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sm9_rate.c
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/* ====================================================================
* Copyright (c) 2018 The GmSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the GmSSL Project.
* (http://gmssl.org/)"
*
* 4. The name "GmSSL Project" must not be used to endorse or promote
* products derived from this software without prior written
* permission. For written permission, please contact
*
* 5. Products derived from this software may not be called "GmSSL"
* nor may "GmSSL" appear in their names without prior written
* permission of the GmSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the GmSSL Project
* (http://gmssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE GmSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE GmSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*/
#include <stdio.h>
#include <string.h>
#include <stdint.h>
#include <openssl/bn.h>
#include <openssl/ec.h>
#include <openssl/err.h>
#include "sm9_lcl.h"
static int fp2_init(fp2_t a, BN_CTX *ctx)
{
a[0] = NULL;
a[1] = NULL;
a[0] = BN_CTX_get(ctx);
a[1] = BN_CTX_get(ctx);
/*
if (!a[1]) {
BN_free(a[0]);
a[0] = NULL;
return 0;
}
*/
return 1;
}
static void fp2_cleanup(fp2_t a)
{
BN_free(a[0]);
BN_free(a[1]);
a[0] = NULL;
a[1] = NULL;
}
static void fp2_clear_cleanup(fp2_t a)
{
BN_clear_free(a[0]);
BN_clear_free(a[1]);
a[0] = NULL;
a[1] = NULL;
}
static int fp2_is_zero(const fp2_t a)
{
return BN_is_zero(a[0])
&& BN_is_zero(a[1]);
}
static int fp2_print(const fp2_t a)
{
printf("%s\n", BN_bn2hex(a[0]));
printf("%s\n", BN_bn2hex(a[1]));
return 1;
}
static int fp2_is_one(const fp2_t a)
{
return BN_is_one(a[0])
&& BN_is_zero(a[1]);
}
static void fp2_set_zero(fp2_t r)
{
BN_zero(r[0]);
BN_zero(r[1]);
}
static int fp2_set_one(fp2_t r)
{
BN_zero(r[1]);
return BN_one(r[0]);
}
static int fp2_copy(fp2_t r, const fp2_t a)
{
return BN_copy(r[0], a[0])
&& BN_copy(r[1], a[1]);
}
static int fp2_set(fp2_t r, const BIGNUM *a0, const BIGNUM *a1)
{
return BN_copy(r[0], a0)
&& BN_copy(r[1], a1);
}
static int fp2_set_hex(fp2_t r, const char *str[2])
{
return BN_hex2bn(&r[0], str[0])
&& BN_hex2bn(&r[1], str[1]);
}
static int fp2_set_u(fp2_t r)
{
BN_zero(r[0]);
return BN_one(r[1]);
}
static int fp2_set_5u(fp2_t r)
{
BN_zero(r[0]);
return BN_set_word(r[1], 5);
}
static int fp2_set_bn(fp2_t r, const BIGNUM *a)
{
BN_zero(r[1]);
return BN_copy(r[0], a) != NULL;
}
static int fp2_set_word(fp2_t r, unsigned long a)
{
BN_zero(r[1]);
return BN_set_word(r[0], a);
}
static int fp2_equ(const fp2_t a, const fp2_t b)
{
return !BN_cmp(a[0], b[0]) && !BN_cmp(a[1], b[1]);
}
#if SM9_TEST
static int fp2_equ_hex(const fp2_t a, const char *str[2], BN_CTX *ctx)
{
fp2_t t;
fp2_init(t, ctx);
fp2_set_hex(t, str);
return fp2_equ(a, t);
}
#endif
#if SM9_TEST
static int fp2_add_word(fp2_t r, const fp2_t a, unsigned long b, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *w = NULL;
if (!(w = BN_CTX_get(ctx))
|| !BN_set_word(w, b)
|| !BN_mod_add(r[0], a[0], w, p, ctx)
|| !BN_copy(r[1], a[1])) {
BN_free(w);
return 0;
}
BN_free(w);
return 1;
}
#endif
static int fp2_add(fp2_t r, const fp2_t a, const fp2_t b, const BIGNUM *p, BN_CTX *ctx)
{
return BN_mod_add(r[0], a[0], b[0], p, ctx)
&& BN_mod_add(r[1], a[1], b[1], p, ctx);
}
static int fp2_dbl(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
return BN_mod_add(r[0], a[0], a[0], p, ctx)
&& BN_mod_add(r[1], a[1], a[1], p, ctx);
}
static int fp2_tri(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t t;
if (!fp2_init(t, ctx)
|| !fp2_dbl(t, a, p, ctx)
|| !fp2_add(r, t, a, p, ctx)) {
fp2_cleanup(t);
return 0;
}
fp2_cleanup(t);
return 1;
}
static int fp2_sub(fp2_t r, const fp2_t a, const fp2_t b, const BIGNUM *p, BN_CTX *ctx)
{
return BN_mod_sub(r[0], a[0], b[0], p, ctx)
&& BN_mod_sub(r[1], a[1], b[1], p, ctx);
}
static int fp2_neg(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
return BN_mod_sub(r[0], p, a[0], p, ctx)
&& BN_mod_sub(r[1], p, a[1], p, ctx);
}
static int fp2_mul(fp2_t r, const fp2_t a, const fp2_t b, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *t = NULL;
BIGNUM *r0 = NULL;
BIGNUM *r1 = NULL;
if (!(t = BN_CTX_get(ctx))
|| !(r0 = BN_CTX_get(ctx))
|| !(r1 = BN_CTX_get(ctx))
/* r0 = a0 * b0 - 2 * a1 * b1 */
|| !BN_mod_mul(r0, a[0], b[0], p, ctx)
|| !BN_mod_mul(t, a[1], b[1], p, ctx)
|| !BN_mod_add(t, t, t, p, ctx)
|| !BN_mod_sub(r0, r0, t, p, ctx)
/* r1 = a0 * b1 + a1 * b0 */
|| !BN_mod_mul(r1, a[0], b[1], p, ctx)
|| !BN_mod_mul(t, a[1], b[0], p, ctx)
|| !BN_mod_add(r1, r1, t, p, ctx)
|| !BN_copy(r[0], r0)
|| !BN_copy(r[1], r1)) {
BN_free(t);
BN_free(r0);
BN_free(r1);
return 0;
}
BN_free(t);
BN_free(r0);
BN_free(r1);
return 1;
}
static int fp2_mul_u(fp2_t r, const fp2_t a, const fp2_t b, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *r0 = NULL;
BIGNUM *r1 = NULL;
BIGNUM *t = NULL;
if (!(r0 = BN_CTX_get(ctx))
|| !(r1 = BN_CTX_get(ctx))
|| !(t = BN_CTX_get(ctx))
/* r0 = -2 * (a0 * b1 + a1 * b0) */
|| !BN_mod_mul(r0, a[0], b[1], p, ctx)
|| !BN_mod_mul(t, a[1], b[0], p, ctx)
|| !BN_mod_add(r0, r0, t, p, ctx)
|| !BN_mod_add(r0, r0, r0, p, ctx)
|| !BN_mod_sub(r0, p, r0, p, ctx)
/* r1 = a0 * b0 - 2 * a1 * b1 */
|| !BN_mod_mul(r1, a[0], b[0], p, ctx)
|| !BN_mod_mul(t, a[1], b[1], p, ctx)
|| !BN_mod_add(t, t, t, p, ctx)
|| !BN_mod_sub(r1, r1, t, p, ctx)
|| !BN_copy(r[0], r0)
|| !BN_copy(r[1], r1)) {
BN_free(r0);
BN_free(r1);
BN_free(t);
return 0;
}
BN_free(r0);
BN_free(r1);
BN_free(t);
return 1;
}
static int fp2_mul_num(fp2_t r, const fp2_t a, const BIGNUM *n, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *r0 = NULL;
BIGNUM *r1 = NULL;
if (!(r0 = BN_CTX_get(ctx))
|| !(r1 = BN_CTX_get(ctx))
|| !BN_mod_mul(r0, a[0], n, p, ctx)
|| !BN_mod_mul(r1, a[1], n, p, ctx)
|| !BN_copy(r[0], r0)
|| !BN_copy(r[1], r1)) {
BN_free(r0);
BN_free(r1);
return 0;
}
BN_free(r0);
BN_free(r1);
return 1;
}
static int fp2_sqr(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *r0 = NULL;
BIGNUM *r1 = NULL;
BIGNUM *t = NULL;
if (!(r0 = BN_CTX_get(ctx))
|| !(r1 = BN_CTX_get(ctx))
||!(t = BN_CTX_get(ctx))
/* r0 = a0^2 - 2 * a1^2 */
|| !BN_mod_sqr(r0, a[0], p, ctx)
|| !BN_mod_sqr(t, a[1], p, ctx)
|| !BN_mod_add(t, t, t, p, ctx)
|| !BN_mod_sub(r0, r0, t, p, ctx)
/* r1 = 2 * a0 * a1 */
|| !BN_mod_mul(r1, a[0], a[1], p, ctx)
|| !BN_mod_add(r1, r1, r1, p, ctx)
|| !BN_copy(r[0], r0)
|| !BN_copy(r[1], r1)) {
BN_free(r0);
BN_free(r1);
BN_free(t);
return 0;
}
BN_free(r0);
BN_free(r1);
BN_free(t);
return 1;
}
static int fp2_sqr_u(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *r0 = NULL;
BIGNUM *r1 = NULL;
BIGNUM *t = NULL;
if (!(r0 = BN_CTX_get(ctx))
|| !(r1 = BN_CTX_get(ctx))
|| !(t = BN_CTX_get(ctx))
/* r0 = -4 * a0 * a1 */
|| !BN_mod_mul(r0, a[0], a[1], p, ctx)
|| !BN_mod_add(r0, r0, r0, p, ctx)
|| !BN_mod_add(r0, r0, r0, p, ctx)
|| !BN_mod_sub(r0, p, r0, p, ctx)
/* r1 = a0^2 - 2 * a1^2 */
|| !BN_mod_sqr(r1, a[0], p, ctx)
|| !BN_mod_sqr(t, a[1], p, ctx)
|| !BN_mod_add(t, t, t, p, ctx)
|| !BN_mod_sub(r1, r1, t, p, ctx)
|| !BN_copy(r[0], r0)
|| !BN_copy(r[1], r1)) {
BN_free(r0);
BN_free(r1);
BN_free(t);
return 0;
}
BN_free(r0);
BN_free(r1);
BN_free(t);
return 1;
}
static int fp2_inv(fp2_t r, const fp2_t a, const BIGNUM *p, BN_CTX *ctx)
{
if (BN_is_zero(a[0])) {
/* r0 = 0 */
BN_zero(r[0]);
/* r1 = -(2 * a1)^-1 */
if (!BN_mod_add(r[1], a[1], a[1], p, ctx)
|| !BN_mod_inverse(r[1], r[1], p, ctx)
|| !BN_mod_sub(r[1], p, r[1], p, ctx)) {
return 0;
}
} else if (BN_is_zero(a[1])) {
/* r1 = 0 */
BN_zero(r[1]);
/* r0 = a0^-1 */
if (!BN_mod_inverse(r[0], a[0], p, ctx)) {
return 0;
}
} else {
BIGNUM *k = NULL;
BIGNUM *t = NULL;
if (!(k = BN_CTX_get(ctx))
|| !(t = BN_CTX_get(ctx))
/* k = (a[0]^2 + 2 * a[1]^2)^-1 */
|| !BN_mod_sqr(k, a[0], p, ctx)
|| !BN_mod_sqr(t, a[1], p, ctx)
|| !BN_mod_add(t, t, t, p, ctx)
|| !BN_mod_add(k, k, t, p, ctx)
|| !BN_mod_inverse(k, k, p, ctx)
/* r[0] = a[0] * k, r[1] = -a[1] * k */
|| !BN_mod_mul(r[0], a[0], k, p, ctx)
|| !BN_mod_mul(r[1], a[1], k, p, ctx)
|| !BN_mod_sub(r[1], p, r[1], p, ctx)) {
BN_free(k);
BN_free(t);
return 0;
}
BN_free(k);
BN_free(t);
}
return 1;
}
#if SM9_TEST
static int fp2_div(fp2_t r, const fp2_t a, const fp2_t b, const BIGNUM *p, BN_CTX *ctx)
{
return fp2_inv(r, b, p, ctx)
&& fp2_mul(r, a, r, p, ctx);
}
#endif
static int fp2_to_bin(const fp2_t a, unsigned char to[64])
{
memset(to, 0, 64);
BN_bn2bin(a[1], to + 32 - BN_num_bytes(a[1]));
BN_bn2bin(a[0], to + 64 - BN_num_bytes(a[0]));
return 1;
}
static int fp2_from_bin(fp2_t a, const unsigned char from[64])
{
return BN_bin2bn(from, 32, a[1])
&& BN_bin2bn(from + 32, 32, a[0]);
}
#if SM9_TEST
static int fp2_test(const BIGNUM *p, BN_CTX *ctx)
{
const char *_a[] = {
"5f25ce2083fc970a6b9fdcd819fb1966d300af2afd58d480c59e02b320852183",
"9acddfef770bcdce452d72461f9d1482a8eff7662e1d591c70a7ce35f2f5710c"};
const char *_b[] = {
"7114f0b7f50ebb85c124558f76f10bd277f71c27384deb67f229e582befde3ee",
"aa2714a30d7b8ae08b987fae8818881fb1952a1f53cda30a35c72841b174d7d"};
const char *add_a_b[] = {
"19fabed87667ab9e56c087179b5d5df4290538071b2bd10cd2584d0dfc31bff4",
"a5705139a7e3867c4de6fa41081e9d04a4094a08235a334d140440ba0e0cbe89"};
const char *dbl_a[] = {
"80b9c4105558723013c0e603e676b88840ecb0ae036ba25a5cc6a3e5db8fd89",
"7f5bbfdeeb73f4aab457393c49ab61c02fed5b8141bfc35cfbe0014402999c9b"};
const char *tri_a[] = {
"67316a6189521e2d6cdbeb38586284ef570f7a35dd8f8ea66b6a6cf17e3e1f0c",
"63e99fce5fdc1b872381003273b9aefdb6eabf9c55622d9d87183452123dc82a"};
const char *sub_a_b[] = {
"a450dd6891918276807f32989898d4d97cfc264edf85d7f4b8e3b85844d88312",
"902b6ea5463415203c73ea4b371b8c00add6a4c438e07eebcd4b5bb1d7de238f"};
const char *neg_a[] = {
"571a31df7ea70fe76a63ce77db93adde4ef1e4201d221a5b1fd19874c2cc23fa",
"1b7220108b97d92390d63909d5f1b2c279029be4ec5d95bf74c7ccf1f05bd471"};
const char *mul_a_b[] = {
"87c654e6949d4f119504b210360cc580fc5365c6d34c1321aec27fcf5a1f15b1",
"36e98d79d712f6a3d1bc6d5ac5a055ee0fcbf088c8744e6e943369538e863eb7"};
const char *mulu_a_b[] = {
"486ce50c547db9aa328ad09a6a4e1b69025ab239899251febd08c880c644c80f",
"87c654e6949d4f119504b210360cc580fc5365c6d34c1321aec27fcf5a1f15b1"};
const char *sqr_a[] = {
"b6011ba4cb9f083149a717c7829eb292c31a0800caf88db28bc71f5a084a0405",
"3a16d18809fca540de3543bdfa3317b45bd8117ce6e6a6be5837fbe70350b684"};
const char *sqru_a[] = {
"42125cefeeaa5c70199923d4012897dc6a4270514cada15f34ffa359dcafd875",
"b6011ba4cb9f083149a717c7829eb292c31a0800caf88db28bc71f5a084a0405"};
const char *inv_a[] = {
"5d25a81c4b20b093804befda14731ad2dfa436a450e8b40cf91939ba94fe84be",
"b317556351e184acb06cf1171069fcf3e9a36b60ca8cd718f55ff0c5769ad325"};
const char *div_a_b[] = {
"107048b3442ccc880691cbeb5005bbeb3e71fbe1ec3899971b6caecd224b7dd9",
"7716a52c4911f52b519d9ec928b56561008469bf3403508d40a324bcd17f4a17"};
const char *inv_1[] = {
"1",
"0"};
const char *inv_u[] = {
"0",
"5b2000000151d378eb01d5a7fac763a290f949a58d3d776df2b7cd93f1a8a2be"};
fp2_t a, b, r;
int ok;
fp2_init(a, ctx);
fp2_init(b, ctx);
fp2_init(r, ctx);
fp2_set_hex(a, _a);
fp2_set_hex(b, _b);
fp2_add(r, a, b, p, ctx);
ok = fp2_equ_hex(r, add_a_b, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_dbl(r, a, p, ctx);
ok = fp2_equ_hex(r, dbl_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_tri(r, a, p, ctx);
ok = fp2_equ_hex(r, tri_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_sub(r, a, b, p, ctx);
ok = fp2_equ_hex(r, sub_a_b, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_neg(r, a, p, ctx);
ok = fp2_equ_hex(r, neg_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_mul(r, a, b, p, ctx);
ok = fp2_equ_hex(r, mul_a_b, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_mul_u(r, a, b, p, ctx);
ok = fp2_equ_hex(r, mulu_a_b, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_sqr(r, a, p, ctx);
ok = fp2_equ_hex(r, sqr_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_sqr_u(r, a, p, ctx);
ok = fp2_equ_hex(r, sqru_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_inv(r, a, p, ctx);
ok = fp2_equ_hex(r, inv_a, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_div(r, a, b, p, ctx);
ok = fp2_equ_hex(r, div_a_b, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_set_one(r);
fp2_inv(r, r, p, ctx);
ok = fp2_equ_hex(r, inv_1, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp2_set_u(r);
fp2_inv(r, r, p, ctx);
ok = fp2_equ_hex(r, inv_u, ctx);
printf("fp2 test %d: %s\n", __LINE__, ok ? "ok" : "error");
return 1;
}
#endif
static int fp4_init(fp4_t a, BN_CTX *ctx)
{
int r;
r = fp2_init(a[0], ctx);
r &= fp2_init(a[1], ctx);
if (!r) {
fp2_cleanup(a[0]);
fp2_cleanup(a[1]);
}
return r;
}
static void fp4_cleanup(fp4_t a)
{
fp2_cleanup(a[0]);
fp2_cleanup(a[1]);
}
#if SM9_TEST
static void fp4_clear_cleanup(fp4_t a)
{
fp2_clear_cleanup(a[0]);
fp2_clear_cleanup(a[1]);
}
#endif
static int fp4_print(const fp4_t a)
{
fp2_print(a[0]);
fp2_print(a[1]);
printf("\n");
return 1;
}
static int fp4_is_zero(const fp4_t a)
{
return fp2_is_zero(a[0])
&& fp2_is_zero(a[1]);
}
static int fp4_is_one(const fp4_t a)
{
return fp2_is_one(a[0])
&& fp2_is_zero(a[1]);
}
static void fp4_set_zero(fp4_t r)
{
fp2_set_zero(r[0]);
fp2_set_zero(r[1]);
}
static int fp4_set_one(fp4_t r)
{
fp2_set_zero(r[1]);
return fp2_set_one(r[0]);
}
static int fp4_set_bn(fp4_t r, const BIGNUM *a)
{
fp2_set_zero(r[1]);
return fp2_set_bn(r[0], a);
}
static int fp4_set_word(fp4_t r, unsigned long a)
{
fp2_set_zero(r[1]);
return fp2_set_word(r[0], a);
}
static int fp4_set_fp2(fp4_t r, const fp2_t a)
{
fp2_set_zero(r[1]);
return fp2_copy(r[0], a);
}
static int fp4_set(fp4_t r, const fp2_t a0, const fp2_t a1)
{
return fp2_copy(r[0], a0)
&& fp2_copy(r[1], a1);
}
static int fp4_set_hex(fp4_t r, const char *str[4])
{
return fp2_set_hex(r[0], str)
&& fp2_set_hex(r[1], str+2);
}
static int fp4_copy(fp4_t r, const fp4_t a)
{
return fp2_copy(r[0], a[0])
&& fp2_copy(r[1], a[1]);
}
static int fp4_set_u(fp4_t r)
{
fp2_set_zero(r[1]);
return fp2_set_u(r[0]);
}
static int fp4_set_v(fp4_t r)
{
fp2_set_zero(r[0]);
return fp2_set_one(r[1]);
}
static int fp4_equ(const fp4_t a, const fp4_t b)
{
return fp2_equ(a[0], b[0])
&& fp2_equ(a[1], b[1]);
}
#if SM9_TEST
static int fp4_equ_hex(const fp4_t a, const char *str[4], BN_CTX *ctx)
{
fp4_t t;
fp4_init(t, ctx);
fp4_set_hex(t, str);
return fp4_equ(a, t);
}
#endif
static int fp4_to_bin(const fp4_t a, unsigned char to[128])
{
return fp2_to_bin(a[1], to)
&& fp2_to_bin(a[0], to + 64);
}
static int fp4_from_bin(fp4_t a, const unsigned char from[128])
{
return fp2_from_bin(a[1], from)
&& fp2_from_bin(a[0], from + 64);
}
static int fp4_add(fp4_t r, const fp4_t a, const fp4_t b, const BIGNUM *p, BN_CTX *ctx)
{
return fp2_add(r[0], a[0], b[0], p, ctx)
&& fp2_add(r[1], a[1], b[1], p, ctx);
}
static int fp4_dbl(fp4_t r, const fp4_t a, const BIGNUM *p, BN_CTX *ctx)
{
return fp2_dbl(r[0], a[0], p, ctx)
&& fp2_dbl(r[1], a[1], p, ctx);
}
static int fp4_sub(fp4_t r, const fp4_t a, const fp4_t b, const BIGNUM *p, BN_CTX *ctx)
{
return fp2_sub(r[0], a[0], b[0], p, ctx)
&& fp2_sub(r[1], a[1], b[1], p, ctx);
}
static int fp4_neg(fp4_t r, const fp4_t a, const BIGNUM *p, BN_CTX *ctx)
{
return fp2_neg(r[0], a[0], p, ctx)
&&fp2_neg(r[1], a[1], p, ctx);
}
static int fp4_mul(fp4_t r, const fp4_t a, const fp4_t b, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t r0, r1, t;
fp2_init(r0, ctx);
fp2_init(r1, ctx);
if (!fp2_init(t, ctx)
/* r0 = a0 * b0 + a1 * b1 * u */
|| !fp2_mul(r0, a[0], b[0], p, ctx)
|| !fp2_mul_u(t, a[1], b[1], p, ctx)
|| !fp2_add(r0, r0, t, p, ctx)
/* r[1] = a[0] * b[1] + a[1] * b[0] */
|| !fp2_mul(r1, a[0], b[1], p, ctx)
|| !fp2_mul(t, a[1], b[0], p, ctx)
|| !fp2_add(r1, r1, t, p, ctx)
|| !fp2_copy(r[0], r0)
|| !fp2_copy(r[1], r1)) {
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 0;
}
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 1;
}
static int fp4_mul_v(fp4_t r, const fp4_t a, const fp4_t b, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t r0, r1, t;
fp2_init(r0, ctx);
fp2_init(r1, ctx);
if (!fp2_init(t, ctx)
/* r0 = a0 * b1 * u + a1 * b0 * u */
|| !fp2_mul_u(r0, a[0], b[1], p, ctx)
|| !fp2_mul_u(t, a[1], b[0], p, ctx)
|| !fp2_add(r0, r0, t, p, ctx)
/* r1 = a0 * b0 + a1 * b1 * u */
|| !fp2_mul(r1, a[0], b[0], p, ctx)
|| !fp2_mul_u(t, a[1], b[1], p, ctx)
|| !fp2_add(r1, r1, t, p, ctx)
|| !fp2_copy(r[0], r0)
|| !fp2_copy(r[1], r1)) {
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 0;
}
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 1;
}
static int fp4_sqr(fp4_t r, const fp4_t a, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t r0, r1, t;
fp2_init(r0, ctx);
fp2_init(r1, ctx);
if (!fp2_init(t, ctx)
/* r0 = a0^2 + a1^2 * u */
|| !fp2_sqr(r0, a[0], p, ctx)
|| !fp2_sqr_u(t, a[1], p, ctx)
|| !fp2_add(r0, r0, t, p, ctx)
/* r1 = 2 * (a0 * a1) */
|| !fp2_mul(r1, a[0], a[1], p, ctx)
|| !fp2_dbl(r1, r1, p, ctx)
|| !fp2_copy(r[0], r0)
|| !fp2_copy(r[1], r1)) {
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 0;
}
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 1;
}
static int fp4_sqr_v(fp4_t r, const fp4_t a, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t r0, r1, t;
fp2_init(r0, ctx);
fp2_init(r1, ctx);
if (!fp2_init(t, ctx)
/* r0 = 2 * (a0 * a1) */
|| !fp2_mul_u(t, a[0], a[1], p, ctx)
|| !fp2_dbl(r0, t, p, ctx)
/* r1 = a0^2 + a1^2 * u */
|| !fp2_sqr(r1, a[0], p, ctx)
|| !fp2_sqr_u(t, a[1], p, ctx)
|| !fp2_add(r1, r1, t, p, ctx)
|| !fp2_copy(r[0], r0)
|| !fp2_copy(r[1], r1)) {
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 0;
}
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(t);
return 1;
}
static int fp4_inv(fp4_t r, const fp4_t a, const BIGNUM *p, BN_CTX *ctx)
{
fp2_t r0, r1, k;
fp2_init(r0, ctx);
fp2_init(r1, ctx);
if (!fp2_init(k, ctx)
/* k = (a1^2 * u - a0^2)^-1 */
|| !fp2_sqr_u(k, a[1], p, ctx)
|| !fp2_sqr(r0, a[0], p, ctx)
|| !fp2_sub(k, k, r0, p, ctx)
|| !fp2_inv(k, k, p, ctx)
/* r0 = -(a0 * k) */
|| !fp2_mul(r0, a[0], k, p, ctx)
|| !fp2_neg(r0, r0, p, ctx)
/* r1 = a1 * k */
|| !fp2_mul(r1, a[1], k, p, ctx)
|| !fp2_copy(r[0], r0)
|| !fp2_copy(r[1], r1)) {
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(k);
return 0;
}
fp2_cleanup(r0);
fp2_cleanup(r1);
fp2_cleanup(k);
return 1;
}
#if SM9_TEST
static int fp4_test(const BIGNUM *p, BN_CTX *ctx)
{
const char *_a[] = {
"bec057c34cec656c05f236d9399cd00c64319632885d200f964e4591dd7ca77",
"55a10432b9095a12c106019c97fa1ed2a484d84bbb750bcf6a378c3f85ba9d09",
"9eb75c7b34e0259a59385602bd2210b844e6b9f6396443eed06dbd701b48a26c",
"76f63f8fb8272b173eaf93cb79e57444c816ef099b3fb11057977d1f3f50eb8"};
const char *_b[] = {
"1dd8569e8b7d7a53a362334330ff5b4e3beeb180466cf7d268c157ff724c2de7",
"48619106bcf6f34107318044223fa5ae3ec74573829f9873e4f06b41d0210762",
"79fdcb2d33f115ef5405c62b509be15adc14cc82abbe6f89978ed0de987377c6",
"71a8d1fd3d68cd689b9ed04872690c41858d98065b2535e70d1a6a8f2547f07e"};
const char *add_a_b[] = {
"29c45c1ac04c40aa63c156b0c499284f0231cae36ef2c9d362263c589023f85e",
"9e02953976004d53c83781e0ba39c480e34c1dbf3e14a4434f27f78155dba46b",
"627527a8662d9497d73a70de182f2acdff08f32dcaa7c49c828cf326d06ad4b5",
"791835f638eb401a0f89c9852a076385d20f06f6f4d930f81293e261193cff36"};
const char *dbl_a[] = {
"17d80af8699d8cad80be46db27339a018c8632c6510ba401f2c9c8b23baf94ee",
"ab4208657212b425820c03392ff43da54909b09776ea179ed46f187f0b753a12",
"872eb8f6671ca442dc6d00b584b55a2b67dae0a1584d9901bb6bdfb8533fff5b",
"edec7f1f704e562e7d5f2796f3cae889902dde13367f6220af2efa3e7ea1d70"};
const char *sub_a_b[] = {
"a453aeddabf4f2f4f3009b7a582938f7ac46fb2dfc93c90a761327818edce20d",
"d3f732bfc1266d1b9d4815875ba792465bd92d838d5735b854720fdb59995a7",
"24b9914e00ef0fab05328fd76c862f5d68d1ed738da5d46538deec9182d52aa6",
"4c0691fbc0bd4c3aae4fd4443ac41247e8e66a355909b405ddcea86ab1fe63b7"};
const char *neg_a[] = {
"aa53fa83cdd4e09b15a487e261f4fa445baf79e7f1f51cdaec0ab6cec5797b06",
"609efbcd499a4cdf14fda9b35d94a8727d6dbaff5f05e30c7b380ee85d96a874",
"1788a384cdc381577ccb554d386cb68cdd0bd954e116aaed1501ddb7c808a311",
"aed09c07072134406218b2133df07000d571245a80c6f3cadff62355ef5c36c5"};
const char *mul_a_b[] = {
"8e897a274c44e47c7db00d58bf08c020472e75f1e008a8a34975a6c947587f80",
"e8b79955f768f30ab48aa1b12b305a71fd12e252f34345d7692d58adf908739",
"a647307d347637d0525d62f9148d9bd7aabfb9c93ec03a7575404e5d4fa64310",
"65cbf741cdf37a3459727a9fcd84b10cc8b1d4c1a3641556de11434b330daf04"};
const char *mulv_a_b[] = {
"a0e8117c6960597af922616050142c70b2817d12ee2db30a0ebcafb960872cf2",
"a647307d347637d0525d62f9148d9bd7aabfb9c93ec03a7575404e5d4fa64310",
"8e897a274c44e47c7db00d58bf08c020472e75f1e008a8a34975a6c947587f80",
"e8b79955f768f30ab48aa1b12b305a71fd12e252f34345d7692d58adf908739"};
const char *sqr_a[] = {
"fb487bb1bee1c8d21956f8b5b7b1d93c5e7087b02666fc475f63b65cf5a2198",
"3a4deaf2a26a4f42fdb3bd34ae1c866a2d1ae5f5d9739d66ec758a38661d7639",
"a089b0d9a76cc56a2db2b56ab0df6e15f7a76ba8ad15e1f3b20accb2245bd827",
"8ad9618cfbada9f4cb296b5f219267785bc4d9b4d3070048e5301972005bb37f"};
const char *sqrv_a[] = {
"56cd3ce60debf9fa15b47fe1a7f8bf998c5b732c8ee7dd26007f036bc5eb23fc",
"a089b0d9a76cc56a2db2b56ab0df6e15f7a76ba8ad15e1f3b20accb2245bd827",
"fb487bb1bee1c8d21956f8b5b7b1d93c5e7087b02666fc475f63b65cf5a2198",
"3a4deaf2a26a4f42fdb3bd34ae1c866a2d1ae5f5d9739d66ec758a38661d7639"};
const char *inv_a[] = {
"7aa3d284401216d78e171627742b5a5dc3af41c15e112ceba1eb9e12ea3780cf",
"99711ed85be3e353d43f87600a9f416b64e1778d92e6b3fc374bc94f59772f70",
"8be97927776cbf6b7a162a5268df1d6a184ecd4ee56cc36273a7127ceabbebd4",
"7b4b924e6c5e548d2c5467e6db40bf35858f690d312d35066821af199a81ff67"};
const char *inv_1[] = {
"1",
"0",
"0",
"0"};
const char *inv_u[] = {
"0",
"5b2000000151d378eb01d5a7fac763a290f949a58d3d776df2b7cd93f1a8a2be",
"0",
"0"};
const char *inv_v[] = {
"0",
"0",
"0",
"5b2000000151d378eb01d5a7fac763a290f949a58d3d776df2b7cd93f1a8a2be"};
fp4_t r, a, b;
int ok;
fp4_init(r, ctx);
fp4_init(a, ctx);
fp4_init(b, ctx);
fp4_set_hex(a, _a);
fp4_set_hex(b, _b);
fp4_add(r, a, b, p, ctx);
ok = fp4_equ_hex(r, add_a_b, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_dbl(r, a, p, ctx);
ok = fp4_equ_hex(r, dbl_a, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_sub(r, a, b, p, ctx);
ok = fp4_equ_hex(r, sub_a_b, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_neg(r, a, p, ctx);
ok = fp4_equ_hex(r, neg_a, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_mul(r, a, b, p, ctx);
ok = fp4_equ_hex(r, mul_a_b, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_mul_v(r, a, b, p, ctx);
ok = fp4_equ_hex(r, mulv_a_b, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_sqr(r, a, p, ctx);
ok = fp4_equ_hex(r, sqr_a, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_sqr_v(r, a, p, ctx);
ok = fp4_equ_hex(r, sqrv_a, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_inv(r, a, p, ctx);
ok = fp4_equ_hex(r, inv_a, ctx);
printf("fp4 test %d: %s\n", __LINE__, ok ? "ok" : "error");
fp4_set_one(r);
fp4_inv(r, r, p, ctx);
ok = fp4_equ_hex(r, inv_1, ctx);