diff --git a/src/sm9_alg.c b/src/sm9_alg.c deleted file mode 100644 index 0c021d73..00000000 --- a/src/sm9_alg.c +++ /dev/null @@ -1,2544 +0,0 @@ -/* - * Copyright 2014-2022 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 -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - - -const sm9_bn_t SM9_ZERO = {0,0,0,0,0,0,0,0}; -const sm9_bn_t SM9_ONE = {1,0,0,0,0,0,0,0}; -static const sm9_bn_t SM9_TWO = {2,0,0,0,0,0,0,0}; -static const sm9_bn_t SM9_FIVE = {5,0,0,0,0,0,0,0}; - - -// p = b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457d -// n = b640000002a3a6f1d603ab4ff58ec74449f2934b18ea8beee56ee19cd69ecf25 -// mu_p = 2^512 // p = 167980e0beb5759a655f73aebdcd1312af2665f6d1e36081c71188f90d5c22146 -// mu_n = 2^512 // n -const sm9_bn_t SM9_P = {0xe351457d, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; -const sm9_bn_t SM9_N = {0xd69ecf25, 0xe56ee19c, 0x18ea8bee, 0x49f2934b, 0xf58ec744, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; -static const sm9_bn_t SM9_P_MINUS_ONE = {0xe351457c, 0xe56f9b27, 0x1a7aeedb, 0x21f2934b, 0xf58ec745, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; -static const sm9_bn_t SM9_N_MINUS_ONE = {0xd69ecf24, 0xe56ee19c, 0x18ea8bee, 0x49f2934b, 0xf58ec744, 0xd603ab4f, 0x02a3a6f1, 0xb6400000}; -static const sm9_barrett_bn_t SM9_MU_P = {0xd5c22146, 0x71188f90, 0x1e36081c, 0xf2665f6d, 0xdcd1312a, 0x55f73aeb, 0xeb5759a6, 0x67980e0b, 0x00000001}; -static const sm9_barrett_bn_t SM9_MU_N = {0xdfc97c2f, 0x74df4fd4, 0xc9c073b0, 0x9c95d85e, 0xdcd1312c, 0x55f73aeb, 0xeb5759a6, 0x67980e0b, 0x00000001}; -static const sm9_barrett_bn_t SM9_MU_N_MINUS_ONE = {0xdfc97c31, 0x74df4fd4, 0xc9c073b0, 0x9c95d85e, 0xdcd1312c, 0x55f73aeb, 0xeb5759a6, 0x67980e0b, 0x00000001}; - - -// P1.X 0x93DE051D62BF718FF5ED0704487D01D6E1E4086909DC3280E8C4E4817C66DDDD -// P1.Y 0x21FE8DDA4F21E607631065125C395BBC1C1C00CBFA6024350C464CD70A3EA616 -const SM9_POINT _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} -}; -const SM9_POINT *SM9_P1 = &_SM9_P1; - - -/* - X : [0x3722755292130b08d2aab97fd34ec120ee265948d19c17abf9b7213baf82d65bn, - 0x85aef3d078640c98597b6027b441a01ff1dd2c190f5e93c454806c11d8806141n], - Y : [0xa7cf28d519be3da65f3170153d278ff247efba98a71a08116215bba5c999a7c7n, - 0x17509b092e845c1266ba0d262cbee6ed0736a96fa347c8bd856dc76b84ebeb96n], - Z : [1n, 0n], -*/ -const SM9_TWIST_POINT _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}}, -}; -const SM9_TWIST_POINT *SM9_P2 = &_SM9_P2; - - -const SM9_TWIST_POINT _SM9_Ppubs = { - {{0x96EA5E32, 0x8F14D656, 0x386A92DD, 0x414D2177, 0x24A3B573, 0x6CE843ED, 0x152D1F78, 0x29DBA116}, - {0x1B94C408, 0x0AB1B679, 0x5E392CFB, 0x1CE0711C, 0x41B56501, 0xE48AFF4B, 0x3084F733, 0x9F64080B}}, - {{0xB4E3216D, 0x0E75C05F, 0x5CDFF073, 0x1006E85F, 0xB7A46F74, 0x1A7CE027, 0xDDA532DA, 0x41E00A53}, - {0xD0EF1C25, 0xE89E1408, 0x1A77F335, 0xAD3E2FDB, 0x47E3A0CB, 0xB57329F4, 0xABEA0112, 0x69850938}}, - {{1,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}}, -}; -const SM9_TWIST_POINT *SM9_Ppubs = &_SM9_Ppubs; - - -void sm9_bn_set_zero(sm9_bn_t r) -{ - sm9_bn_copy(r, SM9_ZERO); -} - -void sm9_bn_set_one(sm9_bn_t r) -{ - sm9_bn_copy(r, SM9_ONE); -} - -int sm9_bn_is_zero(const sm9_bn_t a) -{ - return (sm9_bn_cmp(a, SM9_ZERO) == 0); -} - -int sm9_bn_is_one(const sm9_bn_t a) -{ - return (sm9_bn_cmp(a, SM9_ONE) == 0); -} - -void sm9_bn_to_bytes(const sm9_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); - } -} - -void sm9_bn_from_bytes(sm9_bn_t r, const uint8_t in[32]) -{ - int i; - for (i = 7; i >= 0; i--) { - r[i] = GETU32(in); - in += sizeof(uint32_t); - } -} - -int sm9_bn_from_hex(sm9_bn_t r, const char hex[64]) -{ - uint8_t buf[32]; - size_t len; - if (hex_to_bytes(hex, 64, buf, &len) < 0) { - return -1; - } - sm9_bn_from_bytes(r, buf); - return 1; -} - -void sm9_bn_to_hex(const sm9_bn_t a, char hex[64]) -{ - int i; - for (i = 7; i >= 0; i--) { - (void)sprintf(hex + 8*(7-i), "%08x", (uint32_t)a[i]); - //hex += 8; - } -} - -void sm9_print_bn(const char *prefix, const sm9_bn_t a) -{ - char hex[65] = {0}; - sm9_bn_to_hex(a, hex); - printf("%s\n%s\n", prefix, hex); -} - -void sm9_bn_to_bits(const sm9_bn_t a, char bits[256]) -{ - int i, j; - for (i = 7; i >= 0; i--) { - uint32_t w = (uint32_t)a[i]; - for (j = 0; j < 32; j++) { - *bits++ = (w & 0x80000000) ? '1' : '0'; - w <<= 1; - } - } -} - -int sm9_bn_cmp(const sm9_bn_t a, const sm9_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; -} - -void sm9_bn_copy(sm9_bn_t r, const sm9_bn_t a) -{ - memcpy(r, a, sizeof(sm9_bn_t)); -} - -void sm9_bn_set_word(sm9_bn_t r, uint32_t a) -{ - sm9_bn_set_zero(r); - r[0] = a; -} - -void sm9_bn_add(sm9_bn_t r, const sm9_bn_t a, const sm9_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; - } -} - -void sm9_bn_sub(sm9_bn_t ret, const sm9_bn_t a, const sm9_bn_t b) -{ - int i; - sm9_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; - sm9_bn_copy(ret, r); -} - -int sm9_bn_rand_range(sm9_bn_t r, const sm9_bn_t range) -{ - uint8_t buf[256]; - - do { - rand_bytes(buf, sizeof(buf)); - sm9_bn_from_bytes(r, buf); - } while (sm9_bn_cmp(r, range) >= 0); - return 1; -} - -int sm9_bn_equ(const sm9_bn_t a, const sm9_bn_t b) -{ - int i; - for (i = 0; i < 8; i++) { - if (a[i] != b[i]) - return 0; - } - return 1; -} - -void sm9_fp_add(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) -{ - sm9_bn_add(r, a, b); - if (sm9_bn_cmp(r, SM9_P) >= 0) { - sm9_bn_sub(r, r, SM9_P); - } -} - -void sm9_fp_sub(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) -{ - if (sm9_bn_cmp(a, b) >= 0) { - sm9_bn_sub(r, a, b); - } else { - sm9_bn_t t; - sm9_bn_sub(t, SM9_P, b); - sm9_bn_add(r, t, a); - } -} - -void sm9_fp_dbl(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_add(r, a, a); -} - -void sm9_fp_tri(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_t t; - sm9_fp_dbl(t, a); - sm9_fp_add(r, t, a); -} - -void sm9_fp_div2(sm9_fp_t r, const sm9_fp_t a) -{ - int i; - sm9_bn_copy(r, a); - if (r[0] & 0x01) { - sm9_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; -} - -void sm9_fp_neg(sm9_fp_t r, const sm9_fp_t a) -{ - if (sm9_bn_is_zero(a)) { - sm9_bn_copy(r, a); - } else { - sm9_bn_sub(r, SM9_P, a); - } -} - -int sm9_bn_print(FILE *fp, int fmt, int ind, const char *label, const sm9_bn_t a) -{ - uint8_t buf[32]; - sm9_bn_to_bytes(a, buf); - format_bytes(fp, fmt, ind, label, buf, sizeof(buf)); - return 1; -} - -int sm9_barrett_bn_cmp(const sm9_barrett_bn_t a, const sm9_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; -} - -void sm9_barrett_bn_add(sm9_barrett_bn_t r, const sm9_barrett_bn_t a, const sm9_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; - } -} - -void sm9_barrett_bn_sub(sm9_barrett_bn_t ret, const sm9_barrett_bn_t a, const sm9_barrett_bn_t b) -{ - sm9_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]; - } -} - -// w = -p^-1 mod 2^256 = 0xafd2bac5558a13b3966a4b291522b137181ae39613c8dbaf892bc42c2f2ee42b -// 2^512 mod p = 0x2ea795a656f62fbde479b522d6706e7b88f8105fae1a5d3f27dea312b417e2d2 -const sm9_bn_t SM9_W = {0x2f2ee42b, 0x892bc42c, 0x13c8dbaf, 0x181ae396, 0x1522b137, 0x966a4b29, 0x558a13b3, 0xafd2bac5}; -const sm9_bn_t SM9_2e512modp = {0xb417e2d2, 0x27dea312, 0xae1a5d3f, 0x88f8105f, 0xd6706e7b, 0xe479b522, 0x56f62fbd, 0x2ea795a6}; - -void sm9_fp_to_mont(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_mul_mont(r, a, SM9_2e512modp); -} - -void sm9_fp_from_mont(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_mul_mont(r, a, SM9_ONE); -} - -void sm9_bn_mul(sm9_bn_t r1, sm9_bn_t r2, const sm9_bn_t a, const sm9_bn_t b) -{ - int i, j; - uint64_t s[16]; - uint64_t w; - - for (i = 0; i < 16; 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; - } - for (i = 0; i < 8; i++) { - r1[i] = s[i]; // low 256 - r2[i] = s[i + 8]; // high 256 - } -} - -void sm9_bn_add_512(sm9_bn_t r1, sm9_bn_t r2, - const sm9_bn_t a1, const sm9_bn_t a2, - const sm9_bn_t b1, const sm9_bn_t b2) -{ - int i, over; - - r1[0] = a1[0] + b1[0]; - for (i = 1; i < 8; i++) { - r1[i] = a1[i] + b1[i] + (r1[i-1] >> 32); - } - r2[0] = a2[0] + b2[0] + (r1[7] >> 32); - for (i = 1; i < 8; i++) { - r2[i] = a2[i] + b2[i] + (r2[i-1] >> 32); - } - for (i = 0; i < 7; i++) { - r1[i] &= 0xffffffff; - r2[i] &= 0xffffffff; - } - r1[7] &= 0xffffffff; -} - -void sm9_fp_mul_mont(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) -{ - sm9_bn_t z1, z2, u1, u2; - int i, j; - - // z = x * y mod 2^256 - sm9_bn_mul(z1, z2, a, b); - - // u = z * w mod 2^256 - sm9_bn_mul(u1, u2, z1, SM9_W); - - // s = (x * y + u * p) - sm9_bn_mul(u1, u2, u1, SM9_P); - sm9_bn_add_512(z1, r, z1, z2, u1, u2); - - if (sm9_bn_cmp(r, SM9_P) >= 0) { - sm9_bn_sub(r, r, SM9_P); - } -} - -void sm9_fp_mul(sm9_fp_t r, const sm9_fp_t a, const sm9_fp_t b) -{ - uint64_t s[18]; - sm9_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 < 9; j++) { - w += s[i + j] + zh[i] * SM9_MU_P[j]; - s[i + j] = w & 0xffffffff; - w >>= 32; - } - s[i + 9] = w; - } - for (i = 0; i < 9; i++) { - q[i] = s[9 + i]; - } - - /* q = q * p mod (2^32)^9 */ - for (i = 0; i < 8; i++) { - s[i] = 0; - } - w = 0; - for (j = 0; j < 8; j++) { - w += s[j] + q[0] * SM9_P[j]; - s[j] = w & 0xffffffff; - w >>= 32; - } - s[8] = w; - for (i = 1; i < 9; i++) { - w = 0; - for (j = 0; i + j < 9; j++) { - w += s[i + j] + q[i] * SM9_P[j]; - s[i + j] = w & 0xffffffff; - w >>= 32; - } - } - for (i = 0; i < 9; i++) { - q[i] = s[i]; - } - - /* r = zl - q (mod (2^32)^9) */ - - if (sm9_barrett_bn_cmp(zl, q)) { - sm9_barrett_bn_sub(zl, zl, q); - } else { - sm9_barrett_bn_t c = {0,0,0,0,0,0,0,0,0x100000000}; - sm9_barrett_bn_sub(q, c, q); - sm9_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 - p */ - while (sm9_bn_cmp(r, SM9_P) >= 0) { - - sm9_bn_sub(r, r, SM9_P); - } -} - -void sm9_fp_sqr(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_mul(r, a, a); -} - -void sm9_fp_pow(sm9_fp_t r, const sm9_fp_t a, const sm9_bn_t e) -{ - sm9_fp_t t; - uint32_t w; - int i, j; - - assert(sm9_bn_cmp(e, SM9_P_MINUS_ONE) < 0); - - sm9_bn_set_one(t); - for (i = 7; i >= 0; i--) { - w = (uint32_t)e[i]; - for (j = 0; j < 32; j++) { - sm9_fp_sqr(t, t); - if (w & 0x80000000) - sm9_fp_mul(t, t, a); - w <<= 1; - } - } - sm9_bn_copy(r, t); -} - -void sm9_fp_inv(sm9_fp_t r, const sm9_fp_t a) -{ - sm9_fp_t e; - sm9_bn_sub(e, SM9_P, SM9_TWO); - sm9_fp_pow(r, a, e); -} - -int sm9_fp_from_bytes(sm9_fp_t r, const uint8_t buf[32]) -{ - sm9_bn_from_bytes(r, buf); - if (sm9_bn_cmp(r, SM9_P) >= 0) { - error_print(); - return -1; - } - return 1; -} - -int sm9_fp_from_hex(sm9_fp_t r, const char hex[64]) -{ - if (sm9_bn_from_hex(r, hex) != 1) { - error_print(); - return -1; - } - if (sm9_bn_cmp(r, SM9_P) >= 0) { - error_print(); - return -1; - } - return 1; -} - - -const sm9_fp2_t SM9_FP2_ZERO = {{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}; -const sm9_fp2_t SM9_FP2_ONE = {{1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}; -const sm9_fp2_t SM9_FP2_U = {{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0}}; -static const sm9_fp2_t SM9_FP2_5U = {{0,0,0,0,0,0,0,0},{5,0,0,0,0,0,0,0}}; - -int sm9_fp2_equ(const sm9_fp2_t a, const sm9_fp2_t b) -{ - return (gmssl_secure_memcmp(a, b, sizeof(sm9_fp2_t)) == 0); -} - -void sm9_fp2_copy(sm9_fp2_t r, const sm9_fp2_t a) -{ - memcpy(r, a, sizeof(sm9_fp2_t)); -} - -int sm9_fp2_rand(sm9_fp2_t r) -{ - if (sm9_fp_rand(r[0]) != 1 - || sm9_fp_rand(r[1]) != 1) { - error_print(); - return -1; - } - return 1; -} - -void sm9_fp2_to_bytes(const sm9_fp2_t a, uint8_t buf[64]) -{ - sm9_fp_to_bytes(a[1], buf); - sm9_fp_to_bytes(a[0], buf + 32); -} - -int sm9_fp2_from_bytes(sm9_fp2_t r, const uint8_t buf[64]) -{ - if (sm9_fp_from_bytes(r[1], buf) != 1 - || sm9_fp_from_bytes(r[0], buf + 32) != 1) { - error_print(); - return -1; - } - return 1; -} - -int sm9_fp2_from_hex(sm9_fp2_t r, const char hex[129]) -{ - if (sm9_fp_from_hex(r[1], hex) != 1 - || sm9_fp_from_hex(r[0], hex + 65) != 1) { - error_print(); - return -1; - } - /* - if (hex[64] != SM9_HEX_SEP) { - error_print(); - return -1; - } - */ - return 1; -} - -void sm9_fp2_to_hex(const sm9_fp2_t a, char hex[129]) -{ - sm9_fp_to_hex(a[1], hex); - hex[64] = SM9_HEX_SEP; - sm9_fp_to_hex(a[0], hex + 65); -} - -void sm9_fp2_set_fp(sm9_fp2_t r, const sm9_fp_t a) -{ - sm9_fp_copy(r[0], a); - sm9_fp_set_zero(r[1]); -} - -void sm9_fp2_set(sm9_fp2_t r, const sm9_fp_t a0, const sm9_fp_t a1) -{ - sm9_fp_copy(r[0], a0); - sm9_fp_copy(r[1], a1); -} - -void sm9_fp2_add(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) -{ - sm9_fp_add(r[0], a[0], b[0]); - sm9_fp_add(r[1], a[1], b[1]); -} - -void sm9_fp2_dbl(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_dbl(r[0], a[0]); - sm9_fp_dbl(r[1], a[1]); -} - -void sm9_fp2_tri(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_tri(r[0], a[0]); - sm9_fp_tri(r[1], a[1]); -} - -void sm9_fp2_sub(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) -{ - sm9_fp_sub(r[0], a[0], b[0]); - sm9_fp_sub(r[1], a[1], b[1]); -} - -void sm9_fp2_neg(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_neg(r[0], a[0]); - sm9_fp_neg(r[1], a[1]); -} - -void sm9_fp2_a_mul_u(sm9_fp2_t r, sm9_fp2_t a) { - sm9_fp_t r0; - - sm9_fp_dbl(r0, a[1]); - sm9_fp_neg(r0, r0); - - sm9_fp_copy(r[1], a[0]); - sm9_fp_copy(r[0], r0); -} - -void sm9_fp2_mul(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) -{ - sm9_fp_t r0, r1, t; - - sm9_fp_add(r0, a[0], a[1]); - sm9_fp_add(t, b[0], b[1]); - sm9_fp_mul(r1, t, r0); - - // r0 = a0 * b0 - 2 * a1 * b1 - sm9_fp_mul(r0, a[0], b[0]); - sm9_fp_mul(t, a[1], b[1]); - - // r1 = (a0 + a1) * (b0 + b1) - a0 * b0 - a1 * b1 - sm9_fp_sub(r1, r1, r0); - sm9_fp_sub(r1, r1, t); - - // r0 - sm9_fp_dbl(t, t); - sm9_fp_sub(r0, r0, t); - - sm9_fp_copy(r[0], r0); - sm9_fp_copy(r[1], r1); -} - -void sm9_fp2_mul_u(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) -{ - sm9_fp_t r0, r1, t; - - // r0 = -2 * (a0 * b1 + a1 * b0) - sm9_fp_mul(r0, a[0], b[1]); - sm9_fp_mul(t, a[1], b[0]); - sm9_fp_add(r0, r0, t); - sm9_fp_dbl(r0, r0); - sm9_fp_neg(r0, r0); - - // r1 = a0 * b0 - 2 * a1 * b1 - sm9_fp_mul(r1, a[0], b[0]); - sm9_fp_mul(t, a[1], b[1]); - sm9_fp_dbl(t, t); - sm9_fp_sub(r1, r1, t); - - sm9_fp_copy(r[0], r0); - sm9_fp_copy(r[1], r1); -} - -void sm9_fp2_mul_fp(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp_t k) -{ - sm9_fp_mul(r[0], a[0], k); - sm9_fp_mul(r[1], a[1], k); -} - -void sm9_fp2_sqr(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_t r0, r1, c0, c1; - - // r0 = (a0 + a1) * (a0 - 2a1) + a0 * a1 - sm9_fp_mul(r1, a[0], a[1]); - sm9_fp_add(c0, a[0], a[1]); - sm9_fp_dbl(c1, a[1]); - sm9_fp_sub(c1, a[0], c1); - sm9_fp_mul(r0, c0, c1); - sm9_fp_add(r0, r0, r1); - - // r1 = 2 * a0 * a1 - sm9_fp_dbl(r1, r1); - - sm9_bn_copy(r[0], r0); - sm9_bn_copy(r[1], r1); -} - -void sm9_fp2_sqr_u(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_t r0, r1, t; - - // r0 = -4 * a0 * a1 - sm9_fp_mul(r0, a[0], a[1]); - sm9_fp_dbl(r0, r0); - sm9_fp_dbl(r0, r0); - sm9_fp_neg(r0, r0); - - // r1 = a0^2 - 2 * a1^2 - sm9_fp_sqr(r1, a[0]); - sm9_fp_sqr(t, a[1]); - sm9_fp_dbl(t, t); - sm9_fp_sub(r1, r1, t); - - sm9_fp_copy(r[0], r0); - sm9_fp_copy(r[1], r1); - -} - -void sm9_fp2_inv(sm9_fp2_t r, const sm9_fp2_t a) -{ - if (sm9_fp_is_zero(a[0])) { - // r0 = 0 - sm9_fp_set_zero(r[0]); - // r1 = -(2 * a1)^-1 - sm9_fp_dbl(r[1], a[1]); - sm9_fp_inv(r[1], r[1]); - sm9_fp_neg(r[1], r[1]); - - } else if (sm9_fp_is_zero(a[1])) { - /* r1 = 0 */ - sm9_fp_set_zero(r[1]); - /* r0 = a0^-1 */ - sm9_fp_inv(r[0], a[0]); - - } else { - sm9_fp_t k, t; - - // k = (a[0]^2 + 2 * a[1]^2)^-1 - sm9_fp_sqr(k, a[0]); - sm9_fp_sqr(t, a[1]); - sm9_fp_dbl(t, t); - sm9_fp_add(k, k, t); - sm9_fp_inv(k, k); - - // r[0] = a[0] * k - sm9_fp_mul(r[0], a[0], k); - - // r[1] = -a[1] * k - sm9_fp_mul(r[1], a[1], k); - sm9_fp_neg(r[1], r[1]); - } -} - -void sm9_fp2_div(sm9_fp2_t r, const sm9_fp2_t a, const sm9_fp2_t b) -{ - sm9_fp2_t t; - sm9_fp2_inv(t, b); - sm9_fp2_mul(r, a, t); -} - -void sm9_fp2_div2(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_div2(r[0], a[0]); - sm9_fp_div2(r[1], a[1]); -} - -int sm9_fp2_print(FILE *fp, int fmt, int ind, const char *label, const sm9_fp2_t a) -{ - return 1; -} - - -const sm9_fp4_t SM9_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}}}; -const sm9_fp4_t SM9_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}}}; -const sm9_fp4_t SM9_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}}}; -const sm9_fp4_t SM9_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}}}; - -int sm9_fp4_equ(const sm9_fp4_t a, const sm9_fp4_t b) -{ - return (gmssl_secure_memcmp(a, b, sizeof(sm9_fp4_t)) == 0); -} - -int sm9_fp4_rand(sm9_fp4_t r) -{ - if (sm9_fp2_rand(r[1]) != 1 - || sm9_fp2_rand(r[0]) != 1) { - error_print(); - return -1; - } - return 1; -} - -void sm9_fp4_copy(sm9_fp4_t r, const sm9_fp4_t a) -{ - memcpy(r, a, sizeof(sm9_fp4_t)); -} - -void sm9_fp4_to_bytes(const sm9_fp4_t a, uint8_t buf[128]) -{ - sm9_fp2_to_bytes(a[1], buf); - sm9_fp2_to_bytes(a[0], buf + 64); -} - -int sm9_fp4_from_bytes(sm9_fp4_t r, const uint8_t buf[128]) -{ - if (sm9_fp2_from_bytes(r[1], buf) != 1 - || sm9_fp2_from_bytes(r[0], buf + 64) != 1) { - error_print(); - return -1; - } - return 1; -} - -int sm9_fp4_from_hex(sm9_fp4_t r, const char hex[65 * 4]) -{ - if (sm9_fp2_from_hex(r[1], hex) != 1 - || hex[129] != SM9_HEX_SEP - || sm9_fp2_from_hex(r[0], hex + 130) != 1) { - error_print(); - return -1; - } - return 1; -} - -void sm9_fp4_to_hex(const sm9_fp4_t a, char hex[259]) -{ - sm9_fp2_to_hex(a[1], hex); - hex[129] = SM9_HEX_SEP; - sm9_fp2_to_hex(a[0], hex + 130); -} - -void sm9_fp4_set_fp(sm9_fp4_t r, const sm9_fp_t a) -{ - sm9_fp2_set_fp(r[0], a); - sm9_fp2_set_zero(r[1]); -} - -void sm9_fp4_set_fp2(sm9_fp4_t r, const sm9_fp2_t a) -{ - sm9_fp2_copy(r[0], a); - sm9_fp2_set_zero(r[1]); -} - -void sm9_fp4_set(sm9_fp4_t r, const sm9_fp2_t a0, const sm9_fp2_t a1) -{ - sm9_fp2_copy(r[0], a0); - sm9_fp2_copy(r[1], a1); -} - -void sm9_fp4_set_u(sm9_fp4_t r) -{ - sm9_fp2_set_u(r[0]); - sm9_fp2_set_zero(r[1]); -} - -void sm9_fp4_set_v(sm9_fp4_t r) -{ - sm9_fp2_set_zero(r[0]); - sm9_fp2_set_one(r[1]); -} - -void sm9_fp4_add(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) -{ - sm9_fp2_add(r[0], a[0], b[0]); - sm9_fp2_add(r[1], a[1], b[1]); -} - -void sm9_fp4_dbl(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_dbl(r[0], a[0]); - sm9_fp2_dbl(r[1], a[1]); -} - -void sm9_fp4_sub(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) -{ - sm9_fp2_sub(r[0], a[0], b[0]); - sm9_fp2_sub(r[1], a[1], b[1]); -} - -void sm9_fp4_neg(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_neg(r[0], a[0]); - sm9_fp2_neg(r[1], a[1]); -} - -void sm9_fp4_div2(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_div2(r[0], a[0]); - sm9_fp2_div2(r[1], a[1]); -} - -void sm9_fp4_a_mul_v(sm9_fp4_t r, sm9_fp4_t a) { - sm9_fp2_t r0; - - sm9_fp2_a_mul_u(r0, a[1]); - - sm9_fp2_copy(r[1], a[0]); - sm9_fp2_copy(r[0], r0); -} - -void sm9_fp4_mul(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) -{ - sm9_fp2_t r0, r1, t; - - sm9_fp2_add(r0, a[0], a[1]); - sm9_fp2_add(t, b[0], b[1]); - sm9_fp2_mul(r1, t, r0); - - sm9_fp2_mul(r0, a[0], b[0]); - sm9_fp2_mul(t, a[1], b[1]); - - sm9_fp2_sub(r1, r1, r0); - sm9_fp2_sub(r1, r1, t); - - sm9_fp2_a_mul_u(t, t); - sm9_fp2_add(r0, r0, t); - - sm9_fp2_copy(r[0], r0); - sm9_fp2_copy(r[1], r1); -} - -void sm9_fp4_mul_fp(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp_t k) -{ - sm9_fp2_mul_fp(r[0], a[0], k); - sm9_fp2_mul_fp(r[1], a[1], k); -} - -void sm9_fp4_mul_fp2(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp2_t b0) -{ - sm9_fp2_mul(r[0], a[0], b0); - sm9_fp2_mul(r[1], a[1], b0); -} - -void sm9_fp4_mul_v(sm9_fp4_t r, const sm9_fp4_t a, const sm9_fp4_t b) -{ - sm9_fp2_t r0, r1, t; - - sm9_fp2_mul_u(r0, a[0], b[1]); - sm9_fp2_mul_u(t, a[1], b[0]); - sm9_fp2_add(r0, r0, t); - - sm9_fp2_mul(r1, a[0], b[0]); - sm9_fp2_mul_u(t, a[1], b[1]); - sm9_fp2_add(r1, r1, t); - - sm9_fp2_copy(r[0], r0); - sm9_fp2_copy(r[1], r1); -} - -void sm9_fp4_sqr(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_t r0, r1, t; - - sm9_fp2_add(r1, a[0], a[1]); - sm9_fp2_sqr(r1, r1); - - sm9_fp2_sqr(r0, a[0]); - sm9_fp2_sqr(t, a[1]); - - sm9_fp2_sub(r1, r1, r0); - sm9_fp2_sub(r1, r1, t); - - sm9_fp2_a_mul_u(t, t); - sm9_fp2_add(r0, r0, t); - - sm9_fp2_copy(r[0], r0); - sm9_fp2_copy(r[1], r1); -} - -void sm9_fp4_sqr_v(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_t r0, r1, t; - - sm9_fp2_mul_u(t, a[0], a[1]); - sm9_fp2_dbl(r0, t); - - sm9_fp2_sqr(r1, a[0]); - sm9_fp2_sqr_u(t, a[1]); - sm9_fp2_add(r1, r1, t); - - sm9_fp2_copy(r[0], r0); - sm9_fp2_copy(r[1], r1); -} - -void sm9_fp4_inv(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_t r0, r1, k; - - sm9_fp2_sqr_u(k, a[1]); - sm9_fp2_sqr(r0, a[0]); - sm9_fp2_sub(k, k, r0); - sm9_fp2_inv(k, k); - - sm9_fp2_mul(r0, a[0], k); - sm9_fp2_neg(r0, r0); - - sm9_fp2_mul(r1, a[1], k); - - sm9_fp2_copy(r[0], r0); - sm9_fp2_copy(r[1], r1); -} - -void sm9_fp12_copy(sm9_fp12_t r, const sm9_fp12_t a) -{ - sm9_fp4_copy(r[0], a[0]); - sm9_fp4_copy(r[1], a[1]); - sm9_fp4_copy(r[2], a[2]); -} - -int sm9_fp12_rand(sm9_fp12_t r) -{ - if (sm9_fp4_rand(r[0]) != 1 - || sm9_fp4_rand(r[1]) != 1 - || sm9_fp4_rand(r[2]) != 1) { - error_print(); - return -1; - } - return 1; -} - -void sm9_fp12_set_zero(sm9_fp12_t r) -{ - sm9_fp4_set_zero(r[0]); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_one(sm9_fp12_t r) -{ - sm9_fp4_set_one(r[0]); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -int sm9_fp12_is_one(const sm9_fp12_t a) -{ - return sm9_fp4_is_one(a[0]) - && sm9_fp4_is_zero(a[1]) - && sm9_fp4_is_zero(a[2]); -} - -int sm9_fp12_is_zero(const sm9_fp12_t a) -{ - return sm9_fp4_is_zero(a[0]) - && sm9_fp4_is_zero(a[1]) - && sm9_fp4_is_zero(a[2]); -} - -int sm9_fp12_from_hex(sm9_fp12_t r, const char hex[65 * 12 - 1]) -{ - if (sm9_fp4_from_hex(r[2], hex) != 1 - || hex[65 * 4 - 1] != SM9_HEX_SEP - || sm9_fp4_from_hex(r[1], hex + 65 * 4) != 1 - || hex[65 * 4 - 1] != SM9_HEX_SEP - || sm9_fp4_from_hex(r[0], hex + 65 * 8) != 1) { - error_print(); - return -1; - } - return 1; -} - -void sm9_fp12_to_hex(const sm9_fp12_t a, char hex[65 * 12 - 1]) -{ - sm9_fp4_to_hex(a[2], hex); - hex[65 * 4 - 1] = SM9_HEX_SEP; - sm9_fp4_to_hex(a[1], hex + 65 * 4); - hex[65 * 8 - 1] = SM9_HEX_SEP; - sm9_fp4_to_hex(a[0], hex + 65 * 8); -} - -void sm9_fp12_print(const char *prefix, const sm9_fp12_t a) -{ - char hex[65 * 12]; - sm9_fp12_to_hex(a, hex); - printf("%s\n%s\n", prefix, hex); -} - -void sm9_fp12_set(sm9_fp12_t r, const sm9_fp4_t a0, const sm9_fp4_t a1, const sm9_fp4_t a2) -{ - sm9_fp4_copy(r[0], a0); - sm9_fp4_copy(r[1], a1); - sm9_fp4_copy(r[2], a2); -} - -void sm9_fp12_set_fp(sm9_fp12_t r, const sm9_fp_t a) -{ - sm9_fp4_set_fp(r[0], a); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_fp2(sm9_fp12_t r, const sm9_fp2_t a) -{ - sm9_fp4_set_fp2(r[0], a); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_fp4(sm9_fp12_t r, const sm9_fp4_t a) -{ - sm9_fp4_copy(r[0], a); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_u(sm9_fp12_t r) -{ - sm9_fp4_set_u(r[0]); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_v(sm9_fp12_t r) -{ - sm9_fp4_set_v(r[0]); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_w(sm9_fp12_t r) -{ - sm9_fp4_set_zero(r[0]); - sm9_fp4_set_one(r[1]); - sm9_fp4_set_zero(r[2]); -} - -void sm9_fp12_set_w_sqr(sm9_fp12_t r) -{ - sm9_fp4_set_zero(r[0]); - sm9_fp4_set_zero(r[1]); - sm9_fp4_set_one(r[2]); -} - -int sm9_fp12_equ(const sm9_fp12_t a, const sm9_fp12_t b) -{ - return sm9_fp4_equ(a[0], b[0]) - && sm9_fp4_equ(a[1], b[1]) - && sm9_fp4_equ(a[2], b[2]); -} - -void sm9_fp12_add(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) -{ - sm9_fp4_add(r[0], a[0], b[0]); - sm9_fp4_add(r[1], a[1], b[1]); - sm9_fp4_add(r[2], a[2], b[2]); -} - -void sm9_fp12_dbl(sm9_fp12_t r, const sm9_fp12_t a) -{ - sm9_fp4_dbl(r[0], a[0]); - sm9_fp4_dbl(r[1], a[1]); - sm9_fp4_dbl(r[2], a[2]); -} - -void sm9_fp12_tri(sm9_fp12_t r, const sm9_fp12_t a) -{ - sm9_fp12_t t; - sm9_fp12_dbl(t, a); - sm9_fp12_add(r, t, a); -} - -void sm9_fp12_sub(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) -{ - sm9_fp4_sub(r[0], a[0], b[0]); - sm9_fp4_sub(r[1], a[1], b[1]); - sm9_fp4_sub(r[2], a[2], b[2]); -} - -void sm9_fp12_neg(sm9_fp12_t r, const sm9_fp12_t a) -{ - sm9_fp4_neg(r[0], a[0]); - sm9_fp4_neg(r[1], a[1]); - sm9_fp4_neg(r[2], a[2]); -} - -void sm9_fp12_mul(sm9_fp12_t r, const sm9_fp12_t a, const sm9_fp12_t b) -{ - sm9_fp4_t r0, r1, r2, t, k0, k1, m0, m1, m2; - - sm9_fp4_mul(m0, a[0], b[0]); - sm9_fp4_mul(m1, a[1], b[1]); - sm9_fp4_mul(m2, a[2], b[2]); - - sm9_fp4_add(k0, a[1], a[2]); - sm9_fp4_add(k1, b[1], b[2]); - sm9_fp4_mul(t, k0, k1); - sm9_fp4_sub(t, t, m1); - sm9_fp4_sub(t, t, m2); - sm9_fp4_a_mul_v(t, t); - sm9_fp4_add(r0, t, m0); - - sm9_fp4_add(k0, a[0], a[2]); - sm9_fp4_add(k1, b[0], b[2]); - sm9_fp4_mul(t, k0, k1); - sm9_fp4_sub(t, t, m0); - sm9_fp4_sub(t, t, m2); - sm9_fp4_add(r2, t, m1); - - sm9_fp4_add(k0, a[0], a[1]); - sm9_fp4_add(k1, b[0], b[1]); - sm9_fp4_mul(t, k0, k1); - sm9_fp4_sub(t, t, m0); - sm9_fp4_sub(t, t, m1); - sm9_fp4_a_mul_v(m2, m2); - sm9_fp4_add(r1, t, m2); - - sm9_fp4_copy(r[0], r0); - sm9_fp4_copy(r[1], r1); - sm9_fp4_copy(r[2], r2); -} - -// void sm9_fp12_sqr(sm9_fp12_t r, const sm9_fp12_t a) -// { -// sm9_fp4_t r0, r1, r2, t; - -// sm9_fp4_sqr(r0, a[0]); -// sm9_fp4_mul_v(t, a[1], a[2]); -// sm9_fp4_dbl(t, t); -// sm9_fp4_add(r0, r0, t); - -// sm9_fp4_mul(r1, a[0], a[1]); -// sm9_fp4_dbl(r1, r1); -// sm9_fp4_sqr_v(t, a[2]); -// sm9_fp4_add(r1, r1, t); - -// sm9_fp4_mul(r2, a[0], a[2]); -// sm9_fp4_dbl(r2, r2); -// sm9_fp4_sqr(t, a[1]); -// sm9_fp4_add(r2, r2, t); - -// sm9_fp4_copy(r[0], r0); -// sm9_fp4_copy(r[1], r1); -// sm9_fp4_copy(r[2], r2); -// } - -void sm9_fp12_sqr(sm9_fp12_t r, const sm9_fp12_t a) -{ - sm9_fp4_t h0, h1, h2, t; - sm9_fp4_t s0, s1, s2, s3; - - sm9_fp4_sqr(h0, a[0]); - sm9_fp4_sqr(h1, a[2]); - sm9_fp4_add(s0, a[2], a[0]); - - sm9_fp4_sub(t, s0, a[1]); - sm9_fp4_sqr(s1, t); - - sm9_fp4_add(t, s0, a[1]); - sm9_fp4_sqr(s0, t); - - sm9_fp4_mul(s2, a[1], a[2]); - sm9_fp4_dbl(s2, s2); - - sm9_fp4_add(s3, s0, s1); - sm9_fp4_div2(s3, s3); - - sm9_fp4_sub(t, s3, h1); - sm9_fp4_sub(h2, t, h0); - - sm9_fp4_a_mul_v(h1, h1); - sm9_fp4_add(h1, h1, s0); - sm9_fp4_sub(h1, h1, s2); - sm9_fp4_sub(h1, h1, s3); - - sm9_fp4_a_mul_v(s2, s2); - sm9_fp4_add(h0, h0, s2); - - sm9_fp4_copy(r[0], h0); - sm9_fp4_copy(r[1], h1); - sm9_fp4_copy(r[2], h2); -} - -void sm9_fp12_inv(sm9_fp12_t r, const sm9_fp12_t a) -{ - if (sm9_fp4_is_zero(a[2])) { - sm9_fp4_t k, t; - - sm9_fp4_sqr(k, a[0]); - sm9_fp4_mul(k, k, a[0]); - sm9_fp4_sqr_v(t, a[1]); - sm9_fp4_mul(t, t, a[1]); - sm9_fp4_add(k, k, t); - sm9_fp4_inv(k, k); - - sm9_fp4_sqr(r[2], a[1]); - sm9_fp4_mul(r[2], r[2], k); - - sm9_fp4_mul(r[1], a[0], a[1]); - sm9_fp4_mul(r[1], r[1], k); - sm9_fp4_neg(r[1], r[1]); - - sm9_fp4_sqr(r[0], a[0]); - sm9_fp4_mul(r[0], r[0], k); - - } else { - sm9_fp4_t t0, t1, t2, t3; - - sm9_fp4_sqr(t0, a[1]); - sm9_fp4_mul(t1, a[0], a[2]); - sm9_fp4_sub(t0, t0, t1); - - sm9_fp4_mul(t1, a[0], a[1]); - sm9_fp4_sqr_v(t2, a[2]); - sm9_fp4_sub(t1, t1, t2); - - sm9_fp4_sqr(t2, a[0]); - sm9_fp4_mul_v(t3, a[1], a[2]); - sm9_fp4_sub(t2, t2, t3); - - sm9_fp4_sqr(t3, t1); - sm9_fp4_mul(r[0], t0, t2); - sm9_fp4_sub(t3, t3, r[0]); - sm9_fp4_inv(t3, t3); - sm9_fp4_mul(t3, a[2], t3); - - sm9_fp4_mul(r[0], t2, t3); - - sm9_fp4_mul(r[1], t1, t3); - sm9_fp4_neg(r[1], r[1]); - - sm9_fp4_mul(r[2], t0, t3); - } -} - -void sm9_fp12_pow(sm9_fp12_t r, const sm9_fp12_t a, const sm9_bn_t k) -{ - char kbits[257]; - sm9_fp12_t t; - int i; - - assert(sm9_bn_cmp(k, SM9_P_MINUS_ONE) < 0); - sm9_fp12_set_zero(t); - - sm9_bn_to_bits(k, kbits); - sm9_fp12_set_one(t); - for (i = 0; i < 256; i++) { - sm9_fp12_sqr(t, t); - if (kbits[i] == '1') { - sm9_fp12_mul(t, t, a); - } - } - sm9_fp12_copy(r, t); -} - -void sm9_fp2_conjugate(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp_copy(r[0], a[0]); - sm9_fp_neg (r[1], a[1]); - -} - -void sm9_fp2_frobenius(sm9_fp2_t r, const sm9_fp2_t a) -{ - sm9_fp2_conjugate(r, a); -} - -// beta = 0x6c648de5dc0a3f2cf55acc93ee0baf159f9d411806dc5177f5b21fd3da24d011 -// alpha1 = 0x3f23ea58e5720bdb843c6cfa9c08674947c5c86e0ddd04eda91d8354377b698b -// alpha2 = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 -// alpha3 = 0x6c648de5dc0a3f2cf55acc93ee0baf159f9d411806dc5177f5b21fd3da24d011 -// alpha4 = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65333 -// alpha5 = 0x2d40a38cf6983351711e5f99520347cc57d778a9f8ff4c8a4c949c7fa2a96686 -static const sm9_fp2_t SM9_BETA = {{0xda24d011, 0xf5b21fd3, 0x06dc5177, 0x9f9d4118, 0xee0baf15, 0xf55acc93, 0xdc0a3f2c, 0x6c648de5}, {0}}; -static const sm9_fp_t SM9_ALPHA1 = {0x377b698b, 0xa91d8354, 0x0ddd04ed, 0x47c5c86e, 0x9c086749, 0x843c6cfa, 0xe5720bdb, 0x3f23ea58}; -static const sm9_fp_t SM9_ALPHA2 = {0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, 0x02a3a6f2, 0xf3000000, 0x0, 0x0 }; -static const sm9_fp_t SM9_ALPHA3 = {0xda24d011, 0xf5b21fd3, 0x06dc5177, 0x9f9d4118, 0xee0baf15, 0xf55acc93, 0xdc0a3f2c, 0x6c648de5}; -static const sm9_fp_t SM9_ALPHA4 = {0x7be65333, 0xd5fc1196, 0x4f8b78f4, 0x78027235, 0x02a3a6f2, 0xf3000000, 0x0, 0x0 }; -static const sm9_fp_t SM9_ALPHA5 = {0xa2a96686, 0x4c949c7f, 0xf8ff4c8a, 0x57d778a9, 0x520347cc, 0x711e5f99, 0xf6983351, 0x2d40a38c}; - - -void sm9_fp4_frobenius(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_conjugate(r[0], a[0]); - sm9_fp2_conjugate(r[1], a[1]); - sm9_fp2_mul(r[1], r[1], SM9_BETA); -} - -void sm9_fp4_conjugate(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_copy(r[0], a[0]); - sm9_fp2_neg(r[1], a[1]); -} - -void sm9_fp4_frobenius2(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp4_conjugate(r, a); -} - -void sm9_fp4_frobenius3(sm9_fp4_t r, const sm9_fp4_t a) -{ - sm9_fp2_conjugate(r[0], a[0]); - sm9_fp2_conjugate(r[1], a[1]); - sm9_fp2_mul(r[1], r[1], SM9_BETA); - sm9_fp2_neg(r[1], r[1]); -} - -void sm9_fp12_frobenius(sm9_fp12_t r, const sm9_fp12_t x) -{ - const sm9_fp2_t *xa = x[0]; - const sm9_fp2_t *xb = x[1]; - const sm9_fp2_t *xc = x[2]; - sm9_fp4_t ra; - sm9_fp4_t rb; - sm9_fp4_t rc; - - sm9_fp2_conjugate(ra[0], xa[0]); - sm9_fp2_conjugate(ra[1], xa[1]); - sm9_fp2_mul_fp(ra[1], ra[1], SM9_ALPHA3); - - sm9_fp2_conjugate(rb[0], xb[0]); - sm9_fp2_mul_fp(rb[0], rb[0], SM9_ALPHA1); - sm9_fp2_conjugate(rb[1], xb[1]); - sm9_fp2_mul_fp(rb[1], rb[1], SM9_ALPHA4); - - sm9_fp2_conjugate(rc[0], xc[0]); - sm9_fp2_mul_fp(rc[0], rc[0], SM9_ALPHA2); - sm9_fp2_conjugate(rc[1], xc[1]); - sm9_fp2_mul_fp(rc[1], rc[1], SM9_ALPHA5); - - sm9_fp12_set(r, ra, rb, rc); -} - -void sm9_fp12_frobenius2(sm9_fp12_t r, const sm9_fp12_t x) -{ - sm9_fp4_t a; - sm9_fp4_t b; - sm9_fp4_t c; - - sm9_fp4_conjugate(a, x[0]); - sm9_fp4_conjugate(b, x[1]); - sm9_fp4_mul_fp(b, b, SM9_ALPHA2); - sm9_fp4_conjugate(c, x[2]); - sm9_fp4_mul_fp(c, c, SM9_ALPHA4); - - sm9_fp4_copy(r[0], a); - sm9_fp4_copy(r[1], b); - sm9_fp4_copy(r[2], c); -} - -void sm9_fp12_frobenius3(sm9_fp12_t r, const sm9_fp12_t x) -{ - const sm9_fp2_t *xa = x[0]; - const sm9_fp2_t *xb = x[1]; - const sm9_fp2_t *xc = x[2]; - sm9_fp4_t ra; - sm9_fp4_t rb; - sm9_fp4_t rc; - - sm9_fp2_conjugate(ra[0], xa[0]); - sm9_fp2_conjugate(ra[1], xa[1]); - sm9_fp2_mul(ra[1], ra[1], SM9_BETA); - sm9_fp2_neg(ra[1], ra[1]); - - sm9_fp2_conjugate(rb[0], xb[0]); - sm9_fp2_mul(rb[0], rb[0], SM9_BETA); - sm9_fp2_conjugate(rb[1], xb[1]); - - sm9_fp2_conjugate(rc[0], xc[0]); - sm9_fp2_neg(rc[0], rc[0]); - sm9_fp2_conjugate(rc[1], xc[1]); - sm9_fp2_mul(rc[1], rc[1], SM9_BETA); - - sm9_fp4_copy(r[0], ra); - sm9_fp4_copy(r[1], rb); - sm9_fp4_copy(r[2], rc); -} - -void sm9_fp12_frobenius6(sm9_fp12_t r, const sm9_fp12_t x) -{ - sm9_fp4_t a; - sm9_fp4_t b; - sm9_fp4_t c; - - sm9_fp4_copy(a, x[0]); - sm9_fp4_copy(b, x[1]); - sm9_fp4_copy(c, x[2]); - - sm9_fp4_conjugate(a, a); - sm9_fp4_conjugate(b, b); - sm9_fp4_neg(b, b); - sm9_fp4_conjugate(c, c); - - sm9_fp4_copy(r[0], a); - sm9_fp4_copy(r[1], b); - sm9_fp4_copy(r[2], c); -} - - - -void sm9_point_from_hex(SM9_POINT *R, const char hex[65 * 2]) -{ - sm9_bn_from_hex(R->X, hex); - sm9_bn_from_hex(R->Y, hex + 65); - sm9_bn_set_one(R->Z); -} - -int sm9_point_is_at_infinity(const SM9_POINT *P) { - return sm9_fp_is_zero(P->Z); -} - -void sm9_point_set_infinity(SM9_POINT *R) { - sm9_fp_set_one(R->X); - sm9_fp_set_one(R->Y); - sm9_fp_set_zero(R->Z); -} - -void sm9_point_copy(SM9_POINT *R, const SM9_POINT *P) -{ - *R = *P; -} - -void sm9_point_get_xy(const SM9_POINT *P, sm9_fp_t x, sm9_fp_t y) -{ - sm9_fp_t z_inv; - - assert(!sm9_fp_is_zero(P->Z)); - - if (sm9_fp_is_one(P->Z)) { - sm9_fp_copy(x, P->X); - sm9_fp_copy(y, P->Y); - } - - sm9_fp_inv(z_inv, P->Z); - if (y) - sm9_fp_mul(y, P->Y, z_inv); - sm9_fp_sqr(z_inv, z_inv); - sm9_fp_mul(x, P->X, z_inv); - if (y) - sm9_fp_mul(y, y, z_inv); -} - -int sm9_point_equ(const SM9_POINT *P, const SM9_POINT *Q) -{ - sm9_fp_t t1, t2, t3, t4; - sm9_fp_sqr(t1, P->Z); - sm9_fp_sqr(t2, Q->Z); - sm9_fp_mul(t3, P->X, t2); - sm9_fp_mul(t4, Q->X, t1); - if (!sm9_fp_equ(t3, t4)) { - return 0; - } - sm9_fp_mul(t1, t1, P->Z); - sm9_fp_mul(t2, t2, Q->Z); - sm9_fp_mul(t3, P->Y, t2); - sm9_fp_mul(t4, Q->Y, t1); - return sm9_fp_equ(t3, t4); -} - -int sm9_point_is_on_curve(const SM9_POINT *P) -{ - sm9_fp_t t0, t1, t2; - if (sm9_fp_is_one(P->Z)) { - sm9_fp_sqr(t0, P->Y); - sm9_fp_sqr(t1, P->X); - sm9_fp_mul(t1, t1, P->X); - sm9_fp_add(t1, t1, SM9_FIVE); - } else { - sm9_fp_sqr(t0, P->X); - sm9_fp_mul(t0, t0, P->X); - sm9_fp_sqr(t1, P->Z); - sm9_fp_sqr(t2, t1); - sm9_fp_mul(t1, t1, t2); - sm9_fp_mul(t1, t1, SM9_FIVE); - sm9_fp_add(t1, t0, t1); - sm9_fp_sqr(t0, P->Y); - } - if (sm9_fp_equ(t0, t1) != 1) { - error_print(); - return 0; - } - return 1; -} - -void sm9_point_dbl(SM9_POINT *R, const SM9_POINT *P) -{ - const uint64_t *X1 = P->X; - const uint64_t *Y1 = P->Y; - const uint64_t *Z1 = P->Z; - sm9_fp_t X3, Y3, Z3, T1, T2, T3; - - if (sm9_point_is_at_infinity(P)) { - sm9_point_copy(R, P); - return; - } - - sm9_fp_sqr(T2, X1); - sm9_fp_tri(T2, T2); - sm9_fp_dbl(Y3, Y1); - sm9_fp_mul(Z3, Y3, Z1); - sm9_fp_sqr(Y3, Y3); - sm9_fp_mul(T3, Y3, X1); - sm9_fp_sqr(Y3, Y3); - sm9_fp_div2(Y3, Y3); - sm9_fp_sqr(X3, T2); - sm9_fp_dbl(T1, T3); - sm9_fp_sub(X3, X3, T1); - sm9_fp_sub(T1, T3, X3); - sm9_fp_mul(T1, T1, T2); - sm9_fp_sub(Y3, T1, Y3); - - sm9_fp_copy(R->X, X3); - sm9_fp_copy(R->Y, Y3); - sm9_fp_copy(R->Z, Z3); -} - -void sm9_point_add(SM9_POINT *R, const SM9_POINT *P, const SM9_POINT *Q) -{ - sm9_fp_t x; - sm9_fp_t y; - sm9_point_get_xy(Q, x, y); - - const uint64_t *X1 = P->X; - const uint64_t *Y1 = P->Y; - const uint64_t *Z1 = P->Z; - const uint64_t *x2 = x; - const uint64_t *y2 = y; - sm9_fp_t X3, Y3, Z3, T1, T2, T3, T4; - - if (sm9_point_is_at_infinity(Q)) { - sm9_point_copy(R, P); - return; - } - if (sm9_point_is_at_infinity(P)) { - sm9_point_copy(R, Q); - return; - } - - sm9_fp_sqr(T1, Z1); - sm9_fp_mul(T2, T1, Z1); - sm9_fp_mul(T1, T1, x2); - sm9_fp_mul(T2, T2, y2); - sm9_fp_sub(T1, T1, X1); - sm9_fp_sub(T2, T2, Y1); - - if (sm9_fp_is_zero(T1)) { - if (sm9_fp_is_zero(T2)) { - sm9_point_dbl(R, Q); - return; - } else { - sm9_point_set_infinity(R); - return; - } - } - - sm9_fp_mul(Z3, Z1, T1); - sm9_fp_sqr(T3, T1); - sm9_fp_mul(T4, T3, T1); - sm9_fp_mul(T3, T3, X1); - sm9_fp_dbl(T1, T3); - sm9_fp_sqr(X3, T2); - sm9_fp_sub(X3, X3, T1); - sm9_fp_sub(X3, X3, T4); - sm9_fp_sub(T3, T3, X3); - sm9_fp_mul(T3, T3, T2); - sm9_fp_mul(T4, T4, Y1); - sm9_fp_sub(Y3, T3, T4); - - sm9_fp_copy(R->X, X3); - sm9_fp_copy(R->Y, Y3); - sm9_fp_copy(R->Z, Z3); -} - -void sm9_point_neg(SM9_POINT *R, const SM9_POINT *P) -{ - sm9_fp_copy(R->X, P->X); - sm9_fp_neg(R->Y, P->Y); - sm9_fp_copy(R->Z, P->Z); -} - -void sm9_point_sub(SM9_POINT *R, const SM9_POINT *P, const SM9_POINT *Q) -{ - SM9_POINT _T, *T = &_T; - sm9_point_neg(T, Q); - sm9_point_add(R, P, T); -} - -void sm9_point_mul(SM9_POINT *R, const sm9_bn_t k, const SM9_POINT *P) -{ - char kbits[257]; - SM9_POINT _Q, *Q = &_Q; - int i; - - sm9_bn_to_bits(k, kbits); - sm9_point_set_infinity(Q); - for (i = 0; i < 256; i++) { - sm9_point_dbl(Q, Q); - if (kbits[i] == '1') { - sm9_point_add(Q, Q, P); - } - } - sm9_point_copy(R, Q); -} - -void sm9_point_mul_generator(SM9_POINT *R, const sm9_bn_t k) -{ - sm9_point_mul(R, k, SM9_P1); -} - - -int sm9_point_print(FILE *fp, int fmt, int ind, const char *label, const SM9_POINT *P) -{ - uint8_t buf[65]; - sm9_point_to_uncompressed_octets(P, buf); - format_bytes(fp, fmt, ind, label, buf, sizeof(buf)); - return 1; -} - -int sm9_twist_point_print(FILE *fp, int fmt, int ind, const char *label, const SM9_TWIST_POINT *P) -{ - uint8_t buf[129]; - sm9_twist_point_to_uncompressed_octets(P, buf); - format_bytes(fp, fmt, ind, label, buf, sizeof(buf)); - return 1; -} - -void sm9_twist_point_from_hex(SM9_TWIST_POINT *R, const char hex[65 * 4]) -{ - sm9_fp2_from_hex(R->X, hex); - sm9_fp2_from_hex(R->Y, hex + 65 * 2); - sm9_fp2_set_one(R->Z); -} - -int sm9_twist_point_is_at_infinity(const SM9_TWIST_POINT *P) -{ - return sm9_fp2_is_zero(P->Z); -} - -void sm9_twist_point_set_infinity(SM9_TWIST_POINT *R) -{ - sm9_fp2_set_one(R->X); - sm9_fp2_set_one(R->Y); - sm9_fp2_set_zero(R->Z); -} - -void sm9_twist_point_get_xy(const SM9_TWIST_POINT *P, sm9_fp2_t x, sm9_fp2_t y) -{ - sm9_fp2_t z_inv; - - assert(!sm9_fp2_is_zero(P->Z)); - - if (sm9_fp2_is_one(P->Z)) { - sm9_fp2_copy(x, P->X); - sm9_fp2_copy(y, P->Y); - } - - sm9_fp2_inv(z_inv, P->Z); - if (y) - sm9_fp2_mul(y, P->Y, z_inv); - sm9_fp2_sqr(z_inv, z_inv); - sm9_fp2_mul(x, P->X, z_inv); - if (y) - sm9_fp2_mul(y, y, z_inv); -} - - -int sm9_twist_point_equ(const SM9_TWIST_POINT *P, const SM9_TWIST_POINT *Q) -{ - sm9_fp2_t t1, t2, t3, t4; - - sm9_fp2_sqr(t1, P->Z); - sm9_fp2_sqr(t2, Q->Z); - sm9_fp2_mul(t3, P->X, t2); - sm9_fp2_mul(t4, Q->X, t1); - if (!sm9_fp2_equ(t3, t4)) { - return 0; - } - sm9_fp2_mul(t1, t1, P->Z); - sm9_fp2_mul(t2, t2, Q->Z); - sm9_fp2_mul(t3, P->Y, t2); - sm9_fp2_mul(t4, Q->Y, t1); - return sm9_fp2_equ(t3, t4); -} - -int sm9_twist_point_is_on_curve(const SM9_TWIST_POINT *P) -{ - sm9_fp2_t t0, t1, t2; - - if (sm9_fp2_is_one(P->Z)) { - sm9_fp2_sqr(t0, P->Y); - sm9_fp2_sqr(t1, P->X); - sm9_fp2_mul(t1, t1, P->X); - sm9_fp2_add(t1, t1, SM9_FP2_5U); - - } else { - sm9_fp2_sqr(t0, P->X); - sm9_fp2_mul(t0, t0, P->X); - sm9_fp2_sqr(t1, P->Z); - sm9_fp2_sqr(t2, t1); - sm9_fp2_mul(t1, t1, t2); - sm9_fp2_mul(t1, t1, SM9_FP2_5U); - sm9_fp2_add(t1, t0, t1); - sm9_fp2_sqr(t0, P->Y); - } - - return sm9_fp2_equ(t0, t1); -} - -void sm9_twist_point_neg(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P) -{ - sm9_fp2_copy(R->X, P->X); - sm9_fp2_neg(R->Y, P->Y); - sm9_fp2_copy(R->Z, P->Z); -} - -void sm9_twist_point_dbl(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P) -{ - const sm9_fp_t *X1 = P->X; - const sm9_fp_t *Y1 = P->Y; - const sm9_fp_t *Z1 = P->Z; - sm9_fp2_t X3, Y3, Z3, T1, T2, T3; - - if (sm9_twist_point_is_at_infinity(P)) { - sm9_twist_point_copy(R, P); - return; - } - sm9_fp2_sqr(T2, X1); - sm9_fp2_tri(T2, T2); - sm9_fp2_dbl(Y3, Y1); - sm9_fp2_mul(Z3, Y3, Z1); - sm9_fp2_sqr(Y3, Y3); - sm9_fp2_mul(T3, Y3, X1); - sm9_fp2_sqr(Y3, Y3); - sm9_fp2_div2(Y3, Y3); - sm9_fp2_sqr(X3, T2); - sm9_fp2_dbl(T1, T3); - sm9_fp2_sub(X3, X3, T1); - sm9_fp2_sub(T1, T3, X3); - sm9_fp2_mul(T1, T1, T2); - sm9_fp2_sub(Y3, T1, Y3); - - sm9_fp2_copy(R->X, X3); - sm9_fp2_copy(R->Y, Y3); - sm9_fp2_copy(R->Z, Z3); -} - -void sm9_twist_point_add(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P, const SM9_TWIST_POINT *Q) -{ - const sm9_fp_t *X1 = P->X; - const sm9_fp_t *Y1 = P->Y; - const sm9_fp_t *Z1 = P->Z; - const sm9_fp_t *x2 = Q->X; - const sm9_fp_t *y2 = Q->Y; - sm9_fp2_t X3, Y3, Z3, T1, T2, T3, T4; - - if (sm9_twist_point_is_at_infinity(Q)) { - sm9_twist_point_copy(R, P); - return; - } - if (sm9_twist_point_is_at_infinity(P)) { - sm9_twist_point_copy(R, Q); - return; - } - - sm9_fp2_sqr(T1, Z1); - sm9_fp2_mul(T2, T1, Z1); - sm9_fp2_mul(T1, T1, x2); - sm9_fp2_mul(T2, T2, y2); - sm9_fp2_sub(T1, T1, X1); - sm9_fp2_sub(T2, T2, Y1); - if (sm9_fp2_is_zero(T1)) { - if (sm9_fp2_is_zero(T2)) { - sm9_twist_point_dbl(R, Q); - return; - } else { - sm9_twist_point_set_infinity(R); - return; - } - } - sm9_fp2_mul(Z3, Z1, T1); - sm9_fp2_sqr(T3, T1); - sm9_fp2_mul(T4, T3, T1); - sm9_fp2_mul(T3, T3, X1); - sm9_fp2_dbl(T1, T3); - sm9_fp2_sqr(X3, T2); - sm9_fp2_sub(X3, X3, T1); - sm9_fp2_sub(X3, X3, T4); - sm9_fp2_sub(T3, T3, X3); - sm9_fp2_mul(T3, T3, T2); - sm9_fp2_mul(T4, T4, Y1); - sm9_fp2_sub(Y3, T3, T4); - - sm9_fp2_copy(R->X, X3); - sm9_fp2_copy(R->Y, Y3); - sm9_fp2_copy(R->Z, Z3); -} - -void sm9_twist_point_sub(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P, const SM9_TWIST_POINT *Q) -{ - SM9_TWIST_POINT _T, *T = &_T; - sm9_twist_point_neg(T, Q); - sm9_twist_point_add_full(R, P, T); -} - -void sm9_twist_point_add_full(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P, const SM9_TWIST_POINT *Q) -{ - const sm9_fp_t *X1 = P->X; - const sm9_fp_t *Y1 = P->Y; - const sm9_fp_t *Z1 = P->Z; - const sm9_fp_t *X2 = Q->X; - const sm9_fp_t *Y2 = Q->Y; - const sm9_fp_t *Z2 = Q->Z; - sm9_fp2_t T1, T2, T3, T4, T5, T6, T7, T8; - - if (sm9_twist_point_is_at_infinity(Q)) { - sm9_twist_point_copy(R, P); - return; - } - if (sm9_twist_point_is_at_infinity(P)) { - sm9_twist_point_copy(R, Q); - return; - } - - sm9_fp2_sqr(T1, Z1); - sm9_fp2_sqr(T2, Z2); - sm9_fp2_mul(T3, X2, T1); - sm9_fp2_mul(T4, X1, T2); - sm9_fp2_add(T5, T3, T4); - sm9_fp2_sub(T3, T3, T4); - sm9_fp2_mul(T1, T1, Z1); - sm9_fp2_mul(T1, T1, Y2); - sm9_fp2_mul(T2, T2, Z2); - sm9_fp2_mul(T2, T2, Y1); - sm9_fp2_add(T6, T1, T2); - sm9_fp2_sub(T1, T1, T2); - - if (sm9_fp2_is_zero(T1) && sm9_fp2_is_zero(T3)) { - sm9_twist_point_dbl(R, P); - return; - } - if (sm9_fp2_is_zero(T1) && sm9_fp2_is_zero(T6)) { - sm9_twist_point_set_infinity(R); - return; - } - - sm9_fp2_sqr(T6, T1); - sm9_fp2_mul(T7, T3, Z1); - sm9_fp2_mul(T7, T7, Z2); - sm9_fp2_sqr(T8, T3); - sm9_fp2_mul(T5, T5, T8); - sm9_fp2_mul(T3, T3, T8); - sm9_fp2_mul(T4, T4, T8); - sm9_fp2_sub(T6, T6, T5); - sm9_fp2_sub(T4, T4, T6); - sm9_fp2_mul(T1, T1, T4); - sm9_fp2_mul(T2, T2, T3); - sm9_fp2_sub(T1, T1, T2); - - sm9_fp2_copy(R->X, T6); - sm9_fp2_copy(R->Y, T1); - sm9_fp2_copy(R->Z, T7); -} - -void sm9_twist_point_mul(SM9_TWIST_POINT *R, const sm9_bn_t k, const SM9_TWIST_POINT *P) -{ - SM9_TWIST_POINT _Q, *Q = &_Q; - char kbits[256]; - int i; - - sm9_bn_to_bits(k, kbits); - sm9_twist_point_set_infinity(Q); - for (i = 0; i < 256; i++) { - sm9_twist_point_dbl(Q, Q); - if (kbits[i] == '1') { - sm9_twist_point_add_full(Q, Q, P); - } - } - sm9_twist_point_copy(R, Q); -} - -void sm9_twist_point_mul_generator(SM9_TWIST_POINT *R, const sm9_bn_t k) -{ - sm9_twist_point_mul(R, k, SM9_P2); -} - -void sm9_eval_g_tangent(sm9_fp12_t num, sm9_fp12_t den, const SM9_TWIST_POINT *P, const SM9_POINT *Q) -{ - sm9_fp_t x; - sm9_fp_t y; - sm9_point_get_xy(Q, x, y); - - const sm9_fp_t *XP = P->X; - const sm9_fp_t *YP = P->Y; - const sm9_fp_t *ZP = P->Z; - const uint64_t *xQ = x; - const uint64_t *yQ = y; - - sm9_fp_t *a0 = num[0][0]; - sm9_fp_t *a1 = num[0][1]; - sm9_fp_t *a4 = num[2][0]; - sm9_fp_t *b1 = den[0][1]; - - sm9_fp2_t t0; - sm9_fp2_t t1; - sm9_fp2_t t2; - - - sm9_fp12_set_zero(num); - sm9_fp12_set_zero(den); - - sm9_fp2_sqr(t0, ZP); - sm9_fp2_mul(t1, t0, ZP); - sm9_fp2_mul(b1, t1, YP); - - sm9_fp2_mul_fp(t2, b1, yQ); - sm9_fp2_neg(a1, t2); - - sm9_fp2_sqr(t1, XP); - sm9_fp2_mul(t0, t0, t1); - sm9_fp2_mul_fp(t0, t0, xQ); - sm9_fp2_tri(t0, t0); - sm9_fp2_div2(a4, t0); - - sm9_fp2_mul(t1, t1, XP); - sm9_fp2_tri(t1, t1); - sm9_fp2_div2(t1, t1); - sm9_fp2_sqr(t0, YP); - sm9_fp2_sub(a0, t0, t1); -} - -void sm9_eval_g_line(sm9_fp12_t num, sm9_fp12_t den, const SM9_TWIST_POINT *T, const SM9_TWIST_POINT *P, const SM9_POINT *Q) -{ - sm9_fp_t x; - sm9_fp_t y; - sm9_point_get_xy(Q, x, y); - - const sm9_fp_t *XT = T->X; - const sm9_fp_t *YT = T->Y; - const sm9_fp_t *ZT = T->Z; - const sm9_fp_t *XP = P->X; - const sm9_fp_t *YP = P->Y; - const sm9_fp_t *ZP = P->Z; - const uint64_t *xQ = x; - const uint64_t *yQ = y; - - sm9_fp_t *a0 = num[0][0]; - sm9_fp_t *a1 = num[0][1]; - sm9_fp_t *a4 = num[2][0]; - sm9_fp_t *b1 = den[0][1]; - - sm9_fp2_t T0, T1, T2, T3, T4; - - - sm9_fp12_set_zero(num); - sm9_fp12_set_zero(den); - - sm9_fp2_sqr(T0, ZP); - sm9_fp2_mul(T1, T0, XT); - sm9_fp2_mul(T0, T0, ZP); - sm9_fp2_sqr(T2, ZT); - sm9_fp2_mul(T3, T2, XP); - sm9_fp2_mul(T2, T2, ZT); - sm9_fp2_mul(T2, T2, YP); - sm9_fp2_sub(T1, T1, T3); - sm9_fp2_mul(T1, T1, ZT); - sm9_fp2_mul(T1, T1, ZP); - sm9_fp2_mul(T4, T1, T0); - sm9_fp2_copy(b1, T4); - sm9_fp2_mul(T1, T1, YP); - sm9_fp2_mul(T3, T0, YT); - sm9_fp2_sub(T3, T3, T2); - sm9_fp2_mul(T0, T0, T3); - sm9_fp2_mul_fp(T0, T0, xQ); - sm9_fp2_copy(a4, T0); - sm9_fp2_mul(T3, T3, XP); - sm9_fp2_mul(T3, T3, ZP); - sm9_fp2_sub(T1, T1, T3); - sm9_fp2_copy(a0, T1); - sm9_fp2_mul_fp(T2, T4, yQ); - sm9_fp2_neg(T2, T2); - sm9_fp2_copy(a1, T2); -} - -void sm9_twist_point_pi1(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P) -{ - //const c = 0x3f23ea58e5720bdb843c6cfa9c08674947c5c86e0ddd04eda91d8354377b698bn; - const sm9_fp_t c = { - 0x377b698b, 0xa91d8354, 0x0ddd04ed, 0x47c5c86e, - 0x9c086749, 0x843c6cfa, 0xe5720bdb, 0x3f23ea58, - }; - sm9_fp2_conjugate(R->X, P->X); - sm9_fp2_conjugate(R->Y, P->Y); - sm9_fp2_conjugate(R->Z, P->Z); - sm9_fp2_mul_fp(R->Z, R->Z, c); - -} - -void sm9_twist_point_pi2(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P) -{ - //c = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 - const sm9_fp_t c = { - 0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, - 0x02a3a6f2, 0xf3000000, 0, 0, - }; - sm9_fp2_copy(R->X, P->X); - sm9_fp2_copy(R->Y, P->Y); - sm9_fp2_mul_fp(R->Z, P->Z, c); -} - -void sm9_twist_point_neg_pi2(SM9_TWIST_POINT *R, const SM9_TWIST_POINT *P) -{ - // c = 0xf300000002a3a6f2780272354f8b78f4d5fc11967be65334 - const sm9_fp_t c = { - 0x7be65334, 0xd5fc1196, 0x4f8b78f4, 0x78027235, - 0x02a3a6f2, 0xf3000000, 0, 0, - }; - sm9_fp2_copy(R->X, P->X); - sm9_fp2_neg(R->Y, P->Y); - sm9_fp2_mul_fp(R->Z, P->Z, c); -} - - -void sm9_final_exponent_hard_part(sm9_fp12_t r, const sm9_fp12_t f) -{ - // a2 = 0xd8000000019062ed0000b98b0cb27659 - // a3 = 0x2400000000215d941 - const sm9_bn_t a2 = {0xcb27659, 0x0000b98b, 0x019062ed, 0xd8000000, 0, 0, 0, 0}; - const sm9_bn_t a3 = {0x215d941, 0x40000000, 0x2, 0, 0, 0, 0, 0}; - const sm9_bn_t nine = {9,0,0,0,0,0,0,0}; - sm9_fp12_t t0, t1, t2, t3; - - sm9_fp12_pow(t0, f, a3); - sm9_fp12_inv(t0, t0); - sm9_fp12_frobenius(t1, t0); - sm9_fp12_mul(t1, t0, t1); - - sm9_fp12_mul(t0, t0, t1); - sm9_fp12_frobenius(t2, f); - sm9_fp12_mul(t3, t2, f); - sm9_fp12_pow(t3, t3, nine); - - sm9_fp12_mul(t0, t0, t3); - sm9_fp12_sqr(t3, f); - sm9_fp12_sqr(t3, t3); - sm9_fp12_mul(t0, t0, t3); - sm9_fp12_sqr(t2, t2); - sm9_fp12_mul(t2, t2, t1); - sm9_fp12_frobenius2(t1, f); - sm9_fp12_mul(t1, t1, t2); - - sm9_fp12_pow(t2, t1, a2); - sm9_fp12_mul(t0, t2, t0); - sm9_fp12_frobenius3(t1, f); - sm9_fp12_mul(t1, t1, t0); - - sm9_fp12_copy(r, t1); -} - -void sm9_final_exponent(sm9_fp12_t r, const sm9_fp12_t f) -{ - sm9_fp12_t t0; - sm9_fp12_t t1; - - sm9_fp12_frobenius6(t0, f); - sm9_fp12_inv(t1, f); - sm9_fp12_mul(t0, t0, t1); - sm9_fp12_frobenius2(t1, t0); - sm9_fp12_mul(t0, t0, t1); - sm9_final_exponent_hard_part(t0, t0); - - sm9_fp12_copy(r, t0); -} - -void sm9_pairing(sm9_fp12_t r, const SM9_TWIST_POINT *Q, const SM9_POINT *P) { - const char *abits = "00100000000000000000000000000000000000010000101100020200101000020"; - - SM9_TWIST_POINT _T, *T = &_T; - SM9_TWIST_POINT _Q1, *Q1 = &_Q1; - SM9_TWIST_POINT _Q2, *Q2 = &_Q2; - - sm9_fp12_t f_num; - sm9_fp12_t f_den; - sm9_fp12_t g_num; - sm9_fp12_t g_den; - int i; - - sm9_twist_point_copy(T, Q); - - sm9_fp12_set_one(f_num); - sm9_fp12_set_one(f_den); - - for (i = 0; i < strlen(abits); i++) { - sm9_fp12_sqr(f_num, f_num); - sm9_fp12_sqr(f_den, f_den); - sm9_eval_g_tangent(g_num, g_den, T, P); - sm9_fp12_mul(f_num, f_num, g_num); - sm9_fp12_mul(f_den, f_den, g_den); - - sm9_twist_point_dbl(T, T); - - if (abits[i] == '1') { - sm9_eval_g_line(g_num, g_den, T, Q, P); - sm9_fp12_mul(f_num, f_num, g_num); - sm9_fp12_mul(f_den, f_den, g_den); - sm9_twist_point_add_full(T, T, Q); - } else if (abits[i] == '2') { - sm9_twist_point_neg(Q1, Q); - sm9_eval_g_line(g_num, g_den, T, Q1, P); - sm9_fp12_mul(f_num, f_num, g_num); - sm9_fp12_mul(f_den, f_den, g_den); - sm9_twist_point_add_full(T, T, Q1); - } - } - - sm9_twist_point_pi1(Q1, Q); - sm9_twist_point_neg_pi2(Q2, Q); - - sm9_eval_g_line(g_num, g_den, T, Q1, P); - sm9_fp12_mul(f_num, f_num, g_num); - sm9_fp12_mul(f_den, f_den, g_den); - sm9_twist_point_add_full(T, T, Q1); - - sm9_eval_g_line(g_num, g_den, T, Q2, P); - sm9_fp12_mul(f_num, f_num, g_num); - sm9_fp12_mul(f_den, f_den, g_den); - sm9_twist_point_add_full(T, T, Q2); - - sm9_fp12_inv(f_den, f_den); - sm9_fp12_mul(r, f_num, f_den); - - sm9_final_exponent(r, r); -} - -void sm9_fn_add(sm9_fn_t r, const sm9_fn_t a, const sm9_fn_t b) -{ - sm9_bn_add(r, a, b); - if (sm9_bn_cmp(r, SM9_N) >= 0) { - sm9_bn_sub(r, r, SM9_N); - } -} - -void sm9_fn_sub(sm9_fn_t r, const sm9_fn_t a, const sm9_fn_t b) -{ - if (sm9_bn_cmp(a, b) >= 0) { - sm9_bn_sub(r, a, b); - } else { - sm9_bn_t t; - sm9_bn_sub(t, SM9_N, b); - sm9_bn_add(r, t, a); - } -} - -void sm9_fn_mul(sm9_fn_t r, const sm9_fn_t a, const sm9_fn_t b) -{ - uint64_t s[18]; - sm9_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 < 18; i++) { - s[i] = 0; - } - for (i = 0; i < 9; i++) { - w = 0; - for (j = 0; j < 9; j++) { - w += s[i + j] + zh[i] * SM9_MU_N[j]; - s[i + j] = w & 0xffffffff; - w >>= 32; - } - s[i + 9] = w; - } - for (i = 0; i < 9; i++) { - q[i] = s[9 + i]; - } - - /* q = q * n mod (2^32)^9 */ - for (i = 0; i < 18; i++) { - s[i] = 0; - } - for (i = 0; i < 9; 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 (sm9_barrett_bn_cmp(zl, q)) { - sm9_barrett_bn_sub(zl, zl, q); - } else { - sm9_barrett_bn_t c = {0,0,0,0,0,0,0,0,0x100000000}; - sm9_barrett_bn_sub(q, c, q); - sm9_barrett_bn_add(zl, q, zl); - } - - - for (i = 0; i < 8; i++) { - r[i] = zl[i]; - } - - r[7] += (zl[8] << 32); - - /* while r >= n do: r = r - n */ - while (sm9_bn_cmp(r, SM9_N) >= 0) { - sm9_bn_sub(r, r, SM9_N); - } -} - -void sm9_fn_pow(sm9_fn_t r, const sm9_fn_t a, const sm9_bn_t e) -{ - sm9_fn_t t; - uint32_t w; - int i, j; - - assert(sm9_bn_cmp(e, SM9_N_MINUS_ONE) < 0); - - sm9_bn_set_one(t); - for (i = 7; i >= 0; i--) { - w = (uint32_t)e[i]; - for (j = 0; j < 32; j++) { - sm9_fn_mul(t, t, t); - if (w & 0x80000000) - sm9_fn_mul(t, t, a); - w <<= 1; - } - } - sm9_bn_copy(r, t); -} - -void sm9_fn_inv(sm9_fn_t r, const sm9_fn_t a) -{ - sm9_fn_t e; - sm9_bn_sub(e, SM9_N, SM9_TWO); - sm9_fn_pow(r, a, e); -} - - -// for H1() and H2() -// h = (Ha mod (n-1)) + 1; h in [1, n-1], n is the curve order, Ha is 40 bytes from hash -void sm9_fn_from_hash(sm9_fn_t h, const uint8_t Ha[40]) -{ - uint64_t s[18] = {0}; - sm9_barrett_bn_t zh, zl, q; - uint64_t w; - int i, j; - - /* s = Ha -> int */ - for (int i = 0; i < 10; i++) { - for (int j = 0; j < 4; j++) { - s[i] <<= 8; - s[i] += Ha[4 * (9-i) + j]; - } - } - - /* 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 < 18; i++) { - s[i] = 0; - } - for (i = 0; i < 9; i++) { - w = 0; - for (j = 0; j < 9; j++) { - w += s[i + j] + zh[i] * SM9_MU_N_MINUS_ONE[j]; // - s[i + j] = w & 0xffffffff; - w >>= 32; - } - s[i + 9] = w; - } - for (i = 0; i < 9; i++) { - q[i] = s[9 + i]; - } - - /* q = q * p mod (2^32)^9 */ - for (i = 0; i < 18; i++) { - s[i] = 0; - } - for (i = 0; i < 9; i++) { - w = 0; - for (j = 0; j < 8; j++) { - w += s[i + j] + q[i] * SM9_N_MINUS_ONE[j]; - s[i + j] = w & 0xffffffff; - w >>= 32; - } - s[i + 8] = w; - } - for (i = 0; i < 9; i++) { - q[i] = s[i]; - } - - /* h = zl - q (mod (2^32)^9) */ - - if (sm9_barrett_bn_cmp(zl, q)) { - sm9_barrett_bn_sub(zl, zl, q); - } else { - sm9_barrett_bn_t c = {0,0,0,0,0,0,0,0,0x100000000}; - sm9_barrett_bn_sub(q, c, q); - sm9_barrett_bn_add(zl, q, zl); - } - - for (i = 0; i < 8; i++) { - h[i] = zl[i]; - } - - h[7] += (zl[8] << 32); - - /* while h >= (n-1) do: h = h - (n-1) */ - while (sm9_bn_cmp(h, SM9_N_MINUS_ONE) >= 0) { - sm9_bn_sub(h, h, SM9_N_MINUS_ONE); - } - - sm9_fn_add(h, h, SM9_ONE); -} - -void sm9_fp12_to_bytes(const sm9_fp12_t a, uint8_t buf[32 * 12]) -{ - sm9_fp4_to_bytes(a[2], buf); - sm9_fp4_to_bytes(a[1], buf + 32 * 4); - sm9_fp4_to_bytes(a[0], buf + 32 * 8); -} - -int sm9_fn_from_bytes(sm9_fn_t a, const uint8_t in[32]) -{ - sm9_bn_from_bytes(a, in); - return 1; -} - -int sm9_point_to_uncompressed_octets(const SM9_POINT *P, uint8_t octets[65]) -{ - sm9_fp_t x; - sm9_fp_t y; - sm9_point_get_xy(P, x, y); - octets[0] = 0x04; - sm9_bn_to_bytes(x, octets + 1); - sm9_bn_to_bytes(y, octets + 32 + 1); - return 1; -} - -int sm9_point_from_uncompressed_octets(SM9_POINT *P, const uint8_t octets[65]) -{ - if (octets[0] != 0x04) { - error_print(); - return -1; - } - memset(P, 0, sizeof(*P)); - sm9_bn_from_bytes(P->X, octets + 1); - sm9_bn_from_bytes(P->Y, octets + 32 + 1); - sm9_fp_set_one(P->Z); - if (!sm9_point_is_on_curve(P)) { - error_print(); - return -1; - } - return 1; -} - -int sm9_twist_point_to_uncompressed_octets(const SM9_TWIST_POINT *P, uint8_t octets[129]) -{ - octets[0] = 0x04; - sm9_fp2_t x; - sm9_fp2_t y; - sm9_twist_point_get_xy(P, x, y); - sm9_fp2_to_bytes(x, octets + 1); - sm9_fp2_to_bytes(y, octets + 32 * 2 + 1); - return 1; -} - -int sm9_twist_point_from_uncompressed_octets(SM9_TWIST_POINT *P, const uint8_t octets[129]) -{ - assert(octets[0] == 0x04); - sm9_fp2_from_bytes(P->X, octets + 1); - sm9_fp2_from_bytes(P->Y, octets + 32 * 2 + 1); - sm9_fp2_set_one(P->Z); - if (!sm9_twist_point_is_on_curve(P)) return -1; - return 1; -}