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Update SM2 arithmetic implementations

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Decouple API and implementations. SM2 arithmetic exposes 3 types: GF(p), GF(n), and Point.
This commit is contained in:
Zhi Guan
2024-02-22 11:14:59 +08:00
parent 79a6437c8c
commit c460766320
8 changed files with 1168 additions and 707 deletions
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14
src/sm2_alg.c
View File

@@ -1,5 +1,5 @@
/*
* Copyright 2014-2022 The GmSSL Project. All Rights Reserved.
/*
* Copyright 2014-2024 The GmSSL Project. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
@@ -20,10 +20,6 @@
#include <gmssl/endian.h>
#define sm2_print_bn(label,a) sm2_bn_print(stderr,0,0,label,a) // 这个不应该放在这里，应该放在测试文件中
const SM2_BN SM2_P = {
0xffffffff, 0xffffffff, 0x00000000, 0xffffffff,
0xffffffff, 0xffffffff, 0xffffffff, 0xfffffffe,
@@ -65,7 +61,6 @@ const SM2_BN SM2_TWO = {2,0,0,0,0,0,0,0};
const SM2_BN SM2_THREE = {3,0,0,0,0,0,0,0};
int sm2_bn_check(const SM2_BN a)
{
int err = 0;
@@ -775,8 +770,6 @@ int sm2_fn_rand(SM2_BN r)
return 1;
}
void sm2_jacobian_point_init(SM2_JACOBIAN_POINT *R)
{
memset(R, 0, sizeof(SM2_JACOBIAN_POINT));
@@ -817,7 +810,7 @@ void sm2_jacobian_point_get_xy(const SM2_JACOBIAN_POINT *P, SM2_BN x, SM2_BN y)
}
}
int sm2_jacobian_pointpoint_print(FILE *fp, int fmt, int ind, const char *label, const SM2_JACOBIAN_POINT *P)
int sm2_jacobian_point_print(FILE *fp, int fmt, int ind, const char *label, const SM2_JACOBIAN_POINT *P)
{
int len = 0;
SM2_BN x;
@@ -1321,6 +1314,7 @@ int sm2_point_from_hash(SM2_POINT *R, const uint8_t *data, size_t datalen)
sm2_bn_add(u, SM2_P, SM2_ONE);
sm2_bn_rshift(u, u, 2);
// How many times？
do {
sm3_digest(data, datalen, dgst);

405
src/sm2_lib.c
View File

@@ -1,5 +1,5 @@
/*
* Copyright 2014-2023 The GmSSL Project. All Rights Reserved.
* Copyright 2014-2024 The GmSSL Project. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
@@ -20,144 +20,6 @@
#include <gmssl/endian.h>
extern const SM2_BN SM2_N;
extern const SM2_BN SM2_ONE;
int sm2_do_sign(const SM2_KEY *key, const uint8_t dgst[32], SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_BN d;
SM2_BN d_inv;
SM2_BN e;
SM2_BN k;
SM2_BN x;
SM2_BN t;
SM2_BN r;
SM2_BN s;
//fprintf(stderr, "sm2_do_sign\n");
sm2_bn_from_bytes(d, key->private_key);
// compute (d + 1)^-1 (mod n)
sm2_fn_add(d_inv, d, SM2_ONE); //sm2_bn_print(stderr, 0, 4, "(1+d)", d_inv);
if (sm2_bn_is_zero(d_inv)) {
error_print();
return -1;
}
sm2_fn_inv(d_inv, d_inv); //sm2_bn_print(stderr, 0, 4, "(1+d)^-1", d_inv);
// e = H(M)
sm2_bn_from_bytes(e, dgst); //sm2_bn_print(stderr, 0, 4, "e", e);
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// (x, y) = kG
sm2_jacobian_point_mul_generator(P, k);
sm2_jacobian_point_get_xy(P, x, NULL);
//sm2_bn_print(stderr, 0, 4, "x", x);
// r = e + x (mod n)
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
if (sm2_bn_cmp(x, SM2_N) >= 0) {
sm2_bn_sub(x, x, SM2_N);
}
sm2_fn_add(r, e, x); //sm2_bn_print(stderr, 0, 4, "r = e + x (mod n)", r);
// if r == 0 or r + k == n re-generate k
sm2_bn_add(t, r, k);
if (sm2_bn_is_zero(r) || sm2_bn_cmp(t, SM2_N) == 0) {
//sm2_bn_print(stderr, 0, 4, "r + k", t);
goto retry;
}
// s = ((1 + d)^-1 * (k - r * d)) mod n
sm2_fn_mul(t, r, d); //sm2_bn_print(stderr, 0, 4, "r*d", t);
sm2_fn_sub(k, k, t); //sm2_bn_print(stderr, 0, 4, "k-r*d", k);
sm2_fn_mul(s, d_inv, k); //sm2_bn_print(stderr, 0, 4, "s = ((1 + d)^-1 * (k - r * d)) mod n", s);
// check s != 0
if (sm2_bn_is_zero(s)) {
goto retry;
}
sm2_bn_to_bytes(r, sig->r); //sm2_bn_print_bn(stderr, 0, 4, "r", r);
sm2_bn_to_bytes(s, sig->s); //sm2_bn_print_bn(stderr, 0, 4, "s", s);
gmssl_secure_clear(d, sizeof(d));
gmssl_secure_clear(d_inv, sizeof(d_inv ));
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(t, sizeof(t));
return 1;
}
int sm2_do_verify(const SM2_KEY *key, const uint8_t dgst[32], const SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _R, *R = &_R;
SM2_BN r;
SM2_BN s;
SM2_BN e;
SM2_BN x;
SM2_BN t;
// parse public key
sm2_jacobian_point_from_bytes(P, (const uint8_t *)&key->public_key);
//sm2_jacobian_point_print(stderr, 0, 4, "P", P);
// parse signature values
sm2_bn_from_bytes(r, sig->r); //sm2_bn_print(stderr, 0, 4, "r", r);
sm2_bn_from_bytes(s, sig->s); //sm2_bn_print(stderr, 0, 4, "s", s);
// check r, s in [1, n-1]
if (sm2_bn_is_zero(r) == 1
|| sm2_bn_cmp(r, SM2_N) >= 0
|| sm2_bn_is_zero(s) == 1
|| sm2_bn_cmp(s, SM2_N) >= 0) {
error_print();
return -1;
}
// e = H(M)
sm2_bn_from_bytes(e, dgst); //sm2_bn_print(stderr, 0, 4, "e = H(M)", e);
// t = r + s (mod n), check t != 0
sm2_fn_add(t, r, s); //sm2_bn_print(stderr, 0, 4, "t = r + s (mod n)", t);
if (sm2_bn_is_zero(t)) {
error_print();
return -1;
}
// Q = s * G + t * P
sm2_jacobian_point_mul_sum(R, t, P, s);
sm2_jacobian_point_get_xy(R, x, NULL);
//sm2_bn_print(stderr, 0, 4, "x", x);
// r' = e + x (mod n)
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
if (sm2_bn_cmp(x, SM2_N) >= 0) {
sm2_bn_sub(x, x, SM2_N);
}
sm2_fn_add(e, e, x); //sm2_bn_print(stderr, 0, 4, "e + x (mod n)", e);
// check if r == r'
if (sm2_bn_cmp(e, r) != 0) {
error_print();
return -1;
}
return 1;
}
int sm2_signature_to_der(const SM2_SIGNATURE *sig, uint8_t **out, size_t *outlen)
{
size_t len = 0;
@@ -360,223 +222,6 @@ int sm2_kdf(const uint8_t *in, size_t inlen, size_t outlen, uint8_t *out)
return 1;
}
static int all_zero(const uint8_t *buf, size_t len)
{
size_t i;
for (i = 0; i < len; i++) {
if (buf[i]) {
return 0;
}
}
return 1;
}
int sm2_do_encrypt(const SM2_KEY *key, const uint8_t *in, size_t inlen, SM2_CIPHERTEXT *out)
{
SM2_BN k;
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
SM2_JACOBIAN_POINT _kP, *kP = &_kP;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
if (!(SM2_MIN_PLAINTEXT_SIZE <= inlen && inlen <= SM2_MAX_PLAINTEXT_SIZE)) {
error_print();
return -1;
}
sm2_jacobian_point_from_bytes(P, (uint8_t *)&key->public_key);
// S = h * P, check S != O
// for sm2 curve, h == 1 and S == P
// SM2_POINT can not present point at infinity, do do nothing here
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// output C1 = k * G = (x1, y1)
sm2_jacobian_point_mul_generator(C1, k);
sm2_jacobian_point_to_bytes(C1, (uint8_t *)&out->point);
// k * P = (x2, y2)
sm2_jacobian_point_mul(kP, k, P);
sm2_jacobian_point_to_bytes(kP, x2y2);
// t = KDF(x2 || y2, inlen)
sm2_kdf(x2y2, 64, inlen, out->ciphertext);
// if t is all zero, retry
if (all_zero(out->ciphertext, inlen)) {
goto retry;
}
// output C2 = M xor t
gmssl_memxor(out->ciphertext, out->ciphertext, in, inlen);
out->ciphertext_size = (uint32_t)inlen;
// output C3 = Hash(x2 || m || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, in, inlen);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, out->hash);
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(kP, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return 1;
}
int sm2_do_encrypt_fixlen(const SM2_KEY *key, const uint8_t *in, size_t inlen, int point_size, SM2_CIPHERTEXT *out)
{
unsigned int trys = 200;
SM2_BN k;
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
SM2_JACOBIAN_POINT _kP, *kP = &_kP;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
if (!(SM2_MIN_PLAINTEXT_SIZE <= inlen && inlen <= SM2_MAX_PLAINTEXT_SIZE)) {
error_print();
return -1;
}
switch (point_size) {
case SM2_ciphertext_compact_point_size:
case SM2_ciphertext_typical_point_size:
case SM2_ciphertext_max_point_size:
break;
default:
error_print();
return -1;
}
sm2_jacobian_point_from_bytes(P, (uint8_t *)&key->public_key);
// S = h * P, check S != O
// for sm2 curve, h == 1 and S == P
// SM2_POINT can not present point at infinity, do do nothing here
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// output C1 = k * G = (x1, y1)
sm2_jacobian_point_mul_generator(C1, k);
sm2_jacobian_point_to_bytes(C1, (uint8_t *)&out->point);
// check fixlen
if (trys) {
size_t len = 0;
asn1_integer_to_der(out->point.x, 32, NULL, &len);
asn1_integer_to_der(out->point.y, 32, NULL, &len);
if (len != point_size) {
trys--;
goto retry;
}
} else {
gmssl_secure_clear(k, sizeof(k));
error_print();
return -1;
}
// k * P = (x2, y2)
sm2_jacobian_point_mul(kP, k, P);
sm2_jacobian_point_to_bytes(kP, x2y2);
// t = KDF(x2 || y2, inlen)
sm2_kdf(x2y2, 64, inlen, out->ciphertext);
// if t is all zero, retry
if (all_zero(out->ciphertext, inlen)) {
goto retry;
}
// output C2 = M xor t
gmssl_memxor(out->ciphertext, out->ciphertext, in, inlen);
out->ciphertext_size = (uint32_t)inlen;
// output C3 = Hash(x2 || m || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, in, inlen);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, out->hash);
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(kP, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return 1;
}
int sm2_do_decrypt(const SM2_KEY *key, const SM2_CIPHERTEXT *in, uint8_t *out, size_t *outlen)
{
int ret = -1;
SM2_BN d;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
uint8_t hash[32];
// check C1 is on sm2 curve
sm2_jacobian_point_from_bytes(C1, (uint8_t *)&in->point);
if (!sm2_jacobian_point_is_on_curve(C1)) {
error_print();
return -1;
}
// check if S = h * C1 is point at infinity
// this will not happen, as SM2_POINT can not present point at infinity
// d * C1 = (x2, y2)
sm2_bn_from_bytes(d, key->private_key);
sm2_jacobian_point_mul(C1, d, C1);
// t = KDF(x2 || y2, klen) and check t is not all zeros
sm2_jacobian_point_to_bytes(C1, x2y2);
sm2_kdf(x2y2, 64, in->ciphertext_size, out);
if (all_zero(out, in->ciphertext_size)) {
error_print();
goto end;
}
// M = C2 xor t
gmssl_memxor(out, out, in->ciphertext, in->ciphertext_size);
*outlen = in->ciphertext_size;
// u = Hash(x2 || M || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, out, in->ciphertext_size);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, hash);
// check if u == C3
if (memcmp(in->hash, hash, sizeof(hash)) != 0) {
error_print();
goto end;
}
ret = 1;
end:
gmssl_secure_clear(d, sizeof(d));
gmssl_secure_clear(C1, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return ret;
}
int sm2_ciphertext_to_der(const SM2_CIPHERTEXT *C, uint8_t **out, size_t *outlen)
{
size_t len = 0;
@@ -773,51 +418,3 @@ int sm2_ecdh(const SM2_KEY *key, const uint8_t *peer_public, size_t peer_public_
}
return 1;
}
// (x1, y1) = k * G
// r = e + x1
// s = (k - r * d)/(1 + d) = (k +r - r * d - r)/(1 + d) = (k + r - r(1 +d))/(1 + d) = (k + r)/(1 + d) - r
// = -r + (k + r)*(1 + d)^-1
// = -r + (k + r) * d'
int sm2_do_sign_fast(const SM2_Fn d, const uint8_t dgst[32], SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT R;
SM2_BN e;
SM2_BN k;
SM2_BN x1;
SM2_BN r;
SM2_BN s;
// e = H(M)
sm2_bn_from_bytes(e, dgst);
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k));
// (x1, y1) = kG
sm2_jacobian_point_mul_generator(&R, k);
sm2_jacobian_point_get_xy(&R, x1, NULL);
// r = e + x1 (mod n)
sm2_fn_add(r, e, x1);
// s = (k + r) * d' - r
sm2_bn_add(s, k, r);
sm2_fn_mul(s, s, d);
sm2_fn_sub(s, s, r);
sm2_bn_to_bytes(r, sig->r);
sm2_bn_to_bytes(s, sig->s);
return 1;
}

421
src/sm2_sign.c Normal file
View File

@@ -0,0 +1,421 @@
/*
* Copyright 2014-2024 The GmSSL Project. All Rights Reserved.
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
*
* http://www.apache.org/licenses/LICENSE-2.0
*/
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <gmssl/mem.h>
#include <gmssl/sm2.h>
#include <gmssl/sm3.h>
#include <gmssl/asn1.h>
#include <gmssl/error.h>
#include <gmssl/endian.h>
extern const SM2_BN SM2_N;
extern const SM2_BN SM2_ONE;
int sm2_do_sign(const SM2_KEY *key, const uint8_t dgst[32], SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_BN d;
SM2_BN d_inv;
SM2_BN e;
SM2_BN k;
SM2_BN x;
SM2_BN t;
SM2_BN r;
SM2_BN s;
//fprintf(stderr, "sm2_do_sign\n");
sm2_bn_from_bytes(d, key->private_key);
// compute (d + 1)^-1 (mod n)
sm2_fn_add(d_inv, d, SM2_ONE); //sm2_bn_print(stderr, 0, 4, "(1+d)", d_inv);
if (sm2_bn_is_zero(d_inv)) {
error_print();
return -1;
}
sm2_fn_inv(d_inv, d_inv); //sm2_bn_print(stderr, 0, 4, "(1+d)^-1", d_inv);
// e = H(M)
sm2_bn_from_bytes(e, dgst); //sm2_bn_print(stderr, 0, 4, "e", e);
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// (x, y) = kG
sm2_jacobian_point_mul_generator(P, k);
sm2_jacobian_point_get_xy(P, x, NULL);
//sm2_bn_print(stderr, 0, 4, "x", x);
// r = e + x (mod n)
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
if (sm2_bn_cmp(x, SM2_N) >= 0) {
sm2_bn_sub(x, x, SM2_N);
}
sm2_fn_add(r, e, x); //sm2_bn_print(stderr, 0, 4, "r = e + x (mod n)", r);
// if r == 0 or r + k == n re-generate k
sm2_bn_add(t, r, k);
if (sm2_bn_is_zero(r) || sm2_bn_cmp(t, SM2_N) == 0) {
//sm2_bn_print(stderr, 0, 4, "r + k", t);
goto retry;
}
// s = ((1 + d)^-1 * (k - r * d)) mod n
sm2_fn_mul(t, r, d); //sm2_bn_print(stderr, 0, 4, "r*d", t);
sm2_fn_sub(k, k, t); //sm2_bn_print(stderr, 0, 4, "k-r*d", k);
sm2_fn_mul(s, d_inv, k); //sm2_bn_print(stderr, 0, 4, "s = ((1 + d)^-1 * (k - r * d)) mod n", s);
// check s != 0
if (sm2_bn_is_zero(s)) {
goto retry;
}
sm2_bn_to_bytes(r, sig->r); //sm2_bn_print_bn(stderr, 0, 4, "r", r);
sm2_bn_to_bytes(s, sig->s); //sm2_bn_print_bn(stderr, 0, 4, "s", s);
gmssl_secure_clear(d, sizeof(d));
gmssl_secure_clear(d_inv, sizeof(d_inv ));
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(t, sizeof(t));
return 1;
}
// (x1, y1) = k * G
// r = e + x1
// s = (k - r * d)/(1 + d) = (k +r - r * d - r)/(1 + d) = (k + r - r(1 +d))/(1 + d) = (k + r)/(1 + d) - r
// = -r + (k + r)*(1 + d)^-1
// = -r + (k + r) * d'
int sm2_do_sign_fast(const SM2_Fn d, const uint8_t dgst[32], SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT R;
SM2_BN e;
SM2_BN k;
SM2_BN x1;
SM2_BN r;
SM2_BN s;
// e = H(M)
sm2_bn_from_bytes(e, dgst);
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k));
// (x1, y1) = kG
sm2_jacobian_point_mul_generator(&R, k);
sm2_jacobian_point_get_xy(&R, x1, NULL);
// r = e + x1 (mod n)
sm2_fn_add(r, e, x1);
// s = (k + r) * d' - r
sm2_bn_add(s, k, r);
sm2_fn_mul(s, s, d);
sm2_fn_sub(s, s, r);
sm2_bn_to_bytes(r, sig->r);
sm2_bn_to_bytes(s, sig->s);
return 1;
}
int sm2_do_verify(const SM2_KEY *key, const uint8_t dgst[32], const SM2_SIGNATURE *sig)
{
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _R, *R = &_R;
SM2_BN r;
SM2_BN s;
SM2_BN e;
SM2_BN x;
SM2_BN t;
// parse public key
sm2_jacobian_point_from_bytes(P, (const uint8_t *)&key->public_key);
//sm2_jacobian_point_print(stderr, 0, 4, "P", P);
// parse signature values
sm2_bn_from_bytes(r, sig->r); //sm2_bn_print(stderr, 0, 4, "r", r);
sm2_bn_from_bytes(s, sig->s); //sm2_bn_print(stderr, 0, 4, "s", s);
// check r, s in [1, n-1]
if (sm2_bn_is_zero(r) == 1
|| sm2_bn_cmp(r, SM2_N) >= 0
|| sm2_bn_is_zero(s) == 1
|| sm2_bn_cmp(s, SM2_N) >= 0) {
error_print();
return -1;
}
// e = H(M)
sm2_bn_from_bytes(e, dgst); //sm2_bn_print(stderr, 0, 4, "e = H(M)", e);
// t = r + s (mod n), check t != 0
sm2_fn_add(t, r, s); //sm2_bn_print(stderr, 0, 4, "t = r + s (mod n)", t);
if (sm2_bn_is_zero(t)) {
error_print();
return -1;
}
// Q = s * G + t * P
sm2_jacobian_point_mul_sum(R, t, P, s);
sm2_jacobian_point_get_xy(R, x, NULL);
//sm2_bn_print(stderr, 0, 4, "x", x);
// r' = e + x (mod n)
if (sm2_bn_cmp(e, SM2_N) >= 0) {
sm2_bn_sub(e, e, SM2_N);
}
if (sm2_bn_cmp(x, SM2_N) >= 0) {
sm2_bn_sub(x, x, SM2_N);
}
sm2_fn_add(e, e, x); //sm2_bn_print(stderr, 0, 4, "e + x (mod n)", e);
// check if r == r'
if (sm2_bn_cmp(e, r) != 0) {
error_print();
return -1;
}
return 1;
}
static int all_zero(const uint8_t *buf, size_t len)
{
size_t i;
for (i = 0; i < len; i++) {
if (buf[i]) {
return 0;
}
}
return 1;
}
int sm2_do_encrypt(const SM2_KEY *key, const uint8_t *in, size_t inlen, SM2_CIPHERTEXT *out)
{
SM2_BN k;
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
SM2_JACOBIAN_POINT _kP, *kP = &_kP;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
if (!(SM2_MIN_PLAINTEXT_SIZE <= inlen && inlen <= SM2_MAX_PLAINTEXT_SIZE)) {
error_print();
return -1;
}
sm2_jacobian_point_from_bytes(P, (uint8_t *)&key->public_key);
// S = h * P, check S != O
// for sm2 curve, h == 1 and S == P
// SM2_POINT can not present point at infinity, do do nothing here
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// output C1 = k * G = (x1, y1)
sm2_jacobian_point_mul_generator(C1, k);
sm2_jacobian_point_to_bytes(C1, (uint8_t *)&out->point);
// k * P = (x2, y2)
sm2_jacobian_point_mul(kP, k, P);
sm2_jacobian_point_to_bytes(kP, x2y2);
// t = KDF(x2 || y2, inlen)
sm2_kdf(x2y2, 64, inlen, out->ciphertext);
// if t is all zero, retry
if (all_zero(out->ciphertext, inlen)) {
goto retry;
}
// output C2 = M xor t
gmssl_memxor(out->ciphertext, out->ciphertext, in, inlen);
out->ciphertext_size = (uint32_t)inlen;
// output C3 = Hash(x2 || m || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, in, inlen);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, out->hash);
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(kP, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return 1;
}
int sm2_do_encrypt_fixlen(const SM2_KEY *key, const uint8_t *in, size_t inlen, int point_size, SM2_CIPHERTEXT *out)
{
unsigned int trys = 200;
SM2_BN k;
SM2_JACOBIAN_POINT _P, *P = &_P;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
SM2_JACOBIAN_POINT _kP, *kP = &_kP;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
if (!(SM2_MIN_PLAINTEXT_SIZE <= inlen && inlen <= SM2_MAX_PLAINTEXT_SIZE)) {
error_print();
return -1;
}
switch (point_size) {
case SM2_ciphertext_compact_point_size:
case SM2_ciphertext_typical_point_size:
case SM2_ciphertext_max_point_size:
break;
default:
error_print();
return -1;
}
sm2_jacobian_point_from_bytes(P, (uint8_t *)&key->public_key);
// S = h * P, check S != O
// for sm2 curve, h == 1 and S == P
// SM2_POINT can not present point at infinity, do do nothing here
retry:
// rand k in [1, n - 1]
do {
if (sm2_fn_rand(k) != 1) {
error_print();
return -1;
}
} while (sm2_bn_is_zero(k)); //sm2_bn_print(stderr, 0, 4, "k", k);
// output C1 = k * G = (x1, y1)
sm2_jacobian_point_mul_generator(C1, k);
sm2_jacobian_point_to_bytes(C1, (uint8_t *)&out->point);
// check fixlen
if (trys) {
size_t len = 0;
asn1_integer_to_der(out->point.x, 32, NULL, &len);
asn1_integer_to_der(out->point.y, 32, NULL, &len);
if (len != point_size) {
trys--;
goto retry;
}
} else {
gmssl_secure_clear(k, sizeof(k));
error_print();
return -1;
}
// k * P = (x2, y2)
sm2_jacobian_point_mul(kP, k, P);
sm2_jacobian_point_to_bytes(kP, x2y2);
// t = KDF(x2 || y2, inlen)
sm2_kdf(x2y2, 64, inlen, out->ciphertext);
// if t is all zero, retry
if (all_zero(out->ciphertext, inlen)) {
goto retry;
}
// output C2 = M xor t
gmssl_memxor(out->ciphertext, out->ciphertext, in, inlen);
out->ciphertext_size = (uint32_t)inlen;
// output C3 = Hash(x2 || m || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, in, inlen);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, out->hash);
gmssl_secure_clear(k, sizeof(k));
gmssl_secure_clear(kP, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return 1;
}
int sm2_do_decrypt(const SM2_KEY *key, const SM2_CIPHERTEXT *in, uint8_t *out, size_t *outlen)
{
int ret = -1;
SM2_BN d;
SM2_JACOBIAN_POINT _C1, *C1 = &_C1;
uint8_t x2y2[64];
SM3_CTX sm3_ctx;
uint8_t hash[32];
// check C1 is on sm2 curve
sm2_jacobian_point_from_bytes(C1, (uint8_t *)&in->point);
if (!sm2_jacobian_point_is_on_curve(C1)) {
error_print();
return -1;
}
// check if S = h * C1 is point at infinity
// this will not happen, as SM2_POINT can not present point at infinity
// d * C1 = (x2, y2)
sm2_bn_from_bytes(d, key->private_key);
sm2_jacobian_point_mul(C1, d, C1);
// t = KDF(x2 || y2, klen) and check t is not all zeros
sm2_jacobian_point_to_bytes(C1, x2y2);
sm2_kdf(x2y2, 64, in->ciphertext_size, out);
if (all_zero(out, in->ciphertext_size)) {
error_print();
goto end;
}
// M = C2 xor t
gmssl_memxor(out, out, in->ciphertext, in->ciphertext_size);
*outlen = in->ciphertext_size;
// u = Hash(x2 || M || y2)
sm3_init(&sm3_ctx);
sm3_update(&sm3_ctx, x2y2, 32);
sm3_update(&sm3_ctx, out, in->ciphertext_size);
sm3_update(&sm3_ctx, x2y2 + 32, 32);
sm3_finish(&sm3_ctx, hash);
// check if u == C3
if (memcmp(in->hash, hash, sizeof(hash)) != 0) {
error_print();
goto end;
}
ret = 1;
end:
gmssl_secure_clear(d, sizeof(d));
gmssl_secure_clear(C1, sizeof(SM2_JACOBIAN_POINT));
gmssl_secure_clear(x2y2, sizeof(x2y2));
return ret;
}

532
src/sm2_z256.c
View File

@@ -52,8 +52,35 @@
#include <gmssl/endian.h>
#include <gmssl/sm2_z256.h>
/*
SM2 parameters
// z256
p = 0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffffffffffff
a = 0xfffffffeffffffffffffffffffffffffffffffff00000000fffffffffffffffc
b = 0x28e9fa9e9d9f5e344d5a9e4bcf6509a7f39789f515ab8f92ddbcbd414d940e93
x = 0x32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7
y = 0xbc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0
n = 0xfffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54123
h = 0x1
*/
const uint64_t SM2_Z256_ONE[4] = { 1,0,0,0 };
void sm2_z256_from_bytes(uint64_t r[4], const uint8_t in[32])
{
r[3] = GETU64(in);
r[2] = GETU64(in + 8);
r[1] = GETU64(in + 16);
r[0] = GETU64(in + 24);
}
void sm2_z256_to_bytes(const uint64_t a[4], uint8_t out[32])
{
PUTU64(out, a[3]);
PUTU64(out + 8, a[2]);
PUTU64(out + 16, a[1]);
PUTU64(out + 24, a[0]);
}
void sm2_z256_copy(uint64_t r[4], const uint64_t a[4])
{
@@ -74,22 +101,6 @@ void sm2_z256_copy_conditional(uint64_t dst[4], const uint64_t src[4], uint64_t
dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
}
void sm2_z256_from_bytes(uint64_t r[4], const uint8_t in[32])
{
r[3] = GETU64(in);
r[2] = GETU64(in + 8);
r[1] = GETU64(in + 16);
r[0] = GETU64(in + 24);
}
void sm2_z256_to_bytes(const uint64_t a[4], uint8_t out[32])
{
PUTU64(out, a[3]);
PUTU64(out + 8, a[2]);
PUTU64(out + 16, a[1]);
PUTU64(out + 24, a[0]);
}
static uint64_t is_zero(uint64_t in)
{
in |= (0 - in);
@@ -294,18 +305,18 @@ int sm2_z512_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t
return 1;
}
// z256 mod p
// GF(p)
// p = 2^256 - 2^224 - 2^96 + 2^64 - 1
// = 0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffffffffffff
const uint64_t SM2_Z256_P[4] = {
0xffffffffffffffff, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffeffffffff
0xffffffffffffffff, 0xffffffff00000000, 0xffffffffffffffff, 0xfffffffeffffffff,
};
// mont(1) = 2^256 mod p = 2^224 + 2^96 - 2^64 + 1
// 2^256 - p = 2^224 + 2^96 - 2^64 + 1
const uint64_t SM2_Z256_NEG_P[4] = {
1, ((uint64_t)1 << 32) - 1, 0, ((uint64_t)1 << 32) };
1, ((uint64_t)1 << 32) - 1, 0, ((uint64_t)1 << 32),
};
void sm2_z256_modp_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
{
@@ -373,24 +384,24 @@ void sm2_z256_modp_neg(uint64_t r[4], const uint64_t a[4])
(void)sm2_z256_sub(r, SM2_Z256_P, a);
}
// p' = -p^(-1) mod 2^256
// = fffffffc00000001fffffffe00000000ffffffff000000010000000000000001
// sage: -(IntegerModRing(2^256)(p))^-1
const uint64_t SM2_Z256_P_PRIME[4] = {
0x0000000000000001, 0xffffffff00000001, 0xfffffffe00000000, 0xfffffffc00000001,
};
// montegomery
const uint64_t *SM2_Z256_MONT_ONE = SM2_Z256_NEG_P;
// mont(1) (mod p) = 2^256 mod p = 2^256 - p
const uint64_t *SM2_Z256_MODP_MONT_ONE = SM2_Z256_NEG_P;
// z = xy
// c = (z + (z * p' mod 2^256) * p)/2^256
void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
void sm2_z256_modp_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
{
uint64_t z[8];
uint64_t t[8];
uint64_t c;
// p' = -p^(-1) mod 2^256 = fffffffc00000001fffffffe00000000ffffffff000000010000000000000001
const uint64_t p_[4] = {
0x0000000000000001, 0xffffffff00000001, 0xfffffffe00000000, 0xfffffffc00000001
};
//sm2_z256_print(stderr, 0, 0, "a", a);
//sm2_z256_print(stderr, 0, 0, "b", b);
@@ -399,7 +410,7 @@ void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
//sm2_z512_print(stderr, 0, 0, "z", z);
// t = low(z) * p'
sm2_z256_mul(t, z, p_);
sm2_z256_mul(t, z, SM2_Z256_P_PRIME);
//sm2_z256_print(stderr, 0, 0, "z * p' mod 2^256", t);
// t = low(t) * p
@@ -415,7 +426,7 @@ void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
//sm2_z256_print(stderr, 0, 0, "r", r);
if (c) {
sm2_z256_add(r, r, SM2_Z256_MONT_ONE);
sm2_z256_add(r, r, SM2_Z256_MODP_MONT_ONE);
//sm2_z256_print(stderr, 0, 0, "r1", r);
} else if (sm2_z256_cmp(r, SM2_Z256_P) >= 0) {
@@ -424,12 +435,35 @@ void sm2_z256_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
}
}
void sm2_z256_mont_sqr(uint64_t r[4], const uint64_t a[4])
void sm2_z256_modp_mont_sqr(uint64_t r[4], const uint64_t a[4])
{
sm2_z256_mont_mul(r, a, a);
sm2_z256_modp_mont_mul(r, a, a);
}
void sm2_z256_mont_inv(uint64_t r[4], const uint64_t a[4])
void sm2_z256_modp_mont_exp(uint64_t r[4], const uint64_t a[4], const uint64_t e[4])
{
uint64_t t[4];
uint64_t w;
int i, j;
// t = mont(1) (mod p)
sm2_z256_copy(t, SM2_Z256_MODP_MONT_ONE);
for (i = 3; i >= 0; i--) {
w = e[i];
for (j = 0; j < 64; j++) {
sm2_z256_modp_mont_sqr(t, t);
if (w & 0x8000000000000000) {
sm2_z256_modp_mont_mul(t, t, a);
}
w <<= 1;
}
}
sm2_z256_copy(r, t);
}
void sm2_z256_modp_mont_inv(uint64_t r[4], const uint64_t a[4])
{
uint64_t a1[4];
uint64_t a2[4];
@@ -438,105 +472,264 @@ void sm2_z256_mont_inv(uint64_t r[4], const uint64_t a[4])
uint64_t a5[4];
int i;
sm2_z256_mont_sqr(a1, a);
sm2_z256_mont_mul(a2, a1, a);
sm2_z256_mont_sqr(a3, a2);
sm2_z256_mont_sqr(a3, a3);
sm2_z256_mont_mul(a3, a3, a2);
sm2_z256_mont_sqr(a4, a3);
sm2_z256_mont_sqr(a4, a4);
sm2_z256_mont_sqr(a4, a4);
sm2_z256_mont_sqr(a4, a4);
sm2_z256_mont_mul(a4, a4, a3);
sm2_z256_mont_sqr(a5, a4);
sm2_z256_modp_mont_sqr(a1, a);
sm2_z256_modp_mont_mul(a2, a1, a);
sm2_z256_modp_mont_sqr(a3, a2);
sm2_z256_modp_mont_sqr(a3, a3);
sm2_z256_modp_mont_mul(a3, a3, a2);
sm2_z256_modp_mont_sqr(a4, a3);
sm2_z256_modp_mont_sqr(a4, a4);
sm2_z256_modp_mont_sqr(a4, a4);
sm2_z256_modp_mont_sqr(a4, a4);
sm2_z256_modp_mont_mul(a4, a4, a3);
sm2_z256_modp_mont_sqr(a5, a4);
for (i = 1; i < 8; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a5, a5, a4);
sm2_z256_modp_mont_mul(a5, a5, a4);
for (i = 0; i < 8; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a5, a5, a4);
sm2_z256_modp_mont_mul(a5, a5, a4);
for (i = 0; i < 4; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a5, a5, a3);
sm2_z256_mont_sqr(a5, a5);
sm2_z256_mont_sqr(a5, a5);
sm2_z256_mont_mul(a5, a5, a2);
sm2_z256_mont_sqr(a5, a5);
sm2_z256_mont_mul(a5, a5, a);
sm2_z256_mont_sqr(a4, a5);
sm2_z256_mont_mul(a3, a4, a1);
sm2_z256_mont_sqr(a5, a4);
sm2_z256_modp_mont_mul(a5, a5, a3);
sm2_z256_modp_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
sm2_z256_modp_mont_mul(a5, a5, a2);
sm2_z256_modp_mont_sqr(a5, a5);
sm2_z256_modp_mont_mul(a5, a5, a);
sm2_z256_modp_mont_sqr(a4, a5);
sm2_z256_modp_mont_mul(a3, a4, a1);
sm2_z256_modp_mont_sqr(a5, a4);
for (i = 1; i< 31; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a4, a5, a4);
sm2_z256_mont_sqr(a4, a4);
sm2_z256_mont_mul(a4, a4, a);
sm2_z256_mont_mul(a3, a4, a2);
sm2_z256_modp_mont_mul(a4, a5, a4);
sm2_z256_modp_mont_sqr(a4, a4);
sm2_z256_modp_mont_mul(a4, a4, a);
sm2_z256_modp_mont_mul(a3, a4, a2);
for (i = 0; i < 33; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a2, a5, a3);
sm2_z256_mont_mul(a3, a2, a3);
sm2_z256_modp_mont_mul(a2, a5, a3);
sm2_z256_modp_mont_mul(a3, a2, a3);
for (i = 0; i < 32; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a2, a5, a3);
sm2_z256_mont_mul(a3, a2, a3);
sm2_z256_mont_mul(a4, a2, a4);
sm2_z256_modp_mont_mul(a2, a5, a3);
sm2_z256_modp_mont_mul(a3, a2, a3);
sm2_z256_modp_mont_mul(a4, a2, a4);
for (i = 0; i < 32; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a2, a5, a3);
sm2_z256_mont_mul(a3, a2, a3);
sm2_z256_mont_mul(a4, a2, a4);
sm2_z256_modp_mont_mul(a2, a5, a3);
sm2_z256_modp_mont_mul(a3, a2, a3);
sm2_z256_modp_mont_mul(a4, a2, a4);
for (i = 0; i < 32; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a2, a5, a3);
sm2_z256_mont_mul(a3, a2, a3);
sm2_z256_mont_mul(a4, a2, a4);
sm2_z256_modp_mont_mul(a2, a5, a3);
sm2_z256_modp_mont_mul(a3, a2, a3);
sm2_z256_modp_mont_mul(a4, a2, a4);
for (i = 0; i < 32; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(a2, a5, a3);
sm2_z256_mont_mul(a3, a2, a3);
sm2_z256_mont_mul(a4, a2, a4);
sm2_z256_modp_mont_mul(a2, a5, a3);
sm2_z256_modp_mont_mul(a3, a2, a3);
sm2_z256_modp_mont_mul(a4, a2, a4);
for (i = 0; i < 32; i++) {
sm2_z256_mont_sqr(a5, a5);
sm2_z256_modp_mont_sqr(a5, a5);
}
sm2_z256_mont_mul(r, a4, a5);
sm2_z256_modp_mont_mul(r, a4, a5);
}
// mont(mont(a), 1) = aR * 1 * R^-1 (mod p) = a (mod p)
void sm2_z256_from_mont(uint64_t r[4], const uint64_t a[4])
void sm2_z256_modp_from_mont(uint64_t r[4], const uint64_t a[4])
{
const uint64_t SM2_Z256_ONE[4] = { 1,0,0,0 };
sm2_z256_mont_mul(r, a, SM2_Z256_ONE);
sm2_z256_modp_mont_mul(r, a, SM2_Z256_ONE);
}
// 2^512 (mod p)
const uint64_t SM2_Z256_2e512modp[4] = {
0x0000000200000003, 0x00000002ffffffff, 0x0000000100000001, 0x0000000400000002
};
// mont(a) = a * 2^256 (mod p) = mont_mul(a, 2^512 mod p)
void sm2_z256_to_mont(const uint64_t a[4], uint64_t r[4])
void sm2_z256_modp_to_mont(const uint64_t a[4], uint64_t r[4])
{
// 2^512 (mod p)
const uint64_t SM2_Z256_2e512modp[4] = {
0x0000000200000003, 0x00000002ffffffff, 0x0000000100000001, 0x0000000400000002
};
sm2_z256_mont_mul(r, a, SM2_Z256_2e512modp);
sm2_z256_modp_mont_mul(r, a, SM2_Z256_2e512modp);
}
int sm2_z256_mont_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4])
int sm2_z256_modp_mont_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4])
{
uint64_t r[4];
sm2_z256_from_mont(r, a);
sm2_z256_modp_from_mont(r, a);
sm2_z256_print(fp, ind, fmt, label, r);
return 1;
}
// GF(n)
// n = 0xfffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54123
const uint64_t SM2_Z256_N[4] = {
0x53bbf40939d54123, 0x7203df6b21c6052b, 0xffffffffffffffff, 0xfffffffeffffffff,
};
// 2^256 - n = 0x10000000000000000000000008dfc2094de39fad4ac440bf6c62abedd
const uint64_t SM2_Z256_NEG_N[4] = {
0xac440bf6c62abedd, 0x8dfc2094de39fad4, 0x0000000000000000, 0x0000000100000000,
};
void sm2_z256_modn_add(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
{
uint64_t c;
c = sm2_z256_add(r, a, b);
if (c) {
// a + b - n = (a + b - 2^256) + (2^256 - n)
(void)sm2_z256_add(r, r, SM2_Z256_NEG_N);
return;
}
if (sm2_z256_cmp(r, SM2_Z256_N) >= 0) {
(void)sm2_z256_sub(r, r, SM2_Z256_N);
}
}
void sm2_z256_modn_sub(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
{
uint64_t c;
c = sm2_z256_sub(r, a, b);
if (c) {
// a - b + n = (a - b + 2^256) - (2^256 - n)
(void)sm2_z256_sub(r, r, SM2_Z256_NEG_N);
}
}
void sm2_z256_modn_neg(uint64_t r[4], const uint64_t a[4])
{
(void)sm2_z256_sub(r, SM2_Z256_N, a);
}
// n' = -n^(-1) mod 2^256
// = 0x6f39132f82e4c7bc2b0068d3b08941d4df1e8d34fc8319a5327f9e8872350975
// sage: -(IntegerModRing(2^256)(n))^-1
const uint64_t SM2_Z256_N_PRIME[4] = {
0x327f9e8872350975, 0xdf1e8d34fc8319a5, 0x2b0068d3b08941d4, 0x6f39132f82e4c7bc,
};
// mont(1) (mod n) = 2^256 - n
const uint64_t *SM2_Z256_MODN_MONT_ONE = SM2_Z256_NEG_N;
void sm2_z256_modn_mont_mul(uint64_t r[4], const uint64_t a[4], const uint64_t b[4])
{
uint64_t z[8];
uint64_t t[8];
uint64_t c;
//sm2_z256_print(stderr, 0, 0, "a", a);
//sm2_z256_print(stderr, 0, 0, "b", b);
// z = a * b
sm2_z256_mul(z, a, b);
//sm2_z512_print(stderr, 0, 0, "z", z);
// t = low(z) * n'
sm2_z256_mul(t, z, SM2_Z256_N_PRIME);
//sm2_z256_print(stderr, 0, 0, "z * n' mod 2^256", t);
// t = low(t) * n
sm2_z256_mul(t, t, SM2_Z256_N);
//sm2_z512_print(stderr, 0, 0, "(z * n' mod 2^256) * n", t);
// z = z + t
c = sm2_z512_add(z, z, t);
//sm2_z512_print(stderr, 0, 0, "z", z);
// r = high(r)
sm2_z256_copy(r, z + 4);
//sm2_z256_print(stderr, 0, 0, "r", r);
if (c) {
sm2_z256_add(r, r, SM2_Z256_MODN_MONT_ONE);
//sm2_z256_print(stderr, 0, 0, "r1", r);
} else if (sm2_z256_cmp(r, SM2_Z256_N) >= 0) {
(void)sm2_z256_sub(r, r, SM2_Z256_N);
//sm2_z256_print(stderr, 0, 0, "r2", r);
}
}
void sm2_z256_modn_mont_sqr(uint64_t r[4], const uint64_t a[4])
{
sm2_z256_modn_mont_mul(r, a, a);
}
void sm2_z256_modn_mont_exp(uint64_t r[4], const uint64_t a[4], const uint64_t e[4])
{
uint64_t t[4];
uint64_t w;
int i, j;
// t = mont(1)
sm2_z256_copy(t, SM2_Z256_MODN_MONT_ONE);
for (i = 3; i >= 0; i--) {
w = e[i];
for (j = 0; j < 64; j++) {
sm2_z256_modn_mont_sqr(t, t);
if (w & 0x8000000000000000) {
sm2_z256_modn_mont_mul(t, t, a);
}
w <<= 1;
}
}
sm2_z256_copy(r, t);
}
// n - 2 = 0xfffffffeffffffffffffffffffffffff7203df6b21c6052b53bbf40939d54121
const uint64_t SM2_Z256_N_MINUS_TWO[4] = {
0x53bbf40939d54121, 0x7203df6b21c6052b, 0xffffffffffffffff, 0xfffffffeffffffff,
};
void sm2_z256_modn_mont_inv(uint64_t r[4], const uint64_t a[4])
{
sm2_z256_modn_mont_exp(r, a, SM2_Z256_N_MINUS_TWO);
}
// mont(mont(a), 1) = aR * 1 * R^-1 (mod n) = a (mod p)
void sm2_z256_modn_from_mont(uint64_t r[4], const uint64_t a[4])
{
sm2_z256_modn_mont_mul(r, a, SM2_Z256_ONE);
}
// 2^512 (mod n) = 0x1eb5e412a22b3d3b620fc84c3affe0d43464504ade6fa2fa901192af7c114f20
const uint64_t SM2_Z256_2e512modn[4] = {
0x901192af7c114f20, 0x3464504ade6fa2fa, 0x620fc84c3affe0d4, 0x1eb5e412a22b3d3b,
};
// mont(a) = a * 2^256 (mod n) = mont_mul(a, 2^512 mod n)
void sm2_z256_modn_to_mont(const uint64_t a[4], uint64_t r[4])
{
sm2_z256_modn_mont_mul(r, a, SM2_Z256_2e512modn);
}
int sm2_z256_modn_mont_print(FILE *fp, int ind, int fmt, const char *label, const uint64_t a[4])
{
uint64_t r[4];
sm2_z256_modn_from_mont(r, a);
sm2_z256_print(fp, ind, fmt, label, r);
return 1;
}
// Jacobian Point with Montgomery coordinates
void sm2_z256_point_dbl(SM2_Z256_POINT *R, const SM2_Z256_POINT *A)
@@ -554,75 +747,75 @@ void sm2_z256_point_dbl(SM2_Z256_POINT *R, const SM2_Z256_POINT *A)
// S = 2*Y1
sm2_z256_modp_mul_by_2(S, Y1);
//sm2_z256_mont_print(stderr, 0, 0, "1", S);
//sm2_z256_modp_mont_print(stderr, 0, 0, "1", S);
// Zsqr = Z1^2
sm2_z256_mont_sqr(Zsqr, Z1);
//sm2_z256_mont_print(stderr, 0, 0, "2", Zsqr);
sm2_z256_modp_mont_sqr(Zsqr, Z1);
//sm2_z256_modp_mont_print(stderr, 0, 0, "2", Zsqr);
// S = S^2 = 4*Y1^2
sm2_z256_mont_sqr(S, S);
//sm2_z256_mont_print(stderr, 0, 0, "3", S);
sm2_z256_modp_mont_sqr(S, S);
//sm2_z256_modp_mont_print(stderr, 0, 0, "3", S);
// Z3 = Z1 * Y1
sm2_z256_mont_mul(Z3, Z1, Y1);
//sm2_z256_mont_print(stderr, 0, 0, "4", Z3);
sm2_z256_modp_mont_mul(Z3, Z1, Y1);
//sm2_z256_modp_mont_print(stderr, 0, 0, "4", Z3);
// Z3 = 2 * Z3 = 2*Y1*Z1
sm2_z256_modp_mul_by_2(Z3, Z3);
//sm2_z256_mont_print(stderr, 0, 0, "5", Z3);
//sm2_z256_modp_mont_print(stderr, 0, 0, "5", Z3);
// M = X1 + Zsqr = X1 + Z1^2
sm2_z256_modp_add(M, X1, Zsqr);
//sm2_z256_mont_print(stderr, 0, 0, "6", M);
//sm2_z256_modp_mont_print(stderr, 0, 0, "6", M);
// Zsqr = X1 - Zsqr = X1 - Z1^2
sm2_z256_modp_sub(Zsqr, X1, Zsqr);
//sm2_z256_mont_print(stderr, 0, 0, "7", Zsqr);
//sm2_z256_modp_mont_print(stderr, 0, 0, "7", Zsqr);
// Y3 = S^2 = 16 * Y1^4
sm2_z256_mont_sqr(Y3, S);
//sm2_z256_mont_print(stderr, 0, 0, "8", Y3);
sm2_z256_modp_mont_sqr(Y3, S);
//sm2_z256_modp_mont_print(stderr, 0, 0, "8", Y3);
// Y3 = Y3/2 = 8 * Y1^4
sm2_z256_modp_div_by_2(Y3, Y3);
//sm2_z256_mont_print(stderr, 0, 0, "9", Y3);
//sm2_z256_modp_mont_print(stderr, 0, 0, "9", Y3);
// M = M * Zsqr = (X1 + Z1^2)(X1 - Z1^2)
sm2_z256_mont_mul(M, M, Zsqr);
//sm2_z256_mont_print(stderr, 0, 0, "10", M);
sm2_z256_modp_mont_mul(M, M, Zsqr);
//sm2_z256_modp_mont_print(stderr, 0, 0, "10", M);
// M = 3*M = 3(X1 + Z1^2)(X1 - Z1^2)
sm2_z256_modp_mul_by_3(M, M);
//sm2_z256_mont_print(stderr, 0, 0, "11", M);
//sm2_z256_modp_mont_print(stderr, 0, 0, "11", M);
// S = S * X1 = 4 * X1 * Y1^2
sm2_z256_mont_mul(S, S, X1);
//sm2_z256_mont_print(stderr, 0, 0, "12", S);
sm2_z256_modp_mont_mul(S, S, X1);
//sm2_z256_modp_mont_print(stderr, 0, 0, "12", S);
// tmp0 = 2 * S = 8 * X1 * Y1^2
sm2_z256_modp_mul_by_2(tmp0, S);
//sm2_z256_mont_print(stderr, 0, 0, "13", tmp0);
//sm2_z256_modp_mont_print(stderr, 0, 0, "13", tmp0);
// X3 = M^2 = (3(X1 + Z1^2)(X1 - Z1^2))^2
sm2_z256_mont_sqr(X3, M);
//sm2_z256_mont_print(stderr, 0, 0, "14", X3);
sm2_z256_modp_mont_sqr(X3, M);
//sm2_z256_modp_mont_print(stderr, 0, 0, "14", X3);
// X3 = X3 - tmp0 = (3(X1 + Z1^2)(X1 - Z1^2))^2 - 8 * X1 * Y1^2
sm2_z256_modp_sub(X3, X3, tmp0);
//sm2_z256_mont_print(stderr, 0, 0, "15", X3);
//sm2_z256_modp_mont_print(stderr, 0, 0, "15", X3);
// S = S - X3 = 4 * X1 * Y1^2 - X3
sm2_z256_modp_sub(S, S, X3);
//sm2_z256_mont_print(stderr, 0, 0, "16", S);
//sm2_z256_modp_mont_print(stderr, 0, 0, "16", S);
// S = S * M = 3(X1 + Z1^2)(X1 - Z1^2)(4 * X1 * Y1^2 - X3)
sm2_z256_mont_mul(S, S, M);
//sm2_z256_mont_print(stderr, 0, 0, "17", S);
sm2_z256_modp_mont_mul(S, S, M);
//sm2_z256_modp_mont_print(stderr, 0, 0, "17", S);
// Y3 = S - Y3 = 3(X1 + Z1^2)(X1 - Z1^2)(4 * X1 * Y1^2 - X3) - 8 * Y1^4
sm2_z256_modp_sub(Y3, S, Y3);
//sm2_z256_mont_print(stderr, 0, 0, "18", Y3);
//sm2_z256_modp_mont_print(stderr, 0, 0, "18", Y3);
}
void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT *b)
@@ -660,18 +853,18 @@ void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z2
in1infty = is_zero(in1infty);
in2infty = is_zero(in2infty);
sm2_z256_mont_sqr(Z2sqr, in2_z); /* Z2^2 */
sm2_z256_mont_sqr(Z1sqr, in1_z); /* Z1^2 */
sm2_z256_modp_mont_sqr(Z2sqr, in2_z); /* Z2^2 */
sm2_z256_modp_mont_sqr(Z1sqr, in1_z); /* Z1^2 */
sm2_z256_mont_mul(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
sm2_z256_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
sm2_z256_modp_mont_mul(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
sm2_z256_modp_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
sm2_z256_mont_mul(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
sm2_z256_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
sm2_z256_modp_mont_mul(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
sm2_z256_modp_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
sm2_z256_modp_sub(R, S2, S1); /* R = S2 - S1 */
sm2_z256_mont_mul(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
sm2_z256_mont_mul(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
sm2_z256_modp_mont_mul(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
sm2_z256_modp_mont_mul(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
sm2_z256_modp_sub(H, U2, U1); /* H = U2 - U1 */
/*
@@ -687,13 +880,13 @@ void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z2
}
}
sm2_z256_mont_sqr(Rsqr, R); /* R^2 */
sm2_z256_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
sm2_z256_mont_sqr(Hsqr, H); /* H^2 */
sm2_z256_mont_mul(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
sm2_z256_mont_mul(Hcub, Hsqr, H); /* H^3 */
sm2_z256_modp_mont_sqr(Rsqr, R); /* R^2 */
sm2_z256_modp_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
sm2_z256_modp_mont_sqr(Hsqr, H); /* H^2 */
sm2_z256_modp_mont_mul(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
sm2_z256_modp_mont_mul(Hcub, Hsqr, H); /* H^3 */
sm2_z256_mont_mul(U2, U1, Hsqr); /* U1*H^2 */
sm2_z256_modp_mont_mul(U2, U1, Hsqr); /* U1*H^2 */
sm2_z256_modp_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
sm2_z256_modp_sub(res_x, Rsqr, Hsqr);
@@ -701,8 +894,8 @@ void sm2_z256_point_add(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z2
sm2_z256_modp_sub(res_y, U2, res_x);
sm2_z256_mont_mul(S2, S1, Hcub);
sm2_z256_mont_mul(res_y, R, res_y);
sm2_z256_modp_mont_mul(S2, S1, Hcub);
sm2_z256_modp_mont_mul(res_y, R, res_y);
sm2_z256_modp_sub(res_y, res_y, S2);
sm2_z256_copy_conditional(res_x, in2_x, in1infty);
@@ -739,34 +932,31 @@ void sm2_z256_point_get_affine(const SM2_Z256_POINT *P, uint64_t x[4], uint64_t
uint64_t y_out[4];
// z_inv = 1/Z
sm2_z256_mont_inv(z_inv, P->Z);
sm2_z256_modp_mont_inv(z_inv, P->Z);
// y_out = Y/Z
if (y) {
sm2_z256_mont_mul(y_out, P->Y, z_inv);
sm2_z256_modp_mont_mul(y_out, P->Y, z_inv);
}
// z_inv = 1/Z^2
sm2_z256_mont_sqr(z_inv, z_inv);
sm2_z256_modp_mont_sqr(z_inv, z_inv);
// x_out = X/Z^2
sm2_z256_mont_mul(x_out, P->X, z_inv);
sm2_z256_from_mont(x, x_out);
sm2_z256_modp_mont_mul(x_out, P->X, z_inv);
sm2_z256_modp_from_mont(x, x_out);
if (y) {
// y_out = Y/Z^3
sm2_z256_mont_mul(y_out, y_out, z_inv);
sm2_z256_from_mont(y, y_out);
sm2_z256_modp_mont_mul(y_out, y_out, z_inv);
sm2_z256_modp_from_mont(y, y_out);
}
}
void sm2_z256_point_copy_affine(SM2_Z256_POINT *R, const SM2_Z256_POINT_AFFINE *P)
{
memcpy(R, P, sizeof(SM2_Z256_POINT_AFFINE));
sm2_z256_copy(R->Z, SM2_Z256_MONT_ONE);
sm2_z256_copy(R->Z, SM2_Z256_MODP_MONT_ONE);
}
void sm2_z256_point_add_affine(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const SM2_Z256_POINT_AFFINE *b)
@@ -807,33 +997,33 @@ void sm2_z256_point_add_affine(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const
/* Z1^2 */
sm2_z256_mont_sqr(Z1sqr, in1_z);
sm2_z256_modp_mont_sqr(Z1sqr, in1_z);
/* U2 = X2*Z1^2 */
sm2_z256_mont_mul(U2, in2_x, Z1sqr);
sm2_z256_modp_mont_mul(U2, in2_x, Z1sqr);
/* H = U2 - U1 */
sm2_z256_modp_sub(H, U2, in1_x);
sm2_z256_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
sm2_z256_modp_mont_mul(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
sm2_z256_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
sm2_z256_modp_mont_mul(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
sm2_z256_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
sm2_z256_modp_mont_mul(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
sm2_z256_modp_sub(R, S2, in1_y); /* R = S2 - S1 */
sm2_z256_mont_sqr(Hsqr, H); /* H^2 */
sm2_z256_mont_sqr(Rsqr, R); /* R^2 */
sm2_z256_mont_mul(Hcub, Hsqr, H); /* H^3 */
sm2_z256_modp_mont_sqr(Hsqr, H); /* H^2 */
sm2_z256_modp_mont_sqr(Rsqr, R); /* R^2 */
sm2_z256_modp_mont_mul(Hcub, Hsqr, H); /* H^3 */
sm2_z256_mont_mul(U2, in1_x, Hsqr); /* U1*H^2 */
sm2_z256_modp_mont_mul(U2, in1_x, Hsqr); /* U1*H^2 */
sm2_z256_modp_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
sm2_z256_modp_sub(res_x, Rsqr, Hsqr);
sm2_z256_modp_sub(res_x, res_x, Hcub);
sm2_z256_modp_sub(H, U2, res_x);
sm2_z256_mont_mul(S2, in1_y, Hcub);
sm2_z256_mont_mul(H, H, R);
sm2_z256_modp_mont_mul(S2, in1_y, Hcub);
sm2_z256_modp_mont_mul(H, H, R);
sm2_z256_modp_sub(res_y, H, S2);
sm2_z256_copy_conditional(res_x, in2_x, in1infty);
@@ -842,7 +1032,7 @@ void sm2_z256_point_add_affine(SM2_Z256_POINT *r, const SM2_Z256_POINT *a, const
sm2_z256_copy_conditional(res_y, in2_y, in1infty);
sm2_z256_copy_conditional(res_y, in1_y, in2infty);
sm2_z256_copy_conditional(res_z, SM2_Z256_MONT_ONE, in1infty);
sm2_z256_copy_conditional(res_z, SM2_Z256_MODP_MONT_ONE, in1infty);
sm2_z256_copy_conditional(res_z, in1_z, in2infty);
memcpy(r->X, res_x, sizeof(res_x));
@@ -880,10 +1070,10 @@ int sm2_z256_point_affine_print(FILE *fp, int fmt, int ind, const char *label, c
uint8_t affine[64];
uint64_t a[4];
sm2_z256_from_mont(a, P->x);
sm2_z256_modp_from_mont(a, P->x);
sm2_z256_to_bytes(a, affine);
sm2_z256_from_mont(a, P->y);
sm2_z256_modp_from_mont(a, P->y);
sm2_z256_to_bytes(a, affine + 32);
format_bytes(fp, fmt, ind, label, affine, 64);
@@ -985,7 +1175,6 @@ void sm2_z256_point_mul_sum(SM2_Z256_POINT *R, const uint64_t t[4], const SM2_Z2
sm2_z256_point_add(R, R, &Q);
}
void sm2_z256_point_to_bytes(const SM2_Z256_POINT *P, uint8_t out[64])
{
uint64_t x[4];
@@ -995,10 +1184,3 @@ void sm2_z256_point_to_bytes(const SM2_Z256_POINT *P, uint8_t out[64])
sm2_z256_to_bytes(x, out);
sm2_z256_to_bytes(y, out + 32);
}