- secp256k1_num_set_bin(num, b32, 32);
- if (secp256k1_num_is_zero(num))
- continue;
- if (secp256k1_num_cmp(num, &secp256k1_ge_consts->order) >= 0)
- continue;
- break;
- } while(1);
+void run_scratch_tests(void) {
+ int32_t ecount = 0;
+ secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+ secp256k1_scratch_space *scratch;
+
+ /* Test public API */
+ secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
+
+ scratch = secp256k1_scratch_space_create(none, 1000);
+ CHECK(scratch != NULL);
+ CHECK(ecount == 0);
+
+ /* Test internal API */
+ CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
+ CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 1000);
+
+ /* Allocating 500 bytes with no frame fails */
+ CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
+ CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
+
+ /* ...but pushing a new stack frame does affect the max allocation */
+ CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1 == 1));
+ CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 500); /* 500 - ALIGNMENT */
+ CHECK(secp256k1_scratch_alloc(scratch, 500) != NULL);
+ CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
+
+ CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 0);
+
+ /* ...and this effect is undone by popping the frame */
+ secp256k1_scratch_deallocate_frame(scratch);
+ CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
+ CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
+
+ /* cleanup */
+ secp256k1_scratch_space_destroy(scratch);
+ secp256k1_context_destroy(none);
}
-void test_num_get_set_bin(void) {
- secp256k1_num_t n1,n2;
- random_num_order_test(&n1);
- unsigned char c[32];
- secp256k1_num_get_bin(c, 32, &n1);
- secp256k1_num_set_bin(&n2, c, 32);
- CHECK(secp256k1_num_eq(&n1, &n2));
- for (int i=0; i<32; i++) {
- /* check whether the lower 8 bits correspond to the last byte */
- int low1 = secp256k1_num_shift(&n1, 8);
- int low2 = c[31];
- CHECK(low1 == low2);
- /* shift bits off the byte representation, and compare */
- memmove(c+1, c, 31);
- c[0] = 0;
- secp256k1_num_set_bin(&n2, c, 32);
- CHECK(secp256k1_num_eq(&n1, &n2));
+/***** HASH TESTS *****/
+
+void run_sha256_tests(void) {
+ static const char *inputs[8] = {
+ "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
+ "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
+ "For this sample, this 63-byte string will be used as input data",
+ "This is exactly 64 bytes long, not counting the terminating byte"
+ };
+ static const unsigned char outputs[8][32] = {
+ {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
+ {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
+ {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
+ {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d},
+ {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
+ {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
+ {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
+ {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
+ };
+ int i;
+ for (i = 0; i < 8; i++) {
+ unsigned char out[32];
+ secp256k1_sha256 hasher;
+ secp256k1_sha256_initialize(&hasher);
+ secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+ secp256k1_sha256_finalize(&hasher, out);
+ CHECK(memcmp(out, outputs[i], 32) == 0);
+ if (strlen(inputs[i]) > 0) {
+ int split = secp256k1_rand_int(strlen(inputs[i]));
+ secp256k1_sha256_initialize(&hasher);
+ secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+ secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+ secp256k1_sha256_finalize(&hasher, out);
+ CHECK(memcmp(out, outputs[i], 32) == 0);
+ }
+ }
+}
+
+void run_hmac_sha256_tests(void) {
+ static const char *keys[6] = {
+ "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
+ "\x4a\x65\x66\x65",
+ "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
+ "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
+ "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
+ "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
+ };
+ static const char *inputs[6] = {
+ "\x48\x69\x20\x54\x68\x65\x72\x65",
+ "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
+ "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
+ "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
+ "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
+ "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
+ };
+ static const unsigned char outputs[6][32] = {
+ {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
+ {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
+ {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
+ {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
+ {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
+ {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
+ };
+ int i;
+ for (i = 0; i < 6; i++) {
+ secp256k1_hmac_sha256 hasher;
+ unsigned char out[32];
+ secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+ secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
+ secp256k1_hmac_sha256_finalize(&hasher, out);
+ CHECK(memcmp(out, outputs[i], 32) == 0);
+ if (strlen(inputs[i]) > 0) {
+ int split = secp256k1_rand_int(strlen(inputs[i]));
+ secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
+ secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
+ secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
+ secp256k1_hmac_sha256_finalize(&hasher, out);
+ CHECK(memcmp(out, outputs[i], 32) == 0);
+ }
+ }
+}
+
+void run_rfc6979_hmac_sha256_tests(void) {
+ static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
+ static const unsigned char out1[3][32] = {
+ {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
+ {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
+ {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
+ };
+
+ static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
+ static const unsigned char out2[3][32] = {
+ {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
+ {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
+ {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
+ };
+
+ secp256k1_rfc6979_hmac_sha256 rng;
+ unsigned char out[32];
+ int i;
+
+ secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
+ for (i = 0; i < 3; i++) {
+ secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+ CHECK(memcmp(out, out1[i], 32) == 0);
}
+ secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+
+ secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
+ for (i = 0; i < 3; i++) {
+ secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+ CHECK(memcmp(out, out1[i], 32) != 0);
+ }
+ secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+
+ secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
+ for (i = 0; i < 3; i++) {
+ secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
+ CHECK(memcmp(out, out2[i], 32) == 0);
+ }
+ secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+}
+
+/***** RANDOM TESTS *****/
+
+void test_rand_bits(int rand32, int bits) {
+ /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
+ * get a false negative chance below once in a billion */
+ static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
+ /* We try multiplying the results with various odd numbers, which shouldn't
+ * influence the uniform distribution modulo a power of 2. */
+ static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
+ /* We only select up to 6 bits from the output to analyse */
+ unsigned int usebits = bits > 6 ? 6 : bits;
+ unsigned int maxshift = bits - usebits;
+ /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
+ number, track all observed outcomes, one per bit in a uint64_t. */
+ uint64_t x[6][27] = {{0}};
+ unsigned int i, shift, m;
+ /* Multiply the output of all rand calls with the odd number m, which
+ should not change the uniformity of its distribution. */
+ for (i = 0; i < rounds[usebits]; i++) {
+ uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
+ CHECK((((uint64_t)r) >> bits) == 0);
+ for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+ uint32_t rm = r * mults[m];
+ for (shift = 0; shift <= maxshift; shift++) {
+ x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
+ }
+ }
+ }
+ for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+ for (shift = 0; shift <= maxshift; shift++) {
+ /* Test that the lower usebits bits of x[shift] are 1 */
+ CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
+ }
+ }
+}
+
+/* Subrange must be a whole divisor of range, and at most 64 */
+void test_rand_int(uint32_t range, uint32_t subrange) {
+ /* (1-1/subrange)^rounds < 1/10^9 */
+ int rounds = (subrange * 2073) / 100;
+ int i;
+ uint64_t x = 0;
+ CHECK((range % subrange) == 0);
+ for (i = 0; i < rounds; i++) {
+ uint32_t r = secp256k1_rand_int(range);
+ CHECK(r < range);
+ r = r % subrange;
+ x |= (((uint64_t)1) << r);
+ }
+ /* Test that the lower subrange bits of x are 1. */
+ CHECK(((~x) << (64 - subrange)) == 0);
+}
+
+void run_rand_bits(void) {
+ size_t b;
+ test_rand_bits(1, 32);
+ for (b = 1; b <= 32; b++) {
+ test_rand_bits(0, b);
+ }
+}
+
+void run_rand_int(void) {
+ static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
+ static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
+ unsigned int m, s;
+ for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
+ for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
+ test_rand_int(ms[m] * ss[s], ss[s]);
+ }
+ }
+}
+
+/***** NUM TESTS *****/
+
+#ifndef USE_NUM_NONE
+void random_num_negate(secp256k1_num *num) {
+ if (secp256k1_rand_bits(1)) {
+ secp256k1_num_negate(num);
+ }
+}
+
+void random_num_order_test(secp256k1_num *num) {
+ secp256k1_scalar sc;
+ random_scalar_order_test(&sc);
+ secp256k1_scalar_get_num(num, &sc);
+}
+
+void random_num_order(secp256k1_num *num) {
+ secp256k1_scalar sc;
+ random_scalar_order(&sc);
+ secp256k1_scalar_get_num(num, &sc);
}
void test_num_negate(void) {
- secp256k1_num_t n1;
- secp256k1_num_t n2;
+ secp256k1_num n1;
+ secp256k1_num n2;
random_num_order_test(&n1); /* n1 = R */
random_num_negate(&n1);
secp256k1_num_copy(&n2, &n1); /* n2 = R */
}
void test_num_add_sub(void) {
- int r = secp256k1_rand32();
- secp256k1_num_t n1;
- secp256k1_num_t n2;
+ int i;
+ secp256k1_scalar s;
+ secp256k1_num n1;
+ secp256k1_num n2;
+ secp256k1_num n1p2, n2p1, n1m2, n2m1;
random_num_order_test(&n1); /* n1 = R1 */
- if (r & 1) {
+ if (secp256k1_rand_bits(1)) {
random_num_negate(&n1);
}
random_num_order_test(&n2); /* n2 = R2 */
- if (r & 2) {
+ if (secp256k1_rand_bits(1)) {
random_num_negate(&n2);
}
- secp256k1_num_t n1p2, n2p1, n1m2, n2m1;
secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
CHECK(!secp256k1_num_eq(&n2p1, &n1));
secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
CHECK(secp256k1_num_eq(&n2p1, &n1));
+
+ /* check is_one */
+ secp256k1_scalar_set_int(&s, 1);
+ secp256k1_scalar_get_num(&n1, &s);
+ CHECK(secp256k1_num_is_one(&n1));
+ /* check that 2^n + 1 is never 1 */
+ secp256k1_scalar_get_num(&n2, &s);
+ for (i = 0; i < 250; ++i) {
+ secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */
+ secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */
+ CHECK(!secp256k1_num_is_one(&n1p2));
+ }
+}
+
+void test_num_mod(void) {
+ int i;
+ secp256k1_scalar s;
+ secp256k1_num order, n;
+
+ /* check that 0 mod anything is 0 */
+ random_scalar_order_test(&s);
+ secp256k1_scalar_get_num(&order, &s);
+ secp256k1_scalar_set_int(&s, 0);
+ secp256k1_scalar_get_num(&n, &s);
+ secp256k1_num_mod(&n, &order);
+ CHECK(secp256k1_num_is_zero(&n));
+
+ /* check that anything mod 1 is 0 */
+ secp256k1_scalar_set_int(&s, 1);
+ secp256k1_scalar_get_num(&order, &s);
+ secp256k1_scalar_get_num(&n, &s);
+ secp256k1_num_mod(&n, &order);
+ CHECK(secp256k1_num_is_zero(&n));
+
+ /* check that increasing the number past 2^256 does not break this */
+ random_scalar_order_test(&s);
+ secp256k1_scalar_get_num(&n, &s);
+ /* multiply by 2^8, which'll test this case with high probability */
+ for (i = 0; i < 8; ++i) {
+ secp256k1_num_add(&n, &n, &n);
+ }
+ secp256k1_num_mod(&n, &order);
+ CHECK(secp256k1_num_is_zero(&n));
+}
+
+void test_num_jacobi(void) {
+ secp256k1_scalar sqr;
+ secp256k1_scalar small;
+ secp256k1_scalar five; /* five is not a quadratic residue */
+ secp256k1_num order, n;
+ int i;
+ /* squares mod 5 are 1, 4 */
+ const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
+
+ /* check some small values with 5 as the order */
+ secp256k1_scalar_set_int(&five, 5);
+ secp256k1_scalar_get_num(&order, &five);
+ for (i = 0; i < 10; ++i) {
+ secp256k1_scalar_set_int(&small, i);
+ secp256k1_scalar_get_num(&n, &small);
+ CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
+ }
+
+ /** test large values with 5 as group order */
+ secp256k1_scalar_get_num(&order, &five);
+ /* we first need a scalar which is not a multiple of 5 */
+ do {
+ secp256k1_num fiven;
+ random_scalar_order_test(&sqr);
+ secp256k1_scalar_get_num(&fiven, &five);
+ secp256k1_scalar_get_num(&n, &sqr);
+ secp256k1_num_mod(&n, &fiven);
+ } while (secp256k1_num_is_zero(&n));
+ /* next force it to be a residue. 2 is a nonresidue mod 5 so we can
+ * just multiply by two, i.e. add the number to itself */
+ if (secp256k1_num_jacobi(&n, &order) == -1) {
+ secp256k1_num_add(&n, &n, &n);
+ }
+
+ /* test residue */
+ CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+ /* test nonresidue */
+ secp256k1_num_add(&n, &n, &n);
+ CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+
+ /** test with secp group order as order */
+ secp256k1_scalar_order_get_num(&order);
+ random_scalar_order_test(&sqr);
+ secp256k1_scalar_sqr(&sqr, &sqr);
+ /* test residue */
+ secp256k1_scalar_get_num(&n, &sqr);
+ CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+ /* test nonresidue */
+ secp256k1_scalar_mul(&sqr, &sqr, &five);
+ secp256k1_scalar_get_num(&n, &sqr);
+ CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+ /* test multiple of the order*/
+ CHECK(secp256k1_num_jacobi(&order, &order) == 0);
+
+ /* check one less than the order */
+ secp256k1_scalar_set_int(&small, 1);
+ secp256k1_scalar_get_num(&n, &small);
+ secp256k1_num_sub(&n, &order, &n);
+ CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */
}
void run_num_smalltests(void) {
- for (int i=0; i<100*count; i++) {
- test_num_get_set_bin();
+ int i;
+ for (i = 0; i < 100*count; i++) {
test_num_negate();
test_num_add_sub();
+ test_num_mod();
+ test_num_jacobi();
}
}
+#endif
/***** SCALAR TESTS *****/
void scalar_test(void) {
+ secp256k1_scalar s;
+ secp256k1_scalar s1;
+ secp256k1_scalar s2;
+#ifndef USE_NUM_NONE
+ secp256k1_num snum, s1num, s2num;
+ secp256k1_num order, half_order;
+#endif
unsigned char c[32];
/* Set 's' to a random scalar, with value 'snum'. */
- secp256k1_rand256_test(c);
- secp256k1_scalar_t s;
- secp256k1_scalar_set_b32(&s, c, NULL);
- secp256k1_num_t snum;
- secp256k1_num_set_bin(&snum, c, 32);
- secp256k1_num_mod(&snum, &secp256k1_ge_consts->order);
+ random_scalar_order_test(&s);
/* Set 's1' to a random scalar, with value 's1num'. */
- secp256k1_rand256_test(c);
- secp256k1_scalar_t s1;
- secp256k1_scalar_set_b32(&s1, c, NULL);
- secp256k1_num_t s1num;
- secp256k1_num_set_bin(&s1num, c, 32);
- secp256k1_num_mod(&s1num, &secp256k1_ge_consts->order);
+ random_scalar_order_test(&s1);
/* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
- secp256k1_rand256_test(c);
- secp256k1_scalar_t s2;
- int overflow = 0;
- secp256k1_scalar_set_b32(&s2, c, &overflow);
- secp256k1_num_t s2num;
- secp256k1_num_set_bin(&s2num, c, 32);
- secp256k1_num_mod(&s2num, &secp256k1_ge_consts->order);
+ random_scalar_order_test(&s2);
+ secp256k1_scalar_get_b32(c, &s2);
+
+#ifndef USE_NUM_NONE
+ secp256k1_scalar_get_num(&snum, &s);
+ secp256k1_scalar_get_num(&s1num, &s1);
+ secp256k1_scalar_get_num(&s2num, &s2);
+
+ secp256k1_scalar_order_get_num(&order);
+ half_order = order;
+ secp256k1_num_shift(&half_order, 1);
+#endif
{
+ int i;
/* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
- secp256k1_scalar_t n;
+ secp256k1_scalar n;
secp256k1_scalar_set_int(&n, 0);
- for (int i = 0; i < 256; i += 4) {
- secp256k1_scalar_t t;
+ for (i = 0; i < 256; i += 4) {
+ secp256k1_scalar t;
+ int j;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
- for (int j = 0; j < 4; j++) {
+ for (j = 0; j < 4; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
{
/* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
- secp256k1_scalar_t n;
- secp256k1_scalar_set_int(&n, 0);
+ secp256k1_scalar n;
int i = 0;
+ secp256k1_scalar_set_int(&n, 0);
while (i < 256) {
- int now = (secp256k1_rand32() % 15) + 1;
+ secp256k1_scalar t;
+ int j;
+ int now = secp256k1_rand_int(15) + 1;
if (now + i > 256) {
now = 256 - i;
}
- secp256k1_scalar_t t;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
- for (int j = 0; j < now; j++) {
+ for (j = 0; j < now; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
CHECK(secp256k1_scalar_eq(&n, &s));
}
- {
- /* Test that get_b32 returns the same as get_bin on the number. */
- unsigned char r1[32];
- secp256k1_scalar_get_b32(r1, &s2);
- unsigned char r2[32];
- secp256k1_num_get_bin(r2, 32, &s2num);
- CHECK(memcmp(r1, r2, 32) == 0);
- /* If no overflow occurred when assigning, it should also be equal to the original byte array. */
- CHECK((memcmp(r1, c, 32) == 0) == (overflow == 0));
- }
-
+#ifndef USE_NUM_NONE
{
/* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
- secp256k1_num_t rnum;
+ secp256k1_num rnum;
+ secp256k1_num r2num;
+ secp256k1_scalar r;
secp256k1_num_add(&rnum, &snum, &s2num);
- secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
- secp256k1_scalar_t r;
+ secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_add(&r, &s, &s2);
- secp256k1_num_t r2num;
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
}
{
- /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
- secp256k1_num_t rnum;
+ /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
+ secp256k1_scalar r;
+ secp256k1_num r2num;
+ secp256k1_num rnum;
secp256k1_num_mul(&rnum, &snum, &s2num);
- secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
- secp256k1_scalar_t r;
+ secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_mul(&r, &s, &s2);
- secp256k1_num_t r2num;
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
/* The result can only be zero if at least one of the factors was zero. */
}
{
+ secp256k1_scalar neg;
+ secp256k1_num negnum;
+ secp256k1_num negnum2;
/* Check that comparison with zero matches comparison with zero on the number. */
CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
/* Check that comparison with the half order is equal to testing for high scalar. */
- CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &secp256k1_ge_consts->half_order) > 0));
- secp256k1_scalar_t neg;
+ CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
secp256k1_scalar_negate(&neg, &s);
- secp256k1_num_t negnum;
- secp256k1_num_sub(&negnum, &secp256k1_ge_consts->order, &snum);
- secp256k1_num_mod(&negnum, &secp256k1_ge_consts->order);
+ secp256k1_num_sub(&negnum, &order, &snum);
+ secp256k1_num_mod(&negnum, &order);
/* Check that comparison with the half order is equal to testing for high scalar after negation. */
- CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &secp256k1_ge_consts->half_order) > 0));
+ CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
/* Negating should change the high property, unless the value was already zero. */
CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
- secp256k1_num_t negnum2;
secp256k1_scalar_get_num(&negnum2, &neg);
/* Negating a scalar should be equal to (order - n) mod order on the number. */
CHECK(secp256k1_num_eq(&negnum, &negnum2));
CHECK(secp256k1_scalar_is_zero(&neg));
}
+ {
+ /* Test secp256k1_scalar_mul_shift_var. */
+ secp256k1_scalar r;
+ secp256k1_num one;
+ secp256k1_num rnum;
+ secp256k1_num rnum2;
+ unsigned char cone[1] = {0x01};
+ unsigned int shift = 256 + secp256k1_rand_int(257);
+ secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
+ secp256k1_num_mul(&rnum, &s1num, &s2num);
+ secp256k1_num_shift(&rnum, shift - 1);
+ secp256k1_num_set_bin(&one, cone, 1);
+ secp256k1_num_add(&rnum, &rnum, &one);
+ secp256k1_num_shift(&rnum, 1);
+ secp256k1_scalar_get_num(&rnum2, &r);
+ CHECK(secp256k1_num_eq(&rnum, &rnum2));
+ }
+
+ {
+ /* test secp256k1_scalar_shr_int */
+ secp256k1_scalar r;
+ int i;
+ random_scalar_order_test(&r);
+ for (i = 0; i < 100; ++i) {
+ int low;
+ int shift = 1 + secp256k1_rand_int(15);
+ int expected = r.d[0] % (1 << shift);
+ low = secp256k1_scalar_shr_int(&r, shift);
+ CHECK(expected == low);
+ }
+ }
+#endif
+
{
/* Test that scalar inverses are equal to the inverse of their number modulo the order. */
if (!secp256k1_scalar_is_zero(&s)) {
- secp256k1_scalar_t inv;
+ secp256k1_scalar inv;
+#ifndef USE_NUM_NONE
+ secp256k1_num invnum;
+ secp256k1_num invnum2;
+#endif
secp256k1_scalar_inverse(&inv, &s);
- secp256k1_num_t invnum;
- secp256k1_num_mod_inverse(&invnum, &snum, &secp256k1_ge_consts->order);
- secp256k1_num_t invnum2;
+#ifndef USE_NUM_NONE
+ secp256k1_num_mod_inverse(&invnum, &snum, &order);
secp256k1_scalar_get_num(&invnum2, &inv);
CHECK(secp256k1_num_eq(&invnum, &invnum2));
+#endif
secp256k1_scalar_mul(&inv, &inv, &s);
/* Multiplying a scalar with its inverse must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
secp256k1_scalar_inverse(&inv, &inv);
/* Inverting one must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
+#ifndef USE_NUM_NONE
+ secp256k1_scalar_get_num(&invnum, &inv);
+ CHECK(secp256k1_num_is_one(&invnum));
+#endif
}
}
{
/* Test commutativity of add. */
- secp256k1_scalar_t r1, r2;
+ secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
+ secp256k1_scalar r1, r2;
+ secp256k1_scalar b;
+ int i;
/* Test add_bit. */
- int bit = secp256k1_rand32() % 256;
- secp256k1_scalar_t b;
+ int bit = secp256k1_rand_bits(8);
secp256k1_scalar_set_int(&b, 1);
CHECK(secp256k1_scalar_is_one(&b));
- for (int i = 0; i < bit; i++) {
+ for (i = 0; i < bit; i++) {
secp256k1_scalar_add(&b, &b, &b);
}
- secp256k1_scalar_t r1 = s1, r2 = s1;
- secp256k1_scalar_add(&r1, &r1, &b);
- if (!(secp256k1_scalar_get_bits(&s1, 255, 1) == 1 && secp256k1_scalar_get_bits(&r1, 255, 1) == 0)) {
+ r1 = s1;
+ r2 = s1;
+ if (!secp256k1_scalar_add(&r1, &r1, &b)) {
/* No overflow happened. */
- secp256k1_scalar_add_bit(&r2, bit);
+ secp256k1_scalar_cadd_bit(&r2, bit, 1);
+ CHECK(secp256k1_scalar_eq(&r1, &r2));
+ /* cadd is a noop when flag is zero */
+ secp256k1_scalar_cadd_bit(&r2, bit, 0);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
{
/* Test commutativity of mul. */
- secp256k1_scalar_t r1, r2;
+ secp256k1_scalar r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
{
/* Test associativity of add. */
- secp256k1_scalar_t r1, r2;
+ secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r1, &r1, &s);
secp256k1_scalar_add(&r2, &s2, &s);
{
/* Test associativity of mul. */
- secp256k1_scalar_t r1, r2;
+ secp256k1_scalar r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s2, &s);
{
/* Test distributitivity of mul over add. */
- secp256k1_scalar_t r1, r2, t;
+ secp256k1_scalar r1, r2, t;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s1, &s);
{
/* Test square. */
- secp256k1_scalar_t r1, r2;
+ secp256k1_scalar r1, r2;
secp256k1_scalar_sqr(&r1, &s1);
secp256k1_scalar_mul(&r2, &s1, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
+
+ {
+ /* Test multiplicative identity. */
+ secp256k1_scalar r1, v1;
+ secp256k1_scalar_set_int(&v1,1);
+ secp256k1_scalar_mul(&r1, &s1, &v1);
+ CHECK(secp256k1_scalar_eq(&r1, &s1));
+ }
+
+ {
+ /* Test additive identity. */
+ secp256k1_scalar r1, v0;
+ secp256k1_scalar_set_int(&v0,0);
+ secp256k1_scalar_add(&r1, &s1, &v0);
+ CHECK(secp256k1_scalar_eq(&r1, &s1));
+ }
+
+ {
+ /* Test zero product property. */
+ secp256k1_scalar r1, v0;
+ secp256k1_scalar_set_int(&v0,0);
+ secp256k1_scalar_mul(&r1, &s1, &v0);
+ CHECK(secp256k1_scalar_eq(&r1, &v0));
+ }
+
}
void run_scalar_tests(void) {
- for (int i = 0; i < 128 * count; i++) {
+ int i;
+ for (i = 0; i < 128 * count; i++) {
scalar_test();
}
+
+ {
+ /* (-1)+1 should be zero. */
+ secp256k1_scalar s, o;
+ secp256k1_scalar_set_int(&s, 1);
+ CHECK(secp256k1_scalar_is_one(&s));
+ secp256k1_scalar_negate(&o, &s);
+ secp256k1_scalar_add(&o, &o, &s);
+ CHECK(secp256k1_scalar_is_zero(&o));
+ secp256k1_scalar_negate(&o, &o);
+ CHECK(secp256k1_scalar_is_zero(&o));
+ }
+
+#ifndef USE_NUM_NONE
+ {
+ /* A scalar with value of the curve order should be 0. */
+ secp256k1_num order;
+ secp256k1_scalar zero;
+ unsigned char bin[32];
+ int overflow = 0;
+ secp256k1_scalar_order_get_num(&order);
+ secp256k1_num_get_bin(bin, 32, &order);
+ secp256k1_scalar_set_b32(&zero, bin, &overflow);
+ CHECK(overflow == 1);
+ CHECK(secp256k1_scalar_is_zero(&zero));
+ }
+#endif
+
+ {
+ /* Does check_overflow check catch all ones? */
+ static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
+ 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+ 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
+ );
+ CHECK(secp256k1_scalar_check_overflow(&overflowed));
+ }
+
+ {
+ /* Static test vectors.
+ * These were reduced from ~10^12 random vectors based on comparison-decision
+ * and edge-case coverage on 32-bit and 64-bit implementations.
+ * The responses were generated with Sage 5.9.
+ */
+ secp256k1_scalar x;
+ secp256k1_scalar y;
+ secp256k1_scalar z;
+ secp256k1_scalar zz;
+ secp256k1_scalar one;
+ secp256k1_scalar r1;
+ secp256k1_scalar r2;
+#if defined(USE_SCALAR_INV_NUM)
+ secp256k1_scalar zzv;
+#endif
+ int overflow;
+ unsigned char chal[33][2][32] = {
+ {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
+ 0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
+ {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+ {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
+ 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
+ {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
+ {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
+ 0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
+ 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
+ 0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
+ 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
+ 0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
+ 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
+ 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+ {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+ 0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
+ 0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+ 0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
+ 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
+ {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+ {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
+ 0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+ {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
+ {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+ 0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
+ 0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
+ 0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
+ {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
+ {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
+ 0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
+ 0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
+ 0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
+ {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
+ {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
+ {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
+ 0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+ {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
+ {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+ 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
+ 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
+ {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+ {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
+ 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
+ 0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
+ {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
+ 0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
+ 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+ 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+ 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+ {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
+ 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
+ 0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
+ {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+ 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+ 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
+ 0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
+ 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+ {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+ {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+ 0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
+ {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
+ {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+ 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
+ 0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
+ {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
+ 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+ {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
+ 0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
+ 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
+ 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+ {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
+ 0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
+ 0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
+ {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
+ 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
+ 0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+ 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
+ {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
+ 0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
+ {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+ 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+ 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
+ {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+ 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+ 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
+ };
+ unsigned char res[33][2][32] = {
+ {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
+ 0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
+ 0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
+ 0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
+ {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
+ 0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
+ 0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
+ 0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
+ {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
+ 0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
+ 0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
+ 0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
+ {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
+ 0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
+ 0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
+ 0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
+ {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
+ 0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
+ 0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
+ 0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
+ {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
+ 0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
+ 0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
+ 0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
+ {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
+ 0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
+ 0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
+ 0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
+ {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
+ 0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
+ 0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
+ 0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
+ {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
+ 0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
+ 0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
+ 0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
+ {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
+ 0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
+ 0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
+ 0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
+ {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
+ 0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
+ 0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
+ 0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
+ {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
+ 0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
+ 0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
+ 0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
+ {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
+ 0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
+ 0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
+ 0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
+ {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
+ 0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
+ 0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
+ 0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
+ {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
+ 0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
+ 0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
+ 0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
+ {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
+ 0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
+ 0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
+ 0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
+ {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
+ 0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
+ 0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
+ 0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
+ {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
+ 0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
+ 0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
+ 0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
+ {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
+ 0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
+ 0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
+ 0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
+ {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
+ 0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
+ 0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
+ 0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
+ {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
+ 0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
+ 0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
+ 0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
+ {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
+ 0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
+ 0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
+ 0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
+ {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
+ 0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
+ 0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
+ 0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
+ {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
+ 0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
+ 0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
+ 0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
+ {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
+ 0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
+ 0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
+ 0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
+ {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
+ 0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
+ 0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
+ 0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
+ {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
+ 0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
+ 0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
+ 0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
+ {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
+ 0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
+ 0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
+ 0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
+ {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
+ 0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
+ 0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
+ 0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
+ {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
+ 0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
+ 0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
+ 0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
+ {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
+ 0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
+ 0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
+ 0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
+ {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
+ 0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
+ 0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
+ 0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
+ {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
+ 0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
+ 0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
+ 0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
+ {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
+ 0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
+ 0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
+ 0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
+ {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
+ 0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
+ 0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
+ 0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
+ {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
+ 0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
+ 0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
+ 0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
+ {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
+ 0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
+ 0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
+ 0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
+ {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
+ 0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
+ 0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
+ 0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
+ {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
+ 0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
+ 0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
+ 0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
+ {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
+ 0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
+ 0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
+ 0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+ {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+ 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+ 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+ 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
+ {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+ 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+ 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+ 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+ {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
+ 0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
+ 0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
+ 0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
+ {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
+ 0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
+ 0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
+ 0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
+ {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+ 0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
+ {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+ 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+ 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+ 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+ {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+ 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+ 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+ {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+ {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
+ 0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
+ 0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
+ 0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
+ {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
+ 0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
+ 0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
+ 0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
+ {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
+ 0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
+ 0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
+ 0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
+ {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
+ 0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
+ 0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
+ 0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
+ {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
+ 0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
+ 0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
+ 0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
+ {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
+ 0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
+ 0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
+ 0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
+ {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
+ 0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
+ 0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
+ 0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
+ {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
+ 0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
+ 0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
+ 0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
+ {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
+ 0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
+ 0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
+ 0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
+ {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
+ 0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
+ 0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
+ 0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
+ {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
+ 0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
+ 0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
+ 0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
+ {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
+ 0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
+ 0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
+ 0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
+ {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+ 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+ 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+ 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
+ {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+ 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+ 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+ 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
+ };
+ secp256k1_scalar_set_int(&one, 1);
+ for (i = 0; i < 33; i++) {
+ secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
+ CHECK(!overflow);
+ secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
+ CHECK(!overflow);
+ secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
+ CHECK(!overflow);
+ secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
+ CHECK(!overflow);
+ secp256k1_scalar_mul(&z, &x, &y);
+ CHECK(!secp256k1_scalar_check_overflow(&z));
+ CHECK(secp256k1_scalar_eq(&r1, &z));
+ if (!secp256k1_scalar_is_zero(&y)) {
+ secp256k1_scalar_inverse(&zz, &y);
+ CHECK(!secp256k1_scalar_check_overflow(&zz));
+#if defined(USE_SCALAR_INV_NUM)
+ secp256k1_scalar_inverse_var(&zzv, &y);
+ CHECK(secp256k1_scalar_eq(&zzv, &zz));
+#endif
+ secp256k1_scalar_mul(&z, &z, &zz);
+ CHECK(!secp256k1_scalar_check_overflow(&z));
+ CHECK(secp256k1_scalar_eq(&x, &z));
+ secp256k1_scalar_mul(&zz, &zz, &y);
+ CHECK(!secp256k1_scalar_check_overflow(&zz));
+ CHECK(secp256k1_scalar_eq(&one, &zz));
+ }
+ secp256k1_scalar_mul(&z, &x, &x);
+ CHECK(!secp256k1_scalar_check_overflow(&z));
+ secp256k1_scalar_sqr(&zz, &x);
+ CHECK(!secp256k1_scalar_check_overflow(&zz));
+ CHECK(secp256k1_scalar_eq(&zz, &z));
+ CHECK(secp256k1_scalar_eq(&r2, &zz));
+ }
+ }
}
/***** FIELD TESTS *****/
-void random_fe(secp256k1_fe_t *x) {
+void random_fe(secp256k1_fe *x) {
unsigned char bin[32];
do {
secp256k1_rand256(bin);
} while(1);
}
-void random_fe_non_zero(secp256k1_fe_t *nz) {
+void random_fe_test(secp256k1_fe *x) {
+ unsigned char bin[32];
+ do {
+ secp256k1_rand256_test(bin);
+ if (secp256k1_fe_set_b32(x, bin)) {
+ return;
+ }
+ } while(1);
+}
+
+void random_fe_non_zero(secp256k1_fe *nz) {
int tries = 10;
while (--tries >= 0) {
random_fe(nz);
secp256k1_fe_normalize(nz);
- if (!secp256k1_fe_is_zero(nz))
+ if (!secp256k1_fe_is_zero(nz)) {
break;
+ }
}
/* Infinitesimal probability of spurious failure here */
CHECK(tries >= 0);
}
-void random_fe_non_square(secp256k1_fe_t *ns) {
+void random_fe_non_square(secp256k1_fe *ns) {
+ secp256k1_fe r;
random_fe_non_zero(ns);
- secp256k1_fe_t r;
if (secp256k1_fe_sqrt(&r, ns)) {
secp256k1_fe_negate(ns, ns, 1);
}
}
-int check_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
- secp256k1_fe_t an = *a; secp256k1_fe_normalize(&an);
- secp256k1_fe_t bn = *b; secp256k1_fe_normalize(&bn);
- return secp256k1_fe_equal(&an, &bn);
+int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+ secp256k1_fe an = *a;
+ secp256k1_fe bn = *b;
+ secp256k1_fe_normalize_weak(&an);
+ secp256k1_fe_normalize_var(&bn);
+ return secp256k1_fe_equal_var(&an, &bn);
}
-int check_fe_inverse(const secp256k1_fe_t *a, const secp256k1_fe_t *ai) {
- secp256k1_fe_t x; secp256k1_fe_mul(&x, a, ai);
- secp256k1_fe_t one; secp256k1_fe_set_int(&one, 1);
+int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
+ secp256k1_fe x;
+ secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+ secp256k1_fe_mul(&x, a, ai);
return check_fe_equal(&x, &one);
}
+void run_field_convert(void) {
+ static const unsigned char b32[32] = {
+ 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
+ 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
+ 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
+ 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
+ };
+ static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
+ 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
+ 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
+ );
+ static const secp256k1_fe fe = SECP256K1_FE_CONST(
+ 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
+ 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
+ );
+ secp256k1_fe fe2;
+ unsigned char b322[32];
+ secp256k1_fe_storage fes2;
+ /* Check conversions to fe. */
+ CHECK(secp256k1_fe_set_b32(&fe2, b32));
+ CHECK(secp256k1_fe_equal_var(&fe, &fe2));
+ secp256k1_fe_from_storage(&fe2, &fes);
+ CHECK(secp256k1_fe_equal_var(&fe, &fe2));
+ /* Check conversion from fe. */
+ secp256k1_fe_get_b32(b322, &fe);
+ CHECK(memcmp(b322, b32, 32) == 0);
+ secp256k1_fe_to_storage(&fes2, &fe);
+ CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
+}
+
+int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
+ secp256k1_fe t = *b;
+#ifdef VERIFY
+ t.magnitude = a->magnitude;
+ t.normalized = a->normalized;
+#endif
+ return memcmp(a, &t, sizeof(secp256k1_fe));
+}
+
+void run_field_misc(void) {
+ secp256k1_fe x;
+ secp256k1_fe y;
+ secp256k1_fe z;
+ secp256k1_fe q;
+ secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
+ int i, j;
+ for (i = 0; i < 5*count; i++) {
+ secp256k1_fe_storage xs, ys, zs;
+ random_fe(&x);
+ random_fe_non_zero(&y);
+ /* Test the fe equality and comparison operations. */
+ CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
+ CHECK(secp256k1_fe_equal_var(&x, &x));
+ z = x;
+ secp256k1_fe_add(&z,&y);
+ /* Test fe conditional move; z is not normalized here. */
+ q = x;
+ secp256k1_fe_cmov(&x, &z, 0);
+#ifdef VERIFY
+ CHECK(!x.normalized && x.magnitude == z.magnitude);
+#endif
+ secp256k1_fe_cmov(&x, &x, 1);
+ CHECK(fe_memcmp(&x, &z) != 0);
+ CHECK(fe_memcmp(&x, &q) == 0);
+ secp256k1_fe_cmov(&q, &z, 1);
+#ifdef VERIFY
+ CHECK(!q.normalized && q.magnitude == z.magnitude);
+#endif
+ CHECK(fe_memcmp(&q, &z) == 0);
+ secp256k1_fe_normalize_var(&x);
+ secp256k1_fe_normalize_var(&z);
+ CHECK(!secp256k1_fe_equal_var(&x, &z));
+ secp256k1_fe_normalize_var(&q);
+ secp256k1_fe_cmov(&q, &z, (i&1));
+#ifdef VERIFY
+ CHECK(q.normalized && q.magnitude == 1);
+#endif
+ for (j = 0; j < 6; j++) {
+ secp256k1_fe_negate(&z, &z, j+1);
+ secp256k1_fe_normalize_var(&q);
+ secp256k1_fe_cmov(&q, &z, (j&1));
+#ifdef VERIFY
+ CHECK(!q.normalized && q.magnitude == (j+2));
+#endif
+ }
+ secp256k1_fe_normalize_var(&z);
+ /* Test storage conversion and conditional moves. */
+ secp256k1_fe_to_storage(&xs, &x);
+ secp256k1_fe_to_storage(&ys, &y);
+ secp256k1_fe_to_storage(&zs, &z);
+ secp256k1_fe_storage_cmov(&zs, &xs, 0);
+ secp256k1_fe_storage_cmov(&zs, &zs, 1);
+ CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
+ secp256k1_fe_storage_cmov(&ys, &xs, 1);
+ CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
+ secp256k1_fe_from_storage(&x, &xs);
+ secp256k1_fe_from_storage(&y, &ys);
+ secp256k1_fe_from_storage(&z, &zs);
+ /* Test that mul_int, mul, and add agree. */
+ secp256k1_fe_add(&y, &x);
+ secp256k1_fe_add(&y, &x);
+ z = x;
+ secp256k1_fe_mul_int(&z, 3);
+ CHECK(check_fe_equal(&y, &z));
+ secp256k1_fe_add(&y, &x);
+ secp256k1_fe_add(&z, &x);
+ CHECK(check_fe_equal(&z, &y));
+ z = x;
+ secp256k1_fe_mul_int(&z, 5);
+ secp256k1_fe_mul(&q, &x, &fe5);
+ CHECK(check_fe_equal(&z, &q));
+ secp256k1_fe_negate(&x, &x, 1);
+ secp256k1_fe_add(&z, &x);
+ secp256k1_fe_add(&q, &x);
+ CHECK(check_fe_equal(&y, &z));
+ CHECK(check_fe_equal(&q, &y));
+ }
+}
+
void run_field_inv(void) {
- secp256k1_fe_t x, xi, xii;
- for (int i=0; i<10*count; i++) {
+ secp256k1_fe x, xi, xii;
+ int i;
+ for (i = 0; i < 10*count; i++) {
random_fe_non_zero(&x);
secp256k1_fe_inv(&xi, &x);
CHECK(check_fe_inverse(&x, &xi));
}
void run_field_inv_var(void) {
- secp256k1_fe_t x, xi, xii;
- for (int i=0; i<10*count; i++) {
+ secp256k1_fe x, xi, xii;
+ int i;
+ for (i = 0; i < 10*count; i++) {
random_fe_non_zero(&x);
secp256k1_fe_inv_var(&xi, &x);
CHECK(check_fe_inverse(&x, &xi));
}
}
-void run_field_inv_all(void) {
- secp256k1_fe_t x[16], xi[16], xii[16];
- /* Check it's safe to call for 0 elements */
- secp256k1_fe_inv_all(0, xi, x);
- for (int i=0; i<count; i++) {
- size_t len = (secp256k1_rand32() & 15) + 1;
- for (size_t j=0; j<len; j++)
- random_fe_non_zero(&x[j]);
- secp256k1_fe_inv_all(len, xi, x);
- for (size_t j=0; j<len; j++)
- CHECK(check_fe_inverse(&x[j], &xi[j]));
- secp256k1_fe_inv_all(len, xii, xi);
- for (size_t j=0; j<len; j++)
- CHECK(check_fe_equal(&x[j], &xii[j]));
- }
-}
-
void run_field_inv_all_var(void) {
- secp256k1_fe_t x[16], xi[16], xii[16];
+ secp256k1_fe x[16], xi[16], xii[16];
+ int i;
/* Check it's safe to call for 0 elements */
- secp256k1_fe_inv_all_var(0, xi, x);
- for (int i=0; i<count; i++) {
- size_t len = (secp256k1_rand32() & 15) + 1;
- for (size_t j=0; j<len; j++)
+ secp256k1_fe_inv_all_var(xi, x, 0);
+ for (i = 0; i < count; i++) {
+ size_t j;
+ size_t len = secp256k1_rand_int(15) + 1;
+ for (j = 0; j < len; j++) {
random_fe_non_zero(&x[j]);
- secp256k1_fe_inv_all_var(len, xi, x);
- for (size_t j=0; j<len; j++)
+ }
+ secp256k1_fe_inv_all_var(xi, x, len);
+ for (j = 0; j < len; j++) {
CHECK(check_fe_inverse(&x[j], &xi[j]));
- secp256k1_fe_inv_all_var(len, xii, xi);
- for (size_t j=0; j<len; j++)
+ }
+ secp256k1_fe_inv_all_var(xii, xi, len);
+ for (j = 0; j < len; j++) {
CHECK(check_fe_equal(&x[j], &xii[j]));
+ }
}
}
void run_sqr(void) {
- secp256k1_fe_t x, s;
+ secp256k1_fe x, s;
{
+ int i;
secp256k1_fe_set_int(&x, 1);
secp256k1_fe_negate(&x, &x, 1);
- for (int i=1; i<=512; ++i) {
+ for (i = 1; i <= 512; ++i) {
secp256k1_fe_mul_int(&x, 2);
secp256k1_fe_normalize(&x);
secp256k1_fe_sqr(&s, &x);
}
}
-void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) {
- secp256k1_fe_t r1, r2;
+void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
+ secp256k1_fe r1, r2;
int v = secp256k1_fe_sqrt(&r1, a);
CHECK((v == 0) == (k == NULL));
}
void run_sqrt(void) {
- secp256k1_fe_t ns, x, s, t;
+ secp256k1_fe ns, x, s, t;
+ int i;
/* Check sqrt(0) is 0 */
secp256k1_fe_set_int(&x, 0);
test_sqrt(&s, &x);
/* Check sqrt of small squares (and their negatives) */
- for (int i=1; i<=100; i++) {
+ for (i = 1; i <= 100; i++) {
secp256k1_fe_set_int(&x, i);
secp256k1_fe_sqr(&s, &x);
test_sqrt(&s, &x);
}
/* Consistency checks for large random values */
- for (int i=0; i<10; i++) {
+ for (i = 0; i < 10; i++) {
+ int j;
random_fe_non_square(&ns);
- for (int j=0; j<count; j++) {
+ for (j = 0; j < count; j++) {
random_fe(&x);
secp256k1_fe_sqr(&s, &x);
test_sqrt(&s, &x);
/***** GROUP TESTS *****/
-int ge_equals_ge(const secp256k1_ge_t *a, const secp256k1_ge_t *b) {
- if (a->infinity && b->infinity)
- return 1;
- return check_fe_equal(&a->x, &b->x) && check_fe_equal(&a->y, &b->y);
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
+ CHECK(a->infinity == b->infinity);
+ if (a->infinity) {
+ return;
+ }
+ CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
+ CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
}
-void ge_equals_gej(const secp256k1_ge_t *a, const secp256k1_gej_t *b) {
- secp256k1_ge_t bb;
- secp256k1_gej_t bj = *b;
- secp256k1_ge_set_gej_var(&bb, &bj);
- CHECK(ge_equals_ge(a, &bb));
+/* This compares jacobian points including their Z, not just their geometric meaning. */
+int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
+ secp256k1_gej a2;
+ secp256k1_gej b2;
+ int ret = 1;
+ ret &= a->infinity == b->infinity;
+ if (ret && !a->infinity) {
+ a2 = *a;
+ b2 = *b;
+ secp256k1_fe_normalize(&a2.x);
+ secp256k1_fe_normalize(&a2.y);
+ secp256k1_fe_normalize(&a2.z);
+ secp256k1_fe_normalize(&b2.x);
+ secp256k1_fe_normalize(&b2.y);
+ secp256k1_fe_normalize(&b2.z);
+ ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
+ ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
+ ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
+ }
+ return ret;
}
-void gej_equals_gej(const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
- secp256k1_ge_t aa, bb;
- secp256k1_gej_t aj = *a, bj = *b;
- secp256k1_ge_set_gej_var(&aa, &aj);
- secp256k1_ge_set_gej_var(&bb, &bj);
- CHECK(ge_equals_ge(&aa, &bb));
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+ secp256k1_fe z2s;
+ secp256k1_fe u1, u2, s1, s2;
+ CHECK(a->infinity == b->infinity);
+ if (a->infinity) {
+ return;
+ }
+ /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+ secp256k1_fe_sqr(&z2s, &b->z);
+ secp256k1_fe_mul(&u1, &a->x, &z2s);
+ u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+ secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+ s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+ CHECK(secp256k1_fe_equal_var(&u1, &u2));
+ CHECK(secp256k1_fe_equal_var(&s1, &s2));
}
void test_ge(void) {
- secp256k1_ge_t a, b, i, n;
- random_group_element_test(&a);
- random_group_element_test(&b);
- n = a;
- secp256k1_fe_normalize(&a.y);
- secp256k1_fe_negate(&n.y, &a.y, 1);
- secp256k1_ge_set_infinity(&i);
- random_field_element_magnitude(&a.x);
- random_field_element_magnitude(&a.y);
- random_field_element_magnitude(&b.x);
- random_field_element_magnitude(&b.y);
- random_field_element_magnitude(&n.x);
- random_field_element_magnitude(&n.y);
-
- secp256k1_gej_t aj, bj, ij, nj;
- random_group_element_jacobian_test(&aj, &a);
- random_group_element_jacobian_test(&bj, &b);
- secp256k1_gej_set_infinity(&ij);
- random_group_element_jacobian_test(&nj, &n);
- random_field_element_magnitude(&aj.x);
- random_field_element_magnitude(&aj.y);
- random_field_element_magnitude(&aj.z);
- random_field_element_magnitude(&bj.x);
- random_field_element_magnitude(&bj.y);
- random_field_element_magnitude(&bj.z);
- random_field_element_magnitude(&nj.x);
- random_field_element_magnitude(&nj.y);
- random_field_element_magnitude(&nj.z);
-
- /* gej + gej adds */
- secp256k1_gej_t aaj; secp256k1_gej_add_var(&aaj, &aj, &aj);
- secp256k1_gej_t abj; secp256k1_gej_add_var(&abj, &aj, &bj);
- secp256k1_gej_t aij; secp256k1_gej_add_var(&aij, &aj, &ij);
- secp256k1_gej_t anj; secp256k1_gej_add_var(&anj, &aj, &nj);
- secp256k1_gej_t iaj; secp256k1_gej_add_var(&iaj, &ij, &aj);
- secp256k1_gej_t iij; secp256k1_gej_add_var(&iij, &ij, &ij);
-
- /* gej + ge adds */
- secp256k1_gej_t aa; secp256k1_gej_add_ge_var(&aa, &aj, &a);
- secp256k1_gej_t ab; secp256k1_gej_add_ge_var(&ab, &aj, &b);
- secp256k1_gej_t ai; secp256k1_gej_add_ge_var(&ai, &aj, &i);
- secp256k1_gej_t an; secp256k1_gej_add_ge_var(&an, &aj, &n);
- secp256k1_gej_t ia; secp256k1_gej_add_ge_var(&ia, &ij, &a);
- secp256k1_gej_t ii; secp256k1_gej_add_ge_var(&ii, &ij, &i);
-
- /* const gej + ge adds */
- secp256k1_gej_t aac; secp256k1_gej_add_ge(&aac, &aj, &a);
- secp256k1_gej_t abc; secp256k1_gej_add_ge(&abc, &aj, &b);
- secp256k1_gej_t anc; secp256k1_gej_add_ge(&anc, &aj, &n);
- secp256k1_gej_t iac; secp256k1_gej_add_ge(&iac, &ij, &a);
-
- CHECK(secp256k1_gej_is_infinity(&an));
- CHECK(secp256k1_gej_is_infinity(&anj));
- CHECK(secp256k1_gej_is_infinity(&anc));
- gej_equals_gej(&aa, &aaj);
- gej_equals_gej(&aa, &aac);
- gej_equals_gej(&ab, &abj);
- gej_equals_gej(&ab, &abc);
- gej_equals_gej(&an, &anj);
- gej_equals_gej(&an, &anc);
- gej_equals_gej(&ia, &iaj);
- gej_equals_gej(&ai, &aij);
- gej_equals_gej(&ii, &iij);
- ge_equals_gej(&a, &ai);
- ge_equals_gej(&a, &ai);
- ge_equals_gej(&a, &iaj);
- ge_equals_gej(&a, &iaj);
- ge_equals_gej(&a, &iac);
-}
+ int i, i1;
+#ifdef USE_ENDOMORPHISM
+ int runs = 6;
+#else
+ int runs = 4;
+#endif
+ /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
+ * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
+ * All magnitudes are randomized.
+ * All 17*17 combinations of points are added to each other, using all applicable methods.
+ *
+ * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
+ */
+ secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
+ secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
+ secp256k1_fe *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
+ secp256k1_fe zf;
+ secp256k1_fe zfi2, zfi3;
-void run_ge(void) {
- for (int i = 0; i < 2000*count; i++) {
- test_ge();
+ secp256k1_gej_set_infinity(&gej[0]);
+ secp256k1_ge_clear(&ge[0]);
+ secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
+ for (i = 0; i < runs; i++) {
+ int j;
+ secp256k1_ge g;
+ random_group_element_test(&g);
+#ifdef USE_ENDOMORPHISM
+ if (i >= runs - 2) {
+ secp256k1_ge_mul_lambda(&g, &ge[1]);
+ }
+ if (i >= runs - 1) {
+ secp256k1_ge_mul_lambda(&g, &g);
+ }
+#endif
+ ge[1 + 4 * i] = g;
+ ge[2 + 4 * i] = g;
+ secp256k1_ge_neg(&ge[3 + 4 * i], &g);
+ secp256k1_ge_neg(&ge[4 + 4 * i], &g);
+ secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
+ random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
+ secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
+ random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
+ for (j = 0; j < 4; j++) {
+ random_field_element_magnitude(&ge[1 + j + 4 * i].x);
+ random_field_element_magnitude(&ge[1 + j + 4 * i].y);
+ random_field_element_magnitude(&gej[1 + j + 4 * i].x);
+ random_field_element_magnitude(&gej[1 + j + 4 * i].y);
+ random_field_element_magnitude(&gej[1 + j + 4 * i].z);
+ }
}
-}
-/***** ECMULT TESTS *****/
+ /* Compute z inverses. */
+ {
+ secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs));
+ for (i = 0; i < 4 * runs + 1; i++) {
+ if (i == 0) {
+ /* The point at infinity does not have a meaningful z inverse. Any should do. */
+ do {
+ random_field_element_test(&zs[i]);
+ } while(secp256k1_fe_is_zero(&zs[i]));
+ } else {
+ zs[i] = gej[i].z;
+ }
+ }
+ secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
+ free(zs);
+ }
+
+ /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
+ do {
+ random_field_element_test(&zf);
+ } while(secp256k1_fe_is_zero(&zf));
+ random_field_element_magnitude(&zf);
+ secp256k1_fe_inv_var(&zfi3, &zf);
+ secp256k1_fe_sqr(&zfi2, &zfi3);
+ secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
+
+ for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
+ int i2;
+ for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
+ /* Compute reference result using gej + gej (var). */
+ secp256k1_gej refj, resj;
+ secp256k1_ge ref;
+ secp256k1_fe zr;
+ secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
+ /* Check Z ratio. */
+ if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
+ secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+ CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
+ }
+ secp256k1_ge_set_gej_var(&ref, &refj);
+
+ /* Test gej + ge with Z ratio result (var). */
+ secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
+ ge_equals_gej(&ref, &resj);
+ if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
+ secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+ CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
+ }
+
+ /* Test gej + ge (var, with additional Z factor). */
+ {
+ secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
+ secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
+ secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
+ random_field_element_magnitude(&ge2_zfi.x);
+ random_field_element_magnitude(&ge2_zfi.y);
+ secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
+ ge_equals_gej(&ref, &resj);
+ }
+
+ /* Test gej + ge (const). */
+ if (i2 != 0) {
+ /* secp256k1_gej_add_ge does not support its second argument being infinity. */
+ secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]);
+ ge_equals_gej(&ref, &resj);
+ }
+
+ /* Test doubling (var). */
+ if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
+ secp256k1_fe zr2;
+ /* Normal doubling with Z ratio result. */
+ secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
+ ge_equals_gej(&ref, &resj);
+ /* Check Z ratio. */
+ secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
+ CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
+ /* Normal doubling. */
+ secp256k1_gej_double_var(&resj, &gej[i2], NULL);
+ ge_equals_gej(&ref, &resj);
+ }
+
+ /* Test adding opposites. */
+ if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) {
+ CHECK(secp256k1_ge_is_infinity(&ref));
+ }
+
+ /* Test adding infinity. */
+ if (i1 == 0) {
+ CHECK(secp256k1_ge_is_infinity(&ge[i1]));
+ CHECK(secp256k1_gej_is_infinity(&gej[i1]));
+ ge_equals_gej(&ref, &gej[i2]);
+ }
+ if (i2 == 0) {
+ CHECK(secp256k1_ge_is_infinity(&ge[i2]));
+ CHECK(secp256k1_gej_is_infinity(&gej[i2]));
+ ge_equals_gej(&ref, &gej[i1]);
+ }
+ }
+ }
+
+ /* Test adding all points together in random order equals infinity. */
+ {
+ secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
+ secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej));
+ for (i = 0; i < 4 * runs + 1; i++) {
+ gej_shuffled[i] = gej[i];
+ }
+ for (i = 0; i < 4 * runs + 1; i++) {
+ int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
+ if (swap != i) {
+ secp256k1_gej t = gej_shuffled[i];
+ gej_shuffled[i] = gej_shuffled[swap];
+ gej_shuffled[swap] = t;
+ }
+ }
+ for (i = 0; i < 4 * runs + 1; i++) {
+ secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
+ }
+ CHECK(secp256k1_gej_is_infinity(&sum));
+ free(gej_shuffled);
+ }
+
+ /* Test batch gej -> ge conversion with and without known z ratios. */
+ {
+ secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe));
+ secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
+ for (i = 0; i < 4 * runs + 1; i++) {
+ /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
+ if (i < 4 * runs) {
+ secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
+ }
+ }
+ secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1);
+ for (i = 0; i < 4 * runs + 1; i++) {
+ secp256k1_fe s;
+ random_fe_non_zero(&s);
+ secp256k1_gej_rescale(&gej[i], &s);
+ ge_equals_gej(&ge_set_all[i], &gej[i]);
+ }
+ free(ge_set_all);
+ free(zr);
+ }
+
+ /* Test batch gej -> ge conversion with many infinities. */
+ for (i = 0; i < 4 * runs + 1; i++) {
+ random_group_element_test(&ge[i]);
+ /* randomly set half the points to infinitiy */
+ if(secp256k1_fe_is_odd(&ge[i].x)) {
+ secp256k1_ge_set_infinity(&ge[i]);
+ }
+ secp256k1_gej_set_ge(&gej[i], &ge[i]);
+ }
+ /* batch invert */
+ secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1);
+ /* check result */
+ for (i = 0; i < 4 * runs + 1; i++) {
+ ge_equals_gej(&ge[i], &gej[i]);
+ }
+
+ free(ge);
+ free(gej);
+ free(zinv);
+}
+
+void test_add_neg_y_diff_x(void) {
+ /* The point of this test is to check that we can add two points
+ * whose y-coordinates are negatives of each other but whose x
+ * coordinates differ. If the x-coordinates were the same, these
+ * points would be negatives of each other and their sum is
+ * infinity. This is cool because it "covers up" any degeneracy
+ * in the addition algorithm that would cause the xy coordinates
+ * of the sum to be wrong (since infinity has no xy coordinates).
+ * HOWEVER, if the x-coordinates are different, infinity is the
+ * wrong answer, and such degeneracies are exposed. This is the
+ * root of https://github.com/bitcoin-core/secp256k1/issues/257
+ * which this test is a regression test for.
+ *
+ * These points were generated in sage as
+ * # secp256k1 params
+ * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+ * C = EllipticCurve ([F (0), F (7)])
+ * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+ * N = FiniteField(G.order())
+ *
+ * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
+ * x = polygen(N)
+ * lam = (1 - x^3).roots()[1][0]
+ *
+ * # random "bad pair"
+ * P = C.random_element()
+ * Q = -int(lam) * P
+ * print " P: %x %x" % P.xy()
+ * print " Q: %x %x" % Q.xy()
+ * print "P + Q: %x %x" % (P + Q).xy()
+ */
+ secp256k1_gej aj = SECP256K1_GEJ_CONST(
+ 0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
+ 0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
+ 0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
+ 0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
+ );
+ secp256k1_gej bj = SECP256K1_GEJ_CONST(
+ 0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
+ 0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
+ 0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
+ 0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
+ );
+ secp256k1_gej sumj = SECP256K1_GEJ_CONST(
+ 0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
+ 0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
+ 0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
+ 0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
+ );
+ secp256k1_ge b;
+ secp256k1_gej resj;
+ secp256k1_ge res;
+ secp256k1_ge_set_gej(&b, &bj);
+
+ secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
+ secp256k1_ge_set_gej(&res, &resj);
+ ge_equals_gej(&res, &sumj);
+
+ secp256k1_gej_add_ge(&resj, &aj, &b);
+ secp256k1_ge_set_gej(&res, &resj);
+ ge_equals_gej(&res, &sumj);
+
+ secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
+ secp256k1_ge_set_gej(&res, &resj);
+ ge_equals_gej(&res, &sumj);
+}
+
+void run_ge(void) {
+ int i;
+ for (i = 0; i < count * 32; i++) {
+ test_ge();
+ }
+ test_add_neg_y_diff_x();
+}
+
+void test_ec_combine(void) {
+ secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+ secp256k1_pubkey data[6];
+ const secp256k1_pubkey* d[6];
+ secp256k1_pubkey sd;
+ secp256k1_pubkey sd2;
+ secp256k1_gej Qj;
+ secp256k1_ge Q;
+ int i;
+ for (i = 1; i <= 6; i++) {
+ secp256k1_scalar s;
+ random_scalar_order_test(&s);
+ secp256k1_scalar_add(&sum, &sum, &s);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
+ secp256k1_ge_set_gej(&Q, &Qj);
+ secp256k1_pubkey_save(&data[i - 1], &Q);
+ d[i - 1] = &data[i - 1];
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
+ secp256k1_ge_set_gej(&Q, &Qj);
+ secp256k1_pubkey_save(&sd, &Q);
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
+ CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
+ }
+}
+
+void run_ec_combine(void) {
+ int i;
+ for (i = 0; i < count * 8; i++) {
+ test_ec_combine();
+ }
+}
+
+void test_group_decompress(const secp256k1_fe* x) {
+ /* The input itself, normalized. */
+ secp256k1_fe fex = *x;
+ secp256k1_fe fez;
+ /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
+ secp256k1_ge ge_quad, ge_even, ge_odd;
+ secp256k1_gej gej_quad;
+ /* Return values of the above calls. */
+ int res_quad, res_even, res_odd;
+
+ secp256k1_fe_normalize_var(&fex);
+
+ res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
+ res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
+ res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
+
+ CHECK(res_quad == res_even);
+ CHECK(res_quad == res_odd);
+
+ if (res_quad) {
+ secp256k1_fe_normalize_var(&ge_quad.x);
+ secp256k1_fe_normalize_var(&ge_odd.x);
+ secp256k1_fe_normalize_var(&ge_even.x);
+ secp256k1_fe_normalize_var(&ge_quad.y);
+ secp256k1_fe_normalize_var(&ge_odd.y);
+ secp256k1_fe_normalize_var(&ge_even.y);
+
+ /* No infinity allowed. */
+ CHECK(!ge_quad.infinity);
+ CHECK(!ge_even.infinity);
+ CHECK(!ge_odd.infinity);
+
+ /* Check that the x coordinates check out. */
+ CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
+ CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
+ CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
+
+ /* Check that the Y coordinate result in ge_quad is a square. */
+ CHECK(secp256k1_fe_is_quad_var(&ge_quad.y));
+
+ /* Check odd/even Y in ge_odd, ge_even. */
+ CHECK(secp256k1_fe_is_odd(&ge_odd.y));
+ CHECK(!secp256k1_fe_is_odd(&ge_even.y));
+
+ /* Check secp256k1_gej_has_quad_y_var. */
+ secp256k1_gej_set_ge(&gej_quad, &ge_quad);
+ CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+ do {
+ random_fe_test(&fez);
+ } while (secp256k1_fe_is_zero(&fez));
+ secp256k1_gej_rescale(&gej_quad, &fez);
+ CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+ secp256k1_gej_neg(&gej_quad, &gej_quad);
+ CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+ do {
+ random_fe_test(&fez);
+ } while (secp256k1_fe_is_zero(&fez));
+ secp256k1_gej_rescale(&gej_quad, &fez);
+ CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+ secp256k1_gej_neg(&gej_quad, &gej_quad);
+ CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+ }
+}
+
+void run_group_decompress(void) {
+ int i;
+ for (i = 0; i < count * 4; i++) {
+ secp256k1_fe fe;
+ random_fe_test(&fe);
+ test_group_decompress(&fe);
+ }
+}
+
+/***** ECMULT TESTS *****/
+
+void run_ecmult_chain(void) {
+ /* random starting point A (on the curve) */
+ secp256k1_gej a = SECP256K1_GEJ_CONST(
+ 0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
+ 0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
+ 0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
+ 0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
+ );
+ /* two random initial factors xn and gn */
+ secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
+ 0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
+ 0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
+ );
+ secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
+ 0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
+ 0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
+ );
+ /* two small multipliers to be applied to xn and gn in every iteration: */
+ static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
+ static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
+ /* accumulators with the resulting coefficients to A and G */
+ secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+ secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+ /* actual points */
+ secp256k1_gej x;
+ secp256k1_gej x2;
+ int i;
-void run_ecmult_chain(void) {
- /* random starting point A (on the curve) */
- secp256k1_fe_t ax; VERIFY_CHECK(secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64));
- secp256k1_fe_t ay; VERIFY_CHECK(secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64));
- secp256k1_gej_t a; secp256k1_gej_set_xy(&a, &ax, &ay);
- /* two random initial factors xn and gn */
- static const unsigned char xni[32] = {
- 0x84, 0xcc, 0x54, 0x52, 0xf7, 0xfd, 0xe1, 0xed,
- 0xb4, 0xd3, 0x8a, 0x8c, 0xe9, 0xb1, 0xb8, 0x4c,
- 0xce, 0xf3, 0x1f, 0x14, 0x6e, 0x56, 0x9b, 0xe9,
- 0x70, 0x5d, 0x35, 0x7a, 0x42, 0x98, 0x54, 0x07
- };
- secp256k1_scalar_t xn;
- secp256k1_scalar_set_b32(&xn, xni, NULL);
- static const unsigned char gni[32] = {
- 0xa1, 0xe5, 0x8d, 0x22, 0x55, 0x3d, 0xcd, 0x42,
- 0xb2, 0x39, 0x80, 0x62, 0x5d, 0x4c, 0x57, 0xa9,
- 0x6e, 0x93, 0x23, 0xd4, 0x2b, 0x31, 0x52, 0xe5,
- 0xca, 0x2c, 0x39, 0x90, 0xed, 0xc7, 0xc9, 0xde
- };
- secp256k1_scalar_t gn;
- secp256k1_scalar_set_b32(&gn, gni, NULL);
- /* two small multipliers to be applied to xn and gn in every iteration: */
- static const unsigned char xfi[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0x13,0x37};
- secp256k1_scalar_t xf;
- secp256k1_scalar_set_b32(&xf, xfi, NULL);
- static const unsigned char gfi[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0x71,0x13};
- secp256k1_scalar_t gf;
- secp256k1_scalar_set_b32(&gf, gfi, NULL);
- /* accumulators with the resulting coefficients to A and G */
- secp256k1_scalar_t ae;
- secp256k1_scalar_set_int(&ae, 1);
- secp256k1_scalar_t ge;
- secp256k1_scalar_set_int(&ge, 0);
/* the point being computed */
- secp256k1_gej_t x = a;
- for (int i=0; i<200*count; i++) {
+ x = a;
+ for (i = 0; i < 200*count; i++) {
/* in each iteration, compute X = xn*X + gn*G; */
- secp256k1_ecmult(&x, &x, &xn, &gn);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn);
/* also compute ae and ge: the actual accumulated factors for A and G */
/* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
secp256k1_scalar_mul(&ae, &ae, &xn);
/* verify */
if (i == 19999) {
- char res[132]; int resl = 132;
- secp256k1_gej_get_hex(res, &resl, &x);
- CHECK(strcmp(res, "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)") == 0);
+ /* expected result after 19999 iterations */
+ secp256k1_gej rp = SECP256K1_GEJ_CONST(
+ 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
+ 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
+ 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
+ 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
+ );
+
+ secp256k1_gej_neg(&rp, &rp);
+ secp256k1_gej_add_var(&rp, &rp, &x, NULL);
+ CHECK(secp256k1_gej_is_infinity(&rp));
}
}
/* redo the computation, but directly with the resulting ae and ge coefficients: */
- secp256k1_gej_t x2; secp256k1_ecmult(&x2, &a, &ae, &ge);
- char res[132]; int resl = 132;
- char res2[132]; int resl2 = 132;
- secp256k1_gej_get_hex(res, &resl, &x);
- secp256k1_gej_get_hex(res2, &resl2, &x2);
- CHECK(strcmp(res, res2) == 0);
- CHECK(strlen(res) == 131);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
+ secp256k1_gej_neg(&x2, &x2);
+ secp256k1_gej_add_var(&x2, &x2, &x, NULL);
+ CHECK(secp256k1_gej_is_infinity(&x2));
}
-void test_point_times_order(const secp256k1_gej_t *point) {
+void test_point_times_order(const secp256k1_gej *point) {
/* X * (point + G) + (order-X) * (pointer + G) = 0 */
- secp256k1_scalar_t x;
+ secp256k1_scalar x;
+ secp256k1_scalar nx;
+ secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+ secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+ secp256k1_gej res1, res2;
+ secp256k1_ge res3;
+ unsigned char pub[65];
+ size_t psize = 65;
random_scalar_order_test(&x);
- secp256k1_scalar_t nx;
secp256k1_scalar_negate(&nx, &x);
- secp256k1_gej_t res1, res2;
- secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */
- secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
- secp256k1_gej_add_var(&res1, &res1, &res2);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
+ secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
CHECK(secp256k1_gej_is_infinity(&res1));
+ CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
+ secp256k1_ge_set_gej(&res3, &res1);
+ CHECK(secp256k1_ge_is_infinity(&res3));
+ CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
+ CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
+ psize = 65;
+ CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
+ /* check zero/one edge cases */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
+ secp256k1_ge_set_gej(&res3, &res1);
+ CHECK(secp256k1_ge_is_infinity(&res3));
+ secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
+ secp256k1_ge_set_gej(&res3, &res1);
+ ge_equals_gej(&res3, point);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
+ secp256k1_ge_set_gej(&res3, &res1);
+ ge_equals_ge(&res3, &secp256k1_ge_const_g);
}
void run_point_times_order(void) {
- secp256k1_fe_t x; VERIFY_CHECK(secp256k1_fe_set_hex(&x, "02", 2));
- for (int i=0; i<500; i++) {
- secp256k1_ge_t p;
- if (secp256k1_ge_set_xo(&p, &x, 1)) {
- CHECK(secp256k1_ge_is_valid(&p));
- secp256k1_gej_t j;
+ int i;
+ secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
+ static const secp256k1_fe xr = SECP256K1_FE_CONST(
+ 0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
+ 0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
+ );
+ for (i = 0; i < 500; i++) {
+ secp256k1_ge p;
+ if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
+ secp256k1_gej j;
+ CHECK(secp256k1_ge_is_valid_var(&p));
secp256k1_gej_set_ge(&j, &p);
- CHECK(secp256k1_gej_is_valid(&j));
+ CHECK(secp256k1_gej_is_valid_var(&j));
test_point_times_order(&j);
}
secp256k1_fe_sqr(&x, &x);
}
- char c[65]; int cl=65;
- secp256k1_fe_get_hex(c, &cl, &x);
- CHECK(strcmp(c, "7603CB59B0EF6C63FE6084792A0C378CDB3233A80F8A9A09A877DEAD31B38C45") == 0);
+ secp256k1_fe_normalize_var(&x);
+ CHECK(secp256k1_fe_equal_var(&x, &xr));
+}
+
+void ecmult_const_random_mult(void) {
+ /* random starting point A (on the curve) */
+ secp256k1_ge a = SECP256K1_GE_CONST(
+ 0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
+ 0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
+ 0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
+ 0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
+ );
+ /* random initial factor xn */
+ secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
+ 0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
+ 0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
+ );
+ /* expected xn * A (from sage) */
+ secp256k1_ge expected_b = SECP256K1_GE_CONST(
+ 0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
+ 0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
+ 0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
+ 0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
+ );
+ secp256k1_gej b;
+ secp256k1_ecmult_const(&b, &a, &xn, 256);
+
+ CHECK(secp256k1_ge_is_valid_var(&a));
+ ge_equals_gej(&expected_b, &b);
+}
+
+void ecmult_const_commutativity(void) {
+ secp256k1_scalar a;
+ secp256k1_scalar b;
+ secp256k1_gej res1;
+ secp256k1_gej res2;
+ secp256k1_ge mid1;
+ secp256k1_ge mid2;
+ random_scalar_order_test(&a);
+ random_scalar_order_test(&b);
+
+ secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256);
+ secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256);
+ secp256k1_ge_set_gej(&mid1, &res1);
+ secp256k1_ge_set_gej(&mid2, &res2);
+ secp256k1_ecmult_const(&res1, &mid1, &b, 256);
+ secp256k1_ecmult_const(&res2, &mid2, &a, 256);
+ secp256k1_ge_set_gej(&mid1, &res1);
+ secp256k1_ge_set_gej(&mid2, &res2);
+ ge_equals_ge(&mid1, &mid2);
+}
+
+void ecmult_const_mult_zero_one(void) {
+ secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+ secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+ secp256k1_scalar negone;
+ secp256k1_gej res1;
+ secp256k1_ge res2;
+ secp256k1_ge point;
+ secp256k1_scalar_negate(&negone, &one);
+
+ random_group_element_test(&point);
+ secp256k1_ecmult_const(&res1, &point, &zero, 3);
+ secp256k1_ge_set_gej(&res2, &res1);
+ CHECK(secp256k1_ge_is_infinity(&res2));
+ secp256k1_ecmult_const(&res1, &point, &one, 2);
+ secp256k1_ge_set_gej(&res2, &res1);
+ ge_equals_ge(&res2, &point);
+ secp256k1_ecmult_const(&res1, &point, &negone, 256);
+ secp256k1_gej_neg(&res1, &res1);
+ secp256k1_ge_set_gej(&res2, &res1);
+ ge_equals_ge(&res2, &point);
+}
+
+void ecmult_const_chain_multiply(void) {
+ /* Check known result (randomly generated test problem from sage) */
+ const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
+ 0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
+ 0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
+ );
+ const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
+ 0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
+ 0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
+ 0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
+ 0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
+ );
+ secp256k1_gej point;
+ secp256k1_ge res;
+ int i;
+
+ secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
+ for (i = 0; i < 100; ++i) {
+ secp256k1_ge tmp;
+ secp256k1_ge_set_gej(&tmp, &point);
+ secp256k1_ecmult_const(&point, &tmp, &scalar, 256);
+ }
+ secp256k1_ge_set_gej(&res, &point);
+ ge_equals_gej(&res, &expected_point);
}
-void test_wnaf(const secp256k1_scalar_t *number, int w) {
- secp256k1_scalar_t x, two, t;
+void run_ecmult_const_tests(void) {
+ ecmult_const_mult_zero_one();
+ ecmult_const_random_mult();
+ ecmult_const_commutativity();
+ ecmult_const_chain_multiply();
+}
+
+typedef struct {
+ secp256k1_scalar *sc;
+ secp256k1_ge *pt;
+} ecmult_multi_data;
+
+static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
+ ecmult_multi_data *data = (ecmult_multi_data*) cbdata;
+ *sc = data->sc[idx];
+ *pt = data->pt[idx];
+ return 1;
+}
+
+static int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) {
+ (void)sc;
+ (void)pt;
+ (void)idx;
+ (void)cbdata;
+ return 0;
+}
+
+void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) {
+ int ncount;
+ secp256k1_scalar szero;
+ secp256k1_scalar sc[32];
+ secp256k1_ge pt[32];
+ secp256k1_gej r;
+ secp256k1_gej r2;
+ ecmult_multi_data data;
+ secp256k1_scratch *scratch_empty;
+
+ data.sc = sc;
+ data.pt = pt;
+ secp256k1_scalar_set_int(&szero, 0);
+
+ /* No points to multiply */
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
+
+ /* Check 1- and 2-point multiplies against ecmult */
+ for (ncount = 0; ncount < count; ncount++) {
+ secp256k1_ge ptg;
+ secp256k1_gej ptgj;
+ random_scalar_order(&sc[0]);
+ random_scalar_order(&sc[1]);
+
+ random_group_element_test(&ptg);
+ secp256k1_gej_set_ge(&ptgj, &ptg);
+ pt[0] = ptg;
+ pt[1] = secp256k1_ge_const_g;
+
+ /* only G scalar */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+
+ /* 1-point */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+
+ /* Try to multiply 1 point, but scratch space is empty */
+ scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0);
+ CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
+ secp256k1_scratch_destroy(scratch_empty);
+
+ /* Try to multiply 1 point, but callback returns false */
+ CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
+
+ /* 2-point */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+
+ /* 2-point with G scalar */
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ /* Check infinite outputs of various forms */
+ for (ncount = 0; ncount < count; ncount++) {
+ secp256k1_ge ptg;
+ size_t i, j;
+ size_t sizes[] = { 2, 10, 32 };
+
+ for (j = 0; j < 3; j++) {
+ for (i = 0; i < 32; i++) {
+ random_scalar_order(&sc[i]);
+ secp256k1_ge_set_infinity(&pt[i]);
+ }
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ for (j = 0; j < 3; j++) {
+ for (i = 0; i < 32; i++) {
+ random_group_element_test(&ptg);
+ pt[i] = ptg;
+ secp256k1_scalar_set_int(&sc[i], 0);
+ }
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ for (j = 0; j < 3; j++) {
+ random_group_element_test(&ptg);
+ for (i = 0; i < 16; i++) {
+ random_scalar_order(&sc[2*i]);
+ secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]);
+ pt[2 * i] = ptg;
+ pt[2 * i + 1] = ptg;
+ }
+
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+ CHECK(secp256k1_gej_is_infinity(&r));
+
+ random_scalar_order(&sc[0]);
+ for (i = 0; i < 16; i++) {
+ random_group_element_test(&ptg);
+
+ sc[2*i] = sc[0];
+ sc[2*i+1] = sc[0];
+ pt[2 * i] = ptg;
+ secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]);
+ }
+
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j]));
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ random_group_element_test(&ptg);
+ secp256k1_scalar_set_int(&sc[0], 0);
+ pt[0] = ptg;
+ for (i = 1; i < 32; i++) {
+ pt[i] = ptg;
+
+ random_scalar_order(&sc[i]);
+ secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]);
+ secp256k1_scalar_negate(&sc[i], &sc[i]);
+ }
+
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32));
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ /* Check random points, constant scalar */
+ for (ncount = 0; ncount < count; ncount++) {
+ size_t i;
+ secp256k1_gej_set_infinity(&r);
+
+ random_scalar_order(&sc[0]);
+ for (i = 0; i < 20; i++) {
+ secp256k1_ge ptg;
+ sc[i] = sc[0];
+ random_group_element_test(&ptg);
+ pt[i] = ptg;
+ secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL);
+ }
+
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ /* Check random scalars, constant point */
+ for (ncount = 0; ncount < count; ncount++) {
+ size_t i;
+ secp256k1_ge ptg;
+ secp256k1_gej p0j;
+ secp256k1_scalar rs;
+ secp256k1_scalar_set_int(&rs, 0);
+
+ random_group_element_test(&ptg);
+ for (i = 0; i < 20; i++) {
+ random_scalar_order(&sc[i]);
+ pt[i] = ptg;
+ secp256k1_scalar_add(&rs, &rs, &sc[i]);
+ }
+
+ secp256k1_gej_set_ge(&p0j, &pt[0]);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+ secp256k1_gej_neg(&r2, &r2);
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+
+ /* Sanity check that zero scalars don't cause problems */
+ for (ncount = 0; ncount < 20; ncount++) {
+ random_scalar_order(&sc[ncount]);
+ random_group_element_test(&pt[ncount]);
+ }
+
+ secp256k1_scalar_clear(&sc[0]);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20));
+ secp256k1_scalar_clear(&sc[1]);
+ secp256k1_scalar_clear(&sc[2]);
+ secp256k1_scalar_clear(&sc[3]);
+ secp256k1_scalar_clear(&sc[4]);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6));
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5));
+ CHECK(secp256k1_gej_is_infinity(&r));
+
+ /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */
+ {
+ const size_t TOP = 8;
+ size_t s0i, s1i;
+ size_t t0i, t1i;
+ secp256k1_ge ptg;
+ secp256k1_gej ptgj;
+
+ random_group_element_test(&ptg);
+ secp256k1_gej_set_ge(&ptgj, &ptg);
+
+ for(t0i = 0; t0i < TOP; t0i++) {
+ for(t1i = 0; t1i < TOP; t1i++) {
+ secp256k1_gej t0p, t1p;
+ secp256k1_scalar t0, t1;
+
+ secp256k1_scalar_set_int(&t0, (t0i + 1) / 2);
+ secp256k1_scalar_cond_negate(&t0, t0i & 1);
+ secp256k1_scalar_set_int(&t1, (t1i + 1) / 2);
+ secp256k1_scalar_cond_negate(&t1, t1i & 1);
+
+ secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero);
+
+ for(s0i = 0; s0i < TOP; s0i++) {
+ for(s1i = 0; s1i < TOP; s1i++) {
+ secp256k1_scalar tmp1, tmp2;
+ secp256k1_gej expected, actual;
+
+ secp256k1_ge_set_gej(&pt[0], &t0p);
+ secp256k1_ge_set_gej(&pt[1], &t1p);
+
+ secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2);
+ secp256k1_scalar_cond_negate(&sc[0], s0i & 1);
+ secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2);
+ secp256k1_scalar_cond_negate(&sc[1], s1i & 1);
+
+ secp256k1_scalar_mul(&tmp1, &t0, &sc[0]);
+ secp256k1_scalar_mul(&tmp2, &t1, &sc[1]);
+ secp256k1_scalar_add(&tmp1, &tmp1, &tmp2);
+
+ secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero);
+ CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2));
+ secp256k1_gej_neg(&expected, &expected);
+ secp256k1_gej_add_var(&actual, &actual, &expected, NULL);
+ CHECK(secp256k1_gej_is_infinity(&actual));
+ }
+ }
+ }
+ }
+ }
+}
+
+void test_secp256k1_pippenger_bucket_window_inv(void) {
+ int i;
+
+ CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0);
+ for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) {
+#ifdef USE_ENDOMORPHISM
+ /* Bucket_window of 8 is not used with endo */
+ if (i == 8) {
+ continue;
+ }
+#endif
+ CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i);
+ if (i != PIPPENGER_MAX_BUCKET_WINDOW) {
+ CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i);
+ }
+ }
+}
+
+/**
+ * Probabilistically test the function returning the maximum number of possible points
+ * for a given scratch space.
+ */
+void test_ecmult_multi_pippenger_max_points(void) {
+ size_t scratch_size = secp256k1_rand_int(256);
+ size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
+ secp256k1_scratch *scratch;
+ size_t n_points_supported;
+ int bucket_window = 0;
+
+ for(; scratch_size < max_size; scratch_size+=256) {
+ scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size);
+ CHECK(scratch != NULL);
+ n_points_supported = secp256k1_pippenger_max_points(scratch);
+ if (n_points_supported == 0) {
+ secp256k1_scratch_destroy(scratch);
+ continue;
+ }
+ bucket_window = secp256k1_pippenger_bucket_window(n_points_supported);
+ CHECK(secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points_supported, bucket_window), PIPPENGER_SCRATCH_OBJECTS));
+ secp256k1_scratch_deallocate_frame(scratch);
+ secp256k1_scratch_destroy(scratch);
+ }
+ CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW);
+}
+
+void test_ecmult_multi_batch_size_helper(void) {
+ size_t n_batches, n_batch_points, max_n_batch_points, n;
+
+ max_n_batch_points = 0;
+ n = 1;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0);
+
+ max_n_batch_points = 1;
+ n = 0;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == 0);
+ CHECK(n_batch_points == 0);
+
+ max_n_batch_points = 2;
+ n = 5;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == 3);
+ CHECK(n_batch_points == 2);
+
+ max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH;
+ n = ECMULT_MAX_POINTS_PER_BATCH;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == 1);
+ CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH);
+
+ max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1;
+ n = ECMULT_MAX_POINTS_PER_BATCH + 1;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == 2);
+ CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1);
+
+ max_n_batch_points = 1;
+ n = SIZE_MAX;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == SIZE_MAX);
+ CHECK(n_batch_points == 1);
+
+ max_n_batch_points = 2;
+ n = SIZE_MAX;
+ CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1);
+ CHECK(n_batches == SIZE_MAX/2 + 1);
+ CHECK(n_batch_points == 2);
+}
+
+/**
+ * Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to
+ * 1 <= i <= num points.
+ */
+void test_ecmult_multi_batching(void) {
+ static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD;
+ secp256k1_scalar scG;
+ secp256k1_scalar szero;
+ secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_scalar) * n_points);
+ secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * n_points);
+ secp256k1_gej r;
+ secp256k1_gej r2;
+ ecmult_multi_data data;
+ int i;
+ secp256k1_scratch *scratch;
+
+ secp256k1_gej_set_infinity(&r2);
+ secp256k1_scalar_set_int(&szero, 0);
+
+ /* Get random scalars and group elements and compute result */
+ random_scalar_order(&scG);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG);
+ for(i = 0; i < n_points; i++) {
+ secp256k1_ge ptg;
+ secp256k1_gej ptgj;
+ random_group_element_test(&ptg);
+ secp256k1_gej_set_ge(&ptgj, &ptg);
+ pt[i] = ptg;
+ random_scalar_order(&sc[i]);
+ secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL);
+ secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL);
+ }
+ data.sc = sc;
+ data.pt = pt;
+
+ /* Test with empty scratch space */
+ scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
+ CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
+ secp256k1_scratch_destroy(scratch);
+
+ /* Test with space for 1 point in pippenger. That's not enough because
+ * ecmult_multi selects strauss which requires more memory. */
+ scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
+ CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
+ secp256k1_scratch_destroy(scratch);
+
+ secp256k1_gej_neg(&r2, &r2);
+ for(i = 1; i <= n_points; i++) {
+ if (i > ECMULT_PIPPENGER_THRESHOLD) {
+ int bucket_window = secp256k1_pippenger_bucket_window(i);
+ size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window);
+ scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
+ } else {
+ size_t scratch_size = secp256k1_strauss_scratch_size(i);
+ scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
+ }
+ CHECK(secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
+ secp256k1_gej_add_var(&r, &r, &r2, NULL);
+ CHECK(secp256k1_gej_is_infinity(&r));
+ secp256k1_scratch_destroy(scratch);
+ }
+ free(sc);
+ free(pt);
+}
+
+void run_ecmult_multi_tests(void) {
+ secp256k1_scratch *scratch;
+
+ test_secp256k1_pippenger_bucket_window_inv();
+ test_ecmult_multi_pippenger_max_points();
+ scratch = secp256k1_scratch_create(&ctx->error_callback, 819200);
+ test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
+ test_ecmult_multi(NULL, secp256k1_ecmult_multi_var);
+ test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
+ test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
+ secp256k1_scratch_destroy(scratch);
+
+ /* Run test_ecmult_multi with space for exactly one point */
+ scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
+ test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
+ secp256k1_scratch_destroy(scratch);
+
+ test_ecmult_multi_batch_size_helper();
+ test_ecmult_multi_batching();
+}
+
+void test_wnaf(const secp256k1_scalar *number, int w) {
+ secp256k1_scalar x, two, t;
+ int wnaf[256];
+ int zeroes = -1;
+ int i;
+ int bits;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&two, 2);
- int wnaf[256];
- int bits = secp256k1_ecmult_wnaf(wnaf, number, w);
+ bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
CHECK(bits <= 256);
- int zeroes = -1;
- for (int i=bits-1; i>=0; i--) {
- secp256k1_scalar_mul(&x, &x, &two);
+ for (i = bits-1; i >= 0; i--) {
int v = wnaf[i];
+ secp256k1_scalar_mul(&x, &x, &two);
if (v) {
CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
zeroes=0;
CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
}
+void test_constant_wnaf_negate(const secp256k1_scalar *number) {
+ secp256k1_scalar neg1 = *number;
+ secp256k1_scalar neg2 = *number;
+ int sign1 = 1;
+ int sign2 = 1;
+
+ if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
+ secp256k1_scalar_negate(&neg1, &neg1);
+ sign1 = -1;
+ }
+ sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
+ CHECK(sign1 == sign2);
+ CHECK(secp256k1_scalar_eq(&neg1, &neg2));
+}
+
+void test_constant_wnaf(const secp256k1_scalar *number, int w) {
+ secp256k1_scalar x, shift;
+ int wnaf[256] = {0};
+ int i;
+ int skew;
+ int bits = 256;
+ secp256k1_scalar num = *number;
+
+ secp256k1_scalar_set_int(&x, 0);
+ secp256k1_scalar_set_int(&shift, 1 << w);
+ /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
+#ifdef USE_ENDOMORPHISM
+ for (i = 0; i < 16; ++i) {
+ secp256k1_scalar_shr_int(&num, 8);
+ }
+ bits = 128;
+#endif
+ skew = secp256k1_wnaf_const(wnaf, &num, w, bits);
+
+ for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) {
+ secp256k1_scalar t;
+ int v = wnaf[i];
+ CHECK(v != 0); /* check nonzero */
+ CHECK(v & 1); /* check parity */
+ CHECK(v > -(1 << w)); /* check range above */
+ CHECK(v < (1 << w)); /* check range below */
+
+ secp256k1_scalar_mul(&x, &x, &shift);
+ if (v >= 0) {
+ secp256k1_scalar_set_int(&t, v);
+ } else {
+ secp256k1_scalar_set_int(&t, -v);
+ secp256k1_scalar_negate(&t, &t);
+ }
+ secp256k1_scalar_add(&x, &x, &t);
+ }
+ /* Skew num because when encoding numbers as odd we use an offset */
+ secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
+ CHECK(secp256k1_scalar_eq(&x, &num));
+}
+
+void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
+ secp256k1_scalar x, shift;
+ int wnaf[256] = {0};
+ int i;
+ int skew;
+ secp256k1_scalar num = *number;
+
+ secp256k1_scalar_set_int(&x, 0);
+ secp256k1_scalar_set_int(&shift, 1 << w);
+ /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
+#ifdef USE_ENDOMORPHISM
+ for (i = 0; i < 16; ++i) {
+ secp256k1_scalar_shr_int(&num, 8);
+ }
+#endif
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+
+ for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
+ secp256k1_scalar t;
+ int v = wnaf[i];
+ CHECK(v == 0 || v & 1); /* check parity */
+ CHECK(v > -(1 << w)); /* check range above */
+ CHECK(v < (1 << w)); /* check range below */
+
+ secp256k1_scalar_mul(&x, &x, &shift);
+ if (v >= 0) {
+ secp256k1_scalar_set_int(&t, v);
+ } else {
+ secp256k1_scalar_set_int(&t, -v);
+ secp256k1_scalar_negate(&t, &t);
+ }
+ secp256k1_scalar_add(&x, &x, &t);
+ }
+ /* If skew is 1 then add 1 to num */
+ secp256k1_scalar_cadd_bit(&num, 0, skew == 1);
+ CHECK(secp256k1_scalar_eq(&x, &num));
+}
+
+/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the
+ * rest is 0.*/
+void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) {
+ int i;
+ for (i = WNAF_SIZE(w)-1; i >= 8; --i) {
+ CHECK(wnaf[i] == 0);
+ }
+ for (i = 7; i >= 0; --i) {
+ CHECK(wnaf[i] == wnaf_expected[i]);
+ }
+}
+
+void test_fixed_wnaf_small(void) {
+ int w = 4;
+ int wnaf[256] = {0};
+ int i;
+ int skew;
+ secp256k1_scalar num;
+
+ secp256k1_scalar_set_int(&num, 0);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
+ int v = wnaf[i];
+ CHECK(v == 0);
+ }
+ CHECK(skew == 0);
+
+ secp256k1_scalar_set_int(&num, 1);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ for (i = WNAF_SIZE(w)-1; i >= 1; --i) {
+ int v = wnaf[i];
+ CHECK(v == 0);
+ }
+ CHECK(wnaf[0] == 1);
+ CHECK(skew == 0);
+
+ {
+ int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf };
+ secp256k1_scalar_set_int(&num, 0xffffffff);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+ CHECK(skew == 0);
+ }
+ {
+ int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf };
+ secp256k1_scalar_set_int(&num, 0xeeeeeeee);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+ CHECK(skew == 1);
+ }
+ {
+ int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 };
+ secp256k1_scalar_set_int(&num, 0x01010101);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+ CHECK(skew == 0);
+ }
+ {
+ int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 };
+ secp256k1_scalar_set_int(&num, 0x01ef1ef1);
+ skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+ test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+ CHECK(skew == 0);
+ }
+}
+
void run_wnaf(void) {
- secp256k1_scalar_t n;
- for (int i=0; i<count; i++) {
+ int i;
+ secp256k1_scalar n = {{0}};
+
+ /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
+ * have easier-to-diagnose failure modes */
+ n.d[0] = 1;
+ test_constant_wnaf(&n, 4);
+ n.d[0] = 2;
+ test_constant_wnaf(&n, 4);
+ /* Test 0 */
+ test_fixed_wnaf_small();
+ /* Random tests */
+ for (i = 0; i < count; i++) {
random_scalar_order(&n);
- if (i % 1)
- secp256k1_scalar_negate(&n, &n);
test_wnaf(&n, 4+(i%10));
+ test_constant_wnaf_negate(&n);
+ test_constant_wnaf(&n, 4 + (i % 10));
+ test_fixed_wnaf(&n, 4 + (i % 10));
+ }
+ secp256k1_scalar_set_int(&n, 0);
+ CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
+ CHECK(secp256k1_scalar_is_zero(&n));
+ CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
+ CHECK(secp256k1_scalar_is_zero(&n));
+}
+
+void test_ecmult_constants(void) {
+ /* Test ecmult_gen() for [0..36) and [order-36..0). */
+ secp256k1_scalar x;
+ secp256k1_gej r;
+ secp256k1_ge ng;
+ int i;
+ int j;
+ secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
+ for (i = 0; i < 36; i++ ) {
+ secp256k1_scalar_set_int(&x, i);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
+ for (j = 0; j < i; j++) {
+ if (j == i - 1) {
+ ge_equals_gej(&secp256k1_ge_const_g, &r);
+ }
+ secp256k1_gej_add_ge(&r, &r, &ng);
+ }
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+ for (i = 1; i <= 36; i++ ) {
+ secp256k1_scalar_set_int(&x, i);
+ secp256k1_scalar_negate(&x, &x);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
+ for (j = 0; j < i; j++) {
+ if (j == i - 1) {
+ ge_equals_gej(&ng, &r);
+ }
+ secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
+ }
+ CHECK(secp256k1_gej_is_infinity(&r));
+ }
+}
+
+void run_ecmult_constants(void) {
+ test_ecmult_constants();
+}
+
+void test_ecmult_gen_blind(void) {
+ /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
+ secp256k1_scalar key;
+ secp256k1_scalar b;
+ unsigned char seed32[32];
+ secp256k1_gej pgej;
+ secp256k1_gej pgej2;
+ secp256k1_gej i;
+ secp256k1_ge pge;
+ random_scalar_order_test(&key);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
+ secp256k1_rand256(seed32);
+ b = ctx->ecmult_gen_ctx.blind;
+ i = ctx->ecmult_gen_ctx.initial;
+ secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+ CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
+ CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
+ CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
+ secp256k1_ge_set_gej(&pge, &pgej);
+ ge_equals_gej(&pge, &pgej2);
+}
+
+void test_ecmult_gen_blind_reset(void) {
+ /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
+ secp256k1_scalar b;
+ secp256k1_gej initial;
+ secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
+ b = ctx->ecmult_gen_ctx.blind;
+ initial = ctx->ecmult_gen_ctx.initial;
+ secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
+ CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
+ CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
+}
+
+void run_ecmult_gen_blind(void) {
+ int i;
+ test_ecmult_gen_blind_reset();
+ for (i = 0; i < 10; i++) {
+ test_ecmult_gen_blind();
+ }
+}
+
+#ifdef USE_ENDOMORPHISM
+/***** ENDOMORPHISH TESTS *****/
+void test_scalar_split(void) {
+ secp256k1_scalar full;
+ secp256k1_scalar s1, slam;
+ const unsigned char zero[32] = {0};
+ unsigned char tmp[32];
+
+ random_scalar_order_test(&full);
+ secp256k1_scalar_split_lambda(&s1, &slam, &full);
+
+ /* check that both are <= 128 bits in size */
+ if (secp256k1_scalar_is_high(&s1)) {
+ secp256k1_scalar_negate(&s1, &s1);
+ }
+ if (secp256k1_scalar_is_high(&slam)) {
+ secp256k1_scalar_negate(&slam, &slam);
+ }
+
+ secp256k1_scalar_get_b32(tmp, &s1);
+ CHECK(memcmp(zero, tmp, 16) == 0);
+ secp256k1_scalar_get_b32(tmp, &slam);
+ CHECK(memcmp(zero, tmp, 16) == 0);
+}
+
+void run_endomorphism_tests(void) {
+ test_scalar_split();
+}
+#endif
+
+void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
+ unsigned char pubkeyc[65];
+ secp256k1_pubkey pubkey;
+ secp256k1_ge ge;
+ size_t pubkeyclen;
+ int32_t ecount;
+ ecount = 0;
+ secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+ for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
+ /* Smaller sizes are tested exhaustively elsewhere. */
+ int32_t i;
+ memcpy(&pubkeyc[1], input, 64);
+ VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
+ for (i = 0; i < 256; i++) {
+ /* Try all type bytes. */
+ int xpass;
+ int ypass;
+ int ysign;
+ pubkeyc[0] = i;
+ /* What sign does this point have? */
+ ysign = (input[63] & 1) + 2;
+ /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
+ xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
+ /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
+ ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
+ ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
+ if (xpass || ypass) {
+ /* These cases must parse. */
+ unsigned char pubkeyo[65];
+ size_t outl;
+ memset(&pubkey, 0, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ ecount = 0;
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ outl = 65;
+ VG_UNDEF(pubkeyo, 65);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+ VG_CHECK(pubkeyo, outl);
+ CHECK(outl == 33);
+ CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
+ CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
+ if (ypass) {
+ /* This test isn't always done because we decode with alternative signs, so the y won't match. */
+ CHECK(pubkeyo[0] == ysign);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+ memset(&pubkey, 0, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ secp256k1_pubkey_save(&pubkey, &ge);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ outl = 65;
+ VG_UNDEF(pubkeyo, 65);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+ VG_CHECK(pubkeyo, outl);
+ CHECK(outl == 65);
+ CHECK(pubkeyo[0] == 4);
+ CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
+ }
+ CHECK(ecount == 0);
+ } else {
+ /* These cases must fail to parse. */
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ }
+ }
+ }
+ secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+}
+
+void run_ec_pubkey_parse_test(void) {
+#define SECP256K1_EC_PARSE_TEST_NVALID (12)
+ const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
+ {
+ /* Point with leading and trailing zeros in x and y serialization. */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
+ 0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
+ },
+ {
+ /* Point with x equal to a 3rd root of unity.*/
+ 0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
+ 0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
+ 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+ 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+ },
+ {
+ /* Point with largest x. (1/2) */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+ 0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
+ 0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
+ },
+ {
+ /* Point with largest x. (2/2) */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+ 0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
+ 0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
+ },
+ {
+ /* Point with smallest x. (1/2) */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+ 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+ },
+ {
+ /* Point with smallest x. (2/2) */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+ 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+ },
+ {
+ /* Point with largest y. (1/3) */
+ 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+ 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+ },
+ {
+ /* Point with largest y. (2/3) */
+ 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+ 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+ },
+ {
+ /* Point with largest y. (3/3) */
+ 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+ 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+ },
+ {
+ /* Point with smallest y. (1/3) */
+ 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+ 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ },
+ {
+ /* Point with smallest y. (2/3) */
+ 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+ 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ },
+ {
+ /* Point with smallest y. (3/3) */
+ 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+ 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
+ }
+ };
+#define SECP256K1_EC_PARSE_TEST_NXVALID (4)
+ const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
+ {
+ /* Valid if y overflow ignored (y = 1 mod p). (1/3) */
+ 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+ 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+ },
+ {
+ /* Valid if y overflow ignored (y = 1 mod p). (2/3) */
+ 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+ 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+ },
+ {
+ /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
+ 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+ 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+ },
+ {
+ /* x on curve, y is from y^2 = x^3 + 8. */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
+ }
+ };
+#define SECP256K1_EC_PARSE_TEST_NINVALID (7)
+ const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
+ {
+ /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
+ 0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
+ 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ },
+ {
+ /* Valid if x overflow ignored (x = 1 mod p). */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+ 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+ 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+ },
+ {
+ /* Valid if x overflow ignored (x = 1 mod p). */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+ 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+ 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+ },
+ {
+ /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+ 0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
+ 0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
+ },
+ {
+ /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+ 0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
+ 0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
+ },
+ {
+ /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
+ 0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
+ },
+ {
+ /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
+ 0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
+ }
+ };
+ const unsigned char pubkeyc[66] = {
+ /* Serialization of G. */
+ 0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
+ 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
+ 0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
+ 0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
+ 0xB8, 0x00
+ };
+ unsigned char sout[65];
+ unsigned char shortkey[2];
+ secp256k1_ge ge;
+ secp256k1_pubkey pubkey;
+ size_t len;
+ int32_t i;
+ int32_t ecount;
+ int32_t ecount2;
+ ecount = 0;
+ /* Nothing should be reading this far into pubkeyc. */
+ VG_UNDEF(&pubkeyc[65], 1);
+ secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+ /* Zero length claimed, fail, zeroize, no illegal arg error. */
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(shortkey, 2);
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ /* Length one claimed, fail, zeroize, no illegal arg error. */
+ for (i = 0; i < 256 ; i++) {
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ shortkey[0] = i;
+ VG_UNDEF(&shortkey[1], 1);
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ }
+ /* Length two claimed, fail, zeroize, no illegal arg error. */
+ for (i = 0; i < 65536 ; i++) {
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ shortkey[0] = i & 255;
+ shortkey[1] = i >> 8;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
}
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
+ CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
+ CHECK(ecount == 2);
+ /* NULL input string. Illegal arg and zeroize output. */
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 1);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 2);
+ /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
+ memset(&pubkey, 0xfe, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+ CHECK(ecount == 1);
+ /* Valid parse. */
+ memset(&pubkey, 0, sizeof(pubkey));
+ ecount = 0;
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
+ CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(ecount == 0);
+ VG_UNDEF(&ge, sizeof(ge));
+ CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+ VG_CHECK(&ge.x, sizeof(ge.x));
+ VG_CHECK(&ge.y, sizeof(ge.y));
+ VG_CHECK(&ge.infinity, sizeof(ge.infinity));
+ ge_equals_ge(&secp256k1_ge_const_g, &ge);
+ CHECK(ecount == 0);
+ /* secp256k1_ec_pubkey_serialize illegal args. */
+ ecount = 0;
+ len = 65;
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+ CHECK(ecount == 1);
+ CHECK(len == 0);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+ CHECK(ecount == 2);
+ len = 65;
+ VG_UNDEF(sout, 65);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
+ VG_CHECK(sout, 65);
+ CHECK(ecount == 3);
+ CHECK(len == 0);
+ len = 65;
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
+ CHECK(ecount == 4);
+ CHECK(len == 0);
+ len = 65;
+ VG_UNDEF(sout, 65);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+ VG_CHECK(sout, 65);
+ CHECK(ecount == 4);
+ CHECK(len == 65);
+ /* Multiple illegal args. Should still set arg error only once. */
+ ecount = 0;
+ ecount2 = 11;
+ CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+ CHECK(ecount == 1);
+ /* Does the illegal arg callback actually change the behavior? */
+ secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
+ CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+ CHECK(ecount == 1);
+ CHECK(ecount2 == 10);
+ secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+ /* Try a bunch of prefabbed points with all possible encodings. */
+ for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
+ ec_pubkey_parse_pointtest(valid[i], 1, 1);
+ }
+ for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
+ ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
+ }
+ for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
+ ec_pubkey_parse_pointtest(invalid[i], 0, 0);
+ }
+}
+
+void run_eckey_edge_case_test(void) {
+ const unsigned char orderc[32] = {
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+ 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+ 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+ };
+ const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
+ unsigned char ctmp[33];
+ unsigned char ctmp2[33];
+ secp256k1_pubkey pubkey;
+ secp256k1_pubkey pubkey2;
+ secp256k1_pubkey pubkey_one;
+ secp256k1_pubkey pubkey_negone;
+ const secp256k1_pubkey *pubkeys[3];
+ size_t len;
+ int32_t ecount;
+ /* Group order is too large, reject. */
+ CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ /* Maximum value is too large, reject. */
+ memset(ctmp, 255, 32);
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+ memset(&pubkey, 1, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ /* Zero is too small, reject. */
+ memset(ctmp, 0, 32);
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+ memset(&pubkey, 1, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ /* One must be accepted. */
+ ctmp[31] = 0x01;
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+ memset(&pubkey, 0, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+ pubkey_one = pubkey;
+ /* Group order + 1 is too large, reject. */
+ memcpy(ctmp, orderc, 32);
+ ctmp[31] = 0x42;
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+ memset(&pubkey, 1, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ /* -1 must be accepted. */
+ ctmp[31] = 0x40;
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+ memset(&pubkey, 0, sizeof(pubkey));
+ VG_UNDEF(&pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+ VG_CHECK(&pubkey, sizeof(pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+ pubkey_negone = pubkey;
+ /* Tweak of zero leaves the value unchanged. */
+ memset(ctmp2, 0, 32);
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
+ CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
+ memcpy(&pubkey2, &pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+ CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+ /* Multiply tweak of zero zeroizes the output. */
+ CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
+ CHECK(memcmp(zeros, ctmp, 32) == 0);
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
+ CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+ memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+ /* Overflowing key tweak zeroizes. */
+ memcpy(ctmp, orderc, 32);
+ ctmp[31] = 0x40;
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
+ CHECK(memcmp(zeros, ctmp, 32) == 0);
+ memcpy(ctmp, orderc, 32);
+ ctmp[31] = 0x40;
+ CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
+ CHECK(memcmp(zeros, ctmp, 32) == 0);
+ memcpy(ctmp, orderc, 32);
+ ctmp[31] = 0x40;
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
+ CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+ memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
+ CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+ memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+ /* Private key tweaks results in a key of zero. */
+ ctmp2[31] = 1;
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
+ CHECK(memcmp(zeros, ctmp2, 32) == 0);
+ ctmp2[31] = 1;
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+ CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+ memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+ /* Tweak computation wraps and results in a key of 1. */
+ ctmp2[31] = 2;
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
+ CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
+ ctmp2[31] = 2;
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+ ctmp2[31] = 1;
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
+ CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+ /* Tweak mul * 2 = 1+1. */
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+ ctmp2[31] = 2;
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
+ CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+ /* Test argument errors. */
+ ecount = 0;
+ secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+ CHECK(ecount == 0);
+ /* Zeroize pubkey on parse error. */
+ memset(&pubkey, 0, 32);
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+ CHECK(ecount == 1);
+ CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+ memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+ memset(&pubkey2, 0, 32);
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
+ CHECK(ecount == 2);
+ CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
+ /* Plain argument errors. */
+ ecount = 0;
+ CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+ CHECK(ecount == 0);
+ CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
+ CHECK(ecount == 1);
+ ecount = 0;
+ memset(ctmp2, 0, 32);
+ ctmp2[31] = 4;
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
+ CHECK(ecount == 2);
+ ecount = 0;
+ memset(ctmp2, 0, 32);
+ ctmp2[31] = 4;
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
+ CHECK(ecount == 2);
+ ecount = 0;
+ memset(ctmp2, 0, 32);
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
+ CHECK(ecount == 2);
+ ecount = 0;
+ memset(ctmp2, 0, 32);
+ ctmp2[31] = 1;
+ CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
+ CHECK(ecount == 2);
+ ecount = 0;
+ CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
+ CHECK(ecount == 1);
+ memset(&pubkey, 1, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+ CHECK(ecount == 2);
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ /* secp256k1_ec_pubkey_combine tests. */
+ ecount = 0;
+ pubkeys[0] = &pubkey_one;
+ VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
+ VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
+ VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ CHECK(ecount == 2);
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ CHECK(ecount == 3);
+ pubkeys[0] = &pubkey_negone;
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+ CHECK(ecount == 3);
+ len = 33;
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
+ CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+ /* Result is infinity. */
+ pubkeys[0] = &pubkey_one;
+ pubkeys[1] = &pubkey_negone;
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+ CHECK(ecount == 3);
+ /* Passes through infinity but comes out one. */
+ pubkeys[2] = &pubkey_one;
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+ CHECK(ecount == 3);
+ len = 33;
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
+ CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+ /* Adds to two. */
+ pubkeys[1] = &pubkey_one;
+ memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+ VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
+ VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+ CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+ CHECK(ecount == 3);
+ secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
}
-void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *key, const secp256k1_scalar_t *msg, int *recid) {
- secp256k1_scalar_t nonce;
+void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
+ secp256k1_scalar nonce;
do {
random_scalar_order_test(&nonce);
- } while(!secp256k1_ecdsa_sig_sign(sig, key, msg, &nonce, recid));
+ } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
}
void test_ecdsa_sign_verify(void) {
- secp256k1_scalar_t msg, key;
+ secp256k1_gej pubj;
+ secp256k1_ge pub;
+ secp256k1_scalar one;
+ secp256k1_scalar msg, key;
+ secp256k1_scalar sigr, sigs;
+ int recid;
+ int getrec;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
- secp256k1_gej_t pubj; secp256k1_ecmult_gen(&pubj, &key);
- secp256k1_ge_t pub; secp256k1_ge_set_gej(&pub, &pubj);
- secp256k1_ecdsa_sig_t sig;
- random_sign(&sig, &key, &msg, NULL);
- CHECK(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
- secp256k1_scalar_t one;
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
+ secp256k1_ge_set_gej(&pub, &pubj);
+ getrec = secp256k1_rand_bits(1);
+ random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
+ if (getrec) {
+ CHECK(recid >= 0 && recid < 4);
+ }
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_add(&msg, &msg, &one);
- CHECK(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
+ CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
}
void run_ecdsa_sign_verify(void) {
- for (int i=0; i<10*count; i++) {
+ int i;
+ for (i = 0; i < 10*count; i++) {
test_ecdsa_sign_verify();
}
}
+/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
+static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+ (void)msg32;
+ (void)key32;
+ (void)algo16;
+ memcpy(nonce32, data, 32);
+ return (counter == 0);
+}
+
+static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+ /* Dummy nonce generator that has a fatal error on the first counter value. */
+ if (counter == 0) {
+ return 0;
+ }
+ return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
+}
+
+static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+ /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
+ if (counter < 3) {
+ memset(nonce32, counter==0 ? 0 : 255, 32);
+ if (counter == 2) {
+ nonce32[31]--;
+ }
+ return 1;
+ }
+ if (counter < 5) {
+ static const unsigned char order[] = {
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+ 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+ 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+ };
+ memcpy(nonce32, order, 32);
+ if (counter == 4) {
+ nonce32[31]++;
+ }
+ return 1;
+ }
+ /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
+ /* If someone does fine a case where it retries for secp256k1, we'd like to know. */
+ if (counter > 5) {
+ return 0;
+ }
+ return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
+}
+
+int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
+ static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
+ return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
+}
+
void test_ecdsa_end_to_end(void) {
+ unsigned char extra[32] = {0x00};
unsigned char privkey[32];
unsigned char message[32];
+ unsigned char privkey2[32];
+ secp256k1_ecdsa_signature signature[6];
+ secp256k1_scalar r, s;
+ unsigned char sig[74];
+ size_t siglen = 74;
+ unsigned char pubkeyc[65];
+ size_t pubkeyclen = 65;
+ secp256k1_pubkey pubkey;
+ secp256k1_pubkey pubkey_tmp;
+ unsigned char seckey[300];
+ size_t seckeylen = 300;
/* Generate a random key and message. */
{
- secp256k1_num_t msg, key;
- random_num_order_test(&msg);
- random_num_order_test(&key);
- secp256k1_num_get_bin(privkey, 32, &key);
- secp256k1_num_get_bin(message, 32, &msg);
+ secp256k1_scalar msg, key;
+ random_scalar_order_test(&msg);
+ random_scalar_order_test(&key);
+ secp256k1_scalar_get_b32(privkey, &key);
+ secp256k1_scalar_get_b32(message, &msg);
}
/* Construct and verify corresponding public key. */
- CHECK(secp256k1_ec_seckey_verify(privkey) == 1);
- unsigned char pubkey[65]; int pubkeylen = 65;
- CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, secp256k1_rand32() % 2) == 1);
- CHECK(secp256k1_ec_pubkey_verify(pubkey, pubkeylen));
+ CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+ /* Verify exporting and importing public key. */
+ CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
+ memset(&pubkey, 0, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
+
+ /* Verify negation changes the key and changes it back */
+ memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
+ CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
+ CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
+ CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
+ CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
/* Verify private key import and export. */
- unsigned char seckey[300]; int seckeylen = 300;
- CHECK(secp256k1_ec_privkey_export(privkey, seckey, &seckeylen, secp256k1_rand32() % 2) == 1);
- unsigned char privkey2[32];
- CHECK(secp256k1_ec_privkey_import(privkey2, seckey, seckeylen) == 1);
+ CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
+ CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
CHECK(memcmp(privkey, privkey2, 32) == 0);
/* Optionally tweak the keys using addition. */
- if (secp256k1_rand32() % 3 == 0) {
+ if (secp256k1_rand_int(3) == 0) {
+ int ret1;
+ int ret2;
unsigned char rnd[32];
+ secp256k1_pubkey pubkey2;
secp256k1_rand256_test(rnd);
- int ret1 = secp256k1_ec_privkey_tweak_add(privkey, rnd);
- int ret2 = secp256k1_ec_pubkey_tweak_add(pubkey, pubkeylen, rnd);
+ ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
+ ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
CHECK(ret1 == ret2);
- if (ret1 == 0) return;
- unsigned char pubkey2[65]; int pubkeylen2 = 65;
- CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
- CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
+ if (ret1 == 0) {
+ return;
+ }
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+ CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Optionally tweak the keys using multiplication. */
- if (secp256k1_rand32() % 3 == 0) {
+ if (secp256k1_rand_int(3) == 0) {
+ int ret1;
+ int ret2;
unsigned char rnd[32];
+ secp256k1_pubkey pubkey2;
secp256k1_rand256_test(rnd);
- int ret1 = secp256k1_ec_privkey_tweak_mul(privkey, rnd);
- int ret2 = secp256k1_ec_pubkey_tweak_mul(pubkey, pubkeylen, rnd);
+ ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
+ ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
CHECK(ret1 == ret2);
- if (ret1 == 0) return;
- unsigned char pubkey2[65]; int pubkeylen2 = 65;
- CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
- CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
+ if (ret1 == 0) {
+ return;
+ }
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+ CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Sign. */
- unsigned char signature[72]; int signaturelen = 72;
- while(1) {
- unsigned char rnd[32];
- secp256k1_rand256_test(rnd);
- if (secp256k1_ecdsa_sign(message, 32, signature, &signaturelen, privkey, rnd) == 1) {
- break;
- }
- }
+ CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
+ CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
+ CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
+ extra[31] = 1;
+ CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
+ extra[31] = 0;
+ extra[0] = 1;
+ CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
+ CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
+ CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
+ CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
+ CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
+ CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
+ CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
+ CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
/* Verify. */
- CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) == 1);
- /* Destroy signature and verify again. */
- signature[signaturelen - 1 - secp256k1_rand32() % 20] += 1 + (secp256k1_rand32() % 255);
- CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) != 1);
-
- /* Compact sign. */
- unsigned char csignature[64]; int recid = 0;
- while(1) {
- unsigned char rnd[32];
- secp256k1_rand256_test(rnd);
- if (secp256k1_ecdsa_sign_compact(message, 32, csignature, privkey, rnd, &recid) == 1) {
- break;
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
+ /* Test lower-S form, malleate, verify and fail, test again, malleate again */
+ CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
+ secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
+ secp256k1_scalar_negate(&s, &s);
+ secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
+ CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+ CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+ CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+ CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+ secp256k1_scalar_negate(&s, &s);
+ secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+ CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+ CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
+
+ /* Serialize/parse DER and verify again */
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+ memset(&signature[0], 0, sizeof(signature[0]));
+ CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
+ CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+ /* Serialize/destroy/parse DER and verify again. */
+ siglen = 74;
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+ sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
+ CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
+ secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
+}
+
+void test_random_pubkeys(void) {
+ secp256k1_ge elem;
+ secp256k1_ge elem2;
+ unsigned char in[65];
+ /* Generate some randomly sized pubkeys. */
+ size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
+ if (secp256k1_rand_bits(2) == 0) {
+ len = secp256k1_rand_bits(6);
+ }
+ if (len == 65) {
+ in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
+ } else {
+ in[0] = secp256k1_rand_bits(1) ? 2 : 3;
+ }
+ if (secp256k1_rand_bits(3) == 0) {
+ in[0] = secp256k1_rand_bits(8);
+ }
+ if (len > 1) {
+ secp256k1_rand256(&in[1]);
+ }
+ if (len > 33) {
+ secp256k1_rand256(&in[33]);
+ }
+ if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
+ unsigned char out[65];
+ unsigned char firstb;
+ int res;
+ size_t size = len;
+ firstb = in[0];
+ /* If the pubkey can be parsed, it should round-trip... */
+ CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
+ CHECK(size == len);
+ CHECK(memcmp(&in[1], &out[1], len-1) == 0);
+ /* ... except for the type of hybrid inputs. */
+ if ((in[0] != 6) && (in[0] != 7)) {
+ CHECK(in[0] == out[0]);
+ }
+ size = 65;
+ CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
+ CHECK(size == 65);
+ CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
+ ge_equals_ge(&elem,&elem2);
+ /* Check that the X9.62 hybrid type is checked. */
+ in[0] = secp256k1_rand_bits(1) ? 6 : 7;
+ res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
+ if (firstb == 2 || firstb == 3) {
+ if (in[0] == firstb + 4) {
+ CHECK(res);
+ } else {
+ CHECK(!res);
+ }
+ }
+ if (res) {
+ ge_equals_ge(&elem,&elem2);
+ CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
+ CHECK(memcmp(&in[1], &out[1], 64) == 0);
}
}
- /* Recover. */
- unsigned char recpubkey[65]; int recpubkeylen = 0;
- CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) == 1);
- CHECK(recpubkeylen == pubkeylen);
- CHECK(memcmp(pubkey, recpubkey, pubkeylen) == 0);
- /* Destroy signature and verify again. */
- csignature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
- CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) != 1 ||
- memcmp(pubkey, recpubkey, pubkeylen) != 0);
- CHECK(recpubkeylen == pubkeylen);
+}
+void run_random_pubkeys(void) {
+ int i;
+ for (i = 0; i < 10*count; i++) {
+ test_random_pubkeys();
+ }
}
void run_ecdsa_end_to_end(void) {
- for (int i=0; i<64*count; i++) {
+ int i;
+ for (i = 0; i < 64*count; i++) {
test_ecdsa_end_to_end();
}
}
+int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
+ static const unsigned char zeroes[32] = {0};
+#ifdef ENABLE_OPENSSL_TESTS
+ static const unsigned char max_scalar[32] = {
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+ 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+ 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
+ };
+#endif
+
+ int ret = 0;
+
+ secp256k1_ecdsa_signature sig_der;
+ unsigned char roundtrip_der[2048];
+ unsigned char compact_der[64];
+ size_t len_der = 2048;
+ int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
+
+ secp256k1_ecdsa_signature sig_der_lax;
+ unsigned char roundtrip_der_lax[2048];
+ unsigned char compact_der_lax[64];
+ size_t len_der_lax = 2048;
+ int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
+
+#ifdef ENABLE_OPENSSL_TESTS
+ ECDSA_SIG *sig_openssl;
+ const BIGNUM *r = NULL, *s = NULL;
+ const unsigned char *sigptr;
+ unsigned char roundtrip_openssl[2048];
+ int len_openssl = 2048;
+ int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
+#endif
+
+ parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
+ if (parsed_der) {
+ ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
+ valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
+ }
+ if (valid_der) {
+ ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
+ roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
+ }
+
+ parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
+ if (parsed_der_lax) {
+ ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
+ valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
+ }
+ if (valid_der_lax) {
+ ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
+ roundtrips_der_lax = (len_der_lax == siglen) && memcmp(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 |= (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0) << 14;
+ }
+ ret |= (roundtrips_der != roundtrips_der_lax) << 15;
+ if (parsed_der) {
+ ret |= (!parsed_der_lax) << 16;
+ }
+
+#ifdef ENABLE_OPENSSL_TESTS
+ sig_openssl = ECDSA_SIG_new();
+ sigptr = sig;
+ parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
+ if (parsed_openssl) {
+ ECDSA_SIG_get0(sig_openssl, &r, &s);
+ valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256;
+ if (valid_openssl) {
+ unsigned char tmp[32] = {0};
+ BN_bn2bin(r, tmp + 32 - BN_num_bytes(r));
+ valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+ }
+ if (valid_openssl) {
+ unsigned char tmp[32] = {0};
+ BN_bn2bin(s, tmp + 32 - BN_num_bytes(s));
+ valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+ }
+ }
+ len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
+ if (len_openssl <= 2048) {
+ unsigned char *ptr = roundtrip_openssl;
+ CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
+ roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
+ } else {
+ len_openssl = 0;
+ }
+ ECDSA_SIG_free(sig_openssl);
+
+ ret |= (parsed_der && !parsed_openssl) << 4;
+ ret |= (valid_der && !valid_openssl) << 5;
+ ret |= (roundtrips_openssl && !parsed_der) << 6;
+ ret |= (roundtrips_der != roundtrips_openssl) << 7;
+ if (roundtrips_openssl) {
+ ret |= (len_der != (size_t)len_openssl) << 8;
+ ret |= (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0) << 9;
+ }
+#endif
+ return ret;
+}
+
+static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
+ size_t i;
+ for (i = 0; i < ptrlen; i++) {
+ int shift = ptrlen - 1 - i;
+ if (shift >= 4) {
+ ptr[i] = 0;
+ } else {
+ ptr[i] = (val >> shift) & 0xFF;
+ }
+ }
+}
+
+static void damage_array(unsigned char *sig, size_t *len) {
+ int pos;
+ int action = secp256k1_rand_bits(3);
+ if (action < 1 && *len > 3) {
+ /* Delete a byte. */
+ pos = secp256k1_rand_int(*len);
+ memmove(sig + pos, sig + pos + 1, *len - pos - 1);
+ (*len)--;
+ return;
+ } else if (action < 2 && *len < 2048) {
+ /* Insert a byte. */
+ pos = secp256k1_rand_int(1 + *len);
+ memmove(sig + pos + 1, sig + pos, *len - pos);
+ sig[pos] = secp256k1_rand_bits(8);
+ (*len)++;
+ return;
+ } else if (action < 4) {
+ /* Modify a byte. */
+ sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
+ return;
+ } else { /* action < 8 */
+ /* Modify a bit. */
+ sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
+ return;
+ }
+}
+
+static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
+ int der;
+ int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
+ size_t tlen, elen, glen;
+ int indet;
+ int n;
+
+ *len = 0;
+ der = secp256k1_rand_bits(2) == 0;
+ *certainly_der = der;
+ *certainly_not_der = 0;
+ indet = der ? 0 : secp256k1_rand_int(10) == 0;
+
+ for (n = 0; n < 2; n++) {
+ /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
+ nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
+ /* The length of the number in bytes (the first byte of which will always be nonzero) */
+ nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
+ CHECK(nlen[n] <= 232);
+ /* The top bit of the number. */
+ nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
+ /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
+ nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
+ /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
+ nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
+ if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
+ *certainly_not_der = 1;
+ }
+ CHECK(nlen[n] + nzlen[n] <= 300);
+ /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
+ nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
+ if (!der) {
+ /* nlenlen[n] max 127 bytes */
+ int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+ nlenlen[n] += add;
+ if (add != 0) {
+ *certainly_not_der = 1;
+ }
+ }
+ CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
+ }
+
+ /* The total length of the data to go, so far */
+ tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
+ CHECK(tlen <= 856);
+
+ /* The length of the garbage inside the tuple. */
+ elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
+ if (elen != 0) {
+ *certainly_not_der = 1;
+ }
+ tlen += elen;
+ CHECK(tlen <= 980);
+
+ /* The length of the garbage after the end of the tuple. */
+ glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
+ if (glen != 0) {
+ *certainly_not_der = 1;
+ }
+ CHECK(tlen + glen <= 990);
+
+ /* Write the tuple header. */
+ sig[(*len)++] = 0x30;
+ if (indet) {
+ /* Indeterminate length */
+ sig[(*len)++] = 0x80;
+ *certainly_not_der = 1;
+ } else {
+ int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
+ if (!der) {
+ int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+ tlenlen += add;
+ if (add != 0) {
+ *certainly_not_der = 1;
+ }
+ }
+ if (tlenlen == 0) {
+ /* Short length notation */
+ sig[(*len)++] = tlen;
+ } else {
+ /* Long length notation */
+ sig[(*len)++] = 128 + tlenlen;
+ assign_big_endian(sig + *len, tlenlen, tlen);
+ *len += tlenlen;
+ }
+ tlen += tlenlen;
+ }
+ tlen += 2;
+ CHECK(tlen + glen <= 1119);
+
+ for (n = 0; n < 2; n++) {
+ /* Write the integer header. */
+ sig[(*len)++] = 0x02;
+ if (nlenlen[n] == 0) {
+ /* Short length notation */
+ sig[(*len)++] = nlen[n] + nzlen[n];
+ } else {
+ /* Long length notation. */
+ sig[(*len)++] = 128 + nlenlen[n];
+ assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
+ *len += nlenlen[n];
+ }
+ /* Write zero padding */
+ while (nzlen[n] > 0) {
+ sig[(*len)++] = 0x00;
+ nzlen[n]--;
+ }
+ if (nlen[n] == 32 && !nlow[n]) {
+ /* Special extra 16 0xFF bytes in "high" 32-byte numbers */
+ int i;
+ for (i = 0; i < 16; i++) {
+ sig[(*len)++] = 0xFF;
+ }
+ nlen[n] -= 16;
+ }
+ /* Write first byte of number */
+ if (nlen[n] > 0) {
+ sig[(*len)++] = nhbyte[n];
+ nlen[n]--;
+ }
+ /* Generate remaining random bytes of number */
+ secp256k1_rand_bytes_test(sig + *len, nlen[n]);
+ *len += nlen[n];
+ nlen[n] = 0;
+ }
+
+ /* Generate random garbage inside tuple. */
+ secp256k1_rand_bytes_test(sig + *len, elen);
+ *len += elen;
+
+ /* Generate end-of-contents bytes. */
+ if (indet) {
+ sig[(*len)++] = 0;
+ sig[(*len)++] = 0;
+ tlen += 2;
+ }
+ CHECK(tlen + glen <= 1121);
+
+ /* Generate random garbage outside tuple. */
+ secp256k1_rand_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) {
- const unsigned char msg32[32] = {
- 'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
- 'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
- 'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
- 's', 's', 'a', 'g', 'e', '.', '.', '.'
- };
- const unsigned char sig64[64] = {
- /* Generated by signing the above message with nonce 'This is the nonce we will use...'
- * and secret key 0 (which is not valid), resulting in recid 0. */
- 0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
- 0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
- 0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
- 0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
- 0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
- 0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
- 0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
- 0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
- };
- unsigned char pubkey[65];
- int pubkeylen = 65;
- CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 0));
- CHECK(secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 1));
- CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 2));
- CHECK(!secp256k1_ecdsa_recover_compact(msg32, 32, sig64, pubkey, &pubkeylen, 0, 3));
-
- /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
- const unsigned char sigb64[64] = {
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
- };
- unsigned char pubkeyb[33];
- int pubkeyblen = 33;
- for (int recid = 0; recid < 4; recid++) {
- // (4,4) encoded in DER.
- unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
- // (order + r,4) encoded in DER.
- unsigned char sigbderlong[40] = {
- 0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
- 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
- 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
- 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
- 0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
+ int t;
+ secp256k1_ecdsa_signature sig;
+
+ /* Test the case where ECDSA recomputes a point that is infinity. */
+ {
+ secp256k1_gej keyj;
+ secp256k1_ge key;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 1);
+ secp256k1_scalar_negate(&ss, &ss);
+ secp256k1_scalar_inverse(&ss, &ss);
+ secp256k1_scalar_set_int(&sr, 1);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
+ secp256k1_ge_set_gej(&key, &keyj);
+ msg = ss;
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ }
+
+ /* Verify signature with r of zero fails. */
+ {
+ const unsigned char pubkey_mods_zero[33] = {
+ 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+ 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+ 0x41
+ };
+ secp256k1_ge key;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 1);
+ secp256k1_scalar_set_int(&msg, 0);
+ secp256k1_scalar_set_int(&sr, 0);
+ CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ }
+
+ /* Verify signature with s of zero fails. */
+ {
+ const unsigned char pubkey[33] = {
+ 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x01
+ };
+ secp256k1_ge key;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 0);
+ secp256k1_scalar_set_int(&msg, 0);
+ secp256k1_scalar_set_int(&sr, 1);
+ CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ }
+
+ /* Verify signature with message 0 passes. */
+ {
+ const unsigned char pubkey[33] = {
+ 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x02
+ };
+ const unsigned char pubkey2[33] = {
+ 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+ 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+ 0x43
+ };
+ secp256k1_ge key;
+ secp256k1_ge key2;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 2);
+ secp256k1_scalar_set_int(&msg, 0);
+ secp256k1_scalar_set_int(&sr, 2);
+ CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+ CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+ secp256k1_scalar_negate(&ss, &ss);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+ secp256k1_scalar_set_int(&ss, 1);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+ }
+
+ /* Verify signature with message 1 passes. */
+ {
+ const unsigned char pubkey[33] = {
+ 0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
+ 0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
+ 0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
+ 0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
+ 0x25
+ };
+ const unsigned char pubkey2[33] = {
+ 0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
+ 0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
+ 0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
+ 0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
+ 0x62
+ };
+ const unsigned char csr[32] = {
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+ 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
+ };
+ secp256k1_ge key;
+ secp256k1_ge key2;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 1);
+ secp256k1_scalar_set_int(&msg, 1);
+ secp256k1_scalar_set_b32(&sr, csr, NULL);
+ CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+ CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+ secp256k1_scalar_negate(&ss, &ss);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+ secp256k1_scalar_set_int(&ss, 2);
+ secp256k1_scalar_inverse_var(&ss, &ss);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
+ }
+
+ /* Verify signature with message -1 passes. */
+ {
+ const unsigned char pubkey[33] = {
+ 0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
+ 0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
+ 0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
+ 0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
+ 0xf1
+ };
+ const unsigned char csr[32] = {
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+ 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
+ };
+ secp256k1_ge key;
+ secp256k1_scalar msg;
+ secp256k1_scalar sr, ss;
+ secp256k1_scalar_set_int(&ss, 1);
+ secp256k1_scalar_set_int(&msg, 1);
+ secp256k1_scalar_negate(&msg, &msg);
+ secp256k1_scalar_set_b32(&sr, csr, NULL);
+ CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ secp256k1_scalar_negate(&ss, &ss);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+ secp256k1_scalar_set_int(&ss, 3);
+ secp256k1_scalar_inverse_var(&ss, &ss);
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+ }
+
+ /* Signature where s would be zero. */
+ {
+ secp256k1_pubkey pubkey;
+ size_t siglen;
+ int32_t ecount;
+ unsigned char signature[72];
+ static const unsigned char nonce[32] = {
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ };
+ static const unsigned char nonce2[32] = {
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+ 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+ 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
};
- CHECK(secp256k1_ecdsa_recover_compact(msg32, 32, sigb64, pubkeyb, &pubkeyblen, 1, recid));
- CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 1);
- for (int recid2 = 0; recid2 < 4; recid2++) {
- unsigned char pubkey2b[33];
- int pubkey2blen = 33;
- CHECK(secp256k1_ecdsa_recover_compact(msg32, 32, sigb64, pubkey2b, &pubkey2blen, 1, recid2));
- // Verifying with (order + r,4) should always fail.
- CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbderlong, sizeof(sigbderlong), pubkey2b, pubkey2blen) != 1);
+ const unsigned char key[32] = {
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+ };
+ unsigned char msg[32] = {
+ 0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
+ 0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
+ 0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
+ 0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
+ };
+ ecount = 0;
+ secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
+ msg[31] = 0xaa;
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
+ CHECK(ecount == 0);
+ CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
+ CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
+ CHECK(ecount == 4);
+ CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
+ CHECK(ecount == 5);
+ CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
+ CHECK(ecount == 6);
+ CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
+ CHECK(ecount == 6);
+ CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+ CHECK(ecount == 7);
+ /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
+ CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
+ CHECK(ecount == 8);
+ siglen = 72;
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
+ CHECK(ecount == 9);
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
+ CHECK(ecount == 10);
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
+ CHECK(ecount == 11);
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
+ CHECK(ecount == 11);
+ CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
+ CHECK(ecount == 12);
+ CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
+ CHECK(ecount == 13);
+ CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
+ CHECK(ecount == 13);
+ siglen = 10;
+ /* Too little room for a signature does not fail via ARGCHECK. */
+ CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
+ CHECK(ecount == 13);
+ ecount = 0;
+ CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
+ CHECK(ecount == 1);
+ CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
+ CHECK(ecount == 2);
+ CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
+ CHECK(ecount == 3);
+ CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
+ CHECK(ecount == 4);
+ CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
+ CHECK(ecount == 5);
+ CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
+ CHECK(ecount == 5);
+ memset(signature, 255, 64);
+ CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
+ CHECK(ecount == 5);
+ secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+ }
+
+ /* Nonce function corner cases. */
+ for (t = 0; t < 2; t++) {
+ static const unsigned char zero[32] = {0x00};
+ int i;
+ unsigned char key[32];
+ unsigned char msg[32];
+ secp256k1_ecdsa_signature sig2;
+ secp256k1_scalar sr[512], ss;
+ const unsigned char *extra;
+ extra = t == 0 ? NULL : zero;
+ memset(msg, 0, 32);
+ msg[31] = 1;
+ /* High key results in signature failure. */
+ memset(key, 0xFF, 32);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+ CHECK(is_empty_signature(&sig));
+ /* Zero key results in signature failure. */
+ memset(key, 0, 32);
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+ CHECK(is_empty_signature(&sig));
+ /* Nonce function failure results in signature failure. */
+ key[31] = 1;
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
+ CHECK(is_empty_signature(&sig));
+ /* The retry loop successfully makes its way to the first good value. */
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
+ CHECK(!is_empty_signature(&sig));
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
+ CHECK(!is_empty_signature(&sig2));
+ CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+ /* The default nonce function is deterministic. */
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+ CHECK(!is_empty_signature(&sig2));
+ CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+ /* The default nonce function changes output with different messages. */
+ for(i = 0; i < 256; i++) {
+ int j;
+ msg[0] = i;
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+ CHECK(!is_empty_signature(&sig2));
+ secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
+ for (j = 0; j < i; j++) {
+ CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
+ }
+ }
+ msg[0] = 0;
+ msg[31] = 2;
+ /* The default nonce function changes output with different keys. */
+ for(i = 256; i < 512; i++) {
+ int j;
+ key[0] = i - 256;
+ CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+ CHECK(!is_empty_signature(&sig2));
+ secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
+ for (j = 0; j < i; j++) {
+ CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
+ }
}
- /* Damage signature. */
- sigbder[7]++;
- CHECK(secp256k1_ecdsa_verify(msg32, 32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 0);
+ 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(memcmp(nonce, nonce2, 32) != 0);
+ CHECK(memcmp(nonce, nonce3, 32) != 0);
+ CHECK(memcmp(nonce, nonce4, 32) != 0);
+ CHECK(memcmp(nonce2, nonce3, 32) != 0);
+ CHECK(memcmp(nonce2, nonce4, 32) != 0);
+ CHECK(memcmp(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));
}
}
}
#ifdef ENABLE_OPENSSL_TESTS
-EC_KEY *get_openssl_key(const secp256k1_scalar_t *key) {
+EC_KEY *get_openssl_key(const unsigned char *key32) {
unsigned char privkey[300];
- int privkeylen;
- int compr = secp256k1_rand32() & 1;
+ size_t privkeylen;
const unsigned char* pbegin = privkey;
+ int compr = secp256k1_rand_bits(1);
EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
- CHECK(secp256k1_eckey_privkey_serialize(privkey, &privkeylen, key, compr));
+ CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
CHECK(EC_KEY_check_key(ec_key));
return ec_key;
}
void test_ecdsa_openssl(void) {
- secp256k1_scalar_t key, msg;
+ secp256k1_gej qj;
+ secp256k1_ge q;
+ secp256k1_scalar sigr, sigs;
+ secp256k1_scalar one;
+ secp256k1_scalar msg2;
+ secp256k1_scalar key, msg;
+ EC_KEY *ec_key;
+ unsigned int sigsize = 80;
+ size_t secp_sigsize = 80;
unsigned char message[32];
+ unsigned char signature[80];
+ unsigned char key32[32];
secp256k1_rand256_test(message);
secp256k1_scalar_set_b32(&msg, message, NULL);
random_scalar_order_test(&key);
- secp256k1_gej_t qj;
- secp256k1_ecmult_gen(&qj, &key);
- secp256k1_ge_t q;
+ secp256k1_scalar_get_b32(key32, &key);
+ secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
secp256k1_ge_set_gej(&q, &qj);
- EC_KEY *ec_key = get_openssl_key(&key);
- CHECK(ec_key);
- unsigned char signature[80];
- unsigned int sigsize = 80;
+ ec_key = get_openssl_key(key32);
+ CHECK(ec_key != NULL);
CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
- secp256k1_ecdsa_sig_t sig;
- CHECK(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize));
- CHECK(secp256k1_ecdsa_sig_verify(&sig, &q, &msg));
- secp256k1_scalar_t one;
+ CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
+ CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
secp256k1_scalar_set_int(&one, 1);
- secp256k1_scalar_t msg2;
secp256k1_scalar_add(&msg2, &msg, &one);
- CHECK(!secp256k1_ecdsa_sig_verify(&sig, &q, &msg2));
+ CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
- random_sign(&sig, &key, &msg, NULL);
- int secp_sigsize = 80;
- CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sig));
+ random_sign(&sigr, &sigs, &key, &msg, NULL);
+ CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
EC_KEY_free(ec_key);
}
void run_ecdsa_openssl(void) {
- for (int i=0; i<10*count; i++) {
+ int i;
+ for (i = 0; i < 10*count; i++) {
test_ecdsa_openssl();
}
}
#endif
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/tests_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/tests_impl.h"
+#endif
+
int main(int argc, char **argv) {
+ unsigned char seed16[16] = {0};
+ unsigned char run32[32] = {0};
/* find iteration count */
if (argc > 1) {
count = strtol(argv[1], NULL, 0);
}
/* find random seed */
- uint64_t seed;
if (argc > 2) {
- seed = strtoull(argv[2], NULL, 0);
+ int pos = 0;
+ const char* ch = argv[2];
+ while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
+ unsigned short sh;
+ if (sscanf(ch, "%2hx", &sh)) {
+ seed16[pos] = sh;
+ } else {
+ break;
+ }
+ ch += 2;
+ pos++;
+ }
} else {
FILE *frand = fopen("/dev/urandom", "r");
- if (!frand || !fread(&seed, sizeof(seed), 1, frand)) {
- seed = time(NULL) * 1337;
+ if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) {
+ uint64_t t = time(NULL) * (uint64_t)1337;
+ fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n");
+ seed16[0] ^= t;
+ seed16[1] ^= t >> 8;
+ seed16[2] ^= t >> 16;
+ seed16[3] ^= t >> 24;
+ seed16[4] ^= t >> 32;
+ seed16[5] ^= t >> 40;
+ seed16[6] ^= t >> 48;
+ seed16[7] ^= t >> 56;
+ }
+ if (frand) {
+ fclose(frand);
}
- fclose(frand);
}
- secp256k1_rand_seed(seed);
+ secp256k1_rand_seed(seed16);
printf("test count = %i\n", count);
- printf("random seed = %llu\n", (unsigned long long)seed);
+ printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
/* initialize */
- secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY);
+ run_context_tests(0);
+ run_context_tests(1);
+ run_scratch_tests();
+ ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+ if (secp256k1_rand_bits(1)) {
+ secp256k1_rand256(run32);
+ CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
+ }
+
+ run_rand_bits();
+ run_rand_int();
+ run_sha256_tests();
+ run_hmac_sha256_tests();
+ run_rfc6979_hmac_sha256_tests();
+
+#ifndef USE_NUM_NONE
/* num tests */
run_num_smalltests();
+#endif
/* scalar tests */
run_scalar_tests();
/* field tests */
run_field_inv();
run_field_inv_var();
- run_field_inv_all();
run_field_inv_all_var();
+ run_field_misc();
+ run_field_convert();
run_sqr();
run_sqrt();
/* group tests */
run_ge();
+ run_group_decompress();
/* ecmult tests */
run_wnaf();
run_point_times_order();
run_ecmult_chain();
+ run_ecmult_constants();
+ run_ecmult_gen_blind();
+ run_ecmult_const_tests();
+ run_ecmult_multi_tests();
+ run_ec_combine();
+
+ /* endomorphism tests */
+#ifdef USE_ENDOMORPHISM
+ run_endomorphism_tests();
+#endif
+
+ /* EC point parser test */
+ run_ec_pubkey_parse_test();
+
+ /* EC key edge cases */
+ run_eckey_edge_case_test();
+
+#ifdef ENABLE_MODULE_ECDH
+ /* ecdh tests */
+ run_ecdh_tests();
+#endif
/* ecdsa tests */
+ run_random_pubkeys();
+ run_ecdsa_der_parse();
run_ecdsa_sign_verify();
run_ecdsa_end_to_end();
run_ecdsa_edge_cases();
run_ecdsa_openssl();
#endif
- printf("random run = %llu\n", (unsigned long long)secp256k1_rand32() + ((unsigned long long)secp256k1_rand32() << 32));
+#ifdef ENABLE_MODULE_RECOVERY
+ /* ECDSA pubkey recovery tests */
+ run_recovery_tests();
+#endif
+
+ secp256k1_rand256(run32);
+ printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
/* shutdown */
- secp256k1_stop();
+ secp256k1_context_destroy(ctx);
+
+ printf("no problems found\n");
return 0;
}
projects / secp256k1.git / blobdiff