2011-10-10 13:36:09 +00:00
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/*
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* modp256.c -- modulo P256 arithmetic
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*
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* Copyright (C) 2011 Free Software Initiative of Japan
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* Author: NIIBE Yutaka <gniibe@fsij.org>
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*
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* This file is a part of Gnuk, a GnuPG USB Token implementation.
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*
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* Gnuk is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Gnuk is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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* License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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*/
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/*
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* p256 = 2^256 - 2^224 + 2^192 + 2^96 - 1
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*/
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#include <stdint.h>
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#include <string.h>
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#include "bn.h"
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#include "modp256.h"
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/*
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256 224 192 160 128 96 64 32 0
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2^256
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1 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
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2^256 - 2^224
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0 ffffffff 00000000 00000000 00000000 00000000 00000000 00000000 00000000
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2^256 - 2^224 + 2^192
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0 ffffffff 00000001 00000000 00000000 00000000 00000000 00000000 00000000
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2^256 - 2^224 + 2^192 + 2^96
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0 ffffffff 00000001 00000000 00000000 00000001 00000000 00000000 00000000
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2^256 - 2^224 + 2^192 + 2^96 - 1
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0 ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
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*/
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bn256 p256 = { {0xffffffff, 0xffffffff, 0xffffffff, 0x00000000,
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0x00000000, 0x00000000, 0x00000001, 0xffffffff} };
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/**
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* @brief X = (A + B) mod p256
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*/
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void
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modp256_add (bn256 *X, const bn256 *A, const bn256 *B)
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{
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int carry;
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carry = bn256_add (X, A, B);
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if (carry)
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bn256_sub (X, X, P256);
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}
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/**
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* @brief X = (A - B) mod p256
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*/
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void
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2011-10-11 00:39:21 +00:00
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modp256_sub (bn256 *X, const bn256 *A, const bn256 *B)
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2011-10-10 13:36:09 +00:00
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{
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int borrow;
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borrow = bn256_sub (X, A, B);
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if (borrow)
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bn256_add (X, X, P256);
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}
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/**
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* @brief X = A mod p256
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*/
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void
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2011-10-11 00:39:21 +00:00
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modp256_reduce (bn256 *X, const bn512 *A)
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2011-10-10 13:36:09 +00:00
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{
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bn256 tmp[1];
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#define S1 X
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#define S2 tmp
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#define S3 tmp
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#define S4 tmp
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#define S5 tmp
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#define S6 tmp
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#define S7 tmp
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#define S8 tmp
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#define S9 tmp
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S1->words[7] = A->words[7];
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S1->words[6] = A->words[6];
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S1->words[5] = A->words[5];
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S1->words[4] = A->words[4];
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S1->words[3] = A->words[3];
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S1->words[2] = A->words[2];
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S1->words[1] = A->words[1];
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S1->words[0] = A->words[0];
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/* X = S1 */
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S2->words[7] = A->words[15];
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S2->words[6] = A->words[14];
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S2->words[5] = A->words[13];
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S2->words[4] = A->words[12];
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S2->words[3] = A->words[11];
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S2->words[2] = S2->words[1] = S2->words[0] = 0;
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/* X += 2 * S2 */
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modp256_add (X, X, S2);
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modp256_add (X, X, S2);
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S3->words[7] = 0;
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S3->words[6] = A->words[15];
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S3->words[5] = A->words[14];
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S3->words[4] = A->words[13];
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S3->words[3] = A->words[12];
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S3->words[2] = S3->words[1] = S3->words[0] = 0;
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/* X += 2 * S3 */
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modp256_add (X, X, S3);
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modp256_add (X, X, S3);
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S4->words[7] = A->words[15];
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S4->words[6] = A->words[14];
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S4->words[5] = S4->words[4] = S4->words[3] = 0;
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S4->words[2] = A->words[10];
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S4->words[1] = A->words[9];
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S4->words[0] = A->words[8];
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/* X += S4 */
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modp256_add (X, X, S4);
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S5->words[7] = A->words[8];
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S5->words[6] = A->words[13];
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S5->words[5] = A->words[15];
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S5->words[4] = A->words[14];
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S5->words[3] = A->words[13];
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S5->words[2] = A->words[11];
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S5->words[1] = A->words[10];
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S5->words[0] = A->words[9];
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/* X += S5 */
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modp256_add (X, X, S5);
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S6->words[7] = A->words[10];
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S6->words[6] = A->words[8];
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S6->words[5] = S6->words[4] = S6->words[3] = 0;
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S6->words[2] = A->words[13];
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S6->words[1] = A->words[12];
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S6->words[0] = A->words[11];
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/* X -= S6 */
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modp256_sub (X, X, S6);
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S7->words[7] = A->words[11];
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S7->words[6] = A->words[9];
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S7->words[5] = S7->words[4] = 0;
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S7->words[3] = A->words[15];
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S7->words[2] = A->words[14];
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S7->words[1] = A->words[13];
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S7->words[0] = A->words[12];
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/* X -= S7 */
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modp256_sub (X, X, S7);
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S8->words[7] = A->words[12];
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S8->words[6] = 0;
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S8->words[5] = A->words[10];
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S8->words[4] = A->words[9];
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S8->words[3] = A->words[8];
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S8->words[2] = A->words[15];
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S8->words[1] = A->words[14];
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S8->words[0] = A->words[13];
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/* X -= S8 */
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modp256_sub (X, X, S8);
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S9->words[7] = A->words[13];
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S9->words[6] = 0;
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S9->words[5] = A->words[11];
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S9->words[4] = A->words[10];
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S9->words[3] = A->words[9];
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S9->words[2] = 0;
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S9->words[1] = A->words[15];
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S9->words[0] = A->words[14];
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/* X -= S9 */
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modp256_sub (X, X, S9);
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if (bn256_is_ge (X, P256))
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bn256_sub (X, X, P256);
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}
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/**
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* @brief X = (A * B) mod p256
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*/
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void
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2011-10-11 00:39:21 +00:00
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modp256_mul (bn256 *X, const bn256 *A, const bn256 *B)
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2011-10-10 13:36:09 +00:00
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{
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bn512 AB[1];
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bn256_mul (AB, A, B);
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modp256_reduce (X, AB);
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}
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/**
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* @brief X = A * A mod p256
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*/
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void
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2011-10-11 00:39:21 +00:00
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modp256_sqr (bn256 *X, const bn256 *A)
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2011-10-10 13:36:09 +00:00
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{
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bn512 AA[1];
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bn256_sqr (AA, A);
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modp256_reduce (X, AA);
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}
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/**
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* @brief C = (1 / a) mod p256
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*/
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void
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modp256_inv (bn256 *C, const bn256 *a)
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{
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bn256 u[1], v[1];
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bn256 A[1] = { { { 1, 0, 0, 0, 0, 0, 0, 0 } } };
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memset (C, 0, sizeof (bn256));
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memcpy (u, a, sizeof (bn256));
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memcpy (v, P256, sizeof (bn256));
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while (!bn256_is_zero (u))
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{
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while (bn256_is_even (u))
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{
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bn256_shift (u, u, -1);
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if (bn256_is_even (A))
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bn256_shift (A, A, -1);
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else
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{
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int carry = bn256_add (A, A, P256);
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bn256_shift (A, A, -1);
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if (carry)
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A->words[7] |= 0x80000000;
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}
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}
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while (bn256_is_even (v))
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{
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bn256_shift (v, v, -1);
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if (bn256_is_even (C))
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bn256_shift (C, C, -1);
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else
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{
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int carry = bn256_add (C, C, P256);
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bn256_shift (C, C, -1);
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if (carry)
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C->words[7] |= 0x80000000;
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}
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}
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if (bn256_is_ge (u, v))
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{
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bn256_sub (u, u, v);
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modp256_sub (A, A, C);
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}
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else
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{
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bn256_sub (v, v, u);
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modp256_sub (C, C, A);
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}
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}
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}
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2011-10-11 00:39:21 +00:00
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/**
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* @brief X = (A << shift) mod p256
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* @note shift <= 32
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*/
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void
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modp256_shift (bn256 *X, const bn256 *A, int shift)
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{
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2011-10-11 13:46:39 +00:00
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uint32_t carry;
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bn256 tmp[1];
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2011-10-11 00:39:21 +00:00
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carry = bn256_shift (X, A, shift);
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if (shift < 0)
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return;
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2011-10-11 13:46:39 +00:00
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memset (tmp, 0, sizeof (bn256));
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tmp->words[7] = carry;
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tmp->words[0] = carry;
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modp256_add (X, X, tmp);
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2011-10-11 00:39:21 +00:00
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2011-10-11 13:46:39 +00:00
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tmp->words[7] = 0;
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tmp->words[0] = 0;
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tmp->words[6] = carry;
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tmp->words[3] = carry;
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modp256_sub (X, X, tmp);
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2011-10-11 00:39:21 +00:00
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if (bn256_is_ge (X, P256))
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bn256_sub (X, X, P256);
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}
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