secp256k1

src/tests.c

/***********************************************************************
* Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#ifdef USE_EXTERNAL_DEFAULT_CALLBACKS
#pragma message("Ignoring USE_EXTERNAL_CALLBACKS in tests.")
#undef USE_EXTERNAL_DEFAULT_CALLBACKS
#endif
#if defined(VERIFY) && defined(COVERAGE)
#pragma message("Defining VERIFY for tests being built for coverage analysis support is meaningless.")
#endif
#include "secp256k1.c"
#include "../include/secp256k1.h"
#include "../include/secp256k1_preallocated.h"
#include "testrand_impl.h"
#include "checkmem.h"
#include "testutil.h"
#include "util.h"
#include "unit_test.h"
#include "unit_test.c"
#include "../contrib/lax_der_parsing.c"
#include "../contrib/lax_der_privatekey_parsing.c"
#include "modinv32_impl.h"
#ifdef SECP256K1_WIDEMUL_INT128
#include "modinv64_impl.h"
#include "int128_impl.h"
#endif
#define CONDITIONAL_TEST(cnt, nam) if (COUNT < (cnt)) { printf("Skipping %s (iteration count too low)\n", nam); } else
static secp256k1_context *CTX = NULL;
static secp256k1_context *STATIC_CTX = NULL;
static int all_bytes_equal(const void* s, unsigned char value, size_t n) {
const unsigned char *p = s;
size_t i;
for (i = 0; i < n; i++) {
if (p[i] != value) {
return 0;
}
}
return 1;
}
#define CHECK_COUNTING_CALLBACK_VOID(ctx, expr_or_stmt, callback, callback_setter) do { \
expanded from macro 'CHECK_COUNTING_CALLBACK_VOID'
int32_t _calls_to_callback = 0; \
secp256k1_callback _saved_callback = ctx->callback; \
callback_setter(ctx, counting_callback_fn, &_calls_to_callback); \
{ expr_or_stmt; } \
expanded from macro 'CHECK_COUNTING_CALLBACK_VOID'
ctx->callback = _saved_callback; \
expanded from macro 'CHECK_COUNTING_CALLBACK_VOID'
CHECK(_calls_to_callback == 1); \
expanded from macro 'CHECK_COUNTING_CALLBACK_VOID'
} while(0);
/* CHECK that expr_or_stmt calls the error or illegal callback of ctx exactly once
*
* Useful for checking functions that return void (e.g., API functions that use ARG_CHECK_VOID) */
#define CHECK_ERROR_VOID(ctx, expr_or_stmt) \
CHECK_COUNTING_CALLBACK_VOID(ctx, expr_or_stmt, error_callback, secp256k1_context_set_error_callback)
expanded from macro 'CHECK_ERROR_VOID'
expanded from macro 'CHECK_ERROR_VOID'
#define CHECK_ILLEGAL_VOID(ctx, expr_or_stmt) \
CHECK_COUNTING_CALLBACK_VOID(ctx, expr_or_stmt, illegal_callback, secp256k1_context_set_illegal_callback)
expanded from macro 'CHECK_ILLEGAL_VOID'
expanded from macro 'CHECK_ILLEGAL_VOID'
/* CHECK that
* - expr calls the illegal callback of ctx exactly once and,
* - expr == 0 (or equivalently, expr == NULL)
*
* Useful for checking functions that return an integer or a pointer. */
#define CHECK_ILLEGAL(ctx, expr) CHECK_ILLEGAL_VOID(ctx, CHECK((expr) == 0))
expanded from macro 'CHECK_ILLEGAL'
expanded from macro 'CHECK_ILLEGAL'
#define CHECK_ERROR(ctx, expr) CHECK_ERROR_VOID(ctx, CHECK((expr) == 0))
expanded from macro 'CHECK_ERROR'
expanded from macro 'CHECK_ERROR'
static void counting_callback_fn(const char* str, void* data) {
/* Dummy callback function that just counts. */
int32_t *p;
(void)str;
p = data;
CHECK(*p != INT32_MAX);
(*p)++;
}
static void run_xoshiro256pp_tests(void) {
{
size_t i;
/* Sanity check that we run before the actual seeding. */
for (i = 0; i < sizeof(secp256k1_test_state)/sizeof(secp256k1_test_state[0]); i++) {
CHECK(secp256k1_test_state[i] == 0);
}
}
{
int i;
unsigned char buf32[32];
unsigned char seed16[16] = {
'C', 'H', 'I', 'C', 'K', 'E', 'N', '!',
'C', 'H', 'I', 'C', 'K', 'E', 'N', '!',
};
unsigned char buf32_expected[32] = {
0xAF, 0xCC, 0xA9, 0x16, 0xB5, 0x6C, 0xE3, 0xF0,
0x44, 0x3F, 0x45, 0xE0, 0x47, 0xA5, 0x08, 0x36,
0x4C, 0xCC, 0xC1, 0x18, 0xB2, 0xD8, 0x8F, 0xEF,
0x43, 0x26, 0x15, 0x57, 0x37, 0x00, 0xEF, 0x30,
};
testrand_seed(seed16);
for (i = 0; i < 17; i++) {
testrand256(buf32);
}
CHECK(secp256k1_memcmp_var(buf32, buf32_expected, sizeof(buf32)) == 0);
}
}
static void run_selftest_tests(void) {
/* Test public API */
secp256k1_selftest();
}
static int ecmult_gen_context_eq(const secp256k1_ecmult_gen_context *a, const secp256k1_ecmult_gen_context *b) {
return a->built == b->built
&& secp256k1_scalar_eq(&a->scalar_offset, &b->scalar_offset)
&& secp256k1_ge_eq_var(&a->ge_offset, &b->ge_offset)
&& secp256k1_fe_equal(&a->proj_blind, &b->proj_blind);
}
static int context_eq(const secp256k1_context *a, const secp256k1_context *b) {
return a->declassify == b->declassify
&& ecmult_gen_context_eq(&a->ecmult_gen_ctx, &b->ecmult_gen_ctx)
&& a->illegal_callback.fn == b->illegal_callback.fn
&& a->illegal_callback.data == b->illegal_callback.data
&& a->error_callback.fn == b->error_callback.fn
&& a->error_callback.data == b->error_callback.data;
}
static void run_deprecated_context_flags_test(void) {
/* Check that a context created with any of the flags in the flags array is
* identical to the NONE context. */
unsigned int flags[] = { SECP256K1_CONTEXT_SIGN,
SECP256K1_CONTEXT_VERIFY,
SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY };
secp256k1_context *none_ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
int i;
for (i = 0; i < (int)(sizeof(flags)/sizeof(flags[0])); i++) {
secp256k1_context *tmp_ctx;
CHECK(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE) == secp256k1_context_preallocated_size(flags[i]));
tmp_ctx = secp256k1_context_create(flags[i]);
CHECK(context_eq(none_ctx, tmp_ctx));
secp256k1_context_destroy(tmp_ctx);
}
secp256k1_context_destroy(none_ctx);
}
static void run_ec_illegal_argument_tests(void) {
secp256k1_pubkey pubkey;
secp256k1_pubkey zero_pubkey;
secp256k1_ecdsa_signature sig;
unsigned char ctmp[32];
/* Setup */
memset(ctmp, 1, 32);
memset(&zero_pubkey, 0, sizeof(zero_pubkey));
/* Verify context-type checking illegal-argument errors. */
CHECK_ILLEGAL(STATIC_CTX, secp256k1_ec_pubkey_create(STATIC_CTX, &pubkey, ctmp));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(STATIC_CTX, secp256k1_ecdsa_sign(STATIC_CTX, &sig, ctmp, ctmp, NULL, NULL));
SECP256K1_CHECKMEM_UNDEFINE(&sig, sizeof(sig));
CHECK(secp256k1_ecdsa_sign(CTX, &sig, ctmp, ctmp, NULL, NULL) == 1);
SECP256K1_CHECKMEM_CHECK(&sig, sizeof(sig));
CHECK(secp256k1_ecdsa_verify(CTX, &sig, ctmp, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(STATIC_CTX, &sig, ctmp, &pubkey) == 1);
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp) == 1);
CHECK(secp256k1_ec_pubkey_tweak_add(STATIC_CTX, &pubkey, ctmp) == 1);
CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, ctmp) == 1);
CHECK(secp256k1_ec_pubkey_negate(STATIC_CTX, &pubkey) == 1);
CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey) == 1);
CHECK_ILLEGAL(STATIC_CTX, secp256k1_ec_pubkey_negate(STATIC_CTX, &zero_pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_negate(CTX, NULL));
CHECK(secp256k1_ec_pubkey_tweak_mul(STATIC_CTX, &pubkey, ctmp) == 1);
}
static void run_static_context_tests(int use_prealloc) {
/* Check that deprecated secp256k1_context_no_precomp is an alias to secp256k1_context_static. */
CHECK(secp256k1_context_no_precomp == secp256k1_context_static);
Assuming the condition is false
Loop condition is false. Exiting loop
Taking false branch
{
unsigned char seed[32] = {0x17};
/* Randomizing secp256k1_context_static is not supported. */
CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_randomize(STATIC_CTX, seed));
Loop condition is false. Exiting loop
Taking false branch
CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_randomize(STATIC_CTX, NULL));
Loop condition is false. Exiting loop
Taking false branch
/* Destroying or cloning secp256k1_context_static is not supported. */
if (use_prealloc) {
Taking false branch
Assuming 'use_prealloc' is 0
CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_preallocated_clone_size(STATIC_CTX));
{
secp256k1_context *my_static_ctx = malloc(sizeof(*STATIC_CTX));
CHECK(my_static_ctx != NULL);
memset(my_static_ctx, 0x2a, sizeof(*my_static_ctx));
CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_preallocated_clone(STATIC_CTX, my_static_ctx));
CHECK(all_bytes_equal(my_static_ctx, 0x2a, sizeof(*my_static_ctx)));
free(my_static_ctx);
}
CHECK_ILLEGAL_VOID(STATIC_CTX, secp256k1_context_preallocated_destroy(STATIC_CTX));
} else {
CHECK_ILLEGAL(STATIC_CTX, secp256k1_context_clone(STATIC_CTX));
Loop condition is false. Exiting loop
Taking false branch
CHECK_ILLEGAL_VOID(STATIC_CTX, secp256k1_context_destroy(STATIC_CTX));
Use of memory after it is freed
Use of memory after it is freed
Calling 'secp256k1_context_destroy'
Returning; memory was released via 1st parameter
}
}
{
/* Verify that setting and resetting illegal callback works */
int32_t dummy = 0;
secp256k1_context_set_illegal_callback(STATIC_CTX, counting_callback_fn, &dummy);
CHECK(STATIC_CTX->illegal_callback.fn == counting_callback_fn);
CHECK(STATIC_CTX->illegal_callback.data == &dummy);
secp256k1_context_set_illegal_callback(STATIC_CTX, NULL, NULL);
CHECK(STATIC_CTX->illegal_callback.fn == secp256k1_default_illegal_callback_fn);
CHECK(STATIC_CTX->illegal_callback.data == NULL);
}
}
static void run_all_static_context_tests(void)
{
run_static_context_tests(0);
run_static_context_tests(1);
}
static void run_proper_context_tests(int use_prealloc) {
int32_t dummy = 0;
secp256k1_context *my_ctx, *my_ctx_fresh;
void *my_ctx_prealloc = NULL;
unsigned char seed[32] = {0x17};
secp256k1_gej pubj;
secp256k1_ge pub;
secp256k1_scalar msg, key, nonce;
secp256k1_scalar sigr, sigs;
/* Fresh reference context for comparison */
my_ctx_fresh = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
if (use_prealloc) {
my_ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
CHECK(my_ctx_prealloc != NULL);
my_ctx = secp256k1_context_preallocated_create(my_ctx_prealloc, SECP256K1_CONTEXT_NONE);
} else {
my_ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
}
/* Randomize and reset randomization */
CHECK(context_eq(my_ctx, my_ctx_fresh));
CHECK(secp256k1_context_randomize(my_ctx, seed) == 1);
CHECK(!context_eq(my_ctx, my_ctx_fresh));
CHECK(secp256k1_context_randomize(my_ctx, NULL) == 1);
CHECK(context_eq(my_ctx, my_ctx_fresh));
/* set error callback (to a function that still aborts in case malloc() fails in secp256k1_context_clone() below) */
secp256k1_context_set_error_callback(my_ctx, secp256k1_default_illegal_callback_fn, NULL);
CHECK(my_ctx->error_callback.fn != secp256k1_default_error_callback_fn);
CHECK(my_ctx->error_callback.fn == secp256k1_default_illegal_callback_fn);
/* check if sizes for cloning are consistent */
CHECK(secp256k1_context_preallocated_clone_size(my_ctx) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
/*** 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 = my_ctx;
my_ctx = secp256k1_context_clone(my_ctx);
CHECK(context_eq(ctx_tmp, my_ctx));
secp256k1_context_preallocated_destroy(ctx_tmp);
free(my_ctx_prealloc);
my_ctx_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE));
CHECK(my_ctx_prealloc != NULL);
ctx_tmp = my_ctx;
my_ctx = secp256k1_context_preallocated_clone(my_ctx, my_ctx_prealloc);
CHECK(context_eq(ctx_tmp, my_ctx));
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 = my_ctx;
my_ctx = secp256k1_context_preallocated_clone(my_ctx, prealloc_tmp);
CHECK(context_eq(ctx_tmp, my_ctx));
secp256k1_context_destroy(ctx_tmp);
ctx_tmp = my_ctx;
my_ctx = secp256k1_context_clone(my_ctx);
CHECK(context_eq(ctx_tmp, my_ctx));
secp256k1_context_preallocated_destroy(ctx_tmp);
free(prealloc_tmp);
}
}
/* Verify that the error callback makes it across the clone. */
CHECK(my_ctx->error_callback.fn != secp256k1_default_error_callback_fn);
CHECK(my_ctx->error_callback.fn == secp256k1_default_illegal_callback_fn);
/* And that it resets back to default. */
secp256k1_context_set_error_callback(my_ctx, NULL, NULL);
CHECK(my_ctx->error_callback.fn == secp256k1_default_error_callback_fn);
CHECK(context_eq(my_ctx, my_ctx_fresh));
/* Verify that setting and resetting illegal callback works */
secp256k1_context_set_illegal_callback(my_ctx, counting_callback_fn, &dummy);
CHECK(my_ctx->illegal_callback.fn == counting_callback_fn);
CHECK(my_ctx->illegal_callback.data == &dummy);
secp256k1_context_set_illegal_callback(my_ctx, NULL, NULL);
CHECK(my_ctx->illegal_callback.fn == secp256k1_default_illegal_callback_fn);
CHECK(my_ctx->illegal_callback.data == NULL);
CHECK(context_eq(my_ctx, my_ctx_fresh));
/*** attempt to use them ***/
testutil_random_scalar_order_test(&msg);
testutil_random_scalar_order_test(&key);
secp256k1_ecmult_gen(&my_ctx->ecmult_gen_ctx, &pubj, &key);
secp256k1_ge_set_gej(&pub, &pubj);
/* obtain a working nonce */
do {
testutil_random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(&my_ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try signing */
CHECK(secp256k1_ecdsa_sig_sign(&my_ctx->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
/* try verifying */
CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
/* cleanup */
if (use_prealloc) {
secp256k1_context_preallocated_destroy(my_ctx);
free(my_ctx_prealloc);
} else {
secp256k1_context_destroy(my_ctx);
}
secp256k1_context_destroy(my_ctx_fresh);
/* Defined as no-op. */
secp256k1_context_destroy(NULL);
secp256k1_context_preallocated_destroy(NULL);
}
static void run_all_proper_context_tests(void)
{
run_proper_context_tests(0);
run_proper_context_tests(1);
}
static void run_scratch_tests(void) {
const size_t adj_alloc = ((500 + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT;
size_t checkpoint;
size_t checkpoint_2;
secp256k1_scratch_space *scratch;
secp256k1_scratch_space local_scratch;
/* Test public API */
scratch = secp256k1_scratch_space_create(CTX, 1000);
CHECK(scratch != NULL);
Loop condition is false. Exiting loop
Taking false branch
'scratch' is not equal to null
/* Test internal API */
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000);
Loop condition is false. Exiting loop
Taking false branch
Assuming the condition is true
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1));
Loop condition is false. Exiting loop
Taking false branch
CHECK(scratch->alloc_size == 0);
Loop condition is false. Exiting loop
Taking false branch
Assuming field 'alloc_size' is equal to 0
CHECK(scratch->alloc_size % ALIGNMENT == 0);
Loop condition is false. Exiting loop
Taking false branch
/* Allocating 500 bytes succeeds */
checkpoint = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch);
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500) != NULL);
Loop condition is false. Exiting loop
Taking false branch
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000 - adj_alloc);
Loop condition is false. Exiting loop
Taking false branch
Assuming the condition is true
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
Loop condition is false. Exiting loop
Taking false branch
CHECK(scratch->alloc_size != 0);
Loop condition is false. Exiting loop
Taking false branch
Assuming field 'alloc_size' is not equal to 0
CHECK(scratch->alloc_size % ALIGNMENT == 0);
Loop condition is false. Exiting loop
Taking false branch
Assuming the condition is true
/* Allocating another 501 bytes fails */
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 501) == NULL);
Loop condition is false. Exiting loop
Taking false branch
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000 - adj_alloc);
Loop condition is false. Exiting loop
Taking false branch
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1));
Loop condition is false. Exiting loop
Taking false branch
CHECK(scratch->alloc_size != 0);
Loop condition is false. Exiting loop
Taking false branch
Field 'alloc_size' is not equal to 0
CHECK(scratch->alloc_size % ALIGNMENT == 0);
Loop condition is false. Exiting loop
Taking false branch
/* ...but it succeeds once we apply the checkpoint to undo it */
secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint);
CHECK(scratch->alloc_size == 0);
Loop condition is false. Exiting loop
Taking false branch
CHECK(secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0) == 1000);
Loop condition is false. Exiting loop
Taking false branch
Assuming the condition is true
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500) != NULL);
Loop condition is false. Exiting loop
Taking false branch
CHECK(scratch->alloc_size != 0);
Loop condition is false. Exiting loop
Taking false branch
/* try to apply a bad checkpoint */
checkpoint_2 = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch);
secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint);
CHECK_ERROR_VOID(CTX, secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint_2)); /* checkpoint_2 is after checkpoint */
Loop condition is false. Exiting loop
Taking false branch
CHECK_ERROR_VOID(CTX, secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, (size_t) -1)); /* this is just wildly invalid */
Loop condition is false. Exiting loop
Taking false branch
/* try to use badly initialized scratch space */
secp256k1_scratch_space_destroy(CTX, scratch);
memset(&local_scratch, 0, sizeof(local_scratch));
scratch = &local_scratch;
CHECK_ERROR(CTX, secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, 0));
Loop condition is false. Exiting loop
Taking false branch
CHECK_ERROR(CTX, secp256k1_scratch_alloc(&CTX->error_callback, scratch, 500));
Loop condition is false. Exiting loop
Taking false branch
CHECK_ERROR_VOID(CTX, secp256k1_scratch_space_destroy(CTX, scratch));
Calling 'secp256k1_scratch_space_destroy'
/* Test that large integers do not wrap around in a bad way */
scratch = secp256k1_scratch_space_create(CTX, 1000);
/* Try max allocation with a large number of objects. Only makes sense if
* ALIGNMENT is greater than 1 because otherwise the objects take no extra
* space. */
CHECK(ALIGNMENT <= 1 || !secp256k1_scratch_max_allocation(&CTX->error_callback, scratch, (SIZE_MAX / (ALIGNMENT - 1)) + 1));
/* Try allocating SIZE_MAX to test wrap around which only happens if
* ALIGNMENT > 1, otherwise it returns NULL anyway because the scratch
* space is too small. */
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, SIZE_MAX) == NULL);
secp256k1_scratch_space_destroy(CTX, scratch);
/* cleanup */
secp256k1_scratch_space_destroy(CTX, NULL); /* no-op */
}
static void run_ctz_tests(void) {
static const uint32_t b32[] = {1, 0xffffffff, 0x5e56968f, 0xe0d63129};
static const uint64_t b64[] = {1, 0xffffffffffffffff, 0xbcd02462139b3fc3, 0x98b5f80c769693ef};
int shift;
unsigned i;
for (i = 0; i < sizeof(b32) / sizeof(b32[0]); ++i) {
for (shift = 0; shift < 32; ++shift) {
CHECK(secp256k1_ctz32_var_debruijn(b32[i] << shift) == shift);
CHECK(secp256k1_ctz32_var(b32[i] << shift) == shift);
}
}
for (i = 0; i < sizeof(b64) / sizeof(b64[0]); ++i) {
for (shift = 0; shift < 64; ++shift) {
CHECK(secp256k1_ctz64_var_debruijn(b64[i] << shift) == shift);
CHECK(secp256k1_ctz64_var(b64[i] << shift) == shift);
}
}
}
/***** HASH TESTS *****/
static void run_sha256_known_output_tests(void) {
static const char *inputs[] = {
"", "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",
"aaaaa",
};
static const unsigned int repeat[] = {
1, 1, 1, 1, 1, 1, 1, 1, 1000000/5
};
static const unsigned char outputs[][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},
{0xcd, 0xc7, 0x6e, 0x5c, 0x99, 0x14, 0xfb, 0x92, 0x81, 0xa1, 0xc7, 0xe2, 0x84, 0xd7, 0x3e, 0x67, 0xf1, 0x80, 0x9a, 0x48, 0xa4, 0x97, 0x20, 0x0e, 0x04, 0x6d, 0x39, 0xcc, 0xc7, 0x11, 0x2c, 0xd0},
};
unsigned int i, ninputs;
/* Skip last input vector for low iteration counts */
ninputs = sizeof(inputs)/sizeof(inputs[0]) - 1;
CONDITIONAL_TEST(16, "run_sha256_known_output_tests 1000000") ninputs++;
for (i = 0; i < ninputs; i++) {
unsigned char out[32];
secp256k1_sha256 hasher;
unsigned int j;
/* 1. Run: simply write the input bytestrings */
j = repeat[i];
secp256k1_sha256_initialize(&hasher);
while (j > 0) {
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
j--;
}
secp256k1_sha256_finalize(&hasher, out);
CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
/* 2. Run: split the input bytestrings randomly before writing */
if (strlen(inputs[i]) > 0) {
int split = testrand_int(strlen(inputs[i]));
secp256k1_sha256_initialize(&hasher);
j = repeat[i];
while (j > 0) {
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
j--;
}
secp256k1_sha256_finalize(&hasher, out);
CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
}
}
}
/** SHA256 counter tests
The tests verify that the SHA256 counter doesn't wrap around at message length
2^i bytes for i = 20, ..., 33. This wide range aims at being independent of the
implementation of the counter and it catches multiple natural 32-bit overflows
(e.g., counting bits, counting bytes, counting blocks, ...).
The test vectors have been generated using following Python script which relies
on https://github.com/cloudtools/sha256/ (v0.3 on Python v3.10.2).
```
from sha256 import sha256
from copy import copy
def midstate_c_definition(hasher):
ret = ' {{0x' + hasher.state[0].hex('_', 4).replace('_', ', 0x') + '},\n'
ret += ' {0x00}, ' + str(hex(hasher.state[1])) + '}'
return ret
def output_c_literal(hasher):
return '{0x' + hasher.digest().hex('_').replace('_', ', 0x') + '}'
MESSAGE = b'abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno'
assert(len(MESSAGE) == 64)
BYTE_BOUNDARIES = [(2**b)//len(MESSAGE) - 1 for b in range(20, 34)]
midstates = []
digests = []
hasher = sha256()
for i in range(BYTE_BOUNDARIES[-1] + 1):
if i in BYTE_BOUNDARIES:
midstates.append(midstate_c_definition(hasher))
hasher_copy = copy(hasher)
hasher_copy.update(MESSAGE)
digests.append(output_c_literal(hasher_copy))
hasher.update(MESSAGE)
for x in midstates:
print(x + ',')
for x in digests:
print(x + ',')
```
*/
static void run_sha256_counter_tests(void) {
static const char *input = "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmno";
static const secp256k1_sha256 midstates[] = {
{{0xa2b5c8bb, 0x26c88bb3, 0x2abdc3d2, 0x9def99a3, 0xdfd21a6e, 0x41fe585b, 0x7ef2c440, 0x2b79adda},
{0x00}, 0xfffc0},
{{0xa0d29445, 0x9287de66, 0x76aabd71, 0x41acd765, 0x0c7528b4, 0x84e14906, 0x942faec6, 0xcc5a7b26},
{0x00}, 0x1fffc0},
{{0x50449526, 0xb9f1d657, 0xa0fc13e9, 0x50860f10, 0xa550c431, 0x3fbc97c1, 0x7bbb2d89, 0xdb67bac1},
{0x00}, 0x3fffc0},
{{0x54a6efdc, 0x46762e7b, 0x88bfe73f, 0xbbd149c7, 0x41620c43, 0x1168da7b, 0x2c5960f9, 0xeccffda6},
{0x00}, 0x7fffc0},
{{0x2515a8f5, 0x5faa2977, 0x3a850486, 0xac858cad, 0x7b7276ee, 0x235c0385, 0xc53a157c, 0x7cb3e69c},
{0x00}, 0xffffc0},
{{0x34f39828, 0x409fedb7, 0x4bbdd0fb, 0x3b643634, 0x7806bf2e, 0xe0d1b713, 0xca3f2e1e, 0xe38722c2},
{0x00}, 0x1ffffc0},
{{0x389ef5c5, 0x38c54167, 0x8f5d56ab, 0x582a75cc, 0x8217caef, 0xf10947dd, 0x6a1998a8, 0x048f0b8c},
{0x00}, 0x3ffffc0},
{{0xd6c3f394, 0x0bee43b9, 0x6783f497, 0x29fa9e21, 0x6ce491c1, 0xa81fe45e, 0x2fc3859a, 0x269012d0},
{0x00}, 0x7ffffc0},
{{0x6dd3c526, 0x44d88aa0, 0x806a1bae, 0xfbcc0d32, 0x9d6144f3, 0x9d2bd757, 0x9851a957, 0xb50430ad},
{0x00}, 0xfffffc0},
{{0x2add4021, 0xdfe8a9e6, 0xa56317c6, 0x7a15f5bb, 0x4a48aacd, 0x5d368414, 0x4f00e6f0, 0xd9355023},
{0x00}, 0x1fffffc0},
{{0xb66666b4, 0xdbeac32b, 0x0ea351ae, 0xcba9da46, 0x6278b874, 0x8c508e23, 0xe16ca776, 0x8465bac1},
{0x00}, 0x3fffffc0},
{{0xb6744789, 0x9cce87aa, 0xc4c478b7, 0xf38404d8, 0x2e38ba62, 0xa3f7019b, 0x50458fe7, 0x3047dbec},
{0x00}, 0x7fffffc0},
{{0x8b1297ba, 0xba261a80, 0x2ba1b0dd, 0xfbc67d6d, 0x61072c4e, 0x4b5a2a0f, 0x52872760, 0x2dfeb162},
{0x00}, 0xffffffc0},
{{0x24f33cf7, 0x41ad6583, 0x41c8ff5d, 0xca7ef35f, 0x50395756, 0x021b743e, 0xd7126cd7, 0xd037473a},
{0x00}, 0x1ffffffc0},
};
static const unsigned char outputs[][32] = {
{0x0e, 0x83, 0xe2, 0xc9, 0x4f, 0xb2, 0xb8, 0x2b, 0x89, 0x06, 0x92, 0x78, 0x04, 0x03, 0x48, 0x5c, 0x48, 0x44, 0x67, 0x61, 0x77, 0xa4, 0xc7, 0x90, 0x9e, 0x92, 0x55, 0x10, 0x05, 0xfe, 0x39, 0x15},
{0x1d, 0x1e, 0xd7, 0xb8, 0xa3, 0xa7, 0x8a, 0x79, 0xfd, 0xa0, 0x05, 0x08, 0x9c, 0xeb, 0xf0, 0xec, 0x67, 0x07, 0x9f, 0x8e, 0x3c, 0x0d, 0x8e, 0xf9, 0x75, 0x55, 0x13, 0xc1, 0xe8, 0x77, 0xf8, 0xbb},
{0x66, 0x95, 0x6c, 0xc9, 0xe0, 0x39, 0x65, 0xb6, 0xb0, 0x05, 0xd1, 0xaf, 0xaf, 0xf3, 0x1d, 0xb9, 0xa4, 0xda, 0x6f, 0x20, 0xcd, 0x3a, 0xae, 0x64, 0xc2, 0xdb, 0xee, 0xf5, 0xb8, 0x8d, 0x57, 0x0e},
{0x3c, 0xbb, 0x1c, 0x12, 0x5e, 0x17, 0xfd, 0x54, 0x90, 0x45, 0xa7, 0x7b, 0x61, 0x6c, 0x1d, 0xfe, 0xe6, 0xcc, 0x7f, 0xee, 0xcf, 0xef, 0x33, 0x35, 0x50, 0x62, 0x16, 0x70, 0x2f, 0x87, 0xc3, 0xc9},
{0x53, 0x4d, 0xa8, 0xe7, 0x1e, 0x98, 0x73, 0x8d, 0xd9, 0xa3, 0x54, 0xa5, 0x0e, 0x59, 0x2c, 0x25, 0x43, 0x6f, 0xaa, 0xa2, 0xf5, 0x21, 0x06, 0x3e, 0xc9, 0x82, 0x06, 0x94, 0x98, 0x72, 0x9d, 0xa7},
{0xef, 0x7e, 0xe9, 0x6b, 0xd3, 0xe5, 0xb7, 0x41, 0x4c, 0xc8, 0xd3, 0x07, 0x52, 0x9a, 0x5a, 0x8b, 0x4e, 0x1e, 0x75, 0xa4, 0x17, 0x78, 0xc8, 0x36, 0xcd, 0xf8, 0x2e, 0xd9, 0x57, 0xe3, 0xd7, 0x07},
{0x87, 0x16, 0xfb, 0xf9, 0xa5, 0xf8, 0xc4, 0x56, 0x2b, 0x48, 0x52, 0x8e, 0x2d, 0x30, 0x85, 0xb6, 0x4c, 0x56, 0xb5, 0xd1, 0x16, 0x9c, 0xcf, 0x32, 0x95, 0xad, 0x03, 0xe8, 0x05, 0x58, 0x06, 0x76},
{0x75, 0x03, 0x80, 0x28, 0xf2, 0xa7, 0x63, 0x22, 0x1a, 0x26, 0x9c, 0x68, 0xe0, 0x58, 0xfc, 0x73, 0xeb, 0x42, 0xf6, 0x86, 0x16, 0x24, 0x4b, 0xbc, 0x24, 0xf7, 0x02, 0xc8, 0x3d, 0x90, 0xe2, 0xb0},
{0xdf, 0x49, 0x0f, 0x15, 0x7b, 0x7d, 0xbf, 0xe0, 0xd4, 0xcf, 0x47, 0xc0, 0x80, 0x93, 0x4a, 0x61, 0xaa, 0x03, 0x07, 0x66, 0xb3, 0x38, 0x5d, 0xc8, 0xc9, 0x07, 0x61, 0xfb, 0x97, 0x10, 0x2f, 0xd8},
{0x77, 0x19, 0x40, 0x56, 0x41, 0xad, 0xbc, 0x59, 0xda, 0x1e, 0xc5, 0x37, 0x14, 0x63, 0x7b, 0xfb, 0x79, 0xe2, 0x7a, 0xb1, 0x55, 0x42, 0x99, 0x42, 0x56, 0xfe, 0x26, 0x9d, 0x0f, 0x7e, 0x80, 0xc6},
{0x50, 0xe7, 0x2a, 0x0e, 0x26, 0x44, 0x2f, 0xe2, 0x55, 0x2d, 0xc3, 0x93, 0x8a, 0xc5, 0x86, 0x58, 0x22, 0x8c, 0x0c, 0xbf, 0xb1, 0xd2, 0xca, 0x87, 0x2a, 0xe4, 0x35, 0x26, 0x6f, 0xcd, 0x05, 0x5e},
{0xe4, 0x80, 0x6f, 0xdb, 0x3d, 0x7d, 0xba, 0xde, 0x50, 0x3f, 0xea, 0x00, 0x3d, 0x46, 0x59, 0x64, 0xfd, 0x58, 0x1c, 0xa1, 0xb8, 0x7d, 0x5f, 0xac, 0x94, 0x37, 0x9e, 0xa0, 0xc0, 0x9c, 0x93, 0x8b},
{0x2c, 0xf3, 0xa9, 0xf6, 0x15, 0x25, 0x80, 0x70, 0x76, 0x99, 0x7d, 0xf1, 0xc3, 0x2f, 0xa3, 0x31, 0xff, 0x92, 0x35, 0x2e, 0x8d, 0x04, 0x13, 0x33, 0xd8, 0x0d, 0xdb, 0x4a, 0xf6, 0x8c, 0x03, 0x34},
{0xec, 0x12, 0x24, 0x9f, 0x35, 0xa4, 0x29, 0x8b, 0x9e, 0x4a, 0x95, 0xf8, 0x61, 0xaf, 0x61, 0xc5, 0x66, 0x55, 0x3e, 0x3f, 0x2a, 0x98, 0xea, 0x71, 0x16, 0x6b, 0x1c, 0xd9, 0xe4, 0x09, 0xd2, 0x8e},
};
unsigned int i;
for (i = 0; i < sizeof(midstates)/sizeof(midstates[0]); i++) {
unsigned char out[32];
secp256k1_sha256 hasher = midstates[i];
secp256k1_sha256_write(&hasher, (const unsigned char*)input, strlen(input));
secp256k1_sha256_finalize(&hasher, out);
CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
}
}
/* Tests for the equality of two sha256 structs. This function only produces a
* correct result if an integer multiple of 64 many bytes have been written
* into the hash functions. This function is used by some module tests. */
static void test_sha256_eq(const secp256k1_sha256 *sha1, const secp256k1_sha256 *sha2) {
/* Is buffer fully consumed? */
CHECK((sha1->bytes & 0x3F) == 0);
CHECK(sha1->bytes == sha2->bytes);
CHECK(secp256k1_memcmp_var(sha1->s, sha2->s, sizeof(sha1->s)) == 0);
}
/* Convenience function for using test_sha256_eq to verify the correctness of a
* tagged hash midstate. This function is used by some module tests. */
static void test_sha256_tag_midstate(secp256k1_sha256 *sha_tagged, const unsigned char *tag, size_t taglen) {
secp256k1_sha256 sha;
secp256k1_sha256_initialize_tagged(&sha, tag, taglen);
test_sha256_eq(&sha, sha_tagged);
}
static void run_hmac_sha256_tests(void) {
static const char *keys[6] = {
"\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
"\x4a\x65\x66\x65",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
"\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
"\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
};
static const char *inputs[6] = {
"\x48\x69\x20\x54\x68\x65\x72\x65",
"\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
"\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
"\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
"\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
"\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
};
static const unsigned char outputs[6][32] = {
{0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
{0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
{0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
{0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
{0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
{0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
};
int i;
for (i = 0; i < 6; i++) {
secp256k1_hmac_sha256 hasher;
unsigned char out[32];
secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
secp256k1_hmac_sha256_finalize(&hasher, out);
CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
if (strlen(inputs[i]) > 0) {
int split = testrand_int(strlen(inputs[i]));
secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
secp256k1_hmac_sha256_finalize(&hasher, out);
CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
}
}
}
static void run_rfc6979_hmac_sha256_tests(void) {
static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
static const unsigned char out1[3][32] = {
{0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
{0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
{0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
};
static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
static const unsigned char out2[3][32] = {
{0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
{0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
{0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
};
secp256k1_rfc6979_hmac_sha256 rng;
unsigned char out[32];
int i;
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(secp256k1_memcmp_var(out, out1[i], 32) == 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(secp256k1_memcmp_var(out, out1[i], 32) != 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
for (i = 0; i < 3; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
CHECK(secp256k1_memcmp_var(out, out2[i], 32) == 0);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
}
static void run_tagged_sha256_tests(void) {
unsigned char tag[32] = { 0 };
unsigned char msg[32] = { 0 };
unsigned char hash32[32];
unsigned char hash_expected[32] = {
0x04, 0x7A, 0x5E, 0x17, 0xB5, 0x86, 0x47, 0xC1,
0x3C, 0xC6, 0xEB, 0xC0, 0xAA, 0x58, 0x3B, 0x62,
0xFB, 0x16, 0x43, 0x32, 0x68, 0x77, 0x40, 0x6C,
0xE2, 0x76, 0x55, 0x9A, 0x3B, 0xDE, 0x55, 0xB3
};
/* API test */
CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, sizeof(tag), msg, sizeof(msg)) == 1);
CHECK_ILLEGAL(CTX, secp256k1_tagged_sha256(CTX, NULL, tag, sizeof(tag), msg, sizeof(msg)));
CHECK_ILLEGAL(CTX, secp256k1_tagged_sha256(CTX, hash32, NULL, 0, msg, sizeof(msg)));
CHECK_ILLEGAL(CTX, secp256k1_tagged_sha256(CTX, hash32, tag, sizeof(tag), NULL, 0));
/* Static test vector */
memcpy(tag, "tag", 3);
memcpy(msg, "msg", 3);
CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, 3, msg, 3) == 1);
CHECK(secp256k1_memcmp_var(hash32, hash_expected, sizeof(hash32)) == 0);
}
/***** MODINV TESTS *****/
/* Compute the modular inverse of (odd) x mod 2^64. */
static uint64_t modinv2p64(uint64_t x) {
/* If w = 1/x mod 2^(2^L), then w*(2 - w*x) = 1/x mod 2^(2^(L+1)). See
* Hacker's Delight second edition, Henry S. Warren, Jr., pages 245-247 for
* why. Start with L=0, for which it is true for every odd x that
* 1/x=1 mod 2. Iterating 6 times gives us 1/x mod 2^64. */
int l;
uint64_t w = 1;
CHECK(x & 1);
for (l = 0; l < 6; ++l) w *= (2 - w*x);
return w;
}
/* compute out = (a*b) mod m; if b=NULL, treat b=1; if m=NULL, treat m=infinity.
*
* Out is a 512-bit number (represented as 32 uint16_t's in LE order). The other
* arguments are 256-bit numbers (represented as 16 uint16_t's in LE order). */
static void mulmod256(uint16_t* out, const uint16_t* a, const uint16_t* b, const uint16_t* m) {
uint16_t mul[32];
uint64_t c = 0;
int i, j;
int m_bitlen = 0;
int mul_bitlen = 0;
if (b != NULL) {
/* Compute the product of a and b, and put it in mul. */
for (i = 0; i < 32; ++i) {
for (j = i <= 15 ? 0 : i - 15; j <= i && j <= 15; j++) {
c += (uint64_t)a[j] * b[i - j];
}
mul[i] = c & 0xFFFF;
c >>= 16;
}
CHECK(c == 0);
/* compute the highest set bit in mul */
for (i = 511; i >= 0; --i) {
if ((mul[i >> 4] >> (i & 15)) & 1) {
mul_bitlen = i;
break;
}
}
} else {
/* if b==NULL, set mul=a. */
memcpy(mul, a, 32);
memset(mul + 16, 0, 32);
/* compute the highest set bit in mul */
for (i = 255; i >= 0; --i) {
if ((mul[i >> 4] >> (i & 15)) & 1) {
mul_bitlen = i;
break;
}
}
}
if (m) {
/* Compute the highest set bit in m. */
for (i = 255; i >= 0; --i) {
if ((m[i >> 4] >> (i & 15)) & 1) {
m_bitlen = i;
break;
}
}
/* Try do mul -= m<<i, for i going down to 0, whenever the result is not negative */
for (i = mul_bitlen - m_bitlen; i >= 0; --i) {
uint16_t mul2[32];
int64_t cs;
/* Compute mul2 = mul - m<<i. */
cs = 0; /* accumulator */
for (j = 0; j < 32; ++j) { /* j loops over the output limbs in mul2. */
/* Compute sub: the 16 bits in m that will be subtracted from mul2[j]. */
uint16_t sub = 0;
int p;
for (p = 0; p < 16; ++p) { /* p loops over the bit positions in mul2[j]. */
int bitpos = j * 16 - i + p; /* bitpos is the correspond bit position in m. */
if (bitpos >= 0 && bitpos < 256) {
sub |= ((m[bitpos >> 4] >> (bitpos & 15)) & 1) << p;
}
}
/* Add mul[j]-sub to accumulator, and shift bottom 16 bits out to mul2[j]. */
cs += mul[j];
cs -= sub;
mul2[j] = (cs & 0xFFFF);
cs >>= 16;
}
/* If remainder of subtraction is 0, set mul = mul2. */
if (cs == 0) {
memcpy(mul, mul2, sizeof(mul));
}
}
/* Sanity check: test that all limbs higher than m's highest are zero */
for (i = (m_bitlen >> 4) + 1; i < 32; ++i) {
CHECK(mul[i] == 0);
}
}
memcpy(out, mul, 32);
}
/* Convert a 256-bit number represented as 16 uint16_t's to signed30 notation. */
static void uint16_to_signed30(secp256k1_modinv32_signed30* out, const uint16_t* in) {
int i;
memset(out->v, 0, sizeof(out->v));
for (i = 0; i < 256; ++i) {
out->v[i / 30] |= (int32_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 30);
}
}
/* Convert a 256-bit number in signed30 notation to a representation as 16 uint16_t's. */
static void signed30_to_uint16(uint16_t* out, const secp256k1_modinv32_signed30* in) {
int i;
memset(out, 0, 32);
for (i = 0; i < 256; ++i) {
out[i >> 4] |= (((in->v[i / 30]) >> (i % 30)) & 1) << (i & 15);
}
}
/* Randomly mutate the sign of limbs in signed30 representation, without changing the value. */
static void mutate_sign_signed30(secp256k1_modinv32_signed30* x) {
int i;
for (i = 0; i < 16; ++i) {
int pos = testrand_bits(3);
if (x->v[pos] > 0 && x->v[pos + 1] <= 0x3fffffff) {
x->v[pos] -= 0x40000000;
x->v[pos + 1] += 1;
} else if (x->v[pos] < 0 && x->v[pos + 1] >= 0x3fffffff) {
x->v[pos] += 0x40000000;
x->v[pos + 1] -= 1;
}
}
}
/* Test secp256k1_modinv32{_var}, using inputs in 16-bit limb format, and returning inverse. */
static void test_modinv32_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) {
uint16_t tmp[16];
secp256k1_modinv32_signed30 x;
secp256k1_modinv32_modinfo m;
int i, vartime, nonzero;
uint16_to_signed30(&x, in);
nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4] | x.v[5] | x.v[6] | x.v[7] | x.v[8]) != 0;
uint16_to_signed30(&m.modulus, mod);
/* compute 1/modulus mod 2^30 */
m.modulus_inv30 = modinv2p64(m.modulus.v[0]) & 0x3fffffff;
CHECK(((m.modulus_inv30 * m.modulus.v[0]) & 0x3fffffff) == 1);
/* Test secp256k1_jacobi32_maybe_var. */
if (nonzero) {
int jac;
uint16_t sqr[16], negone[16];
mulmod256(sqr, in, in, mod);
uint16_to_signed30(&x, sqr);
/* Compute jacobi symbol of in^2, which must be 1 (or uncomputable). */
jac = secp256k1_jacobi32_maybe_var(&x, &m);
CHECK(jac == 0 || jac == 1);
/* Then compute the jacobi symbol of -(in^2). x and -x have opposite
* jacobi symbols if and only if (mod % 4) == 3. */
negone[0] = mod[0] - 1;
for (i = 1; i < 16; ++i) negone[i] = mod[i];
mulmod256(sqr, sqr, negone, mod);
uint16_to_signed30(&x, sqr);
jac = secp256k1_jacobi32_maybe_var(&x, &m);
CHECK(jac == 0 || jac == 1 - (mod[0] & 2));
}
uint16_to_signed30(&x, in);
mutate_sign_signed30(&m.modulus);
for (vartime = 0; vartime < 2; ++vartime) {
/* compute inverse */
(vartime ? secp256k1_modinv32_var : secp256k1_modinv32)(&x, &m);
/* produce output */
signed30_to_uint16(out, &x);
/* check if the inverse times the input is 1 (mod m), unless x is 0. */
mulmod256(tmp, out, in, mod);
CHECK(tmp[0] == nonzero);
for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0);
/* invert again */
(vartime ? secp256k1_modinv32_var : secp256k1_modinv32)(&x, &m);
/* check if the result is equal to the input */
signed30_to_uint16(tmp, &x);
for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]);
}
}
#ifdef SECP256K1_WIDEMUL_INT128
/* Convert a 256-bit number represented as 16 uint16_t's to signed62 notation. */
static void uint16_to_signed62(secp256k1_modinv64_signed62* out, const uint16_t* in) {
int i;
memset(out->v, 0, sizeof(out->v));
for (i = 0; i < 256; ++i) {
out->v[i / 62] |= (int64_t)(((in[i >> 4]) >> (i & 15)) & 1) << (i % 62);
}
}
/* Convert a 256-bit number in signed62 notation to a representation as 16 uint16_t's. */
static void signed62_to_uint16(uint16_t* out, const secp256k1_modinv64_signed62* in) {
int i;
memset(out, 0, 32);
for (i = 0; i < 256; ++i) {
out[i >> 4] |= (((in->v[i / 62]) >> (i % 62)) & 1) << (i & 15);
}
}
/* Randomly mutate the sign of limbs in signed62 representation, without changing the value. */
static void mutate_sign_signed62(secp256k1_modinv64_signed62* x) {
static const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
int i;
for (i = 0; i < 8; ++i) {
int pos = testrand_bits(2);
if (x->v[pos] > 0 && x->v[pos + 1] <= M62) {
x->v[pos] -= (M62 + 1);
x->v[pos + 1] += 1;
} else if (x->v[pos] < 0 && x->v[pos + 1] >= -M62) {
x->v[pos] += (M62 + 1);
x->v[pos + 1] -= 1;
}
}
}
/* Test secp256k1_modinv64{_var}, using inputs in 16-bit limb format, and returning inverse. */
static void test_modinv64_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod) {
static const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
uint16_t tmp[16];
secp256k1_modinv64_signed62 x;
secp256k1_modinv64_modinfo m;
int i, vartime, nonzero;
uint16_to_signed62(&x, in);
nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4]) != 0;
uint16_to_signed62(&m.modulus, mod);
/* compute 1/modulus mod 2^62 */
m.modulus_inv62 = modinv2p64(m.modulus.v[0]) & M62;
CHECK(((m.modulus_inv62 * m.modulus.v[0]) & M62) == 1);
/* Test secp256k1_jacobi64_maybe_var. */
if (nonzero) {
int jac;
uint16_t sqr[16], negone[16];
mulmod256(sqr, in, in, mod);
uint16_to_signed62(&x, sqr);
/* Compute jacobi symbol of in^2, which must be 1 (or uncomputable). */
jac = secp256k1_jacobi64_maybe_var(&x, &m);
CHECK(jac == 0 || jac == 1);
/* Then compute the jacobi symbol of -(in^2). x and -x have opposite
* jacobi symbols if and only if (mod % 4) == 3. */
negone[0] = mod[0] - 1;
for (i = 1; i < 16; ++i) negone[i] = mod[i];
mulmod256(sqr, sqr, negone, mod);
uint16_to_signed62(&x, sqr);
jac = secp256k1_jacobi64_maybe_var(&x, &m);
CHECK(jac == 0 || jac == 1 - (mod[0] & 2));
}
uint16_to_signed62(&x, in);
mutate_sign_signed62(&m.modulus);
for (vartime = 0; vartime < 2; ++vartime) {
/* compute inverse */
(vartime ? secp256k1_modinv64_var : secp256k1_modinv64)(&x, &m);
/* produce output */
signed62_to_uint16(out, &x);
/* check if the inverse times the input is 1 (mod m), unless x is 0. */
mulmod256(tmp, out, in, mod);
CHECK(tmp[0] == nonzero);
for (i = 1; i < 16; ++i) CHECK(tmp[i] == 0);
/* invert again */
(vartime ? secp256k1_modinv64_var : secp256k1_modinv64)(&x, &m);
/* check if the result is equal to the input */
signed62_to_uint16(tmp, &x);
for (i = 0; i < 16; ++i) CHECK(tmp[i] == in[i]);
}
}
#endif
/* test if a and b are coprime */
static int coprime(const uint16_t* a, const uint16_t* b) {
uint16_t x[16], y[16], t[16];
int i;
int iszero;
memcpy(x, a, 32);
memcpy(y, b, 32);
/* simple gcd loop: while x!=0, (x,y)=(y%x,x) */
while (1) {
iszero = 1;
for (i = 0; i < 16; ++i) {
if (x[i] != 0) {
iszero = 0;
break;
}
}
if (iszero) break;
mulmod256(t, y, NULL, x);
memcpy(y, x, 32);
memcpy(x, t, 32);
}
/* return whether y=1 */
if (y[0] != 1) return 0;
for (i = 1; i < 16; ++i) {
if (y[i] != 0) return 0;
}
return 1;
}
static void run_modinv_tests(void) {
/* Fixed test cases. Each tuple is (input, modulus, output), each as 16x16 bits in LE order. */
static const uint16_t CASES[][3][16] = {
/* Test cases triggering edge cases in divsteps */
/* Test case known to need 713 divsteps */
{{0x1513, 0x5389, 0x54e9, 0x2798, 0x1957, 0x66a0, 0x8057, 0x3477,
0x7784, 0x1052, 0x326a, 0x9331, 0x6506, 0xa95c, 0x91f3, 0xfb5e},
{0x2bdd, 0x8df4, 0xcc61, 0x481f, 0xdae5, 0x5ca7, 0xf43b, 0x7d54,
0x13d6, 0x469b, 0x2294, 0x20f4, 0xb2a4, 0xa2d1, 0x3ff1, 0xfd4b},
{0xffd8, 0xd9a0, 0x456e, 0x81bb, 0xbabd, 0x6cea, 0x6dbd, 0x73ab,
0xbb94, 0x3d3c, 0xdf08, 0x31c4, 0x3e32, 0xc179, 0x2486, 0xb86b}},
/* Test case known to need 589 divsteps, reaching delta=-140 and
delta=141. */
{{0x3fb1, 0x903b, 0x4eb7, 0x4813, 0xd863, 0x26bf, 0xd89f, 0xa8a9,
0x02fe, 0x57c6, 0x554a, 0x4eab, 0x165e, 0x3d61, 0xee1e, 0x456c},
{0x9295, 0x823b, 0x5c1f, 0x5386, 0x48e0, 0x02ff, 0x4c2a, 0xa2da,
0xe58f, 0x967c, 0xc97e, 0x3f5a, 0x69fb, 0x52d9, 0x0a86, 0xb4a3},
{0x3d30, 0xb893, 0xa809, 0xa7a8, 0x26f5, 0x5b42, 0x55be, 0xf4d0,
0x12c2, 0x7e6a, 0xe41a, 0x90c7, 0xebfa, 0xf920, 0x304e, 0x1419}},
/* Test case known to need 650 divsteps, and doing 65 consecutive (f,g/2) steps. */
{{0x8583, 0x5058, 0xbeae, 0xeb69, 0x48bc, 0x52bb, 0x6a9d, 0xcc94,
0x2a21, 0x87d5, 0x5b0d, 0x42f6, 0x5b8a, 0x2214, 0xe9d6, 0xa040},
{0x7531, 0x27cb, 0x7e53, 0xb739, 0x6a5f, 0x83f5, 0xa45c, 0xcb1d,
0x8a87, 0x1c9c, 0x51d7, 0x851c, 0xb9d8, 0x1fbe, 0xc241, 0xd4a3},
{0xcdb4, 0x275c, 0x7d22, 0xa906, 0x0173, 0xc054, 0x7fdf, 0x5005,
0x7fb8, 0x9059, 0xdf51, 0x99df, 0x2654, 0x8f6e, 0x070f, 0xb347}},
/* example needing 713 divsteps; delta=-2..3 */
{{0xe2e9, 0xee91, 0x4345, 0xe5ad, 0xf3ec, 0x8f42, 0x0364, 0xd5c9,
0xff49, 0xbef5, 0x4544, 0x4c7c, 0xae4b, 0xfd9d, 0xb35b, 0xda9d},
{0x36e7, 0x8cca, 0x2ed0, 0x47b3, 0xaca4, 0xb374, 0x7d2a, 0x0772,
0x6bdb, 0xe0a7, 0x900b, 0xfe10, 0x788c, 0x6f22, 0xd909, 0xf298},
{0xd8c6, 0xba39, 0x13ed, 0x198c, 0x16c8, 0xb837, 0xa5f2, 0x9797,
0x0113, 0x882a, 0x15b5, 0x324c, 0xabee, 0xe465, 0x8170, 0x85ac}},
/* example needing 713 divsteps; delta=-2..3 */
{{0xd5b7, 0x2966, 0x040e, 0xf59a, 0x0387, 0xd96d, 0xbfbc, 0xd850,
0x2d96, 0x872a, 0xad81, 0xc03c, 0xbb39, 0xb7fa, 0xd904, 0xef78},
{0x6279, 0x4314, 0xfdd3, 0x1568, 0x0982, 0x4d13, 0x625f, 0x010c,
0x22b1, 0x0cc3, 0xf22d, 0x5710, 0x1109, 0x5751, 0x7714, 0xfcf2},
{0xdb13, 0x5817, 0x232e, 0xe456, 0xbbbc, 0x6fbe, 0x4572, 0xa358,
0xc76d, 0x928e, 0x0162, 0x5314, 0x8325, 0x5683, 0xe21b, 0xda88}},
/* example needing 713 divsteps; delta=-2..3 */
{{0xa06f, 0x71ee, 0x3bac, 0x9ebb, 0xdeaa, 0x09ed, 0x1cf7, 0x9ec9,
0x7158, 0x8b72, 0x5d53, 0x5479, 0x5c75, 0xbb66, 0x9125, 0xeccc},
{0x2941, 0xd46c, 0x3cd4, 0x4a9d, 0x5c4a, 0x256b, 0xbd6c, 0x9b8e,
0x8fe0, 0x8a14, 0xffe8, 0x2496, 0x618d, 0xa9d7, 0x5018, 0xfb29},
{0x437c, 0xbd60, 0x7590, 0x94bb, 0x0095, 0xd35e, 0xd4fe, 0xd6da,
0x0d4e, 0x5342, 0x4cd2, 0x169b, 0x661c, 0x1380, 0xed2d, 0x85c1}},
/* example reaching delta=-64..65; 661 divsteps */
{{0xfde4, 0x68d6, 0x6c48, 0x7f77, 0x1c78, 0x96de, 0x2fd9, 0xa6c2,
0xbbb5, 0xd319, 0x69cf, 0xd4b3, 0xa321, 0xcda0, 0x172e, 0xe530},
{0xd9e3, 0x0f60, 0x3d86, 0xeeab, 0x25ee, 0x9582, 0x2d50, 0xfe16,
0xd4e2, 0xe3ba, 0x94e2, 0x9833, 0x6c5e, 0x8982, 0x13b6, 0xe598},
{0xe675, 0xf55a, 0x10f6, 0xabde, 0x5113, 0xecaa, 0x61ae, 0xad9f,
0x0c27, 0xef33, 0x62e5, 0x211d, 0x08fa, 0xa78d, 0xc675, 0x8bae}},
/* example reaching delta=-64..65; 661 divsteps */
{{0x21bf, 0x52d5, 0x8fd4, 0xaa18, 0x156a, 0x7247, 0xebb8, 0x5717,
0x4eb5, 0x1421, 0xb58f, 0x3b0b, 0x5dff, 0xe533, 0xb369, 0xd28a},
{0x9f6b, 0xe463, 0x2563, 0xc74d, 0x6d81, 0x636a, 0x8fc8, 0x7a94,
0x9429, 0x1585, 0xf35e, 0x7ff5, 0xb64f, 0x9720, 0xba74, 0xe108},
{0xa5ab, 0xea7b, 0xfe5e, 0x8a85, 0x13be, 0x7934, 0xe8a0, 0xa187,
0x86b5, 0xe477, 0xb9a4, 0x75d7, 0x538f, 0xdd70, 0xc781, 0xb67d}},
/* example reaching delta=-64..65; 661 divsteps */
{{0xa41a, 0x3e8d, 0xf1f5, 0x9493, 0x868c, 0x5103, 0x2725, 0x3ceb,
0x6032, 0x3624, 0xdc6b, 0x9120, 0xbf4c, 0x8821, 0x91ad, 0xb31a},
{0x5c0b, 0xdda5, 0x20f8, 0x32a1, 0xaf73, 0x6ec5, 0x4779, 0x43d6,
0xd454, 0x9573, 0xbf84, 0x5a58, 0xe04e, 0x307e, 0xd1d5, 0xe230},
{0xda15, 0xbcd6, 0x7180, 0xabd3, 0x04e6, 0x6986, 0xc0d7, 0x90bb,
0x3a4d, 0x7c95, 0xaaab, 0x9ab3, 0xda34, 0xa7f6, 0x9636, 0x6273}},
/* example doing 123 consecutive (f,g/2) steps; 615 divsteps */
{{0xb4d6, 0xb38f, 0x00aa, 0xebda, 0xd4c2, 0x70b8, 0x9dad, 0x58ee,
0x68f8, 0x48d3, 0xb5ff, 0xf422, 0x9e46, 0x2437, 0x18d0, 0xd9cc},
{0x5c83, 0xfed7, 0x97f5, 0x3f07, 0xcaad, 0x95b1, 0xb4a4, 0xb005,
0x23af, 0xdd27, 0x6c0d, 0x932c, 0xe2b2, 0xe3ae, 0xfb96, 0xdf67},
{0x3105, 0x0127, 0xfd48, 0x039b, 0x35f1, 0xbc6f, 0x6c0a, 0xb572,
0xe4df, 0xebad, 0x8edc, 0xb89d, 0x9555, 0x4c26, 0x1fef, 0x997c}},
/* example doing 123 consecutive (f,g/2) steps; 614 divsteps */
{{0x5138, 0xd474, 0x385f, 0xc964, 0x00f2, 0x6df7, 0x862d, 0xb185,
0xb264, 0xe9e1, 0x466c, 0xf39e, 0xafaf, 0x5f41, 0x47e2, 0xc89d},
{0x8607, 0x9c81, 0x46a2, 0x7dcc, 0xcb0c, 0x9325, 0xe149, 0x2bde,
0x6632, 0x2869, 0xa261, 0xb163, 0xccee, 0x22ae, 0x91e0, 0xcfd5},
{0x831c, 0xda22, 0xb080, 0xba7a, 0x26e2, 0x54b0, 0x073b, 0x5ea0,
0xed4b, 0xcb3d, 0xbba1, 0xbec8, 0xf2ad, 0xae0d, 0x349b, 0x17d1}},
/* example doing 123 consecutive (f,g/2) steps; 614 divsteps */
{{0xe9a5, 0xb4ad, 0xd995, 0x9953, 0xcdff, 0x50d7, 0xf715, 0x9dc7,
0x3e28, 0x15a9, 0x95a3, 0x8554, 0x5b5e, 0xad1d, 0x6d57, 0x3d50},
{0x3ad9, 0xbd60, 0x5cc7, 0x6b91, 0xadeb, 0x71f6, 0x7cc4, 0xa58a,
0x2cce, 0xf17c, 0x38c9, 0x97ed, 0x65fb, 0x3fa6, 0xa6bc, 0xeb24},
{0xf96c, 0x1963, 0x8151, 0xa0cc, 0x299b, 0xf277, 0x001a, 0x16bb,
0xfd2e, 0x532d, 0x0410, 0xe117, 0x6b00, 0x44ec, 0xca6a, 0x1745}},
/* example doing 446 (f,g/2) steps; 523 divsteps */
{{0x3758, 0xa56c, 0xe41e, 0x4e47, 0x0975, 0xa82b, 0x107c, 0x89cf,
0x2093, 0x5a0c, 0xda37, 0xe007, 0x6074, 0x4f68, 0x2f5a, 0xbb8a},
{0x4beb, 0xa40f, 0x2c42, 0xd9d6, 0x97e8, 0xca7c, 0xd395, 0x894f,
0x1f50, 0x8067, 0xa233, 0xb850, 0x1746, 0x1706, 0xbcda, 0xdf32},
{0x762a, 0xceda, 0x4c45, 0x1ca0, 0x8c37, 0xd8c5, 0xef57, 0x7a2c,
0x6e98, 0xe38a, 0xc50e, 0x2ca9, 0xcb85, 0x24d5, 0xc29c, 0x61f6}},
/* example doing 446 (f,g/2) steps; 523 divsteps */
{{0x6f38, 0x74ad, 0x7332, 0x4073, 0x6521, 0xb876, 0xa370, 0xa6bd,
0xcea5, 0xbd06, 0x969f, 0x77c6, 0x1e69, 0x7c49, 0x7d51, 0xb6e7},
{0x3f27, 0x4be4, 0xd81e, 0x1396, 0xb21f, 0x92aa, 0x6dc3, 0x6283,
0x6ada, 0x3ca2, 0xc1e5, 0x8b9b, 0xd705, 0x5598, 0x8ba1, 0xe087},
{0x6a22, 0xe834, 0xbc8d, 0xcee9, 0x42fc, 0xfc77, 0x9c45, 0x1ca8,
0xeb66, 0xed74, 0xaaf9, 0xe75f, 0xfe77, 0x46d2, 0x179b, 0xbf3e}},
/* example doing 336 (f,(f+g)/2) steps; 693 divsteps */
{{0x7ea7, 0x444e, 0x84ea, 0xc447, 0x7c1f, 0xab97, 0x3de6, 0x5878,
0x4e8b, 0xc017, 0x03e0, 0xdc40, 0xbbd0, 0x74ce, 0x0169, 0x7ab5},
{0x4023, 0x154f, 0xfbe4, 0x8195, 0xfda0, 0xef54, 0x9e9a, 0xc703,
0x2803, 0xf760, 0x6302, 0xed5b, 0x7157, 0x6456, 0xdd7d, 0xf14b},
{0xb6fb, 0xe3b3, 0x0733, 0xa77e, 0x44c5, 0x3003, 0xc937, 0xdd4d,
0x5355, 0x14e9, 0x184e, 0xcefe, 0xe6b5, 0xf2e0, 0x0a28, 0x5b74}},
/* example doing 336 (f,(f+g)/2) steps; 687 divsteps */
{{0xa893, 0xb5f4, 0x1ede, 0xa316, 0x242c, 0xbdcc, 0xb017, 0x0836,
0x3a37, 0x27fb, 0xfb85, 0x251e, 0xa189, 0xb15d, 0xa4b8, 0xc24c},
{0xb0b7, 0x57ba, 0xbb6d, 0x9177, 0xc896, 0xc7f2, 0x43b4, 0x85a6,
0xe6c4, 0xe50e, 0x3109, 0x7ca5, 0xd73d, 0x13ff, 0x0c3d, 0xcd62},
{0x48ca, 0xdb34, 0xe347, 0x2cef, 0x4466, 0x10fb, 0x7ee1, 0x6344,
0x4308, 0x966d, 0xd4d1, 0xb099, 0x994f, 0xd025, 0x2187, 0x5866}},
/* example doing 267 (g,(g-f)/2) steps; 678 divsteps */
{{0x0775, 0x1754, 0x01f6, 0xdf37, 0xc0be, 0x8197, 0x072f, 0x6cf5,
0x8b36, 0x8069, 0x5590, 0xb92d, 0x6084, 0x47a4, 0x23fe, 0xddd5},
{0x8e1b, 0xda37, 0x27d9, 0x312e, 0x3a2f, 0xef6d, 0xd9eb, 0x8153,
0xdcba, 0x9fa3, 0x9f80, 0xead5, 0x134d, 0x2ebb, 0x5ec0, 0xe032},
{0x1cb6, 0x5a61, 0x1bed, 0x77d6, 0xd5d1, 0x7498, 0xef33, 0x2dd2,
0x1089, 0xedbd, 0x6958, 0x16ae, 0x336c, 0x45e6, 0x4361, 0xbadc}},
/* example doing 267 (g,(g-f)/2) steps; 676 divsteps */
{{0x0207, 0xf948, 0xc430, 0xf36b, 0xf0a7, 0x5d36, 0x751f, 0x132c,
0x6f25, 0xa630, 0xca1f, 0xc967, 0xaf9c, 0x34e7, 0xa38f, 0xbe9f},
{0x5fb9, 0x7321, 0x6561, 0x5fed, 0x54ec, 0x9c3a, 0xee0e, 0x6717,
0x49af, 0xb896, 0xf4f5, 0x451c, 0x722a, 0xf116, 0x64a9, 0xcf0b},
{0xf4d7, 0xdb47, 0xfef2, 0x4806, 0x4cb8, 0x18c7, 0xd9a7, 0x4951,
0x14d8, 0x5c3a, 0xd22d, 0xd7b2, 0x750c, 0x3de7, 0x8b4a, 0x19aa}},
/* Test cases triggering edge cases in divsteps variant starting with delta=1/2 */
/* example needing 590 divsteps; delta=-5/2..7/2 */
{{0x9118, 0xb640, 0x53d7, 0x30ab, 0x2a23, 0xd907, 0x9323, 0x5b3a,
0xb6d4, 0x538a, 0x7637, 0xfe97, 0xfd05, 0x3cc0, 0x453a, 0xfb7e},
{0x6983, 0x4f75, 0x4ad1, 0x48ad, 0xb2d9, 0x521d, 0x3dbc, 0x9cc0,
0x4b60, 0x0ac6, 0xd3be, 0x0fb6, 0xd305, 0x3895, 0x2da5, 0xfdf8},
{0xcec1, 0x33ac, 0xa801, 0x8194, 0xe36c, 0x65ef, 0x103b, 0xca54,
0xfa9b, 0xb41d, 0x9b52, 0xb6f7, 0xa611, 0x84aa, 0x3493, 0xbf54}},
/* example needing 590 divsteps; delta=-3/2..5/2 */
{{0xb5f2, 0x42d0, 0x35e8, 0x8ca0, 0x4b62, 0x6e1d, 0xbdf3, 0x890e,
0x8c82, 0x23d8, 0xc79a, 0xc8e8, 0x789e, 0x353d, 0x9766, 0xea9d},
{0x6fa1, 0xacba, 0x4b7a, 0x5de1, 0x95d0, 0xc845, 0xebbf, 0x6f5a,
0x30cf, 0x52db, 0x69b7, 0xe278, 0x4b15, 0x8411, 0x2ab2, 0xf3e7},
{0xf12c, 0x9d6d, 0x95fa, 0x1878, 0x9f13, 0x4fb5, 0x3c8b, 0xa451,
0x7182, 0xc4b6, 0x7e2a, 0x7bb7, 0x6e0e, 0x5b68, 0xde55, 0x9927}},
/* example needing 590 divsteps; delta=-3/2..5/2 */
{{0x229c, 0x4ef8, 0x1e93, 0xe5dc, 0xcde5, 0x6d62, 0x263b, 0xad11,
0xced0, 0x88ff, 0xae8e, 0x3183, 0x11d2, 0xa50b, 0x350d, 0xeb40},
{0x3157, 0xe2ea, 0x8a02, 0x0aa3, 0x5ae1, 0xb26c, 0xea27, 0x6805,
0x87e2, 0x9461, 0x37c1, 0x2f8d, 0x85d2, 0x77a8, 0xf805, 0xeec9},
{0x6f4e, 0x2748, 0xf7e5, 0xd8d3, 0xabe2, 0x7270, 0xc4e0, 0xedc7,
0xf196, 0x78ca, 0x9139, 0xd8af, 0x72c6, 0xaf2f, 0x85d2, 0x6cd3}},
/* example needing 590 divsteps; delta=-5/2..7/2 */
{{0xdce8, 0xf1fe, 0x6708, 0x021e, 0xf1ca, 0xd609, 0x5443, 0x85ce,
0x7a05, 0x8f9c, 0x90c3, 0x52e7, 0x8e1d, 0x97b8, 0xc0bf, 0xf2a1},
{0xbd3d, 0xed11, 0x1625, 0xb4c5, 0x844c, 0xa413, 0x2569, 0xb9ba,
0xcd35, 0xff84, 0xcd6e, 0x7f0b, 0x7d5d, 0x10df, 0x3efe, 0xfbe5},
{0xa9dd, 0xafef, 0xb1b7, 0x4c8d, 0x50e4, 0xafbf, 0x2d5a, 0xb27c,
0x0653, 0x66b6, 0x5d36, 0x4694, 0x7e35, 0xc47c, 0x857f, 0x32c5}},
/* example needing 590 divsteps; delta=-3/2..5/2 */
{{0x7902, 0xc9f8, 0x926b, 0xaaeb, 0x90f8, 0x1c89, 0xcce3, 0x96b7,
0x28b2, 0x87a2, 0x136d, 0x695a, 0xa8df, 0x9061, 0x9e31, 0xee82},
{0xd3a9, 0x3c02, 0x818c, 0x6b81, 0x34b3, 0xebbb, 0xe2c8, 0x7712,
0xbfd6, 0x8248, 0xa6f4, 0xba6f, 0x03bb, 0xfb54, 0x7575, 0xfe89},
{0x8246, 0x0d63, 0x478e, 0xf946, 0xf393, 0x0451, 0x08c2, 0x5919,
0x5fd6, 0x4c61, 0xbeb7, 0x9a15, 0x30e1, 0x55fc, 0x6a01, 0x3724}},
/* example reaching delta=-127/2..129/2; 571 divsteps */
{{0x3eff, 0x926a, 0x77f5, 0x1fff, 0x1a5b, 0xf3ef, 0xf64b, 0x8681,
0xf800, 0xf9bc, 0x761d, 0xe268, 0x62b0, 0xa032, 0xba9c, 0xbe56},
{0xb8f9, 0x00e7, 0x47b7, 0xdffc, 0xfd9d, 0x5abb, 0xa19b, 0x1868,
0x31fd, 0x3b29, 0x3674, 0x5449, 0xf54d, 0x1d19, 0x6ac7, 0xff6f},
{0xf1d7, 0x3551, 0x5682, 0x9adf, 0xe8aa, 0x19a5, 0x8340, 0x71db,
0xb7ab, 0x4cfd, 0xf661, 0x632c, 0xc27e, 0xd3c6, 0xdf42, 0xd306}},
/* example reaching delta=-127/2..129/2; 571 divsteps */
{{0x0000, 0x0000, 0x0000, 0x0000, 0x3aff, 0x2ed7, 0xf2e0, 0xabc7,
0x8aee, 0x166e, 0x7ed0, 0x9ac7, 0x714a, 0xb9c5, 0x4d58, 0xad6c},
{0x9cf9, 0x47e2, 0xa421, 0xb277, 0xffc2, 0x2747, 0x6486, 0x94c1,
0x1d99, 0xd49b, 0x1096, 0x991a, 0xe986, 0xae02, 0xe89b, 0xea36},
{0x1fb4, 0x98d8, 0x19b7, 0x80e9, 0xcdac, 0xaa5a, 0xf1e6, 0x0074,
0xe393, 0xed8b, 0x8d5c, 0xe17d, 0x81b3, 0xc16d, 0x54d3, 0x9be3}},
/* example reaching delta=-127/2..129/2; 571 divsteps */
{{0xd047, 0x7e36, 0x3157, 0x7ab6, 0xb4d9, 0x8dae, 0x7534, 0x4f5d,
0x489e, 0xa8ab, 0x8a3d, 0xd52c, 0x62af, 0xa032, 0xba9c, 0xbe56},
{0xb1f1, 0x737f, 0x5964, 0x5afb, 0x3712, 0x8ef9, 0x19f7, 0x9669,
0x664d, 0x03ad, 0xc352, 0xf7a5, 0xf545, 0x1d19, 0x6ac7, 0xff6f},
{0xa834, 0x5256, 0x27bc, 0x33bd, 0xba11, 0x5a7b, 0x791e, 0xe6c0,
0x9ac4, 0x9370, 0x1130, 0x28b4, 0x2b2e, 0x231b, 0x082a, 0x796e}},
/* example doing 123 consecutive (f,g/2) steps; 554 divsteps */
{{0x6ab1, 0x6ea0, 0x1a99, 0xe0c2, 0xdd45, 0x645d, 0x8dbc, 0x466a,
0xfa64, 0x4289, 0xd3f7, 0xfc8f, 0x2894, 0xe3c5, 0xa008, 0xcc14},
{0xc75f, 0xc083, 0x4cc2, 0x64f2, 0x2aff, 0x4c12, 0x8461, 0xc4ae,
0xbbfa, 0xb336, 0xe4b2, 0x3ac5, 0x2c22, 0xf56c, 0x5381, 0xe943},
{0xcd80, 0x760d, 0x4395, 0xb3a6, 0xd497, 0xf583, 0x82bd, 0x1daa,
0xbe92, 0x2613, 0xfdfb, 0x869b, 0x0425, 0xa333, 0x7056, 0xc9c5}},
/* example doing 123 consecutive (f,g/2) steps; 554 divsteps */
{{0x71d4, 0x64df, 0xec4f, 0x74d8, 0x7e0c, 0x40d3, 0x7073, 0x4cc8,
0x2a2a, 0xb1ff, 0x8518, 0x6513, 0xb0ea, 0x640a, 0x62d9, 0xd5f4},
{0xdc75, 0xd937, 0x3b13, 0x1d36, 0xdf83, 0xd034, 0x1c1c, 0x4332,
0x4cc3, 0xeeec, 0x7d94, 0x6771, 0x3384, 0x74b0, 0x947d, 0xf2c4},
{0x0a82, 0x37a4, 0x12d5, 0xec97, 0x972c, 0xe6bf, 0xc348, 0xa0a9,
0xc50c, 0xdc7c, 0xae30, 0x19d1, 0x0fca, 0x35e1, 0xd6f6, 0x81ee}},
/* example doing 123 consecutive (f,g/2) steps; 554 divsteps */
{{0xa6b1, 0xabc5, 0x5bbc, 0x7f65, 0xdd32, 0xaa73, 0xf5a3, 0x1982,
0xced4, 0xe949, 0x0fd6, 0x2bc4, 0x2bd7, 0xe3c5, 0xa008, 0xcc14},
{0x4b5f, 0x8f96, 0xa375, 0xfbcf, 0x1c7d, 0xf1ec, 0x03f5, 0xb35d,
0xb999, 0xdb1f, 0xc9a1, 0xb4c7, 0x1dd5, 0xf56c, 0x5381, 0xe943},
{0xaa3d, 0x38b9, 0xf17d, 0xeed9, 0x9988, 0x69ee, 0xeb88, 0x1495,
0x203f, 0x18c8, 0x82b7, 0xdcb2, 0x34a7, 0x6b00, 0x6998, 0x589a}},
/* example doing 453 (f,g/2) steps; 514 divsteps */
{{0xa478, 0xe60d, 0x3244, 0x60e6, 0xada3, 0xfe50, 0xb6b1, 0x2eae,
0xd0ef, 0xa7b1, 0xef63, 0x05c0, 0xe213, 0x443e, 0x4427, 0x2448},
{0x258f, 0xf9ef, 0xe02b, 0x92dd, 0xd7f3, 0x252b, 0xa503, 0x9089,
0xedff, 0x96c1, 0xfe3a, 0x3a39, 0x198a, 0x981d, 0x0627, 0xedb7},
{0x595a, 0x45be, 0x8fb0, 0x2265, 0xc210, 0x02b8, 0xdce9, 0xe241,
0xcab6, 0xbf0d, 0x0049, 0x8d9a, 0x2f51, 0xae54, 0x5785, 0xb411}},
/* example doing 453 (f,g/2) steps; 514 divsteps */
{{0x48f0, 0x7db3, 0xdafe, 0x1c92, 0x5912, 0xe11a, 0xab52, 0xede1,
0x3182, 0x8980, 0x5d2b, 0x9b5b, 0x8718, 0xda27, 0x1683, 0x1de2},
{0x168f, 0x6f36, 0xce7a, 0xf435, 0x19d4, 0xda5e, 0x2351, 0x9af5,
0xb003, 0x0ef5, 0x3b4c, 0xecec, 0xa9f0, 0x78e1, 0xdfef, 0xe823},
{0x5f55, 0xfdcc, 0xb233, 0x2914, 0x84f0, 0x97d1, 0x9cf4, 0x2159,
0xbf56, 0xb79c, 0x17a3, 0x7cef, 0xd5de, 0x34f0, 0x5311, 0x4c54}},
/* example doing 510 (f,(f+g)/2) steps; 512 divsteps */
{{0x2789, 0x2e04, 0x6e0e, 0xb6cd, 0xe4de, 0x4dbf, 0x228d, 0x7877,
0xc335, 0x806b, 0x38cd, 0x8049, 0xa73b, 0xcfa2, 0x82f7, 0x9e19},
{0xc08d, 0xb99d, 0xb8f3, 0x663d, 0xbbb3, 0x1284, 0x1485, 0x1d49,
0xc98f, 0x9e78, 0x1588, 0x11e3, 0xd91a, 0xa2c7, 0xfff1, 0xc7b9},
{0x1e1f, 0x411d, 0x7c49, 0x0d03, 0xe789, 0x2f8e, 0x5d55, 0xa95e,
0x826e, 0x8de5, 0x52a0, 0x1abc, 0x4cd7, 0xd13a, 0x4395, 0x63e1}},
/* example doing 510 (f,(f+g)/2) steps; 512 divsteps */
{{0xd5a1, 0xf786, 0x555c, 0xb14b, 0x44ae, 0x535f, 0x4a49, 0xffc3,
0xf497, 0x70d1, 0x57c8, 0xa933, 0xc85a, 0x1910, 0x75bf, 0x960b},
{0xfe53, 0x5058, 0x496d, 0xfdff, 0x6fb8, 0x4100, 0x92bd, 0xe0c4,
0xda89, 0xe0a4, 0x841b, 0x43d4, 0xa388, 0x957f, 0x99ca, 0x9abf},
{0xe530, 0x05bc, 0xfeec, 0xfc7e, 0xbcd3, 0x1239, 0x54cb, 0x7042,
0xbccb, 0x139e, 0x9076, 0x0203, 0x6068, 0x90c7, 0x1ddf, 0x488d}},
/* example doing 228 (g,(g-f)/2) steps; 538 divsteps */
{{0x9488, 0xe54b, 0x0e43, 0x81d2, 0x06e7, 0x4b66, 0x36d0, 0x53d6,
0x2b68, 0x22ec, 0x3fa9, 0xc1a7, 0x9ad2, 0xa596, 0xb3ac, 0xdf42},
{0xe31f, 0x0b28, 0x5f3b, 0xc1ff, 0x344c, 0xbf5f, 0xd2ec, 0x2936,
0x9995, 0xdeb2, 0xae6c, 0x2852, 0xa2c6, 0xb306, 0x8120, 0xe305},
{0xa56e, 0xfb98, 0x1537, 0x4d85, 0x619e, 0x866c, 0x3cd4, 0x779a,
0xdd66, 0xa80d, 0xdc2f, 0xcae4, 0xc74c, 0x5175, 0xa65d, 0x605e}},
/* example doing 228 (g,(g-f)/2) steps; 537 divsteps */
{{0x8cd5, 0x376d, 0xd01b, 0x7176, 0x19ef, 0xcf09, 0x8403, 0x5e52,
0x83c1, 0x44de, 0xb91e, 0xb33d, 0xe15c, 0x51e7, 0xbad8, 0x6359},
{0x3b75, 0xf812, 0x5f9e, 0xa04e, 0x92d3, 0x226e, 0x540e, 0x7c9a,
0x31c6, 0x46d2, 0x0b7b, 0xdb4a, 0xe662, 0x4950, 0x0265, 0xf76f},
{0x09ed, 0x692f, 0xe8f1, 0x3482, 0xab54, 0x36b4, 0x8442, 0x6ae9,
0x4329, 0x6505, 0x183b, 0x1c1d, 0x482d, 0x7d63, 0xb44f, 0xcc09}},
/* Test cases with the group order as modulus. */
/* Test case with the group order as modulus, needing 635 divsteps. */
{{0x95ed, 0x6c01, 0xd113, 0x5ff1, 0xd7d0, 0x29cc, 0x5817, 0x6120,
0xca8e, 0xaad1, 0x25ae, 0x8e84, 0x9af6, 0x30bf, 0xf0ed, 0x1686},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x1631, 0xbf4a, 0x286a, 0x2716, 0x469f, 0x2ac8, 0x1312, 0xe9bc,
0x04f4, 0x304b, 0x9931, 0x113b, 0xd932, 0xc8f4, 0x0d0d, 0x01a1}},
/* example with group size as modulus needing 631 divsteps */
{{0x85ed, 0xc284, 0x9608, 0x3c56, 0x19b6, 0xbb5b, 0x2850, 0xdab7,
0xa7f5, 0xe9ab, 0x06a4, 0x5bbb, 0x1135, 0xa186, 0xc424, 0xc68b},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x8479, 0x450a, 0x8fa3, 0xde05, 0xb2f5, 0x7793, 0x7269, 0xbabb,
0xc3b3, 0xd49b, 0x3377, 0x03c6, 0xe694, 0xc760, 0xd3cb, 0x2811}},
/* example with group size as modulus needing 565 divsteps starting at delta=1/2 */
{{0x8432, 0x5ceb, 0xa847, 0x6f1e, 0x51dd, 0x535a, 0x6ddc, 0x70ce,
0x6e70, 0xc1f6, 0x18f2, 0x2a7e, 0xc8e7, 0x39f8, 0x7e96, 0xebbf},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x257e, 0x449f, 0x689f, 0x89aa, 0x3989, 0xb661, 0x376c, 0x1e32,
0x654c, 0xee2e, 0xf4e2, 0x33c8, 0x3f2f, 0x9716, 0x6046, 0xcaa3}},
/* Test case with the group size as modulus, needing 981 divsteps with
broken eta handling. */
{{0xfeb9, 0xb877, 0xee41, 0x7fa3, 0x87da, 0x94c4, 0x9d04, 0xc5ae,
0x5708, 0x0994, 0xfc79, 0x0916, 0xbf32, 0x3ad8, 0xe11c, 0x5ca2},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0f12, 0x075e, 0xce1c, 0x6f92, 0xc80f, 0xca92, 0x9a04, 0x6126,
0x4b6c, 0x57d6, 0xca31, 0x97f3, 0x1f99, 0xf4fd, 0xda4d, 0x42ce}},
/* Test case with the group size as modulus, input = 0. */
{{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}},
/* Test case with the group size as modulus, input = 1. */
{{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}},
/* Test case with the group size as modulus, input = 2. */
{{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x20a1, 0x681b, 0x2f46, 0xdfe9, 0x501d, 0x57a4, 0x6e73, 0x5d57,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}},
/* Test case with the group size as modulus, input = group - 1. */
{{0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x4141, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x4140, 0xd036, 0x5e8c, 0xbfd2, 0xa03b, 0xaf48, 0xdce6, 0xbaae,
0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}},
/* Test cases with the field size as modulus. */
/* Test case with the field size as modulus, needing 637 divsteps. */
{{0x9ec3, 0x1919, 0xca84, 0x7c11, 0xf996, 0x06f3, 0x5408, 0x6688,
0x1320, 0xdb8a, 0x632a, 0x0dcb, 0x8a84, 0x6bee, 0x9c95, 0xe34e},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x18e5, 0x19b6, 0xdf92, 0x1aaa, 0x09fb, 0x8a3f, 0x52b0, 0x8701,
0xac0c, 0x2582, 0xda44, 0x9bcc, 0x6828, 0x1c53, 0xbd8f, 0xbd2c}},
/* example with field size as modulus needing 637 divsteps */
{{0xaec3, 0xa7cf, 0x2f2d, 0x0693, 0x5ad5, 0xa8ff, 0x7ec7, 0x30ff,
0x0c8b, 0xc242, 0xcab2, 0x063a, 0xf86e, 0x6057, 0x9cbd, 0xf6d8},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0310, 0x579d, 0xcb38, 0x9030, 0x3ded, 0x9bb9, 0x1234, 0x63ce,
0x0c63, 0x8e3d, 0xacfe, 0x3c20, 0xdc85, 0xf859, 0x919e, 0x1d45}},
/* example with field size as modulus needing 564 divsteps starting at delta=1/2 */
{{0x63ae, 0x8d10, 0x0071, 0xdb5c, 0xb454, 0x78d1, 0x744a, 0x5f8e,
0xe4d8, 0x87b1, 0x8e62, 0x9590, 0xcede, 0xa070, 0x36b4, 0x7f6f},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0xfdc8, 0xe8d5, 0xbe15, 0x9f86, 0xa5fe, 0xf18e, 0xa7ff, 0xd291,
0xf4c2, 0x9c87, 0xf150, 0x073e, 0x69b8, 0xf7c4, 0xee4b, 0xc7e6}},
/* Test case with the field size as modulus, needing 935 divsteps with
broken eta handling. */
{{0x1b37, 0xbdc3, 0x8bcd, 0x25e3, 0x1eae, 0x567d, 0x30b6, 0xf0d8,
0x9277, 0x0cf8, 0x9c2e, 0xecd7, 0x631d, 0xe38f, 0xd4f8, 0x5c93},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x1622, 0xe05b, 0xe880, 0x7de9, 0x3e45, 0xb682, 0xee6c, 0x67ed,
0xa179, 0x15db, 0x6b0d, 0xa656, 0x7ccb, 0x8ef7, 0xa2ff, 0xe279}},
/* Test case with the field size as modulus, input = 0. */
{{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}},
/* Test case with the field size as modulus, input = 1. */
{{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000}},
/* Test case with the field size as modulus, input = 2. */
{{0x0002, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0xfe18, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff}},
/* Test case with the field size as modulus, input = field - 1. */
{{0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff},
{0xfc2e, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}},
/* Selected from a large number of random inputs to reach small/large
* d/e values in various configurations. */
{{0x3a08, 0x23e1, 0x4d8c, 0xe606, 0x3263, 0x67af, 0x9bf1, 0x9d70,
0xf5fd, 0x12e4, 0x03c8, 0xb9ca, 0xe847, 0x8c5d, 0x6322, 0xbd30},
{0x8359, 0x59dd, 0x1831, 0x7c1a, 0x1e83, 0xaee1, 0x770d, 0xcea8,
0xfbb1, 0xeed6, 0x10b5, 0xe2c6, 0x36ea, 0xee17, 0xe32c, 0xffff},
{0x1727, 0x0f36, 0x6f85, 0x5d0c, 0xca6c, 0x3072, 0x9628, 0x5842,
0xcb44, 0x7c2b, 0xca4f, 0x62e5, 0x29b1, 0x6ffd, 0x9055, 0xc196}},
{{0x905d, 0x41c8, 0xa2ff, 0x295b, 0x72bb, 0x4679, 0x6d01, 0x2c98,
0xb3e0, 0xc537, 0xa310, 0xe07e, 0xe72f, 0x4999, 0x1148, 0xf65e},
{0x5b41, 0x4239, 0x3c37, 0x5130, 0x30e3, 0xff35, 0xc51f, 0x1a43,
0xdb23, 0x13cf, 0x9f49, 0xf70c, 0x5e70, 0xd411, 0x3005, 0xf8c6},
{0xc30e, 0x68f0, 0x201a, 0xe10c, 0x864a, 0x6243, 0xe946, 0x43ae,
0xf3f1, 0x52dc, 0x1f7f, 0x50d4, 0x2797, 0x064c, 0x5ca4, 0x90e3}},
{{0xf1b5, 0xc6e5, 0xd2c4, 0xff95, 0x27c5, 0x0c92, 0x5d19, 0x7ae5,
0x4fbe, 0x5438, 0x99e1, 0x880d, 0xd892, 0xa05c, 0x6ffd, 0x7eac},
{0x2153, 0xcc9d, 0xfc6c, 0x8358, 0x49a1, 0x01e2, 0xcef0, 0x4969,
0xd69a, 0x8cef, 0xf5b2, 0xfd95, 0xdcc2, 0x71f4, 0x6ae2, 0xceeb},
{0x9b2e, 0xcdc6, 0x0a5c, 0x7317, 0x9084, 0xe228, 0x56cf, 0xd512,
0x628a, 0xce21, 0x3473, 0x4e13, 0x8823, 0x1ed0, 0x34d0, 0xbfa3}},
{{0x5bae, 0x53e5, 0x5f4d, 0x21ca, 0xb875, 0x8ecf, 0x9aa6, 0xbe3c,
0x9f96, 0x7b82, 0x375d, 0x4d3e, 0x491c, 0xb1eb, 0x04c9, 0xb6c8},
{0xfcfd, 0x10b7, 0x73b2, 0xd23b, 0xa357, 0x67da, 0x0d9f, 0x8702,
0xa037, 0xff8e, 0x0e8b, 0x1801, 0x2c5c, 0x4e6e, 0x4558, 0xfff2},
{0xc50f, 0x5654, 0x6713, 0x5ef5, 0xa7ce, 0xa647, 0xc832, 0x69ce,
0x1d5c, 0x4310, 0x0746, 0x5a01, 0x96ea, 0xde4b, 0xa88b, 0x5543}},
{{0xdc7f, 0x5e8c, 0x89d1, 0xb077, 0xd521, 0xcf90, 0x32fa, 0x5737,
0x839e, 0x1464, 0x007c, 0x09c6, 0x9371, 0xe8ea, 0xc1cb, 0x75c4},
{0xe3a3, 0x107f, 0xa82a, 0xa375, 0x4578, 0x60f4, 0x75c9, 0x5ee4,
0x3fd7, 0x2736, 0x2871, 0xd3d2, 0x5f1d, 0x1abb, 0xa764, 0xffff},
{0x45c6, 0x1f2e, 0xb14c, 0x84d7, 0x7bb7, 0x5a04, 0x0504, 0x3f33,
0x5cc1, 0xb07a, 0x6a6c, 0x786f, 0x647f, 0xe1d7, 0x78a2, 0x4cf4}},
{{0xc006, 0x356f, 0x8cd2, 0x967b, 0xb49e, 0x2d4e, 0x14bf, 0x4bcb,
0xddab, 0xd3f9, 0xa068, 0x2c1c, 0xd242, 0xa56d, 0xf2c7, 0x5f97},
{0x465b, 0xb745, 0x0e0d, 0x69a9, 0x987d, 0xcb37, 0xf637, 0xb311,
0xc4d6, 0x2ddb, 0xf68f, 0x2af9, 0x959d, 0x3f53, 0x98f2, 0xf640},
{0xc0f2, 0x6bfb, 0xf5c3, 0x91c1, 0x6b05, 0x0825, 0x5ca0, 0x7df7,
0x9d55, 0x6d9e, 0xfe94, 0x2ad9, 0xd9f0, 0xe68b, 0xa72b, 0xd1b2}},
{{0x2279, 0x61ba, 0x5bc6, 0x136b, 0xf544, 0x717c, 0xafda, 0x02bd,
0x79af, 0x1fad, 0xea09, 0x81bb, 0x932b, 0x32c9, 0xdf1d, 0xe576},
{0x8215, 0x7817, 0xca82, 0x43b0, 0x9b06, 0xea65, 0x1291, 0x0621,
0x0089, 0x46fe, 0xc5a6, 0xddd7, 0x8065, 0xc6a0, 0x214b, 0xfc64},
{0x04bf, 0x6f2a, 0x86b2, 0x841a, 0x4a95, 0xc632, 0x97b7, 0x5821,
0x2b18, 0x1bb0, 0x3e97, 0x935e, 0xcc7d, 0x066b, 0xd513, 0xc251}},
{{0x76e8, 0x5bc2, 0x3eaa, 0x04fc, 0x9974, 0x92c1, 0x7c15, 0xfa89,
0x1151, 0x36ee, 0x48b2, 0x049c, 0x5f16, 0xcee4, 0x925b, 0xe98e},
{0x913f, 0x0a2d, 0xa185, 0x9fea, 0xda5a, 0x4025, 0x40d7, 0x7cfa,
0x88ca, 0xbbe8, 0xb265, 0xb7e4, 0x6cb1, 0xed64, 0xc6f9, 0xffb5},
{0x6ab1, 0x1a86, 0x5009, 0x152b, 0x1cc4, 0xe2c8, 0x960b, 0x19d0,
0x3554, 0xc562, 0xd013, 0xcf91, 0x10e1, 0x7933, 0xe195, 0xcf49}},
{{0x9cb5, 0xd2d7, 0xc6ed, 0xa818, 0xb495, 0x06ee, 0x0f4a, 0x06e3,
0x4c5a, 0x80ce, 0xd49a, 0x4cd7, 0x7487, 0x92af, 0xe516, 0x676c},
{0xd6e9, 0x6b85, 0x619a, 0xb52c, 0x20a0, 0x2f79, 0x3545, 0x1edd,
0x5a6f, 0x8082, 0x9b80, 0xf8f8, 0xc78a, 0xd0a3, 0xadf4, 0xffff},
{0x01c2, 0x2118, 0xef5e, 0xa877, 0x046a, 0xd2c2, 0x2ad5, 0x951c,
0x8900, 0xa5c9, 0x8d0f, 0x6b61, 0x55d3, 0xd572, 0x48de, 0x9219}},
{{0x5114, 0x0644, 0x23dd, 0x01d3, 0xc101, 0xa659, 0xea17, 0x640f,
0xf767, 0x2644, 0x9cec, 0xd8ba, 0xd6da, 0x9156, 0x8aeb, 0x875a},
{0xc1bf, 0xdae9, 0xe96b, 0xce77, 0xf7a1, 0x3e99, 0x5c2e, 0x973b,
0xd048, 0x5bd0, 0x4e8a, 0xcb85, 0xce39, 0x37f5, 0x815d, 0xffff},
{0x48cc, 0x35b6, 0x26d4, 0x2ea6, 0x50d6, 0xa2f9, 0x64b6, 0x03bf,
0xd00c, 0xe057, 0x3343, 0xfb79, 0x3ce5, 0xf717, 0xc5af, 0xe185}},
{{0x13ff, 0x6c76, 0x2077, 0x16e0, 0xd5ca, 0xf2ad, 0x8dba, 0x8f49,
0x7887, 0x16f9, 0xb646, 0xfc87, 0xfa31, 0x5096, 0xf08c, 0x3fbe},
{0x8139, 0x6fd7, 0xf6df, 0xa7bf, 0x6699, 0x5361, 0x6f65, 0x13c8,
0xf4d1, 0xe28f, 0xc545, 0x0a8c, 0x5274, 0xb0a6, 0xffff, 0xffff},
{0x22ca, 0x0cd6, 0xc1b5, 0xb064, 0x44a7, 0x297b, 0x495f, 0x34ac,
0xfa95, 0xec62, 0xf08d, 0x621c, 0x66a6, 0xba94, 0x84c6, 0x8ee0}},
{{0xaa30, 0x312e, 0x439c, 0x4e88, 0x2e2f, 0x32dc, 0xb880, 0xa28e,
0xf795, 0xc910, 0xb406, 0x8dd7, 0xb187, 0xa5a5, 0x38f1, 0xe49e},
{0xfb19, 0xf64a, 0xba6a, 0x8ec2, 0x7255, 0xce89, 0x2cf9, 0x9cba,
0xe1fe, 0x50da, 0x1705, 0xac52, 0xe3d4, 0x4269, 0x0648, 0xfd77},
{0xb4c8, 0x6e8a, 0x2b5f, 0x4c2d, 0x5a67, 0xa7bb, 0x7d6d, 0x5569,
0xa0ea, 0x244a, 0xc0f2, 0xf73d, 0x58cf, 0xac7f, 0xd32b, 0x3018}},
{{0xc953, 0x1ae1, 0xae46, 0x8709, 0x19c2, 0xa986, 0x9abe, 0x1611,
0x0395, 0xd5ab, 0xf0f6, 0xb5b0, 0x5b2b, 0x0317, 0x80ba, 0x376d},
{0xfe77, 0xbc03, 0xac2f, 0x9d00, 0xa175, 0x293d, 0x3b56, 0x0e3a,
0x0a9c, 0xf40c, 0x690e, 0x1508, 0x95d4, 0xddc4, 0xe805, 0xffff},
{0xb1ce, 0x0929, 0xa5fe, 0x4b50, 0x9d5d, 0x8187, 0x2557, 0x4376,
0x11ba, 0xdcef, 0xc1f3, 0xd531, 0x1824, 0x93f6, 0xd81f, 0x8f83}},
{{0xb8d2, 0xb900, 0x4a0c, 0x7188, 0xa5bf, 0x1b0b, 0x2ae5, 0xa35b,
0x98e0, 0x610c, 0x86db, 0x2487, 0xa267, 0x002c, 0xebb6, 0xc5f4},
{0x9cdd, 0x1c1b, 0x2f06, 0x43d1, 0xce47, 0xc334, 0x6e60, 0xc016,
0x989e, 0x0ab2, 0x0cac, 0x1196, 0xe2d9, 0x2e04, 0xc62b, 0xffff},
{0xdc36, 0x1f05, 0x6aa9, 0x7a20, 0x944f, 0x2fd3, 0xa553, 0xdb4f,
0xbd5c, 0x3a75, 0x25d4, 0xe20e, 0xa387, 0x1410, 0xdbb1, 0x1b60}},
{{0x76b3, 0x2207, 0x4930, 0x5dd7, 0x65a0, 0xd55c, 0xb443, 0x53b7,
0x5c22, 0x818a, 0xb2e7, 0x9de8, 0x9985, 0xed45, 0x33b1, 0x53e8},
{0x7913, 0x44e1, 0xf15b, 0x5edd, 0x34f3, 0x4eba, 0x0758, 0x7104,
0x32d9, 0x28f3, 0x4401, 0x85c5, 0xb695, 0xb899, 0xc0f2, 0xffff},
{0x7f43, 0xd202, 0x24c9, 0x69f3, 0x74dc, 0x1a69, 0xeaee, 0x5405,
0x1755, 0x4bb8, 0x04e3, 0x2fd2, 0xada8, 0x39eb, 0x5b4d, 0x96ca}},
{{0x807b, 0x7112, 0xc088, 0xdafd, 0x02fa, 0x9d95, 0x5e42, 0xc033,
0xde0a, 0xeecf, 0x8e90, 0x8da1, 0xb17e, 0x9a5b, 0x4c6d, 0x1914},
{0x4871, 0xd1cb, 0x47d7, 0x327f, 0x09ec, 0x97bb, 0x2fae, 0xd346,
0x6b78, 0x3707, 0xfeb2, 0xa6ab, 0x13df, 0x76b0, 0x8fb9, 0xffb3},
{0x179e, 0xb63b, 0x4784, 0x231e, 0x9f42, 0x7f1a, 0xa3fb, 0xdd8c,
0xd1eb, 0xb4c9, 0x8ca7, 0x018c, 0xf691, 0x576c, 0xa7d6, 0xce27}},
{{0x5f45, 0x7c64, 0x083d, 0xedd5, 0x08a0, 0x0c64, 0x6c6f, 0xec3c,
0xe2fb, 0x352c, 0x9303, 0x75e4, 0xb4e0, 0x8b09, 0xaca4, 0x7025},
{0x1025, 0xb482, 0xfed5, 0xa678, 0x8966, 0x9359, 0x5329, 0x98bb,
0x85b2, 0x73ba, 0x9982, 0x6fdc, 0xf190, 0xbe8c, 0xdc5c, 0xfd93},
{0x83a2, 0x87a4, 0xa680, 0x52a1, 0x1ba1, 0x8848, 0x5db7, 0x9744,
0x409c, 0x0745, 0x0e1e, 0x1cfc, 0x00cd, 0xf573, 0x2071, 0xccaa}},
{{0xf61f, 0x63d4, 0x536c, 0x9eb9, 0x5ddd, 0xbb11, 0x9014, 0xe904,
0xfe01, 0x6b45, 0x1858, 0xcb5b, 0x4c38, 0x43e1, 0x381d, 0x7f94},
{0xf61f, 0x63d4, 0xd810, 0x7ca3, 0x8a04, 0x4b83, 0x11fc, 0xdf94,
0x4169, 0xbd05, 0x608e, 0x7151, 0x4fbf, 0xb31a, 0x38a7, 0xa29b},
{0xe621, 0xdfa5, 0x3d06, 0x1d03, 0x81e6, 0x00da, 0x53a6, 0x965e,
0x93e5, 0x2164, 0x5b61, 0x59b8, 0xa629, 0x8d73, 0x699a, 0x6111}},
{{0x4cc3, 0xd29e, 0xf4a3, 0x3428, 0x2048, 0xeec9, 0x5f50, 0x99a4,
0x6de9, 0x05f2, 0x5aa9, 0x5fd2, 0x98b4, 0x1adc, 0x225f, 0x777f},
{0xe649, 0x37da, 0x5ba6, 0x5765, 0x3f4a, 0x8a1c, 0x2e79, 0xf550,
0x1a54, 0xcd1e, 0x7218, 0x3c3c, 0x6311, 0xfe28, 0x95fb, 0xed97},
{0xe9b6, 0x0c47, 0x3f0e, 0x849b, 0x11f8, 0xe599, 0x5e4d, 0xd618,
0xa06d, 0x33a0, 0x9a3e, 0x44db, 0xded8, 0x10f0, 0x94d2, 0x81fb}},
{{0x2e59, 0x7025, 0xd413, 0x455a, 0x1ce3, 0xbd45, 0x7263, 0x27f7,
0x23e3, 0x518e, 0xbe06, 0xc8c4, 0xe332, 0x4276, 0x68b4, 0xb166},
{0x596f, 0x0cf6, 0xc8ec, 0x787b, 0x04c1, 0x473c, 0xd2b8, 0x8d54,
0x9cdf, 0x77f2, 0xd3f3, 0x6735, 0x0638, 0xf80e, 0x9467, 0xc6aa},
{0xc7e7, 0x1822, 0xb62a, 0xec0d, 0x89cd, 0x7846, 0xbfa2, 0x35d5,
0xfa38, 0x870f, 0x494b, 0x1697, 0x8b17, 0xf904, 0x10b6, 0x9822}},
{{0x6d5b, 0x1d4f, 0x0aaf, 0x807b, 0x35fb, 0x7ee8, 0x00c6, 0x059a,
0xddf0, 0x1fb1, 0xc38a, 0xd78e, 0x2aa4, 0x79e7, 0xad28, 0xc3f1},
{0xe3bb, 0x174e, 0xe0a8, 0x74b6, 0xbd5b, 0x35f6, 0x6d23, 0x6328,
0xc11f, 0x83e1, 0xf928, 0xa918, 0x838e, 0xbf43, 0xe243, 0xfffb},
{0x9cf2, 0x6b8b, 0x3476, 0x9d06, 0xdcf2, 0xdb8a, 0x89cd, 0x4857,
0x75c2, 0xabb8, 0x490b, 0xc9bd, 0x890e, 0xe36e, 0xd552, 0xfffa}},
{{0x2f09, 0x9d62, 0xa9fc, 0xf090, 0xd6d1, 0x9d1d, 0x1828, 0xe413,
0xc92b, 0x3d5a, 0x1373, 0x368c, 0xbaf2, 0x2158, 0x71eb, 0x08a3},
{0x2f09, 0x1d62, 0x4630, 0x0de1, 0x06dc, 0xf7f1, 0xc161, 0x1e92,
0x7495, 0x97e4, 0x94b6, 0xa39e, 0x4f1b, 0x18f8, 0x7bd4, 0x0c4c},
{0xeb3d, 0x723d, 0x0907, 0x525b, 0x463a, 0x49a8, 0xc6b8, 0xce7f,
0x740c, 0x0d7d, 0xa83b, 0x457f, 0xae8e, 0xc6af, 0xd331, 0x0475}},
{{0x6abd, 0xc7af, 0x3e4e, 0x95fd, 0x8fc4, 0xee25, 0x1f9c, 0x0afe,
0x291d, 0xcde0, 0x48f4, 0xb2e8, 0xf7af, 0x8f8d, 0x0bd6, 0x078d},
{0x4037, 0xbf0e, 0x2081, 0xf363, 0x13b2, 0x381e, 0xfb6e, 0x818e,
0x27e4, 0x5662, 0x18b0, 0x0cd2, 0x81f5, 0x9415, 0x0d6c, 0xf9fb},
{0xd205, 0x0981, 0x0498, 0x1f08, 0xdb93, 0x1732, 0x0579, 0x1424,
0xad95, 0x642f, 0x050c, 0x1d6d, 0xfc95, 0xfc4a, 0xd41b, 0x3521}},
{{0xf23a, 0x4633, 0xaef4, 0x1a92, 0x3c8b, 0x1f09, 0x30f3, 0x4c56,
0x2a2f, 0x4f62, 0xf5e4, 0x8329, 0x63cc, 0xb593, 0xec6a, 0xc428},
{0x93a7, 0xfcf6, 0x606d, 0xd4b2, 0x2aad, 0x28b4, 0xc65b, 0x8998,
0x4e08, 0xd178, 0x0900, 0xc82b, 0x7470, 0xa342, 0x7c0f, 0xffff},
{0x315f, 0xf304, 0xeb7b, 0xe5c3, 0x1451, 0x6311, 0x8f37, 0x93a8,
0x4a38, 0xa6c6, 0xe393, 0x1087, 0x6301, 0xd673, 0x4ec4, 0xffff}},
{{0x892e, 0xeed0, 0x1165, 0xcbc1, 0x5545, 0xa280, 0x7243, 0x10c9,
0x9536, 0x36af, 0xb3fc, 0x2d7c, 0xe8a5, 0x09d6, 0xe1d4, 0xe85d},
{0xae09, 0xc28a, 0xd777, 0xbd80, 0x23d6, 0xf980, 0xeb7c, 0x4e0e,
0xf7dc, 0x6475, 0xf10a, 0x2d33, 0x5dfd, 0x797a, 0x7f1c, 0xf71a},
{0x4064, 0x8717, 0xd091, 0x80b0, 0x4527, 0x8442, 0xac8b, 0x9614,
0xc633, 0x35f5, 0x7714, 0x2e83, 0x4aaa, 0xd2e4, 0x1acd, 0x0562}},
{{0xdb64, 0x0937, 0x308b, 0x53b0, 0x00e8, 0xc77f, 0x2f30, 0x37f7,
0x79ce, 0xeb7f, 0xde81, 0x9286, 0xafda, 0x0e62, 0xae00, 0x0067},
{0x2cc7, 0xd362, 0xb161, 0x0557, 0x4ff2, 0xb9c8, 0x06fe, 0x5f2b,
0xde33, 0x0190, 0x28c6, 0xb886, 0xee2b, 0x5a4e, 0x3289, 0x0185},
{0x4215, 0x923e, 0xf34f, 0xb362, 0x88f8, 0xceec, 0xafdd, 0x7f42,
0x0c57, 0x56b2, 0xa366, 0x6a08, 0x0826, 0xfb8f, 0x1b03, 0x0163}},
{{0xa4ba, 0x8408, 0x810a, 0xdeba, 0x47a3, 0x853a, 0xeb64, 0x2f74,
0x3039, 0x038c, 0x7fbb, 0x498e, 0xd1e9, 0x46fb, 0x5691, 0x32a4},
{0xd749, 0xb49d, 0x20b7, 0x2af6, 0xd34a, 0xd2da, 0x0a10, 0xf781,
0x58c9, 0x171f, 0x3cb6, 0x6337, 0x88cd, 0xcf1e, 0xb246, 0x7351},
{0xf729, 0xcf0a, 0x96ea, 0x032c, 0x4a8f, 0x42fe, 0xbac8, 0xec65,
0x1510, 0x0d75, 0x4c17, 0x8d29, 0xa03f, 0x8b7e, 0x2c49, 0x0000}},
{{0x0fa4, 0x8e1c, 0x3788, 0xba3c, 0x8d52, 0xd89d, 0x12c8, 0xeced,
0x9fe6, 0x9b88, 0xecf3, 0xe3c8, 0xac48, 0x76ed, 0xf23e, 0xda79},
{0x1103, 0x227c, 0x5b00, 0x3fcf, 0xc5d0, 0x2d28, 0x8020, 0x4d1c,
0xc6b9, 0x67f9, 0x6f39, 0x989a, 0xda53, 0x3847, 0xd416, 0xe0d0},
{0xdd8e, 0xcf31, 0x3710, 0x7e44, 0xa511, 0x933c, 0x0cc3, 0x5145,
0xf632, 0x5e1d, 0x038f, 0x5ce7, 0x7265, 0xda9d, 0xded6, 0x08f8}},
{{0xe2c8, 0x91d5, 0xa5f5, 0x735f, 0x6b58, 0x56dc, 0xb39d, 0x5c4a,
0x57d0, 0xa1c2, 0xd92f, 0x9ad4, 0xf7c4, 0x51dd, 0xaf5c, 0x0096},
{0x1739, 0x7207, 0x7505, 0xbf35, 0x42de, 0x0a29, 0xa962, 0xdedf,
0x53e8, 0x12bf, 0xcde7, 0xd8e2, 0x8d4d, 0x2c4b, 0xb1b1, 0x0628},
{0x992d, 0xe3a7, 0xb422, 0xc198, 0x23ab, 0xa6ef, 0xb45d, 0x50da,
0xa738, 0x014a, 0x2310, 0x85fb, 0x5fe8, 0x1b18, 0x1774, 0x03a7}},
{{0x1f16, 0x2b09, 0x0236, 0xee90, 0xccf9, 0x9775, 0x8130, 0x4c91,
0x9091, 0x310b, 0x6dc4, 0x86f6, 0xc2e8, 0xef60, 0xfc0e, 0xf3a4},
{0x9f49, 0xac15, 0x02af, 0x110f, 0xc59d, 0x5677, 0xa1a9, 0x38d5,
0x914f, 0xa909, 0x3a3a, 0x4a39, 0x3703, 0xea30, 0x73da, 0xffad},
{0x15ed, 0xdd16, 0x83c7, 0x270a, 0x862f, 0xd8ad, 0xcaa1, 0x5f41,
0x99a9, 0x3fc8, 0x7bb2, 0x360a, 0xb06d, 0xfadc, 0x1b36, 0xffa8}},
{{0xc4e0, 0xb8fd, 0x5106, 0xe169, 0x754c, 0xa58c, 0xc413, 0x8224,
0x5483, 0x63ec, 0xd477, 0x8473, 0x4778, 0x9281, 0x0000, 0x0000},
{0x85e1, 0xff54, 0xb200, 0xe413, 0xf4f4, 0x4c0f, 0xfcec, 0xc183,
0x60d3, 0x1b0c, 0x3834, 0x601c, 0x943c, 0xbe6e, 0x0002, 0x0000},
{0xf4f8, 0xfd5e, 0x61ef, 0xece8, 0x9199, 0xe5c4, 0x05a6, 0xe6c3,
0xc4ae, 0x8b28, 0x66b1, 0x8a95, 0x9ece, 0x8f4a, 0x0001, 0x0000}},
{{0xeae9, 0xa1b4, 0xc6d8, 0x2411, 0x2b5a, 0x1dd0, 0x2dc9, 0xb57b,
0x5ccd, 0x4957, 0xaf59, 0xa04b, 0x5f42, 0xab7c, 0x2826, 0x526f},
{0xf407, 0x165a, 0xb724, 0x2f12, 0x2ea1, 0x470b, 0x4464, 0xbd35,
0x606f, 0xd73e, 0x50d3, 0x8a7f, 0x8029, 0x7ffc, 0xbe31, 0x6cfb},
{0x8171, 0x1f4c, 0xced2, 0x9c99, 0x6d7e, 0x5a0f, 0xfefb, 0x59e3,
0xa0c8, 0xabd9, 0xc4c5, 0x57d3, 0xbfa3, 0x4f11, 0x96a2, 0x5a7d}},
{{0xe068, 0x4cc0, 0x8bcd, 0xc903, 0x9e52, 0xb3e1, 0xd745, 0x0995,
0xdd8f, 0xf14b, 0xd2ac, 0xd65a, 0xda1d, 0xa742, 0xbac5, 0x474c},
{0x7481, 0xf2ad, 0x9757, 0x2d82, 0xb683, 0xb16b, 0x0002, 0x7b60,
0x8f0c, 0x2594, 0x8f64, 0x3b7a, 0x3552, 0x8d9d, 0xb9d7, 0x67eb},
{0xcaab, 0xb9a1, 0xf966, 0xe311, 0x5b34, 0x0fa0, 0x6abc, 0x8134,
0xab3d, 0x90f6, 0x1984, 0x9232, 0xec17, 0x74e5, 0x2ceb, 0x434e}},
{{0x0fb1, 0x7a55, 0x1a5c, 0x53eb, 0xd7b3, 0x7a01, 0xca32, 0x31f6,
0x3b74, 0x679e, 0x1501, 0x6c57, 0xdb20, 0x8b7c, 0xd7d0, 0x8097},
{0xb127, 0xb20c, 0xe3a2, 0x96f3, 0xe0d8, 0xd50c, 0x14b4, 0x0b40,
0x6eeb, 0xa258, 0x99db, 0x3c8c, 0x0f51, 0x4198, 0x3887, 0xffd0},
{0x0273, 0x9f8c, 0x9669, 0xbbba, 0x1c49, 0x767c, 0xc2af, 0x59f0,
0x1366, 0xd397, 0x63ac, 0x6fe8, 0x1a9a, 0x1259, 0x01d0, 0x0016}},
{{0x7876, 0x2a35, 0xa24a, 0x433e, 0x5501, 0x573c, 0xd76d, 0xcb82,
0x1334, 0xb4a6, 0xf290, 0xc797, 0xeae9, 0x2b83, 0x1e2b, 0x8b14},
{0x3885, 0x8aef, 0x9dea, 0x2b8c, 0xdd7c, 0xd7cd, 0xb0cc, 0x05ee,
0x361b, 0x3800, 0xb0d4, 0x4c23, 0xbd3f, 0x5180, 0x9783, 0xff80},
{0xab36, 0x3104, 0xdae8, 0x0704, 0x4a28, 0x6714, 0x824b, 0x0051,
0x8134, 0x1f6a, 0x712d, 0x1f03, 0x03b2, 0xecac, 0x377d, 0xfef9}}
};
int i, j, ok;
/* Test known inputs/outputs */
for (i = 0; (size_t)i < sizeof(CASES) / sizeof(CASES[0]); ++i) {
uint16_t out[16];
test_modinv32_uint16(out, CASES[i][0], CASES[i][1]);
for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]);
#ifdef SECP256K1_WIDEMUL_INT128
test_modinv64_uint16(out, CASES[i][0], CASES[i][1]);
for (j = 0; j < 16; ++j) CHECK(out[j] == CASES[i][2][j]);
#endif
}
for (i = 0; i < 100 * COUNT; ++i) {
/* 256-bit numbers in 16-uint16_t's notation */
static const uint16_t ZERO[16] = {0};
uint16_t xd[16]; /* the number (in range [0,2^256)) to be inverted */
uint16_t md[16]; /* the modulus (odd, in range [3,2^256)) */
uint16_t id[16]; /* the inverse of xd mod md */
/* generate random xd and md, so that md is odd, md>1, xd<md, and gcd(xd,md)=1 */
do {
/* generate random xd and md (with many subsequent 0s and 1s) */
testrand256_test((unsigned char*)xd);
testrand256_test((unsigned char*)md);
md[0] |= 1; /* modulus must be odd */
/* If modulus is 1, find another one. */
ok = md[0] != 1;
for (j = 1; j < 16; ++j) ok |= md[j] != 0;
mulmod256(xd, xd, NULL, md); /* Make xd = xd mod md */
} while (!(ok && coprime(xd, md)));
test_modinv32_uint16(id, xd, md);
#ifdef SECP256K1_WIDEMUL_INT128
test_modinv64_uint16(id, xd, md);
#endif
/* In a few cases, also test with input=0 */
if (i < COUNT) {
test_modinv32_uint16(id, ZERO, md);
#ifdef SECP256K1_WIDEMUL_INT128
test_modinv64_uint16(id, ZERO, md);
#endif
}
}
}
/***** INT128 TESTS *****/
#ifdef SECP256K1_WIDEMUL_INT128
/* Add two 256-bit numbers (represented as 16 uint16_t's in LE order) together mod 2^256. */
static void add256(uint16_t* out, const uint16_t* a, const uint16_t* b) {
int i;
uint32_t carry = 0;
for (i = 0; i < 16; ++i) {
carry += a[i];
carry += b[i];
out[i] = carry;
carry >>= 16;
}
}
/* Negate a 256-bit number (represented as 16 uint16_t's in LE order) mod 2^256. */
static void neg256(uint16_t* out, const uint16_t* a) {
int i;
uint32_t carry = 1;
for (i = 0; i < 16; ++i) {
carry += (uint16_t)~a[i];
out[i] = carry;
carry >>= 16;
}
}
/* Right-shift a 256-bit number (represented as 16 uint16_t's in LE order). */
static void rshift256(uint16_t* out, const uint16_t* a, int n, int sign_extend) {
uint16_t sign = sign_extend && (a[15] >> 15);
int i, j;
for (i = 15; i >= 0; --i) {
uint16_t v = 0;
for (j = 0; j < 16; ++j) {
int frompos = i*16 + j + n;
if (frompos >= 256) {
v |= sign << j;
} else {
v |= ((uint16_t)((a[frompos >> 4] >> (frompos & 15)) & 1)) << j;
}
}
out[i] = v;
}
}
/* Load a 64-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */
static void load256u64(uint16_t* out, uint64_t v, int is_signed) {
int i;
uint64_t sign = is_signed && (v >> 63) ? UINT64_MAX : 0;
for (i = 0; i < 4; ++i) {
out[i] = v >> (16 * i);
}
for (i = 4; i < 16; ++i) {
out[i] = sign;
}
}
/* Load a 128-bit unsigned integer into an array of 16 uint16_t's in LE order representing a 256-bit value. */
static void load256two64(uint16_t* out, uint64_t hi, uint64_t lo, int is_signed) {
int i;
uint64_t sign = is_signed && (hi >> 63) ? UINT64_MAX : 0;
for (i = 0; i < 4; ++i) {
out[i] = lo >> (16 * i);
}
for (i = 4; i < 8; ++i) {
out[i] = hi >> (16 * (i - 4));
}
for (i = 8; i < 16; ++i) {
out[i] = sign;
}
}
/* Check whether the 256-bit value represented by array of 16-bit values is in range -2^127 < v < 2^127. */
static int int256is127(const uint16_t* v) {
int all_0 = ((v[7] & 0x8000) == 0), all_1 = ((v[7] & 0x8000) == 0x8000);
int i;
for (i = 8; i < 16; ++i) {
if (v[i] != 0) all_0 = 0;
if (v[i] != 0xffff) all_1 = 0;
}
return all_0 || all_1;
}
static void load256u128(uint16_t* out, const secp256k1_uint128* v) {
uint64_t lo = secp256k1_u128_to_u64(v), hi = secp256k1_u128_hi_u64(v);
load256two64(out, hi, lo, 0);
}
static void load256i128(uint16_t* out, const secp256k1_int128* v) {
uint64_t lo;
int64_t hi;
secp256k1_int128 c = *v;
lo = secp256k1_i128_to_u64(&c);
secp256k1_i128_rshift(&c, 64);
hi = secp256k1_i128_to_i64(&c);
load256two64(out, hi, lo, 1);
}
static void run_int128_test_case(void) {
unsigned char buf[32];
uint64_t v[4];
secp256k1_int128 swa, swz;
secp256k1_uint128 uwa, uwz;
uint64_t ub, uc;
int64_t sb, sc;
uint16_t rswa[16], rswz[32], rswr[32], ruwa[16], ruwz[32], ruwr[32];
uint16_t rub[16], ruc[16], rsb[16], rsc[16];
int i;
/* Generate 32-byte random value. */
testrand256_test(buf);
/* Convert into 4 64-bit integers. */
for (i = 0; i < 4; ++i) {
uint64_t vi = 0;
int j;
for (j = 0; j < 8; ++j) vi = (vi << 8) + buf[8*i + j];
v[i] = vi;
}
/* Convert those into a 128-bit value and two 64-bit values (signed and unsigned). */
secp256k1_u128_load(&uwa, v[1], v[0]);
secp256k1_i128_load(&swa, v[1], v[0]);
ub = v[2];
sb = v[2];
uc = v[3];
sc = v[3];
/* Load those also into 16-bit array representations. */
load256u128(ruwa, &uwa);
load256i128(rswa, &swa);
load256u64(rub, ub, 0);
load256u64(rsb, sb, 1);
load256u64(ruc, uc, 0);
load256u64(rsc, sc, 1);
/* test secp256k1_u128_mul */
mulmod256(ruwr, rub, ruc, NULL);
secp256k1_u128_mul(&uwz, ub, uc);
load256u128(ruwz, &uwz);
CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
/* test secp256k1_u128_accum_mul */
mulmod256(ruwr, rub, ruc, NULL);
add256(ruwr, ruwr, ruwa);
uwz = uwa;
secp256k1_u128_accum_mul(&uwz, ub, uc);
load256u128(ruwz, &uwz);
CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
/* test secp256k1_u128_accum_u64 */
add256(ruwr, rub, ruwa);
uwz = uwa;
secp256k1_u128_accum_u64(&uwz, ub);
load256u128(ruwz, &uwz);
CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
/* test secp256k1_u128_rshift */
rshift256(ruwr, ruwa, uc % 128, 0);
uwz = uwa;
secp256k1_u128_rshift(&uwz, uc % 128);
load256u128(ruwz, &uwz);
CHECK(secp256k1_memcmp_var(ruwr, ruwz, 16) == 0);
/* test secp256k1_u128_to_u64 */
CHECK(secp256k1_u128_to_u64(&uwa) == v[0]);
/* test secp256k1_u128_hi_u64 */
CHECK(secp256k1_u128_hi_u64(&uwa) == v[1]);
/* test secp256k1_u128_from_u64 */
secp256k1_u128_from_u64(&uwz, ub);
load256u128(ruwz, &uwz);
CHECK(secp256k1_memcmp_var(rub, ruwz, 16) == 0);
/* test secp256k1_u128_check_bits */
{
int uwa_bits = 0;
int j;
for (j = 0; j < 128; ++j) {
if (ruwa[j / 16] >> (j % 16)) uwa_bits = 1 + j;
}
for (j = 0; j < 128; ++j) {
CHECK(secp256k1_u128_check_bits(&uwa, j) == (uwa_bits <= j));
}
}
/* test secp256k1_i128_mul */
mulmod256(rswr, rsb, rsc, NULL);
secp256k1_i128_mul(&swz, sb, sc);
load256i128(rswz, &swz);
CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
/* test secp256k1_i128_accum_mul */
mulmod256(rswr, rsb, rsc, NULL);
add256(rswr, rswr, rswa);
if (int256is127(rswr)) {
swz = swa;
secp256k1_i128_accum_mul(&swz, sb, sc);
load256i128(rswz, &swz);
CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
}
/* test secp256k1_i128_det */
{
uint16_t rsd[16], rse[16], rst[32];
int64_t sd = v[0], se = v[1];
load256u64(rsd, sd, 1);
load256u64(rse, se, 1);
mulmod256(rst, rsc, rsd, NULL);
neg256(rst, rst);
mulmod256(rswr, rsb, rse, NULL);
add256(rswr, rswr, rst);
secp256k1_i128_det(&swz, sb, sc, sd, se);
load256i128(rswz, &swz);
CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
}
/* test secp256k1_i128_rshift */
rshift256(rswr, rswa, uc % 127, 1);
swz = swa;
secp256k1_i128_rshift(&swz, uc % 127);
load256i128(rswz, &swz);
CHECK(secp256k1_memcmp_var(rswr, rswz, 16) == 0);
/* test secp256k1_i128_to_u64 */
CHECK(secp256k1_i128_to_u64(&swa) == v[0]);
/* test secp256k1_i128_from_i64 */
secp256k1_i128_from_i64(&swz, sb);
load256i128(rswz, &swz);
CHECK(secp256k1_memcmp_var(rsb, rswz, 16) == 0);
/* test secp256k1_i128_to_i64 */
CHECK(secp256k1_i128_to_i64(&swz) == sb);
/* test secp256k1_i128_eq_var */
{
int expect = (uc & 1);
swz = swa;
if (!expect) {
/* Make sure swz != swa */
uint64_t v0c = v[0], v1c = v[1];
if (ub & 64) {
v1c ^= (((uint64_t)1) << (ub & 63));
} else {
v0c ^= (((uint64_t)1) << (ub & 63));
}
secp256k1_i128_load(&swz, v1c, v0c);
}
CHECK(secp256k1_i128_eq_var(&swa, &swz) == expect);
}
/* test secp256k1_i128_check_pow2 (sign == 1) */
{
int expect = (uc & 1);
int pos = ub % 127;
if (expect) {
/* If expect==1, set swz to exactly 2^pos. */
uint64_t hi = 0;
uint64_t lo = 0;
if (pos >= 64) {
hi = (((uint64_t)1) << (pos & 63));
} else {
lo = (((uint64_t)1) << (pos & 63));
}
secp256k1_i128_load(&swz, hi, lo);
} else {
/* If expect==0, set swz = swa, but update expect=1 if swa happens to equal 2^pos. */
if (pos >= 64) {
if ((v[1] == (((uint64_t)1) << (pos & 63))) && v[0] == 0) expect = 1;
} else {
if ((v[0] == (((uint64_t)1) << (pos & 63))) && v[1] == 0) expect = 1;
}
swz = swa;
}
CHECK(secp256k1_i128_check_pow2(&swz, pos, 1) == expect);
}
/* test secp256k1_i128_check_pow2 (sign == -1) */
{
int expect = (uc & 1);
int pos = ub % 127;
if (expect) {
/* If expect==1, set swz to exactly -2^pos. */
uint64_t hi = ~(uint64_t)0;
uint64_t lo = ~(uint64_t)0;
if (pos >= 64) {
hi <<= (pos & 63);
lo = 0;
} else {
lo <<= (pos & 63);
}
secp256k1_i128_load(&swz, hi, lo);
} else {
/* If expect==0, set swz = swa, but update expect=1 if swa happens to equal -2^pos. */
if (pos >= 64) {
if ((v[1] == ((~(uint64_t)0) << (pos & 63))) && v[0] == 0) expect = 1;
} else {
if ((v[0] == ((~(uint64_t)0) << (pos & 63))) && v[1] == ~(uint64_t)0) expect = 1;
}
swz = swa;
}
CHECK(secp256k1_i128_check_pow2(&swz, pos, -1) == expect);
}
}
static void run_int128_tests(void) {
{ /* secp256k1_u128_accum_mul */
secp256k1_uint128 res;
/* Check secp256k1_u128_accum_mul overflow */
secp256k1_u128_mul(&res, UINT64_MAX, UINT64_MAX);
secp256k1_u128_accum_mul(&res, UINT64_MAX, UINT64_MAX);
CHECK(secp256k1_u128_to_u64(&res) == 2);
CHECK(secp256k1_u128_hi_u64(&res) == 18446744073709551612U);
}
{ /* secp256k1_u128_accum_mul */
secp256k1_int128 res;
/* Compute INT128_MAX = 2^127 - 1 with secp256k1_i128_accum_mul */
secp256k1_i128_mul(&res, INT64_MAX, INT64_MAX);
secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MAX);
CHECK(secp256k1_i128_to_u64(&res) == 2);
secp256k1_i128_accum_mul(&res, 4, 9223372036854775807);
secp256k1_i128_accum_mul(&res, 1, 1);
CHECK(secp256k1_i128_to_u64(&res) == UINT64_MAX);
secp256k1_i128_rshift(&res, 64);
CHECK(secp256k1_i128_to_i64(&res) == INT64_MAX);
/* Compute INT128_MIN = - 2^127 with secp256k1_i128_accum_mul */
secp256k1_i128_mul(&res, INT64_MAX, INT64_MIN);
CHECK(secp256k1_i128_to_u64(&res) == (uint64_t)INT64_MIN);
secp256k1_i128_accum_mul(&res, INT64_MAX, INT64_MIN);
CHECK(secp256k1_i128_to_u64(&res) == 0);
secp256k1_i128_accum_mul(&res, 2, INT64_MIN);
CHECK(secp256k1_i128_to_u64(&res) == 0);
secp256k1_i128_rshift(&res, 64);
CHECK(secp256k1_i128_to_i64(&res) == INT64_MIN);
}
{
/* Randomized tests. */
int i;
for (i = 0; i < 256 * COUNT; ++i) run_int128_test_case();
}
}
#endif
/***** SCALAR TESTS *****/
static void scalar_test(void) {
secp256k1_scalar s;
secp256k1_scalar s1;
secp256k1_scalar s2;
unsigned char c[32];
/* Set 's' to a random scalar, with value 'snum'. */
testutil_random_scalar_order_test(&s);
/* Set 's1' to a random scalar, with value 's1num'. */
testutil_random_scalar_order_test(&s1);
/* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
testutil_random_scalar_order_test(&s2);
secp256k1_scalar_get_b32(c, &s2);
{
int i;
/* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar n;
secp256k1_scalar_set_int(&n, 0);
for (i = 0; i < 256; i += 4) {
secp256k1_scalar t;
int j;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_limb32(&s, 256 - 4 - i, 4));
for (j = 0; j < 4; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
{
/* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar n;
int i = 0;
secp256k1_scalar_set_int(&n, 0);
while (i < 256) {
secp256k1_scalar t;
int j;
int now = testrand_int(15) + 1;
if (now + i > 256) {
now = 256 - i;
}
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
for (j = 0; j < now; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
i += now;
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
{
/* Test commutativity of add. */
secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
secp256k1_scalar r1, r2;
secp256k1_scalar b;
int i;
/* Test add_bit. */
int bit = testrand_bits(8);
secp256k1_scalar_set_int(&b, 1);
CHECK(secp256k1_scalar_is_one(&b));
for (i = 0; i < bit; i++) {
secp256k1_scalar_add(&b, &b, &b);
}
r1 = s1;
r2 = s1;
if (!secp256k1_scalar_add(&r1, &r1, &b)) {
/* No overflow happened. */
secp256k1_scalar_cadd_bit(&r2, bit, 1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
/* cadd is a noop when flag is zero */
secp256k1_scalar_cadd_bit(&r2, bit, 0);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
{
/* Test commutativity of mul. */
secp256k1_scalar r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test associativity of add. */
secp256k1_scalar r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r1, &r1, &s);
secp256k1_scalar_add(&r2, &s2, &s);
secp256k1_scalar_add(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test associativity of mul. */
secp256k1_scalar r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s2, &s);
secp256k1_scalar_mul(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test distributitivity of mul over add. */
secp256k1_scalar r1, r2, t;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s1, &s);
secp256k1_scalar_mul(&t, &s2, &s);
secp256k1_scalar_add(&r2, &r2, &t);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test multiplicative identity. */
secp256k1_scalar r1;
secp256k1_scalar_mul(&r1, &s1, &secp256k1_scalar_one);
CHECK(secp256k1_scalar_eq(&r1, &s1));
}
{
/* Test additive identity. */
secp256k1_scalar r1;
secp256k1_scalar_add(&r1, &s1, &secp256k1_scalar_zero);
CHECK(secp256k1_scalar_eq(&r1, &s1));
}
{
/* Test zero product property. */
secp256k1_scalar r1;
secp256k1_scalar_mul(&r1, &s1, &secp256k1_scalar_zero);
CHECK(secp256k1_scalar_eq(&r1, &secp256k1_scalar_zero));
}
{
/* Test halving. */
secp256k1_scalar r;
secp256k1_scalar_add(&r, &s, &s);
secp256k1_scalar_half(&r, &r);
CHECK(secp256k1_scalar_eq(&r, &s));
}
}
static void run_scalar_set_b32_seckey_tests(void) {
unsigned char b32[32];
secp256k1_scalar s1;
secp256k1_scalar s2;
/* Usually set_b32 and set_b32_seckey give the same result */
testutil_random_scalar_order_b32(b32);
secp256k1_scalar_set_b32(&s1, b32, NULL);
CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 1);
CHECK(secp256k1_scalar_eq(&s1, &s2) == 1);
memset(b32, 0, sizeof(b32));
CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0);
memset(b32, 0xFF, sizeof(b32));
CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0);
}
static void run_scalar_tests(void) {
int i;
for (i = 0; i < 128 * COUNT; i++) {
scalar_test();
}
for (i = 0; i < COUNT; i++) {
run_scalar_set_b32_seckey_tests();
}
{
/* Check that the scalar constants secp256k1_scalar_zero and
secp256k1_scalar_one contain the expected values. */
secp256k1_scalar zero, one;
CHECK(secp256k1_scalar_is_zero(&secp256k1_scalar_zero));
secp256k1_scalar_set_int(&zero, 0);
CHECK(secp256k1_scalar_eq(&zero, &secp256k1_scalar_zero));
CHECK(secp256k1_scalar_is_one(&secp256k1_scalar_one));
secp256k1_scalar_set_int(&one, 1);
CHECK(secp256k1_scalar_eq(&one, &secp256k1_scalar_one));
}
{
/* (-1)+1 should be zero. */
secp256k1_scalar o;
secp256k1_scalar_negate(&o, &secp256k1_scalar_one);
secp256k1_scalar_add(&o, &o, &secp256k1_scalar_one);
CHECK(secp256k1_scalar_is_zero(&o));
secp256k1_scalar_negate(&o, &o);
CHECK(secp256k1_scalar_is_zero(&o));
}
{
/* Test that halving and doubling roundtrips on some fixed values. */
static const secp256k1_scalar HALF_TESTS[] = {
/* 0 */
SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0),
/* 1 */
SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1),
/* -1 */
SECP256K1_SCALAR_CONST(0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffeul, 0xbaaedce6ul, 0xaf48a03bul, 0xbfd25e8cul, 0xd0364140ul),
/* -2 (largest odd value) */
SECP256K1_SCALAR_CONST(0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffeul, 0xbaaedce6ul, 0xaf48a03bul, 0xbfd25e8cul, 0xd036413Ful),
/* Half the secp256k1 order */
SECP256K1_SCALAR_CONST(0x7ffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0x5d576e73ul, 0x57a4501dul, 0xdfe92f46ul, 0x681b20a0ul),
/* Half the secp256k1 order + 1 */
SECP256K1_SCALAR_CONST(0x7ffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0x5d576e73ul, 0x57a4501dul, 0xdfe92f46ul, 0x681b20a1ul),
/* 2^255 */
SECP256K1_SCALAR_CONST(0x80000000ul, 0, 0, 0, 0, 0, 0, 0),
/* 2^255 - 1 */
SECP256K1_SCALAR_CONST(0x7ffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful, 0xfffffffful),
};
unsigned n;
for (n = 0; n < sizeof(HALF_TESTS) / sizeof(HALF_TESTS[0]); ++n) {
secp256k1_scalar s;
secp256k1_scalar_half(&s, &HALF_TESTS[n]);
secp256k1_scalar_add(&s, &s, &s);
CHECK(secp256k1_scalar_eq(&s, &HALF_TESTS[n]));
secp256k1_scalar_add(&s, &s, &s);
secp256k1_scalar_half(&s, &s);
CHECK(secp256k1_scalar_eq(&s, &HALF_TESTS[n]));
}
}
{
/* 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 r1;
secp256k1_scalar r2;
secp256k1_scalar zzv;
int overflow;
unsigned char chal[33][2][32] = {
{{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
{{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
{0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
{0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
{0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
{0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
{{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
{0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
{{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
{{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
{0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
{{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
{{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
{0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
{{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
{0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
{{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
{0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
{{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
{0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
{{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
{0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
{{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
};
unsigned char res[33][2][32] = {
{{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
{0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
{{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
{0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
{{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
{0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
{{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
{0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
{{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
{0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
{{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
{0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
{{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
{0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
{{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
{0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
{{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
{0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
{{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
{0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
{{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
{0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
{{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
{0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
{{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
{0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
{{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
{0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
{{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
{0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
{{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
{0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
{{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
{0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
{{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
{0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
{{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
{0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
{{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
{0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
{{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
{0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
{{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
{{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
{0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
{{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
{0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
{{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
{0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
{{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
{0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
{{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
{0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
{{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
{0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
{{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
};
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_eq(&r1, &z));
if (!secp256k1_scalar_is_zero(&y)) {
secp256k1_scalar_inverse(&zz, &y);
secp256k1_scalar_inverse_var(&zzv, &y);
CHECK(secp256k1_scalar_eq(&zzv, &zz));
secp256k1_scalar_mul(&z, &z, &zz);
CHECK(secp256k1_scalar_eq(&x, &z));
secp256k1_scalar_mul(&zz, &zz, &y);
CHECK(secp256k1_scalar_eq(&secp256k1_scalar_one, &zz));
}
secp256k1_scalar_mul(&z, &x, &x);
CHECK(secp256k1_scalar_eq(&r2, &z));
}
}
}
/***** FIELD TESTS *****/
static void random_fe_non_square(secp256k1_fe *ns) {
secp256k1_fe r;
testutil_random_fe_non_zero(ns);
if (secp256k1_fe_sqrt(&r, ns)) {
secp256k1_fe_negate(ns, ns, 1);
}
}
static int fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
secp256k1_fe an = *a;
secp256k1_fe bn = *b;
secp256k1_fe_normalize_weak(&an);
return secp256k1_fe_equal(&an, &bn);
}
static 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_limit(&fe2, b32));
CHECK(secp256k1_fe_equal(&fe, &fe2));
secp256k1_fe_from_storage(&fe2, &fes);
CHECK(secp256k1_fe_equal(&fe, &fe2));
/* Check conversion from fe. */
secp256k1_fe_get_b32(b322, &fe);
CHECK(secp256k1_memcmp_var(b322, b32, 32) == 0);
secp256k1_fe_to_storage(&fes2, &fe);
CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0);
}
static void run_field_be32_overflow(void) {
{
static const unsigned char zero_overflow[32] = {
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F,
};
static const unsigned char zero[32] = { 0x00 };
unsigned char out[32];
secp256k1_fe fe;
CHECK(secp256k1_fe_set_b32_limit(&fe, zero_overflow) == 0);
secp256k1_fe_set_b32_mod(&fe, zero_overflow);
CHECK(secp256k1_fe_normalizes_to_zero(&fe) == 1);
secp256k1_fe_normalize(&fe);
CHECK(secp256k1_fe_is_zero(&fe) == 1);
secp256k1_fe_get_b32(out, &fe);
CHECK(secp256k1_memcmp_var(out, zero, 32) == 0);
}
{
static const unsigned char one_overflow[32] = {
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30,
};
static const unsigned char one[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 out[32];
secp256k1_fe fe;
CHECK(secp256k1_fe_set_b32_limit(&fe, one_overflow) == 0);
secp256k1_fe_set_b32_mod(&fe, one_overflow);
secp256k1_fe_normalize(&fe);
CHECK(secp256k1_fe_cmp_var(&fe, &secp256k1_fe_one) == 0);
secp256k1_fe_get_b32(out, &fe);
CHECK(secp256k1_memcmp_var(out, one, 32) == 0);
}
{
static const unsigned char ff_overflow[32] = {
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
};
static const unsigned char ff[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, 0x01, 0x00, 0x00, 0x03, 0xD0,
};
unsigned char out[32];
secp256k1_fe fe;
const secp256k1_fe fe_ff = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0x01, 0x000003d0);
CHECK(secp256k1_fe_set_b32_limit(&fe, ff_overflow) == 0);
secp256k1_fe_set_b32_mod(&fe, ff_overflow);
secp256k1_fe_normalize(&fe);
CHECK(secp256k1_fe_cmp_var(&fe, &fe_ff) == 0);
secp256k1_fe_get_b32(out, &fe);
CHECK(secp256k1_memcmp_var(out, ff, 32) == 0);
}
}
/* Returns true if two field elements have the same representation. */
static int fe_identical(const secp256k1_fe *a, const secp256k1_fe *b) {
int ret = 1;
/* Compare the struct member that holds the limbs. */
ret &= (secp256k1_memcmp_var(a->n, b->n, sizeof(a->n)) == 0);
return ret;
}
static void run_field_half(void) {
secp256k1_fe t, u;
int m;
/* Check magnitude 0 input */
secp256k1_fe_get_bounds(&t, 0);
secp256k1_fe_half(&t);
#ifdef VERIFY
CHECK(t.magnitude == 1);
CHECK(t.normalized == 0);
#endif
CHECK(secp256k1_fe_normalizes_to_zero(&t));
/* Check non-zero magnitudes in the supported range */
for (m = 1; m < 32; m++) {
/* Check max-value input */
secp256k1_fe_get_bounds(&t, m);
u = t;
secp256k1_fe_half(&u);
#ifdef VERIFY
CHECK(u.magnitude == (m >> 1) + 1);
CHECK(u.normalized == 0);
#endif
secp256k1_fe_normalize_weak(&u);
secp256k1_fe_add(&u, &u);
CHECK(fe_equal(&t, &u));
/* Check worst-case input: ensure the LSB is 1 so that P will be added,
* which will also cause all carries to be 1, since all limbs that can
* generate a carry are initially even and all limbs of P are odd in
* every existing field implementation. */
secp256k1_fe_get_bounds(&t, m);
CHECK(t.n[0] > 0);
CHECK((t.n[0] & 1) == 0);
--t.n[0];
u = t;
secp256k1_fe_half(&u);
#ifdef VERIFY
CHECK(u.magnitude == (m >> 1) + 1);
CHECK(u.normalized == 0);
#endif
secp256k1_fe_normalize_weak(&u);
secp256k1_fe_add(&u, &u);
CHECK(fe_equal(&t, &u));
}
}
static void run_field_misc(void) {
secp256k1_fe x;
secp256k1_fe y;
secp256k1_fe z;
secp256k1_fe q;
int v;
secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
int i, j;
for (i = 0; i < 1000 * COUNT; i++) {
secp256k1_fe_storage xs, ys, zs;
if (i & 1) {
testutil_random_fe(&x);
} else {
testutil_random_fe_test(&x);
}
testutil_random_fe_non_zero(&y);
v = testrand_bits(15);
/* Test that fe_add_int is equivalent to fe_set_int + fe_add. */
secp256k1_fe_set_int(&q, v); /* q = v */
z = x; /* z = x */
secp256k1_fe_add(&z, &q); /* z = x+v */
q = x; /* q = x */
secp256k1_fe_add_int(&q, v); /* q = x+v */
CHECK(fe_equal(&q, &z));
/* Test the fe equality and comparison operations. */
CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
CHECK(secp256k1_fe_equal(&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);
CHECK((x.magnitude == q.magnitude) || (x.magnitude == z.magnitude));
CHECK((x.magnitude >= q.magnitude) && (x.magnitude >= z.magnitude));
#endif
x = q;
secp256k1_fe_cmov(&x, &x, 1);
CHECK(!fe_identical(&x, &z));
CHECK(fe_identical(&x, &q));
secp256k1_fe_cmov(&q, &z, 1);
#ifdef VERIFY
CHECK(!q.normalized);
CHECK((q.magnitude == x.magnitude) || (q.magnitude == z.magnitude));
CHECK((q.magnitude >= x.magnitude) && (q.magnitude >= z.magnitude));
#endif
CHECK(fe_identical(&q, &z));
q = z;
secp256k1_fe_normalize_var(&x);
secp256k1_fe_normalize_var(&z);
CHECK(!secp256k1_fe_equal(&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_unchecked(&z, &z, j+1);
secp256k1_fe_normalize_var(&q);
secp256k1_fe_cmov(&q, &z, (j&1));
#ifdef VERIFY
CHECK(!q.normalized && q.magnitude == z.magnitude);
#endif
}
secp256k1_fe_normalize_var(&z);
/* Test storage conversion and conditional moves. */
secp256k1_fe_to_storage(&xs, &x);
secp256k1_fe_to_storage(&ys, &y);
secp256k1_fe_to_storage(&zs, &z);
secp256k1_fe_storage_cmov(&zs, &xs, 0);
secp256k1_fe_storage_cmov(&zs, &zs, 1);
CHECK(secp256k1_memcmp_var(&xs, &zs, sizeof(xs)) != 0);
secp256k1_fe_storage_cmov(&ys, &xs, 1);
CHECK(secp256k1_memcmp_var(&xs, &ys, sizeof(xs)) == 0);
secp256k1_fe_from_storage(&x, &xs);
secp256k1_fe_from_storage(&y, &ys);
secp256k1_fe_from_storage(&z, &zs);
/* Test that mul_int, mul, and add agree. */
secp256k1_fe_add(&y, &x);
secp256k1_fe_add(&y, &x);
z = x;
secp256k1_fe_mul_int(&z, 3);
CHECK(fe_equal(&y, &z));
secp256k1_fe_add(&y, &x);
secp256k1_fe_add(&z, &x);
CHECK(fe_equal(&z, &y));
z = x;
secp256k1_fe_mul_int(&z, 5);
secp256k1_fe_mul(&q, &x, &fe5);
CHECK(fe_equal(&z, &q));
secp256k1_fe_negate(&x, &x, 1);
secp256k1_fe_add(&z, &x);
secp256k1_fe_add(&q, &x);
CHECK(fe_equal(&y, &z));
CHECK(fe_equal(&q, &y));
/* Check secp256k1_fe_half. */
z = x;
secp256k1_fe_half(&z);
secp256k1_fe_add(&z, &z);
CHECK(fe_equal(&x, &z));
secp256k1_fe_add(&z, &z);
secp256k1_fe_half(&z);
CHECK(fe_equal(&x, &z));
}
}
static void test_fe_mul(const secp256k1_fe* a, const secp256k1_fe* b, int use_sqr)
{
secp256k1_fe c, an, bn;
/* Variables in BE 32-byte format. */
unsigned char a32[32], b32[32], c32[32];
/* Variables in LE 16x uint16_t format. */
uint16_t a16[16], b16[16], c16[16];
/* Field modulus in LE 16x uint16_t format. */
static const uint16_t m16[16] = {
0xfc2f, 0xffff, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
};
uint16_t t16[32];
int i;
/* Compute C = A * B in fe format. */
c = *a;
if (use_sqr) {
secp256k1_fe_sqr(&c, &c);
} else {
secp256k1_fe_mul(&c, &c, b);
}
/* Convert A, B, C into LE 16x uint16_t format. */
an = *a;
bn = *b;
secp256k1_fe_normalize_var(&c);
secp256k1_fe_normalize_var(&an);
secp256k1_fe_normalize_var(&bn);
secp256k1_fe_get_b32(a32, &an);
secp256k1_fe_get_b32(b32, &bn);
secp256k1_fe_get_b32(c32, &c);
for (i = 0; i < 16; ++i) {
a16[i] = a32[31 - 2*i] + ((uint16_t)a32[30 - 2*i] << 8);
b16[i] = b32[31 - 2*i] + ((uint16_t)b32[30 - 2*i] << 8);
c16[i] = c32[31 - 2*i] + ((uint16_t)c32[30 - 2*i] << 8);
}
/* Compute T = A * B in LE 16x uint16_t format. */
mulmod256(t16, a16, b16, m16);
/* Compare */
CHECK(secp256k1_memcmp_var(t16, c16, 32) == 0);
}
static void run_fe_mul(void) {
int i;
for (i = 0; i < 100 * COUNT; ++i) {
secp256k1_fe a, b, c, d;
testutil_random_fe(&a);
testutil_random_fe_magnitude(&a, 8);
testutil_random_fe(&b);
testutil_random_fe_magnitude(&b, 8);
testutil_random_fe_test(&c);
testutil_random_fe_magnitude(&c, 8);
testutil_random_fe_test(&d);
testutil_random_fe_magnitude(&d, 8);
test_fe_mul(&a, &a, 1);
test_fe_mul(&c, &c, 1);
test_fe_mul(&a, &b, 0);
test_fe_mul(&a, &c, 0);
test_fe_mul(&c, &b, 0);
test_fe_mul(&c, &d, 0);
}
}
static void run_sqr(void) {
int i;
secp256k1_fe x, y, lhs, rhs, tmp;
secp256k1_fe_set_int(&x, 1);
secp256k1_fe_negate(&x, &x, 1);
for (i = 1; i <= 512; ++i) {
secp256k1_fe_mul_int(&x, 2);
secp256k1_fe_normalize(&x);
/* Check that (x+y)*(x-y) = x^2 - y*2 for some random values y */
testutil_random_fe_test(&y);
lhs = x;
secp256k1_fe_add(&lhs, &y); /* lhs = x+y */
secp256k1_fe_negate(&tmp, &y, 1); /* tmp = -y */
secp256k1_fe_add(&tmp, &x); /* tmp = x-y */
secp256k1_fe_mul(&lhs, &lhs, &tmp); /* lhs = (x+y)*(x-y) */
secp256k1_fe_sqr(&rhs, &x); /* rhs = x^2 */
secp256k1_fe_sqr(&tmp, &y); /* tmp = y^2 */
secp256k1_fe_negate(&tmp, &tmp, 1); /* tmp = -y^2 */
secp256k1_fe_add(&rhs, &tmp); /* rhs = x^2 - y^2 */
CHECK(fe_equal(&lhs, &rhs));
}
}
static void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
secp256k1_fe r1, r2;
int v = secp256k1_fe_sqrt(&r1, a);
CHECK((v == 0) == (k == NULL));
if (k != NULL) {
/* Check that the returned root is +/- the given known answer */
secp256k1_fe_negate(&r2, &r1, 1);
secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k);
secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2);
CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2));
}
}
static void run_sqrt(void) {
secp256k1_fe ns, x, s, t;
int i;
/* Check sqrt(0) is 0 */
secp256k1_fe_set_int(&x, 0);
secp256k1_fe_sqr(&s, &x);
test_sqrt(&s, &x);
/* Check sqrt of small squares (and their negatives) */
for (i = 1; i <= 100; i++) {
secp256k1_fe_set_int(&x, i);
secp256k1_fe_sqr(&s, &x);
test_sqrt(&s, &x);
secp256k1_fe_negate(&t, &s, 1);
test_sqrt(&t, NULL);
}
/* Consistency checks for large random values */
for (i = 0; i < 10; i++) {
int j;
random_fe_non_square(&ns);
for (j = 0; j < COUNT; j++) {
testutil_random_fe(&x);
secp256k1_fe_sqr(&s, &x);
CHECK(secp256k1_fe_is_square_var(&s));
test_sqrt(&s, &x);
secp256k1_fe_negate(&t, &s, 1);
CHECK(!secp256k1_fe_is_square_var(&t));
test_sqrt(&t, NULL);
secp256k1_fe_mul(&t, &s, &ns);
test_sqrt(&t, NULL);
}
}
}
/***** FIELD/SCALAR INVERSE TESTS *****/
static const secp256k1_scalar scalar_minus_one = SECP256K1_SCALAR_CONST(
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE,
0xBAAEDCE6, 0xAF48A03B, 0xBFD25E8C, 0xD0364140
);
static const secp256k1_fe fe_minus_one = SECP256K1_FE_CONST(
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFC2E
);
/* These tests test the following identities:
*
* for x==0: 1/x == 0
* for x!=0: x*(1/x) == 1
* for x!=0 and x!=1: 1/(1/x - 1) + 1 == -1/(x-1)
*/
static void test_inverse_scalar(secp256k1_scalar* out, const secp256k1_scalar* x, int var)
{
secp256k1_scalar l, r, t;
(var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, x); /* l = 1/x */
if (out) *out = l;
if (secp256k1_scalar_is_zero(x)) {
CHECK(secp256k1_scalar_is_zero(&l));
return;
}
secp256k1_scalar_mul(&t, x, &l); /* t = x*(1/x) */
CHECK(secp256k1_scalar_is_one(&t)); /* x*(1/x) == 1 */
secp256k1_scalar_add(&r, x, &scalar_minus_one); /* r = x-1 */
if (secp256k1_scalar_is_zero(&r)) return;
(var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&r, &r); /* r = 1/(x-1) */
secp256k1_scalar_add(&l, &scalar_minus_one, &l); /* l = 1/x-1 */
(var ? secp256k1_scalar_inverse_var : secp256k1_scalar_inverse)(&l, &l); /* l = 1/(1/x-1) */
secp256k1_scalar_add(&l, &l, &secp256k1_scalar_one); /* l = 1/(1/x-1)+1 */
secp256k1_scalar_add(&l, &r, &l); /* l = 1/(1/x-1)+1 + 1/(x-1) */
CHECK(secp256k1_scalar_is_zero(&l)); /* l == 0 */
}
static void test_inverse_field(secp256k1_fe* out, const secp256k1_fe* x, int var)
{
secp256k1_fe l, r, t;
(var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&l, x) ; /* l = 1/x */
if (out) *out = l;
t = *x; /* t = x */
if (secp256k1_fe_normalizes_to_zero_var(&t)) {
CHECK(secp256k1_fe_normalizes_to_zero(&l));
return;
}
secp256k1_fe_mul(&t, x, &l); /* t = x*(1/x) */
secp256k1_fe_add(&t, &fe_minus_one); /* t = x*(1/x)-1 */
CHECK(secp256k1_fe_normalizes_to_zero(&t)); /* x*(1/x)-1 == 0 */
r = *x; /* r = x */
secp256k1_fe_add(&r, &fe_minus_one); /* r = x-1 */
if (secp256k1_fe_normalizes_to_zero_var(&r)) return;
(var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&r, &r); /* r = 1/(x-1) */
secp256k1_fe_add(&l, &fe_minus_one); /* l = 1/x-1 */
(var ? secp256k1_fe_inv_var : secp256k1_fe_inv)(&l, &l); /* l = 1/(1/x-1) */
secp256k1_fe_add_int(&l, 1); /* l = 1/(1/x-1)+1 */
secp256k1_fe_add(&l, &r); /* l = 1/(1/x-1)+1 + 1/(x-1) */
CHECK(secp256k1_fe_normalizes_to_zero_var(&l)); /* l == 0 */
}
static void run_inverse_tests(void)
{
/* Fixed test cases for field inverses: pairs of (x, 1/x) mod p. */
static const secp256k1_fe fe_cases[][2] = {
/* 0 */
{SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0),
SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)},
/* 1 */
{SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1),
SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1)},
/* -1 */
{SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e),
SECP256K1_FE_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xfffffc2e)},
/* 2 */
{SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2),
SECP256K1_FE_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7ffffe18)},
/* 2**128 */
{SECP256K1_FE_CONST(0, 0, 0, 1, 0, 0, 0, 0),
SECP256K1_FE_CONST(0xbcb223fe, 0xdc24a059, 0xd838091d, 0xd2253530, 0xffffffff, 0xffffffff, 0xffffffff, 0x434dd931)},
/* Input known to need 637 divsteps */
{SECP256K1_FE_CONST(0xe34e9c95, 0x6bee8a84, 0x0dcb632a, 0xdb8a1320, 0x66885408, 0x06f3f996, 0x7c11ca84, 0x19199ec3),
SECP256K1_FE_CONST(0xbd2cbd8f, 0x1c536828, 0x9bccda44, 0x2582ac0c, 0x870152b0, 0x8a3f09fb, 0x1aaadf92, 0x19b618e5)},
/* Input known to need 567 divsteps starting with delta=1/2. */
{SECP256K1_FE_CONST(0xf6bc3ba3, 0x636451c4, 0x3e46357d, 0x2c21d619, 0x0988e234, 0x15985661, 0x6672982b, 0xa7549bfc),
SECP256K1_FE_CONST(0xb024fdc7, 0x5547451e, 0x426c585f, 0xbd481425, 0x73df6b75, 0xeef6d9d0, 0x389d87d4, 0xfbb440ba)},
/* Input known to need 566 divsteps starting with delta=1/2. */
{SECP256K1_FE_CONST(0xb595d81b, 0x2e3c1e2f, 0x482dbc65, 0xe4865af7, 0x9a0a50aa, 0x29f9e618, 0x6f87d7a5, 0x8d1063ae),
SECP256K1_FE_CONST(0xc983337c, 0x5d5c74e1, 0x49918330, 0x0b53afb5, 0xa0428a0b, 0xce6eef86, 0x059bd8ef, 0xe5b908de)},
/* Set of 10 inputs accessing all 128 entries in the modinv32 divsteps_var table */
{SECP256K1_FE_CONST(0x00000000, 0x00000000, 0xe0ff1f80, 0x1f000000, 0x00000000, 0x00000000, 0xfeff0100, 0x00000000),
SECP256K1_FE_CONST(0x9faf9316, 0x77e5049d, 0x0b5e7a1b, 0xef70b893, 0x18c9e30c, 0x045e7fd7, 0x29eddf8c, 0xd62e9e3d)},
{SECP256K1_FE_CONST(0x621a538d, 0x511b2780, 0x35688252, 0x53f889a4, 0x6317c3ac, 0x32ba0a46, 0x6277c0d1, 0xccd31192),
SECP256K1_FE_CONST(0x38513b0c, 0x5eba856f, 0xe29e882e, 0x9b394d8c, 0x34bda011, 0xeaa66943, 0x6a841a4c, 0x6ae8bcff)},
{SECP256K1_FE_CONST(0x00000200, 0xf0ffff1f, 0x00000000, 0x0000e0ff, 0xffffffff, 0xfffcffff, 0xffffffff, 0xffff0100),
SECP256K1_FE_CONST(0x5da42a52, 0x3640de9e, 0x13e64343, 0x0c7591b7, 0x6c1e3519, 0xf048c5b6, 0x0484217c, 0xedbf8b2f)},
{SECP256K1_FE_CONST(0xd1343ef9, 0x4b952621, 0x7c52a2ee, 0x4ea1281b, 0x4ab46410, 0x9f26998d, 0xa686a8ff, 0x9f2103e8),
SECP256K1_FE_CONST(0x84044385, 0x9a4619bf, 0x74e35b6d, 0xa47e0c46, 0x6b7fb47d, 0x9ffab128, 0xb0775aa3, 0xcb318bd1)},
{SECP256K1_FE_CONST(0xb27235d2, 0xc56a52be, 0x210db37a, 0xd50d23a4, 0xbe621bdd, 0x5df22c6a, 0xe926ba62, 0xd2e4e440),
SECP256K1_FE_CONST(0x67a26e54, 0x483a9d3c, 0xa568469e, 0xd258ab3d, 0xb9ec9981, 0xdca9b1bd, 0x8d2775fe, 0x53ae429b)},
{SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00e0ffff, 0xffffff83, 0xffffffff, 0x3f00f00f, 0x000000e0, 0xffffffff),
SECP256K1_FE_CONST(0x310e10f8, 0x23bbfab0, 0xac94907d, 0x076c9a45, 0x8d357d7f, 0xc763bcee, 0x00d0e615, 0x5a6acef6)},
{SECP256K1_FE_CONST(0xfeff0300, 0x001c0000, 0xf80700c0, 0x0ff0ffff, 0xffffffff, 0x0fffffff, 0xffff0100, 0x7f0000fe),
SECP256K1_FE_CONST(0x28e2fdb4, 0x0709168b, 0x86f598b0, 0x3453a370, 0x530cf21f, 0x32f978d5, 0x1d527a71, 0x59269b0c)},
{SECP256K1_FE_CONST(0xc2591afa, 0x7bb98ef7, 0x090bb273, 0x85c14f87, 0xbb0b28e0, 0x54d3c453, 0x85c66753, 0xd5574d2f),
SECP256K1_FE_CONST(0xfdca70a2, 0x70ce627c, 0x95e66fae, 0x848a6dbb, 0x07ffb15c, 0x5f63a058, 0xba4140ed, 0x6113b503)},
{SECP256K1_FE_CONST(0xf5475db3, 0xedc7b5a3, 0x411c047e, 0xeaeb452f, 0xc625828e, 0x1cf5ad27, 0x8eec1060, 0xc7d3e690),
SECP256K1_FE_CONST(0x5eb756c0, 0xf963f4b9, 0xdc6a215e, 0xec8cc2d8, 0x2e9dec01, 0xde5eb88d, 0x6aba7164, 0xaecb2c5a)},
{SECP256K1_FE_CONST(0x00000000, 0x00f8ffff, 0xffffffff, 0x01000000, 0xe0ff1f00, 0x00000000, 0xffffff7f, 0x00000000),
SECP256K1_FE_CONST(0xe0d2e3d8, 0x49b6157d, 0xe54e88c2, 0x1a7f02ca, 0x7dd28167, 0xf1125d81, 0x7bfa444e, 0xbe110037)},
/* Selection of randomly generated inputs that reach high/low d/e values in various configurations. */
{SECP256K1_FE_CONST(0x13cc08a4, 0xd8c41f0f, 0x179c3e67, 0x54c46c67, 0xc4109221, 0x09ab3b13, 0xe24d9be1, 0xffffe950),
SECP256K1_FE_CONST(0xb80c8006, 0xd16abaa7, 0xcabd71e5, 0xcf6714f4, 0x966dd3d0, 0x64767a2d, 0xe92c4441, 0x51008cd1)},
{SECP256K1_FE_CONST(0xaa6db990, 0x95efbca1, 0x3cc6ff71, 0x0602e24a, 0xf49ff938, 0x99fffc16, 0x46f40993, 0xc6e72057),
SECP256K1_FE_CONST(0xd5d3dd69, 0xb0c195e5, 0x285f1d49, 0xe639e48c, 0x9223f8a9, 0xca1d731d, 0x9ca482f9, 0xa5b93e06)},
{SECP256K1_FE_CONST(0x1c680eac, 0xaeabffd8, 0x9bdc4aee, 0x1781e3de, 0xa3b08108, 0x0015f2e0, 0x94449e1b, 0x2f67a058),
SECP256K1_FE_CONST(0x7f083f8d, 0x31254f29, 0x6510f475, 0x245c373d, 0xc5622590, 0x4b323393, 0x32ed1719, 0xc127444b)},
{SECP256K1_FE_CONST(0x147d44b3, 0x012d83f8, 0xc160d386, 0x1a44a870, 0x9ba6be96, 0x8b962707, 0x267cbc1a, 0xb65b2f0a),
SECP256K1_FE_CONST(0x555554ff, 0x170aef1e, 0x50a43002, 0xe51fbd36, 0xafadb458, 0x7a8aded1, 0x0ca6cd33, 0x6ed9087c)},
{SECP256K1_FE_CONST(0x12423796, 0x22f0fe61, 0xf9ca017c, 0x5384d107, 0xa1fbf3b2, 0x3b018013, 0x916a3c37, 0x4000b98c),
SECP256K1_FE_CONST(0x20257700, 0x08668f94, 0x1177e306, 0x136c01f5, 0x8ed1fbd2, 0x95ec4589, 0xae38edb9, 0xfd19b6d7)},
{SECP256K1_FE_CONST(0xdcf2d030, 0x9ab42cb4, 0x93ffa181, 0xdcd23619, 0x39699b52, 0x08909a20, 0xb5a17695, 0x3a9dcf21),
SECP256K1_FE_CONST(0x1f701dea, 0xe211fb1f, 0x4f37180d, 0x63a0f51c, 0x29fe1e40, 0xa40b6142, 0x2e7b12eb, 0x982b06b6)},
{SECP256K1_FE_CONST(0x79a851f6, 0xa6314ed3, 0xb35a55e6, 0xca1c7d7f, 0xe32369ea, 0xf902432e, 0x375308c5, 0xdfd5b600),
SECP256K1_FE_CONST(0xcaae00c5, 0xe6b43851, 0x9dabb737, 0x38cba42c, 0xa02c8549, 0x7895dcbf, 0xbd183d71, 0xafe4476a)},
{SECP256K1_FE_CONST(0xede78fdd, 0xcfc92bf1, 0x4fec6c6c, 0xdb8d37e2, 0xfb66bc7b, 0x28701870, 0x7fa27c9a, 0x307196ec),
SECP256K1_FE_CONST(0x68193a6c, 0x9a8b87a7, 0x2a760c64, 0x13e473f6, 0x23ae7bed, 0x1de05422, 0x88865427, 0xa3418265)},
{SECP256K1_FE_CONST(0xa40b2079, 0xb8f88e89, 0xa7617997, 0x89baf5ae, 0x174df343, 0x75138eae, 0x2711595d, 0x3fc3e66c),
SECP256K1_FE_CONST(0x9f99c6a5, 0x6d685267, 0xd4b87c37, 0x9d9c4576, 0x358c692b, 0x6bbae0ed, 0x3389c93d, 0x7fdd2655)},
{SECP256K1_FE_CONST(0x7c74c6b6, 0xe98d9151, 0x72645cf1, 0x7f06e321, 0xcefee074, 0x15b2113a, 0x10a9be07, 0x08a45696),
SECP256K1_FE_CONST(0x8c919a88, 0x898bc1e0, 0x77f26f97, 0x12e655b7, 0x9ba0ac40, 0xe15bb19e, 0x8364cc3b, 0xe227a8ee)},
{SECP256K1_FE_CONST(0x109ba1ce, 0xdafa6d4a, 0xa1cec2b2, 0xeb1069f4, 0xb7a79e5b, 0xec6eb99b, 0xaec5f643, 0xee0e723e),
SECP256K1_FE_CONST(0x93d13eb8, 0x4bb0bcf9, 0xe64f5a71, 0xdbe9f359, 0x7191401c, 0x6f057a4a, 0xa407fe1b, 0x7ecb65cc)},
{SECP256K1_FE_CONST(0x3db076cd, 0xec74a5c9, 0xf61dd138, 0x90e23e06, 0xeeedd2d0, 0x74cbc4e0, 0x3dbe1e91, 0xded36a78),
SECP256K1_FE_CONST(0x3f07f966, 0x8e2a1e09, 0x706c71df, 0x02b5e9d5, 0xcb92ddbf, 0xcdd53010, 0x16545564, 0xe660b107)},
{SECP256K1_FE_CONST(0xe31c73ed, 0xb4c4b82c, 0x02ae35f7, 0x4cdec153, 0x98b522fd, 0xf7d2460c, 0x6bf7c0f8, 0x4cf67b0d),
SECP256K1_FE_CONST(0x4b8f1faf, 0x94e8b070, 0x19af0ff6, 0xa319cd31, 0xdf0a7ffb, 0xefaba629, 0x59c50666, 0x1fe5b843)},
{SECP256K1_FE_CONST(0x4c8b0e6e, 0x83392ab6, 0xc0e3e9f1, 0xbbd85497, 0x16698897, 0xf552d50d, 0x79652ddb, 0x12f99870),
SECP256K1_FE_CONST(0x56d5101f, 0xd23b7949, 0x17dc38d6, 0xf24022ef, 0xcf18e70a, 0x5cc34424, 0x438544c3, 0x62da4bca)},
{SECP256K1_FE_CONST(0xb0e040e2, 0x40cc35da, 0x7dd5c611, 0x7fccb178, 0x28888137, 0xbc930358, 0xea2cbc90, 0x775417dc),
SECP256K1_FE_CONST(0xca37f0d4, 0x016dd7c8, 0xab3ae576, 0x96e08d69, 0x68ed9155, 0xa9b44270, 0x900ae35d, 0x7c7800cd)},
{SECP256K1_FE_CONST(0x8a32ea49, 0x7fbb0bae, 0x69724a9d, 0x8e2105b2, 0xbdf69178, 0x862577ef, 0x35055590, 0x667ddaef),
SECP256K1_FE_CONST(0xd02d7ead, 0xc5e190f0, 0x559c9d72, 0xdaef1ffc, 0x64f9f425, 0xf43645ea, 0x7341e08d, 0x11768e96)},
{SECP256K1_FE_CONST(0xa3592d98, 0x9abe289d, 0x579ebea6, 0xbb0857a8, 0xe242ab73, 0x85f9a2ce, 0xb6998f0f, 0xbfffbfc6),
SECP256K1_FE_CONST(0x093c1533, 0x32032efa, 0x6aa46070, 0x0039599e, 0x589c35f4, 0xff525430, 0x7fe3777a, 0x44b43ddc)},
{SECP256K1_FE_CONST(0x647178a3, 0x229e607b, 0xcc98521a, 0xcce3fdd9, 0x1e1bc9c9, 0x97fb7c6a, 0x61b961e0, 0x99b10709),
SECP256K1_FE_CONST(0x98217c13, 0xd51ddf78, 0x96310e77, 0xdaebd908, 0x602ca683, 0xcb46d07a, 0xa1fcf17e, 0xc8e2feb3)},
{SECP256K1_FE_CONST(0x7334627c, 0x73f98968, 0x99464b4b, 0xf5964958, 0x1b95870d, 0xc658227e, 0x5e3235d8, 0xdcab5787),
SECP256K1_FE_CONST(0x000006fd, 0xc7e9dd94, 0x40ae367a, 0xe51d495c, 0x07603b9b, 0x2d088418, 0x6cc5c74c, 0x98514307)},
{SECP256K1_FE_CONST(0x82e83876, 0x96c28938, 0xa50dd1c5, 0x605c3ad1, 0xc048637d, 0x7a50825f, 0x335ed01a, 0x00005760),
SECP256K1_FE_CONST(0xb0393f9f, 0x9f2aa55e, 0xf5607e2e, 0x5287d961, 0x60b3e704, 0xf3e16e80, 0xb4f9a3ea, 0xfec7f02d)},
{SECP256K1_FE_CONST(0xc97b6cec, 0x3ee6b8dc, 0x98d24b58, 0x3c1970a1, 0xfe06297a, 0xae813529, 0xe76bb6bd, 0x771ae51d),
SECP256K1_FE_CONST(0x0507c702, 0xd407d097, 0x47ddeb06, 0xf6625419, 0x79f48f79, 0x7bf80d0b, 0xfc34b364, 0x253a5db1)},
{SECP256K1_FE_CONST(0xd559af63, 0x77ea9bc4, 0x3cf1ad14, 0x5c7a4bbb, 0x10e7d18b, 0x7ce0dfac, 0x380bb19d, 0x0bb99bd3),
SECP256K1_FE_CONST(0x00196119, 0xb9b00d92, 0x34edfdb5, 0xbbdc42fc, 0xd2daa33a, 0x163356ca, 0xaa8754c8, 0xb0ec8b0b)},
{SECP256K1_FE_CONST(0x8ddfa3dc, 0x52918da0, 0x640519dc, 0x0af8512a, 0xca2d33b2, 0xbde52514, 0xda9c0afc, 0xcb29fce4),
SECP256K1_FE_CONST(0xb3e4878d, 0x5cb69148, 0xcd54388b, 0xc23acce0, 0x62518ba8, 0xf09def92, 0x7b31e6aa, 0x6ba35b02)},
{SECP256K1_FE_CONST(0xf8207492, 0xe3049f0a, 0x65285f2b, 0x0bfff996, 0x00ca112e, 0xc05da837, 0x546d41f9, 0x5194fb91),
SECP256K1_FE_CONST(0x7b7ee50b, 0xa8ed4bbd, 0xf6469930, 0x81419a5c, 0x071441c7, 0x290d046e, 0x3b82ea41, 0x611c5f95)},
{SECP256K1_FE_CONST(0x050f7c80, 0x5bcd3c6b, 0x823cb724, 0x5ce74db7, 0xa4e39f5c, 0xbd8828d7, 0xfd4d3e07, 0x3ec2926a),
SECP256K1_FE_CONST(0x000d6730, 0xb0171314, 0x4764053d, 0xee157117, 0x48fd61da, 0xdea0b9db, 0x1d5e91c6, 0xbdc3f59e)},
{SECP256K1_FE_CONST(0x3e3ea8eb, 0x05d760cf, 0x23009263, 0xb3cb3ac9, 0x088f6f0d, 0x3fc182a3, 0xbd57087c, 0xe67c62f9),
SECP256K1_FE_CONST(0xbe988716, 0xa29c1bf6, 0x4456aed6, 0xab1e4720, 0x49929305, 0x51043bf4, 0xebd833dd, 0xdd511e8b)},
{SECP256K1_FE_CONST(0x6964d2a9, 0xa7fa6501, 0xa5959249, 0x142f4029, 0xea0c1b5f, 0x2f487ef6, 0x301ac80a, 0x768be5cd),
SECP256K1_FE_CONST(0x3918ffe4, 0x07492543, 0xed24d0b7, 0x3df95f8f, 0xaffd7cb4, 0x0de2191c, 0x9ec2f2ad, 0x2c0cb3c6)},
{SECP256K1_FE_CONST(0x37c93520, 0xf6ddca57, 0x2b42fd5e, 0xb5c7e4de, 0x11b5b81c, 0xb95e91f3, 0x95c4d156, 0x39877ccb),
SECP256K1_FE_CONST(0x9a94b9b5, 0x57eb71ee, 0x4c975b8b, 0xac5262a8, 0x077b0595, 0xe12a6b1f, 0xd728edef, 0x1a6bf956)}
};
/* Fixed test cases for scalar inverses: pairs of (x, 1/x) mod n. */
static const secp256k1_scalar scalar_cases[][2] = {
/* 0 */
{SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0),
SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0)},
/* 1 */
{SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1),
SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1)},
/* -1 */
{SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140),
SECP256K1_SCALAR_CONST(0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe, 0xbaaedce6, 0xaf48a03b, 0xbfd25e8c, 0xd0364140)},
/* 2 */
{SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 2),
SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x5d576e73, 0x57a4501d, 0xdfe92f46, 0x681b20a1)},
/* 2**128 */
{SECP256K1_SCALAR_CONST(0, 0, 0, 1, 0, 0, 0, 0),
SECP256K1_SCALAR_CONST(0x50a51ac8, 0x34b9ec24, 0x4b0dff66, 0x5588b13e, 0x9984d5b3, 0xcf80ef0f, 0xd6a23766, 0xa3ee9f22)},
/* Input known to need 635 divsteps */
{SECP256K1_SCALAR_CONST(0xcb9f1d35, 0xdd4416c2, 0xcd71bf3f, 0x6365da66, 0x3c9b3376, 0x8feb7ae9, 0x32a5ef60, 0x19199ec3),
SECP256K1_SCALAR_CONST(0x1d7c7bba, 0xf1893d53, 0xb834bd09, 0x36b411dc, 0x42c2e42f, 0xec72c428, 0x5e189791, 0x8e9bc708)},
/* Input known to need 566 divsteps starting with delta=1/2. */
{SECP256K1_SCALAR_CONST(0x7e3c993d, 0xa4272488, 0xbc015b49, 0x2db54174, 0xd382083a, 0xebe6db35, 0x80f82eff, 0xcd132c72),
SECP256K1_SCALAR_CONST(0x086f34a0, 0x3e631f76, 0x77418f28, 0xcc84ac95, 0x6304439d, 0x365db268, 0x312c6ded, 0xd0b934f8)},
/* Input known to need 565 divsteps starting with delta=1/2. */
{SECP256K1_SCALAR_CONST(0xbad7e587, 0x3f307859, 0x60d93147, 0x8a18491e, 0xb38a9fd5, 0x254350d3, 0x4b1f0e4b, 0x7dd6edc4),
SECP256K1_SCALAR_CONST(0x89f2df26, 0x39e2b041, 0xf19bd876, 0xd039c8ac, 0xc2223add, 0x29c4943e, 0x6632d908, 0x515f467b)},
/* Selection of randomly generated inputs that reach low/high d/e values in various configurations. */
{SECP256K1_SCALAR_CONST(0x1950d757, 0xb37a5809, 0x435059bb, 0x0bb8997e, 0x07e1e3c8, 0x5e5d7d2c, 0x6a0ed8e3, 0xdbde180e),
SECP256K1_SCALAR_CONST(0xbf72af9b, 0x750309e2, 0x8dda230b, 0xfe432b93, 0x7e25e475, 0x4388251e, 0x633d894b, 0x3bcb6f8c)},
{SECP256K1_SCALAR_CONST(0x9bccf4e7, 0xc5a515e3, 0x50637aa9, 0xbb65a13f, 0x391749a1, 0x62de7d4e, 0xf6d7eabb, 0x3cd10ce0),
SECP256K1_SCALAR_CONST(0xaf2d5623, 0xb6385a33, 0xcd0365be, 0x5e92a70d, 0x7f09179c, 0x3baaf30f, 0x8f9cc83b, 0x20092f67)},
{SECP256K1_SCALAR_CONST(0x73a57111, 0xb242952a, 0x5c5dee59, 0xf3be2ace, 0xa30a7659, 0xa46e5f47, 0xd21267b1, 0x39e642c9),
SECP256K1_SCALAR_CONST(0xa711df07, 0xcbcf13ef, 0xd61cc6be, 0xbcd058ce, 0xb02cf157, 0x272d4a18, 0x86d0feb3, 0xcd5fa004)},
{SECP256K1_SCALAR_CONST(0x04884963, 0xce0580b1, 0xba547030, 0x3c691db3, 0x9cd2c84f, 0x24c7cebd, 0x97ebfdba, 0x3e785ec2),
SECP256K1_SCALAR_CONST(0xaaaaaf14, 0xd7c99ba7, 0x517ce2c1, 0x78a28b4c, 0x3769a851, 0xe5c5a03d, 0x4cc28f33, 0x0ec4dc5d)},
{SECP256K1_SCALAR_CONST(0x1679ed49, 0x21f537b1, 0x815cb8ae, 0x9efc511c, 0x5b9fa037, 0x0b0f275e, 0x6c985281, 0x6c4a9905),
SECP256K1_SCALAR_CONST(0xb14ac3d5, 0x62b52999, 0xef34ead1, 0xffca4998, 0x0294341a, 0x1f8172aa, 0xea1624f9, 0x302eea62)},
{SECP256K1_SCALAR_CONST(0x626b37c0, 0xf0057c35, 0xee982f83, 0x452a1fd3, 0xea826506, 0x48b08a9d, 0x1d2c4799, 0x4ad5f6ec),
SECP256K1_SCALAR_CONST(0xe38643b7, 0x567bfc2f, 0x5d2f1c15, 0xe327239c, 0x07112443, 0x69509283, 0xfd98e77a, 0xdb71c1e8)},
{SECP256K1_SCALAR_CONST(0x1850a3a7, 0x759efc56, 0x54f287b2, 0x14d1234b, 0xe263bbc9, 0xcf4d8927, 0xd5f85f27, 0x965bd816),
SECP256K1_SCALAR_CONST(0x3b071831, 0xcac9619a, 0xcceb0596, 0xf614d63b, 0x95d0db2f, 0xc6a00901, 0x8eaa2621, 0xabfa0009)},
{SECP256K1_SCALAR_CONST(0x94ae5d06, 0xa27dc400, 0x487d72be, 0xaa51ebed, 0xe475b5c0, 0xea675ffc, 0xf4df627a, 0xdca4222f),
SECP256K1_SCALAR_CONST(0x01b412ed, 0xd7830956, 0x1532537e, 0xe5e3dc99, 0x8fd3930a, 0x54f8d067, 0x32ef5760, 0x594438a5)},
{SECP256K1_SCALAR_CONST(0x1f24278a, 0xb5bfe374, 0xa328dbbc, 0xebe35f48, 0x6620e009, 0xd58bb1b4, 0xb5a6bf84, 0x8815f63a),
SECP256K1_SCALAR_CONST(0xfe928416, 0xca5ba2d3, 0xfde513da, 0x903a60c7, 0x9e58ad8a, 0x8783bee4, 0x083a3843, 0xa608c914)},
{SECP256K1_SCALAR_CONST(0xdc107d58, 0x274f6330, 0x67dba8bc, 0x26093111, 0x5201dfb8, 0x968ce3f5, 0xf34d1bd4, 0xf2146504),
SECP256K1_SCALAR_CONST(0x660cfa90, 0x13c3d93e, 0x7023b1e5, 0xedd09e71, 0x6d9c9d10, 0x7a3d2cdb, 0xdd08edc3, 0xaa78fcfb)},
{SECP256K1_SCALAR_CONST(0x7cd1e905, 0xc6f02776, 0x2f551cc7, 0x5da61cff, 0x7da05389, 0x1119d5a4, 0x631c7442, 0x894fd4f7),
SECP256K1_SCALAR_CONST(0xff20862a, 0x9d3b1a37, 0x1628803b, 0x3004ccae, 0xaa23282a, 0xa89a1109, 0xd94ece5e, 0x181bdc46)},
{SECP256K1_SCALAR_CONST(0x5b9dade8, 0x23d26c58, 0xcd12d818, 0x25b8ae97, 0x3dea04af, 0xf482c96b, 0xa062f254, 0x9e453640),
SECP256K1_SCALAR_CONST(0x50c38800, 0x15fa53f4, 0xbe1e5392, 0x5c9b120a, 0x262c22c7, 0x18fa0816, 0x5f2baab4, 0x8cb5db46)},
{SECP256K1_SCALAR_CONST(0x11cdaeda, 0x969c464b, 0xef1f4ab0, 0x5b01d22e, 0x656fd098, 0x882bea84, 0x65cdbe7a, 0x0c19ff03),
SECP256K1_SCALAR_CONST(0x1968d0fa, 0xac46f103, 0xb55f1f72, 0xb3820bed, 0xec6b359a, 0x4b1ae0ad, 0x7e38e1fb, 0x295ccdfb)},
{SECP256K1_SCALAR_CONST(0x2c351aa1, 0x26e91589, 0x194f8a1e, 0x06561f66, 0x0cb97b7f, 0x10914454, 0x134d1c03, 0x157266b4),
SECP256K1_SCALAR_CONST(0xbe49ada6, 0x92bd8711, 0x41b176c4, 0xa478ba95, 0x14883434, 0x9d1cd6f3, 0xcc4b847d, 0x22af80f5)},
{SECP256K1_SCALAR_CONST(0x6ba07c6e, 0x13a60edb, 0x6247f5c3, 0x84b5fa56, 0x76fe3ec5, 0x80426395, 0xf65ec2ae, 0x623ba730),
SECP256K1_SCALAR_CONST(0x25ac23f7, 0x418cd747, 0x98376f9d, 0x4a11c7bf, 0x24c8ebfe, 0x4c8a8655, 0x345f4f52, 0x1c515595)},
{SECP256K1_SCALAR_CONST(0x9397a712, 0x8abb6951, 0x2d4a3d54, 0x703b1c2a, 0x0661dca8, 0xd75c9b31, 0xaed4d24b, 0xd2ab2948),
SECP256K1_SCALAR_CONST(0xc52e8bef, 0xd55ce3eb, 0x1c897739, 0xeb9fb606, 0x36b9cd57, 0x18c51cc2, 0x6a87489e, 0xffd0dcf3)},
{SECP256K1_SCALAR_CONST(0xe6a808cc, 0xeb437888, 0xe97798df, 0x4e224e44, 0x7e3b380a, 0x207c1653, 0x889f3212, 0xc6738b6f),
SECP256K1_SCALAR_CONST(0x31f9ae13, 0xd1e08b20, 0x757a2e5e, 0x5243a0eb, 0x8ae35f73, 0x19bb6122, 0xb910f26b, 0xda70aa55)},
{SECP256K1_SCALAR_CONST(0xd0320548, 0xab0effe7, 0xa70779e0, 0x61a347a6, 0xb8c1e010, 0x9d5281f8, 0x2ee588a6, 0x80000000),
SECP256K1_SCALAR_CONST(0x1541897e, 0x78195c90, 0x7583dd9e, 0x728b6100, 0xbce8bc6d, 0x7a53b471, 0x5dcd9e45, 0x4425fcaf)},
{SECP256K1_SCALAR_CONST(0x93d623f1, 0xd45b50b0, 0x796e9186, 0x9eac9407, 0xd30edc20, 0xef6304cf, 0x250494e7, 0xba503de9),
SECP256K1_SCALAR_CONST(0x7026d638, 0x1178b548, 0x92043952, 0x3c7fb47c, 0xcd3ea236, 0x31d82b01, 0x612fc387, 0x80b9b957)},
{SECP256K1_SCALAR_CONST(0xf860ab39, 0x55f5d412, 0xa4d73bcc, 0x3b48bd90, 0xc248ffd3, 0x13ca10be, 0x8fba84cc, 0xdd28d6a3),
SECP256K1_SCALAR_CONST(0x5c32fc70, 0xe0b15d67, 0x76694700, 0xfe62be4d, 0xeacdb229, 0x7a4433d9, 0x52155cd0, 0x7649ab59)},
{SECP256K1_SCALAR_CONST(0x4e41311c, 0x0800af58, 0x7a690a8e, 0xe175c9ba, 0x6981ab73, 0xac532ea8, 0x5c1f5e63, 0x6ac1f189),
SECP256K1_SCALAR_CONST(0xfffffff9, 0xd075982c, 0x7fbd3825, 0xc05038a2, 0x4533b91f, 0x94ec5f45, 0xb280b28f, 0x842324dc)},
{SECP256K1_SCALAR_CONST(0x48e473bf, 0x3555eade, 0xad5d7089, 0x2424c4e4, 0x0a99397c, 0x2dc796d8, 0xb7a43a69, 0xd0364141),
SECP256K1_SCALAR_CONST(0x634976b2, 0xa0e47895, 0x1ec38593, 0x266d6fd0, 0x6f602644, 0x9bb762f1, 0x7180c704, 0xe23a4daa)},
{SECP256K1_SCALAR_CONST(0xbe83878d, 0x3292fc54, 0x26e71c62, 0x556ccedc, 0x7cbb8810, 0x4032a720, 0x34ead589, 0xe4d6bd13),
SECP256K1_SCALAR_CONST(0x6cd150ad, 0x25e59d0f, 0x74cbae3d, 0x6377534a, 0x1e6562e8, 0xb71b9d18, 0xe1e5d712, 0x8480abb3)},
{SECP256K1_SCALAR_CONST(0xcdddf2e5, 0xefc15f88, 0xc9ee06de, 0x8a846ca9, 0x28561581, 0x68daa5fb, 0xd1cf3451, 0xeb1782d0),
SECP256K1_SCALAR_CONST(0xffffffd9, 0xed8d2af4, 0x993c865a, 0x23e9681a, 0x3ca3a3dc, 0xe6d5a46e, 0xbd86bd87, 0x61b55c70)},
{SECP256K1_SCALAR_CONST(0xb6a18f1f, 0x04872df9, 0x08165ec4, 0x319ca19c, 0x6c0359ab, 0x1f7118fb, 0xc2ef8082, 0xca8b7785),
SECP256K1_SCALAR_CONST(0xff55b19b, 0x0f1ac78c, 0x0f0c88c2, 0x2358d5ad, 0x5f455e4e, 0x3330b72f, 0x274dc153, 0xffbf272b)},
{SECP256K1_SCALAR_CONST(0xea4898e5, 0x30eba3e8, 0xcf0e5c3d, 0x06ec6844, 0x01e26fb6, 0x75636225, 0xc5d08f4c, 0x1decafa0),
SECP256K1_SCALAR_CONST(0xe5a014a8, 0xe3c4ec1e, 0xea4f9b32, 0xcfc7b386, 0x00630806, 0x12c08d02, 0x6407ccc2, 0xb067d90e)},
{SECP256K1_SCALAR_CONST(0x70e9aea9, 0x7e933af0, 0x8a23bfab, 0x23e4b772, 0xff951863, 0x5ffcf47d, 0x6bebc918, 0x2ca58265),
SECP256K1_SCALAR_CONST(0xf4e00006, 0x81bc6441, 0x4eb6ec02, 0xc194a859, 0x80ad7c48, 0xba4e9afb, 0x8b6bdbe0, 0x989d8f77)},
{SECP256K1_SCALAR_CONST(0x3c56c774, 0x46efe6f0, 0xe93618b8, 0xf9b5a846, 0xd247df61, 0x83b1e215, 0x06dc8bcc, 0xeefc1bf5),
SECP256K1_SCALAR_CONST(0xfff8937a, 0x2cd9586b, 0x43c25e57, 0xd1cefa7a, 0x9fb91ed3, 0x95b6533d, 0x8ad0de5b, 0xafb93f00)},
{SECP256K1_SCALAR_CONST(0xfb5c2772, 0x5cb30e83, 0xe38264df, 0xe4e3ebf3, 0x392aa92e, 0xa68756a1, 0x51279ac5, 0xb50711a8),
SECP256K1_SCALAR_CONST(0x000013af, 0x1105bfe7, 0xa6bbd7fb, 0x3d638f99, 0x3b266b02, 0x072fb8bc, 0x39251130, 0x2e0fd0ea)}
};
int i, var, testrand;
unsigned char b32[32];
secp256k1_fe x_fe;
secp256k1_scalar x_scalar;
memset(b32, 0, sizeof(b32));
/* Test fixed test cases through test_inverse_{scalar,field}, both ways. */
for (i = 0; (size_t)i < sizeof(fe_cases)/sizeof(fe_cases[0]); ++i) {
for (var = 0; var <= 1; ++var) {
test_inverse_field(&x_fe, &fe_cases[i][0], var);
CHECK(fe_equal(&x_fe, &fe_cases[i][1]));
test_inverse_field(&x_fe, &fe_cases[i][1], var);
CHECK(fe_equal(&x_fe, &fe_cases[i][0]));
}
}
for (i = 0; (size_t)i < sizeof(scalar_cases)/sizeof(scalar_cases[0]); ++i) {
for (var = 0; var <= 1; ++var) {
test_inverse_scalar(&x_scalar, &scalar_cases[i][0], var);
CHECK(secp256k1_scalar_eq(&x_scalar, &scalar_cases[i][1]));
test_inverse_scalar(&x_scalar, &scalar_cases[i][1], var);
CHECK(secp256k1_scalar_eq(&x_scalar, &scalar_cases[i][0]));
}
}
/* Test inputs 0..999 and their respective negations. */
for (i = 0; i < 1000; ++i) {
b32[31] = i & 0xff;
b32[30] = (i >> 8) & 0xff;
secp256k1_scalar_set_b32(&x_scalar, b32, NULL);
secp256k1_fe_set_b32_mod(&x_fe, b32);
for (var = 0; var <= 1; ++var) {
test_inverse_scalar(NULL, &x_scalar, var);
test_inverse_field(NULL, &x_fe, var);
}
secp256k1_scalar_negate(&x_scalar, &x_scalar);
secp256k1_fe_negate(&x_fe, &x_fe, 1);
for (var = 0; var <= 1; ++var) {
test_inverse_scalar(NULL, &x_scalar, var);
test_inverse_field(NULL, &x_fe, var);
}
}
/* test 128*count random inputs; half with testrand256_test, half with testrand256 */
for (testrand = 0; testrand <= 1; ++testrand) {
for (i = 0; i < 64 * COUNT; ++i) {
(testrand ? testrand256_test : testrand256)(b32);
secp256k1_scalar_set_b32(&x_scalar, b32, NULL);
secp256k1_fe_set_b32_mod(&x_fe, b32);
for (var = 0; var <= 1; ++var) {
test_inverse_scalar(NULL, &x_scalar, var);
test_inverse_field(NULL, &x_fe, var);
}
}
}
}
/***** HSORT TESTS *****/
static void test_heap_swap(void) {
unsigned char a[600];
unsigned char e[sizeof(a)];
memset(a, 21, 200);
memset(a + 200, 99, 200);
memset(a + 400, 42, 200);
memset(e, 42, 200);
memset(e + 200, 99, 200);
memset(e + 400, 21, 200);
secp256k1_heap_swap(a, 0, 2, 200);
CHECK(secp256k1_memcmp_var(a, e, sizeof(a)) == 0);
}
static void test_hsort_is_sorted(unsigned char *elements, size_t n, size_t len) {
size_t i;
for (i = 1; i < n; i++) {
CHECK(secp256k1_memcmp_var(&elements[(i-1) * len], &elements[i * len], len) <= 0);
}
}
struct test_hsort_cmp_data {
size_t counter;
size_t element_len;
};
static int test_hsort_cmp(const void *ele1, const void *ele2, void *data) {
struct test_hsort_cmp_data *d = (struct test_hsort_cmp_data *) data;
d->counter += 1;
return secp256k1_memcmp_var((unsigned char *)ele1, (unsigned char *)ele2, d->element_len);
}
#define NUM 65
#define MAX_ELEMENT_LEN 65
static void test_hsort(size_t element_len) {
unsigned char elements[NUM * MAX_ELEMENT_LEN] = { 0 };
struct test_hsort_cmp_data data;
int i;
VERIFY_CHECK(element_len <= MAX_ELEMENT_LEN);
data.counter = 0;
data.element_len = element_len;
secp256k1_hsort(elements, 0, element_len, test_hsort_cmp, &data);
CHECK(data.counter == 0);
secp256k1_hsort(elements, 1, element_len, test_hsort_cmp, &data);
CHECK(data.counter == 0);
secp256k1_hsort(elements, NUM, element_len, test_hsort_cmp, &data);
CHECK(data.counter >= NUM - 1);
test_hsort_is_sorted(elements, NUM, element_len);
/* Test hsort with array of random length n */
for (i = 0; i < COUNT; i++) {
int n = testrand_int(NUM);
testrand_bytes_test(elements, n*element_len);
secp256k1_hsort(elements, n, element_len, test_hsort_cmp, &data);
test_hsort_is_sorted(elements, n, element_len);
}
}
#undef NUM
#undef MAX_ELEMENT_LEN
static void run_hsort_tests(void) {
test_heap_swap();
test_hsort(1);
test_hsort(64);
test_hsort(65);
}
/***** GROUP TESTS *****/
/* This compares jacobian points including their Z, not just their geometric meaning. */
static 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;
}
static void test_ge(void) {
int i, i1;
int runs = 6;
/* 25 points are used:
* - infinity
* - for each of four random points p1 p2 p3 p4, we add the point, its
* negation, and then those two again but with randomized Z coordinate.
* - The same is then done for lambda*p1 and lambda^2*p1.
*/
secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&CTX->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
secp256k1_fe zf, r;
secp256k1_fe zfi2, zfi3;
secp256k1_gej_set_infinity(&gej[0]);
secp256k1_ge_set_infinity(&ge[0]);
for (i = 0; i < runs; i++) {
int j, k;
secp256k1_ge g;
testutil_random_ge_test(&g);
if (i >= runs - 2) {
secp256k1_ge_mul_lambda(&g, &ge[1]);
CHECK(!secp256k1_ge_eq_var(&g, &ge[1]));
}
if (i >= runs - 1) {
secp256k1_ge_mul_lambda(&g, &g);
}
ge[1 + 4 * i] = g;
ge[2 + 4 * i] = g;
secp256k1_ge_neg(&ge[3 + 4 * i], &g);
secp256k1_ge_neg(&ge[4 + 4 * i], &g);
secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
testutil_random_ge_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
testutil_random_ge_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
for (j = 0; j < 4; j++) {
testutil_random_ge_x_magnitude(&ge[1 + j + 4 * i]);
testutil_random_ge_y_magnitude(&ge[1 + j + 4 * i]);
testutil_random_gej_x_magnitude(&gej[1 + j + 4 * i]);
testutil_random_gej_y_magnitude(&gej[1 + j + 4 * i]);
testutil_random_gej_z_magnitude(&gej[1 + j + 4 * i]);
}
for (j = 0; j < 4; ++j) {
for (k = 0; k < 4; ++k) {
int expect_equal = (j >> 1) == (k >> 1);
CHECK(secp256k1_ge_eq_var(&ge[1 + j + 4 * i], &ge[1 + k + 4 * i]) == expect_equal);
CHECK(secp256k1_gej_eq_var(&gej[1 + j + 4 * i], &gej[1 + k + 4 * i]) == expect_equal);
CHECK(secp256k1_gej_eq_ge_var(&gej[1 + j + 4 * i], &ge[1 + k + 4 * i]) == expect_equal);
CHECK(secp256k1_gej_eq_ge_var(&gej[1 + k + 4 * i], &ge[1 + j + 4 * i]) == expect_equal);
}
}
}
/* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
testutil_random_fe_non_zero_test(&zf);
testutil_random_fe_magnitude(&zf, 8);
secp256k1_fe_inv_var(&zfi3, &zf);
secp256k1_fe_sqr(&zfi2, &zfi3);
secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
/* Generate random r */
testutil_random_fe_non_zero_test(&r);
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(&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);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
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(&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);
testutil_random_ge_x_magnitude(&ge2_zfi);
testutil_random_ge_y_magnitude(&ge2_zfi);
secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
}
/* 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]);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
}
/* 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);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
/* Check Z ratio. */
secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
CHECK(secp256k1_fe_equal(&zr2, &resj.z));
/* Normal doubling. */
secp256k1_gej_double_var(&resj, &gej[i2], NULL);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
/* Constant-time doubling. */
secp256k1_gej_double(&resj, &gej[i2]);
CHECK(secp256k1_gej_eq_ge_var(&resj, &ref));
}
/* 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]));
CHECK(secp256k1_gej_eq_ge_var(&gej[i2], &ref));
}
if (i2 == 0) {
CHECK(secp256k1_ge_is_infinity(&ge[i2]));
CHECK(secp256k1_gej_is_infinity(&gej[i2]));
CHECK(secp256k1_gej_eq_ge_var(&gej[i1], &ref));
}
}
}
/* 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 + testrand_int(4 * runs + 1 - i);
if (swap != i) {
secp256k1_gej t = gej_shuffled[i];
gej_shuffled[i] = gej_shuffled[swap];
gej_shuffled[swap] = t;
}
}
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
}
CHECK(secp256k1_gej_is_infinity(&sum));
free(gej_shuffled);
}
/* Test batch gej -> ge conversion without known z ratios. */
{
secp256k1_ge *ge_set_all_var = (secp256k1_ge *)checked_malloc(&CTX->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&CTX->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge));
secp256k1_ge_set_all_gej_var(&ge_set_all_var[0], &gej[0], 4 * runs + 1);
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_fe s;
testutil_random_fe_non_zero(&s);
secp256k1_gej_rescale(&gej[i], &s);
CHECK(secp256k1_gej_eq_ge_var(&gej[i], &ge_set_all_var[i]));
}
/* Skip infinity at &gej[0]. */
secp256k1_ge_set_all_gej(&ge_set_all[1], &gej[1], 4 * runs);
for (i = 1; i < 4 * runs + 1; i++) {
secp256k1_fe s;
testutil_random_fe_non_zero(&s);
secp256k1_gej_rescale(&gej[i], &s);
CHECK(secp256k1_gej_eq_ge_var(&gej[i], &ge_set_all[i]));
CHECK(secp256k1_ge_eq_var(&ge_set_all_var[i], &ge_set_all[i]));
}
/* Test with an array of length 1. */
secp256k1_ge_set_all_gej_var(ge_set_all_var, &gej[1], 1);
secp256k1_ge_set_all_gej(ge_set_all, &gej[1], 1);
CHECK(secp256k1_gej_eq_ge_var(&gej[1], &ge_set_all_var[1]));
CHECK(secp256k1_gej_eq_ge_var(&gej[1], &ge_set_all[1]));
CHECK(secp256k1_ge_eq_var(&ge_set_all_var[1], &ge_set_all[1]));
/* Test with an array of length 0. */
secp256k1_ge_set_all_gej_var(NULL, NULL, 0);
secp256k1_ge_set_all_gej(NULL, NULL, 0);
free(ge_set_all_var);
free(ge_set_all);
}
/* Test that all elements have X coordinates on the curve. */
for (i = 1; i < 4 * runs + 1; i++) {
secp256k1_fe n;
CHECK(secp256k1_ge_x_on_curve_var(&ge[i].x));
/* And the same holds after random rescaling. */
secp256k1_fe_mul(&n, &zf, &ge[i].x);
CHECK(secp256k1_ge_x_frac_on_curve_var(&n, &zf));
}
/* Test correspondence of secp256k1_ge_x{,_frac}_on_curve_var with ge_set_xo. */
{
secp256k1_fe n;
secp256k1_ge q;
int ret_on_curve, ret_frac_on_curve, ret_set_xo;
secp256k1_fe_mul(&n, &zf, &r);
ret_on_curve = secp256k1_ge_x_on_curve_var(&r);
ret_frac_on_curve = secp256k1_ge_x_frac_on_curve_var(&n, &zf);
ret_set_xo = secp256k1_ge_set_xo_var(&q, &r, 0);
CHECK(ret_on_curve == ret_frac_on_curve);
CHECK(ret_on_curve == ret_set_xo);
if (ret_set_xo) CHECK(secp256k1_fe_equal(&r, &q.x));
}
/* Test batch gej -> ge conversion with many infinities. */
for (i = 0; i < 4 * runs + 1; i++) {
int odd;
testutil_random_ge_test(&ge[i]);
odd = secp256k1_fe_is_odd(&ge[i].x);
CHECK(odd == 0 || odd == 1);
/* randomly set half the points to infinity */
if (odd == i % 2) {
secp256k1_ge_set_infinity(&ge[i]);
}
secp256k1_gej_set_ge(&gej[i], &ge[i]);
}
/* batch convert */
secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1);
/* check result */
for (i = 0; i < 4 * runs + 1; i++) {
CHECK(secp256k1_gej_eq_ge_var(&gej[i], &ge[i]));
}
/* Test batch gej -> ge conversion with all infinities. */
for (i = 0; i < 4 * runs + 1; i++) {
secp256k1_gej_set_infinity(&gej[i]);
}
/* batch convert */
secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1);
/* check result */
for (i = 0; i < 4 * runs + 1; i++) {
CHECK(secp256k1_ge_is_infinity(&ge[i]));
}
free(ge);
free(gej);
}
static void test_initialized_inf(void) {
secp256k1_ge p;
secp256k1_gej pj, npj, infj1, infj2, infj3;
secp256k1_fe zinv;
/* Test that adding P+(-P) results in a fully initialized infinity*/
testutil_random_ge_test(&p);
secp256k1_gej_set_ge(&pj, &p);
secp256k1_gej_neg(&npj, &pj);
secp256k1_gej_add_var(&infj1, &pj, &npj, NULL);
CHECK(secp256k1_gej_is_infinity(&infj1));
CHECK(secp256k1_fe_is_zero(&infj1.x));
CHECK(secp256k1_fe_is_zero(&infj1.y));
CHECK(secp256k1_fe_is_zero(&infj1.z));
secp256k1_gej_add_ge_var(&infj2, &npj, &p, NULL);
CHECK(secp256k1_gej_is_infinity(&infj2));
CHECK(secp256k1_fe_is_zero(&infj2.x));
CHECK(secp256k1_fe_is_zero(&infj2.y));
CHECK(secp256k1_fe_is_zero(&infj2.z));
secp256k1_fe_set_int(&zinv, 1);
secp256k1_gej_add_zinv_var(&infj3, &npj, &p, &zinv);
CHECK(secp256k1_gej_is_infinity(&infj3));
CHECK(secp256k1_fe_is_zero(&infj3.x));
CHECK(secp256k1_fe_is_zero(&infj3.y));
CHECK(secp256k1_fe_is_zero(&infj3.z));
}
static 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
*
* load("secp256k1_params.sage")
*
* # random "bad pair"
* P = C.random_element()
* Q = -int(LAMBDA) * 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);
CHECK(secp256k1_gej_eq_ge_var(&sumj, &res));
secp256k1_gej_add_ge(&resj, &aj, &b);
secp256k1_ge_set_gej(&res, &resj);
CHECK(secp256k1_gej_eq_ge_var(&sumj, &res));
secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
secp256k1_ge_set_gej(&res, &resj);
CHECK(secp256k1_gej_eq_ge_var(&sumj, &res));
}
static void test_ge_bytes(void) {
int i;
for (i = 0; i < COUNT + 1; i++) {
unsigned char buf[64];
secp256k1_ge p, q;
if (i == 0) {
secp256k1_ge_set_infinity(&p);
} else {
testutil_random_ge_test(&p);
}
if (!secp256k1_ge_is_infinity(&p)) {
secp256k1_ge_to_bytes(buf, &p);
secp256k1_ge_from_bytes(&q, buf);
CHECK(secp256k1_ge_eq_var(&p, &q));
secp256k1_ge_from_bytes_ext(&q, buf);
CHECK(secp256k1_ge_eq_var(&p, &q));
}
secp256k1_ge_to_bytes_ext(buf, &p);
secp256k1_ge_from_bytes_ext(&q, buf);
CHECK(secp256k1_ge_eq_var(&p, &q));
}
}
static void run_ge(void) {
int i;
for (i = 0; i < COUNT * 32; i++) {
test_ge();
}
test_add_neg_y_diff_x();
test_initialized_inf();
test_ge_bytes();
}
static void test_gej_cmov(const secp256k1_gej *a, const secp256k1_gej *b) {
secp256k1_gej t = *a;
secp256k1_gej_cmov(&t, b, 0);
CHECK(gej_xyz_equals_gej(&t, a));
secp256k1_gej_cmov(&t, b, 1);
CHECK(gej_xyz_equals_gej(&t, b));
}
static void run_gej(void) {
int i;
secp256k1_gej a, b;
/* Tests for secp256k1_gej_cmov */
for (i = 0; i < COUNT; i++) {
secp256k1_gej_set_infinity(&a);
secp256k1_gej_set_infinity(&b);
test_gej_cmov(&a, &b);
testutil_random_gej_test(&a);
test_gej_cmov(&a, &b);
test_gej_cmov(&b, &a);
b = a;
test_gej_cmov(&a, &b);
testutil_random_gej_test(&b);
test_gej_cmov(&a, &b);
test_gej_cmov(&b, &a);
}
/* Tests for secp256k1_gej_eq_var */
for (i = 0; i < COUNT; i++) {
secp256k1_fe fe;
testutil_random_gej_test(&a);
testutil_random_gej_test(&b);
CHECK(!secp256k1_gej_eq_var(&a, &b));
b = a;
testutil_random_fe_non_zero_test(&fe);
secp256k1_gej_rescale(&a, &fe);
CHECK(secp256k1_gej_eq_var(&a, &b));
}
}
static void test_ec_combine(void) {
secp256k1_scalar sum = secp256k1_scalar_zero;
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;
testutil_random_scalar_order_test(&s);
secp256k1_scalar_add(&sum, &sum, &s);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &Qj, &s);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&data[i - 1], &Q);
d[i - 1] = &data[i - 1];
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &Qj, &sum);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(&sd, &Q);
CHECK(secp256k1_ec_pubkey_combine(CTX, &sd2, d, i) == 1);
CHECK(secp256k1_memcmp_var(&sd, &sd2, sizeof(sd)) == 0);
}
}
static void run_ec_combine(void) {
int i;
for (i = 0; i < COUNT * 8; i++) {
test_ec_combine();
}
}
static void test_group_decompress(const secp256k1_fe* x) {
/* The input itself, normalized. */
secp256k1_fe fex = *x;
/* Results of set_xo_var(..., 0), set_xo_var(..., 1). */
secp256k1_ge ge_even, ge_odd;
/* Return values of the above calls. */
int res_even, res_odd;
secp256k1_fe_normalize_var(&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_even == res_odd);
if (res_even) {
secp256k1_fe_normalize_var(&ge_odd.x);
secp256k1_fe_normalize_var(&ge_even.x);
secp256k1_fe_normalize_var(&ge_odd.y);
secp256k1_fe_normalize_var(&ge_even.y);
/* No infinity allowed. */
CHECK(!ge_even.infinity);
CHECK(!ge_odd.infinity);
/* Check that the x coordinates check out. */
CHECK(secp256k1_fe_equal(&ge_even.x, x));
CHECK(secp256k1_fe_equal(&ge_odd.x, x));
/* 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));
}
}
static void run_group_decompress(void) {
int i;
for (i = 0; i < COUNT * 4; i++) {
secp256k1_fe fe;
testutil_random_fe_test(&fe);
test_group_decompress(&fe);
}
}
/***** ECMULT TESTS *****/
static void test_pre_g_table(const secp256k1_ge_storage * pre_g, size_t n) {
/* Tests the pre_g / pre_g_128 tables for consistency.
* For independent verification we take a "geometric" approach to verification.
* We check that every entry is on-curve.
* We check that for consecutive entries p and q, that p + gg - q = 0 by checking
* (1) p, gg, and -q are colinear.
* (2) p, gg, and -q are all distinct.
* where gg is twice the generator, where the generator is the first table entry.
*
* Checking the table's generators are correct is done in run_ecmult_pre_g.
*/
secp256k1_gej g2;
secp256k1_ge p, q, gg;
secp256k1_fe dpx, dpy, dqx, dqy;
size_t i;
CHECK(0 < n);
secp256k1_ge_from_storage(&p, &pre_g[0]);
CHECK(secp256k1_ge_is_valid_var(&p));
secp256k1_gej_set_ge(&g2, &p);
secp256k1_gej_double_var(&g2, &g2, NULL);
secp256k1_ge_set_gej_var(&gg, &g2);
for (i = 1; i < n; ++i) {
secp256k1_fe_negate(&dpx, &p.x, 1); secp256k1_fe_add(&dpx, &gg.x); secp256k1_fe_normalize_weak(&dpx);
secp256k1_fe_negate(&dpy, &p.y, 1); secp256k1_fe_add(&dpy, &gg.y); secp256k1_fe_normalize_weak(&dpy);
/* Check that p is not equal to gg */
CHECK(!secp256k1_fe_normalizes_to_zero_var(&dpx) || !secp256k1_fe_normalizes_to_zero_var(&dpy));
secp256k1_ge_from_storage(&q, &pre_g[i]);
CHECK(secp256k1_ge_is_valid_var(&q));
secp256k1_fe_negate(&dqx, &q.x, 1); secp256k1_fe_add(&dqx, &gg.x);
dqy = q.y; secp256k1_fe_add(&dqy, &gg.y);
/* Check that -q is not equal to gg */
CHECK(!secp256k1_fe_normalizes_to_zero_var(&dqx) || !secp256k1_fe_normalizes_to_zero_var(&dqy));
/* Check that -q is not equal to p */
CHECK(!secp256k1_fe_equal(&dpx, &dqx) || !secp256k1_fe_equal(&dpy, &dqy));
/* Check that p, -q and gg are colinear */
secp256k1_fe_mul(&dpx, &dpx, &dqy);
secp256k1_fe_mul(&dpy, &dpy, &dqx);
CHECK(secp256k1_fe_equal(&dpx, &dpy));
p = q;
}
}
static void run_ecmult_pre_g(void) {
secp256k1_ge_storage gs;
secp256k1_gej gj;
secp256k1_ge g;
size_t i;
/* Check that the pre_g and pre_g_128 tables are consistent. */
test_pre_g_table(secp256k1_pre_g, ECMULT_TABLE_SIZE(WINDOW_G));
test_pre_g_table(secp256k1_pre_g_128, ECMULT_TABLE_SIZE(WINDOW_G));
/* Check the first entry from the pre_g table. */
secp256k1_ge_to_storage(&gs, &secp256k1_ge_const_g);
CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g[0], sizeof(gs)) == 0);
/* Check the first entry from the pre_g_128 table. */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
for (i = 0; i < 128; ++i) {
secp256k1_gej_double_var(&gj, &gj, NULL);
}
secp256k1_ge_set_gej(&g, &gj);
secp256k1_ge_to_storage(&gs, &g);
CHECK(secp256k1_memcmp_var(&gs, &secp256k1_pre_g_128[0], sizeof(gs)) == 0);
}
static 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_one;
secp256k1_scalar ge = secp256k1_scalar_zero;
/* actual points */
secp256k1_gej x;
secp256k1_gej x2;
int i;
/* the point being computed */
x = a;
for (i = 0; i < 200*COUNT; i++) {
/* in each iteration, compute X = xn*X + gn*G; */
secp256k1_ecmult(&x, &x, &xn, &gn);
/* also compute ae and ge: the actual accumulated factors for A and G */
/* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
secp256k1_scalar_mul(&ae, &ae, &xn);
secp256k1_scalar_mul(&ge, &ge, &xn);
secp256k1_scalar_add(&ge, &ge, &gn);
/* modify xn and gn */
secp256k1_scalar_mul(&xn, &xn, &xf);
secp256k1_scalar_mul(&gn, &gn, &gf);
/* verify */
if (i == 19999) {
/* expected result after 19999 iterations */
secp256k1_gej rp = SECP256K1_GEJ_CONST(
0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
);
CHECK(secp256k1_gej_eq_var(&rp, &x));
}
}
/* redo the computation, but directly with the resulting ae and ge coefficients: */
secp256k1_ecmult(&x2, &a, &ae, &ge);
CHECK(secp256k1_gej_eq_var(&x, &x2));
}
static void test_point_times_order(const secp256k1_gej *point) {
/* X * (point + G) + (order-X) * (pointer + G) = 0 */
secp256k1_scalar x;
secp256k1_scalar nx;
secp256k1_gej res1, res2;
secp256k1_ge res3;
unsigned char pub[65];
size_t psize = 65;
testutil_random_scalar_order_test(&x);
secp256k1_scalar_negate(&nx, &x);
secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */
secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
CHECK(secp256k1_gej_is_infinity(&res1));
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
psize = 65;
CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
/* check zero/one edge cases */
secp256k1_ecmult(&res1, point, &secp256k1_scalar_zero, &secp256k1_scalar_zero);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
secp256k1_ecmult(&res1, point, &secp256k1_scalar_one, &secp256k1_scalar_zero);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_gej_eq_ge_var(point, &res3));
secp256k1_ecmult(&res1, point, &secp256k1_scalar_zero, &secp256k1_scalar_one);
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_eq_var(&secp256k1_ge_const_g, &res3));
}
/* These scalars reach large (in absolute value) outputs when fed to secp256k1_scalar_split_lambda.
*
* They are computed as:
* - For a in [-2, -1, 0, 1, 2]:
* - For b in [-3, -1, 1, 3]:
* - Output (a*LAMBDA + (ORDER+b)/2) % ORDER
*/
static const secp256k1_scalar scalars_near_split_bounds[20] = {
SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fc),
SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fd),
SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fe),
SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6ff),
SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632d),
SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632e),
SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632f),
SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf76330),
SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b209f),
SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a0),
SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a1),
SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a2),
SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede11),
SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede12),
SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede13),
SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede14),
SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a42),
SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a43),
SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a44),
SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a45)
};
static void test_ecmult_target(const secp256k1_scalar* target, int mode) {
/* Mode: 0=ecmult_gen, 1=ecmult, 2=ecmult_const */
secp256k1_scalar n1, n2;
secp256k1_ge p;
secp256k1_gej pj, p1j, p2j, ptj;
/* Generate random n1,n2 such that n1+n2 = -target. */
testutil_random_scalar_order_test(&n1);
secp256k1_scalar_add(&n2, &n1, target);
secp256k1_scalar_negate(&n2, &n2);
/* Generate a random input point. */
if (mode != 0) {
testutil_random_ge_test(&p);
secp256k1_gej_set_ge(&pj, &p);
}
/* EC multiplications */
if (mode == 0) {
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &p1j, &n1);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &p2j, &n2);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &ptj, target);
} else if (mode == 1) {
secp256k1_ecmult(&p1j, &pj, &n1, &secp256k1_scalar_zero);
secp256k1_ecmult(&p2j, &pj, &n2, &secp256k1_scalar_zero);
secp256k1_ecmult(&ptj, &pj, target, &secp256k1_scalar_zero);
} else {
secp256k1_ecmult_const(&p1j, &p, &n1);
secp256k1_ecmult_const(&p2j, &p, &n2);
secp256k1_ecmult_const(&ptj, &p, target);
}
/* Add them all up: n1*P + n2*P + target*P = (n1+n2+target)*P = (n1+n1-n1-n2)*P = 0. */
secp256k1_gej_add_var(&ptj, &ptj, &p1j, NULL);
secp256k1_gej_add_var(&ptj, &ptj, &p2j, NULL);
CHECK(secp256k1_gej_is_infinity(&ptj));
}
static void run_ecmult_near_split_bound(void) {
int i;
unsigned j;
for (i = 0; i < 4*COUNT; ++i) {
for (j = 0; j < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++j) {
test_ecmult_target(&scalars_near_split_bounds[j], 0);
test_ecmult_target(&scalars_near_split_bounds[j], 1);
test_ecmult_target(&scalars_near_split_bounds[j], 2);
}
}
}
static void run_point_times_order(void) {
int i;
secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
static const secp256k1_fe xr = SECP256K1_FE_CONST(
0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
);
for (i = 0; i < 500; i++) {
secp256k1_ge p;
if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
secp256k1_gej j;
CHECK(secp256k1_ge_is_valid_var(&p));
secp256k1_gej_set_ge(&j, &p);
test_point_times_order(&j);
}
secp256k1_fe_sqr(&x, &x);
}
secp256k1_fe_normalize_var(&x);
CHECK(secp256k1_fe_equal(&x, &xr));
}
static void ecmult_const_random_mult(void) {
/* random starting point A (on the curve) */
secp256k1_ge a = SECP256K1_GE_CONST(
0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
);
/* random initial factor xn */
secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
);
/* expected xn * A (from sage) */
secp256k1_ge expected_b = SECP256K1_GE_CONST(
0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
);
secp256k1_gej b;
secp256k1_ecmult_const(&b, &a, &xn);
CHECK(secp256k1_ge_is_valid_var(&a));
CHECK(secp256k1_gej_eq_ge_var(&b, &expected_b));
}
static void ecmult_const_commutativity(void) {
secp256k1_scalar a;
secp256k1_scalar b;
secp256k1_gej res1;
secp256k1_gej res2;
secp256k1_ge mid1;
secp256k1_ge mid2;
testutil_random_scalar_order_test(&a);
testutil_random_scalar_order_test(&b);
secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
secp256k1_ecmult_const(&res1, &mid1, &b);
secp256k1_ecmult_const(&res2, &mid2, &a);
secp256k1_ge_set_gej(&mid1, &res1);
secp256k1_ge_set_gej(&mid2, &res2);
CHECK(secp256k1_ge_eq_var(&mid1, &mid2));
}
static void ecmult_const_mult_zero_one(void) {
secp256k1_scalar s;
secp256k1_scalar negone;
secp256k1_gej res1;
secp256k1_ge res2;
secp256k1_ge point;
secp256k1_ge inf;
testutil_random_scalar_order_test(&s);
secp256k1_scalar_negate(&negone, &secp256k1_scalar_one);
testutil_random_ge_test(&point);
secp256k1_ge_set_infinity(&inf);
/* 0*point */
secp256k1_ecmult_const(&res1, &point, &secp256k1_scalar_zero);
CHECK(secp256k1_gej_is_infinity(&res1));
/* s*inf */
secp256k1_ecmult_const(&res1, &inf, &s);
CHECK(secp256k1_gej_is_infinity(&res1));
/* 1*point */
secp256k1_ecmult_const(&res1, &point, &secp256k1_scalar_one);
secp256k1_ge_set_gej(&res2, &res1);
CHECK(secp256k1_ge_eq_var(&res2, &point));
/* -1*point */
secp256k1_ecmult_const(&res1, &point, &negone);
secp256k1_gej_neg(&res1, &res1);
secp256k1_ge_set_gej(&res2, &res1);
CHECK(secp256k1_ge_eq_var(&res2, &point));
}
static void ecmult_const_check_result(const secp256k1_ge *A, const secp256k1_scalar* q, const secp256k1_gej *res) {
secp256k1_gej pointj, res2j;
secp256k1_ge res2;
secp256k1_gej_set_ge(&pointj, A);
secp256k1_ecmult(&res2j, &pointj, q, &secp256k1_scalar_zero);
secp256k1_ge_set_gej(&res2, &res2j);
CHECK(secp256k1_gej_eq_ge_var(res, &res2));
}
static void ecmult_const_edges(void) {
secp256k1_scalar q;
secp256k1_ge point;
secp256k1_gej res;
size_t i;
size_t cases = 1 + sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]);
/* We are trying to reach the following edge cases (variables are defined as
* in ecmult_const_impl.h):
* 1. i = 0: s = 0 <=> q = -K
* 2. i > 0: v1, v2 large values
* <=> s1, s2 large values
* <=> s = scalars_near_split_bounds[i]
* <=> q = 2*scalars_near_split_bounds[i] - K
*/
for (i = 0; i < cases; ++i) {
secp256k1_scalar_negate(&q, &secp256k1_ecmult_const_K);
if (i > 0) {
secp256k1_scalar_add(&q, &q, &scalars_near_split_bounds[i - 1]);
secp256k1_scalar_add(&q, &q, &scalars_near_split_bounds[i - 1]);
}
testutil_random_ge_test(&point);
secp256k1_ecmult_const(&res, &point, &q);
ecmult_const_check_result(&point, &q, &res);
}
}
static void ecmult_const_mult_xonly(void) {
int i;
/* Test correspondence between secp256k1_ecmult_const and secp256k1_ecmult_const_xonly. */
for (i = 0; i < 2*COUNT; ++i) {
secp256k1_ge base;
secp256k1_gej basej, resj;
secp256k1_fe n, d, resx, v;
secp256k1_scalar q;
int res;
/* Random base point. */
testutil_random_ge_test(&base);
/* Random scalar to multiply it with. */
testutil_random_scalar_order_test(&q);
/* If i is odd, n=d*base.x for random non-zero d */
if (i & 1) {
testutil_random_fe_non_zero_test(&d);
secp256k1_fe_mul(&n, &base.x, &d);
} else {
n = base.x;
}
/* Perform x-only multiplication. */
res = secp256k1_ecmult_const_xonly(&resx, &n, (i & 1) ? &d : NULL, &q, i & 2);
CHECK(res);
/* Perform normal multiplication. */
secp256k1_gej_set_ge(&basej, &base);
secp256k1_ecmult(&resj, &basej, &q, NULL);
/* Check that resj's X coordinate corresponds with resx. */
secp256k1_fe_sqr(&v, &resj.z);
secp256k1_fe_mul(&v, &v, &resx);
CHECK(fe_equal(&v, &resj.x));
}
/* Test that secp256k1_ecmult_const_xonly correctly rejects X coordinates not on curve. */
for (i = 0; i < 2*COUNT; ++i) {
secp256k1_fe x, n, d, r;
int res;
secp256k1_scalar q;
testutil_random_scalar_order_test(&q);
/* Generate random X coordinate not on the curve. */
do {
testutil_random_fe_test(&x);
} while (secp256k1_ge_x_on_curve_var(&x));
/* If i is odd, n=d*x for random non-zero d. */
if (i & 1) {
testutil_random_fe_non_zero_test(&d);
secp256k1_fe_mul(&n, &x, &d);
} else {
n = x;
}
res = secp256k1_ecmult_const_xonly(&r, &n, (i & 1) ? &d : NULL, &q, 0);
CHECK(res == 0);
}
}
static void ecmult_const_chain_multiply(void) {
/* Check known result (randomly generated test problem from sage) */
const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
);
const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
);
secp256k1_gej point;
secp256k1_ge res;
int i;
secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
for (i = 0; i < 100; ++i) {
secp256k1_ge tmp;
secp256k1_ge_set_gej(&tmp, &point);
secp256k1_ecmult_const(&point, &tmp, &scalar);
}
secp256k1_ge_set_gej(&res, &point);
CHECK(secp256k1_gej_eq_ge_var(&expected_point, &res));
}
static void run_ecmult_const_tests(void) {
ecmult_const_mult_zero_one();
ecmult_const_edges();
ecmult_const_random_mult();
ecmult_const_commutativity();
ecmult_const_chain_multiply();
ecmult_const_mult_xonly();
}
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;
}
static void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) {
int ncount;
secp256k1_scalar sc[32];
secp256k1_ge pt[32];
secp256k1_gej r;
secp256k1_gej r2;
ecmult_multi_data data;
data.sc = sc;
data.pt = pt;
/* No points to multiply */
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
/* Check 1- and 2-point multiplies against ecmult */
for (ncount = 0; ncount < COUNT; ncount++) {
secp256k1_ge ptg;
secp256k1_gej ptgj;
testutil_random_scalar_order(&sc[0]);
testutil_random_scalar_order(&sc[1]);
testutil_random_ge_test(&ptg);
secp256k1_gej_set_ge(&ptgj, &ptg);
pt[0] = ptg;
pt[1] = secp256k1_ge_const_g;
/* only G scalar */
secp256k1_ecmult(&r2, &ptgj, &secp256k1_scalar_zero, &sc[0]);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0));
CHECK(secp256k1_gej_eq_var(&r, &r2));
/* 1-point */
secp256k1_ecmult(&r2, &ptgj, &sc[0], &secp256k1_scalar_zero);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 1));
CHECK(secp256k1_gej_eq_var(&r, &r2));
/* Try to multiply 1 point, but callback returns false */
CHECK(!ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_false_callback, &data, 1));
/* 2-point */
secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 2));
CHECK(secp256k1_gej_eq_var(&r, &r2));
/* 2-point with G scalar */
secp256k1_ecmult(&r2, &ptgj, &sc[0], &sc[1]);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1));
CHECK(secp256k1_gej_eq_var(&r, &r2));
}
/* 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++) {
testutil_random_scalar_order(&sc[i]);
secp256k1_ge_set_infinity(&pt[i]);
}
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
for (j = 0; j < 3; j++) {
for (i = 0; i < 32; i++) {
testutil_random_ge_test(&ptg);
pt[i] = ptg;
secp256k1_scalar_set_int(&sc[i], 0);
}
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
for (j = 0; j < 3; j++) {
testutil_random_ge_test(&ptg);
for (i = 0; i < 16; i++) {
testutil_random_scalar_order(&sc[2*i]);
secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]);
pt[2 * i] = ptg;
pt[2 * i + 1] = ptg;
}
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
testutil_random_scalar_order(&sc[0]);
for (i = 0; i < 16; i++) {
testutil_random_ge_test(&ptg);
sc[2*i] = sc[0];
sc[2*i+1] = sc[0];
pt[2 * i] = ptg;
secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]);
}
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, sizes[j]));
CHECK(secp256k1_gej_is_infinity(&r));
}
testutil_random_ge_test(&ptg);
secp256k1_scalar_set_int(&sc[0], 0);
pt[0] = ptg;
for (i = 1; i < 32; i++) {
pt[i] = ptg;
testutil_random_scalar_order(&sc[i]);
secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]);
secp256k1_scalar_negate(&sc[i], &sc[i]);
}
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, 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);
testutil_random_scalar_order(&sc[0]);
for (i = 0; i < 20; i++) {
secp256k1_ge ptg;
sc[i] = sc[0];
testutil_random_ge_test(&ptg);
pt[i] = ptg;
secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL);
}
secp256k1_ecmult(&r2, &r, &sc[0], &secp256k1_scalar_zero);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 20));
CHECK(secp256k1_gej_eq_var(&r, &r2));
}
/* 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);
testutil_random_ge_test(&ptg);
for (i = 0; i < 20; i++) {
testutil_random_scalar_order(&sc[i]);
pt[i] = ptg;
secp256k1_scalar_add(&rs, &rs, &sc[i]);
}
secp256k1_gej_set_ge(&p0j, &pt[0]);
secp256k1_ecmult(&r2, &p0j, &rs, &secp256k1_scalar_zero);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 20));
CHECK(secp256k1_gej_eq_var(&r, &r2));
}
/* Sanity check that zero scalars don't cause problems */
for (ncount = 0; ncount < 20; ncount++) {
testutil_random_scalar_order(&sc[ncount]);
testutil_random_ge_test(&pt[ncount]);
}
secp256k1_scalar_set_int(&sc[0], 0);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 20));
secp256k1_scalar_set_int(&sc[1], 0);
secp256k1_scalar_set_int(&sc[2], 0);
secp256k1_scalar_set_int(&sc[3], 0);
secp256k1_scalar_set_int(&sc[4], 0);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 6));
CHECK(ecmult_multi(&CTX->error_callback, scratch, &r, &secp256k1_scalar_zero, 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;
testutil_random_ge_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(&t0p, &ptgj, &t0, &secp256k1_scalar_zero);
secp256k1_ecmult(&t1p, &ptgj, &t1, &secp256k1_scalar_zero);
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(&expected, &ptgj, &tmp1, &secp256k1_scalar_zero);
CHECK(ecmult_multi(&CTX->error_callback, scratch, &actual, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 2));
CHECK(secp256k1_gej_eq_var(&actual, &expected));
}
}
}
}
}
}
static int test_ecmult_multi_random(secp256k1_scratch *scratch) {
/* Large random test for ecmult_multi_* functions which exercises:
* - Few or many inputs (0 up to 128, roughly exponentially distributed).
* - Few or many 0*P or a*INF inputs (roughly uniformly distributed).
* - Including or excluding an nonzero a*G term (or such a term at all).
* - Final expected result equal to infinity or not (roughly 50%).
* - ecmult_multi_var, ecmult_strauss_single_batch, ecmult_pippenger_single_batch
*/
/* These 4 variables define the eventual input to the ecmult_multi function.
* g_scalar is the G scalar fed to it (or NULL, possibly, if g_scalar=0), and
* scalars[0..filled-1] and gejs[0..filled-1] are the scalars and points
* which form its normal inputs. */
int filled = 0;
secp256k1_scalar g_scalar = secp256k1_scalar_zero;
secp256k1_scalar scalars[128];
secp256k1_gej gejs[128];
/* The expected result, and the computed result. */
secp256k1_gej expected, computed;
/* Temporaries. */
secp256k1_scalar sc_tmp;
secp256k1_ge ge_tmp;
/* Variables needed for the actual input to ecmult_multi. */
secp256k1_ge ges[128];
ecmult_multi_data data;
int i;
/* Which multiplication function to use */
int fn = testrand_int(3);
secp256k1_ecmult_multi_func ecmult_multi = fn == 0 ? secp256k1_ecmult_multi_var :
fn == 1 ? secp256k1_ecmult_strauss_batch_single :
secp256k1_ecmult_pippenger_batch_single;
/* Simulate exponentially distributed num. */
int num_bits = 2 + testrand_int(6);
/* Number of (scalar, point) inputs (excluding g). */
int num = testrand_int((1 << num_bits) + 1);
/* Number of those which are nonzero. */
int num_nonzero = testrand_int(num + 1);
/* Whether we're aiming to create an input with nonzero expected result. */
int nonzero_result = testrand_bits(1);
/* Whether we will provide nonzero g multiplicand. In some cases our hand
* is forced here based on num_nonzero and nonzero_result. */
int g_nonzero = num_nonzero == 0 ? nonzero_result :
num_nonzero == 1 && !nonzero_result ? 1 :
(int)testrand_bits(1);
/* Which g_scalar pointer to pass into ecmult_multi(). */
const secp256k1_scalar* g_scalar_ptr = (g_nonzero || testrand_bits(1)) ? &g_scalar : NULL;
/* How many EC multiplications were performed in this function. */
int mults = 0;
/* How many randomization steps to apply to the input list. */
int rands = (int)testrand_bits(3);
if (rands > num_nonzero) rands = num_nonzero;
secp256k1_gej_set_infinity(&expected);
secp256k1_gej_set_infinity(&gejs[0]);
secp256k1_scalar_set_int(&scalars[0], 0);
if (g_nonzero) {
/* If g_nonzero, set g_scalar to nonzero value r. */
testutil_random_scalar_order_test(&g_scalar);
if (!nonzero_result) {
/* If expected=0 is desired, add a (a*r, -(1/a)*g) term to compensate. */
CHECK(num_nonzero > filled);
testutil_random_scalar_order_test(&sc_tmp);
secp256k1_scalar_mul(&scalars[filled], &sc_tmp, &g_scalar);
secp256k1_scalar_inverse_var(&sc_tmp, &sc_tmp);
secp256k1_scalar_negate(&sc_tmp, &sc_tmp);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &gejs[filled], &sc_tmp);
++filled;
++mults;
}
}
if (nonzero_result && filled < num_nonzero) {
/* If a nonzero result is desired, and there is space, add a random nonzero term. */
testutil_random_scalar_order_test(&scalars[filled]);
testutil_random_ge_test(&ge_tmp);
secp256k1_gej_set_ge(&gejs[filled], &ge_tmp);
++filled;
}
if (nonzero_result) {
/* Compute the expected result using normal ecmult. */
CHECK(filled <= 1);
secp256k1_ecmult(&expected, &gejs[0], &scalars[0], &g_scalar);
mults += filled + g_nonzero;
}
/* At this point we have expected = scalar_g*G + sum(scalars[i]*gejs[i] for i=0..filled-1). */
CHECK(filled <= 1 + !nonzero_result);
CHECK(filled <= num_nonzero);
/* Add entries to scalars,gejs so that there are num of them. All the added entries
* either have scalar=0 or point=infinity, so these do not change the expected result. */
while (filled < num) {
if (testrand_bits(1)) {
secp256k1_gej_set_infinity(&gejs[filled]);
testutil_random_scalar_order_test(&scalars[filled]);
} else {
secp256k1_scalar_set_int(&scalars[filled], 0);
testutil_random_ge_test(&ge_tmp);
secp256k1_gej_set_ge(&gejs[filled], &ge_tmp);
}
++filled;
}
/* Now perform cheapish transformations on gejs and scalars, for indices
* 0..num_nonzero-1, which do not change the expected result, but may
* convert some of them to be both non-0-scalar and non-infinity-point. */
for (i = 0; i < rands; ++i) {
int j;
secp256k1_scalar v, iv;
/* Shuffle the entries. */
for (j = 0; j < num_nonzero; ++j) {
int k = testrand_int(num_nonzero - j);
if (k != 0) {
secp256k1_gej gej = gejs[j];
secp256k1_scalar sc = scalars[j];
gejs[j] = gejs[j + k];
scalars[j] = scalars[j + k];
gejs[j + k] = gej;
scalars[j + k] = sc;
}
}
/* Perturb all consecutive pairs of inputs:
* a*P + b*Q -> (a+b)*P + b*(Q-P). */
for (j = 0; j + 1 < num_nonzero; j += 2) {
secp256k1_gej gej;
secp256k1_scalar_add(&scalars[j], &scalars[j], &scalars[j+1]);
secp256k1_gej_neg(&gej, &gejs[j]);
secp256k1_gej_add_var(&gejs[j+1], &gejs[j+1], &gej, NULL);
}
/* Transform the last input: a*P -> (v*a) * ((1/v)*P). */
CHECK(num_nonzero >= 1);
testutil_random_scalar_order_test(&v);
secp256k1_scalar_inverse(&iv, &v);
secp256k1_scalar_mul(&scalars[num_nonzero - 1], &scalars[num_nonzero - 1], &v);
secp256k1_ecmult(&gejs[num_nonzero - 1], &gejs[num_nonzero - 1], &iv, NULL);
++mults;
}
/* Shuffle all entries (0..num-1). */
for (i = 0; i < num; ++i) {
int j = testrand_int(num - i);
if (j != 0) {
secp256k1_gej gej = gejs[i];
secp256k1_scalar sc = scalars[i];
gejs[i] = gejs[i + j];
scalars[i] = scalars[i + j];
gejs[i + j] = gej;
scalars[i + j] = sc;
}
}
/* Compute affine versions of all inputs. */
secp256k1_ge_set_all_gej_var(ges, gejs, filled);
/* Invoke ecmult_multi code. */
data.sc = scalars;
data.pt = ges;
CHECK(ecmult_multi(&CTX->error_callback, scratch, &computed, g_scalar_ptr, ecmult_multi_callback, &data, filled));
mults += num_nonzero + g_nonzero;
/* Compare with expected result. */
CHECK(secp256k1_gej_eq_var(&computed, &expected));
return mults;
}
static void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) {
secp256k1_scalar sc;
secp256k1_ge pt;
secp256k1_gej r;
ecmult_multi_data data;
secp256k1_scratch *scratch_empty;
testutil_random_ge_test(&pt);
testutil_random_scalar_order(&sc);
data.sc = &sc;
data.pt = &pt;
/* Try to multiply 1 point, but scratch space is empty.*/
scratch_empty = secp256k1_scratch_create(&CTX->error_callback, 0);
CHECK(!ecmult_multi(&CTX->error_callback, scratch_empty, &r, &secp256k1_scalar_zero, ecmult_multi_callback, &data, 1));
secp256k1_scratch_destroy(&CTX->error_callback, scratch_empty);
}
static void test_secp256k1_pippenger_bucket_window_inv(void) {
int i;
CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0);
for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) {
/* Bucket_window of 8 is not used with endo */
if (i == 8) {
continue;
}
CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i);
if (i != PIPPENGER_MAX_BUCKET_WINDOW) {
CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i);
}
}
}
/**
* Probabilistically test the function returning the maximum number of possible points
* for a given scratch space.
*/
static void test_ecmult_multi_pippenger_max_points(void) {
size_t scratch_size = testrand_bits(8);
size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
secp256k1_scratch *scratch;
size_t n_points_supported;
int bucket_window = 0;
for(; scratch_size < max_size; scratch_size+=256) {
size_t i;
size_t total_alloc;
size_t checkpoint;
scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size);
CHECK(scratch != NULL);
checkpoint = secp256k1_scratch_checkpoint(&CTX->error_callback, scratch);
n_points_supported = secp256k1_pippenger_max_points(&CTX->error_callback, scratch);
if (n_points_supported == 0) {
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
continue;
}
bucket_window = secp256k1_pippenger_bucket_window(n_points_supported);
/* allocate `total_alloc` bytes over `PIPPENGER_SCRATCH_OBJECTS` many allocations */
total_alloc = secp256k1_pippenger_scratch_size(n_points_supported, bucket_window);
for (i = 0; i < PIPPENGER_SCRATCH_OBJECTS - 1; i++) {
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, 1));
total_alloc--;
}
CHECK(secp256k1_scratch_alloc(&CTX->error_callback, scratch, total_alloc));
secp256k1_scratch_apply_checkpoint(&CTX->error_callback, scratch, checkpoint);
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
}
CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW);
}
static 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.
*/
static void test_ecmult_multi_batching(void) {
static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD;
secp256k1_scalar scG;
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);
/* Get random scalars and group elements and compute result */
testutil_random_scalar_order(&scG);
secp256k1_ecmult(&r2, &r2, &secp256k1_scalar_zero, &scG);
for(i = 0; i < n_points; i++) {
secp256k1_ge ptg;
secp256k1_gej ptgj;
testutil_random_ge_test(&ptg);
secp256k1_gej_set_ge(&ptgj, &ptg);
pt[i] = ptg;
testutil_random_scalar_order(&sc[i]);
secp256k1_ecmult(&ptgj, &ptgj, &sc[i], NULL);
secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL);
}
data.sc = sc;
data.pt = pt;
secp256k1_gej_neg(&r2, &r2);
/* Test with empty scratch space. It should compute the correct result using
* ecmult_mult_simple algorithm which doesn't require a scratch space. */
scratch = secp256k1_scratch_create(&CTX->error_callback, 0);
CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
/* Test with space for 1 point in pippenger. That's not enough because
* ecmult_multi selects strauss which requires more memory. It should
* therefore select the simple algorithm. */
scratch = secp256k1_scratch_create(&CTX->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
for(i = 1; i <= n_points; i++) {
if (i > ECMULT_PIPPENGER_THRESHOLD) {
int bucket_window = secp256k1_pippenger_bucket_window(i);
size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window);
scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
} else {
size_t scratch_size = secp256k1_strauss_scratch_size(i);
scratch = secp256k1_scratch_create(&CTX->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
}
CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
secp256k1_gej_add_var(&r, &r, &r2, NULL);
CHECK(secp256k1_gej_is_infinity(&r));
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
}
free(sc);
free(pt);
}
static void run_ecmult_multi_tests(void) {
secp256k1_scratch *scratch;
int64_t todo = (int64_t)320 * COUNT;
test_secp256k1_pippenger_bucket_window_inv();
test_ecmult_multi_pippenger_max_points();
scratch = secp256k1_scratch_create(&CTX->error_callback, 819200);
test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
test_ecmult_multi(NULL, secp256k1_ecmult_multi_var);
test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single);
test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single);
while (todo > 0) {
todo -= test_ecmult_multi_random(scratch);
}
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
/* Run test_ecmult_multi with space for exactly one point */
scratch = secp256k1_scratch_create(&CTX->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
secp256k1_scratch_destroy(&CTX->error_callback, scratch);
test_ecmult_multi_batch_size_helper();
test_ecmult_multi_batching();
}
static void test_wnaf(const secp256k1_scalar *number, int w) {
secp256k1_scalar x, two, t;
int wnaf[256];
int zeroes = -1;
int i;
int bits;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&two, 2);
bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
CHECK(bits <= 256);
for (i = bits-1; i >= 0; i--) {
int v = wnaf[i];
secp256k1_scalar_mul(&x, &x, &two);
if (v) {
CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
zeroes=0;
CHECK((v & 1) == 1); /* check non-zero elements are odd */
CHECK(v <= (1 << (w-1)) - 1); /* check range below */
CHECK(v >= -(1 << (w-1)) - 1); /* check range above */
} else {
CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */
zeroes++;
}
if (v >= 0) {
secp256k1_scalar_set_int(&t, v);
} else {
secp256k1_scalar_set_int(&t, -v);
secp256k1_scalar_negate(&t, &t);
}
secp256k1_scalar_add(&x, &x, &t);
}
CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
}
static 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, unused;
secp256k1_scalar_set_int(&x, 0);
secp256k1_scalar_set_int(&shift, 1 << w);
/* Make num a 128-bit scalar. */
secp256k1_scalar_split_128(&num, &unused, number);
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.*/
static 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]);
}
}
static 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);
}
}
static void run_wnaf(void) {
int i;
secp256k1_scalar n;
/* Test 0 for fixed wnaf */
test_fixed_wnaf_small();
/* Random tests */
for (i = 0; i < COUNT; i++) {
testutil_random_scalar_order(&n);
test_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));
}
static int test_ecmult_accumulate_cb(secp256k1_scalar* sc, secp256k1_ge* pt, size_t idx, void* data) {
const secp256k1_scalar* indata = (const secp256k1_scalar*)data;
*sc = *indata;
*pt = secp256k1_ge_const_g;
CHECK(idx == 0);
return 1;
}
static void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar* x, secp256k1_scratch* scratch) {
/* Compute x*G in 6 different ways, serialize it uncompressed, and feed it into acc. */
secp256k1_gej rj1, rj2, rj3, rj4, rj5, rj6, gj, infj;
secp256k1_ge r;
unsigned char bytes[65];
size_t size = 65;
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
secp256k1_gej_set_infinity(&infj);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &rj1, x);
secp256k1_ecmult(&rj2, &gj, x, &secp256k1_scalar_zero);
secp256k1_ecmult(&rj3, &infj, &secp256k1_scalar_zero, x);
CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &rj4, x, NULL, NULL, 0));
CHECK(secp256k1_ecmult_multi_var(&CTX->error_callback, scratch, &rj5, &secp256k1_scalar_zero, test_ecmult_accumulate_cb, (void*)x, 1));
secp256k1_ecmult_const(&rj6, &secp256k1_ge_const_g, x);
secp256k1_ge_set_gej_var(&r, &rj1);
CHECK(secp256k1_gej_eq_ge_var(&rj2, &r));
CHECK(secp256k1_gej_eq_ge_var(&rj3, &r));
CHECK(secp256k1_gej_eq_ge_var(&rj4, &r));
CHECK(secp256k1_gej_eq_ge_var(&rj5, &r));
CHECK(secp256k1_gej_eq_ge_var(&rj6, &r));
if (secp256k1_ge_is_infinity(&r)) {
/* Store infinity as 0x00 */
const unsigned char zerobyte[1] = {0};
secp256k1_sha256_write(acc, zerobyte, 1);
} else {
/* Store other points using their uncompressed serialization. */
secp256k1_eckey_pubkey_serialize(&r, bytes, &size, 0);
CHECK(size == 65);
secp256k1_sha256_write(acc, bytes, size);
}
}
static void test_ecmult_constants_2bit(void) {
/* Using test_ecmult_accumulate, test ecmult for:
* - For i in 0..36:
* - Key i
* - Key -i
* - For i in 0..255:
* - For j in 1..255 (only odd values):
* - Key (j*2^i) mod order
*/
secp256k1_scalar x;
secp256k1_sha256 acc;
unsigned char b32[32];
int i, j;
secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(CTX, 65536);
/* Expected hash of all the computed points; created with an independent
* implementation. */
static const unsigned char expected32[32] = {
0xe4, 0x71, 0x1b, 0x4d, 0x14, 0x1e, 0x68, 0x48,
0xb7, 0xaf, 0x47, 0x2b, 0x4c, 0xd2, 0x04, 0x14,
0x3a, 0x75, 0x87, 0x60, 0x1a, 0xf9, 0x63, 0x60,
0xd0, 0xcb, 0x1f, 0xaa, 0x85, 0x9a, 0xb7, 0xb4
};
secp256k1_sha256_initialize(&acc);
for (i = 0; i <= 36; ++i) {
secp256k1_scalar_set_int(&x, i);
test_ecmult_accumulate(&acc, &x, scratch);
secp256k1_scalar_negate(&x, &x);
test_ecmult_accumulate(&acc, &x, scratch);
};
for (i = 0; i < 256; ++i) {
for (j = 1; j < 256; j += 2) {
int k;
secp256k1_scalar_set_int(&x, j);
for (k = 0; k < i; ++k) secp256k1_scalar_add(&x, &x, &x);
test_ecmult_accumulate(&acc, &x, scratch);
}
}
secp256k1_sha256_finalize(&acc, b32);
CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
secp256k1_scratch_space_destroy(CTX, scratch);
}
static void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsigned char* expected32) {
/* Using test_ecmult_accumulate, test ecmult for:
* - Key 0
* - Key 1
* - Key -1
* - For i in range(iter):
* - Key SHA256(LE32(prefix) || LE16(i))
*/
secp256k1_scalar x;
secp256k1_sha256 acc;
unsigned char b32[32];
unsigned char inp[6];
size_t i;
secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(CTX, 65536);
inp[0] = prefix & 0xFF;
inp[1] = (prefix >> 8) & 0xFF;
inp[2] = (prefix >> 16) & 0xFF;
inp[3] = (prefix >> 24) & 0xFF;
secp256k1_sha256_initialize(&acc);
secp256k1_scalar_set_int(&x, 0);
test_ecmult_accumulate(&acc, &x, scratch);
secp256k1_scalar_set_int(&x, 1);
test_ecmult_accumulate(&acc, &x, scratch);
secp256k1_scalar_negate(&x, &x);
test_ecmult_accumulate(&acc, &x, scratch);
for (i = 0; i < iter; ++i) {
secp256k1_sha256 gen;
inp[4] = i & 0xff;
inp[5] = (i >> 8) & 0xff;
secp256k1_sha256_initialize(&gen);
secp256k1_sha256_write(&gen, inp, sizeof(inp));
secp256k1_sha256_finalize(&gen, b32);
secp256k1_scalar_set_b32(&x, b32, NULL);
test_ecmult_accumulate(&acc, &x, scratch);
}
secp256k1_sha256_finalize(&acc, b32);
CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0);
secp256k1_scratch_space_destroy(CTX, scratch);
}
static void run_ecmult_constants(void) {
/* Expected hashes of all points in the tests below. Computed using an
* independent implementation. */
static const unsigned char expected32_6bit20[32] = {
0x68, 0xb6, 0xed, 0x6f, 0x28, 0xca, 0xc9, 0x7f,
0x8e, 0x8b, 0xd6, 0xc0, 0x61, 0x79, 0x34, 0x6e,
0x5a, 0x8f, 0x2b, 0xbc, 0x3e, 0x1f, 0xc5, 0x2e,
0x2a, 0xd0, 0x45, 0x67, 0x7f, 0x95, 0x95, 0x8e
};
static const unsigned char expected32_8bit8[32] = {
0x8b, 0x65, 0x8e, 0xea, 0x86, 0xae, 0x3c, 0x95,
0x90, 0xb6, 0x77, 0xa4, 0x8c, 0x76, 0xd9, 0xec,
0xf5, 0xab, 0x8a, 0x2f, 0xfd, 0xdb, 0x19, 0x12,
0x1a, 0xee, 0xe6, 0xb7, 0x6e, 0x05, 0x3f, 0xc6
};
/* For every combination of 6 bit positions out of 256, restricted to
* 20-bit windows (i.e., the first and last bit position are no more than
* 19 bits apart), all 64 bit patterns occur in the input scalars used in
* this test. */
CONDITIONAL_TEST(1, "test_ecmult_constants_sha 1024") {
test_ecmult_constants_sha(4808378u, 1024, expected32_6bit20);
}
/* For every combination of 8 consecutive bit positions, all 256 bit
* patterns occur in the input scalars used in this test. */
CONDITIONAL_TEST(3, "test_ecmult_constants_sha 2048") {
test_ecmult_constants_sha(1607366309u, 2048, expected32_8bit8);
}
CONDITIONAL_TEST(16, "test_ecmult_constants_2bit") {
test_ecmult_constants_2bit();
}
}
static 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_ge p;
secp256k1_ge pge;
testutil_random_scalar_order_test(&key);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pgej, &key);
testrand256(seed32);
b = CTX->ecmult_gen_ctx.scalar_offset;
p = CTX->ecmult_gen_ctx.ge_offset;
secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, seed32);
CHECK(!secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.scalar_offset));
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pgej2, &key);
CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
CHECK(!secp256k1_ge_eq_var(&p, &CTX->ecmult_gen_ctx.ge_offset));
secp256k1_ge_set_gej(&pge, &pgej);
CHECK(secp256k1_gej_eq_ge_var(&pgej2, &pge));
}
static void test_ecmult_gen_blind_reset(void) {
/* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
secp256k1_scalar b;
secp256k1_ge p1, p2;
secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0);
b = CTX->ecmult_gen_ctx.scalar_offset;
p1 = CTX->ecmult_gen_ctx.ge_offset;
secp256k1_ecmult_gen_blind(&CTX->ecmult_gen_ctx, 0);
CHECK(secp256k1_scalar_eq(&b, &CTX->ecmult_gen_ctx.scalar_offset));
p2 = CTX->ecmult_gen_ctx.ge_offset;
CHECK(secp256k1_ge_eq_var(&p1, &p2));
}
/* Verify that ecmult_gen for scalars gn for which gn + scalar_offset = {-1,0,1}. */
static void test_ecmult_gen_edge_cases(void) {
int i;
secp256k1_gej res1, res2, res3;
secp256k1_scalar gn = secp256k1_scalar_one; /* gn = 1 */
secp256k1_scalar_add(&gn, &gn, &CTX->ecmult_gen_ctx.scalar_offset); /* gn = 1 + scalar_offset */
secp256k1_scalar_negate(&gn, &gn); /* gn = -1 - scalar_offset */
for (i = -1; i < 2; ++i) {
Loop condition is true. Entering loop body
/* Run test with gn = i - scalar_offset (so that the ecmult_gen recoded value represents i). */
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &res1, &gn);
secp256k1_ecmult(&res2, NULL, &secp256k1_scalar_zero, &gn);
Calling 'secp256k1_ecmult'
Passing null pointer value via 2nd parameter 'a'
secp256k1_ecmult_const(&res3, &secp256k1_ge_const_g, &gn);
CHECK(secp256k1_gej_eq_var(&res1, &res2));
CHECK(secp256k1_gej_eq_var(&res1, &res3));
secp256k1_scalar_add(&gn, &gn, &secp256k1_scalar_one);
}
}
static void run_ecmult_gen_blind(void) {
int i;
test_ecmult_gen_blind_reset();
test_ecmult_gen_edge_cases();
for (i = 0; i < 10; i++) {
test_ecmult_gen_blind();
}
}
/***** ENDOMORPHISH TESTS *****/
static void test_scalar_split(const secp256k1_scalar* full) {
secp256k1_scalar s, s1, slam;
const unsigned char zero[32] = {0};
unsigned char tmp[32];
secp256k1_scalar_split_lambda(&s1, &slam, full);
Calling 'secp256k1_scalar_split_lambda'
/* check slam*lambda + s1 == full */
secp256k1_scalar_mul(&s, &secp256k1_const_lambda, &slam);
secp256k1_scalar_add(&s, &s, &s1);
CHECK(secp256k1_scalar_eq(&s, full));
/* check that both are <= 128 bits in size */
if (secp256k1_scalar_is_high(&s1)) {
secp256k1_scalar_negate(&s1, &s1);
}
if (secp256k1_scalar_is_high(&slam)) {
secp256k1_scalar_negate(&slam, &slam);
}
secp256k1_scalar_get_b32(tmp, &s1);
CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0);
secp256k1_scalar_get_b32(tmp, &slam);
CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0);
}
static void run_endomorphism_tests(void) {
unsigned i;
static secp256k1_scalar s;
test_scalar_split(&secp256k1_scalar_zero);
Calling 'test_scalar_split'
test_scalar_split(&secp256k1_scalar_one);
secp256k1_scalar_negate(&s,&secp256k1_scalar_one);
test_scalar_split(&s);
test_scalar_split(&secp256k1_const_lambda);
secp256k1_scalar_add(&s, &secp256k1_const_lambda, &secp256k1_scalar_one);
test_scalar_split(&s);
for (i = 0; i < 100U * COUNT; ++i) {
secp256k1_scalar full;
testutil_random_scalar_order_test(&full);
test_scalar_split(&full);
}
for (i = 0; i < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++i) {
test_scalar_split(&scalars_near_split_bounds[i]);
}
}
static 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;
for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
/* Smaller sizes are tested exhaustively elsewhere. */
int32_t i;
memcpy(&pubkeyc[1], input, 64);
SECP256K1_CHECKMEM_UNDEFINE(&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));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
SECP256K1_CHECKMEM_UNDEFINE(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
SECP256K1_CHECKMEM_CHECK(pubkeyo, outl);
CHECK(outl == 33);
CHECK(secp256k1_memcmp_var(&pubkeyo[1], &pubkeyc[1], 32) == 0);
CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
if (ypass) {
/* This test isn't always done because we decode with alternative signs, so the y won't match. */
CHECK(pubkeyo[0] == ysign);
CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 1);
memset(&pubkey, 0, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
secp256k1_pubkey_save(&pubkey, &ge);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
outl = 65;
SECP256K1_CHECKMEM_UNDEFINE(pubkeyo, 65);
CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
SECP256K1_CHECKMEM_CHECK(pubkeyo, outl);
CHECK(outl == 65);
CHECK(pubkeyo[0] == 4);
CHECK(secp256k1_memcmp_var(&pubkeyo[1], input, 64) == 0);
}
} else {
/* These cases must fail to parse. */
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
}
}
}
}
static 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] = { 0 };
secp256k1_ge ge;
secp256k1_pubkey pubkey;
size_t len;
int32_t i;
/* Nothing should be reading this far into pubkeyc. */
SECP256K1_CHECKMEM_UNDEFINE(&pubkeyc[65], 1);
/* Zero length claimed, fail, zeroize, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(shortkey, 2);
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 0) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
/* Length one claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 256 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
shortkey[0] = i;
SECP256K1_CHECKMEM_UNDEFINE(&shortkey[1], 1);
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 1) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
}
/* Length two claimed, fail, zeroize, no illegal arg error. */
for (i = 0; i < 65536 ; i++) {
memset(&pubkey, 0xfe, sizeof(pubkey));
shortkey[0] = i & 255;
shortkey[1] = i >> 8;
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, shortkey, 2) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
}
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&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);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
/* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_parse(CTX, NULL, pubkeyc, 65));
/* NULL input string. Illegal arg and zeroize output. */
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_parse(CTX, &pubkey, NULL, 65));
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
/* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 64) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
/* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
memset(&pubkey, 0xfe, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 66) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_pubkey_load(CTX, &ge, &pubkey));
/* Valid parse. */
memset(&pubkey, 0, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, 65) == 1);
CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_static, &pubkey, pubkeyc, 65) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&ge, sizeof(ge));
CHECK(secp256k1_pubkey_load(CTX, &ge, &pubkey) == 1);
SECP256K1_CHECKMEM_CHECK(&ge.x, sizeof(ge.x));
SECP256K1_CHECKMEM_CHECK(&ge.y, sizeof(ge.y));
SECP256K1_CHECKMEM_CHECK(&ge.infinity, sizeof(ge.infinity));
CHECK(secp256k1_ge_eq_var(&ge, &secp256k1_ge_const_g));
/* secp256k1_ec_pubkey_serialize illegal args. */
len = 65;
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_serialize(CTX, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED));
CHECK(len == 0);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_serialize(CTX, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED));
len = 65;
SECP256K1_CHECKMEM_UNDEFINE(sout, 65);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_serialize(CTX, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED));
SECP256K1_CHECKMEM_CHECK(sout, 65);
CHECK(len == 0);
len = 65;
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_serialize(CTX, sout, &len, &pubkey, ~0));
CHECK(len == 0);
len = 65;
SECP256K1_CHECKMEM_UNDEFINE(sout, 65);
CHECK(secp256k1_ec_pubkey_serialize(CTX, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
SECP256K1_CHECKMEM_CHECK(sout, 65);
CHECK(len == 65);
/* Multiple illegal args. Should still set arg error only once. */
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_parse(CTX, NULL, NULL, 65));
/* 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);
}
}
static void run_eckey_edge_case_test(void) {
const unsigned char *orderc = secp256k1_group_order_bytes;
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;
/* Group order is too large, reject. */
CHECK(secp256k1_ec_seckey_verify(CTX, orderc) == 0);
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, orderc) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* Maximum value is too large, reject. */
memset(ctmp, 255, 32);
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* Zero is too small, reject. */
memset(ctmp, 0, 32);
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* One must be accepted. */
ctmp[31] = 0x01;
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1);
memset(&pubkey, 0, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
pubkey_one = pubkey;
/* Group order + 1 is too large, reject. */
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x42;
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0);
memset(&pubkey, 1, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* -1 must be accepted. */
ctmp[31] = 0x40;
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1);
memset(&pubkey, 0, sizeof(pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, ctmp) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
pubkey_negone = pubkey;
/* Tweak of zero leaves the value unchanged. */
memset(ctmp2, 0, 32);
CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, ctmp2) == 1);
CHECK(secp256k1_memcmp_var(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
memcpy(&pubkey2, &pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1);
CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Multiply tweak of zero zeroizes the output. */
CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, ctmp2) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, ctmp2) == 0);
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing
seckey, the seckey is zeroized. */
memcpy(ctmp, orderc, 32);
memset(ctmp2, 0, 32);
ctmp2[31] = 0x01;
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp2) == 1);
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 0);
CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, ctmp2) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
memcpy(ctmp, orderc, 32);
CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, ctmp2) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
/* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing
tweak, the seckey is zeroized. */
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp, orderc) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
CHECK(secp256k1_ec_seckey_tweak_mul(CTX, ctmp, orderc) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
/* If pubkey_tweak_add or pubkey_tweak_mul are called with an overflowing
tweak, the pubkey is zeroized. */
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, orderc) == 0);
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, orderc) == 0);
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* If the resulting key in secp256k1_ec_seckey_tweak_add and
* secp256k1_ec_pubkey_tweak_add is 0 the functions fail and in the latter
* case the pubkey is zeroized. */
memcpy(ctmp, orderc, 32);
ctmp[31] = 0x40;
memset(ctmp2, 0, 32);
ctmp2[31] = 1;
CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp2, ctmp) == 0);
CHECK(secp256k1_memcmp_var(zeros, ctmp2, 32) == 0);
ctmp2[31] = 1;
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 0);
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
/* Tweak computation wraps and results in a key of 1. */
ctmp2[31] = 2;
CHECK(secp256k1_ec_seckey_tweak_add(CTX, ctmp2, ctmp) == 1);
CHECK(secp256k1_memcmp_var(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
ctmp2[31] = 2;
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1);
ctmp2[31] = 1;
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, ctmp2) == 1);
CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Tweak mul * 2 = 1+1. */
CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2) == 1);
ctmp2[31] = 2;
CHECK(secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey2, ctmp2) == 1);
CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
/* Zeroize pubkey on parse error. */
memset(&pubkey, 0, 32);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, ctmp2));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
memcpy(&pubkey, &pubkey2, sizeof(pubkey));
memset(&pubkey2, 0, 32);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey2, ctmp2));
CHECK(secp256k1_memcmp_var(&pubkey2, zeros, sizeof(pubkey2)) == 0);
/* Plain argument errors. */
CHECK(secp256k1_ec_seckey_verify(CTX, ctmp) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ec_seckey_verify(CTX, NULL));
memset(ctmp2, 0, 32);
ctmp2[31] = 4;
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_add(CTX, NULL, ctmp2));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, NULL));
memset(ctmp2, 0, 32);
ctmp2[31] = 4;
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_mul(CTX, NULL, ctmp2));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, NULL));
memset(ctmp2, 0, 32);
CHECK_ILLEGAL(CTX, secp256k1_ec_seckey_tweak_add(CTX, NULL, ctmp2));
CHECK_ILLEGAL(CTX, secp256k1_ec_seckey_tweak_add(CTX, ctmp, NULL));
memset(ctmp2, 0, 32);
ctmp2[31] = 1;
CHECK_ILLEGAL(CTX, secp256k1_ec_seckey_tweak_mul(CTX, NULL, ctmp2));
CHECK_ILLEGAL(CTX, secp256k1_ec_seckey_tweak_mul(CTX, ctmp, NULL));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_create(CTX, NULL, ctmp));
memset(&pubkey, 1, sizeof(pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_create(CTX, &pubkey, NULL));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* secp256k1_ec_pubkey_combine tests. */
pubkeys[0] = &pubkey_one;
SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[0], sizeof(secp256k1_pubkey *));
SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[1], sizeof(secp256k1_pubkey *));
SECP256K1_CHECKMEM_UNDEFINE(&pubkeys[2], sizeof(secp256k1_pubkey *));
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 0));
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_combine(CTX, NULL, pubkeys, 1));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_combine(CTX, &pubkey, NULL, 1));
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
pubkeys[0] = &pubkey_negone;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 1) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
len = 33;
CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0);
/* Result is infinity. */
pubkeys[0] = &pubkey_one;
pubkeys[1] = &pubkey_negone;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 2) == 0);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
/* Passes through infinity but comes out one. */
pubkeys[2] = &pubkey_one;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 3) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
len = 33;
CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_ec_pubkey_serialize(CTX, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0);
/* Adds to two. */
pubkeys[1] = &pubkey_one;
memset(&pubkey, 255, sizeof(secp256k1_pubkey));
SECP256K1_CHECKMEM_UNDEFINE(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_ec_pubkey_combine(CTX, &pubkey, pubkeys, 2) == 1);
SECP256K1_CHECKMEM_CHECK(&pubkey, sizeof(secp256k1_pubkey));
CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
}
static void run_eckey_negate_test(void) {
unsigned char seckey[32];
unsigned char seckey_tmp[32];
testutil_random_scalar_order_b32(seckey);
memcpy(seckey_tmp, seckey, 32);
/* Verify negation changes the key and changes it back */
CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 1);
CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) != 0);
CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 1);
CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
/* Negating all 0s fails */
memset(seckey, 0, 32);
memset(seckey_tmp, 0, 32);
CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 0);
/* Check that seckey is not modified */
CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
/* Negating an overflowing seckey fails and the seckey is zeroed. In this
* test, the seckey has 16 random bytes to ensure that ec_seckey_negate
* doesn't just set seckey to a constant value in case of failure. */
testutil_random_scalar_order_b32(seckey);
memset(seckey, 0xFF, 16);
memset(seckey_tmp, 0, 32);
CHECK(secp256k1_ec_seckey_negate(CTX, seckey) == 0);
CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
}
static void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
secp256k1_scalar nonce;
do {
testutil_random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(&CTX->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
}
static void test_ecdsa_sign_verify(void) {
secp256k1_gej pubj;
secp256k1_ge pub;
secp256k1_scalar one;
secp256k1_scalar msg, key;
secp256k1_scalar sigr, sigs;
int getrec;
int recid;
testutil_random_scalar_order_test(&msg);
testutil_random_scalar_order_test(&key);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &pubj, &key);
secp256k1_ge_set_gej(&pub, &pubj);
getrec = testrand_bits(1);
/* The specific way in which this conditional is written sidesteps a potential bug in clang.
See the commit messages of the commit that introduced this comment for details. */
if (getrec) {
random_sign(&sigr, &sigs, &key, &msg, &recid);
CHECK(recid >= 0 && recid < 4);
} else {
random_sign(&sigr, &sigs, &key, &msg, NULL);
}
CHECK(secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_add(&msg, &msg, &one);
CHECK(!secp256k1_ecdsa_sig_verify(&sigr, &sigs, &pub, &msg));
}
static void run_ecdsa_sign_verify(void) {
int i;
for (i = 0; i < 10*COUNT; i++) {
test_ecdsa_sign_verify();
}
}
/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
(void)msg32;
(void)key32;
(void)algo16;
memcpy(nonce32, data, 32);
return (counter == 0);
}
static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
/* Dummy nonce generator that has a fatal error on the first counter value. */
if (counter == 0) {
return 0;
}
return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
}
static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
/* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
if (counter < 3) {
memset(nonce32, counter==0 ? 0 : 255, 32);
if (counter == 2) {
nonce32[31]--;
}
return 1;
}
if (counter < 5) {
memcpy(nonce32, secp256k1_group_order_bytes, 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);
}
static int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
return secp256k1_memcmp_var(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
}
static void test_ecdsa_end_to_end(void) {
unsigned char extra[32] = {0x00};
unsigned char privkey[32];
unsigned char message[32];
unsigned char privkey2[32];
secp256k1_ecdsa_signature signature[6];
secp256k1_scalar r, s;
unsigned char sig[74];
size_t siglen = 74;
unsigned char pubkeyc[65];
size_t pubkeyclen = 65;
secp256k1_pubkey pubkey;
secp256k1_pubkey pubkey_tmp;
unsigned char seckey[300];
size_t seckeylen = 300;
/* Generate a random key and message. */
{
secp256k1_scalar msg, key;
testutil_random_scalar_order_test(&msg);
testutil_random_scalar_order_test(&key);
secp256k1_scalar_get_b32(privkey, &key);
secp256k1_scalar_get_b32(message, &msg);
}
/* Construct and verify corresponding public key. */
CHECK(secp256k1_ec_seckey_verify(CTX, privkey) == 1);
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, privkey) == 1);
/* Verify exporting and importing public key. */
CHECK(secp256k1_ec_pubkey_serialize(CTX, pubkeyc, &pubkeyclen, &pubkey, testrand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
memset(&pubkey, 0, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pubkeyc, pubkeyclen) == 1);
/* Verify negation changes the key and changes it back */
memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey_tmp) == 1);
CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
CHECK(secp256k1_ec_pubkey_negate(CTX, &pubkey_tmp) == 1);
CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
/* Verify private key import and export. */
CHECK(ec_privkey_export_der(CTX, seckey, &seckeylen, privkey, testrand_bits(1) == 1));
CHECK(ec_privkey_import_der(CTX, privkey2, seckey, seckeylen) == 1);
CHECK(secp256k1_memcmp_var(privkey, privkey2, 32) == 0);
/* Optionally tweak the keys using addition. */
if (testrand_int(3) == 0) {
int ret1;
int ret2;
unsigned char rnd[32];
secp256k1_pubkey pubkey2;
testrand256_test(rnd);
ret1 = secp256k1_ec_seckey_tweak_add(CTX, privkey, rnd);
ret2 = secp256k1_ec_pubkey_tweak_add(CTX, &pubkey, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) {
return;
}
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, privkey) == 1);
CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Optionally tweak the keys using multiplication. */
if (testrand_int(3) == 0) {
int ret1;
int ret2;
unsigned char rnd[32];
secp256k1_pubkey pubkey2;
testrand256_test(rnd);
ret1 = secp256k1_ec_seckey_tweak_mul(CTX, privkey, rnd);
ret2 = secp256k1_ec_pubkey_tweak_mul(CTX, &pubkey, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) {
return;
}
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey2, privkey) == 1);
CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
}
/* Sign. */
CHECK(secp256k1_ecdsa_sign(CTX, &signature[0], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign(CTX, &signature[4], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign(CTX, &signature[1], message, privkey, NULL, extra) == 1);
extra[31] = 1;
CHECK(secp256k1_ecdsa_sign(CTX, &signature[2], message, privkey, NULL, extra) == 1);
extra[31] = 0;
extra[0] = 1;
CHECK(secp256k1_ecdsa_sign(CTX, &signature[3], message, privkey, NULL, extra) == 1);
CHECK(secp256k1_memcmp_var(&signature[0], &signature[4], sizeof(signature[0])) == 0);
CHECK(secp256k1_memcmp_var(&signature[0], &signature[1], sizeof(signature[0])) != 0);
CHECK(secp256k1_memcmp_var(&signature[0], &signature[2], sizeof(signature[0])) != 0);
CHECK(secp256k1_memcmp_var(&signature[0], &signature[3], sizeof(signature[0])) != 0);
CHECK(secp256k1_memcmp_var(&signature[1], &signature[2], sizeof(signature[0])) != 0);
CHECK(secp256k1_memcmp_var(&signature[1], &signature[3], sizeof(signature[0])) != 0);
CHECK(secp256k1_memcmp_var(&signature[2], &signature[3], sizeof(signature[0])) != 0);
/* Verify. */
CHECK(secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(CTX, &signature[1], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(CTX, &signature[2], message, &pubkey) == 1);
CHECK(secp256k1_ecdsa_verify(CTX, &signature[3], message, &pubkey) == 1);
/* Test lower-S form, malleate, verify and fail, test again, malleate again */
CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[0]));
secp256k1_ecdsa_signature_load(CTX, &r, &s, &signature[0]);
secp256k1_scalar_negate(&s, &s);
secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 0);
CHECK(secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5]));
CHECK(secp256k1_ecdsa_signature_normalize(CTX, &signature[5], &signature[5]));
CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5]));
CHECK(!secp256k1_ecdsa_signature_normalize(CTX, &signature[5], &signature[5]));
CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 1);
secp256k1_scalar_negate(&s, &s);
secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
CHECK(!secp256k1_ecdsa_signature_normalize(CTX, NULL, &signature[5]));
CHECK(secp256k1_ecdsa_verify(CTX, &signature[5], message, &pubkey) == 1);
CHECK(secp256k1_memcmp_var(&signature[5], &signature[0], 64) == 0);
/* Serialize/parse DER and verify again */
CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, sig, &siglen, &signature[0]) == 1);
memset(&signature[0], 0, sizeof(signature[0]));
CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &signature[0], sig, siglen) == 1);
CHECK(secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 1);
/* Serialize/destroy/parse DER and verify again. */
siglen = 74;
CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, sig, &siglen, &signature[0]) == 1);
sig[testrand_int(siglen)] += 1 + testrand_int(255);
CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &signature[0], sig, siglen) == 0 ||
secp256k1_ecdsa_verify(CTX, &signature[0], message, &pubkey) == 0);
}
static void test_random_pubkeys(void) {
secp256k1_ge elem;
secp256k1_ge elem2;
unsigned char in[65];
/* Generate some randomly sized pubkeys. */
size_t len = testrand_bits(2) == 0 ? 65 : 33;
if (testrand_bits(2) == 0) {
len = testrand_bits(6);
}
if (len == 65) {
in[0] = testrand_bits(1) ? 4 : (testrand_bits(1) ? 6 : 7);
} else {
in[0] = testrand_bits(1) ? 2 : 3;
}
if (testrand_bits(3) == 0) {
in[0] = testrand_bits(8);
}
if (len > 1) {
testrand256(&in[1]);
}
if (len > 33) {
testrand256(&in[33]);
}
if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
unsigned char out[65];
unsigned char firstb;
int res;
size_t size = len;
firstb = in[0];
/* If the pubkey can be parsed, it should round-trip... */
CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
CHECK(size == len);
CHECK(secp256k1_memcmp_var(&in[1], &out[1], len-1) == 0);
/* ... except for the type of hybrid inputs. */
if ((in[0] != 6) && (in[0] != 7)) {
CHECK(in[0] == out[0]);
}
size = 65;
CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
CHECK(size == 65);
CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
CHECK(secp256k1_ge_eq_var(&elem2, &elem));
/* Check that the X9.62 hybrid type is checked. */
in[0] = testrand_bits(1) ? 6 : 7;
res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
if (firstb == 2 || firstb == 3) {
if (in[0] == firstb + 4) {
CHECK(res);
} else {
CHECK(!res);
}
}
if (res) {
CHECK(secp256k1_ge_eq_var(&elem, &elem2));
CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
CHECK(secp256k1_memcmp_var(&in[1], &out[1], 64) == 0);
}
}
}
static void run_pubkey_comparison(void) {
unsigned char pk1_ser[33] = {
0x02,
0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11,
0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23
};
const unsigned char pk2_ser[33] = {
0x02,
0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d,
0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c
};
secp256k1_pubkey pk1;
secp256k1_pubkey pk2;
CHECK(secp256k1_ec_pubkey_parse(CTX, &pk1, pk1_ser, sizeof(pk1_ser)) == 1);
CHECK(secp256k1_ec_pubkey_parse(CTX, &pk2, pk2_ser, sizeof(pk2_ser)) == 1);
CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_ec_pubkey_cmp(CTX, NULL, &pk2) < 0));
CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, NULL) > 0));
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk2) < 0);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk1) > 0);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk1) == 0);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk2) == 0);
{
secp256k1_pubkey pk_tmp;
memset(&pk_tmp, 0, sizeof(pk_tmp)); /* illegal pubkey */
CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk_tmp, &pk2) < 0));
{
int32_t ecount = 0;
secp256k1_context_set_illegal_callback(CTX, counting_callback_fn, &ecount);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk_tmp, &pk_tmp) == 0);
CHECK(ecount == 2);
secp256k1_context_set_illegal_callback(CTX, NULL, NULL);
}
CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk_tmp) > 0));
}
/* Make pk2 the same as pk1 but with 3 rather than 2. Note that in
* an uncompressed encoding, these would have the opposite ordering */
pk1_ser[0] = 3;
CHECK(secp256k1_ec_pubkey_parse(CTX, &pk2, pk1_ser, sizeof(pk1_ser)) == 1);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk1, &pk2) < 0);
CHECK(secp256k1_ec_pubkey_cmp(CTX, &pk2, &pk1) > 0);
}
static void test_sort_helper(secp256k1_pubkey *pk, size_t *pk_order, size_t n_pk) {
size_t i;
const secp256k1_pubkey *pk_test[5];
for (i = 0; i < n_pk; i++) {
pk_test[i] = &pk[pk_order[i]];
}
secp256k1_ec_pubkey_sort(CTX, pk_test, n_pk);
for (i = 0; i < n_pk; i++) {
CHECK(secp256k1_memcmp_var(pk_test[i], &pk[i], sizeof(*pk_test[i])) == 0);
}
}
static void permute(size_t *arr, size_t n) {
size_t i;
for (i = n - 1; i >= 1; i--) {
size_t tmp, j;
j = testrand_int(i + 1);
tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
}
static void test_sort_api(void) {
secp256k1_pubkey pks[2];
const secp256k1_pubkey *pks_ptr[2];
pks_ptr[0] = &pks[0];
pks_ptr[1] = &pks[1];
testutil_random_pubkey_test(&pks[0]);
testutil_random_pubkey_test(&pks[1]);
CHECK(secp256k1_ec_pubkey_sort(CTX, pks_ptr, 2) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_sort(CTX, NULL, 2));
CHECK(secp256k1_ec_pubkey_sort(CTX, pks_ptr, 0) == 1);
/* Test illegal public keys */
memset(&pks[0], 0, sizeof(pks[0]));
CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_ec_pubkey_sort(CTX, pks_ptr, 2) == 1));
memset(&pks[1], 0, sizeof(pks[1]));
{
int32_t ecount = 0;
secp256k1_context_set_illegal_callback(CTX, counting_callback_fn, &ecount);
CHECK(secp256k1_ec_pubkey_sort(CTX, pks_ptr, 2) == 1);
CHECK(ecount == 2);
secp256k1_context_set_illegal_callback(CTX, NULL, NULL);
}
}
static void test_sort(void) {
secp256k1_pubkey pk[5];
unsigned char pk_ser[5][33] = {
{ 0x02, 0x08 },
{ 0x02, 0x0b },
{ 0x02, 0x0c },
{ 0x03, 0x05 },
{ 0x03, 0x0a },
};
int i;
size_t pk_order[5] = { 0, 1, 2, 3, 4 };
for (i = 0; i < 5; i++) {
CHECK(secp256k1_ec_pubkey_parse(CTX, &pk[i], pk_ser[i], sizeof(pk_ser[i])));
}
permute(pk_order, 1);
test_sort_helper(pk, pk_order, 1);
permute(pk_order, 2);
test_sort_helper(pk, pk_order, 2);
permute(pk_order, 3);
test_sort_helper(pk, pk_order, 3);
for (i = 0; i < COUNT; i++) {
permute(pk_order, 4);
test_sort_helper(pk, pk_order, 4);
}
for (i = 0; i < COUNT; i++) {
permute(pk_order, 5);
test_sort_helper(pk, pk_order, 5);
}
/* Check that sorting also works for random pubkeys */
for (i = 0; i < COUNT; i++) {
int j;
const secp256k1_pubkey *pk_ptr[5];
for (j = 0; j < 5; j++) {
testutil_random_pubkey_test(&pk[j]);
pk_ptr[j] = &pk[j];
}
secp256k1_ec_pubkey_sort(CTX, pk_ptr, 5);
for (j = 1; j < 5; j++) {
CHECK(secp256k1_ec_pubkey_sort_cmp(&pk_ptr[j - 1], &pk_ptr[j], CTX) <= 0);
}
}
}
/* Test vectors from BIP-MuSig2 */
static void test_sort_vectors(void) {
enum { N_PUBKEYS = 6 };
unsigned char pk_ser[N_PUBKEYS][33] = {
{ 0x02, 0xDD, 0x30, 0x8A, 0xFE, 0xC5, 0x77, 0x7E, 0x13, 0x12, 0x1F,
0xA7, 0x2B, 0x9C, 0xC1, 0xB7, 0xCC, 0x01, 0x39, 0x71, 0x53, 0x09,
0xB0, 0x86, 0xC9, 0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xB8 },
{ 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34,
0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83,
0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 },
{ 0x03, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, 0x36, 0x18,
0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2,
0xDE, 0xCE, 0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 },
{ 0x02, 0x35, 0x90, 0xA9, 0x4E, 0x76, 0x8F, 0x8E, 0x18, 0x15, 0xC2,
0xF2, 0x4B, 0x4D, 0x80, 0xA8, 0xE3, 0x14, 0x93, 0x16, 0xC3, 0x51,
0x8C, 0xE7, 0xB7, 0xAD, 0x33, 0x83, 0x68, 0xD0, 0x38, 0xCA, 0x66 },
{ 0x02, 0xDD, 0x30, 0x8A, 0xFE, 0xC5, 0x77, 0x7E, 0x13, 0x12, 0x1F,
0xA7, 0x2B, 0x9C, 0xC1, 0xB7, 0xCC, 0x01, 0x39, 0x71, 0x53, 0x09,
0xB0, 0x86, 0xC9, 0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xFF },
{ 0x02, 0xDD, 0x30, 0x8A, 0xFE, 0xC5, 0x77, 0x7E, 0x13, 0x12, 0x1F,
0xA7, 0x2B, 0x9C, 0xC1, 0xB7, 0xCC, 0x01, 0x39, 0x71, 0x53, 0x09,
0xB0, 0x86, 0xC9, 0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xB8 }
};
secp256k1_pubkey pubkeys[N_PUBKEYS];
secp256k1_pubkey *sorted[N_PUBKEYS];
const secp256k1_pubkey *pks_ptr[N_PUBKEYS];
int i;
sorted[0] = &pubkeys[3];
sorted[1] = &pubkeys[0];
sorted[2] = &pubkeys[0];
sorted[3] = &pubkeys[4];
sorted[4] = &pubkeys[1];
sorted[5] = &pubkeys[2];
for (i = 0; i < N_PUBKEYS; i++) {
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkeys[i], pk_ser[i], sizeof(pk_ser[i])));
pks_ptr[i] = &pubkeys[i];
}
CHECK(secp256k1_ec_pubkey_sort(CTX, pks_ptr, N_PUBKEYS) == 1);
for (i = 0; i < N_PUBKEYS; i++) {
CHECK(secp256k1_memcmp_var(pks_ptr[i], sorted[i], sizeof(secp256k1_pubkey)) == 0);
}
}
static void run_pubkey_sort(void) {
test_sort_api();
test_sort();
test_sort_vectors();
}
static void run_random_pubkeys(void) {
int i;
for (i = 0; i < 10*COUNT; i++) {
test_random_pubkeys();
}
}
static void run_ecdsa_end_to_end(void) {
int i;
for (i = 0; i < 64*COUNT; i++) {
test_ecdsa_end_to_end();
}
}
static int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
static const unsigned char zeroes[32] = {0};
int ret = 0;
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;
parsed_der = secp256k1_ecdsa_signature_parse_der(CTX, &sig_der, sig, siglen);
if (parsed_der) {
ret |= (!secp256k1_ecdsa_signature_serialize_compact(CTX, compact_der, &sig_der)) << 0;
valid_der = (secp256k1_memcmp_var(compact_der, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der + 32, zeroes, 32) != 0);
}
if (valid_der) {
ret |= (!secp256k1_ecdsa_signature_serialize_der(CTX, roundtrip_der, &len_der, &sig_der)) << 1;
roundtrips_der = (len_der == siglen) && secp256k1_memcmp_var(roundtrip_der, sig, siglen) == 0;
}
parsed_der_lax = ecdsa_signature_parse_der_lax(CTX, &sig_der_lax, sig, siglen);
if (parsed_der_lax) {
ret |= (!secp256k1_ecdsa_signature_serialize_compact(CTX, compact_der_lax, &sig_der_lax)) << 10;
valid_der_lax = (secp256k1_memcmp_var(compact_der_lax, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der_lax + 32, zeroes, 32) != 0);
}
if (valid_der_lax) {
ret |= (!secp256k1_ecdsa_signature_serialize_der(CTX, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
roundtrips_der_lax = (len_der_lax == siglen) && secp256k1_memcmp_var(roundtrip_der_lax, sig, siglen) == 0;
}
if (certainly_der) {
ret |= (!parsed_der) << 2;
}
if (certainly_not_der) {
ret |= (parsed_der) << 17;
}
if (valid_der) {
ret |= (!roundtrips_der) << 3;
}
if (valid_der) {
ret |= (!roundtrips_der_lax) << 12;
ret |= (len_der != len_der_lax) << 13;
ret |= ((len_der != len_der_lax) || (secp256k1_memcmp_var(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14;
}
ret |= (roundtrips_der != roundtrips_der_lax) << 15;
if (parsed_der) {
ret |= (!parsed_der_lax) << 16;
}
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 = testrand_bits(3);
if (action < 1 && *len > 3) {
/* Delete a byte. */
pos = testrand_int(*len);
memmove(sig + pos, sig + pos + 1, *len - pos - 1);
(*len)--;
return;
} else if (action < 2 && *len < 2048) {
/* Insert a byte. */
pos = testrand_int(1 + *len);
memmove(sig + pos + 1, sig + pos, *len - pos);
sig[pos] = testrand_bits(8);
(*len)++;
return;
} else if (action < 4) {
/* Modify a byte. */
sig[testrand_int(*len)] += 1 + testrand_int(255);
return;
} else { /* action < 8 */
/* Modify a bit. */
sig[testrand_int(*len)] ^= 1 << testrand_bits(3);
return;
}
}
static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
int der;
int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
size_t tlen, elen, glen;
int indet;
int n;
*len = 0;
der = testrand_bits(2) == 0;
*certainly_der = der;
*certainly_not_der = 0;
indet = der ? 0 : testrand_int(10) == 0;
for (n = 0; n < 2; n++) {
/* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
nlow[n] = der ? 1 : (testrand_bits(3) != 0);
/* The length of the number in bytes (the first byte of which will always be nonzero) */
nlen[n] = nlow[n] ? testrand_int(33) : 32 + testrand_int(200) * testrand_bits(3) / 8;
CHECK(nlen[n] <= 232);
/* The top bit of the number. */
nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : testrand_bits(1));
/* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + testrand_bits(7) : 1 + testrand_int(127));
/* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? testrand_int(3) : testrand_int(300 - nlen[n]) * testrand_bits(3) / 8);
if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
*certainly_not_der = 1;
}
CHECK(nlen[n] + nzlen[n] <= 300);
/* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
if (!der) {
/* nlenlen[n] max 127 bytes */
int add = testrand_int(127 - nlenlen[n]) * testrand_bits(4) * testrand_bits(4) / 256;
nlenlen[n] += add;
if (add != 0) {
*certainly_not_der = 1;
}
}
CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
}
/* The total length of the data to go, so far */
tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
CHECK(tlen <= 856);
/* The length of the garbage inside the tuple. */
elen = (der || indet) ? 0 : testrand_int(980 - tlen) * testrand_bits(3) / 8;
if (elen != 0) {
*certainly_not_der = 1;
}
tlen += elen;
CHECK(tlen <= 980);
/* The length of the garbage after the end of the tuple. */
glen = der ? 0 : testrand_int(990 - tlen) * testrand_bits(3) / 8;
if (glen != 0) {
*certainly_not_der = 1;
}
CHECK(tlen + glen <= 990);
/* Write the tuple header. */
sig[(*len)++] = 0x30;
if (indet) {
/* Indeterminate length */
sig[(*len)++] = 0x80;
*certainly_not_der = 1;
} else {
int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
if (!der) {
int add = testrand_int(127 - tlenlen) * testrand_bits(4) * testrand_bits(4) / 256;
tlenlen += add;
if (add != 0) {
*certainly_not_der = 1;
}
}
if (tlenlen == 0) {
/* Short length notation */
sig[(*len)++] = tlen;
} else {
/* Long length notation */
sig[(*len)++] = 128 + tlenlen;
assign_big_endian(sig + *len, tlenlen, tlen);
*len += tlenlen;
}
tlen += tlenlen;
}
tlen += 2;
CHECK(tlen + glen <= 1119);
for (n = 0; n < 2; n++) {
/* Write the integer header. */
sig[(*len)++] = 0x02;
if (nlenlen[n] == 0) {
/* Short length notation */
sig[(*len)++] = nlen[n] + nzlen[n];
} else {
/* Long length notation. */
sig[(*len)++] = 128 + nlenlen[n];
assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
*len += nlenlen[n];
}
/* Write zero padding */
while (nzlen[n] > 0) {
sig[(*len)++] = 0x00;
nzlen[n]--;
}
if (nlen[n] == 32 && !nlow[n]) {
/* Special extra 16 0xFF bytes in "high" 32-byte numbers */
int i;
for (i = 0; i < 16; i++) {
sig[(*len)++] = 0xFF;
}
nlen[n] -= 16;
}
/* Write first byte of number */
if (nlen[n] > 0) {
sig[(*len)++] = nhbyte[n];
nlen[n]--;
}
/* Generate remaining random bytes of number */
testrand_bytes_test(sig + *len, nlen[n]);
*len += nlen[n];
nlen[n] = 0;
}
/* Generate random garbage inside tuple. */
testrand_bytes_test(sig + *len, elen);
*len += elen;
/* Generate end-of-contents bytes. */
if (indet) {
sig[(*len)++] = 0;
sig[(*len)++] = 0;
tlen += 2;
}
CHECK(tlen + glen <= 1121);
/* Generate random garbage outside tuple. */
testrand_bytes_test(sig + *len, glen);
*len += glen;
tlen += glen;
CHECK(tlen <= 1121);
CHECK(tlen == *len);
}
static 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. */
static void test_ecdsa_edge_cases(void) {
int t;
secp256k1_ecdsa_signature sig;
/* Test the case where ECDSA recomputes a point that is infinity. */
{
secp256k1_gej keyj;
secp256k1_ge key;
secp256k1_scalar msg;
secp256k1_scalar sr, ss;
secp256k1_scalar_set_int(&ss, 1);
secp256k1_scalar_negate(&ss, &ss);
secp256k1_scalar_inverse(&ss, &ss);
secp256k1_scalar_set_int(&sr, 1);
secp256k1_ecmult_gen(&CTX->ecmult_gen_ctx, &keyj, &sr);
secp256k1_ge_set_gej(&key, &keyj);
msg = ss;
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
Calling 'secp256k1_ecdsa_sig_verify'
}
/* 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( &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(&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(&sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_set_int(&ss, 1);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0);
}
/* Verify signature with message 1 passes. */
{
const unsigned char pubkey[33] = {
0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
0x25
};
const unsigned char pubkey2[33] = {
0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
0x62
};
const unsigned char csr[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
};
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(&sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 1);
secp256k1_scalar_set_int(&ss, 2);
secp256k1_scalar_inverse_var(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key2, &msg) == 0);
}
/* Verify signature with message -1 passes. */
{
const unsigned char pubkey[33] = {
0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
0xf1
};
const unsigned char csr[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
};
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(&sr, &ss, &key, &msg) == 1);
secp256k1_scalar_negate(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 1);
secp256k1_scalar_set_int(&ss, 3);
secp256k1_scalar_inverse_var(&ss, &ss);
CHECK(secp256k1_ecdsa_sig_verify(&sr, &ss, &key, &msg) == 0);
}
/* Signature where s would be zero. */
{
secp256k1_pubkey pubkey;
size_t siglen;
unsigned char signature[72];
static const unsigned char nonce[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
};
static const unsigned char nonce2[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
};
const unsigned char key[32] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
};
unsigned char msg[32] = {
0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
};
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_ILLEGAL(CTX, secp256k1_ecdsa_sign(CTX, NULL, msg, key, precomputed_nonce_function, nonce2));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_sign(CTX, &sig, NULL, key, precomputed_nonce_function, nonce2));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_sign(CTX, &sig, msg, NULL, precomputed_nonce_function, nonce2));
CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
CHECK(secp256k1_ec_pubkey_create(CTX, &pubkey, key) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_verify(CTX, NULL, msg, &pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_verify(CTX, &sig, NULL, &pubkey));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_verify(CTX, &sig, msg, NULL));
CHECK(secp256k1_ecdsa_verify(CTX, &sig, msg, &pubkey) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ec_pubkey_create(CTX, &pubkey, NULL));
/* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_verify(CTX, &sig, msg, &pubkey));
siglen = 72;
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_serialize_der(CTX, NULL, &siglen, &sig));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_serialize_der(CTX, signature, NULL, &sig));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_serialize_der(CTX, signature, &siglen, NULL));
CHECK(secp256k1_ecdsa_signature_serialize_der(CTX, signature, &siglen, &sig) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_parse_der(CTX, NULL, signature, siglen));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_parse_der(CTX, &sig, NULL, siglen));
CHECK(secp256k1_ecdsa_signature_parse_der(CTX, &sig, signature, siglen) == 1);
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_ILLEGAL(CTX, secp256k1_ecdsa_signature_normalize(CTX, NULL, NULL));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_serialize_compact(CTX, NULL, &sig));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_serialize_compact(CTX, signature, NULL));
CHECK(secp256k1_ecdsa_signature_serialize_compact(CTX, signature, &sig) == 1);
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_parse_compact(CTX, NULL, signature));
CHECK_ILLEGAL(CTX, secp256k1_ecdsa_signature_parse_compact(CTX, &sig, NULL));
CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, &sig, signature) == 1);
memset(signature, 255, 64);
CHECK(secp256k1_ecdsa_signature_parse_compact(CTX, &sig, signature) == 0);
}
/* Nonce function corner cases. */
for (t = 0; t < 2; t++) {
static const unsigned char zero[32] = {0x00};
int i;
unsigned char key[32];
unsigned char msg[32];
secp256k1_ecdsa_signature sig2;
secp256k1_scalar sr[512], ss;
const unsigned char *extra;
extra = t == 0 ? NULL : zero;
memset(msg, 0, 32);
msg[31] = 1;
/* High key results in signature failure. */
memset(key, 0xFF, 32);
CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, NULL, extra) == 0);
CHECK(is_empty_signature(&sig));
/* Zero key results in signature failure. */
memset(key, 0, 32);
CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, NULL, extra) == 0);
CHECK(is_empty_signature(&sig));
/* Nonce function failure results in signature failure. */
key[31] = 1;
CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, nonce_function_test_fail, extra) == 0);
CHECK(is_empty_signature(&sig));
/* The retry loop successfully makes its way to the first good value. */
CHECK(secp256k1_ecdsa_sign(CTX, &sig, msg, key, nonce_function_test_retry, extra) == 1);
CHECK(!is_empty_signature(&sig));
CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
CHECK(!is_empty_signature(&sig2));
CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0);
/* The default nonce function is deterministic. */
CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0);
/* The default nonce function changes output with different messages. */
for(i = 0; i < 256; i++) {
int j;
msg[0] = i;
CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
secp256k1_ecdsa_signature_load(CTX, &sr[i], &ss, &sig2);
for (j = 0; j < i; j++) {
CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
}
}
msg[0] = 0;
msg[31] = 2;
/* The default nonce function changes output with different keys. */
for(i = 256; i < 512; i++) {
int j;
key[0] = i - 256;
CHECK(secp256k1_ecdsa_sign(CTX, &sig2, msg, key, NULL, extra) == 1);
CHECK(!is_empty_signature(&sig2));
secp256k1_ecdsa_signature_load(CTX, &sr[i], &ss, &sig2);
for (j = 0; j < i; j++) {
CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
}
}
key[0] = 0;
}
{
/* Check that optional nonce arguments do not have equivalent effect. */
const unsigned char zeros[32] = {0};
unsigned char nonce[32];
unsigned char nonce2[32];
unsigned char nonce3[32];
unsigned char nonce4[32];
SECP256K1_CHECKMEM_UNDEFINE(nonce,32);
SECP256K1_CHECKMEM_UNDEFINE(nonce2,32);
SECP256K1_CHECKMEM_UNDEFINE(nonce3,32);
SECP256K1_CHECKMEM_UNDEFINE(nonce4,32);
CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
SECP256K1_CHECKMEM_CHECK(nonce,32);
CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
SECP256K1_CHECKMEM_CHECK(nonce2,32);
CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
SECP256K1_CHECKMEM_CHECK(nonce3,32);
CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
SECP256K1_CHECKMEM_CHECK(nonce4,32);
CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0);
CHECK(secp256k1_memcmp_var(nonce, nonce3, 32) != 0);
CHECK(secp256k1_memcmp_var(nonce, nonce4, 32) != 0);
CHECK(secp256k1_memcmp_var(nonce2, nonce3, 32) != 0);
CHECK(secp256k1_memcmp_var(nonce2, nonce4, 32) != 0);
CHECK(secp256k1_memcmp_var(nonce3, nonce4, 32) != 0);
}
/* Privkey export where pubkey is the point at infinity. */
{
unsigned char privkey[300];
const unsigned char *seckey = secp256k1_group_order_bytes;
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));
}
}
static void run_ecdsa_edge_cases(void) {
test_ecdsa_edge_cases();
}
/** Wycheproof tests
The tests check for known attacks (range checks in (r,s), arithmetic errors, malleability).
*/
static void test_ecdsa_wycheproof(void) {
#include "wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h"
int t;
for (t = 0; t < SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS; t++) {
secp256k1_ecdsa_signature signature;
secp256k1_sha256 hasher;
secp256k1_pubkey pubkey;
const unsigned char *msg, *sig, *pk;
unsigned char out[32] = {0};
int actual_verify = 0;
memset(&pubkey, 0, sizeof(pubkey));
pk = &wycheproof_ecdsa_public_keys[testvectors[t].pk_offset];
CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, pk, 65) == 1);
secp256k1_sha256_initialize(&hasher);
msg = &wycheproof_ecdsa_messages[testvectors[t].msg_offset];
secp256k1_sha256_write(&hasher, msg, testvectors[t].msg_len);
secp256k1_sha256_finalize(&hasher, out);
sig = &wycheproof_ecdsa_signatures[testvectors[t].sig_offset];
if (secp256k1_ecdsa_signature_parse_der(CTX, &signature, sig, testvectors[t].sig_len) == 1) {
actual_verify = secp256k1_ecdsa_verify(CTX, (const secp256k1_ecdsa_signature *)&signature, out, &pubkey);
}
CHECK(testvectors[t].expected_verify == actual_verify);
}
}
/* Tests cases from Wycheproof test suite. */
static void run_ecdsa_wycheproof(void) {
test_ecdsa_wycheproof();
}
#ifdef ENABLE_MODULE_ECDH
# include "modules/ecdh/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_RECOVERY
# include "modules/recovery/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_EXTRAKEYS
# include "modules/extrakeys/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_SCHNORRSIG
# include "modules/schnorrsig/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_MUSIG
# include "modules/musig/tests_impl.h"
#endif
#ifdef ENABLE_MODULE_ELLSWIFT
# include "modules/ellswift/tests_impl.h"
#endif
static void run_secp256k1_memczero_test(void) {
unsigned char buf1[6] = {1, 2, 3, 4, 5, 6};
unsigned char buf2[sizeof(buf1)];
/* secp256k1_memczero(..., ..., 0) is a noop. */
memcpy(buf2, buf1, sizeof(buf1));
secp256k1_memczero(buf1, sizeof(buf1), 0);
CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0);
/* secp256k1_memczero(..., ..., 1) zeros the buffer. */
memset(buf2, 0, sizeof(buf2));
secp256k1_memczero(buf1, sizeof(buf1) , 1);
CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0);
}
static void run_secp256k1_is_zero_array_test(void) {
unsigned char buf1[3] = {0, 1};
unsigned char buf2[3] = {1, 0};
CHECK(secp256k1_is_zero_array(buf1, 0) == 1);
CHECK(secp256k1_is_zero_array(buf1, 1) == 1);
CHECK(secp256k1_is_zero_array(buf1, 2) == 0);
CHECK(secp256k1_is_zero_array(buf2, 1) == 0);
CHECK(secp256k1_is_zero_array(buf2, 2) == 0);
}
static void run_secp256k1_byteorder_tests(void) {
{
const uint32_t x = 0xFF03AB45;
const unsigned char x_be[4] = {0xFF, 0x03, 0xAB, 0x45};
unsigned char buf[4];
uint32_t x_;
secp256k1_write_be32(buf, x);
CHECK(secp256k1_memcmp_var(buf, x_be, sizeof(buf)) == 0);
x_ = secp256k1_read_be32(buf);
CHECK(x == x_);
}
{
const uint64_t x = 0xCAFE0123BEEF4567;
const unsigned char x_be[8] = {0xCA, 0xFE, 0x01, 0x23, 0xBE, 0xEF, 0x45, 0x67};
unsigned char buf[8];
uint64_t x_;
secp256k1_write_be64(buf, x);
CHECK(secp256k1_memcmp_var(buf, x_be, sizeof(buf)) == 0);
x_ = secp256k1_read_be64(buf);
CHECK(x == x_);
}
}
static void int_cmov_test(void) {
int r = INT_MAX;
int a = 0;
secp256k1_int_cmov(&r, &a, 0);
CHECK(r == INT_MAX);
r = 0; a = INT_MAX;
secp256k1_int_cmov(&r, &a, 1);
CHECK(r == INT_MAX);
a = 0;
secp256k1_int_cmov(&r, &a, 1);
CHECK(r == 0);
a = 1;
secp256k1_int_cmov(&r, &a, 1);
CHECK(r == 1);
r = 1; a = 0;
secp256k1_int_cmov(&r, &a, 0);
CHECK(r == 1);
}
static void fe_cmov_test(void) {
static const secp256k1_fe zero = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0);
static const secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
static const secp256k1_fe max = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
);
secp256k1_fe r = max;
secp256k1_fe a = zero;
secp256k1_fe_cmov(&r, &a, 0);
CHECK(fe_identical(&r, &max));
r = zero; a = max;
secp256k1_fe_cmov(&r, &a, 1);
CHECK(fe_identical(&r, &max));
a = zero;
secp256k1_fe_cmov(&r, &a, 1);
CHECK(fe_identical(&r, &zero));
a = one;
secp256k1_fe_cmov(&r, &a, 1);
CHECK(fe_identical(&r, &one));
r = one; a = zero;
secp256k1_fe_cmov(&r, &a, 0);
CHECK(fe_identical(&r, &one));
}
static void fe_storage_cmov_test(void) {
static const secp256k1_fe_storage zero = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0);
static const secp256k1_fe_storage one = SECP256K1_FE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
static const secp256k1_fe_storage max = SECP256K1_FE_STORAGE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
);
secp256k1_fe_storage r = max;
secp256k1_fe_storage a = zero;
secp256k1_fe_storage_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
r = zero; a = max;
secp256k1_fe_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
a = zero;
secp256k1_fe_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
a = one;
secp256k1_fe_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
r = one; a = zero;
secp256k1_fe_storage_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
}
static void scalar_cmov_test(void) {
static const secp256k1_scalar max = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364140UL
);
secp256k1_scalar r = max;
secp256k1_scalar a = secp256k1_scalar_zero;
secp256k1_scalar_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
r = secp256k1_scalar_zero; a = max;
secp256k1_scalar_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
a = secp256k1_scalar_zero;
secp256k1_scalar_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &secp256k1_scalar_zero, sizeof(r)) == 0);
a = secp256k1_scalar_one;
secp256k1_scalar_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &secp256k1_scalar_one, sizeof(r)) == 0);
r = secp256k1_scalar_one; a = secp256k1_scalar_zero;
secp256k1_scalar_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &secp256k1_scalar_one, sizeof(r)) == 0);
}
static void ge_storage_cmov_test(void) {
static const secp256k1_ge_storage zero = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
static const secp256k1_ge_storage one = SECP256K1_GE_STORAGE_CONST(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1);
static const secp256k1_ge_storage max = SECP256K1_GE_STORAGE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
);
secp256k1_ge_storage r = max;
secp256k1_ge_storage a = zero;
secp256k1_ge_storage_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
r = zero; a = max;
secp256k1_ge_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
a = zero;
secp256k1_ge_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
a = one;
secp256k1_ge_storage_cmov(&r, &a, 1);
CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
r = one; a = zero;
secp256k1_ge_storage_cmov(&r, &a, 0);
CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
}
static void run_cmov_tests(void) {
int_cmov_test();
fe_cmov_test();
fe_storage_cmov_test();
scalar_cmov_test();
ge_storage_cmov_test();
}
/* --------------------------------------------------------- */
/* Test Registry */
/* --------------------------------------------------------- */
/* --- Special test cases that must run before RNG initialization --- */
static const struct tf_test_entry tests_no_rng[] = {
CASE(xoshiro256pp_tests),
};
static const struct tf_test_module registry_modules_no_rng = MAKE_TEST_MODULE(no_rng);
/* --- Standard test cases start here --- */
static const struct tf_test_entry tests_general[] = {
CASE(selftest_tests),
CASE(all_proper_context_tests),
CASE(all_static_context_tests),
CASE(deprecated_context_flags_test),
CASE(scratch_tests),
};
static const struct tf_test_entry tests_integer[] = {
#ifdef SECP256K1_WIDEMUL_INT128
CASE(int128_tests),
#endif
CASE(ctz_tests),
CASE(modinv_tests),
CASE(inverse_tests),
};
static const struct tf_test_entry tests_hash[] = {
CASE(sha256_known_output_tests),
CASE(sha256_counter_tests),
CASE(hmac_sha256_tests),
CASE(rfc6979_hmac_sha256_tests),
CASE(tagged_sha256_tests),
};
static const struct tf_test_entry tests_scalar[] = {
CASE(scalar_tests),
};
static const struct tf_test_entry tests_field[] = {
CASE(field_half),
CASE(field_misc),
CASE(field_convert),
CASE(field_be32_overflow),
CASE(fe_mul),
CASE(sqr),
CASE(sqrt),
};
static const struct tf_test_entry tests_group[] = {
CASE(ge),
CASE(gej),
CASE(group_decompress),
};
static const struct tf_test_entry tests_ecmult[] = {
CASE(ecmult_pre_g),
CASE(wnaf),
CASE(point_times_order),
CASE(ecmult_near_split_bound),
CASE(ecmult_chain),
CASE(ecmult_constants),
CASE(ecmult_gen_blind),
CASE(ecmult_const_tests),
CASE(ecmult_multi_tests),
CASE(ec_combine),
};
static const struct tf_test_entry tests_ec[] = {
CASE(endomorphism_tests),
CASE(ec_pubkey_parse_test),
CASE(eckey_edge_case_test),
CASE(eckey_negate_test),
};
static const struct tf_test_entry tests_ecdsa[] = {
CASE(ec_illegal_argument_tests),
CASE(pubkey_comparison),
CASE(pubkey_sort),
CASE(random_pubkeys),
CASE(ecdsa_der_parse),
CASE(ecdsa_sign_verify),
CASE(ecdsa_end_to_end),
CASE(ecdsa_edge_cases),
CASE(ecdsa_wycheproof),
};
static const struct tf_test_entry tests_utils[] = {
CASE(hsort_tests),
CASE(secp256k1_memczero_test),
CASE(secp256k1_is_zero_array_test),
CASE(secp256k1_byteorder_tests),
CASE(cmov_tests),
};
/* Register test modules */
static const struct tf_test_module registry_modules[] = {
MAKE_TEST_MODULE(general),
MAKE_TEST_MODULE(integer),
MAKE_TEST_MODULE(hash),
MAKE_TEST_MODULE(scalar),
MAKE_TEST_MODULE(field),
MAKE_TEST_MODULE(group),
MAKE_TEST_MODULE(ecmult),
MAKE_TEST_MODULE(ec),
#ifdef ENABLE_MODULE_ECDH
MAKE_TEST_MODULE(ecdh),
#endif
MAKE_TEST_MODULE(ecdsa),
#ifdef ENABLE_MODULE_RECOVERY
/* ECDSA pubkey recovery tests */
MAKE_TEST_MODULE(recovery),
#endif
#ifdef ENABLE_MODULE_EXTRAKEYS
MAKE_TEST_MODULE(extrakeys),
#endif
#ifdef ENABLE_MODULE_SCHNORRSIG
MAKE_TEST_MODULE(schnorrsig),
#endif
#ifdef ENABLE_MODULE_MUSIG
MAKE_TEST_MODULE(musig),
#endif
#ifdef ENABLE_MODULE_ELLSWIFT
MAKE_TEST_MODULE(ellswift),
#endif
MAKE_TEST_MODULE(utils),
};
/* Setup test environment */
static int setup(void) {
/* Create a global context available to all tests */
CTX = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
/* Randomize the context only with probability 15/16
to make sure we test without context randomization from time to time.
TODO Reconsider this when recalibrating the tests. */
if (testrand_bits(4)) {
unsigned char rand32[32];
testrand256(rand32);
CHECK(secp256k1_context_randomize(CTX, rand32));
}
/* Make a writable copy of secp256k1_context_static in order to test the effect of API functions
that write to the context. The API does not support cloning the static context, so we use
memcpy instead. The user is not supposed to copy a context but we should still ensure that
the API functions handle copies of the static context gracefully. */
STATIC_CTX = malloc(sizeof(*secp256k1_context_static));
CHECK(STATIC_CTX != NULL);
memcpy(STATIC_CTX, secp256k1_context_static, sizeof(secp256k1_context));
CHECK(!secp256k1_context_is_proper(STATIC_CTX));
return 0;
}
/* Shutdown test environment */
static int teardown(void) {
free(STATIC_CTX);
secp256k1_context_destroy(CTX);
return 0;
}
int main(int argc, char **argv) {
struct tf_framework tf = {0};
tf.registry_modules = registry_modules;
tf.num_modules = sizeof(registry_modules) / sizeof(registry_modules[0]);
tf.registry_no_rng = &registry_modules_no_rng;
/* Add context creation/destruction functions */
tf.fn_setup = setup;
tf.fn_teardown = teardown;
/* Init and run framework */
if (tf_init(&tf, argc, argv) != 0) return EXIT_FAILURE;
return tf_run(&tf);
}