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566 lines
13 KiB
566 lines
13 KiB
/**
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* Copyright (c) 2013 Tomas Dzetkulic
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* Copyright (c) 2013 Pavol Rusnak
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES
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* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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* OTHER DEALINGS IN THE SOFTWARE.
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*/
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#include <stdio.h>
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#include <string.h>
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#include "bignum.h"
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#include "secp256k1.h"
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inline uint32_t read_be(const uint8_t *data)
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{
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return (((uint32_t)data[0]) << 24) |
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(((uint32_t)data[1]) << 16) |
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(((uint32_t)data[2]) << 8) |
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(((uint32_t)data[3]));
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}
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inline void write_be(uint8_t *data, uint32_t x)
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{
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data[0] = x >> 24;
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data[1] = x >> 16;
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data[2] = x >> 8;
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data[3] = x;
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}
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void bn_read_be(const uint8_t *in_number, bignum256 *out_number)
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{
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int i;
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uint64_t temp = 0;
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for (i = 0; i < 8; i++) {
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temp += (((uint64_t)read_be(in_number + (7 - i) * 4)) << (2 * i));
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out_number->val[i]= temp & 0x3FFFFFFF;
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temp >>= 30;
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}
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out_number->val[8] = temp;
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}
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void bn_write_be(const bignum256 *in_number, uint8_t *out_number)
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{
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int i, shift = 30 + 16 - 32;
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uint64_t temp = in_number->val[8];
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for (i = 0; i < 8; i++) {
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temp <<= 30;
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temp |= in_number->val[7 - i];
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write_be(out_number + i * 4, temp >> shift);
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shift -= 2;
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}
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}
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void bn_zero(bignum256 *a)
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{
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int i;
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for (i = 0; i < 9; i++) {
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a->val[i] = 0;
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}
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}
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int bn_is_zero(const bignum256 *a)
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{
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int i;
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for (i = 0; i < 9; i++) {
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if (a->val[i] != 0) return 0;
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}
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return 1;
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}
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int bn_is_less(const bignum256 *a, const bignum256 *b)
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{
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int i;
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for (i = 8; i >= 0; i--) {
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if (a->val[i] < b->val[i]) return 1;
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if (a->val[i] > b->val[i]) return 0;
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}
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return 0;
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}
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int bn_is_equal(const bignum256 *a, const bignum256 *b) {
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int i;
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for (i = 0; i < 9; i++) {
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if (a->val[i] != b->val[i]) return 0;
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}
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return 1;
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}
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int bn_bitlen(const bignum256 *a) {
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int i = 8, j;
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while (i >= 0 && a->val[i] == 0) i--;
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if (i == -1) return 0;
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j = 29;
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while ((a->val[i] & (1 << j)) == 0) j--;
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return i * 30 + j + 1;
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}
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void bn_lshift(bignum256 *a)
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{
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int i;
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for (i = 8; i > 0; i--) {
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a->val[i] = ((a->val[i] << 1) & 0x3FFFFFFF) | ((a->val[i - 1] & 0x20000000) >> 29);
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}
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a->val[0] = (a->val[0] << 1) & 0x3FFFFFFF;
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}
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void bn_rshift(bignum256 *a)
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{
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int i;
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for (i = 0; i < 8; i++) {
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a->val[i] = (a->val[i] >> 1) | ((a->val[i + 1] & 1) << 29);
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}
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a->val[8] >>= 1;
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}
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// assumes x < 2*prime, result < prime
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void bn_mod(bignum256 *x, const bignum256 *prime)
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{
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int i = 8;
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uint32_t temp;
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// compare numbers
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while (i >= 0 && prime->val[i] == x->val[i]) i--;
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// if equal
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if (i == -1) {
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// set x to zero
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bn_zero(x);
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} else {
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// if x is greater
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if (x->val[i] > prime->val[i]) {
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// substract p from x
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temp = 0x40000000u;
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for (i = 0; i < 9; i++) {
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temp += x->val[i] - prime->val[i];
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x->val[i] = temp & 0x3FFFFFFF;
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temp >>= 30;
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temp += 0x3FFFFFFFu;
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}
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}
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}
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}
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// a = a + b
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void bn_addi(bignum256 *a, uint32_t b)
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{
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uint64_t t = a->val[0];
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t += b;
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a->val[0] = t & 0x3FFFFFFFu;
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t >>= 30;
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a->val[1] += t;
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}
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// a = a * b
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void bn_muli(bignum256 *a, uint32_t b)
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{
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uint64_t t = 0;
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int i;
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for (i = 0; i < 8; i++) {
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t = (uint64_t)(a->val[i]) * b + t;
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a->val[i] = t & 0x3FFFFFFFu;
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t >>= 30;
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}
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a->val[8] += t;
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}
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// x = k * x
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// both inputs and result may be bigger than prime but not bigger than 2 * prime
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void bn_multiply(const bignum256 *k, bignum256 *x, const bignum256 *prime)
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{
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int i, j;
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uint64_t temp = 0;
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uint32_t res[18], coef;
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// compute lower half of long multiplication
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for (i = 0; i < 9; i++)
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{
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for (j = 0; j <= i; j++) {
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temp += k->val[j] * (uint64_t)x->val[i - j];
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}
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res[i] = temp & 0x3FFFFFFFu;
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temp >>= 30;
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}
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// compute upper half
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for (; i < 17; i++)
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{
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for (j = i - 8; j < 9 ; j++) {
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temp += k->val[j] * (uint64_t)x->val[i - j];
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}
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res[i] = temp & 0x3FFFFFFFu;
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temp >>= 30;
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}
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res[17] = temp;
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// compute modulo p division is only estimated so this may give result greater than prime but not bigger than 2 * prime
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for (i = 16; i >= 8; i--) {
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// estimate (res / prime)
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coef = (res[i] >> 16) + (res[i + 1] << 14);
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// substract (coef * prime) from res
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temp = 0x1000000000000000llu + res[i - 8] - prime->val[0] * (uint64_t)coef;
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res[i - 8] = temp & 0x3FFFFFFF;
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for (j = 1; j < 9; j++) {
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temp >>= 30;
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temp += 0xFFFFFFFC0000000llu + res[i - 8 + j] - prime->val[j] * (uint64_t)coef;
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res[i - 8 + j] = temp & 0x3FFFFFFF;
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}
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}
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// store the result
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for (i = 0; i < 9; i++) {
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x->val[i] = res[i];
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}
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}
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// result is smaller than 2*prime
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void bn_fast_mod(bignum256 *x, const bignum256 *prime)
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{
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int j;
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uint32_t coef;
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uint64_t temp;
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coef = x->val[8] >> 16;
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if (!coef) return;
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// substract (coef * prime) from x
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temp = 0x1000000000000000llu + x->val[0] - prime->val[0] * (uint64_t)coef;
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x->val[0] = temp & 0x3FFFFFFF;
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for (j = 1; j < 9; j++) {
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temp >>= 30;
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temp += 0xFFFFFFFC0000000llu + x->val[j] - prime->val[j] * (uint64_t)coef;
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x->val[j] = temp & 0x3FFFFFFF;
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}
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}
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// square root of x = x^((p+1)/4)
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// http://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus
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void bn_sqrt(bignum256 *x, const bignum256 *prime)
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{
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uint32_t i, j, limb;
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bignum256 res, p;
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bn_zero(&res); res.val[0] = 1;
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memcpy(&p, prime, sizeof(bignum256));
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p.val[0] += 1;
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bn_rshift(&p);
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bn_rshift(&p);
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for (i = 0; i < 9; i++) {
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limb = p.val[i];
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for (j = 0; j < 30; j++) {
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if (i == 8 && limb == 0) break;
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if (limb & 1) {
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bn_multiply(x, &res, prime);
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}
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limb >>= 1;
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bn_multiply(x, x, prime);
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}
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}
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bn_mod(&res, prime);
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memcpy(x, &res, sizeof(bignum256));
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}
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#if ! USE_INVERSE_FAST
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#if USE_PRECOMPUTED_IV
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#warning USE_PRECOMPUTED_IV will not be used
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#endif
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// in field G_prime, small but slow
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void bn_inverse(bignum256 *x, const bignum256 *prime)
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{
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uint32_t i, j, limb;
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bignum256 res;
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bn_zero(&res); res.val[0] = 1;
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for (i = 0; i < 9; i++) {
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limb = prime->val[i];
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// this is not enough in general but fine for secp256k1 because prime->val[0] > 1
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if (i == 0) limb -= 2;
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for (j = 0; j < 30; j++) {
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if (i == 8 && limb == 0) break;
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if (limb & 1) {
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bn_multiply(x, &res, prime);
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}
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limb >>= 1;
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bn_multiply(x, x, prime);
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}
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}
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bn_mod(&res, prime);
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memcpy(x, &res, sizeof(bignum256));
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}
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#else
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// in field G_prime, big but fast
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void bn_inverse(bignum256 *x, const bignum256 *prime)
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{
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int i, j, k, len1, len2, mask;
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uint32_t u[9], v[9], s[10], r[10], temp, temp2;
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bn_fast_mod(x, prime);
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bn_mod(x, prime);
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for (i = 0; i < 9; i++) {
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u[i] = prime->val[i];
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v[i] = x->val[i];
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}
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len1 = 9;
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s[0] = 1;
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r[0] = 0;
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len2 = 1;
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k = 0;
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for (;;) {
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for (i = 0; i < len1; i++) {
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if (v[i]) break;
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}
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if (i == len1) break;
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for (;;) {
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for (i = 0; i < 30; i++) {
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if (u[0] & (1 << i)) break;
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}
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if (i == 0) break;
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mask = (1 << i) - 1;
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for (j = 0; j + 1 < len1; j++) {
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u[j] = (u[j] >> i) | ((u[j + 1] & mask) << (30 - i));
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}
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u[j] = (u[j] >> i);
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mask = (1 << (30 - i)) - 1;
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s[len2] = s[len2 - 1] >> (30 - i);
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for (j = len2 - 1; j > 0; j--) {
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s[j] = (s[j - 1] >> (30 - i)) | ((s[j] & mask) << i);
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}
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s[0] = (s[0] & mask) << i;
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if (s[len2]) {
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r[len2] = 0;
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len2++;
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}
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k += i;
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}
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for (;;) {
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for (i = 0; i < 30; i++) {
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if (v[0] & (1 << i)) break;
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}
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if (i == 0) break;
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mask = (1 << i) - 1;
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for (j = 0; j + 1 < len1; j++) {
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v[j] = (v[j] >> i) | ((v[j + 1] & mask) << (30 - i));
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}
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v[j] = (v[j] >> i);
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mask = (1 << (30 - i)) - 1;
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r[len2] = r[len2 - 1] >> (30 - i);
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for (j = len2 - 1; j > 0; j--) {
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r[j] = (r[j - 1] >> (30 - i)) | ((r[j] & mask) << i);
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}
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r[0] = (r[0] & mask) << i;
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if (r[len2]) {
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s[len2] = 0;
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len2++;
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}
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k += i;
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}
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i = len1 - 1;
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while (i > 0 && u[i] == v[i]) i--;
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if (u[i] > v[i]) {
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temp = 0x40000000u + u[0] - v[0];
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u[0] = (temp >> 1) & 0x1FFFFFFF;
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temp >>= 30;
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for (i = 1; i < len1; i++) {
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temp += 0x3FFFFFFFu + u[i] - v[i];
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u[i - 1] += (temp & 1) << 29;
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u[i] = (temp >> 1) & 0x1FFFFFFF;
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temp >>= 30;
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}
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temp = temp2 = 0;
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for (i = 0; i < len2; i++) {
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temp += s[i] + r[i];
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temp2 += s[i] << 1;
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r[i] = temp & 0x3FFFFFFF;
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s[i] = temp2 & 0x3FFFFFFF;
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temp >>= 30;
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temp2 >>= 30;
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}
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if (temp != 0 || temp2 != 0) {
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r[len2] = temp;
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s[len2] = temp2;
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len2++;
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}
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} else {
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temp = 0x40000000u + v[0] - u[0];
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v[0] = (temp >> 1) & 0x1FFFFFFF;
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temp >>= 30;
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for (i = 1; i < len1; i++) {
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temp += 0x3FFFFFFFu + v[i] - u[i];
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v[i - 1] += (temp & 1) << 29;
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v[i] = (temp >> 1) & 0x1FFFFFFF;
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temp >>= 30;
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}
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temp = temp2 = 0;
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for (i = 0; i < len2; i++) {
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temp += s[i] + r[i];
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temp2 += r[i] << 1;
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s[i] = temp & 0x3FFFFFFF;
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r[i] = temp2 & 0x3FFFFFFF;
|
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temp >>= 30;
|
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temp2 >>= 30;
|
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}
|
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if (temp != 0 || temp2 != 0) {
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s[len2] = temp;
|
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r[len2] = temp2;
|
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len2++;
|
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}
|
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}
|
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if (u[len1 - 1] == 0 && v[len1 - 1] == 0) len1--;
|
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k++;
|
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}
|
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i = 8;
|
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while (i > 0 && r[i] == prime->val[i]) i--;
|
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if (r[i] >= prime->val[i]) {
|
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temp = 1;
|
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for (i = 0; i < 9; i++) {
|
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temp += 0x3FFFFFFF + r[i] - prime->val[i];
|
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r[i] = temp & 0x3FFFFFFF;
|
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temp >>= 30;
|
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}
|
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}
|
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temp = 1;
|
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for (i = 0; i < 9; i++) {
|
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temp += 0x3FFFFFFF + prime->val[i] - r[i];
|
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r[i] = temp & 0x3FFFFFFF;
|
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temp >>= 30;
|
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}
|
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int done = 0;
|
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#if USE_PRECOMPUTED_IV
|
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if (prime == &prime256k1) {
|
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for (j = 0; j < 9; j++) {
|
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x->val[j] = r[j];
|
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}
|
|
bn_multiply(secp256k1_iv + k - 256, x, prime);
|
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bn_fast_mod(x, prime);
|
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done = 1;
|
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}
|
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#endif
|
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if (!done) {
|
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for (j = 0; j < k; j++) {
|
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if (r[0] & 1) {
|
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temp = r[0] + prime->val[0];
|
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r[0] = (temp >> 1) & 0x1FFFFFFF;
|
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temp >>= 30;
|
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for (i = 1; i < 9; i++) {
|
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temp += r[i] + prime->val[i];
|
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r[i - 1] += (temp & 1) << 29;
|
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r[i] = (temp >> 1) & 0x1FFFFFFF;
|
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temp >>= 30;
|
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}
|
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} else {
|
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for (i = 0; i < 8; i++) {
|
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r[i] = (r[i] >> 1) | ((r[i + 1] & 1) << 29);
|
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}
|
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r[8] = r[8] >> 1;
|
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}
|
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}
|
|
for (j = 0; j < 9; j++) {
|
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x->val[j] = r[j];
|
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}
|
|
}
|
|
}
|
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#endif
|
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|
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void bn_normalize(bignum256 *a) {
|
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int i;
|
|
uint32_t tmp = 0;
|
|
for (i = 0; i < 9; i++) {
|
|
tmp += a->val[i];
|
|
a->val[i] = tmp & 0x3FFFFFFF;
|
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tmp >>= 30;
|
|
}
|
|
}
|
|
|
|
void bn_addmod(bignum256 *a, const bignum256 *b, const bignum256 *prime)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 9; i++) {
|
|
a->val[i] += b->val[i];
|
|
}
|
|
bn_normalize(a);
|
|
bn_fast_mod(a, prime);
|
|
bn_mod(a, prime);
|
|
}
|
|
|
|
void bn_addmodi(bignum256 *a, uint32_t b, const bignum256 *prime) {
|
|
a->val[0] += b;
|
|
bn_normalize(a);
|
|
bn_fast_mod(a, prime);
|
|
bn_mod(a, prime);
|
|
}
|
|
|
|
// res = a - b
|
|
// b < 2*prime; result not normalized
|
|
void bn_substract(const bignum256 *a, const bignum256 *b, bignum256 *res)
|
|
{
|
|
int i;
|
|
uint32_t temp = 0;
|
|
for (i = 0; i < 9; i++) {
|
|
temp += a->val[i] + 2u * prime256k1.val[i] - b->val[i];
|
|
res->val[i] = temp & 0x3FFFFFFF;
|
|
temp >>= 30;
|
|
}
|
|
}
|
|
|
|
// res = a - b ; a > b
|
|
void bn_substract_noprime(const bignum256 *a, const bignum256 *b, bignum256 *res)
|
|
{
|
|
int i;
|
|
uint32_t tmp = 1;
|
|
for (i = 0; i < 9; i++) {
|
|
tmp += 0x3FFFFFFF + a->val[i] - b->val[i];
|
|
res->val[i] = tmp & 0x3FFFFFFF;
|
|
tmp >>= 30;
|
|
}
|
|
}
|
|
|
|
// a / 58 = a (+r)
|
|
void bn_divmod58(bignum256 *a, uint32_t *r)
|
|
{
|
|
int i;
|
|
uint32_t rem, tmp;
|
|
rem = a->val[8] % 58;
|
|
a->val[8] /= 58;
|
|
for (i = 7; i >= 0; i--) {
|
|
// 2^30 == 18512790*58 + 4
|
|
tmp = rem * 4 + a->val[i];
|
|
a->val[i] = rem * 18512790 + (tmp / 58);
|
|
rem = tmp % 58;
|
|
}
|
|
*r = rem;
|
|
}
|
|
|
|
#if BN_PRINT
|
|
void bn_print(const bignum256 *a)
|
|
{
|
|
printf("%04x", a->val[8] & 0x0000FFFF);
|
|
printf("%08x", (a->val[7] << 2) | ((a->val[6] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[6] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[5] << 2) | ((a->val[4] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[4] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[3] << 2) | ((a->val[2] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[2] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[1] << 2) | ((a->val[0] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[0] & 0x0FFFFFFF);
|
|
}
|
|
|
|
void bn_print_raw(const bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 0; i <= 8; i++) {
|
|
printf("0x%08x, ", a->val[i]);
|
|
}
|
|
}
|
|
#endif
|