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sm9_math.c
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/*
* Copyright (c) 2014 - 2020 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 <stdlib.h>
#include <assert.h>
#include <gmssl/hex.h>
#include "endian.h"
typedef uint64_t bn_t[8];
typedef bn_t fp_t;
typedef bn_t fn_t;
typedef uint64_t barrett_bn_t[9];
typedef fp_t fp2_t[2];
typedef fp2_t fp4_t[2];
typedef fp4_t fp12_t[3];
static const bn_t ZERO = {0,0,0,0,0,0,0,0};
static const bn_t ONE = {1,0,0,0,0,0,0,0};
static const bn_t TWO = {2,0,0,0,0,0,0,0};
static const bn_t FIVE = {5,0,0,0,0,0,0,0};
// p = b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457d
// n = b640000002a3a6f1d603ab4ff58ec74449f2934b18ea8beee56ee19cd69ecf25
// mu = 2^512 // p = 167980e0beb5759a655f73aebdcd1312af2665f6d1e36081c71188f90d5c22146
static const bn_t SM9_P = {0xe351457d, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000};
static const bn_t SM9_P_MINUS_ONE = {0xe351457c, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000};
static const bn_t SM9_N = {0xd69ecf25, 0xe56ee19c, 0x18ea8bee, 0x49f2934b, 0xf58ec744, 0xd603ab4f, 0x02a3a6f1, 0xb6400000};
static const bn_t SM9_MU = {0xd5c22146, 0x71188f90, 0x1e36081c, 0xf2665f6d, 0xdcd1312a, 0x55f73aeb, 0xeb5759a6, 0x167980e0b};
typedef struct {
fp_t X;
fp_t Y;
fp_t Z;
} point_t;
// P1.X 0x93DE051D62BF718FF5ED0704487D01D6E1E4086909DC3280E8C4E4817C66DDDD
// P1.Y 0x21FE8DDA4F21E607631065125C395BBC1C1C00CBFA6024350C464CD70A3EA616
static const point_t _SM9_P1 = {
{0x7c66dddd, 0xe8c4e481, 0x09dc3280, 0xe1e40869, 0x487d01d6, 0xf5ed0704, 0x62bf718f, 0x93de051d},
{0x0a3ea616, 0x0c464cd7, 0xfa602435, 0x1c1c00cb, 0x5c395bbc, 0x63106512, 0x4f21e607, 0x21fe8dda},
{1,0,0,0,0,0,0,0}
};
static const point_t *SM9_P1 = &_SM9_P1;
typedef struct {
fp2_t X;
fp2_t Y;
fp2_t Z;
} twist_point_t;
/*
X : [0x3722755292130b08d2aab97fd34ec120ee265948d19c17abf9b7213baf82d65bn,
0x85aef3d078640c98597b6027b441a01ff1dd2c190f5e93c454806c11d8806141n],
Y : [0xa7cf28d519be3da65f3170153d278ff247efba98a71a08116215bba5c999a7c7n,
0x17509b092e845c1266ba0d262cbee6ed0736a96fa347c8bd856dc76b84ebeb96n],
Z : [1n, 0n],
*/
static const twist_point_t _SM9_P2 = {
{{0xAF82D65B, 0xF9B7213B, 0xD19C17AB, 0xEE265948, 0xD34EC120, 0xD2AAB97F, 0x92130B08, 0x37227552},
{0xD8806141, 0x54806C11, 0x0F5E93C4, 0xF1DD2C19, 0xB441A01F, 0x597B6027, 0x78640C98, 0x85AEF3D0}},
{{0xC999A7C7, 0x6215BBA5, 0xA71A0811, 0x47EFBA98, 0x3D278FF2, 0x5F317015, 0x19BE3DA6, 0xA7CF28D5},
{0x84EBEB96, 0x856DC76B, 0xA347C8BD, 0x0736A96F, 0x2CBEE6ED, 0x66BA0D26, 0x2E845C12, 0x17509B09}},
{{1,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}},
};
static const twist_point_t *SM9_P2 = &_SM9_P2;
#define bn_init(r) memset((r),0,sizeof(bn_t))
#define bn_clean(r) memset((r),0,sizeof(bn_t))
#define bn_set_zero(r) memset((r),0,sizeof(bn_t))
#define bn_set_one(r) memcpy((r),&ONE,sizeof(bn_t))
#define bn_copy(r,a) memcpy((r),(a),sizeof(bn_t))
#define bn_is_zero(a) (memcmp((a),&ZERO, sizeof(bn_t)) == 0)
#define bn_is_one(a) (memcmp((a),&ONE, sizeof(bn_t)) == 0)
static void bn_to_bytes(const bn_t a, uint8_t out[32])
{
int i;
for (i = 7; i >= 0; i--) {
PUTU32(out, (uint32_t)a[i]);
out += sizeof(uint32_t);
}
}
static void bn_from_bytes(bn_t r, const uint8_t in[32])
{
int i;
for (i = 7; i >= 0; i--) {
r[i] = GETU32(in);
in += sizeof(uint32_t);
}
}
static int bn_from_hex(bn_t r, const char hex[65])
{
uint8_t buf[32];
size_t len;
if (hex_to_bytes(hex, 64, buf, &len) < 0) {
return -1;
}
bn_from_bytes(r, buf);
return 0;
}
static void bn_to_hex(const bn_t a, char hex[65])
{
int i;
for (i = 7; i >= 0; i--) {
(void)sprintf(hex, "%08x", (uint32_t)a[i]);
hex += 8;
}
hex[64] = '0';
}
static void print_bn(const char *prefix, const bn_t a)
{
char hex[65];
bn_to_hex(a, hex);
printf("%s\n%s\n", prefix, hex);
}
static void bn_to_bits(const bn_t a, char bits[256])
{
int i, j;
for (i = 7; i >= 0; i--) {
uint32_t w = a[i];
for (j = 0; j < 32; j++) {
*bits++ = (w & 0x80000000) ? '1' : '0';
w <<= 1;
}
}
}
static int bn_cmp(const bn_t a, const bn_t b)
{
int i;
for (i = 7; i >= 0; i--) {
if (a[i] > b[i])
return 1;
if (a[i] < b[i])
return -1;
}
return 0;
}
static int bn_equ_hex(const bn_t a, const char *hex)
{
bn_t b;
bn_from_hex(b, hex);
return (bn_cmp(a, b) == 0);
}
static void bn_set_word(bn_t r, uint32_t a)
{
bn_set_zero(r);
r[0] = a;
}
static void bn_add(bn_t r, const bn_t a, const bn_t b)
{
int i;
r[0] = a[0] + b[0];
for (i = 1; i < 8; i++) {
r[i] = a[i] + b[i] + (r[i-1] >> 32);
}
for (i = 0; i < 7; i++) {
r[i] &= 0xffffffff;
}
}
static void bn_sub(bn_t ret, const bn_t a, const bn_t b)
{
int i;
bn_t r;
r[0] = ((uint64_t)1 << 32) + a[0] - b[0];
for (i = 1; i < 7; i++) {
r[i] = 0xffffffff + a[i] - b[i] + (r[i - 1] >> 32);
r[i - 1] &= 0xffffffff;
}
r[i] = a[i] - b[i] + (r[i - 1] >> 32) - 1;
r[i - 1] &= 0xffffffff;
bn_copy(ret, r);
}
static void bn_rand_range(bn_t r, const bn_t range)
{
FILE *fp;
uint8_t buf[256];
fp = fopen("/dev/urandom", "rb");
do {
fread(buf, 1, 256, fp);
bn_from_bytes(r, buf);
} while (bn_cmp(r, range) >= 0);
fclose(fp);
}
#define fp_init(a) bn_init(a)
#define fp_clean(a) bn_clean(a)
#define fp_is_zero(a) bn_is_zero(a)
#define fp_is_one(a) bn_is_one(a)
#define fp_set_zero(a) bn_set_zero(a)
#define fp_set_one(a) bn_set_one(a)
#define fp_from_hex(a,s) bn_from_hex((a),(s))
#define fp_to_hex(a,s) bn_to_hex((a),(s))
#define fp_copy(r,a) bn_copy((r),(a))
static int fp_equ(const fp_t a, const fp_t b)
{
int i;
for (i = 0; i < 8; i++) {
if (a[i] != b[i])
return 0;
}
return 1;
}
static void fp_add(fp_t r, const fp_t a, const fp_t b)
{
bn_add(r, a, b);
if (bn_cmp(r, SM9_P) >= 0)
return bn_sub(r, r, SM9_P);
}
static void fp_sub(fp_t r, const fp_t a, const fp_t b)
{
if (bn_cmp(a, b) >= 0) {
bn_sub(r, a, b);
} else {
bn_t t;
bn_sub(t, SM9_P, b);
bn_add(r, t, a);
}
}
static void fp_dbl(fp_t r, const fp_t a)
{
fp_add(r, a, a);
}
static void fp_tri(fp_t r, const fp_t a)
{
fp_t t;
fp_dbl(t, a);
fp_add(r, t, a);
}
static void fp_div2(fp_t r, const fp_t a)
{
int i;
bn_copy(r, a);
if (r[0] & 0x01) {
bn_add(r, r, SM9_P);
}
for (i = 0; i < 7; i++) {
r[i] = (r[i] >> 1) | ((r[i + 1] & 0x01) << 31);
}
r[i] >>= 1;
}
static void fp_neg(fp_t r, const fp_t a)
{
if (bn_is_zero(a)) {
bn_copy(r, a);
} else {
bn_sub(r, SM9_P, a);
}
}
static int barrett_bn_cmp(const barrett_bn_t a, const barrett_bn_t b)
{
int i;
for (i = 8; i >= 0; i--) {
if (a[i] > b[i])
return 1;
if (a[i] < b[i])
return -1;
}
return 0;
}
static void barrett_bn_add(barrett_bn_t r, const barrett_bn_t a, const barrett_bn_t b)
{
int i;
r[0] = a[0] + b[0];
for (i = 1; i < 9; i++) {
r[i] = a[i] + b[i] + (r[i-1] >> 32);
}
for (i = 0; i < 8; i++) {
r[i] &= 0xffffffff;
}
}
static void barrett_bn_sub(barrett_bn_t ret, const barrett_bn_t a, const barrett_bn_t b)
{
barrett_bn_t r;
int i;
r[0] = ((uint64_t)1 << 32) + a[0] - b[0];
for (i = 1; i < 8; i++) {
r[i] = 0xffffffff + a[i] - b[i] + (r[i - 1] >> 32);
r[i - 1] &= 0xffffffff;
}
r[i] = a[i] - b[i] + (r[i - 1] >> 32) - 1;
r[i - 1] &= 0xffffffff;
for (i = 0; i < 9; i++) {
ret[i] = r[i];
}
}
static void fp_mul(fp_t r, const fp_t a, const fp_t b)
{
uint64_t s[17];
barrett_bn_t zh, zl, q;
uint64_t w;
int i, j;
/* z = a * b */
for (i = 0; i < 8; i++) {
s[i] = 0;
}
for (i = 0; i < 8; i++) {
w = 0;
for (j = 0; j < 8; j++) {
w += s[i + j] + a[i] * b[j];
s[i + j] = w & 0xffffffff;
w >>= 32;
}
s[i + 8] = w;
}
/* zl = z mod (2^32)^9 = z[0..8]
* zh = z // (2^32)^7 = z[7..15] */
for (i = 0; i < 9; i++) {
zl[i] = s[i];
zh[i] = s[7 + i];
}
/* q = zh * mu // (2^32)^9 */
for (i = 0; i < 9; i++) {
s[i] = 0;
}
for (i = 0; i < 9; i++) {
w = 0;
for (j = 0; j < 8; j++) {
w += s[i + j] + zh[i] * SM9_MU[j];
s[i + j] = w & 0xffffffff;
w >>= 32;
}
s[i + 8] = w;
}
for (i = 0; i < 8; i++) {
q[i] = s[9 + i];
}
/* q = q * n mod (2^32)^9 */
for (i = 0; i < 8; i++) {
s[i] = 0;
}
for (i = 0; i < 8; i++) {
w = 0;
for (j = 0; j < 8; j++) {
w += s[i + j] + q[i] * SM9_N[j];
s[i + j] = w & 0xffffffff;
w >>= 32;
}
s[i + 8] = w;
}
for (i = 0; i < 9; i++) {
q[i] = s[i];
}
/* r = zl - q (mod (2^32)^9) */
if (barrett_bn_cmp(zl, q)) {
barrett_bn_sub(zl, zl, q);
} else {
barrett_bn_t c = {0,0,0,0,0,0,0,0,0x100000000};
barrett_bn_sub(q, c, q);
barrett_bn_add(zl, q, zl);
}
for (i = 0; i < 8; i++) {
r[i] = zl[i];
}
r[7] += zl[8] << 32;
/* while r >= p do: r = r - n */
while (bn_cmp(r, SM9_N) >= 0) {
bn_sub(r, r, SM9_N);
}
}
static void fp_sqr(fp_t r, const fp_t a)
{
fp_mul(r, a, a);
}
static void fp_pow(fp_t r, const fp_t a, const bn_t e)
{
fp_t t;
uint32_t w;
int i, j;
assert(bn_cmp(e, SM9_P_MINUS_ONE) < 0);
bn_set_one(t);
for (i = 7; i >= 0; i--) {
w = (uint32_t)e[i];
for (j = 0; j < 32; j++) {
fp_sqr(t, t);
if (w & 0x80000000)
fp_mul(t, t, a);
w <<= 1;
}
}
bn_copy(r, t);
}
static void fp_inv(fp_t r, const fp_t a)
{
fp_t e;
bn_sub(e, SM9_P, TWO);
fp_pow(r, a, e);
}
static void fn_add(fn_t r, const fn_t a, const fn_t b)
{
}
static void fn_sub(fn_t r, const fn_t a, const fn_t b)
{
}
static void fn_neg(fn_t r, const fn_t a)
{
}
static void fn_inv(fn_t r, const fn_t a)
{
}
static const fp2_t FP2_ZERO = {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}};
static const fp2_t FP2_ONE = {{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}};
static const fp2_t FP2_U = {{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0}};
static const fp2_t FP2_5U = {{0,0,0,0,0,0,0,0},{5,0,0,0,0,0,0,0}};
#define fp2_init(a) memset((a), 0, sizeof(fp2_t))
#define fp2_clean(a) memset((a), 0, sizeof(fp2_t))
#define fp2_is_zero(a) (memcmp((a), &FP2_ZERO, sizeof(fp2_t)) == 0)
#define fp2_is_one(a) (memcmp((a), &FP2_ONE, sizeof(fp2_t)) == 0)
#define fp2_copy(r,a) memcpy((r), (a), sizeof(fp2_t))
#define fp2_equ(a,b) (memcmp((a),(b),sizeof(fp2_t)) == 0)
static void fp2_from_hex(fp2_t r, const char hex[65 * 2])
{
fp_from_hex(r[1], hex);
fp_from_hex(r[0], hex + 65);
}
static void fp2_to_hex(const fp2_t a, char hex[65 * 2])
{
fp_to_hex(a[1], hex);
hex[64] = '\n';
fp_to_hex(a[0], hex + 65);
}
static void fp2_print(const char *prefix, const fp2_t a)
{
char hex[65 * 2];
fp2_to_hex(a, hex);
printf("%s\n%s\n", prefix, hex);
}
#define fp2_set_zero(a) memset((a), 0, sizeof(fp2_t))
#define fp2_set_one(a) memcpy((a), &FP2_ONE, sizeof(fp2_t))
static void fp2_set_fp(fp2_t r, const fp_t a)
{
fp_copy(r[0], a);
fp_set_zero(r[1]);
}
#define fp2_set_u(a) memcpy((a), &FP2_U, sizeof(fp2_t))
static void fp2_set(fp2_t r, const fp_t a0, const fp_t a1)
{
fp_copy(r[0], a0);
fp_copy(r[1], a1);
}
static void fp2_add(fp2_t r, const fp2_t a, const fp2_t b)
{
fp_add(r[0], a[0], b[0]);
fp_add(r[1], a[1], b[1]);
}
static void fp2_dbl(fp2_t r, const fp2_t a)
{
fp_dbl(r[0], a[0]);
fp_dbl(r[1], a[1]);
}
static void fp2_tri(fp2_t r, const fp2_t a)
{
fp_tri(r[0], a[0]);
fp_tri(r[1], a[1]);
}
static void fp2_sub(fp2_t r, const fp2_t a, const fp2_t b)
{
fp_sub(r[0], a[0], b[0]);
fp_sub(r[1], a[1], b[1]);
}
static void fp2_neg(fp2_t r, const fp2_t a)
{
fp_neg(r[0], a[0]);
fp_neg(r[1], a[1]);
}
static void fp2_mul(fp2_t r, const fp2_t a, const fp2_t b)
{
fp_t r0, r1, t;
// r0 = a0 * b0 - 2 * a1 * b1
fp_mul(r0, a[0], b[0]);
fp_mul(t, a[1], b[1]);
fp_dbl(t, t);
fp_sub(r0, r0, t);
// r1 = a0 * b1 + a1 * b0
fp_mul(r1, a[0], b[1]);
fp_mul(t, a[1], b[0]);
fp_add(r1, r1, t);
fp_copy(r[0], r0);
fp_copy(r[1], r1);
}
static void fp2_mul_u(fp2_t r, const fp2_t a, const fp2_t b)
{
fp_t r0, r1, t;
// r0 = -2 * (a0 * b1 + a1 * b0)
fp_mul(r0, a[0], b[1]);
fp_mul(t, a[1], b[0]);
fp_add(r0, r0, t);
fp_dbl(r0, r0);
fp_neg(r0, r0);
// r1 = a0 * b0 - 2 * a1 * b1
fp_mul(r1, a[0], b[0]);
fp_mul(t, a[1], b[1]);
fp_dbl(t, t);
fp_sub(r1, r1, t);
fp_copy(r[0], r0);
fp_copy(r[1], r1);
}
static void fp2_mul_fp(fp2_t r, const fp2_t a, const fp_t k)
{
fp_mul(r[0], a[0], k);
fp_mul(r[1], a[1], k);
}
static void fp2_sqr(fp2_t r, const fp2_t a)
{
fp_t r0, r1, t;
// a0^2 - 2 * a1^2
fp_sqr(r0, a[0]);
fp_sqr(t, a[1]);
fp_dbl(t, t);
fp_sub(r0, r0, t);
// r1 = 2 * a0 * a1
fp_mul(r1, a[0], a[1]);
fp_dbl(r1, r1);
bn_copy(r[0], r0);
bn_copy(r[1], r1);
}
static void fp2_sqr_u(fp2_t r, const fp2_t a)
{
fp_t r0, r1, t;
// r0 = -4 * a0 * a1
fp_mul(r0, a[0], a[1]);
fp_dbl(r0, r0);
fp_dbl(r0, r0);
fp_neg(r0, r0);
// r1 = a0^2 - 2 * a1^2
fp_sqr(r1, a[0]);
fp_sqr(t, a[1]);
fp_dbl(t, t);
fp_sub(r1, r1, t);
fp_copy(r[0], r0);
fp_copy(r[1], r1);
}
static void fp2_inv(fp2_t r, const fp2_t a)
{
if (fp_is_zero(a[0])) {
// r0 = 0
fp_set_zero(r[0]);
// r1 = -(2 * a1)^-1
fp_dbl(r[1], a[1]);
fp_inv(r[1], r[1]);
fp_neg(r[1], r[1]);
} else if (fp_is_zero(a[1])) {
/* r1 = 0 */
fp_set_zero(r[1]);
/* r0 = a0^-1 */
fp_inv(r[0], a[0]);
} else {
fp_t k, t;
// k = (a[0]^2 + 2 * a[1]^2)^-1
fp_sqr(k, a[0]);
fp_sqr(t, a[1]);
fp_dbl(t, t);
fp_add(k, k, t);
fp_inv(k, k);
// r[0] = a[0] * k
fp_mul(r[0], a[0], k);
// r[1] = -a[1] * k
fp_mul(r[1], a[1], k);
fp_neg(r[1], r[1]);
}
}
static void fp2_div(fp2_t r, const fp2_t a, const fp2_t b)
{
fp2_t t;
fp2_inv(t, b);
fp2_mul(r, a, t);
}
static void fp2_div2(fp2_t r, const fp2_t a)
{
fp_div2(r[0], a[0]);
fp_div2(r[1], a[1]);
}
static const fp4_t FP4_ZERO = {{{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}}};
static const fp4_t FP4_ONE = {{{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}, {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}};
static const fp4_t FP4_U = {{{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0}}, {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}};
static const fp4_t FP4_V = {{{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}, {{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}};
#define fp4_init(r) memcpy((r), &FP4_ZERO, sizeof(fp4_t))
#define fp4_clean(r) memcpy((r), &FP4_ZERO, sizeof(fp4_t))
#define fp4_set_zero(r) memcpy((r), &FP4_ZERO, sizeof(fp4_t))
#define fp4_set_one(r) memcpy((r), &FP4_ONE, sizeof(fp4_t))
#define fp4_is_zero(a) (memcmp((a), &FP4_ZERO, sizeof(fp4_t)) == 0)
#define fp4_is_one(a) (memcmp((a), &FP4_ONE, sizeof(fp4_t)) == 0)
#define fp4_equ(a,b) (memcmp((a), (b), sizeof(fp4_t)) == 0)
#define fp4_copy(r,a) memcpy((r), (a), sizeof(fp4_t))
static void fp4_from_hex(fp4_t r, const char hex[65 * 4])
{
fp2_from_hex(r[1], hex);
fp2_from_hex(r[0], hex + 65 * 2);
}
static void fp4_to_hex(const fp4_t a, char hex[65 * 4])
{
fp2_to_hex(a[1], hex);
hex[65 + 64] = '\n';
fp2_to_hex(a[0], hex + 65 * 2);
}
static void fp4_set_fp(fp4_t r, const fp_t a)
{
fp2_set_fp(r[0], a);
fp2_set_zero(r[1]);
}
static void fp4_set_fp2(fp4_t r, const fp2_t a)
{
fp2_copy(r[0], a);
fp2_set_zero(r[1]);
}
static void fp4_set(fp4_t r, const fp2_t a0, const fp2_t a1)
{
fp2_copy(r[0], a0);
fp2_copy(r[1], a1);
}
/*
static void fp4_set_one(fp4_t r)
{
fp2_set_one(r[0]);
fp2_set_zero(r[1]);
}
*/
static void fp4_set_u(fp4_t r)
{
fp2_set_u(r[0]);
fp2_set_zero(r[1]);
}
static void fp4_set_v(fp4_t r)
{
fp2_set_zero(r[0]);
fp2_set_one(r[1]);
}
static void fp4_add(fp4_t r, const fp4_t a, const fp4_t b)
{
fp2_add(r[0], a[0], b[0]);
fp2_add(r[1], a[1], b[1]);
}
static void fp4_dbl(fp4_t r, const fp4_t a)
{
fp2_dbl(r[0], a[0]);
fp2_dbl(r[1], a[1]);
}
static void fp4_sub(fp4_t r, const fp4_t a, const fp4_t b)
{
fp2_sub(r[0], a[0], b[0]);
fp2_sub(r[1], a[1], b[1]);
}
static void fp4_neg(fp4_t r, const fp4_t a)
{
fp2_neg(r[0], a[0]);
fp2_neg(r[1], a[1]);
}
static void fp4_mul(fp4_t r, const fp4_t a, const fp4_t b)
{
fp2_t r0, r1, t;
fp2_mul(r0, a[0], b[0]);
fp2_mul_u(t, a[1], b[1]);
fp2_add(r0, r0, t);
fp2_mul(r1, a[0], b[1]);
fp2_mul(t, a[1], b[0]);
fp2_add(r1, r1, t);
fp2_copy(r[0], r0);
fp2_copy(r[1], r1);
}
static void fp4_mul_fp(fp4_t r, const fp4_t a, const fp_t k)
{
fp2_mul_fp(r[0], a[0], k);
fp2_mul_fp(r[1], a[1], k);
}
static void fp4_mul_fp2(fp4_t r, const fp4_t a, const fp2_t b0)
{
fp2_mul(r[0], a[0], b0);
fp2_mul(r[1], a[1], b0);
}
static void fp4_mul_v(fp4_t r, const fp4_t a, const fp4_t b)
{
fp2_t r0, r1, t;
fp2_mul_u(r0, a[0], b[1]);
fp2_mul_u(t, a[1], b[0]);
fp2_add(r0, r0, t);
fp2_mul(r1, a[0], b[0]);
fp2_mul_u(t, a[1], b[1]);
fp2_add(r1, r1, t);
fp2_copy(r[0], r0);
fp2_copy(r[1], r1);
}
static void fp4_sqr(fp4_t r, const fp4_t a)
{
fp2_t r0, r1, t;
fp2_sqr(r0, a[0]);
fp2_sqr_u(t, a[1]);
fp2_add(r0, r0, t);
fp2_mul(r1, a[0], a[1]);
fp2_dbl(r1, r1);
fp2_copy(r[0], r0);
fp2_copy(r[1], r1);
}
static void fp4_sqr_v(fp4_t r, const fp4_t a)
{
fp2_t r0, r1, t;
fp2_mul_u(t, a[0], a[1]);
fp2_dbl(r0, t);
fp2_sqr(r1, a[0]);
fp2_sqr_u(t, a[1]);
fp2_add(r1, r1, t);
fp2_copy(r[0], r0);
fp2_copy(r[1], r1);
}
static void fp4_inv(fp4_t r, const fp4_t a)
{
fp2_t r0, r1, k;
fp2_sqr_u(k, a[1]);
fp2_sqr(r0, a[0]);
fp2_sub(k, k, r0);
fp2_inv(k, k);
fp2_mul(r0, a[0], k);
fp2_neg(r0, r0);
fp2_mul(r1, a[1], k);
fp2_copy(r[0], r0);
fp2_copy(r[1], r1);
}
#define fp12_init(r) memset((r), 0, sizeof(fp12_t))
#define fp12_clean(r) memset((r), 0, sizeof(fp12_t))
#define fp12_set_zero(r) memset((r), 0, sizeof(fp12_t))
#define fp12_copy(r, a) memcpy((r), (a), sizeof(fp12_t))
static void fp12_set_one(fp12_t r)
{
fp4_set_one(r[0]);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static int fp12_is_one(const fp12_t a)
{
return fp4_is_one(a[0])
&& fp4_is_zero(a[1])
&& fp4_is_zero(a[2]);
}
static int fp12_is_zero(const fp12_t a)
{
return fp4_is_zero(a[0])
&& fp4_is_zero(a[1])
&& fp4_is_zero(a[2]);
}
static void fp12_from_hex(fp12_t r, const char hex[65 * 12])
{
fp4_from_hex(r[2], hex);
fp4_from_hex(r[1], hex + 65 * 4);
fp4_from_hex(r[0], hex + 65 * 8);
}
static void fp12_to_hex(const fp12_t a, char hex[65 * 12])
{
fp4_to_hex(a[2], hex);
hex[65 * 4 - 1] = '\n';
fp4_to_hex(a[1], hex + 65 * 4);
hex[65 * 8 - 1] = '\n';
fp4_to_hex(a[0], hex + 65 * 8);
}
static void fp12_print(const char *prefix, const fp12_t a)
{
char hex[65 * 12];
fp12_to_hex(a, hex);
printf("%s\n%s\n", prefix, hex);
}
static void fp12_set(fp12_t r, const fp4_t a0, const fp4_t a1, const fp4_t a2)
{
fp4_copy(r[0], a0);
fp4_copy(r[1], a1);
fp4_copy(r[2], a2);
}
static void fp12_set_fp(fp12_t r, const fp_t a)
{
fp4_set_fp(r[0], a);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_fp2(fp12_t r, const fp2_t a)
{
fp4_set_fp2(r[0], a);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_fp4(fp12_t r, const fp4_t a)
{
fp4_copy(r[0], a);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_u(fp12_t r)
{
fp4_set_u(r[0]);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_v(fp12_t r)
{
fp4_set_v(r[0]);
fp4_set_zero(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_w(fp12_t r)
{
fp4_set_zero(r[0]);
fp4_set_one(r[1]);
fp4_set_zero(r[2]);
}
static void fp12_set_w_sqr(fp12_t r)
{
fp4_set_zero(r[0]);
fp4_set_zero(r[1]);
fp4_set_one(r[2]);
}
static int fp12_equ(const fp12_t a, const fp12_t b)
{
return fp4_equ(a[0], b[0])