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Update libsecp256k1

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This commit is contained in:
Gustav Simonsson
2015-09-28 17:46:17 +02:00
parent 7977e87ce1
commit 1d20b0247c
86 changed files with 6279 additions and 2772 deletions
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32
crypto/secp256k1/libsecp256k1/src/basic-config.h Normal file
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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_BASIC_CONFIG_
#define _SECP256K1_BASIC_CONFIG_
#ifdef USE_BASIC_CONFIG
#undef USE_ASM_X86_64
#undef USE_ENDOMORPHISM
#undef USE_FIELD_10X26
#undef USE_FIELD_5X52
#undef USE_FIELD_INV_BUILTIN
#undef USE_FIELD_INV_NUM
#undef USE_NUM_GMP
#undef USE_NUM_NONE
#undef USE_SCALAR_4X64
#undef USE_SCALAR_8X32
#undef USE_SCALAR_INV_BUILTIN
#undef USE_SCALAR_INV_NUM
#define USE_NUM_NONE 1
#define USE_FIELD_INV_BUILTIN 1
#define USE_SCALAR_INV_BUILTIN 1
#define USE_FIELD_10X26 1
#define USE_SCALAR_8X32 1
#endif // USE_BASIC_CONFIG
#endif // _SECP256K1_BASIC_CONFIG_

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crypto/secp256k1/libsecp256k1/src/bench.h Normal file
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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_BENCH_H_
#define _SECP256K1_BENCH_H_
#include <stdio.h>
#include <math.h>
#include "sys/time.h"
static double gettimedouble(void) {
struct timeval tv;
gettimeofday(&tv, NULL);
return tv.tv_usec * 0.000001 + tv.tv_sec;
}
void print_number(double x) {
double y = x;
int c = 0;
if (y < 0.0) {
y = -y;
}
while (y < 100.0) {
y *= 10.0;
c++;
}
printf("%.*f", c, x);
}
void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) {
int i;
double min = HUGE_VAL;
double sum = 0.0;
double max = 0.0;
for (i = 0; i < count; i++) {
double begin, total;
if (setup != NULL) {
setup(data);
}
begin = gettimedouble();
benchmark(data);
total = gettimedouble() - begin;
if (teardown != NULL) {
teardown(data);
}
if (total < min) {
min = total;
}
if (total > max) {
max = total;
}
sum += total;
}
printf("%s: min ", name);
print_number(min * 1000000.0 / iter);
printf("us / avg ");
print_number((sum / count) * 1000000.0 / iter);
printf("us / max ");
print_number(max * 1000000.0 / iter);
printf("us\n");
}
#endif

53
crypto/secp256k1/libsecp256k1/src/bench_ecdh.c Normal file
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/**********************************************************************
* Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <string.h>
#include "include/secp256k1.h"
#include "include/secp256k1_ecdh.h"
#include "util.h"
#include "bench.h"
typedef struct {
secp256k1_context *ctx;
secp256k1_pubkey point;
unsigned char scalar[32];
} bench_ecdh_t;
static void bench_ecdh_setup(void* arg) {
int i;
bench_ecdh_t *data = (bench_ecdh_t*)arg;
const unsigned char point[] = {
0x03,
0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
};
data->ctx = secp256k1_context_create(0);
for (i = 0; i < 32; i++) {
data->scalar[i] = i + 1;
}
CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
}
static void bench_ecdh(void* arg) {
int i;
unsigned char res[32];
bench_ecdh_t *data = (bench_ecdh_t*)arg;
for (i = 0; i < 20000; i++) {
CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar) == 1);
}
}
int main(void) {
bench_ecdh_t data;
run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, 20000);
return 0;
}

354
crypto/secp256k1/libsecp256k1/src/bench_internal.c Normal file
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/**********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <stdio.h>
#include "include/secp256k1.h"
#include "util.h"
#include "hash_impl.h"
#include "num_impl.h"
#include "field_impl.h"
#include "group_impl.h"
#include "scalar_impl.h"
#include "ecmult_const_impl.h"
#include "ecmult_impl.h"
#include "bench.h"
#include "secp256k1.c"
typedef struct {
secp256k1_scalar scalar_x, scalar_y;
secp256k1_fe fe_x, fe_y;
secp256k1_ge ge_x, ge_y;
secp256k1_gej gej_x, gej_y;
unsigned char data[64];
int wnaf[256];
} bench_inv_t;
void bench_setup(void* arg) {
bench_inv_t *data = (bench_inv_t*)arg;
static const unsigned char init_x[32] = {
0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13,
0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35,
0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59,
0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83
};
static const unsigned char init_y[32] = {
0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83,
0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5,
0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9,
0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3
};
secp256k1_scalar_set_b32(&data->scalar_x, init_x, NULL);
secp256k1_scalar_set_b32(&data->scalar_y, init_y, NULL);
secp256k1_fe_set_b32(&data->fe_x, init_x);
secp256k1_fe_set_b32(&data->fe_y, init_y);
CHECK(secp256k1_ge_set_xo_var(&data->ge_x, &data->fe_x, 0));
CHECK(secp256k1_ge_set_xo_var(&data->ge_y, &data->fe_y, 1));
secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
memcpy(data->data, init_x, 32);
memcpy(data->data + 32, init_y, 32);
}
void bench_scalar_add(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_scalar_negate(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_scalar_negate(&data->scalar_x, &data->scalar_x);
}
}
void bench_scalar_sqr(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_scalar_sqr(&data->scalar_x, &data->scalar_x);
}
}
void bench_scalar_mul(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_scalar_mul(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
#ifdef USE_ENDOMORPHISM
void bench_scalar_split(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_scalar l, r;
secp256k1_scalar_split_lambda(&l, &r, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
#endif
void bench_scalar_inverse(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000; i++) {
secp256k1_scalar_inverse(&data->scalar_x, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_scalar_inverse_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000; i++) {
secp256k1_scalar_inverse_var(&data->scalar_x, &data->scalar_x);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_field_normalize(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_fe_normalize(&data->fe_x);
}
}
void bench_field_normalize_weak(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 2000000; i++) {
secp256k1_fe_normalize_weak(&data->fe_x);
}
}
void bench_field_mul(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_fe_mul(&data->fe_x, &data->fe_x, &data->fe_y);
}
}
void bench_field_sqr(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_fe_sqr(&data->fe_x, &data->fe_x);
}
}
void bench_field_inverse(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_inv(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_field_inverse_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_inv_var(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_field_sqrt_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_fe_sqrt_var(&data->fe_x, &data->fe_x);
secp256k1_fe_add(&data->fe_x, &data->fe_y);
}
}
void bench_group_double_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL);
}
}
void bench_group_add_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL);
}
}
void bench_group_add_affine(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_ge(&data->gej_x, &data->gej_x, &data->ge_y);
}
}
void bench_group_add_affine_var(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 200000; i++) {
secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL);
}
}
void bench_ecmult_wnaf(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_wnaf_const(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A);
secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
}
}
void bench_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_sha256_t sha;
for (i = 0; i < 20000; i++) {
secp256k1_sha256_initialize(&sha);
secp256k1_sha256_write(&sha, data->data, 32);
secp256k1_sha256_finalize(&sha, data->data);
}
}
void bench_hmac_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_hmac_sha256_t hmac;
for (i = 0; i < 20000; i++) {
secp256k1_hmac_sha256_initialize(&hmac, data->data, 32);
secp256k1_hmac_sha256_write(&hmac, data->data, 32);
secp256k1_hmac_sha256_finalize(&hmac, data->data);
}
}
void bench_rfc6979_hmac_sha256(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_rfc6979_hmac_sha256_t rng;
for (i = 0; i < 20000; i++) {
secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
}
}
void bench_context_verify(void* arg) {
int i;
(void)arg;
for (i = 0; i < 20; i++) {
secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
}
}
void bench_context_sign(void* arg) {
int i;
(void)arg;
for (i = 0; i < 200; i++) {
secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
}
}
int have_flag(int argc, char** argv, char *flag) {
char** argm = argv + argc;
argv++;
if (argv == argm) {
return 1;
}
while (argv != NULL && argv != argm) {
if (strcmp(*argv, flag) == 0) {
return 1;
}
argv++;
}
return 0;
}
int main(int argc, char **argv) {
bench_inv_t data;
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, 200000);
#ifdef USE_ENDOMORPHISM
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, 20000);
#endif
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000);
if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, 2000000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt_var", bench_field_sqrt_var, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, 200000);
if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
return 0;
}

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crypto/secp256k1/libsecp256k1/src/bench_recover.c Normal file
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/**********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include "include/secp256k1.h"
#include "include/secp256k1_recovery.h"
#include "util.h"
#include "bench.h"
typedef struct {
secp256k1_context *ctx;
unsigned char msg[32];
unsigned char sig[64];
} bench_recover_t;
void bench_recover(void* arg) {
int i;
bench_recover_t *data = (bench_recover_t*)arg;
secp256k1_pubkey pubkey;
unsigned char pubkeyc[33];
for (i = 0; i < 20000; i++) {
int j;
size_t pubkeylen = 33;
secp256k1_ecdsa_recoverable_signature sig;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2));
CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg));
CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
for (j = 0; j < 32; j++) {
data->sig[j + 32] = data->msg[j]; /* Move former message to S. */
data->msg[j] = data->sig[j]; /* Move former R to message. */
data->sig[j] = pubkeyc[j + 1]; /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
}
}
}
void bench_recover_setup(void* arg) {
int i;
bench_recover_t *data = (bench_recover_t*)arg;
for (i = 0; i < 32; i++) {
data->msg[i] = 1 + i;
}
for (i = 0; i < 64; i++) {
data->sig[i] = 65 + i;
}
}
int main(void) {
bench_recover_t data;
data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, 20000);
secp256k1_context_destroy(data.ctx);
return 0;
}

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crypto/secp256k1/libsecp256k1/src/bench_schnorr_verify.c Normal file
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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <stdio.h>
#include <string.h>
#include "include/secp256k1.h"
#include "include/secp256k1_schnorr.h"
#include "util.h"
#include "bench.h"
typedef struct {
unsigned char key[32];
unsigned char sig[64];
unsigned char pubkey[33];
size_t pubkeylen;
} benchmark_schnorr_sig_t;
typedef struct {
secp256k1_context *ctx;
unsigned char msg[32];
benchmark_schnorr_sig_t sigs[64];
int numsigs;
} benchmark_schnorr_verify_t;
static void benchmark_schnorr_init(void* arg) {
int i, k;
benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
for (i = 0; i < 32; i++) {
data->msg[i] = 1 + i;
}
for (k = 0; k < data->numsigs; k++) {
secp256k1_pubkey pubkey;
for (i = 0; i < 32; i++) {
data->sigs[k].key[i] = 33 + i + k;
}
secp256k1_schnorr_sign(data->ctx, data->sigs[k].sig, data->msg, data->sigs[k].key, NULL, NULL);
data->sigs[k].pubkeylen = 33;
CHECK(secp256k1_ec_pubkey_create(data->ctx, &pubkey, data->sigs[k].key));
CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
}
}
static void benchmark_schnorr_verify(void* arg) {
int i;
benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
for (i = 0; i < 20000 / data->numsigs; i++) {
secp256k1_pubkey pubkey;
data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->sigs[0].pubkey, data->sigs[0].pubkeylen));
CHECK(secp256k1_schnorr_verify(data->ctx, data->sigs[0].sig, data->msg, &pubkey) == ((i & 0xFF) == 0));
data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
}
}
int main(void) {
benchmark_schnorr_verify_t data;
data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
data.numsigs = 1;
run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
secp256k1_context_destroy(data.ctx);
return 0;
}

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include "include/secp256k1.h"
#include "util.h"
#include "bench.h"
typedef struct {
secp256k1_context* ctx;
unsigned char msg[32];
unsigned char key[32];
} bench_sign_t;
static void bench_sign_setup(void* arg) {
int i;
bench_sign_t *data = (bench_sign_t*)arg;
for (i = 0; i < 32; i++) {
data->msg[i] = i + 1;
}
for (i = 0; i < 32; i++) {
data->key[i] = i + 65;
}
}
static void bench_sign(void* arg) {
int i;
bench_sign_t *data = (bench_sign_t*)arg;
unsigned char sig[74];
for (i = 0; i < 20000; i++) {
size_t siglen = 74;
int j;
secp256k1_ecdsa_signature signature;
CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
for (j = 0; j < 32; j++) {
data->msg[j] = sig[j];
data->key[j] = sig[j + 32];
}
}
}
int main(void) {
bench_sign_t data;
data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
run_benchmark("ecdsa_sign", bench_sign, bench_sign_setup, NULL, &data, 10, 20000);
secp256k1_context_destroy(data.ctx);
return 0;
}

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#include <stdio.h>
#include <string.h>
#include "include/secp256k1.h"
#include "util.h"
#include "bench.h"
typedef struct {
secp256k1_context *ctx;
unsigned char msg[32];
unsigned char key[32];
unsigned char sig[72];
size_t siglen;
unsigned char pubkey[33];
size_t pubkeylen;
} benchmark_verify_t;
static void benchmark_verify(void* arg) {
int i;
benchmark_verify_t* data = (benchmark_verify_t*)arg;
for (i = 0; i < 20000; i++) {
secp256k1_pubkey pubkey;
secp256k1_ecdsa_signature sig;
data->sig[data->siglen - 1] ^= (i & 0xFF);
data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
data->sig[data->siglen - 1] ^= (i & 0xFF);
data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
}
}
int main(void) {
int i;
secp256k1_pubkey pubkey;
secp256k1_ecdsa_signature sig;
benchmark_verify_t data;
data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
for (i = 0; i < 32; i++) {
data.msg[i] = 1 + i;
}
for (i = 0; i < 32; i++) {
data.key[i] = 33 + i;
}
data.siglen = 72;
CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, 20000);
secp256k1_context_destroy(data.ctx);
return 0;
}

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECDSA_
#define _SECP256K1_ECDSA_
#include <stddef.h>
#include "scalar.h"
#include "group.h"
#include "ecmult.h"
static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECDSA_IMPL_H_
#define _SECP256K1_ECDSA_IMPL_H_
#include "scalar.h"
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecmult_gen.h"
#include "ecdsa.h"
/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
* sage: for t in xrange(1023, -1, -1):
* .. p = 2**256 - 2**32 - t
* .. if p.is_prime():
* .. print '%x'%p
* .. break
* 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
* 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
*/
static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
);
/** Difference between field and order, values 'p' and 'n' values defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
* sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
* '14551231950b75fc4402da1722fc9baee'
*/
static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
);
static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
unsigned char ra[32] = {0}, sa[32] = {0};
const unsigned char *rp;
const unsigned char *sp;
size_t lenr;
size_t lens;
int overflow;
if (sig[0] != 0x30) {
return 0;
}
lenr = sig[3];
if (5+lenr >= size) {
return 0;
}
lens = sig[lenr+5];
if (sig[1] != lenr+lens+4) {
return 0;
}
if (lenr+lens+6 > size) {
return 0;
}
if (sig[2] != 0x02) {
return 0;
}
if (lenr == 0) {
return 0;
}
if (sig[lenr+4] != 0x02) {
return 0;
}
if (lens == 0) {
return 0;
}
sp = sig + 6 + lenr;
while (lens > 0 && sp[0] == 0) {
lens--;
sp++;
}
if (lens > 32) {
return 0;
}
rp = sig + 4;
while (lenr > 0 && rp[0] == 0) {
lenr--;
rp++;
}
if (lenr > 32) {
return 0;
}
memcpy(ra + 32 - lenr, rp, lenr);
memcpy(sa + 32 - lens, sp, lens);
overflow = 0;
secp256k1_scalar_set_b32(rr, ra, &overflow);
if (overflow) {
return 0;
}
secp256k1_scalar_set_b32(rs, sa, &overflow);
if (overflow) {
return 0;
}
return 1;
}
static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
unsigned char r[33] = {0}, s[33] = {0};
unsigned char *rp = r, *sp = s;
size_t lenR = 33, lenS = 33;
secp256k1_scalar_get_b32(&r[1], ar);
secp256k1_scalar_get_b32(&s[1], as);
while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
if (*size < 6+lenS+lenR) {
*size = 6 + lenS + lenR;
return 0;
}
*size = 6 + lenS + lenR;
sig[0] = 0x30;
sig[1] = 4 + lenS + lenR;
sig[2] = 0x02;
sig[3] = lenR;
memcpy(sig+4, rp, lenR);
sig[4+lenR] = 0x02;
sig[5+lenR] = lenS;
memcpy(sig+lenR+6, sp, lenS);
return 1;
}
static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
unsigned char c[32];
secp256k1_scalar sn, u1, u2;
secp256k1_fe xr;
secp256k1_gej pubkeyj;
secp256k1_gej pr;
if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
return 0;
}
secp256k1_scalar_inverse_var(&sn, sigs);
secp256k1_scalar_mul(&u1, &sn, message);
secp256k1_scalar_mul(&u2, &sn, sigr);
secp256k1_gej_set_ge(&pubkeyj, pubkey);
secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
if (secp256k1_gej_is_infinity(&pr)) {
return 0;
}
secp256k1_scalar_get_b32(c, sigr);
secp256k1_fe_set_b32(&xr, c);
/** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
* in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
* compute the remainder modulo n, and compare it to xr. However:
*
* xr == X(pr) mod n
* <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
* [Since 2 * n > p, h can only be 0 or 1]
* <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
* [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
* <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
* [Multiplying both sides of the equations by pr.z^2 mod p]
* <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
*
* Thus, we can avoid the inversion, but we have to check both cases separately.
* secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
*/
if (secp256k1_gej_eq_x_var(&xr, &pr)) {
/* xr.x == xr * xr.z^2 mod p, so the signature is valid. */
return 1;
}
if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
/* xr + p >= n, so we can skip testing the second case. */
return 0;
}
secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
if (secp256k1_gej_eq_x_var(&xr, &pr)) {
/* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
return 1;
}
return 0;
}
static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
unsigned char brx[32];
secp256k1_fe fx;
secp256k1_ge x;
secp256k1_gej xj;
secp256k1_scalar rn, u1, u2;
secp256k1_gej qj;
if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
return 0;
}
secp256k1_scalar_get_b32(brx, sigr);
VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
if (recid & 2) {
if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
return 0;
}
secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
}
if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
return 0;
}
secp256k1_gej_set_ge(&xj, &x);
secp256k1_scalar_inverse_var(&rn, sigr);
secp256k1_scalar_mul(&u1, &rn, message);
secp256k1_scalar_negate(&u1, &u1);
secp256k1_scalar_mul(&u2, &rn, sigs);
secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
secp256k1_ge_set_gej_var(pubkey, &qj);
return !secp256k1_gej_is_infinity(&qj);
}
static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
unsigned char b[32];
secp256k1_gej rp;
secp256k1_ge r;
secp256k1_scalar n;
int overflow = 0;
secp256k1_ecmult_gen(ctx, &rp, nonce);
secp256k1_ge_set_gej(&r, &rp);
secp256k1_fe_normalize(&r.x);
secp256k1_fe_normalize(&r.y);
secp256k1_fe_get_b32(b, &r.x);
secp256k1_scalar_set_b32(sigr, b, &overflow);
if (secp256k1_scalar_is_zero(sigr)) {
/* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature. */
secp256k1_gej_clear(&rp);
secp256k1_ge_clear(&r);
return 0;
}
if (recid) {
*recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
}
secp256k1_scalar_mul(&n, sigr, seckey);
secp256k1_scalar_add(&n, &n, message);
secp256k1_scalar_inverse(sigs, nonce);
secp256k1_scalar_mul(sigs, sigs, &n);
secp256k1_scalar_clear(&n);
secp256k1_gej_clear(&rp);
secp256k1_ge_clear(&r);
if (secp256k1_scalar_is_zero(sigs)) {
return 0;
}
if (secp256k1_scalar_is_high(sigs)) {
secp256k1_scalar_negate(sigs, sigs);
if (recid) {
*recid ^= 1;
}
}
return 1;
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECKEY_
#define _SECP256K1_ECKEY_
#include <stddef.h>
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
#include "ecmult_gen.h"
static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, unsigned int flags);
static int secp256k1_eckey_privkey_parse(secp256k1_scalar *key, const unsigned char *privkey, size_t privkeylen);
static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context *ctx, unsigned char *privkey, size_t *privkeylen, const secp256k1_scalar *key, unsigned int flags);
static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECKEY_IMPL_H_
#define _SECP256K1_ECKEY_IMPL_H_
#include "eckey.h"
#include "scalar.h"
#include "field.h"
#include "group.h"
#include "ecmult_gen.h"
static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
secp256k1_fe x;
return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == 0x03);
} else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
secp256k1_fe x, y;
if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
return 0;
}
secp256k1_ge_set_xy(elem, &x, &y);
if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07)) {
return 0;
}
return secp256k1_ge_is_valid_var(elem);
} else {
return 0;
}
}
static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, unsigned int flags) {
if (secp256k1_ge_is_infinity(elem)) {
return 0;
}
secp256k1_fe_normalize_var(&elem->x);
secp256k1_fe_normalize_var(&elem->y);
secp256k1_fe_get_b32(&pub[1], &elem->x);
if (flags & SECP256K1_EC_COMPRESSED) {
*size = 33;
pub[0] = 0x02 | (secp256k1_fe_is_odd(&elem->y) ? 0x01 : 0x00);
} else {
*size = 65;
pub[0] = 0x04;
secp256k1_fe_get_b32(&pub[33], &elem->y);
}
return 1;
}
static int secp256k1_eckey_privkey_parse(secp256k1_scalar *key, const unsigned char *privkey, size_t privkeylen) {
unsigned char c[32] = {0};
const unsigned char *end = privkey + privkeylen;
int lenb = 0;
int len = 0;
int overflow = 0;
/* sequence header */
if (end < privkey+1 || *privkey != 0x30) {
return 0;
}
privkey++;
/* sequence length constructor */
if (end < privkey+1 || !(*privkey & 0x80)) {
return 0;
}
lenb = *privkey & ~0x80; privkey++;
if (lenb < 1 || lenb > 2) {
return 0;
}
if (end < privkey+lenb) {
return 0;
}
/* sequence length */
len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
privkey += lenb;
if (end < privkey+len) {
return 0;
}
/* sequence element 0: version number (=1) */
if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
return 0;
}
privkey += 3;
/* sequence element 1: octet string, up to 32 bytes */
if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
return 0;
}
memcpy(c + 32 - privkey[1], privkey + 2, privkey[1]);
secp256k1_scalar_set_b32(key, c, &overflow);
memset(c, 0, 32);
return !overflow;
}
static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context *ctx, unsigned char *privkey, size_t *privkeylen, const secp256k1_scalar *key, unsigned int flags) {
secp256k1_gej rp;
secp256k1_ge r;
size_t pubkeylen = 0;
secp256k1_ecmult_gen(ctx, &rp, key);
secp256k1_ge_set_gej(&r, &rp);
if (flags & SECP256K1_EC_COMPRESSED) {
static const unsigned char begin[] = {
0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,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,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x21,0x02,0x79,0xBE,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,
0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_scalar_get_b32(ptr, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 1)) {
return 0;
}
ptr += pubkeylen;
*privkeylen = ptr - privkey;
} else {
static const unsigned char begin[] = {
0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
};
static const unsigned char middle[] = {
0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,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,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
0x41,0x04,0x79,0xBE,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,
0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
};
unsigned char *ptr = privkey;
memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
secp256k1_scalar_get_b32(ptr, key); ptr += 32;
memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 0)) {
return 0;
}
ptr += pubkeylen;
*privkeylen = ptr - privkey;
}
return 1;
}
static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
secp256k1_scalar_add(key, key, tweak);
if (secp256k1_scalar_is_zero(key)) {
return 0;
}
return 1;
}
static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
secp256k1_gej pt;
secp256k1_scalar one;
secp256k1_gej_set_ge(&pt, key);
secp256k1_scalar_set_int(&one, 1);
secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
if (secp256k1_gej_is_infinity(&pt)) {
return 0;
}
secp256k1_ge_set_gej(key, &pt);
return 1;
}
static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
if (secp256k1_scalar_is_zero(tweak)) {
return 0;
}
secp256k1_scalar_mul(key, key, tweak);
return 1;
}
static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
secp256k1_scalar zero;
secp256k1_gej pt;
if (secp256k1_scalar_is_zero(tweak)) {
return 0;
}
secp256k1_scalar_set_int(&zero, 0);
secp256k1_gej_set_ge(&pt, key);
secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero);
secp256k1_ge_set_gej(key, &pt);
return 1;
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_
#define _SECP256K1_ECMULT_
#include "num.h"
#include "group.h"
typedef struct {
/* For accelerating the computation of a*P + b*G: */
secp256k1_ge_storage (*pre_g)[]; /* odd multiples of the generator */
#ifdef USE_ENDOMORPHISM
secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
#endif
} secp256k1_ecmult_context;
static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
/** Double multiply: R = na*A + ng*G */
static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
#endif

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/**********************************************************************
* Copyright (c) 2015 Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_CONST_
#define _SECP256K1_ECMULT_CONST_
#include "scalar.h"
#include "group.h"
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
#endif

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/**********************************************************************
* Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_CONST_IMPL_
#define _SECP256K1_ECMULT_CONST_IMPL_
#include "scalar.h"
#include "group.h"
#include "ecmult_const.h"
#include "ecmult_impl.h"
#ifdef USE_ENDOMORPHISM
#define WNAF_BITS 128
#else
#define WNAF_BITS 256
#endif
#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
int m; \
int abs_n = (n) * (((n) > 0) * 2 - 1); \
int idx_n = abs_n / 2; \
secp256k1_fe neg_y; \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
/* This loop is used to avoid secret data in array indices. See
* the comment in ecmult_gen_impl.h for rationale. */ \
secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
} \
(r)->infinity = 0; \
secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
} while(0)
/** Convert a number to WNAF notation. The number becomes represented by sum(2^{wi} * wnaf[i], i=0..return_val)
* with the following guarantees:
* - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
* - each wnaf[i] is nonzero
* - the number of words set is returned; this is always (WNAF_BITS + w - 1) / w
*
* Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
* CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
*
* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
*/
static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
int global_sign;
int skew = 0;
int word = 0;
/* 1 2 3 */
int u_last;
int u;
#ifdef USE_ENDOMORPHISM
int flip;
int bit;
secp256k1_scalar neg_s;
int not_neg_one;
/* If we are using the endomorphism, we cannot handle even numbers by negating
* them, since we are working with 128-bit numbers whose negations would be 256
* bits, eliminating the performance advantage. Instead we use a technique from
* Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
* or 2 (for odd) to the number we are encoding, then compensating after the
* multiplication. */
/* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */
flip = secp256k1_scalar_is_high(&s);
/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
bit = flip ^ (s.d[0] & 1);
/* We check for negative one, since adding 2 to it will cause an overflow */
secp256k1_scalar_negate(&neg_s, &s);
not_neg_one = !secp256k1_scalar_is_one(&neg_s);
secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
/* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
* that we added two to it and flipped it. In fact for -1 these operations are
* identical. We only flipped, but since skewing is required (in the sense that
* the skew must be 1 or 2, never zero) and flipping is not, we need to change
* our flags to claim that we only skewed. */
global_sign = secp256k1_scalar_cond_negate(&s, flip);
global_sign *= not_neg_one * 2 - 1;
skew = 1 << bit;
#else
/* Otherwise, we just negate to force oddness */
int is_even = secp256k1_scalar_is_even(&s);
global_sign = secp256k1_scalar_cond_negate(&s, is_even);
#endif
/* 4 */
u_last = secp256k1_scalar_shr_int(&s, w);
while (word * w < WNAF_BITS) {
int sign;
int even;
/* 4.1 4.4 */
u = secp256k1_scalar_shr_int(&s, w);
/* 4.2 */
even = ((u & 1) == 0);
sign = 2 * (u_last > 0) - 1;
u += sign * even;
u_last -= sign * even * (1 << w);
/* 4.3, adapted for global sign change */
wnaf[word++] = u_last * global_sign;
u_last = u;
}
wnaf[word] = u * global_sign;
VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
VERIFY_CHECK(word == WNAF_SIZE(w));
return skew;
}
static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ge tmpa;
secp256k1_fe Z;
#ifdef USE_ENDOMORPHISM
secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
int skew_1;
int skew_lam;
secp256k1_scalar q_1, q_lam;
#else
int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)];
#endif
int i;
secp256k1_scalar sc = *scalar;
/* build wnaf representation for q. */
#ifdef USE_ENDOMORPHISM
/* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
/* no need for zero correction when using endomorphism since even
* numbers have one added to them anyway */
skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1);
skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
#else
int is_zero = secp256k1_scalar_is_zero(scalar);
/* the wNAF ladder cannot handle zero, so bump this to one .. we will
* correct the result after the fact */
sc.d[0] += is_zero;
VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc));
secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1);
#endif
/* Calculate odd multiples of a.
* All multiples are brought to the same Z 'denominator', which is stored
* in Z. Due to secp256k1' isomorphism we can do all operations pretending
* that the Z coordinate was 1, use affine addition formulae, and correct
* the Z coordinate of the result once at the end.
*/
secp256k1_gej_set_ge(r, a);
secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_fe_normalize_weak(&pre_a[i].y);
}
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
#endif
/* first loop iteration (separated out so we can directly set r, rather
* than having it start at infinity, get doubled several times, then have
* its new value added to it) */
#ifdef USE_ENDOMORPHISM
i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
secp256k1_gej_set_ge(r, &tmpa);
i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
secp256k1_gej_add_ge(r, r, &tmpa);
#else
i = wnaf[WNAF_SIZE(WINDOW_A - 1)];
VERIFY_CHECK(i != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
secp256k1_gej_set_ge(r, &tmpa);
#endif
/* remaining loop iterations */
for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
int n;
int j;
for (j = 0; j < WINDOW_A - 1; ++j) {
secp256k1_gej_double_nonzero(r, r, NULL);
}
#ifdef USE_ENDOMORPHISM
n = wnaf_1[i];
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
VERIFY_CHECK(n != 0);
secp256k1_gej_add_ge(r, r, &tmpa);
n = wnaf_lam[i];
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
VERIFY_CHECK(n != 0);
secp256k1_gej_add_ge(r, r, &tmpa);
#else
n = wnaf[i];
VERIFY_CHECK(n != 0);
ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
secp256k1_gej_add_ge(r, r, &tmpa);
#endif
}
secp256k1_fe_mul(&r->z, &r->z, &Z);
#ifdef USE_ENDOMORPHISM
{
/* Correct for wNAF skew */
secp256k1_ge correction = *a;
secp256k1_ge_storage correction_1_stor;
secp256k1_ge_storage correction_lam_stor;
secp256k1_ge_storage a2_stor;
secp256k1_gej tmpj;
secp256k1_gej_set_ge(&tmpj, &correction);
secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
secp256k1_ge_set_gej(&correction, &tmpj);
secp256k1_ge_to_storage(&correction_1_stor, a);
secp256k1_ge_to_storage(&correction_lam_stor, a);
secp256k1_ge_to_storage(&a2_stor, &correction);
/* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
/* Apply the correction */
secp256k1_ge_from_storage(&correction, &correction_1_stor);
secp256k1_ge_neg(&correction, &correction);
secp256k1_gej_add_ge(r, r, &correction);
secp256k1_ge_from_storage(&correction, &correction_lam_stor);
secp256k1_ge_neg(&correction, &correction);
secp256k1_ge_mul_lambda(&correction, &correction);
secp256k1_gej_add_ge(r, r, &correction);
}
#else
/* correct for zero */
r->infinity |= is_zero;
#endif
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_GEN_
#define _SECP256K1_ECMULT_GEN_
#include "scalar.h"
#include "group.h"
typedef struct {
/* For accelerating the computation of a*G:
* To harden against timing attacks, use the following mechanism:
* * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
* * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
* * U_i = U * 2^i (for i=0..62)
* * U_i = U * (1-2^63) (for i=63)
* where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
* For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
* precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
* None of the resulting prec group elements have a known scalar, and neither do any of
* the intermediate sums while computing a*G.
*/
secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
secp256k1_scalar blind;
secp256k1_gej initial;
} secp256k1_ecmult_gen_context;
static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb);
static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb);
static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
/** Multiply with the generator: R = a*G */
static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
#define _SECP256K1_ECMULT_GEN_IMPL_H_
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"
#include "hash_impl.h"
#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
#include "ecmult_static_context.h"
#endif
static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
ctx->prec = NULL;
}
static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
secp256k1_ge prec[1024];
secp256k1_gej gj;
secp256k1_gej nums_gej;
int i, j;
#endif
if (ctx->prec != NULL) {
return;
}
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
{
static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
secp256k1_fe nums_x;
secp256k1_ge nums_ge;
VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
secp256k1_gej_set_ge(&nums_gej, &nums_ge);
/* Add G to make the bits in x uniformly distributed. */
secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
}
/* compute prec. */
{
secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
secp256k1_gej gbase;
secp256k1_gej numsbase;
gbase = gj; /* 16^j * G */
numsbase = nums_gej; /* 2^j * nums. */
for (j = 0; j < 64; j++) {
/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
precj[j*16] = numsbase;
for (i = 1; i < 16; i++) {
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
}
/* Multiply gbase by 16. */
for (i = 0; i < 4; i++) {
secp256k1_gej_double_var(&gbase, &gbase, NULL);
}
/* Multiply numbase by 2. */
secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
if (j == 62) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
}
}
secp256k1_ge_set_all_gej_var(1024, prec, precj, cb);
}
for (j = 0; j < 64; j++) {
for (i = 0; i < 16; i++) {
secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
}
}
#else
(void)cb;
ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
#endif
secp256k1_ecmult_gen_blind(ctx, NULL);
}
static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
return ctx->prec != NULL;
}
static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
if (src->prec == NULL) {
dst->prec = NULL;
} else {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
memcpy(dst->prec, src->prec, sizeof(*dst->prec));
#else
(void)cb;
dst->prec = src->prec;
#endif
dst->initial = src->initial;
dst->blind = src->blind;
}
}
static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
free(ctx->prec);
#endif
secp256k1_scalar_clear(&ctx->blind);
secp256k1_gej_clear(&ctx->initial);
ctx->prec = NULL;
}
static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
secp256k1_ge add;
secp256k1_ge_storage adds;
secp256k1_scalar gnb;
int bits;
int i, j;
memset(&adds, 0, sizeof(adds));
*r = ctx->initial;
/* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
secp256k1_scalar_add(&gnb, gn, &ctx->blind);
add.infinity = 0;
for (j = 0; j < 64; j++) {
bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
for (i = 0; i < 16; i++) {
/** This uses a conditional move to avoid any secret data in array indexes.
* _Any_ use of secret indexes has been demonstrated to result in timing
* sidechannels, even when the cache-line access patterns are uniform.
* See also:
* "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
* (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
* "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
* by Dag Arne Osvik, Adi Shamir, and Eran Tromer
* (http://www.tau.ac.il/~tromer/papers/cache.pdf)
*/
secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
}
secp256k1_ge_from_storage(&add, &adds);
secp256k1_gej_add_ge(r, r, &add);
}
bits = 0;
secp256k1_ge_clear(&add);
secp256k1_scalar_clear(&gnb);
}
/* Setup blinding values for secp256k1_ecmult_gen. */
static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
secp256k1_scalar b;
secp256k1_gej gb;
secp256k1_fe s;
unsigned char nonce32[32];
secp256k1_rfc6979_hmac_sha256_t rng;
int retry;
unsigned char keydata[64] = {0};
if (seed32 == NULL) {
/* When seed is NULL, reset the initial point and blinding value. */
secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
secp256k1_gej_neg(&ctx->initial, &ctx->initial);
secp256k1_scalar_set_int(&ctx->blind, 1);
}
/* The prior blinding value (if not reset) is chained forward by including it in the hash. */
secp256k1_scalar_get_b32(nonce32, &ctx->blind);
/** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
* and guards against weak or adversarial seeds. This is a simpler and safer interface than
* asking the caller for blinding values directly and expecting them to retry on failure.
*/
memcpy(keydata, nonce32, 32);
if (seed32 != NULL) {
memcpy(keydata + 32, seed32, 32);
}
secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
memset(keydata, 0, sizeof(keydata));
/* Retry for out of range results to achieve uniformity. */
do {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
retry = !secp256k1_fe_set_b32(&s, nonce32);
retry |= secp256k1_fe_is_zero(&s);
} while (retry);
/* Randomize the projection to defend against multiplier sidechannels. */
secp256k1_gej_rescale(&ctx->initial, &s);
secp256k1_fe_clear(&s);
do {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
secp256k1_scalar_set_b32(&b, nonce32, &retry);
/* A blinding value of 0 works, but would undermine the projection hardening. */
retry |= secp256k1_scalar_is_zero(&b);
} while (retry);
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
memset(nonce32, 0, 32);
secp256k1_ecmult_gen(ctx, &gb, &b);
secp256k1_scalar_negate(&b, &b);
ctx->blind = b;
ctx->initial = gb;
secp256k1_scalar_clear(&b);
secp256k1_gej_clear(&gb);
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_ECMULT_IMPL_H_
#define _SECP256K1_ECMULT_IMPL_H_
#include "group.h"
#include "scalar.h"
#include "ecmult.h"
/* optimal for 128-bit and 256-bit exponents. */
#define WINDOW_A 5
/** larger numbers may result in slightly better performance, at the cost of
exponentially larger precomputed tables. */
#ifdef USE_ENDOMORPHISM
/** Two tables for window size 15: 1.375 MiB. */
#define WINDOW_G 15
#else
/** One table for window size 16: 1.375 MiB. */
#define WINDOW_G 16
#endif
/** The number of entries a table with precomputed multiples needs to have. */
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
* the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
* contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
* Prej's Z values are undefined, except for the last value.
*/
static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
secp256k1_gej d;
secp256k1_ge a_ge, d_ge;
int i;
VERIFY_CHECK(!a->infinity);
secp256k1_gej_double_var(&d, a, NULL);
/*
* Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
* of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
*/
d_ge.x = d.x;
d_ge.y = d.y;
d_ge.infinity = 0;
secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
prej[0].x = a_ge.x;
prej[0].y = a_ge.y;
prej[0].z = a->z;
prej[0].infinity = 0;
zr[0] = d.z;
for (i = 1; i < n; i++) {
secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
}
/*
* Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
* the final point's z coordinate is actually used though, so just update that.
*/
secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
}
/** Fill a table 'pre' with precomputed odd multiples of a.
*
* There are two versions of this function:
* - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
* resulting point set to a single constant Z denominator, stores the X and Y
* coordinates as ge_storage points in pre, and stores the global Z in rz.
* It only operates on tables sized for WINDOW_A wnaf multiples.
* - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
* resulting point set to actually affine points, and stores those in pre.
* It operates on tables of any size, but uses heap-allocated temporaries.
*
* To compute a*P + b*G, we compute a table for P using the first function,
* and for G using the second (which requires an inverse, but it only needs to
* happen once).
*/
static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
/* Compute the odd multiples in Jacobian form. */
secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
/* Bring them to the same Z denominator. */
secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
}
static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
int i;
/* Compute the odd multiples in Jacobian form. */
secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
/* Convert them in batch to affine coordinates. */
secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
/* Convert them to compact storage form. */
for (i = 0; i < n; i++) {
secp256k1_ge_to_storage(&pre[i], &prea[i]);
}
free(prea);
free(prej);
free(zr);
}
/** The following two macro retrieves a particular odd multiple from a table
* of precomputed multiples. */
#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
*(r) = (pre)[((n)-1)/2]; \
} else { \
secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
} \
} while(0)
#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
VERIFY_CHECK(((n) & 1) == 1); \
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
if ((n) > 0) { \
secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
} else { \
secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
secp256k1_ge_neg((r), (r)); \
} \
} while(0)
static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
ctx->pre_g = NULL;
#ifdef USE_ENDOMORPHISM
ctx->pre_g_128 = NULL;
#endif
}
static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
secp256k1_gej gj;
if (ctx->pre_g != NULL) {
return;
}
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* precompute the tables with odd multiples */
secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
#ifdef USE_ENDOMORPHISM
{
secp256k1_gej g_128j;
int i;
ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
/* calculate 2^128*generator */
g_128j = gj;
for (i = 0; i < 128; i++) {
secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
}
secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
}
#endif
}
static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
if (src->pre_g == NULL) {
dst->pre_g = NULL;
} else {
size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g, src->pre_g, size);
}
#ifdef USE_ENDOMORPHISM
if (src->pre_g_128 == NULL) {
dst->pre_g_128 = NULL;
} else {
size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
memcpy(dst->pre_g_128, src->pre_g_128, size);
}
#endif
}
static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
return ctx->pre_g != NULL;
}
static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
free(ctx->pre_g);
#ifdef USE_ENDOMORPHISM
free(ctx->pre_g_128);
#endif
secp256k1_ecmult_context_init(ctx);
}
/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
* with the following guarantees:
* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
* - the number of set values in wnaf is returned. This number is at most 256, and at most one more
* than the number of bits in the (absolute value) of the input.
*/
static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
secp256k1_scalar s = *a;
int last_set_bit = -1;
int bit = 0;
int sign = 1;
int carry = 0;
VERIFY_CHECK(wnaf != NULL);
VERIFY_CHECK(0 <= len && len <= 256);
VERIFY_CHECK(a != NULL);
VERIFY_CHECK(2 <= w && w <= 31);
memset(wnaf, 0, len * sizeof(wnaf[0]));
if (secp256k1_scalar_get_bits(&s, 255, 1)) {
secp256k1_scalar_negate(&s, &s);
sign = -1;
}
while (bit < len) {
int now;
int word;
if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
bit++;
continue;
}
now = w;
if (now > len - bit) {
now = len - bit;
}
word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
carry = (word >> (w-1)) & 1;
word -= carry << w;
wnaf[bit] = sign * word;
last_set_bit = bit;
bit += now;
}
#ifdef VERIFY
CHECK(carry == 0);
while (bit < 256) {
CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
}
#endif
return last_set_bit + 1;
}
static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_ge tmpa;
secp256k1_fe Z;
#ifdef USE_ENDOMORPHISM
secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
secp256k1_scalar na_1, na_lam;
/* Splitted G factors. */
secp256k1_scalar ng_1, ng_128;
int wnaf_na_1[130];
int wnaf_na_lam[130];
int bits_na_1;
int bits_na_lam;
int wnaf_ng_1[129];
int bits_ng_1;
int wnaf_ng_128[129];
int bits_ng_128;
#else
int wnaf_na[256];
int bits_na;
int wnaf_ng[256];
int bits_ng;
#endif
int i;
int bits;
#ifdef USE_ENDOMORPHISM
/* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
secp256k1_scalar_split_lambda(&na_1, &na_lam, na);
/* build wnaf representation for na_1 and na_lam. */
bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, 130, &na_1, WINDOW_A);
bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
VERIFY_CHECK(bits_na_1 <= 130);
VERIFY_CHECK(bits_na_lam <= 130);
bits = bits_na_1;
if (bits_na_lam > bits) {
bits = bits_na_lam;
}
#else
/* build wnaf representation for na. */
bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A);
bits = bits_na;
#endif
/* Calculate odd multiples of a.
* All multiples are brought to the same Z 'denominator', which is stored
* in Z. Due to secp256k1' isomorphism we can do all operations pretending
* that the Z coordinate was 1, use affine addition formulae, and correct
* the Z coordinate of the result once at the end.
* The exception is the precomputed G table points, which are actually
* affine. Compared to the base used for other points, they have a Z ratio
* of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
* isomorphism to efficiently add with a known Z inverse.
*/
secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
#ifdef USE_ENDOMORPHISM
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
}
/* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
/* Build wnaf representation for ng_1 and ng_128 */
bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G);
bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
if (bits_ng_1 > bits) {
bits = bits_ng_1;
}
if (bits_ng_128 > bits) {
bits = bits_ng_128;
}
#else
bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G);
if (bits_ng > bits) {
bits = bits_ng;
}
#endif
secp256k1_gej_set_infinity(r);
for (i = bits - 1; i >= 0; i--) {
int n;
secp256k1_gej_double_var(r, r, NULL);
#ifdef USE_ENDOMORPHISM
if (i < bits_na_1 && (n = wnaf_na_1[i])) {
ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#else
if (i < bits_na && (n = wnaf_na[i])) {
ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
}
if (i < bits_ng && (n = wnaf_ng[i])) {
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
}
#endif
}
if (!r->infinity) {
secp256k1_fe_mul(&r->z, &r->z, &Z);
}
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_
#define _SECP256K1_FIELD_
/** Field element module.
*
* Field elements can be represented in several ways, but code accessing
* it (and implementations) need to take certain properaties into account:
* - Each field element can be normalized or not.
* - Each field element has a magnitude, which represents how far away
* its representation is away from normalization. Normalized elements
* always have a magnitude of 1, but a magnitude of 1 doesn't imply
* normality.
*/
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_FIELD_10X26)
#include "field_10x26.h"
#elif defined(USE_FIELD_5X52)
#include "field_5x52.h"
#else
#error "Please select field implementation"
#endif
/** Normalize a field element. */
static void secp256k1_fe_normalize(secp256k1_fe *r);
/** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
/** Normalize a field element, without constant-time guarantee. */
static void secp256k1_fe_normalize_var(secp256k1_fe *r);
/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
* implementation may optionally normalize the input, but this should not be relied upon. */
static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
* implementation may optionally normalize the input, but this should not be relied upon. */
static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
/** Set a field element equal to a small integer. Resulting field element is normalized. */
static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
/** Verify whether a field element is zero. Requires the input to be normalized. */
static int secp256k1_fe_is_zero(const secp256k1_fe *a);
/** Check the "oddness" of a field element. Requires the input to be normalized. */
static int secp256k1_fe_is_odd(const secp256k1_fe *a);
/** Compare two field elements. Requires magnitude-1 inputs. */
static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
/** Compare two field elements. Requires both inputs to be normalized */
static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
* as an argument. The magnitude of the output is one higher. */
static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
* small integer. */
static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
/** Sets a field element to be the (modular) square root (if any exist) of another. Requires the
* input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be
* normalized). Return value indicates whether a square root was found. */
static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a);
/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
* at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
* at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
* outputs must not overlap in memory. */
static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a);
/** Convert a field element to the storage type. */
static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
/** Convert a field element back from the storage type. */
static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
#include <stdint.h>
typedef struct {
/* X = sum(i=0..9, elem[i]*2^26) mod n */
uint32_t n[10];
#ifdef VERIFY
int magnitude;
int normalized;
#endif
} secp256k1_fe;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) & 0x3FFFFFFUL, \
(((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
(((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
(((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
(((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
(((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
(((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
(((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
(((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
(((uint32_t)d7) >> 10) \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
typedef struct {
uint32_t n[8];
} secp256k1_fe_storage;
#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_REPR_
#define _SECP256K1_FIELD_REPR_
#include <stdint.h>
typedef struct {
/* X = sum(i=0..4, elem[i]*2^52) mod n */
uint64_t n[5];
#ifdef VERIFY
int magnitude;
int normalized;
#endif
} secp256k1_fe;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
typedef struct {
uint64_t n[4];
} secp256k1_fe_storage;
#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
(d0) | (((uint64_t)(d1)) << 32), \
(d2) | (((uint64_t)(d3)) << 32), \
(d4) | (((uint64_t)(d5)) << 32), \
(d6) | (((uint64_t)(d7)) << 32) \
}}
#endif

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/**********************************************************************
* Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
/**
* Changelog:
* - March 2013, Diederik Huys: original version
* - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm
* - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly
*/
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
/**
* Registers: rdx:rax = multiplication accumulator
* r9:r8 = c
* r15:rcx = d
* r10-r14 = a0-a4
* rbx = b
* rdi = r
* rsi = a / t?
*/
uint64_t tmp1, tmp2, tmp3;
__asm__ __volatile__(
"movq 0(%%rsi),%%r10\n"
"movq 8(%%rsi),%%r11\n"
"movq 16(%%rsi),%%r12\n"
"movq 24(%%rsi),%%r13\n"
"movq 32(%%rsi),%%r14\n"
/* d += a3 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r13\n"
"movq %%rax,%%rcx\n"
"movq %%rdx,%%r15\n"
/* d += a2 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d = a0 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c = a4 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r14\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += (c & M) * R */
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* t3 (tmp1) = d & M */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
"movq %%rsi,%q1\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* d += a4 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a0 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += c * R */
"movq %%r8,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* t4 = d & M (%%rsi) */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* tx = t4 >> 48 (tmp3) */
"movq %%rsi,%%rax\n"
"shrq $48,%%rax\n"
"movq %%rax,%q3\n"
/* t4 &= (M >> 4) (tmp2) */
"movq $0xffffffffffff,%%rax\n"
"andq %%rax,%%rsi\n"
"movq %%rsi,%q2\n"
/* c = a0 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r10\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += a4 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a1 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* u0 = d & M (%%rsi) */
"movq %%rcx,%%rsi\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* u0 = (u0 << 4) | tx (%%rsi) */
"shlq $4,%%rsi\n"
"movq %q3,%%rax\n"
"orq %%rax,%%rsi\n"
/* c += u0 * (R >> 4) */
"movq $0x1000003d1,%%rax\n"
"mulq %%rsi\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[0] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,0(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a1 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a0 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a4 * b2 */
"movq 16(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a2 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c += (d & M) * R */
"movq %%rcx,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 */
"shrdq $52,%%r15,%%rcx\n"
"xorq %%r15,%%r15\n"
/* r[1] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,8(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a2 * b0 */
"movq 0(%%rbx),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a1 * b1 */
"movq 8(%%rbx),%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* c += a0 * b2 (last use of %%r10 = a0) */
"movq 16(%%rbx),%%rax\n"
"mulq %%r10\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */
"movq %q2,%%rsi\n"
"movq %q1,%%r10\n"
/* d += a4 * b3 */
"movq 24(%%rbx),%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* d += a3 * b4 */
"movq 32(%%rbx),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rcx\n"
"adcq %%rdx,%%r15\n"
/* c += (d & M) * R */
"movq %%rcx,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 (%%rcx only) */
"shrdq $52,%%r15,%%rcx\n"
/* r[2] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,16(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += t3 */
"addq %%r10,%%r8\n"
/* c += d * R */
"movq %%rcx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[3] = c & M */
"movq %%r8,%%rax\n"
"movq $0xfffffffffffff,%%rdx\n"
"andq %%rdx,%%rax\n"
"movq %%rax,24(%%rdi)\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* c += t4 (%%r8 only) */
"addq %%rsi,%%r8\n"
/* r[4] = c */
"movq %%r8,32(%%rdi)\n"
: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
: "b"(b), "D"(r)
: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
);
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
/**
* Registers: rdx:rax = multiplication accumulator
* r9:r8 = c
* rcx:rbx = d
* r10-r14 = a0-a4
* r15 = M (0xfffffffffffff)
* rdi = r
* rsi = a / t?
*/
uint64_t tmp1, tmp2, tmp3;
__asm__ __volatile__(
"movq 0(%%rsi),%%r10\n"
"movq 8(%%rsi),%%r11\n"
"movq 16(%%rsi),%%r12\n"
"movq 24(%%rsi),%%r13\n"
"movq 32(%%rsi),%%r14\n"
"movq $0xfffffffffffff,%%r15\n"
/* d = (a0*2) * a3 */
"leaq (%%r10,%%r10,1),%%rax\n"
"mulq %%r13\n"
"movq %%rax,%%rbx\n"
"movq %%rdx,%%rcx\n"
/* d += (a1*2) * a2 */
"leaq (%%r11,%%r11,1),%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c = a4 * a4 */
"movq %%r14,%%rax\n"
"mulq %%r14\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += (c & M) * R */
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* t3 (tmp1) = d & M */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
"movq %%rsi,%q1\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* a4 *= 2 */
"addq %%r14,%%r14\n"
/* d += a0 * a4 */
"movq %%r10,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d+= (a1*2) * a3 */
"leaq (%%r11,%%r11,1),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += a2 * a2 */
"movq %%r12,%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += c * R */
"movq %%r8,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* t4 = d & M (%%rsi) */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* tx = t4 >> 48 (tmp3) */
"movq %%rsi,%%rax\n"
"shrq $48,%%rax\n"
"movq %%rax,%q3\n"
/* t4 &= (M >> 4) (tmp2) */
"movq $0xffffffffffff,%%rax\n"
"andq %%rax,%%rsi\n"
"movq %%rsi,%q2\n"
/* c = a0 * a0 */
"movq %%r10,%%rax\n"
"mulq %%r10\n"
"movq %%rax,%%r8\n"
"movq %%rdx,%%r9\n"
/* d += a1 * a4 */
"movq %%r11,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += (a2*2) * a3 */
"leaq (%%r12,%%r12,1),%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* u0 = d & M (%%rsi) */
"movq %%rbx,%%rsi\n"
"andq %%r15,%%rsi\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* u0 = (u0 << 4) | tx (%%rsi) */
"shlq $4,%%rsi\n"
"movq %q3,%%rax\n"
"orq %%rax,%%rsi\n"
/* c += u0 * (R >> 4) */
"movq $0x1000003d1,%%rax\n"
"mulq %%rsi\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[0] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,0(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* a0 *= 2 */
"addq %%r10,%%r10\n"
/* c += a0 * a1 */
"movq %%r10,%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a2 * a4 */
"movq %%r12,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* d += a3 * a3 */
"movq %%r13,%%rax\n"
"mulq %%r13\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c += (d & M) * R */
"movq %%rbx,%%rax\n"
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 */
"shrdq $52,%%rcx,%%rbx\n"
"xorq %%rcx,%%rcx\n"
/* r[1] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,8(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += a0 * a2 (last use of %%r10) */
"movq %%r10,%%rax\n"
"mulq %%r12\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */
"movq %q2,%%rsi\n"
"movq %q1,%%r10\n"
/* c += a1 * a1 */
"movq %%r11,%%rax\n"
"mulq %%r11\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d += a3 * a4 */
"movq %%r13,%%rax\n"
"mulq %%r14\n"
"addq %%rax,%%rbx\n"
"adcq %%rdx,%%rcx\n"
/* c += (d & M) * R */
"movq %%rbx,%%rax\n"
"andq %%r15,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* d >>= 52 (%%rbx only) */
"shrdq $52,%%rcx,%%rbx\n"
/* r[2] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,16(%%rdi)\n"
/* c >>= 52 */
"shrdq $52,%%r9,%%r8\n"
"xorq %%r9,%%r9\n"
/* c += t3 */
"addq %%r10,%%r8\n"
/* c += d * R */
"movq %%rbx,%%rax\n"
"movq $0x1000003d10,%%rdx\n"
"mulq %%rdx\n"
"addq %%rax,%%r8\n"
"adcq %%rdx,%%r9\n"
/* r[3] = c & M */
"movq %%r8,%%rax\n"
"andq %%r15,%%rax\n"
"movq %%rax,24(%%rdi)\n"
/* c >>= 52 (%%r8 only) */
"shrdq $52,%%r9,%%r8\n"
/* c += t4 (%%r8 only) */
"addq %%rsi,%%r8\n"
/* r[4] = c */
"movq %%r8,32(%%rdi)\n"
: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
: "D"(r)
: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
);
}
#endif

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crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h Normal file
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@ -0,0 +1,456 @@
/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
#define _SECP256K1_FIELD_REPR_IMPL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include <string.h>
#include "util.h"
#include "num.h"
#include "field.h"
#if defined(USE_ASM_X86_64)
#include "field_5x52_asm_impl.h"
#else
#include "field_5x52_int128_impl.h"
#endif
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
* represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
* each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
* is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
* accept any input with magnitude at most M, and have different rules for propagating magnitude to their
* output.
*/
#ifdef VERIFY
static void secp256k1_fe_verify(const secp256k1_fe *a) {
const uint64_t *d = a->n;
int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
/* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
r &= (a->magnitude >= 0);
r &= (a->magnitude <= 2048);
if (a->normalized) {
r &= (a->magnitude <= 1);
if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
r &= (d[0] < 0xFFFFEFFFFFC2FULL);
}
}
VERIFY_CHECK(r == 1);
}
#else
static void secp256k1_fe_verify(const secp256k1_fe *a) {
(void)a;
}
#endif
static void secp256k1_fe_normalize(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
/* Apply the final reduction (for constant-time behaviour, we do it always) */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
if (x) {
t0 += 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
}
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
uint64_t z0, z1;
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
uint64_t t0, t1, t2, t3, t4;
uint64_t z0, z1;
uint64_t x;
t0 = r->n[0];
t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
x = t4 >> 48;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
z0 = t0 & 0xFFFFFFFFFFFFFULL;
z1 = z0 ^ 0x1000003D0ULL;
/* Fast return path should catch the majority of cases */
if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
return 0;
}
t1 = r->n[1];
t2 = r->n[2];
t3 = r->n[3];
t4 &= 0x0FFFFFFFFFFFFULL;
t1 += (t0 >> 52);
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
const uint64_t *t = a->n;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
}
SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return a->n[0] & 1;
}
SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
int i;
#ifdef VERIFY
a->magnitude = 0;
a->normalized = 1;
#endif
for (i=0; i<5; i++) {
a->n[i] = 0;
}
}
static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
int i;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
VERIFY_CHECK(b->normalized);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
#endif
for (i = 4; i >= 0; i--) {
if (a->n[i] > b->n[i]) {
return 1;
}
if (a->n[i] < b->n[i]) {
return -1;
}
}
return 0;
}
static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
int i;
r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
for (i=0; i<32; i++) {
int j;
for (j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
}
}
if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
return 0;
}
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
return 1;
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
int i;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
for (i=0; i<32; i++) {
int j;
int c = 0;
for (j=0; j<2; j++) {
int limb = (8*i+4*j)/52;
int shift = (8*i+4*j)%52;
c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
}
r[31-i] = c;
}
}
SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= m);
secp256k1_fe_verify(a);
#endif
r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
#ifdef VERIFY
r->magnitude = m + 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
r->n[0] *= a;
r->n[1] *= a;
r->n[2] *= a;
r->n[3] *= a;
r->n[4] *= a;
#ifdef VERIFY
r->magnitude *= a;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
#ifdef VERIFY
secp256k1_fe_verify(a);
#endif
r->n[0] += a->n[0];
r->n[1] += a->n[1];
r->n[2] += a->n[2];
r->n[3] += a->n[3];
r->n[4] += a->n[4];
#ifdef VERIFY
r->magnitude += a->magnitude;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
VERIFY_CHECK(b->magnitude <= 8);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
VERIFY_CHECK(r != b);
#endif
secp256k1_fe_mul_inner(r->n, a->n, b->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
secp256k1_fe_verify(a);
#endif
secp256k1_fe_sqr_inner(r->n, a->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
uint64_t mask0, mask1;
mask0 = flag + ~((uint64_t)0);
mask1 = ~mask0;
r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
#ifdef VERIFY
if (a->magnitude > r->magnitude) {
r->magnitude = a->magnitude;
}
r->normalized &= a->normalized;
#endif
}
static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
uint64_t mask0, mask1;
mask0 = flag + ~((uint64_t)0);
mask1 = ~mask0;
r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
}
static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
#endif
r->n[0] = a->n[0] | a->n[1] << 52;
r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
}
static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
r->n[4] = a->n[3] >> 16;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
#endif
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
#include <stdint.h>
#ifdef VERIFY
#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
#else
#define VERIFY_BITS(x, n) do { } while(0)
#endif
SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
uint128_t c, d;
uint64_t t3, t4, tx, u0;
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
VERIFY_BITS(a[0], 56);
VERIFY_BITS(a[1], 56);
VERIFY_BITS(a[2], 56);
VERIFY_BITS(a[3], 56);
VERIFY_BITS(a[4], 52);
VERIFY_BITS(b[0], 56);
VERIFY_BITS(b[1], 56);
VERIFY_BITS(b[2], 56);
VERIFY_BITS(b[3], 56);
VERIFY_BITS(b[4], 52);
VERIFY_CHECK(r != b);
/* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
* px is a shorthand for sum(a[i]*b[x-i], i=0..x).
* Note that [x 0 0 0 0 0] = [x*R].
*/
d = (uint128_t)a0 * b[3]
+ (uint128_t)a1 * b[2]
+ (uint128_t)a2 * b[1]
+ (uint128_t)a3 * b[0];
VERIFY_BITS(d, 114);
/* [d 0 0 0] = [p3 0 0 0] */
c = (uint128_t)a4 * b[4];
VERIFY_BITS(c, 112);
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (c & M) * R; c >>= 52;
VERIFY_BITS(d, 115);
VERIFY_BITS(c, 60);
/* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
t3 = d & M; d >>= 52;
VERIFY_BITS(t3, 52);
VERIFY_BITS(d, 63);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (uint128_t)a0 * b[4]
+ (uint128_t)a1 * b[3]
+ (uint128_t)a2 * b[2]
+ (uint128_t)a3 * b[1]
+ (uint128_t)a4 * b[0];
VERIFY_BITS(d, 115);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
d += c * R;
VERIFY_BITS(d, 116);
/* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
t4 = d & M; d >>= 52;
VERIFY_BITS(t4, 52);
VERIFY_BITS(d, 64);
/* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
tx = (t4 >> 48); t4 &= (M >> 4);
VERIFY_BITS(tx, 4);
VERIFY_BITS(t4, 48);
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
c = (uint128_t)a0 * b[0];
VERIFY_BITS(c, 112);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
d += (uint128_t)a1 * b[4]
+ (uint128_t)a2 * b[3]
+ (uint128_t)a3 * b[2]
+ (uint128_t)a4 * b[1];
VERIFY_BITS(d, 115);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = d & M; d >>= 52;
VERIFY_BITS(u0, 52);
VERIFY_BITS(d, 63);
/* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
/* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = (u0 << 4) | tx;
VERIFY_BITS(u0, 56);
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)u0 * (R >> 4);
VERIFY_BITS(c, 115);
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
r[0] = c & M; c >>= 52;
VERIFY_BITS(r[0], 52);
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)a0 * b[1]
+ (uint128_t)a1 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (uint128_t)a2 * b[4]
+ (uint128_t)a3 * b[3]
+ (uint128_t)a4 * b[2];
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
r[1] = c & M; c >>= 52;
VERIFY_BITS(r[1], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (uint128_t)a0 * b[2]
+ (uint128_t)a1 * b[1]
+ (uint128_t)a2 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (uint128_t)a3 * b[4]
+ (uint128_t)a4 * b[3];
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[2] = c & M; c >>= 52;
VERIFY_BITS(r[2], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += d * R + t3;;
VERIFY_BITS(c, 100);
/* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[3] = c & M; c >>= 52;
VERIFY_BITS(r[3], 52);
VERIFY_BITS(c, 48);
/* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += t4;
VERIFY_BITS(c, 49);
/* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[4] = c;
VERIFY_BITS(r[4], 49);
/* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
uint128_t c, d;
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
int64_t t3, t4, tx, u0;
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
VERIFY_BITS(a[0], 56);
VERIFY_BITS(a[1], 56);
VERIFY_BITS(a[2], 56);
VERIFY_BITS(a[3], 56);
VERIFY_BITS(a[4], 52);
/** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
* px is a shorthand for sum(a[i]*a[x-i], i=0..x).
* Note that [x 0 0 0 0 0] = [x*R].
*/
d = (uint128_t)(a0*2) * a3
+ (uint128_t)(a1*2) * a2;
VERIFY_BITS(d, 114);
/* [d 0 0 0] = [p3 0 0 0] */
c = (uint128_t)a4 * a4;
VERIFY_BITS(c, 112);
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (c & M) * R; c >>= 52;
VERIFY_BITS(d, 115);
VERIFY_BITS(c, 60);
/* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
t3 = d & M; d >>= 52;
VERIFY_BITS(t3, 52);
VERIFY_BITS(d, 63);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
a4 *= 2;
d += (uint128_t)a0 * a4
+ (uint128_t)(a1*2) * a3
+ (uint128_t)a2 * a2;
VERIFY_BITS(d, 115);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
d += c * R;
VERIFY_BITS(d, 116);
/* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
t4 = d & M; d >>= 52;
VERIFY_BITS(t4, 52);
VERIFY_BITS(d, 64);
/* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
tx = (t4 >> 48); t4 &= (M >> 4);
VERIFY_BITS(tx, 4);
VERIFY_BITS(t4, 48);
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
c = (uint128_t)a0 * a0;
VERIFY_BITS(c, 112);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
d += (uint128_t)a1 * a4
+ (uint128_t)(a2*2) * a3;
VERIFY_BITS(d, 114);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = d & M; d >>= 52;
VERIFY_BITS(u0, 52);
VERIFY_BITS(d, 62);
/* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
/* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
u0 = (u0 << 4) | tx;
VERIFY_BITS(u0, 56);
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (uint128_t)u0 * (R >> 4);
VERIFY_BITS(c, 113);
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
r[0] = c & M; c >>= 52;
VERIFY_BITS(r[0], 52);
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
a0 *= 2;
c += (uint128_t)a0 * a1;
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (uint128_t)a2 * a4
+ (uint128_t)a3 * a3;
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
r[1] = c & M; c >>= 52;
VERIFY_BITS(r[1], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (uint128_t)a0 * a2
+ (uint128_t)a1 * a1;
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (uint128_t)a3 * a4;
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[2] = c & M; c >>= 52;
VERIFY_BITS(r[2], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += d * R + t3;;
VERIFY_BITS(c, 100);
/* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[3] = c & M; c >>= 52;
VERIFY_BITS(r[3], 52);
VERIFY_BITS(c, 48);
/* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += t4;
VERIFY_BITS(c, 49);
/* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[4] = c;
VERIFY_BITS(r[4], 49);
/* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_FIELD_IMPL_H_
#define _SECP256K1_FIELD_IMPL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include "util.h"
#if defined(USE_FIELD_10X26)
#include "field_10x26_impl.h"
#elif defined(USE_FIELD_5X52)
#include "field_5x52_impl.h"
#else
#error "Please select field implementation"
#endif
SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
secp256k1_fe na;
secp256k1_fe_negate(&na, a, 1);
secp256k1_fe_add(&na, b);
return secp256k1_fe_normalizes_to_zero_var(&na);
}
static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
int j;
/** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
* { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
* 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
secp256k1_fe_sqr(&x2, a);
secp256k1_fe_mul(&x2, &x2, a);
secp256k1_fe_sqr(&x3, &x2);
secp256k1_fe_mul(&x3, &x3, a);
x6 = x3;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x6, &x6);
}
secp256k1_fe_mul(&x6, &x6, &x3);
x9 = x6;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x9, &x9);
}
secp256k1_fe_mul(&x9, &x9, &x3);
x11 = x9;
for (j=0; j<2; j++) {
secp256k1_fe_sqr(&x11, &x11);
}
secp256k1_fe_mul(&x11, &x11, &x2);
x22 = x11;
for (j=0; j<11; j++) {
secp256k1_fe_sqr(&x22, &x22);
}
secp256k1_fe_mul(&x22, &x22, &x11);
x44 = x22;
for (j=0; j<22; j++) {
secp256k1_fe_sqr(&x44, &x44);
}
secp256k1_fe_mul(&x44, &x44, &x22);
x88 = x44;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x88, &x88);
}
secp256k1_fe_mul(&x88, &x88, &x44);
x176 = x88;
for (j=0; j<88; j++) {
secp256k1_fe_sqr(&x176, &x176);
}
secp256k1_fe_mul(&x176, &x176, &x88);
x220 = x176;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x220, &x220);
}
secp256k1_fe_mul(&x220, &x220, &x44);
x223 = x220;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x223, &x223);
}
secp256k1_fe_mul(&x223, &x223, &x3);
/* The final result is then assembled using a sliding window over the blocks. */
t1 = x223;
for (j=0; j<23; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x22);
for (j=0; j<6; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x2);
secp256k1_fe_sqr(&t1, &t1);
secp256k1_fe_sqr(r, &t1);
/* Check that a square root was actually calculated */
secp256k1_fe_sqr(&t1, r);
return secp256k1_fe_equal_var(&t1, a);
}
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
int j;
/** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
* { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
* [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
secp256k1_fe_sqr(&x2, a);
secp256k1_fe_mul(&x2, &x2, a);
secp256k1_fe_sqr(&x3, &x2);
secp256k1_fe_mul(&x3, &x3, a);
x6 = x3;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x6, &x6);
}
secp256k1_fe_mul(&x6, &x6, &x3);
x9 = x6;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x9, &x9);
}
secp256k1_fe_mul(&x9, &x9, &x3);
x11 = x9;
for (j=0; j<2; j++) {
secp256k1_fe_sqr(&x11, &x11);
}
secp256k1_fe_mul(&x11, &x11, &x2);
x22 = x11;
for (j=0; j<11; j++) {
secp256k1_fe_sqr(&x22, &x22);
}
secp256k1_fe_mul(&x22, &x22, &x11);
x44 = x22;
for (j=0; j<22; j++) {
secp256k1_fe_sqr(&x44, &x44);
}
secp256k1_fe_mul(&x44, &x44, &x22);
x88 = x44;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x88, &x88);
}
secp256k1_fe_mul(&x88, &x88, &x44);
x176 = x88;
for (j=0; j<88; j++) {
secp256k1_fe_sqr(&x176, &x176);
}
secp256k1_fe_mul(&x176, &x176, &x88);
x220 = x176;
for (j=0; j<44; j++) {
secp256k1_fe_sqr(&x220, &x220);
}
secp256k1_fe_mul(&x220, &x220, &x44);
x223 = x220;
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&x223, &x223);
}
secp256k1_fe_mul(&x223, &x223, &x3);
/* The final result is then assembled using a sliding window over the blocks. */
t1 = x223;
for (j=0; j<23; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x22);
for (j=0; j<5; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, a);
for (j=0; j<3; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(&t1, &t1, &x2);
for (j=0; j<2; j++) {
secp256k1_fe_sqr(&t1, &t1);
}
secp256k1_fe_mul(r, a, &t1);
}
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
#if defined(USE_FIELD_INV_BUILTIN)
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
secp256k1_num n, m;
static const secp256k1_fe negone = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
);
/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
static const unsigned char prime[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
};
unsigned char b[32];
secp256k1_fe c = *a;
secp256k1_fe_normalize_var(&c);
secp256k1_fe_get_b32(b, &c);
secp256k1_num_set_bin(&n, b, 32);
secp256k1_num_set_bin(&m, prime, 32);
secp256k1_num_mod_inverse(&n, &n, &m);
secp256k1_num_get_bin(b, 32, &n);
VERIFY_CHECK(secp256k1_fe_set_b32(r, b));
/* Verify the result is the (unique) valid inverse using non-GMP code. */
secp256k1_fe_mul(&c, &c, r);
secp256k1_fe_add(&c, &negone);
CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
#else
#error "Please select field inverse implementation"
#endif
}
static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a) {
secp256k1_fe u;
size_t i;
if (len < 1) {
return;
}
VERIFY_CHECK((r + len <= a) || (a + len <= r));
r[0] = a[0];
i = 0;
while (++i < len) {
secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]);
}
secp256k1_fe_inv_var(&u, &r[--i]);
while (i > 0) {
size_t j = i--;
secp256k1_fe_mul(&r[j], &r[i], &u);
secp256k1_fe_mul(&u, &u, &a[j]);
}
r[0] = u;
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#define USE_BASIC_CONFIG 1
#include "basic-config.h"
#include "include/secp256k1.h"
#include "field_impl.h"
#include "scalar_impl.h"
#include "group_impl.h"
#include "ecmult_gen_impl.h"
static void default_error_callback_fn(const char* str, void* data) {
(void)data;
fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
abort();
}
static const secp256k1_callback default_error_callback = {
default_error_callback_fn,
NULL
};
int main(int argc, char **argv) {
secp256k1_ecmult_gen_context ctx;
int inner;
int outer;
FILE* fp;
(void)argc;
(void)argv;
fp = fopen("src/ecmult_static_context.h","w");
if (fp == NULL) {
fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n");
return -1;
}
fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
fprintf(fp, "#include \"group.h\"\n");
fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = {\n");
secp256k1_ecmult_gen_context_init(&ctx);
secp256k1_ecmult_gen_context_build(&ctx, &default_error_callback);
for(outer = 0; outer != 64; outer++) {
fprintf(fp,"{\n");
for(inner = 0; inner != 16; inner++) {
fprintf(fp," SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
if (inner != 15) {
fprintf(fp,",\n");
} else {
fprintf(fp,"\n");
}
}
if (outer != 63) {
fprintf(fp,"},\n");
} else {
fprintf(fp,"}\n");
}
}
fprintf(fp,"};\n");
secp256k1_ecmult_gen_context_clear(&ctx);
fprintf(fp, "#undef SC\n");
fprintf(fp, "#endif\n");
fclose(fp);
return 0;
}

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_GROUP_
#define _SECP256K1_GROUP_
#include "num.h"
#include "field.h"
/** A group element of the secp256k1 curve, in affine coordinates. */
typedef struct {
secp256k1_fe x;
secp256k1_fe y;
int infinity; /* whether this represents the point at infinity */
} secp256k1_ge;
#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
/** A group element of the secp256k1 curve, in jacobian coordinates. */
typedef struct {
secp256k1_fe x; /* actual X: x/z^2 */
secp256k1_fe y; /* actual Y: y/z^3 */
secp256k1_fe z;
int infinity; /* whether this represents the point at infinity */
} secp256k1_gej;
#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
typedef struct {
secp256k1_fe_storage x;
secp256k1_fe_storage y;
} secp256k1_ge_storage;
#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
/** Set a group element equal to the point at infinity */
static void secp256k1_ge_set_infinity(secp256k1_ge *r);
/** Set a group element equal to the point with given X and Y coordinates */
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
* for Y. Return value indicates whether the result is valid. */
static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
/** Check whether a group element is the point at infinity. */
static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
/** Check whether a group element is valid (i.e., on the curve). */
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
/** Set a group element equal to another which is given in jacobian coordinates */
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb);
/** Set a batch of group elements equal to the inputs given in jacobian
* coordinates (with known z-ratios). zr must contain the known z-ratios such
* that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr);
/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
* the same global z "denominator". zr must contain the known z-ratios such
* that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
* coordinates of the result are stored in r, the common z coordinate is
* stored in globalz. */
static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
/** Set a group element (jacobian) equal to the point at infinity. */
static void secp256k1_gej_set_infinity(secp256k1_gej *r);
/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
static void secp256k1_gej_set_xy(secp256k1_gej *r, const secp256k1_fe *x, const secp256k1_fe *y);
/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
/** Compare the X coordinate of a group element (jacobian). */
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
/** Check whether a group element is the point at infinity. */
static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
* a may not be zero. Constant time. */
static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
#ifdef USE_ENDOMORPHISM
/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
#endif
/** Clear a secp256k1_gej to prevent leaking sensitive information. */
static void secp256k1_gej_clear(secp256k1_gej *r);
/** Clear a secp256k1_ge to prevent leaking sensitive information. */
static void secp256k1_ge_clear(secp256k1_ge *r);
/** Convert a group element to the storage type. */
static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
/** Convert a group element back from the storage type. */
static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_GROUP_IMPL_H_
#define _SECP256K1_GROUP_IMPL_H_
#include <string.h>
#include "num.h"
#include "field.h"
#include "group.h"
/** Generator for secp256k1, value 'g' defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
*/
static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
);
static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
secp256k1_fe zi2;
secp256k1_fe zi3;
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
r->infinity = a->infinity;
}
static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
r->infinity = 1;
}
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
}
static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
return a->infinity;
}
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
*r = *a;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
r->infinity = a->infinity;
secp256k1_fe_inv(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
r->infinity = a->infinity;
if (a->infinity) {
return;
}
secp256k1_fe_inv_var(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_mul(&z3, &a->z, &z2);
secp256k1_fe_mul(&a->x, &a->x, &z2);
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
}
static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb) {
secp256k1_fe *az;
secp256k1_fe *azi;
size_t i;
size_t count = 0;
az = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * len);
for (i = 0; i < len; i++) {
if (!a[i].infinity) {
az[count++] = a[i].z;
}
}
azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
secp256k1_fe_inv_all_var(count, azi, az);
free(az);
count = 0;
for (i = 0; i < len; i++) {
r[i].infinity = a[i].infinity;
if (!a[i].infinity) {
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &azi[count++]);
}
}
free(azi);
}
static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr) {
size_t i = len - 1;
secp256k1_fe zi;
if (len > 0) {
/* Compute the inverse of the last z coordinate, and use it to compute the last affine output. */
secp256k1_fe_inv(&zi, &a[i].z);
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
/* Work out way backwards, using the z-ratios to scale the x/y values. */
while (i > 0) {
secp256k1_fe_mul(&zi, &zi, &zr[i]);
i--;
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
}
}
}
static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
size_t i = len - 1;
secp256k1_fe zs;
if (len > 0) {
/* The z of the final point gives us the "global Z" for the table. */
r[i].x = a[i].x;
r[i].y = a[i].y;
*globalz = a[i].z;
r[i].infinity = 0;
zs = zr[i];
/* Work our way backwards, using the z-ratios to scale the x/y values. */
while (i > 0) {
if (i != len - 1) {
secp256k1_fe_mul(&zs, &zs, &zr[i]);
}
i--;
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
}
}
}
static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
r->infinity = 1;
secp256k1_fe_set_int(&r->x, 0);
secp256k1_fe_set_int(&r->y, 0);
secp256k1_fe_set_int(&r->z, 0);
}
static void secp256k1_gej_set_xy(secp256k1_gej *r, const secp256k1_fe *x, const secp256k1_fe *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
secp256k1_fe_set_int(&r->z, 1);
}
static void secp256k1_gej_clear(secp256k1_gej *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
}
static void secp256k1_ge_clear(secp256k1_ge *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
}
static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
secp256k1_fe x2, x3, c;
r->x = *x;
secp256k1_fe_sqr(&x2, x);
secp256k1_fe_mul(&x3, x, &x2);
r->infinity = 0;
secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&c, &x3);
if (!secp256k1_fe_sqrt_var(&r->y, &c)) {
return 0;
}
secp256k1_fe_normalize_var(&r->y);
if (secp256k1_fe_is_odd(&r->y) != odd) {
secp256k1_fe_negate(&r->y, &r->y, 1);
}
return 1;
}
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
}
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
secp256k1_fe r, r2;
VERIFY_CHECK(!a->infinity);
secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
r2 = a->x; secp256k1_fe_normalize_weak(&r2);
return secp256k1_fe_equal_var(&r, &r2);
}
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
r->z = a->z;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
}
static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
return a->infinity;
}
static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
secp256k1_fe y2, x3, z2, z6;
if (a->infinity) {
return 0;
}
/** y^2 = x^3 + 7
* (Y/Z^3)^2 = (X/Z^2)^3 + 7
* Y^2 / Z^6 = X^3 / Z^6 + 7
* Y^2 = X^3 + 7*Z^6
*/
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_sqr(&z2, &a->z);
secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
secp256k1_fe_mul_int(&z6, 7);
secp256k1_fe_add(&x3, &z6);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
secp256k1_fe y2, x3, c;
if (a->infinity) {
return 0;
}
/* y^2 = x^3 + 7 */
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_set_int(&c, 7);
secp256k1_fe_add(&x3, &c);
secp256k1_fe_normalize_weak(&x3);
return secp256k1_fe_equal_var(&y2, &x3);
}
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
/* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate */
secp256k1_fe t1,t2,t3,t4;
/** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
* Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
* y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
*/
r->infinity = a->infinity;
if (r->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
return;
}
if (rzr != NULL) {
*rzr = a->y;
secp256k1_fe_normalize_weak(rzr);
secp256k1_fe_mul_int(rzr, 2);
}
secp256k1_fe_mul(&r->z, &a->z, &a->y);
secp256k1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */
secp256k1_fe_sqr(&t1, &a->x);
secp256k1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */
secp256k1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */
secp256k1_fe_sqr(&t3, &a->y);
secp256k1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */
secp256k1_fe_sqr(&t4, &t3);
secp256k1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */
secp256k1_fe_mul(&t3, &t3, &a->x); /* T3 = 2*X*Y^2 (1) */
r->x = t3;
secp256k1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */
secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
secp256k1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */
secp256k1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */
secp256k1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */
secp256k1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */
secp256k1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
secp256k1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */
secp256k1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
}
static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
secp256k1_gej_double_var(r, a, rzr);
}
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
/* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
*r = *b;
return;
}
if (b->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z22, &b->z);
secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_mul(&u1, &a->x, &z22);
secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, rzr);
} else {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 0);
}
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
secp256k1_fe_mul(&h, &h, &b->z);
if (rzr != NULL) {
*rzr = h;
}
secp256k1_fe_mul(&r->z, &a->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
/* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
secp256k1_gej_set_ge(r, b);
return;
}
if (b->infinity) {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 1);
}
*r = *a;
return;
}
r->infinity = 0;
secp256k1_fe_sqr(&z12, &a->z);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, rzr);
} else {
if (rzr != NULL) {
secp256k1_fe_set_int(rzr, 0);
}
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
if (rzr != NULL) {
*rzr = h;
}
secp256k1_fe_mul(&r->z, &a->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
/* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
if (b->infinity) {
*r = *a;
return;
}
if (a->infinity) {
secp256k1_fe bzinv2, bzinv3;
r->infinity = b->infinity;
secp256k1_fe_sqr(&bzinv2, bzinv);
secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
secp256k1_fe_set_int(&r->z, 1);
return;
}
r->infinity = 0;
/** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
* secp256k1's isomorphism we can multiply the Z coordinates on both sides
* by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
* This means that (rx,ry,rz) can be calculated as
* (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
* The variable az below holds the modified Z coordinate for a, which is used
* for the computation of rx and ry, but not for rz.
*/
secp256k1_fe_mul(&az, &a->z, bzinv);
secp256k1_fe_sqr(&z12, &az);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
secp256k1_gej_double_var(r, a, NULL);
} else {
r->infinity = 1;
}
return;
}
secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_mul(&h3, &h, &h2);
r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
secp256k1_fe_mul(&t, &u1, &h2);
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
secp256k1_fe_add(&r->y, &h3);
}
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
/* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
secp256k1_fe m_alt, rr_alt;
int infinity, degenerate;
VERIFY_CHECK(!b->infinity);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
/** In:
* Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
* In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
* we find as solution for a unified addition/doubling formula:
* lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
* x3 = lambda^2 - (x1 + x2)
* 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
*
* Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
* U1 = X1*Z2^2, U2 = X2*Z1^2
* S1 = Y1*Z2^3, S2 = Y2*Z1^3
* Z = Z1*Z2
* T = U1+U2
* M = S1+S2
* Q = T*M^2
* R = T^2-U1*U2
* X3 = 4*(R^2-Q)
* Y3 = 4*(R*(3*Q-2*R^2)-M^4)
* Z3 = 2*M*Z
* (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
*
* This formula has the benefit of being the same for both addition
* of distinct points and doubling. However, it breaks down in the
* case that either point is infinity, or that y1 = -y2. We handle
* these cases in the following ways:
*
* - If b is infinity we simply bail by means of a VERIFY_CHECK.
*
* - If a is infinity, we detect this, and at the end of the
* computation replace the result (which will be meaningless,
* but we compute to be constant-time) with b.x : b.y : 1.
*
* - If a = -b, we have y1 = -y2, which is a degenerate case.
* But here the answer is infinity, so we simply set the
* infinity flag of the result, overriding the computed values
* without even needing to cmov.
*
* - If y1 = -y2 but x1 != x2, which does occur thanks to certain
* properties of our curve (specifically, 1 has nontrivial cube
* roots in our field, and the curve equation has no x coefficient)
* then the answer is not infinity but also not given by the above
* equation. In this case, we cmov in place an alternate expression
* for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
* expressions for lambda are defined, they are equal, and can be
* obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
* then substitution of x^3 + 7 for y^2 (using the curve equation).
* For all pairs of nonzero points (a, b) at least one is defined,
* so this covers everything.
*/
secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */
secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */
secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */
secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */
secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */
/** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
* case that Z = z1z2 = 0, and this is special-cased later on). */
degenerate = secp256k1_fe_normalizes_to_zero(&m) &
secp256k1_fe_normalizes_to_zero(&rr);
/* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
* This means either x1 == beta*x2 or beta*x1 == x2, where beta is
* a nontrivial cube root of one. In either case, an alternate
* non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
* so we set R/M equal to this. */
rr_alt = s1;
secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */
secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
secp256k1_fe_cmov(&m_alt, &m, !degenerate);
/* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
* From here on out Ralt and Malt represent the numerator
* and denominator of lambda; R and M represent the explicit
* expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */
secp256k1_fe_mul(&q, &n, &t); /* q = Q = T*Malt^2 (1) */
/* These two lines use the observation that either M == Malt or M == 0,
* so M^3 * Malt is either Malt^4 (which is computed by squaring), or
* zero (which is "computed" by cmov). So the cost is one squaring
* versus two multiplications. */
secp256k1_fe_sqr(&n, &n);
secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */
secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */
secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Malt*Z (1) */
infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
secp256k1_fe_mul_int(&r->z, 2); /* r->z = Z3 = 2*Malt*Z (2) */
secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */
secp256k1_fe_add(&t, &q); /* t = Ralt^2-Q (3) */
secp256k1_fe_normalize_weak(&t);
r->x = t; /* r->x = Ralt^2-Q (1) */
secp256k1_fe_mul_int(&t, 2); /* t = 2*x3 (2) */
secp256k1_fe_add(&t, &q); /* t = 2*x3 - Q: (4) */
secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*x3 - Q) (1) */
secp256k1_fe_add(&t, &n); /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
secp256k1_fe_negate(&r->y, &t, 3); /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_mul_int(&r->x, 4); /* r->x = X3 = 4*(Ralt^2-Q) */
secp256k1_fe_mul_int(&r->y, 4); /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
/** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
r->infinity = infinity;
}
static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
/* Operations: 4 mul, 1 sqr */
secp256k1_fe zz;
VERIFY_CHECK(!secp256k1_fe_is_zero(s));
secp256k1_fe_sqr(&zz, s);
secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */
secp256k1_fe_mul(&r->y, &r->y, &zz);
secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */
secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */
}
static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
secp256k1_fe x, y;
VERIFY_CHECK(!a->infinity);
x = a->x;
secp256k1_fe_normalize(&x);
y = a->y;
secp256k1_fe_normalize(&y);
secp256k1_fe_to_storage(&r->x, &x);
secp256k1_fe_to_storage(&r->y, &y);
}
static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
secp256k1_fe_from_storage(&r->x, &a->x);
secp256k1_fe_from_storage(&r->y, &a->y);
r->infinity = 0;
}
static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
}
#ifdef USE_ENDOMORPHISM
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
static const secp256k1_fe beta = SECP256K1_FE_CONST(
0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
);
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, &beta);
}
#endif
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_HASH_
#define _SECP256K1_HASH_
#include <stdlib.h>
#include <stdint.h>
typedef struct {
uint32_t s[32];
uint32_t buf[16]; /* In big endian */
size_t bytes;
} secp256k1_sha256_t;
static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash);
static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t size);
static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32);
typedef struct {
secp256k1_sha256_t inner, outer;
} secp256k1_hmac_sha256_t;
static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t size);
static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size);
static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32);
typedef struct {
unsigned char v[32];
unsigned char k[32];
int retry;
} secp256k1_rfc6979_hmac_sha256_t;
static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen);
static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen);
static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng);
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_HASH_IMPL_H_
#define _SECP256K1_HASH_IMPL_H_
#include "hash.h"
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z))))
#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y))))
#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10))
#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7))
#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3))
#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10))
#define Round(a,b,c,d,e,f,g,h,k,w) do { \
uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \
uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \
(d) += t1; \
(h) = t1 + t2; \
} while(0)
#ifdef WORDS_BIGENDIAN
#define BE32(x) (x)
#else
#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
#endif
static void secp256k1_sha256_initialize(secp256k1_sha256_t *hash) {
hash->s[0] = 0x6a09e667ul;
hash->s[1] = 0xbb67ae85ul;
hash->s[2] = 0x3c6ef372ul;
hash->s[3] = 0xa54ff53aul;
hash->s[4] = 0x510e527ful;
hash->s[5] = 0x9b05688cul;
hash->s[6] = 0x1f83d9abul;
hash->s[7] = 0x5be0cd19ul;
hash->bytes = 0;
}
/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) {
uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0]));
Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1]));
Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2]));
Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3]));
Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4]));
Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5]));
Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6]));
Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7]));
Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8]));
Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9]));
Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10]));
Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11]));
Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12]));
Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13]));
Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14]));
Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15]));
Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0));
Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0));
Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1));
Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2));
Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3));
Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4));
Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5));
Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6));
Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7));
Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8));
Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9));
Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10));
Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11));
Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12));
Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13));
Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14));
Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15));
Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0));
s[0] += a;
s[1] += b;
s[2] += c;
s[3] += d;
s[4] += e;
s[5] += f;
s[6] += g;
s[7] += h;
}
static void secp256k1_sha256_write(secp256k1_sha256_t *hash, const unsigned char *data, size_t len) {
size_t bufsize = hash->bytes & 0x3F;
hash->bytes += len;
while (bufsize + len >= 64) {
/* Fill the buffer, and process it. */
memcpy(((unsigned char*)hash->buf) + bufsize, data, 64 - bufsize);
data += 64 - bufsize;
len -= 64 - bufsize;
secp256k1_sha256_transform(hash->s, hash->buf);
bufsize = 0;
}
if (len) {
/* Fill the buffer with what remains. */
memcpy(((unsigned char*)hash->buf) + bufsize, data, len);
}
}
static void secp256k1_sha256_finalize(secp256k1_sha256_t *hash, unsigned char *out32) {
static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
uint32_t sizedesc[2];
uint32_t out[8];
int i = 0;
sizedesc[0] = BE32(hash->bytes >> 29);
sizedesc[1] = BE32(hash->bytes << 3);
secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8);
for (i = 0; i < 8; i++) {
out[i] = BE32(hash->s[i]);
hash->s[i] = 0;
}
memcpy(out32, (const unsigned char*)out, 32);
}
static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256_t *hash, const unsigned char *key, size_t keylen) {
int n;
unsigned char rkey[64];
if (keylen <= 64) {
memcpy(rkey, key, keylen);
memset(rkey + keylen, 0, 64 - keylen);
} else {
secp256k1_sha256_t sha256;
secp256k1_sha256_initialize(&sha256);
secp256k1_sha256_write(&sha256, key, keylen);
secp256k1_sha256_finalize(&sha256, rkey);
memset(rkey + 32, 0, 32);
}
secp256k1_sha256_initialize(&hash->outer);
for (n = 0; n < 64; n++) {
rkey[n] ^= 0x5c;
}
secp256k1_sha256_write(&hash->outer, rkey, 64);
secp256k1_sha256_initialize(&hash->inner);
for (n = 0; n < 64; n++) {
rkey[n] ^= 0x5c ^ 0x36;
}
secp256k1_sha256_write(&hash->inner, rkey, 64);
memset(rkey, 0, 64);
}
static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256_t *hash, const unsigned char *data, size_t size) {
secp256k1_sha256_write(&hash->inner, data, size);
}
static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsigned char *out32) {
unsigned char temp[32];
secp256k1_sha256_finalize(&hash->inner, temp);
secp256k1_sha256_write(&hash->outer, temp, 32);
memset(temp, 0, 32);
secp256k1_sha256_finalize(&hash->outer, out32);
}
static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen) {
secp256k1_hmac_sha256_t hmac;
static const unsigned char zero[1] = {0x00};
static const unsigned char one[1] = {0x01};
memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */
memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
/* RFC6979 3.2.d. */
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, zero, 1);
secp256k1_hmac_sha256_write(&hmac, key, keylen);
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
/* RFC6979 3.2.f. */
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, one, 1);
secp256k1_hmac_sha256_write(&hmac, key, keylen);
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
rng->retry = 0;
}
static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen) {
/* RFC6979 3.2.h. */
static const unsigned char zero[1] = {0x00};
if (rng->retry) {
secp256k1_hmac_sha256_t hmac;
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_write(&hmac, zero, 1);
secp256k1_hmac_sha256_finalize(&hmac, rng->k);
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
}
while (outlen > 0) {
secp256k1_hmac_sha256_t hmac;
int now = outlen;
secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
secp256k1_hmac_sha256_finalize(&hmac, rng->v);
if (now > 32) {
now = 32;
}
memcpy(out, rng->v, now);
out += now;
outlen -= now;
}
rng->retry = 1;
}
static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng) {
memset(rng->k, 0, 32);
memset(rng->v, 0, 32);
rng->retry = 0;
}
#undef Round
#undef sigma0
#undef sigma1
#undef Sigma0
#undef Sigma1
#undef Ch
#undef Maj
#undef ReadBE32
#undef WriteBE32
#endif

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package org.bitcoin;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
import com.google.common.base.Preconditions;
/**
* This class holds native methods to handle ECDSA verification.
* You can find an example library that can be used for this at
* https://github.com/sipa/secp256k1
*/
public class NativeSecp256k1 {
public static final boolean enabled;
static {
boolean isEnabled = true;
try {
System.loadLibrary("javasecp256k1");
} catch (UnsatisfiedLinkError e) {
isEnabled = false;
}
enabled = isEnabled;
}
private static ThreadLocal<ByteBuffer> nativeECDSABuffer = new ThreadLocal<ByteBuffer>();
/**
* Verifies the given secp256k1 signature in native code.
* Calling when enabled == false is undefined (probably library not loaded)
*
* @param data The data which was signed, must be exactly 32 bytes
* @param signature The signature
* @param pub The public key which did the signing
*/
public static boolean verify(byte[] data, byte[] signature, byte[] pub) {
Preconditions.checkArgument(data.length == 32 && signature.length <= 520 && pub.length <= 520);
ByteBuffer byteBuff = nativeECDSABuffer.get();
if (byteBuff == null) {
byteBuff = ByteBuffer.allocateDirect(32 + 8 + 520 + 520);
byteBuff.order(ByteOrder.nativeOrder());
nativeECDSABuffer.set(byteBuff);
}
byteBuff.rewind();
byteBuff.put(data);
byteBuff.putInt(signature.length);
byteBuff.putInt(pub.length);
byteBuff.put(signature);
byteBuff.put(pub);
return secp256k1_ecdsa_verify(byteBuff) == 1;
}
/**
* @param byteBuff signature format is byte[32] data,
* native-endian int signatureLength, native-endian int pubkeyLength,
* byte[signatureLength] signature, byte[pubkeyLength] pub
* @returns 1 for valid signature, anything else for invalid
*/
private static native int secp256k1_ecdsa_verify(ByteBuffer byteBuff);
}

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#include "org_bitcoin_NativeSecp256k1.h"
#include "include/secp256k1.h"
JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
(JNIEnv* env, jclass classObject, jobject byteBufferObject)
{
unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
int sigLen = *((int*)(data + 32));
int pubLen = *((int*)(data + 32 + 4));
return secp256k1_ecdsa_verify(data, 32, data+32+8, sigLen, data+32+8+sigLen, pubLen);
}
static void __javasecp256k1_attach(void) __attribute__((constructor));
static void __javasecp256k1_detach(void) __attribute__((destructor));
static void __javasecp256k1_attach(void) {
secp256k1_start(SECP256K1_START_VERIFY);
}
static void __javasecp256k1_detach(void) {
secp256k1_stop();
}

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/* DO NOT EDIT THIS FILE - it is machine generated */
#include <jni.h>
/* Header for class org_bitcoin_NativeSecp256k1 */
#ifndef _Included_org_bitcoin_NativeSecp256k1
#define _Included_org_bitcoin_NativeSecp256k1
#ifdef __cplusplus
extern "C" {
#endif
/*
* Class: org_bitcoin_NativeSecp256k1
* Method: secp256k1_ecdsa_verify
* Signature: (Ljava/nio/ByteBuffer;)I
*/
JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
(JNIEnv *, jclass, jobject);
#ifdef __cplusplus
}
#endif
#endif

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include_HEADERS += include/secp256k1_ecdh.h
noinst_HEADERS += src/modules/ecdh/main_impl.h
noinst_HEADERS += src/modules/ecdh/tests_impl.h
if USE_BENCHMARK
noinst_PROGRAMS += bench_ecdh
bench_ecdh_SOURCES = src/bench_ecdh.c
bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_ecdh_LDFLAGS = -static
endif

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/**********************************************************************
* Copyright (c) 2015 Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_MODULE_ECDH_MAIN_
#define _SECP256K1_MODULE_ECDH_MAIN_
#include "include/secp256k1_ecdh.h"
#include "ecmult_const_impl.h"
int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const secp256k1_pubkey *point, const unsigned char *scalar) {
int ret = 0;
int overflow = 0;
secp256k1_gej res;
secp256k1_ge pt;
secp256k1_scalar s;
ARG_CHECK(result != NULL);
ARG_CHECK(point != NULL);
ARG_CHECK(scalar != NULL);
(void)ctx;
secp256k1_pubkey_load(ctx, &pt, point);
secp256k1_scalar_set_b32(&s, scalar, &overflow);
if (overflow || secp256k1_scalar_is_zero(&s)) {
ret = 0;
} else {
unsigned char x[32];
unsigned char y[1];
secp256k1_sha256_t sha;
secp256k1_ecmult_const(&res, &pt, &s);
secp256k1_ge_set_gej(&pt, &res);
/* Compute a hash of the point in compressed form
* Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not
* expect its output to be secret and has a timing sidechannel. */
secp256k1_fe_normalize(&pt.x);
secp256k1_fe_normalize(&pt.y);
secp256k1_fe_get_b32(x, &pt.x);
y[0] = 0x02 | secp256k1_fe_is_odd(&pt.y);
secp256k1_sha256_initialize(&sha);
secp256k1_sha256_write(&sha, y, sizeof(y));
secp256k1_sha256_write(&sha, x, sizeof(x));
secp256k1_sha256_finalize(&sha, result);
ret = 1;
}
secp256k1_scalar_clear(&s);
return ret;
}
#endif

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/**********************************************************************
* Copyright (c) 2015 Andrew Poelstra *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_MODULE_ECDH_TESTS_
#define _SECP256K1_MODULE_ECDH_TESTS_
void test_ecdh_generator_basepoint(void) {
unsigned char s_one[32] = { 0 };
secp256k1_pubkey point[2];
int i;
s_one[31] = 1;
/* Check against pubkey creation when the basepoint is the generator */
for (i = 0; i < 100; ++i) {
secp256k1_sha256_t sha;
unsigned char s_b32[32];
unsigned char output_ecdh[32];
unsigned char output_ser[32];
unsigned char point_ser[33];
size_t point_ser_len = sizeof(point_ser);
secp256k1_scalar s;
random_scalar_order(&s);
secp256k1_scalar_get_b32(s_b32, &s);
/* compute using ECDH function */
CHECK(secp256k1_ec_pubkey_create(ctx, &point[0], s_one) == 1);
CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32) == 1);
/* compute "explicitly" */
CHECK(secp256k1_ec_pubkey_create(ctx, &point[1], s_b32) == 1);
CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
CHECK(point_ser_len == sizeof(point_ser));
secp256k1_sha256_initialize(&sha);
secp256k1_sha256_write(&sha, point_ser, point_ser_len);
secp256k1_sha256_finalize(&sha, output_ser);
/* compare */
CHECK(memcmp(output_ecdh, output_ser, sizeof(output_ser)) == 0);
}
}
void test_bad_scalar(void) {
unsigned char s_zero[32] = { 0 };
unsigned char s_overflow[32] = {
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
};
unsigned char s_rand[32] = { 0 };
unsigned char output[32];
secp256k1_scalar rand;
secp256k1_pubkey point;
/* Create random point */
random_scalar_order(&rand);
secp256k1_scalar_get_b32(s_rand, &rand);
CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_rand) == 1);
/* Try to multiply it by bad values */
CHECK(secp256k1_ecdh(ctx, output, &point, s_zero) == 0);
CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 0);
/* ...and a good one */
s_overflow[31] -= 1;
CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 1);
}
void run_ecdh_tests(void) {
test_ecdh_generator_basepoint();
test_bad_scalar();
}
#endif

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include_HEADERS += include/secp256k1_recovery.h
noinst_HEADERS += src/modules/recovery/main_impl.h
noinst_HEADERS += src/modules/recovery/tests_impl.h
if USE_BENCHMARK
noinst_PROGRAMS += bench_recover
bench_recover_SOURCES = src/bench_recover.c
bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_recover_LDFLAGS = -static
endif

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/**********************************************************************
* Copyright (c) 2013-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_MODULE_RECOVERY_MAIN_
#define _SECP256K1_MODULE_RECOVERY_MAIN_
#include "include/secp256k1_recovery.h"
static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) {
(void)ctx;
if (sizeof(secp256k1_scalar) == 32) {
/* When the secp256k1_scalar type is exactly 32 byte, use its
* representation inside secp256k1_ecdsa_signature, as conversion is very fast.
* Note that secp256k1_ecdsa_signature_save must use the same representation. */
memcpy(r, &sig->data[0], 32);
memcpy(s, &sig->data[32], 32);
} else {
secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
}
*recid = sig->data[64];
}
static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) {
if (sizeof(secp256k1_scalar) == 32) {
memcpy(&sig->data[0], r, 32);
memcpy(&sig->data[32], s, 32);
} else {
secp256k1_scalar_get_b32(&sig->data[0], r);
secp256k1_scalar_get_b32(&sig->data[32], s);
}
sig->data[64] = recid;
}
int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) {
secp256k1_scalar r, s;
int ret = 1;
int overflow = 0;
(void)ctx;
ARG_CHECK(sig != NULL);
ARG_CHECK(input64 != NULL);
ARG_CHECK(recid >= 0 && recid <= 3);
secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
ret &= !overflow;
secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
ret &= !overflow;
if (ret) {
secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid);
} else {
memset(sig, 0, sizeof(*sig));
}
return ret;
}
int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) {
secp256k1_scalar r, s;
(void)ctx;
ARG_CHECK(output64 != NULL);
ARG_CHECK(sig != NULL);
secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig);
secp256k1_scalar_get_b32(&output64[0], &r);
secp256k1_scalar_get_b32(&output64[32], &s);
return 1;
}
int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) {
secp256k1_scalar r, s;
int recid;
(void)ctx;
ARG_CHECK(sig != NULL);
ARG_CHECK(sigin != NULL);
secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin);
secp256k1_ecdsa_signature_save(sig, &r, &s);
return 1;
}
int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
secp256k1_scalar r, s;
secp256k1_scalar sec, non, msg;
int recid;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(signature != NULL);
ARG_CHECK(seckey != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
/* Fail if the secret key is invalid. */
if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
unsigned int count = 0;
secp256k1_scalar_set_b32(&msg, msg32, NULL);
while (1) {
unsigned char nonce32[32];
ret = noncefp(nonce32, seckey, msg32, NULL, (void*)noncedata, count);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&non, nonce32, &overflow);
memset(nonce32, 0, 32);
if (!secp256k1_scalar_is_zero(&non) && !overflow) {
if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) {
break;
}
}
count++;
}
secp256k1_scalar_clear(&msg);
secp256k1_scalar_clear(&non);
secp256k1_scalar_clear(&sec);
}
if (ret) {
secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid);
} else {
memset(signature, 0, sizeof(*signature));
}
return ret;
}
int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) {
secp256k1_ge q;
secp256k1_scalar r, s;
secp256k1_scalar m;
int recid;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(signature != NULL);
ARG_CHECK(pubkey != NULL);
secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
ARG_CHECK(recid >= 0 && recid < 4);
secp256k1_scalar_set_b32(&m, msg32, NULL);
if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
secp256k1_pubkey_save(pubkey, &q);
return 1;
} else {
memset(pubkey, 0, sizeof(*pubkey));
return 0;
}
}
#endif

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/**********************************************************************
* Copyright (c) 2013-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_MODULE_RECOVERY_TESTS_
#define _SECP256K1_MODULE_RECOVERY_TESTS_
void test_ecdsa_recovery_end_to_end(void) {
unsigned char extra[32] = {0x00};
unsigned char privkey[32];
unsigned char message[32];
secp256k1_ecdsa_signature signature[5];
secp256k1_ecdsa_recoverable_signature rsignature[5];
unsigned char sig[74];
secp256k1_pubkey pubkey;
secp256k1_pubkey recpubkey;
int recid = 0;
/* Generate a random key and message. */
{
secp256k1_scalar msg, key;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_scalar_get_b32(privkey, &key);
secp256k1_scalar_get_b32(message, &msg);
}
/* Construct and verify corresponding public key. */
CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
/* Serialize/parse compact and verify/recover. */
extra[0] = 0;
CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[0], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[4], message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[1], message, privkey, NULL, extra) == 1);
extra[31] = 1;
CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[2], message, privkey, NULL, extra) == 1);
extra[31] = 0;
extra[0] = 1;
CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1);
CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
memset(&rsignature[4], 0, sizeof(rsignature[4]));
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
/* Parse compact (with recovery id) and recover. */
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1);
CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
/* Serialize/destroy/parse signature and verify again. */
CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
sig[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0);
/* Recover again */
CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 ||
memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
}
/* Tests several edge cases. */
void test_ecdsa_recovery_edge_cases(void) {
const unsigned char msg32[32] = {
'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
's', 's', 'a', 'g', 'e', '.', '.', '.'
};
const unsigned char sig64[64] = {
/* Generated by signing the above message with nonce 'This is the nonce we will use...'
* and secret key 0 (which is not valid), resulting in recid 0. */
0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
};
secp256k1_pubkey pubkey;
/* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
const unsigned char sigb64[64] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
};
secp256k1_pubkey pubkeyb;
secp256k1_ecdsa_recoverable_signature rsig;
secp256k1_ecdsa_signature sig;
int recid;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 0));
CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 1));
CHECK(secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 2));
CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 3));
CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
for (recid = 0; recid < 4; recid++) {
int i;
int recid2;
/* (4,4) encoded in DER. */
unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
unsigned char sigbderalt1[39] = {
0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
};
unsigned char sigbderalt2[39] = {
0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
};
unsigned char sigbderalt3[40] = {
0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
};
unsigned char sigbderalt4[40] = {
0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
};
/* (order + r,4) encoded in DER. */
unsigned char sigbderlong[40] = {
0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
};
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
for (recid2 = 0; recid2 < 4; recid2++) {
secp256k1_pubkey pubkey2b;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid2) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &pubkey2b, &rsig, msg32) == 1);
/* Verifying with (order + r,4) should always fail. */
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderlong, sizeof(sigbderlong)) == 0);
}
/* DER parsing tests. */
/* Zero length r/s. */
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0);
/* Leading zeros. */
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt1, sizeof(sigbderalt1)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt2, sizeof(sigbderalt2)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
sigbderalt3[4] = 1;
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0);
sigbderalt4[7] = 1;
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0);
/* Damage signature. */
sigbder[7]++;
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
sigbder[7]--;
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, 6) == 0);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder) - 1) == 0);
for(i = 0; i < 8; i++) {
int c;
unsigned char orig = sigbder[i];
/*Try every single-byte change.*/
for (c = 0; c < 256; c++) {
if (c == orig ) {
continue;
}
sigbder[i] = c;
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
}
sigbder[i] = orig;
}
}
/* Test r/s equal to zero */
{
/* (1,1) encoded in DER. */
unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01};
unsigned char sigc64[64] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
};
secp256k1_pubkey pubkeyc;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyc, &rsig, msg32) == 1);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 1);
sigcder[4] = 0;
sigc64[31] = 0;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
sigcder[4] = 1;
sigcder[7] = 0;
sigc64[31] = 1;
sigc64[63] = 0;
CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
}
}
void run_recovery_tests(void) {
int i;
for (i = 0; i < 64*count; i++) {
test_ecdsa_recovery_end_to_end();
}
test_ecdsa_recovery_edge_cases();
}
#endif

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include_HEADERS += include/secp256k1_schnorr.h
noinst_HEADERS += src/modules/schnorr/main_impl.h
noinst_HEADERS += src/modules/schnorr/schnorr.h
noinst_HEADERS += src/modules/schnorr/schnorr_impl.h
noinst_HEADERS += src/modules/schnorr/tests_impl.h
if USE_BENCHMARK
noinst_PROGRAMS += bench_schnorr_verify
bench_schnorr_verify_SOURCES = src/bench_schnorr_verify.c
bench_schnorr_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
bench_schnorr_verify_LDFLAGS = -static
endif

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/**********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef SECP256K1_MODULE_SCHNORR_MAIN
#define SECP256K1_MODULE_SCHNORR_MAIN
#include "include/secp256k1_schnorr.h"
#include "modules/schnorr/schnorr_impl.h"
static void secp256k1_schnorr_msghash_sha256(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
secp256k1_sha256_t sha;
secp256k1_sha256_initialize(&sha);
secp256k1_sha256_write(&sha, r32, 32);
secp256k1_sha256_write(&sha, msg32, 32);
secp256k1_sha256_finalize(&sha, h32);
}
static const unsigned char secp256k1_schnorr_algo16[17] = "Schnorr+SHA256 ";
int secp256k1_schnorr_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
secp256k1_scalar sec, non;
int ret = 0;
int overflow = 0;
unsigned int count = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sig64 != NULL);
ARG_CHECK(seckey != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
secp256k1_scalar_set_b32(&sec, seckey, NULL);
while (1) {
unsigned char nonce32[32];
ret = noncefp(nonce32, msg32, seckey, secp256k1_schnorr_algo16, (void*)noncedata, count);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&non, nonce32, &overflow);
memset(nonce32, 0, 32);
if (!secp256k1_scalar_is_zero(&non) && !overflow) {
if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, NULL, secp256k1_schnorr_msghash_sha256, msg32)) {
break;
}
}
count++;
}
if (!ret) {
memset(sig64, 0, 64);
}
secp256k1_scalar_clear(&non);
secp256k1_scalar_clear(&sec);
return ret;
}
int secp256k1_schnorr_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
secp256k1_ge q;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sig64 != NULL);
ARG_CHECK(pubkey != NULL);
secp256k1_pubkey_load(ctx, &q, pubkey);
return secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32);
}
int secp256k1_schnorr_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *sig64, const unsigned char *msg32) {
secp256k1_ge q;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sig64 != NULL);
ARG_CHECK(pubkey != NULL);
if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32)) {
secp256k1_pubkey_save(pubkey, &q);
return 1;
} else {
memset(pubkey, 0, sizeof(*pubkey));
return 0;
}
}
int secp256k1_schnorr_generate_nonce_pair(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, unsigned char *privnonce32, const unsigned char *sec32, const unsigned char *msg32, secp256k1_nonce_function noncefp, const void* noncedata) {
int count = 0;
int ret = 1;
secp256k1_gej Qj;
secp256k1_ge Q;
secp256k1_scalar sec;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sec32 != NULL);
ARG_CHECK(pubnonce != NULL);
ARG_CHECK(privnonce32 != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
do {
int overflow;
ret = noncefp(privnonce32, sec32, msg32, secp256k1_schnorr_algo16, (void*)noncedata, count++);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&sec, privnonce32, &overflow);
if (overflow || secp256k1_scalar_is_zero(&sec)) {
continue;
}
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sec);
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(pubnonce, &Q);
break;
} while(1);
secp256k1_scalar_clear(&sec);
if (!ret) {
memset(pubnonce, 0, sizeof(*pubnonce));
}
return ret;
}
int secp256k1_schnorr_partial_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *sec32, const secp256k1_pubkey *pubnonce_others, const unsigned char *secnonce32) {
int overflow = 0;
secp256k1_scalar sec, non;
secp256k1_ge pubnon;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sig64 != NULL);
ARG_CHECK(sec32 != NULL);
ARG_CHECK(secnonce32 != NULL);
ARG_CHECK(pubnonce_others != NULL);
secp256k1_scalar_set_b32(&sec, sec32, &overflow);
if (overflow || secp256k1_scalar_is_zero(&sec)) {
return -1;
}
secp256k1_scalar_set_b32(&non, secnonce32, &overflow);
if (overflow || secp256k1_scalar_is_zero(&non)) {
return -1;
}
secp256k1_pubkey_load(ctx, &pubnon, pubnonce_others);
return secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, &pubnon, secp256k1_schnorr_msghash_sha256, msg32);
}
int secp256k1_schnorr_partial_combine(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char * const *sig64sin, int n) {
ARG_CHECK(sig64 != NULL);
ARG_CHECK(n >= 1);
ARG_CHECK(sig64sin != NULL);
return secp256k1_schnorr_sig_combine(sig64, n, sig64sin);
}
#endif

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/***********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php. *
***********************************************************************/
#ifndef _SECP256K1_MODULE_SCHNORR_H_
#define _SECP256K1_MODULE_SCHNORR_H_
#include "scalar.h"
#include "group.h"
typedef void (*secp256k1_schnorr_msghash)(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32);
static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
static int secp256k1_schnorr_sig_combine(unsigned char *sig64, int n, const unsigned char * const *sig64ins);
#endif

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/***********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php. *
***********************************************************************/
#ifndef _SECP256K1_SCHNORR_IMPL_H_
#define _SECP256K1_SCHNORR_IMPL_H_
#include <string.h>
#include "schnorr.h"
#include "num.h"
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecmult_gen.h"
/**
* Custom Schnorr-based signature scheme. They support multiparty signing, public key
* recovery and batch validation.
*
* Rationale for verifying R's y coordinate:
* In order to support batch validation and public key recovery, the full R point must
* be known to verifiers, rather than just its x coordinate. In order to not risk
* being more strict in batch validation than normal validation, validators must be
* required to reject signatures with incorrect y coordinate. This is only possible
* by including a (relatively slow) field inverse, or a field square root. However,
* batch validation offers potentially much higher benefits than this cost.
*
* Rationale for having an implicit y coordinate oddness:
* If we commit to having the full R point known to verifiers, there are two mechanism.
* Either include its oddness in the signature, or give it an implicit fixed value.
* As the R y coordinate can be flipped by a simple negation of the nonce, we choose the
* latter, as it comes with nearly zero impact on signing or validation performance, and
* saves a byte in the signature.
*
* Signing:
* Inputs: 32-byte message m, 32-byte scalar key x (!=0), 32-byte scalar nonce k (!=0)
*
* Compute point R = k * G. Reject nonce if R's y coordinate is odd (or negate nonce).
* Compute 32-byte r, the serialization of R's x coordinate.
* Compute scalar h = Hash(r || m). Reject nonce if h == 0 or h >= order.
* Compute scalar s = k - h * x.
* The signature is (r, s).
*
*
* Verification:
* Inputs: 32-byte message m, public key point Q, signature: (32-byte r, scalar s)
*
* Signature is invalid if s >= order.
* Signature is invalid if r >= p.
* Compute scalar h = Hash(r || m). Signature is invalid if h == 0 or h >= order.
* Option 1 (faster for single verification):
* Compute point R = h * Q + s * G. Signature is invalid if R is infinity or R's y coordinate is odd.
* Signature is valid if the serialization of R's x coordinate equals r.
* Option 2 (allows batch validation and pubkey recovery):
* Decompress x coordinate r into point R, with odd y coordinate. Fail if R is not on the curve.
* Signature is valid if R + h * Q + s * G == 0.
*/
static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Rj;
secp256k1_ge Ra;
unsigned char h32[32];
secp256k1_scalar h, s;
int overflow;
secp256k1_scalar n;
if (secp256k1_scalar_is_zero(key) || secp256k1_scalar_is_zero(nonce)) {
return 0;
}
n = *nonce;
secp256k1_ecmult_gen(ctx, &Rj, &n);
if (pubnonce != NULL) {
secp256k1_gej_add_ge(&Rj, &Rj, pubnonce);
}
secp256k1_ge_set_gej(&Ra, &Rj);
secp256k1_fe_normalize(&Ra.y);
if (secp256k1_fe_is_odd(&Ra.y)) {
/* R's y coordinate is odd, which is not allowed (see rationale above).
Force it to be even by negating the nonce. Note that this even works
for multiparty signing, as the R point is known to all participants,
which can all decide to flip the sign in unison, resulting in the
overall R point to be negated too. */
secp256k1_scalar_negate(&n, &n);
}
secp256k1_fe_normalize(&Ra.x);
secp256k1_fe_get_b32(sig64, &Ra.x);
hash(h32, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, h32, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
secp256k1_scalar_clear(&n);
return 0;
}
secp256k1_scalar_mul(&s, &h, key);
secp256k1_scalar_negate(&s, &s);
secp256k1_scalar_add(&s, &s, &n);
secp256k1_scalar_clear(&n);
secp256k1_scalar_get_b32(sig64 + 32, &s);
return 1;
}
static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Qj, Rj;
secp256k1_ge Ra;
secp256k1_fe Rx;
secp256k1_scalar h, s;
unsigned char hh[32];
int overflow;
if (secp256k1_ge_is_infinity(pubkey)) {
return 0;
}
hash(hh, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, hh, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
return 0;
}
overflow = 0;
secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
if (overflow) {
return 0;
}
if (!secp256k1_fe_set_b32(&Rx, sig64)) {
return 0;
}
secp256k1_gej_set_ge(&Qj, pubkey);
secp256k1_ecmult(ctx, &Rj, &Qj, &h, &s);
if (secp256k1_gej_is_infinity(&Rj)) {
return 0;
}
secp256k1_ge_set_gej_var(&Ra, &Rj);
secp256k1_fe_normalize_var(&Ra.y);
if (secp256k1_fe_is_odd(&Ra.y)) {
return 0;
}
return secp256k1_fe_equal_var(&Rx, &Ra.x);
}
static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Qj, Rj;
secp256k1_ge Ra;
secp256k1_fe Rx;
secp256k1_scalar h, s;
unsigned char hh[32];
int overflow;
hash(hh, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, hh, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
return 0;
}
overflow = 0;
secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
if (overflow) {
return 0;
}
if (!secp256k1_fe_set_b32(&Rx, sig64)) {
return 0;
}
if (!secp256k1_ge_set_xo_var(&Ra, &Rx, 0)) {
return 0;
}
secp256k1_gej_set_ge(&Rj, &Ra);
secp256k1_scalar_inverse_var(&h, &h);
secp256k1_scalar_negate(&s, &s);
secp256k1_scalar_mul(&s, &s, &h);
secp256k1_ecmult(ctx, &Qj, &Rj, &h, &s);
if (secp256k1_gej_is_infinity(&Qj)) {
return 0;
}
secp256k1_ge_set_gej(pubkey, &Qj);
return 1;
}
static int secp256k1_schnorr_sig_combine(unsigned char *sig64, int n, const unsigned char * const *sig64ins) {
secp256k1_scalar s = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
int i;
for (i = 0; i < n; i++) {
secp256k1_scalar si;
int overflow;
secp256k1_scalar_set_b32(&si, sig64ins[i] + 32, &overflow);
if (overflow) {
return -1;
}
if (i) {
if (memcmp(sig64ins[i - 1], sig64ins[i], 32) != 0) {
return -1;
}
}
secp256k1_scalar_add(&s, &s, &si);
}
if (secp256k1_scalar_is_zero(&s)) {
return 0;
}
memcpy(sig64, sig64ins[0], 32);
secp256k1_scalar_get_b32(sig64 + 32, &s);
secp256k1_scalar_clear(&s);
return 1;
}
#endif

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/**********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef SECP256K1_MODULE_SCHNORR_TESTS
#define SECP256K1_MODULE_SCHNORR_TESTS
#include "include/secp256k1_schnorr.h"
void test_schnorr_end_to_end(void) {
unsigned char privkey[32];
unsigned char message[32];
unsigned char schnorr_signature[64];
secp256k1_pubkey pubkey, recpubkey;
/* Generate a random key and message. */
{
secp256k1_scalar key;
random_scalar_order_test(&key);
secp256k1_scalar_get_b32(privkey, &key);
secp256k1_rand256_test(message);
}
/* Construct and verify corresponding public key. */
CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
/* Schnorr sign. */
CHECK(secp256k1_schnorr_sign(ctx, schnorr_signature, message, privkey, NULL, NULL) == 1);
CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 1);
CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) == 1);
CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
/* Destroy signature and verify again. */
schnorr_signature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 0);
CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) != 1 ||
memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
}
/** Horribly broken hash function. Do not use for anything but tests. */
void test_schnorr_hash(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
int i;
for (i = 0; i < 32; i++) {
h32[i] = r32[i] ^ msg32[i];
}
}
void test_schnorr_sign_verify(void) {
unsigned char msg32[32];
unsigned char sig64[3][64];
secp256k1_gej pubkeyj[3];
secp256k1_ge pubkey[3];
secp256k1_scalar nonce[3], key[3];
int i = 0;
int k;
secp256k1_rand256_test(msg32);
for (k = 0; k < 3; k++) {
random_scalar_order_test(&key[k]);
do {
random_scalar_order_test(&nonce[k]);
if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64[k], &key[k], &nonce[k], NULL, &test_schnorr_hash, msg32)) {
break;
}
} while(1);
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubkeyj[k], &key[k]);
secp256k1_ge_set_gej_var(&pubkey[k], &pubkeyj[k]);
CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32));
for (i = 0; i < 4; i++) {
int pos = secp256k1_rand32() % 64;
int mod = 1 + (secp256k1_rand32() % 255);
sig64[k][pos] ^= mod;
CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32) == 0);
sig64[k][pos] ^= mod;
}
}
}
void test_schnorr_threshold(void) {
unsigned char msg[32];
unsigned char sec[5][32];
secp256k1_pubkey pub[5];
unsigned char nonce[5][32];
secp256k1_pubkey pubnonce[5];
unsigned char sig[5][64];
const unsigned char* sigs[5];
unsigned char allsig[64];
const secp256k1_pubkey* pubs[5];
secp256k1_pubkey allpub;
int n, i;
int damage;
int ret = 0;
damage = (secp256k1_rand32() % 2) ? (1 + (secp256k1_rand32() % 4)) : 0;
secp256k1_rand256_test(msg);
n = 2 + (secp256k1_rand32() % 4);
for (i = 0; i < n; i++) {
do {
secp256k1_rand256_test(sec[i]);
} while (!secp256k1_ec_seckey_verify(ctx, sec[i]));
CHECK(secp256k1_ec_pubkey_create(ctx, &pub[i], sec[i]));
CHECK(secp256k1_schnorr_generate_nonce_pair(ctx, &pubnonce[i], nonce[i], msg, sec[i], NULL, NULL));
pubs[i] = &pub[i];
}
if (damage == 1) {
nonce[secp256k1_rand32() % n][secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
} else if (damage == 2) {
sec[secp256k1_rand32() % n][secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
}
for (i = 0; i < n; i++) {
secp256k1_pubkey allpubnonce;
const secp256k1_pubkey *pubnonces[4];
int j;
for (j = 0; j < i; j++) {
pubnonces[j] = &pubnonce[j];
}
for (j = i + 1; j < n; j++) {
pubnonces[j - 1] = &pubnonce[j];
}
CHECK(secp256k1_ec_pubkey_combine(ctx, &allpubnonce, pubnonces, n - 1));
ret |= (secp256k1_schnorr_partial_sign(ctx, sig[i], msg, sec[i], &allpubnonce, nonce[i]) != 1) * 1;
sigs[i] = sig[i];
}
if (damage == 3) {
sig[secp256k1_rand32() % n][secp256k1_rand32() % 64] ^= 1 + (secp256k1_rand32() % 255);
}
ret |= (secp256k1_ec_pubkey_combine(ctx, &allpub, pubs, n) != 1) * 2;
if ((ret & 1) == 0) {
ret |= (secp256k1_schnorr_partial_combine(ctx, allsig, sigs, n) != 1) * 4;
}
if (damage == 4) {
allsig[secp256k1_rand32() % 32] ^= 1 + (secp256k1_rand32() % 255);
}
if ((ret & 7) == 0) {
ret |= (secp256k1_schnorr_verify(ctx, allsig, msg, &allpub) != 1) * 8;
}
CHECK((ret == 0) == (damage == 0));
}
void test_schnorr_recovery(void) {
unsigned char msg32[32];
unsigned char sig64[64];
secp256k1_ge Q;
secp256k1_rand256_test(msg32);
secp256k1_rand256_test(sig64);
secp256k1_rand256_test(sig64 + 32);
if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1) {
CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1);
}
}
void run_schnorr_tests(void) {
int i;
for (i = 0; i < 32*count; i++) {
test_schnorr_end_to_end();
}
for (i = 0; i < 32 * count; i++) {
test_schnorr_sign_verify();
}
for (i = 0; i < 16 * count; i++) {
test_schnorr_recovery();
}
for (i = 0; i < 10 * count; i++) {
test_schnorr_threshold();
}
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_
#define _SECP256K1_NUM_
#ifndef USE_NUM_NONE
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_NUM_GMP)
#include "num_gmp.h"
#else
#error "Please select num implementation"
#endif
/** Copy a number. */
static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
/** Convert a number's absolute value to a binary big-endian string.
* There must be enough place. */
static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a);
/** Set a number to the value of a binary big-endian string. */
static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen);
/** Compute a modular inverse. The input must be less than the modulus. */
static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
/** Compare the absolute value of two numbers. */
static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
/** Test whether two number are equal (including sign). */
static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
/** Add two (signed) numbers. */
static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
/** Subtract two (signed) numbers. */
static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
/** Multiply two (signed) numbers. */
static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
even if r was negative. */
static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
/** Right-shift the passed number by bits bits. */
static void secp256k1_num_shift(secp256k1_num *r, int bits);
/** Check whether a number is zero. */
static int secp256k1_num_is_zero(const secp256k1_num *a);
/** Check whether a number is strictly negative. */
static int secp256k1_num_is_neg(const secp256k1_num *a);
/** Change a number's sign. */
static void secp256k1_num_negate(secp256k1_num *r);
#endif
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_REPR_
#define _SECP256K1_NUM_REPR_
#include <gmp.h>
#define NUM_LIMBS ((256+GMP_NUMB_BITS-1)/GMP_NUMB_BITS)
typedef struct {
mp_limb_t data[2*NUM_LIMBS];
int neg;
int limbs;
} secp256k1_num;
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_REPR_IMPL_H_
#define _SECP256K1_NUM_REPR_IMPL_H_
#include <string.h>
#include <stdlib.h>
#include <gmp.h>
#include "util.h"
#include "num.h"
#ifdef VERIFY
static void secp256k1_num_sanity(const secp256k1_num *a) {
VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
}
#else
#define secp256k1_num_sanity(a) do { } while(0)
#endif
static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
*r = *a;
}
static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
unsigned char tmp[65];
int len = 0;
int shift = 0;
if (a->limbs>1 || a->data[0] != 0) {
len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
}
while (shift < len && tmp[shift] == 0) shift++;
VERIFY_CHECK(len-shift <= (int)rlen);
memset(r, 0, rlen - len + shift);
if (len > shift) {
memcpy(r + rlen - len + shift, tmp + shift, len - shift);
}
memset(tmp, 0, sizeof(tmp));
}
static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) {
int len;
VERIFY_CHECK(alen > 0);
VERIFY_CHECK(alen <= 64);
len = mpn_set_str(r->data, a, alen, 256);
if (len == 0) {
r->data[0] = 0;
len = 1;
}
VERIFY_CHECK(len <= NUM_LIMBS*2);
r->limbs = len;
r->neg = 0;
while (r->limbs > 1 && r->data[r->limbs-1]==0) {
r->limbs--;
}
}
static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
r->limbs = a->limbs;
if (c != 0) {
VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
r->data[r->limbs++] = c;
}
}
static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
VERIFY_CHECK(c == 0);
r->limbs = a->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) {
r->limbs--;
}
}
static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
secp256k1_num_sanity(r);
secp256k1_num_sanity(m);
if (r->limbs >= m->limbs) {
mp_limb_t t[2*NUM_LIMBS];
mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
memset(t, 0, sizeof(t));
r->limbs = m->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) {
r->limbs--;
}
}
if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
secp256k1_num_sub_abs(r, m, r);
r->neg = 0;
}
}
static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
int i;
mp_limb_t g[NUM_LIMBS+1];
mp_limb_t u[NUM_LIMBS+1];
mp_limb_t v[NUM_LIMBS+1];
mp_size_t sn;
mp_size_t gn;
secp256k1_num_sanity(a);
secp256k1_num_sanity(m);
/** mpn_gcdext computes: (G,S) = gcdext(U,V), where
* * G = gcd(U,V)
* * G = U*S + V*T
* * U has equal or more limbs than V, and V has no padding
* If we set U to be (a padded version of) a, and V = m:
* G = a*S + m*T
* G = a*S mod m
* Assuming G=1:
* S = 1/a mod m
*/
VERIFY_CHECK(m->limbs <= NUM_LIMBS);
VERIFY_CHECK(m->data[m->limbs-1] != 0);
for (i = 0; i < m->limbs; i++) {
u[i] = (i < a->limbs) ? a->data[i] : 0;
v[i] = m->data[i];
}
sn = NUM_LIMBS+1;
gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
VERIFY_CHECK(gn == 1);
VERIFY_CHECK(g[0] == 1);
r->neg = a->neg ^ m->neg;
if (sn < 0) {
mpn_sub(r->data, m->data, m->limbs, r->data, -sn);
r->limbs = m->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) {
r->limbs--;
}
} else {
r->limbs = sn;
}
memset(g, 0, sizeof(g));
memset(u, 0, sizeof(u));
memset(v, 0, sizeof(v));
}
static int secp256k1_num_is_zero(const secp256k1_num *a) {
return (a->limbs == 1 && a->data[0] == 0);
}
static int secp256k1_num_is_neg(const secp256k1_num *a) {
return (a->limbs > 1 || a->data[0] != 0) && a->neg;
}
static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
if (a->limbs > b->limbs) {
return 1;
}
if (a->limbs < b->limbs) {
return -1;
}
return mpn_cmp(a->data, b->data, a->limbs);
}
static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
if (a->limbs > b->limbs) {
return 0;
}
if (a->limbs < b->limbs) {
return 0;
}
if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) {
return 0;
}
return mpn_cmp(a->data, b->data, a->limbs) == 0;
}
static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
r->neg = a->neg;
if (a->limbs >= b->limbs) {
secp256k1_num_add_abs(r, a, b);
} else {
secp256k1_num_add_abs(r, b, a);
}
} else {
if (secp256k1_num_cmp(a, b) > 0) {
r->neg = a->neg;
secp256k1_num_sub_abs(r, a, b);
} else {
r->neg = b->neg ^ bneg;
secp256k1_num_sub_abs(r, b, a);
}
}
}
static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 0);
}
static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 1);
}
static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
mp_limb_t tmp[2*NUM_LIMBS+1];
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
r->limbs = 1;
r->neg = 0;
r->data[0] = 0;
return;
}
if (a->limbs >= b->limbs) {
mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
} else {
mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
}
r->limbs = a->limbs + b->limbs;
if (r->limbs > 1 && tmp[r->limbs - 1]==0) {
r->limbs--;
}
VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
mpn_copyi(r->data, tmp, r->limbs);
r->neg = a->neg ^ b->neg;
memset(tmp, 0, sizeof(tmp));
}
static void secp256k1_num_shift(secp256k1_num *r, int bits) {
if (bits % GMP_NUMB_BITS) {
/* Shift within limbs. */
mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
}
if (bits >= GMP_NUMB_BITS) {
int i;
/* Shift full limbs. */
for (i = 0; i < r->limbs; i++) {
int index = i + (bits / GMP_NUMB_BITS);
if (index < r->limbs && index < 2*NUM_LIMBS) {
r->data[i] = r->data[index];
} else {
r->data[i] = 0;
}
}
}
while (r->limbs>1 && r->data[r->limbs-1]==0) {
r->limbs--;
}
}
static void secp256k1_num_negate(secp256k1_num *r) {
r->neg ^= 1;
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_IMPL_H_
#define _SECP256K1_NUM_IMPL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include "num.h"
#if defined(USE_NUM_GMP)
#include "num_gmp_impl.h"
#elif defined(USE_NUM_NONE)
/* Nothing. */
#else
#error "Please select num implementation"
#endif
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_
#define _SECP256K1_SCALAR_
#include "num.h"
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_SCALAR_4X64)
#include "scalar_4x64.h"
#elif defined(USE_SCALAR_8X32)
#include "scalar_8x32.h"
#else
#error "Please select scalar implementation"
#endif
/** Clear a scalar to prevent the leak of sensitive data. */
static void secp256k1_scalar_clear(secp256k1_scalar *r);
/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
/** Access bits from a scalar. Not constant time. */
static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
/** Set a scalar from a big endian byte array. */
static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
/** Set a scalar to an unsigned integer. */
static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
/** Convert a scalar to a byte array. */
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
/** Multiply two scalars (modulo the group order). */
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
/** Shift a scalar right by some amount strictly between 0 and 16, returning
* the low bits that were shifted off */
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
/** Compute the square of a scalar (modulo the group order). */
static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
/** Compute the inverse of a scalar (modulo the group order). */
static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
/** Compute the complement of a scalar (modulo the group order). */
static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
/** Check whether a scalar equals zero. */
static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
/** Check whether a scalar equals one. */
static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
/** Check whether a scalar, considered as an nonnegative integer, is even. */
static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
/** Check whether a scalar is higher than the group order divided by 2. */
static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
/** Conditionally negate a number, in constant time.
* Returns -1 if the number was negated, 1 otherwise */
static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
#ifndef USE_NUM_NONE
/** Convert a scalar to a number. */
static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
/** Get the order of the group as a number. */
static void secp256k1_scalar_order_get_num(secp256k1_num *r);
#endif
/** Compare two scalars. */
static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
#ifdef USE_ENDOMORPHISM
/** Find r1 and r2 such that r1+r2*2^128 = a. */
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
#endif
/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_
#define _SECP256K1_SCALAR_REPR_
#include <stdint.h>
/** A scalar modulo the group order of the secp256k1 curve. */
typedef struct {
uint64_t d[4];
} secp256k1_scalar;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
#define _SECP256K1_SCALAR_REPR_IMPL_H_
/* Limbs of the secp256k1 order. */
#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
/* Limbs of 2^256 minus the secp256k1 order. */
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
#define SECP256K1_N_C_2 (1)
/* Limbs of half the secp256k1 order. */
#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
r->d[0] = 0;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
}
SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
r->d[0] = v;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK(count < 32);
VERIFY_CHECK(offset + count <= 256);
if ((offset + count - 1) >> 6 == offset >> 6) {
return secp256k1_scalar_get_bits(a, offset, count);
} else {
VERIFY_CHECK((offset >> 6) + 1 < 4);
return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
}
}
SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
no |= (a->d[2] < SECP256K1_N_2);
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
no |= (a->d[1] < SECP256K1_N_1);
yes |= (a->d[1] > SECP256K1_N_1) & ~no;
yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
return yes;
}
SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
uint128_t t;
VERIFY_CHECK(overflow <= 1);
t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint64_t)r->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
return overflow;
}
static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
int overflow;
uint128_t t = (uint128_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
overflow = t + secp256k1_scalar_check_overflow(r);
VERIFY_CHECK(overflow == 0 || overflow == 1);
secp256k1_scalar_reduce(r, overflow);
return overflow;
}
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
uint128_t t;
VERIFY_CHECK(bit < 256);
bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */
t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
#ifdef VERIFY
VERIFY_CHECK((t >> 64) == 0);
VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
#endif
}
static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56;
r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56;
over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
if (overflow) {
*overflow = over;
}
}
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
}
SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
}
static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
r->d[0] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
r->d[1] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
r->d[2] = t & nonzero; t >>= 64;
t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
r->d[3] = t & nonzero;
}
SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
}
static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
no |= (a->d[3] < SECP256K1_N_H_3);
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
return yes;
}
static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
/* If we are flag = 0, mask = 00...00 and this is a no-op;
* if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
uint64_t mask = !flag - 1;
uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
r->d[0] = t & nonzero; t >>= 64;
t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
r->d[1] = t & nonzero; t >>= 64;
t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
r->d[2] = t & nonzero; t >>= 64;
t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
r->d[3] = t & nonzero;
return 2 * (mask == 0) - 1;
}
/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd(a,b) { \
uint64_t tl, th; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c1 += th; /* overflow is handled on the next line */ \
c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
}
/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
#define muladd_fast(a,b) { \
uint64_t tl, th; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c1 += th; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK(c1 >= th); \
}
/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd2(a,b) { \
uint64_t tl, th, th2, tl2; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c0 += tl2; /* overflow is handled on the next line */ \
th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \
c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
c1 += th2; /* overflow is handled on the next line */ \
c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
}
/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
#define sumadd(a) { \
unsigned int over; \
c0 += (a); /* overflow is handled on the next line */ \
over = (c0 < (a)) ? 1 : 0; \
c1 += over; /* overflow is handled on the next line */ \
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
}
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
#define sumadd_fast(a) { \
c0 += (a); /* overflow is handled on the next line */ \
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
VERIFY_CHECK(c2 == 0); \
}
/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */
#define extract(n) { \
(n) = c0; \
c0 = c1; \
c1 = c2; \
c2 = 0; \
}
/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */
#define extract_fast(n) { \
(n) = c0; \
c0 = c1; \
c1 = 0; \
VERIFY_CHECK(c2 == 0); \
}
static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
#ifdef USE_ASM_X86_64
/* Reduce 512 bits into 385. */
uint64_t m0, m1, m2, m3, m4, m5, m6;
uint64_t p0, p1, p2, p3, p4;
uint64_t c;
__asm__ __volatile__(
/* Preload. */
"movq 32(%%rsi), %%r11\n"
"movq 40(%%rsi), %%r12\n"
"movq 48(%%rsi), %%r13\n"
"movq 56(%%rsi), %%r14\n"
/* Initialize r8,r9,r10 */
"movq 0(%%rsi), %%r8\n"
"movq $0, %%r9\n"
"movq $0, %%r10\n"
/* (r8,r9) += n0 * c0 */
"movq %8, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* extract m0 */
"movq %%r8, %q0\n"
"movq $0, %%r8\n"
/* (r9,r10) += l1 */
"addq 8(%%rsi), %%r9\n"
"adcq $0, %%r10\n"
/* (r9,r10,r8) += n1 * c0 */
"movq %8, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += n0 * c1 */
"movq %9, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* extract m1 */
"movq %%r9, %q1\n"
"movq $0, %%r9\n"
/* (r10,r8,r9) += l2 */
"addq 16(%%rsi), %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n2 * c0 */
"movq %8, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n1 * c1 */
"movq %9, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += n0 */
"addq %%r11, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* extract m2 */
"movq %%r10, %q2\n"
"movq $0, %%r10\n"
/* (r8,r9,r10) += l3 */
"addq 24(%%rsi), %%r8\n"
"adcq $0, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n3 * c0 */
"movq %8, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n2 * c1 */
"movq %9, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += n1 */
"addq %%r12, %%r8\n"
"adcq $0, %%r9\n"
"adcq $0, %%r10\n"
/* extract m3 */
"movq %%r8, %q3\n"
"movq $0, %%r8\n"
/* (r9,r10,r8) += n3 * c1 */
"movq %9, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += n2 */
"addq %%r13, %%r9\n"
"adcq $0, %%r10\n"
"adcq $0, %%r8\n"
/* extract m4 */
"movq %%r9, %q4\n"
/* (r10,r8) += n3 */
"addq %%r14, %%r10\n"
"adcq $0, %%r8\n"
/* extract m5 */
"movq %%r10, %q5\n"
/* extract m6 */
"movq %%r8, %q6\n"
: "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
: "S"(l), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
/* Reduce 385 bits into 258. */
__asm__ __volatile__(
/* Preload */
"movq %q9, %%r11\n"
"movq %q10, %%r12\n"
"movq %q11, %%r13\n"
/* Initialize (r8,r9,r10) */
"movq %q5, %%r8\n"
"movq $0, %%r9\n"
"movq $0, %%r10\n"
/* (r8,r9) += m4 * c0 */
"movq %12, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* extract p0 */
"movq %%r8, %q0\n"
"movq $0, %%r8\n"
/* (r9,r10) += m1 */
"addq %q6, %%r9\n"
"adcq $0, %%r10\n"
/* (r9,r10,r8) += m5 * c0 */
"movq %12, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += m4 * c1 */
"movq %13, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* extract p1 */
"movq %%r9, %q1\n"
"movq $0, %%r9\n"
/* (r10,r8,r9) += m2 */
"addq %q7, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m6 * c0 */
"movq %12, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m5 * c1 */
"movq %13, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += m4 */
"addq %%r11, %%r10\n"
"adcq $0, %%r8\n"
"adcq $0, %%r9\n"
/* extract p2 */
"movq %%r10, %q2\n"
/* (r8,r9) += m3 */
"addq %q8, %%r8\n"
"adcq $0, %%r9\n"
/* (r8,r9) += m6 * c1 */
"movq %13, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* (r8,r9) += m5 */
"addq %%r12, %%r8\n"
"adcq $0, %%r9\n"
/* extract p3 */
"movq %%r8, %q3\n"
/* (r9) += m6 */
"addq %%r13, %%r9\n"
/* extract p4 */
"movq %%r9, %q4\n"
: "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
: "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
/* Reduce 258 bits into 256. */
__asm__ __volatile__(
/* Preload */
"movq %q5, %%r10\n"
/* (rax,rdx) = p4 * c0 */
"movq %7, %%rax\n"
"mulq %%r10\n"
/* (rax,rdx) += p0 */
"addq %q1, %%rax\n"
"adcq $0, %%rdx\n"
/* extract r0 */
"movq %%rax, 0(%q6)\n"
/* Move to (r8,r9) */
"movq %%rdx, %%r8\n"
"movq $0, %%r9\n"
/* (r8,r9) += p1 */
"addq %q2, %%r8\n"
"adcq $0, %%r9\n"
/* (r8,r9) += p4 * c1 */
"movq %8, %%rax\n"
"mulq %%r10\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
/* Extract r1 */
"movq %%r8, 8(%q6)\n"
"movq $0, %%r8\n"
/* (r9,r8) += p4 */
"addq %%r10, %%r9\n"
"adcq $0, %%r8\n"
/* (r9,r8) += p2 */
"addq %q3, %%r9\n"
"adcq $0, %%r8\n"
/* Extract r2 */
"movq %%r9, 16(%q6)\n"
"movq $0, %%r9\n"
/* (r8,r9) += p3 */
"addq %q4, %%r8\n"
"adcq $0, %%r9\n"
/* Extract r3 */
"movq %%r8, 24(%q6)\n"
/* Extract c */
"movq %%r9, %q0\n"
: "=g"(c)
: "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
: "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
#else
uint128_t c;
uint64_t c0, c1, c2;
uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
uint64_t m0, m1, m2, m3, m4, m5;
uint32_t m6;
uint64_t p0, p1, p2, p3;
uint32_t p4;
/* Reduce 512 bits into 385. */
/* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
c0 = l[0]; c1 = 0; c2 = 0;
muladd_fast(n0, SECP256K1_N_C_0);
extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
sumadd(n0);
extract(m2);
sumadd(l[3]);
muladd(n3, SECP256K1_N_C_0);
muladd(n2, SECP256K1_N_C_1);
sumadd(n1);
extract(m3);
muladd(n3, SECP256K1_N_C_1);
sumadd(n2);
extract(m4);
sumadd_fast(n3);
extract_fast(m5);
VERIFY_CHECK(c0 <= 1);
m6 = c0;
/* Reduce 385 bits into 258. */
/* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
c0 = m0; c1 = 0; c2 = 0;
muladd_fast(m4, SECP256K1_N_C_0);
extract_fast(p0);
sumadd_fast(m1);
muladd(m5, SECP256K1_N_C_0);
muladd(m4, SECP256K1_N_C_1);
extract(p1);
sumadd(m2);
muladd(m6, SECP256K1_N_C_0);
muladd(m5, SECP256K1_N_C_1);
sumadd(m4);
extract(p2);
sumadd_fast(m3);
muladd_fast(m6, SECP256K1_N_C_1);
sumadd_fast(m5);
extract_fast(p3);
p4 = c0 + m6;
VERIFY_CHECK(p4 <= 2);
/* Reduce 258 bits into 256. */
/* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p2 + (uint128_t)p4;
r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p3;
r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
#endif
/* Final reduction of r. */
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
}
static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
#ifdef USE_ASM_X86_64
const uint64_t *pb = b->d;
__asm__ __volatile__(
/* Preload */
"movq 0(%%rdi), %%r15\n"
"movq 8(%%rdi), %%rbx\n"
"movq 16(%%rdi), %%rcx\n"
"movq 0(%%rdx), %%r11\n"
"movq 8(%%rdx), %%r12\n"
"movq 16(%%rdx), %%r13\n"
"movq 24(%%rdx), %%r14\n"
/* (rax,rdx) = a0 * b0 */
"movq %%r15, %%rax\n"
"mulq %%r11\n"
/* Extract l0 */
"movq %%rax, 0(%%rsi)\n"
/* (r8,r9,r10) = (rdx) */
"movq %%rdx, %%r8\n"
"xorq %%r9, %%r9\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += a0 * b1 */
"movq %%r15, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a1 * b0 */
"movq %%rbx, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l1 */
"movq %%r8, 8(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += a0 * b2 */
"movq %%r15, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a1 * b1 */
"movq %%rbx, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a2 * b0 */
"movq %%rcx, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l2 */
"movq %%r9, 16(%%rsi)\n"
"xorq %%r9, %%r9\n"
/* (r10,r8,r9) += a0 * b3 */
"movq %%r15, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* Preload a3 */
"movq 24(%%rdi), %%r15\n"
/* (r10,r8,r9) += a1 * b2 */
"movq %%rbx, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += a2 * b1 */
"movq %%rcx, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += a3 * b0 */
"movq %%r15, %%rax\n"
"mulq %%r11\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* Extract l3 */
"movq %%r10, 24(%%rsi)\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += a1 * b3 */
"movq %%rbx, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a2 * b2 */
"movq %%rcx, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a3 * b1 */
"movq %%r15, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l4 */
"movq %%r8, 32(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += a2 * b3 */
"movq %%rcx, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a3 * b2 */
"movq %%r15, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l5 */
"movq %%r9, 40(%%rsi)\n"
/* (r10,r8) += a3 * b3 */
"movq %%r15, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
/* Extract l6 */
"movq %%r10, 48(%%rsi)\n"
/* Extract l7 */
"movq %%r8, 56(%%rsi)\n"
: "+d"(pb)
: "S"(l), "D"(a->d)
: "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
#else
/* 160 bit accumulator. */
uint64_t c0 = 0, c1 = 0;
uint32_t c2 = 0;
/* l[0..7] = a[0..3] * b[0..3]. */
muladd_fast(a->d[0], b->d[0]);
extract_fast(l[0]);
muladd(a->d[0], b->d[1]);
muladd(a->d[1], b->d[0]);
extract(l[1]);
muladd(a->d[0], b->d[2]);
muladd(a->d[1], b->d[1]);
muladd(a->d[2], b->d[0]);
extract(l[2]);
muladd(a->d[0], b->d[3]);
muladd(a->d[1], b->d[2]);
muladd(a->d[2], b->d[1]);
muladd(a->d[3], b->d[0]);
extract(l[3]);
muladd(a->d[1], b->d[3]);
muladd(a->d[2], b->d[2]);
muladd(a->d[3], b->d[1]);
extract(l[4]);
muladd(a->d[2], b->d[3]);
muladd(a->d[3], b->d[2]);
extract(l[5]);
muladd_fast(a->d[3], b->d[3]);
extract_fast(l[6]);
VERIFY_CHECK(c1 == 0);
l[7] = c0;
#endif
}
static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
#ifdef USE_ASM_X86_64
__asm__ __volatile__(
/* Preload */
"movq 0(%%rdi), %%r11\n"
"movq 8(%%rdi), %%r12\n"
"movq 16(%%rdi), %%r13\n"
"movq 24(%%rdi), %%r14\n"
/* (rax,rdx) = a0 * a0 */
"movq %%r11, %%rax\n"
"mulq %%r11\n"
/* Extract l0 */
"movq %%rax, 0(%%rsi)\n"
/* (r8,r9,r10) = (rdx,0) */
"movq %%rdx, %%r8\n"
"xorq %%r9, %%r9\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += 2 * a0 * a1 */
"movq %%r11, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l1 */
"movq %%r8, 8(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += 2 * a0 * a2 */
"movq %%r11, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* (r9,r10,r8) += a1 * a1 */
"movq %%r12, %%rax\n"
"mulq %%r12\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l2 */
"movq %%r9, 16(%%rsi)\n"
"xorq %%r9, %%r9\n"
/* (r10,r8,r9) += 2 * a0 * a3 */
"movq %%r11, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* (r10,r8,r9) += 2 * a1 * a2 */
"movq %%r12, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
"adcq $0, %%r9\n"
/* Extract l3 */
"movq %%r10, 24(%%rsi)\n"
"xorq %%r10, %%r10\n"
/* (r8,r9,r10) += 2 * a1 * a3 */
"movq %%r12, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* (r8,r9,r10) += a2 * a2 */
"movq %%r13, %%rax\n"
"mulq %%r13\n"
"addq %%rax, %%r8\n"
"adcq %%rdx, %%r9\n"
"adcq $0, %%r10\n"
/* Extract l4 */
"movq %%r8, 32(%%rsi)\n"
"xorq %%r8, %%r8\n"
/* (r9,r10,r8) += 2 * a2 * a3 */
"movq %%r13, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
"addq %%rax, %%r9\n"
"adcq %%rdx, %%r10\n"
"adcq $0, %%r8\n"
/* Extract l5 */
"movq %%r9, 40(%%rsi)\n"
/* (r10,r8) += a3 * a3 */
"movq %%r14, %%rax\n"
"mulq %%r14\n"
"addq %%rax, %%r10\n"
"adcq %%rdx, %%r8\n"
/* Extract l6 */
"movq %%r10, 48(%%rsi)\n"
/* Extract l7 */
"movq %%r8, 56(%%rsi)\n"
:
: "S"(l), "D"(a->d)
: "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory");
#else
/* 160 bit accumulator. */
uint64_t c0 = 0, c1 = 0;
uint32_t c2 = 0;
/* l[0..7] = a[0..3] * b[0..3]. */
muladd_fast(a->d[0], a->d[0]);
extract_fast(l[0]);
muladd2(a->d[0], a->d[1]);
extract(l[1]);
muladd2(a->d[0], a->d[2]);
muladd(a->d[1], a->d[1]);
extract(l[2]);
muladd2(a->d[0], a->d[3]);
muladd2(a->d[1], a->d[2]);
extract(l[3]);
muladd2(a->d[1], a->d[3]);
muladd(a->d[2], a->d[2]);
extract(l[4]);
muladd2(a->d[2], a->d[3]);
extract(l[5]);
muladd_fast(a->d[3], a->d[3]);
extract_fast(l[6]);
VERIFY_CHECK(c1 == 0);
l[7] = c0;
#endif
}
#undef sumadd
#undef sumadd_fast
#undef muladd
#undef muladd_fast
#undef muladd2
#undef extract
#undef extract_fast
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint64_t l[8];
secp256k1_scalar_mul_512(l, a, b);
secp256k1_scalar_reduce_512(r, l);
}
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
int ret;
VERIFY_CHECK(n > 0);
VERIFY_CHECK(n < 16);
ret = r->d[0] & ((1 << n) - 1);
r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
r->d[3] = (r->d[3] >> n);
return ret;
}
static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint64_t l[8];
secp256k1_scalar_sqr_512(l, a);
secp256k1_scalar_reduce_512(r, l);
}
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
r1->d[0] = a->d[0];
r1->d[1] = a->d[1];
r1->d[2] = 0;
r1->d[3] = 0;
r2->d[0] = a->d[2];
r2->d[1] = a->d[3];
r2->d[2] = 0;
r2->d[3] = 0;
}
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
}
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
uint64_t l[8];
unsigned int shiftlimbs;
unsigned int shiftlow;
unsigned int shifthigh;
VERIFY_CHECK(shift >= 256);
secp256k1_scalar_mul_512(l, a, b);
shiftlimbs = shift >> 6;
shiftlow = shift & 0x3F;
shifthigh = 64 - shiftlow;
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
}
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_
#define _SECP256K1_SCALAR_REPR_
#include <stdint.h>
/** A scalar modulo the group order of the secp256k1 curve. */
typedef struct {
uint32_t d[8];
} secp256k1_scalar;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
#endif

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/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
#define _SECP256K1_SCALAR_REPR_IMPL_H_
/* Limbs of the secp256k1 order. */
#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
/* Limbs of 2^256 minus the secp256k1 order. */
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
#define SECP256K1_N_C_2 (~SECP256K1_N_2)
#define SECP256K1_N_C_3 (~SECP256K1_N_3)
#define SECP256K1_N_C_4 (1)
/* Limbs of half the secp256k1 order. */
#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
r->d[0] = 0;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
r->d[4] = 0;
r->d[5] = 0;
r->d[6] = 0;
r->d[7] = 0;
}
SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
r->d[0] = v;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
r->d[4] = 0;
r->d[5] = 0;
r->d[6] = 0;
r->d[7] = 0;
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
}
SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
VERIFY_CHECK(count < 32);
VERIFY_CHECK(offset + count <= 256);
if ((offset + count - 1) >> 5 == offset >> 5) {
return secp256k1_scalar_get_bits(a, offset, count);
} else {
VERIFY_CHECK((offset >> 5) + 1 < 8);
return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
}
}
SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
no |= (a->d[4] < SECP256K1_N_4);
yes |= (a->d[4] > SECP256K1_N_4) & ~no;
no |= (a->d[3] < SECP256K1_N_3) & ~yes;
yes |= (a->d[3] > SECP256K1_N_3) & ~no;
no |= (a->d[2] < SECP256K1_N_2) & ~yes;
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
no |= (a->d[1] < SECP256K1_N_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_1) & ~no;
yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
return yes;
}
SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
uint64_t t;
VERIFY_CHECK(overflow <= 1);
t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[5];
r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[6];
r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
t += (uint64_t)r->d[7];
r->d[7] = t & 0xFFFFFFFFUL;
return overflow;
}
static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
int overflow;
uint64_t t = (uint64_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[1] + b->d[1];
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[2] + b->d[2];
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[4] + b->d[4];
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[5] + b->d[5];
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[6] + b->d[6];
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)a->d[7] + b->d[7];
r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
overflow = t + secp256k1_scalar_check_overflow(r);
VERIFY_CHECK(overflow == 0 || overflow == 1);
secp256k1_scalar_reduce(r, overflow);
return overflow;
}
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
uint64_t t;
VERIFY_CHECK(bit < 256);
bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */
t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
r->d[7] = t & 0xFFFFFFFFULL;
#ifdef VERIFY
VERIFY_CHECK((t >> 32) == 0);
VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
#endif
}
static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
int over;
r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
if (overflow) {
*overflow = over;
}
}
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
}
SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
}
static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
r->d[0] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
r->d[1] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
r->d[2] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
r->d[3] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
r->d[4] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
r->d[5] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
r->d[6] = t & nonzero; t >>= 32;
t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
r->d[7] = t & nonzero;
}
SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
}
static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
no |= (a->d[7] < SECP256K1_N_H_7);
yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
return yes;
}
static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
/* If we are flag = 0, mask = 00...00 and this is a no-op;
* if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
uint32_t mask = !flag - 1;
uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
r->d[0] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
r->d[1] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
r->d[2] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
r->d[3] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
r->d[4] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
r->d[5] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
r->d[6] = t & nonzero; t >>= 32;
t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
r->d[7] = t & nonzero;
return 2 * (mask == 0) - 1;
}
/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd(a,b) { \
uint32_t tl, th; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c1 += th; /* overflow is handled on the next line */ \
c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
}
/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
#define muladd_fast(a,b) { \
uint32_t tl, th; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
c0 += tl; /* overflow is handled on the next line */ \
th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c1 += th; /* never overflows by contract (verified in the next line) */ \
VERIFY_CHECK(c1 >= th); \
}
/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd2(a,b) { \
uint32_t tl, th, th2, tl2; \
{ \
uint64_t t = (uint64_t)a * b; \
th = t >> 32; /* at most 0xFFFFFFFE */ \
tl = t; \
} \
th2 = th + th; /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
tl2 = tl + tl; /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \
c0 += tl2; /* overflow is handled on the next line */ \
th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \
c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
c1 += th2; /* overflow is handled on the next line */ \
c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
}
/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
#define sumadd(a) { \
unsigned int over; \
c0 += (a); /* overflow is handled on the next line */ \
over = (c0 < (a)) ? 1 : 0; \
c1 += over; /* overflow is handled on the next line */ \
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
}
/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
#define sumadd_fast(a) { \
c0 += (a); /* overflow is handled on the next line */ \
c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
VERIFY_CHECK(c2 == 0); \
}
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
#define extract(n) { \
(n) = c0; \
c0 = c1; \
c1 = c2; \
c2 = 0; \
}
/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
#define extract_fast(n) { \
(n) = c0; \
c0 = c1; \
c1 = 0; \
VERIFY_CHECK(c2 == 0); \
}
static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
uint64_t c;
uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
/* 96 bit accumulator. */
uint32_t c0, c1, c2;
/* Reduce 512 bits into 385. */
/* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
c0 = l[0]; c1 = 0; c2 = 0;
muladd_fast(n0, SECP256K1_N_C_0);
extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
muladd(n0, SECP256K1_N_C_2);
extract(m2);
sumadd(l[3]);
muladd(n3, SECP256K1_N_C_0);
muladd(n2, SECP256K1_N_C_1);
muladd(n1, SECP256K1_N_C_2);
muladd(n0, SECP256K1_N_C_3);
extract(m3);
sumadd(l[4]);
muladd(n4, SECP256K1_N_C_0);
muladd(n3, SECP256K1_N_C_1);
muladd(n2, SECP256K1_N_C_2);
muladd(n1, SECP256K1_N_C_3);
sumadd(n0);
extract(m4);
sumadd(l[5]);
muladd(n5, SECP256K1_N_C_0);
muladd(n4, SECP256K1_N_C_1);
muladd(n3, SECP256K1_N_C_2);
muladd(n2, SECP256K1_N_C_3);
sumadd(n1);
extract(m5);
sumadd(l[6]);
muladd(n6, SECP256K1_N_C_0);
muladd(n5, SECP256K1_N_C_1);
muladd(n4, SECP256K1_N_C_2);
muladd(n3, SECP256K1_N_C_3);
sumadd(n2);
extract(m6);
sumadd(l[7]);
muladd(n7, SECP256K1_N_C_0);
muladd(n6, SECP256K1_N_C_1);
muladd(n5, SECP256K1_N_C_2);
muladd(n4, SECP256K1_N_C_3);
sumadd(n3);
extract(m7);
muladd(n7, SECP256K1_N_C_1);
muladd(n6, SECP256K1_N_C_2);
muladd(n5, SECP256K1_N_C_3);
sumadd(n4);
extract(m8);
muladd(n7, SECP256K1_N_C_2);
muladd(n6, SECP256K1_N_C_3);
sumadd(n5);
extract(m9);
muladd(n7, SECP256K1_N_C_3);
sumadd(n6);
extract(m10);
sumadd_fast(n7);
extract_fast(m11);
VERIFY_CHECK(c0 <= 1);
m12 = c0;
/* Reduce 385 bits into 258. */
/* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
c0 = m0; c1 = 0; c2 = 0;
muladd_fast(m8, SECP256K1_N_C_0);
extract_fast(p0);
sumadd_fast(m1);
muladd(m9, SECP256K1_N_C_0);
muladd(m8, SECP256K1_N_C_1);
extract(p1);
sumadd(m2);
muladd(m10, SECP256K1_N_C_0);
muladd(m9, SECP256K1_N_C_1);
muladd(m8, SECP256K1_N_C_2);
extract(p2);
sumadd(m3);
muladd(m11, SECP256K1_N_C_0);
muladd(m10, SECP256K1_N_C_1);
muladd(m9, SECP256K1_N_C_2);
muladd(m8, SECP256K1_N_C_3);
extract(p3);
sumadd(m4);
muladd(m12, SECP256K1_N_C_0);
muladd(m11, SECP256K1_N_C_1);
muladd(m10, SECP256K1_N_C_2);
muladd(m9, SECP256K1_N_C_3);
sumadd(m8);
extract(p4);
sumadd(m5);
muladd(m12, SECP256K1_N_C_1);
muladd(m11, SECP256K1_N_C_2);
muladd(m10, SECP256K1_N_C_3);
sumadd(m9);
extract(p5);
sumadd(m6);
muladd(m12, SECP256K1_N_C_2);
muladd(m11, SECP256K1_N_C_3);
sumadd(m10);
extract(p6);
sumadd_fast(m7);
muladd_fast(m12, SECP256K1_N_C_3);
sumadd_fast(m11);
extract_fast(p7);
p8 = c0 + m12;
VERIFY_CHECK(p8 <= 2);
/* Reduce 258 bits into 256. */
/* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
c += p4 + (uint64_t)p8;
r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
c += p5;
r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
c += p6;
r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
c += p7;
r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
/* Final reduction of r. */
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
}
static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
/* 96 bit accumulator. */
uint32_t c0 = 0, c1 = 0, c2 = 0;
/* l[0..15] = a[0..7] * b[0..7]. */
muladd_fast(a->d[0], b->d[0]);
extract_fast(l[0]);
muladd(a->d[0], b->d[1]);
muladd(a->d[1], b->d[0]);
extract(l[1]);
muladd(a->d[0], b->d[2]);
muladd(a->d[1], b->d[1]);
muladd(a->d[2], b->d[0]);
extract(l[2]);
muladd(a->d[0], b->d[3]);
muladd(a->d[1], b->d[2]);
muladd(a->d[2], b->d[1]);
muladd(a->d[3], b->d[0]);
extract(l[3]);
muladd(a->d[0], b->d[4]);
muladd(a->d[1], b->d[3]);
muladd(a->d[2], b->d[2]);
muladd(a->d[3], b->d[1]);
muladd(a->d[4], b->d[0]);
extract(l[4]);
muladd(a->d[0], b->d[5]);
muladd(a->d[1], b->d[4]);
muladd(a->d[2], b->d[3]);
muladd(a->d[3], b->d[2]);
muladd(a->d[4], b->d[1]);
muladd(a->d[5], b->d[0]);
extract(l[5]);
muladd(a->d[0], b->d[6]);
muladd(a->d[1], b->d[5]);
muladd(a->d[2], b->d[4]);
muladd(a->d[3], b->d[3]);
muladd(a->d[4], b->d[2]);
muladd(a->d[5], b->d[1]);
muladd(a->d[6], b->d[0]);
extract(l[6]);
muladd(a->d[0], b->d[7]);
muladd(a->d[1], b->d[6]);
muladd(a->d[2], b->d[5]);
muladd(a->d[3], b->d[4]);
muladd(a->d[4], b->d[3]);
muladd(a->d[5], b->d[2]);
muladd(a->d[6], b->d[1]);
muladd(a->d[7], b->d[0]);
extract(l[7]);
muladd(a->d[1], b->d[7]);
muladd(a->d[2], b->d[6]);
muladd(a->d[3], b->d[5]);
muladd(a->d[4], b->d[4]);
muladd(a->d[5], b->d[3]);
muladd(a->d[6], b->d[2]);
muladd(a->d[7], b->d[1]);
extract(l[8]);
muladd(a->d[2], b->d[7]);
muladd(a->d[3], b->d[6]);
muladd(a->d[4], b->d[5]);
muladd(a->d[5], b->d[4]);
muladd(a->d[6], b->d[3]);
muladd(a->d[7], b->d[2]);
extract(l[9]);
muladd(a->d[3], b->d[7]);
muladd(a->d[4], b->d[6]);
muladd(a->d[5], b->d[5]);
muladd(a->d[6], b->d[4]);
muladd(a->d[7], b->d[3]);
extract(l[10]);
muladd(a->d[4], b->d[7]);
muladd(a->d[5], b->d[6]);
muladd(a->d[6], b->d[5]);
muladd(a->d[7], b->d[4]);
extract(l[11]);
muladd(a->d[5], b->d[7]);
muladd(a->d[6], b->d[6]);
muladd(a->d[7], b->d[5]);
extract(l[12]);
muladd(a->d[6], b->d[7]);
muladd(a->d[7], b->d[6]);
extract(l[13]);
muladd_fast(a->d[7], b->d[7]);
extract_fast(l[14]);
VERIFY_CHECK(c1 == 0);
l[15] = c0;
}
static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
/* 96 bit accumulator. */
uint32_t c0 = 0, c1 = 0, c2 = 0;
/* l[0..15] = a[0..7]^2. */
muladd_fast(a->d[0], a->d[0]);
extract_fast(l[0]);
muladd2(a->d[0], a->d[1]);
extract(l[1]);
muladd2(a->d[0], a->d[2]);
muladd(a->d[1], a->d[1]);
extract(l[2]);
muladd2(a->d[0], a->d[3]);
muladd2(a->d[1], a->d[2]);
extract(l[3]);
muladd2(a->d[0], a->d[4]);
muladd2(a->d[1], a->d[3]);
muladd(a->d[2], a->d[2]);
extract(l[4]);
muladd2(a->d[0], a->d[5]);
muladd2(a->d[1], a->d[4]);
muladd2(a->d[2], a->d[3]);
extract(l[5]);
muladd2(a->d[0], a->d[6]);
muladd2(a->d[1], a->d[5]);
muladd2(a->d[2], a->d[4]);
muladd(a->d[3], a->d[3]);
extract(l[6]);
muladd2(a->d[0], a->d[7]);
muladd2(a->d[1], a->d[6]);
muladd2(a->d[2], a->d[5]);
muladd2(a->d[3], a->d[4]);
extract(l[7]);
muladd2(a->d[1], a->d[7]);
muladd2(a->d[2], a->d[6]);
muladd2(a->d[3], a->d[5]);
muladd(a->d[4], a->d[4]);
extract(l[8]);
muladd2(a->d[2], a->d[7]);
muladd2(a->d[3], a->d[6]);
muladd2(a->d[4], a->d[5]);
extract(l[9]);
muladd2(a->d[3], a->d[7]);
muladd2(a->d[4], a->d[6]);
muladd(a->d[5], a->d[5]);
extract(l[10]);
muladd2(a->d[4], a->d[7]);
muladd2(a->d[5], a->d[6]);
extract(l[11]);
muladd2(a->d[5], a->d[7]);
muladd(a->d[6], a->d[6]);
extract(l[12]);
muladd2(a->d[6], a->d[7]);
extract(l[13]);
muladd_fast(a->d[7], a->d[7]);
extract_fast(l[14]);
VERIFY_CHECK(c1 == 0);
l[15] = c0;
}
#undef sumadd
#undef sumadd_fast
#undef muladd
#undef muladd_fast
#undef muladd2
#undef extract
#undef extract_fast
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
uint32_t l[16];
secp256k1_scalar_mul_512(l, a, b);
secp256k1_scalar_reduce_512(r, l);
}
static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
int ret;
VERIFY_CHECK(n > 0);
VERIFY_CHECK(n < 16);
ret = r->d[0] & ((1 << n) - 1);
r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
r->d[7] = (r->d[7] >> n);
return ret;
}
static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint32_t l[16];
secp256k1_scalar_sqr_512(l, a);
secp256k1_scalar_reduce_512(r, l);
}
#ifdef USE_ENDOMORPHISM
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
r1->d[0] = a->d[0];
r1->d[1] = a->d[1];
r1->d[2] = a->d[2];
r1->d[3] = a->d[3];
r1->d[4] = 0;
r1->d[5] = 0;
r1->d[6] = 0;
r1->d[7] = 0;
r2->d[0] = a->d[4];
r2->d[1] = a->d[5];
r2->d[2] = a->d[6];
r2->d[3] = a->d[7];
r2->d[4] = 0;
r2->d[5] = 0;
r2->d[6] = 0;
r2->d[7] = 0;
}
#endif
SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
}
SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
uint32_t l[16];
unsigned int shiftlimbs;
unsigned int shiftlow;
unsigned int shifthigh;
VERIFY_CHECK(shift >= 256);
secp256k1_scalar_mul_512(l, a, b);
shiftlimbs = shift >> 5;
shiftlow = shift & 0x1F;
shifthigh = 32 - shiftlow;
r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
}
#endif

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@ -0,0 +1,337 @@
/**********************************************************************
* Copyright (c) 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_SCALAR_IMPL_H_
#define _SECP256K1_SCALAR_IMPL_H_
#include <string.h>
#include "group.h"
#include "scalar.h"
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#if defined(USE_SCALAR_4X64)
#include "scalar_4x64_impl.h"
#elif defined(USE_SCALAR_8X32)
#include "scalar_8x32_impl.h"
#else
#error "Please select scalar implementation"
#endif
#ifndef USE_NUM_NONE
static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
unsigned char c[32];
secp256k1_scalar_get_b32(c, a);
secp256k1_num_set_bin(r, c, 32);
}
/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
static const unsigned char order[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
secp256k1_num_set_bin(r, order, 32);
}
#endif
static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
secp256k1_scalar *t;
int i;
/* First compute x ^ (2^N - 1) for some values of N. */
secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
secp256k1_scalar_sqr(&x2, x);
secp256k1_scalar_mul(&x2, &x2, x);
secp256k1_scalar_sqr(&x3, &x2);
secp256k1_scalar_mul(&x3, &x3, x);
secp256k1_scalar_sqr(&x4, &x3);
secp256k1_scalar_mul(&x4, &x4, x);
secp256k1_scalar_sqr(&x6, &x4);
secp256k1_scalar_sqr(&x6, &x6);
secp256k1_scalar_mul(&x6, &x6, &x2);
secp256k1_scalar_sqr(&x7, &x6);
secp256k1_scalar_mul(&x7, &x7, x);
secp256k1_scalar_sqr(&x8, &x7);
secp256k1_scalar_mul(&x8, &x8, x);
secp256k1_scalar_sqr(&x15, &x8);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x15, &x15);
}
secp256k1_scalar_mul(&x15, &x15, &x7);
secp256k1_scalar_sqr(&x30, &x15);
for (i = 0; i < 14; i++) {
secp256k1_scalar_sqr(&x30, &x30);
}
secp256k1_scalar_mul(&x30, &x30, &x15);
secp256k1_scalar_sqr(&x60, &x30);
for (i = 0; i < 29; i++) {
secp256k1_scalar_sqr(&x60, &x60);
}
secp256k1_scalar_mul(&x60, &x60, &x30);
secp256k1_scalar_sqr(&x120, &x60);
for (i = 0; i < 59; i++) {
secp256k1_scalar_sqr(&x120, &x120);
}
secp256k1_scalar_mul(&x120, &x120, &x60);
secp256k1_scalar_sqr(&x127, &x120);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x127, &x127);
}
secp256k1_scalar_mul(&x127, &x127, &x7);
/* Then accumulate the final result (t starts at x127). */
t = &x127;
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 5; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 4; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 10; i++) { /* 0000000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 9; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 4; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 8; i++) { /* 000000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 6; i++) { /* 00000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 8; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(r, t, &x6); /* 111111 */
}
SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
/* d[0] is present and is the lowest word for all representations */
return !(a->d[0] & 1);
}
static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
#if defined(USE_SCALAR_INV_BUILTIN)
secp256k1_scalar_inverse(r, x);
#elif defined(USE_SCALAR_INV_NUM)
unsigned char b[32];
secp256k1_num n, m;
secp256k1_scalar t = *x;
secp256k1_scalar_get_b32(b, &t);
secp256k1_num_set_bin(&n, b, 32);
secp256k1_scalar_order_get_num(&m);
secp256k1_num_mod_inverse(&n, &n, &m);
secp256k1_num_get_bin(b, 32, &n);
secp256k1_scalar_set_b32(r, b, NULL);
/* Verify that the inverse was computed correctly, without GMP code. */
secp256k1_scalar_mul(&t, &t, r);
CHECK(secp256k1_scalar_is_one(&t));
#else
#error "Please select scalar inverse implementation"
#endif
}
#ifdef USE_ENDOMORPHISM
/**
* The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
* lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
* 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
*
* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
* and k2 have a small size.
* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
*
* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
*
* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
*
* g1, g2 are precomputed constants used to replace division with a rounded multiplication
* when decomposing the scalar for an endomorphism-based point multiplication.
*
* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
*
* The derivation is described in the paper "Efficient Software Implementation of Public-Key
* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
* Section 4.3 (here we use a somewhat higher-precision estimate):
* d = a1*b2 - b1*a2
* g1 = round((2^272)*b2/d)
* g2 = round((2^272)*b1/d)
*
* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
*
* The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
*/
static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
secp256k1_scalar c1, c2;
static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
);
static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
);
static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
);
static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
);
static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
);
VERIFY_CHECK(r1 != a);
VERIFY_CHECK(r2 != a);
/* these _var calls are constant time since the shift amount is constant */
secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
secp256k1_scalar_mul(&c1, &c1, &minus_b1);
secp256k1_scalar_mul(&c2, &c2, &minus_b2);
secp256k1_scalar_add(r2, &c1, &c2);
secp256k1_scalar_mul(r1, r2, &minus_lambda);
secp256k1_scalar_add(r1, r1, a);
}
#endif
#endif

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/**********************************************************************
* Copyright (c) 2013-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#define SECP256K1_BUILD (1)
#include "include/secp256k1.h"
#include "util.h"
#include "num_impl.h"
#include "field_impl.h"
#include "scalar_impl.h"
#include "group_impl.h"
#include "ecmult_impl.h"
#include "ecmult_const_impl.h"
#include "ecmult_gen_impl.h"
#include "ecdsa_impl.h"
#include "eckey_impl.h"
#include "hash_impl.h"
#define ARG_CHECK(cond) do { \
if (EXPECT(!(cond), 0)) { \
secp256k1_callback_call(&ctx->illegal_callback, #cond); \
return 0; \
} \
} while(0)
static void default_illegal_callback_fn(const char* str, void* data) {
(void)data;
fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
abort();
}
static const secp256k1_callback default_illegal_callback = {
default_illegal_callback_fn,
NULL
};
static void default_error_callback_fn(const char* str, void* data) {
(void)data;
fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
abort();
}
static const secp256k1_callback default_error_callback = {
default_error_callback_fn,
NULL
};
struct secp256k1_context_struct {
secp256k1_ecmult_context ecmult_ctx;
secp256k1_ecmult_gen_context ecmult_gen_ctx;
secp256k1_callback illegal_callback;
secp256k1_callback error_callback;
};
secp256k1_context* secp256k1_context_create(unsigned int flags) {
secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context));
ret->illegal_callback = default_illegal_callback;
ret->error_callback = default_error_callback;
secp256k1_ecmult_context_init(&ret->ecmult_ctx);
secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
if (flags & SECP256K1_CONTEXT_SIGN) {
secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback);
}
if (flags & SECP256K1_CONTEXT_VERIFY) {
secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback);
}
return ret;
}
secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context));
ret->illegal_callback = ctx->illegal_callback;
ret->error_callback = ctx->error_callback;
secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback);
secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback);
return ret;
}
void secp256k1_context_destroy(secp256k1_context* ctx) {
if (ctx != NULL) {
secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
free(ctx);
}
}
void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
if (fun == NULL) {
fun = default_illegal_callback_fn;
}
ctx->illegal_callback.fn = fun;
ctx->illegal_callback.data = data;
}
void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
if (fun == NULL) {
fun = default_error_callback_fn;
}
ctx->error_callback.fn = fun;
ctx->error_callback.data = data;
}
static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) {
if (sizeof(secp256k1_ge_storage) == 64) {
/* When the secp256k1_ge_storage type is exactly 64 byte, use its
* representation inside secp256k1_pubkey, as conversion is very fast.
* Note that secp256k1_pubkey_save must use the same representation. */
secp256k1_ge_storage s;
memcpy(&s, &pubkey->data[0], 64);
secp256k1_ge_from_storage(ge, &s);
} else {
/* Otherwise, fall back to 32-byte big endian for X and Y. */
secp256k1_fe x, y;
secp256k1_fe_set_b32(&x, pubkey->data);
secp256k1_fe_set_b32(&y, pubkey->data + 32);
secp256k1_ge_set_xy(ge, &x, &y);
}
ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
return 1;
}
static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
if (sizeof(secp256k1_ge_storage) == 64) {
secp256k1_ge_storage s;
secp256k1_ge_to_storage(&s, ge);
memcpy(&pubkey->data[0], &s, 64);
} else {
VERIFY_CHECK(!secp256k1_ge_is_infinity(ge));
secp256k1_fe_normalize_var(&ge->x);
secp256k1_fe_normalize_var(&ge->y);
secp256k1_fe_get_b32(pubkey->data, &ge->x);
secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
}
}
int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) {
secp256k1_ge Q;
(void)ctx;
if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
memset(pubkey, 0, sizeof(*pubkey));
return 0;
}
secp256k1_pubkey_save(pubkey, &Q);
secp256k1_ge_clear(&Q);
return 1;
}
int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) {
secp256k1_ge Q;
(void)ctx;
return (secp256k1_pubkey_load(ctx, &Q, pubkey) &&
secp256k1_eckey_pubkey_serialize(&Q, output, outputlen, flags));
}
static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
(void)ctx;
if (sizeof(secp256k1_scalar) == 32) {
/* When the secp256k1_scalar type is exactly 32 byte, use its
* representation inside secp256k1_ecdsa_signature, as conversion is very fast.
* Note that secp256k1_ecdsa_signature_save must use the same representation. */
memcpy(r, &sig->data[0], 32);
memcpy(s, &sig->data[32], 32);
} else {
secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
}
}
static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) {
if (sizeof(secp256k1_scalar) == 32) {
memcpy(&sig->data[0], r, 32);
memcpy(&sig->data[32], s, 32);
} else {
secp256k1_scalar_get_b32(&sig->data[0], r);
secp256k1_scalar_get_b32(&sig->data[32], s);
}
}
int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
secp256k1_scalar r, s;
(void)ctx;
ARG_CHECK(sig != NULL);
ARG_CHECK(input != NULL);
if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) {
secp256k1_ecdsa_signature_save(sig, &r, &s);
return 1;
} else {
memset(sig, 0, sizeof(*sig));
return 0;
}
}
int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) {
secp256k1_scalar r, s;
(void)ctx;
ARG_CHECK(output != NULL);
ARG_CHECK(outputlen != NULL);
ARG_CHECK(sig != NULL);
secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s);
}
int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
secp256k1_ge q;
secp256k1_scalar r, s;
secp256k1_scalar m;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(sig != NULL);
ARG_CHECK(pubkey != NULL);
secp256k1_scalar_set_b32(&m, msg32, NULL);
secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
return (secp256k1_pubkey_load(ctx, &q, pubkey) &&
secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
}
static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
unsigned char keydata[112];
int keylen = 64;
secp256k1_rfc6979_hmac_sha256_t rng;
unsigned int i;
/* We feed a byte array to the PRNG as input, consisting of:
* - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
* - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
* - optionally 16 extra bytes with the algorithm name (the extra data bytes
* are set to zeroes when not present, while the algorithm name is).
*/
memcpy(keydata, key32, 32);
memcpy(keydata + 32, msg32, 32);
if (data != NULL) {
memcpy(keydata + 64, data, 32);
keylen = 96;
}
if (algo16 != NULL) {
memset(keydata + keylen, 0, 96 - keylen);
memcpy(keydata + 96, algo16, 16);
keylen = 112;
}
secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, keylen);
memset(keydata, 0, sizeof(keydata));
for (i = 0; i <= counter; i++) {
secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
}
secp256k1_rfc6979_hmac_sha256_finalize(&rng);
return 1;
}
const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
secp256k1_scalar r, s;
secp256k1_scalar sec, non, msg;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(msg32 != NULL);
ARG_CHECK(signature != NULL);
ARG_CHECK(seckey != NULL);
if (noncefp == NULL) {
noncefp = secp256k1_nonce_function_default;
}
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
/* Fail if the secret key is invalid. */
if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
unsigned int count = 0;
secp256k1_scalar_set_b32(&msg, msg32, NULL);
while (1) {
unsigned char nonce32[32];
ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
if (!ret) {
break;
}
secp256k1_scalar_set_b32(&non, nonce32, &overflow);
memset(nonce32, 0, 32);
if (!overflow && !secp256k1_scalar_is_zero(&non)) {
if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
break;
}
}
count++;
}
secp256k1_scalar_clear(&msg);
secp256k1_scalar_clear(&non);
secp256k1_scalar_clear(&sec);
}
if (ret) {
secp256k1_ecdsa_signature_save(signature, &r, &s);
} else {
memset(signature, 0, sizeof(*signature));
}
return ret;
}
int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) {
secp256k1_scalar sec;
int ret;
int overflow;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(seckey != NULL);
(void)ctx;
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
ret = !overflow && !secp256k1_scalar_is_zero(&sec);
secp256k1_scalar_clear(&sec);
return ret;
}
int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) {
secp256k1_gej pj;
secp256k1_ge p;
secp256k1_scalar sec;
int overflow;
int ret = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
ARG_CHECK(pubkey != NULL);
ARG_CHECK(seckey != NULL);
secp256k1_scalar_set_b32(&sec, seckey, &overflow);
ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec));
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec);
secp256k1_ge_set_gej(&p, &pj);
secp256k1_pubkey_save(pubkey, &p);
secp256k1_scalar_clear(&sec);
if (!ret) {
memset(pubkey, 0, sizeof(*pubkey));
}
return ret;
}
int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
secp256k1_scalar term;
secp256k1_scalar sec;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(seckey != NULL);
ARG_CHECK(tweak != NULL);
(void)ctx;
secp256k1_scalar_set_b32(&term, tweak, &overflow);
secp256k1_scalar_set_b32(&sec, seckey, NULL);
ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term);
if (ret) {
secp256k1_scalar_get_b32(seckey, &sec);
}
secp256k1_scalar_clear(&sec);
secp256k1_scalar_clear(&term);
return ret;
}
int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
secp256k1_ge p;
secp256k1_scalar term;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(pubkey != NULL);
ARG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&term, tweak, &overflow);
if (!overflow && secp256k1_pubkey_load(ctx, &p, pubkey)) {
ret = secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term);
if (ret) {
secp256k1_pubkey_save(pubkey, &p);
} else {
memset(pubkey, 0, sizeof(*pubkey));
}
}
return ret;
}
int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
secp256k1_scalar factor;
secp256k1_scalar sec;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(seckey != NULL);
ARG_CHECK(tweak != NULL);
(void)ctx;
secp256k1_scalar_set_b32(&factor, tweak, &overflow);
secp256k1_scalar_set_b32(&sec, seckey, NULL);
ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor);
if (ret) {
secp256k1_scalar_get_b32(seckey, &sec);
}
secp256k1_scalar_clear(&sec);
secp256k1_scalar_clear(&factor);
return ret;
}
int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
secp256k1_ge p;
secp256k1_scalar factor;
int ret = 0;
int overflow = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
ARG_CHECK(pubkey != NULL);
ARG_CHECK(tweak != NULL);
secp256k1_scalar_set_b32(&factor, tweak, &overflow);
if (!overflow && secp256k1_pubkey_load(ctx, &p, pubkey)) {
ret = secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor);
if (ret) {
secp256k1_pubkey_save(pubkey, &p);
} else {
memset(pubkey, 0, sizeof(*pubkey));
}
}
return ret;
}
int secp256k1_ec_privkey_export(const secp256k1_context* ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *seckey, unsigned int flags) {
secp256k1_scalar key;
int ret = 0;
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(seckey != NULL);
ARG_CHECK(privkey != NULL);
ARG_CHECK(privkeylen != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
secp256k1_scalar_set_b32(&key, seckey, NULL);
ret = secp256k1_eckey_privkey_serialize(&ctx->ecmult_gen_ctx, privkey, privkeylen, &key, flags);
secp256k1_scalar_clear(&key);
return ret;
}
int secp256k1_ec_privkey_import(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *privkey, size_t privkeylen) {
secp256k1_scalar key;
int ret = 0;
ARG_CHECK(seckey != NULL);
ARG_CHECK(privkey != NULL);
(void)ctx;
ret = secp256k1_eckey_privkey_parse(&key, privkey, privkeylen);
if (ret) {
secp256k1_scalar_get_b32(seckey, &key);
}
secp256k1_scalar_clear(&key);
return ret;
}
int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) {
VERIFY_CHECK(ctx != NULL);
ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
return 1;
}
int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, int n) {
int i;
secp256k1_gej Qj;
secp256k1_ge Q;
ARG_CHECK(pubnonce != NULL);
ARG_CHECK(n >= 1);
ARG_CHECK(pubnonces != NULL);
secp256k1_gej_set_infinity(&Qj);
for (i = 0; i < n; i++) {
secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
secp256k1_gej_add_ge(&Qj, &Qj, &Q);
}
if (secp256k1_gej_is_infinity(&Qj)) {
memset(pubnonce, 0, sizeof(*pubnonce));
return 0;
}
secp256k1_ge_set_gej(&Q, &Qj);
secp256k1_pubkey_save(pubnonce, &Q);
return 1;
}
#ifdef ENABLE_MODULE_ECDH
# include "modules/ecdh/main_impl.h"
#endif
#ifdef ENABLE_MODULE_SCHNORR
# include "modules/schnorr/main_impl.h"
#endif
#ifdef ENABLE_MODULE_RECOVERY
# include "modules/recovery/main_impl.h"
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_TESTRAND_H_
#define _SECP256K1_TESTRAND_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
/* A non-cryptographic RNG used only for test infrastructure. */
/** Seed the pseudorandom number generator for testing. */
SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
/** Generate a pseudorandom 32-bit number. */
static uint32_t secp256k1_rand32(void);
/** Generate a pseudorandom 32-byte array. */
static void secp256k1_rand256(unsigned char *b32);
/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
static void secp256k1_rand256_test(unsigned char *b32);
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_TESTRAND_IMPL_H_
#define _SECP256K1_TESTRAND_IMPL_H_
#include <stdint.h>
#include <string.h>
#include "testrand.h"
#include "hash.h"
static secp256k1_rfc6979_hmac_sha256_t secp256k1_test_rng;
static uint32_t secp256k1_test_rng_precomputed[8];
static int secp256k1_test_rng_precomputed_used = 8;
SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
}
SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
if (secp256k1_test_rng_precomputed_used == 8) {
secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
secp256k1_test_rng_precomputed_used = 0;
}
return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
}
static void secp256k1_rand256(unsigned char *b32) {
secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
}
static void secp256k1_rand256_test(unsigned char *b32) {
int bits=0;
uint64_t ent = 0;
int entleft = 0;
memset(b32, 0, 32);
while (bits < 256) {
int now;
uint32_t val;
if (entleft < 12) {
ent |= ((uint64_t)secp256k1_rand32()) << entleft;
entleft += 32;
}
now = 1 + ((ent % 64)*((ent >> 6) % 32)+16)/31;
val = 1 & (ent >> 11);
ent >>= 12;
entleft -= 12;
while (now > 0 && bits < 256) {
b32[bits / 8] |= val << (bits % 8);
now--;
bits++;
}
}
}
#endif

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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_UTIL_H_
#define _SECP256K1_UTIL_H_
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>
typedef struct {
void (*fn)(const char *text, void* data);
const void* data;
} secp256k1_callback;
static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
cb->fn(text, (void*)cb->data);
}
#ifdef DETERMINISTIC
#define TEST_FAILURE(msg) do { \
fprintf(stderr, "%s\n", msg); \
abort(); \
} while(0);
#else
#define TEST_FAILURE(msg) do { \
fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \
abort(); \
} while(0)
#endif
#ifdef HAVE_BUILTIN_EXPECT
#define EXPECT(x,c) __builtin_expect((x),(c))
#else
#define EXPECT(x,c) (x)
#endif
#ifdef DETERMINISTIC
#define CHECK(cond) do { \
if (EXPECT(!(cond), 0)) { \
TEST_FAILURE("test condition failed"); \
} \
} while(0)
#else
#define CHECK(cond) do { \
if (EXPECT(!(cond), 0)) { \
TEST_FAILURE("test condition failed: " #cond); \
} \
} while(0)
#endif
/* Like assert(), but when VERIFY is defined, and side-effect safe. */
#ifdef VERIFY
#define VERIFY_CHECK CHECK
#define VERIFY_SETUP(stmt) do { stmt; } while(0)
#else
#define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
#define VERIFY_SETUP(stmt)
#endif
static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
void *ret = malloc(size);
if (ret == NULL) {
secp256k1_callback_call(cb, "Out of memory");
}
return ret;
}
/* Macro for restrict, when available and not in a VERIFY build. */
#if defined(SECP256K1_BUILD) && defined(VERIFY)
# define SECP256K1_RESTRICT
#else
# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
# if SECP256K1_GNUC_PREREQ(3,0)
# define SECP256K1_RESTRICT __restrict__
# elif (defined(_MSC_VER) && _MSC_VER >= 1400)
# define SECP256K1_RESTRICT __restrict
# else
# define SECP256K1_RESTRICT
# endif
# else
# define SECP256K1_RESTRICT restrict
# endif
#endif
#if defined(_WIN32)
# define I64FORMAT "I64d"
# define I64uFORMAT "I64u"
#else
# define I64FORMAT "lld"
# define I64uFORMAT "llu"
#endif
#if defined(HAVE___INT128)
# if defined(__GNUC__)
# define SECP256K1_GNUC_EXT __extension__
# else
# define SECP256K1_GNUC_EXT
# endif
SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
#endif
#endif