2010-03-03 19:20:03 +00:00
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/* bigint.c */
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/*
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2012-03-28 02:25:11 +00:00
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This file is part of the ARM-Crypto-Lib.
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2010-03-03 19:20:03 +00:00
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Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de)
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This program is free software: you can redistribute it and/or modify
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it 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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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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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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* \file bigint.c
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* \author Daniel Otte
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* \date 2010-02-22
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*
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* \license GPLv3 or later
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*
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*/
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2010-03-18 18:53:47 +00:00
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#define STRING2(x) #x
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#define STRING(x) STRING2(x)
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#define STR_LINE STRING(__LINE__)
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2010-03-03 19:20:03 +00:00
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#include "bigint.h"
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#include <string.h>
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2012-03-28 02:25:11 +00:00
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2013-09-19 23:57:40 +00:00
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#define DEBUG 1
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2012-03-28 02:25:11 +00:00
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2012-09-29 13:59:59 +00:00
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#if DEBUG || 1
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2010-03-18 18:53:47 +00:00
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#include "cli.h"
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2013-09-19 23:57:40 +00:00
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#include "uart_i.h"
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2010-03-18 18:53:47 +00:00
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#include "bigint_io.h"
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2012-09-29 13:59:59 +00:00
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#include <stdio.h>
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2012-03-28 02:25:11 +00:00
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#endif
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2010-03-03 19:20:03 +00:00
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#ifndef MAX
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#define MAX(a,b) (((a)>(b))?(a):(b))
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#endif
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#ifndef MIN
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2013-09-19 23:57:40 +00:00
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#define MIN(a,b) (((a) < (b)) ? (a) : (b))
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2010-03-03 19:20:03 +00:00
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#endif
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2014-02-14 22:10:30 +00:00
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#define SET_FBS(a, v) do {(a)->info &= ~BIGINT_FBS_MASK; (a)->info |= (v);} while(0)
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#define GET_FBS(a) ((a)->info & BIGINT_FBS_MASK)
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2010-03-03 19:20:03 +00:00
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#define SET_NEG(a) (a)->info |= BIGINT_NEG_MASK
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#define SET_POS(a) (a)->info &= ~BIGINT_NEG_MASK
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2013-09-19 23:57:40 +00:00
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#define XCHG(a,b) do{(a) ^= (b); (b) ^= (a); (a) ^= (b);} while(0)
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2012-06-20 21:58:55 +00:00
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#define XCHG_PTR(a,b) do{ a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
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b = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
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2013-09-19 23:57:40 +00:00
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a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));} while(0)
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2010-03-03 19:20:03 +00:00
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2013-09-19 23:57:40 +00:00
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#define GET_SIGN(a) ((a)->info & BIGINT_NEG_MASK)
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2010-03-03 19:20:03 +00:00
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/******************************************************************************/
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2013-02-17 09:44:36 +00:00
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void bigint_adjust(bigint_t *a){
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2014-02-14 22:10:30 +00:00
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while (a->length_W != 0 && a->wordv[a->length_W - 1] == 0) {
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2012-09-07 21:34:12 +00:00
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a->length_W--;
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2010-03-03 19:20:03 +00:00
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}
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2014-02-14 22:10:30 +00:00
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if (a->length_W == 0) {
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2010-03-03 19:20:03 +00:00
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a->info=0;
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return;
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}
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2012-03-28 02:25:11 +00:00
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bigint_word_t t;
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2014-02-14 22:10:30 +00:00
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uint8_t i = BIGINT_WORD_SIZE - 1;
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t = a->wordv[a->length_W - 1];
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while ((t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) == 0 && i) {
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t <<= 1;
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2010-03-03 19:20:03 +00:00
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i--;
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}
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SET_FBS(a, i);
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}
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/******************************************************************************/
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2013-09-19 23:57:40 +00:00
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bigint_length_t bigint_length_b(const bigint_t *a){
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2012-09-07 21:34:12 +00:00
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if(!a->length_W || a->length_W==0){
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2012-03-28 02:25:11 +00:00
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return 0;
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}
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2012-09-07 21:34:12 +00:00
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return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a);
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2012-03-28 02:25:11 +00:00
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}
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/******************************************************************************/
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2013-09-19 23:57:40 +00:00
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bigint_length_t bigint_length_B(const bigint_t *a){
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2012-09-07 21:34:12 +00:00
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return a->length_W * sizeof(bigint_word_t);
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2012-03-28 02:25:11 +00:00
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}
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/******************************************************************************/
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2014-02-15 00:23:43 +00:00
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int32_t bigint_get_first_set_bit(const bigint_t *a){
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2014-02-14 22:10:30 +00:00
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if(a->length_W == 0) {
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2014-02-15 00:23:43 +00:00
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return -1;
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2012-03-28 02:25:11 +00:00
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}
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2014-02-14 22:10:30 +00:00
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return (a->length_W-1) * sizeof(bigint_word_t) * CHAR_BIT + GET_FBS(a);
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2012-03-28 02:25:11 +00:00
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}
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/******************************************************************************/
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2014-02-15 00:23:43 +00:00
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int32_t bigint_get_last_set_bit(const bigint_t *a){
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uint32_t r = 0;
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uint8_t b = 0;
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bigint_word_t x = 1;
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if (a->length_W == 0) {
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return -1;
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2012-03-28 02:25:11 +00:00
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}
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2014-02-15 00:23:43 +00:00
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while (a->wordv[r] == 0 && r < a->length_W) {
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2012-03-28 02:25:11 +00:00
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++r;
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}
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2014-02-15 00:23:43 +00:00
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if (a->wordv[r] == 0) {
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2012-03-28 02:25:11 +00:00
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return (uint32_t)(-1);
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}
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2014-02-15 00:23:43 +00:00
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while ((x&a->wordv[r])==0) {
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2012-03-28 02:25:11 +00:00
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++b;
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x <<= 1;
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}
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2014-02-15 00:23:43 +00:00
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return r * BIGINT_WORD_SIZE + b;
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2012-03-28 02:25:11 +00:00
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}
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/******************************************************************************/
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2013-02-17 09:44:36 +00:00
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void bigint_copy(bigint_t *dest, const bigint_t *src){
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2012-09-29 13:59:59 +00:00
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if(dest->wordv != src->wordv){
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memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t));
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}
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dest->length_W = src->length_W;
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2010-03-03 19:20:03 +00:00
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dest->info = src->info;
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}
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/******************************************************************************/
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/* this should be implemented in assembly */
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2013-02-17 09:44:36 +00:00
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void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
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2013-09-19 23:57:40 +00:00
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bigint_length_t i;
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2012-06-20 21:58:55 +00:00
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bigint_wordplus_t t = 0LL;
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2013-09-19 23:57:40 +00:00
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if (a->length_W < b->length_W) {
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XCHG_PTR(a, b);
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2010-03-03 19:20:03 +00:00
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}
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2013-09-19 23:57:40 +00:00
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for(i = 0; i < b->length_W; ++i) {
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2012-03-28 02:25:11 +00:00
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t += a->wordv[i];
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t += b->wordv[i];
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dest->wordv[i] = (bigint_word_t)t;
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2012-06-20 21:58:55 +00:00
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t >>= BIGINT_WORD_SIZE;
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2010-03-03 19:20:03 +00:00
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}
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2013-09-19 23:57:40 +00:00
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for(; i < a->length_W; ++i){
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2012-03-28 02:25:11 +00:00
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t += a->wordv[i];
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dest->wordv[i] = (bigint_word_t)t;
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2012-06-20 21:58:55 +00:00
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t >>= BIGINT_WORD_SIZE;
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}
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if(t){
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dest->wordv[i++] = (bigint_word_t)t;
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2010-03-03 19:20:03 +00:00
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}
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2012-09-07 21:34:12 +00:00
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dest->length_W = i;
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2013-09-19 23:57:40 +00:00
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SET_POS(dest);
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2010-03-03 19:20:03 +00:00
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bigint_adjust(dest);
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}
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2011-01-02 23:22:27 +00:00
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2010-03-03 19:20:03 +00:00
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/******************************************************************************/
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/* this should be implemented in assembly */
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2013-09-19 23:57:40 +00:00
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void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){
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2012-09-07 21:34:12 +00:00
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if(a->length_W == 0){
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2012-06-20 21:58:55 +00:00
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return;
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}
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if(scale == 0){
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bigint_add_u(dest, dest, a);
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return;
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}
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bigint_t x;
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2012-09-29 13:59:59 +00:00
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#if BIGINT_WORD_SIZE == 8
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memset(dest->wordv + dest->length_W, 0, MAX(dest->length_W, a->length_W + scale) - dest->length_W);
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2012-06-20 21:58:55 +00:00
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x.wordv = dest->wordv + scale;
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2012-09-29 13:59:59 +00:00
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x.length_W = dest->length_W - scale;
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if((int16_t)x.length_W < 0){
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x.length_W = 0;
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x.info = 0;
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} else {
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x.info = dest->info;
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}
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2012-03-28 02:25:11 +00:00
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bigint_add_u(&x, &x, a);
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2012-09-07 21:34:12 +00:00
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dest->length_W = x.length_W + scale;
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2012-03-28 02:25:11 +00:00
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dest->info = 0;
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bigint_adjust(dest);
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#else
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2012-06-20 21:58:55 +00:00
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bigint_t s;
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2013-09-19 23:57:40 +00:00
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bigint_length_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
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2012-09-07 21:34:12 +00:00
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bigint_word_t bv[a->length_W + 1];
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2012-06-20 21:58:55 +00:00
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s.wordv = bv;
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2012-09-07 21:34:12 +00:00
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bv[0] = bv[a->length_W] = 0;
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memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_W * sizeof(bigint_word_t));
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s.length_W = a->length_W + 1;
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2012-06-20 21:58:55 +00:00
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bigint_adjust(&s);
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2012-09-07 21:34:12 +00:00
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memset(dest->wordv + dest->length_W, 0, (MAX(dest->length_W, s.length_W + word_shift) - dest->length_W) * sizeof(bigint_word_t));
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2012-06-20 21:58:55 +00:00
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x.wordv = dest->wordv + word_shift;
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2012-09-07 21:34:12 +00:00
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x.length_W = dest->length_W - word_shift;
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if((int16_t)x.length_W < 0){
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x.length_W = 0;
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2012-06-20 21:58:55 +00:00
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x.info = 0;
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}else{
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x.info = dest->info;
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}
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bigint_add_u(&x, &x, &s);
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2012-09-07 21:34:12 +00:00
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dest->length_W = x.length_W + word_shift;
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2012-06-20 21:58:55 +00:00
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dest->info = 0;
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bigint_adjust(dest);
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2012-03-28 02:25:11 +00:00
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#endif
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2010-03-03 19:20:03 +00:00
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}
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/******************************************************************************/
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/* this should be implemented in assembly */
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2013-02-17 09:44:36 +00:00
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void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
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2013-09-19 23:57:40 +00:00
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int8_t borrow = 0;
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2010-03-03 19:20:03 +00:00
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int8_t r;
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2014-02-14 22:10:30 +00:00
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bigint_wordplus_signed_t t = 0;
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2013-09-19 23:57:40 +00:00
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bigint_length_t i;
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2012-09-29 13:59:59 +00:00
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if(b->length_W == 0){
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2012-03-28 02:25:11 +00:00
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bigint_copy(dest, a);
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2010-03-03 19:20:03 +00:00
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SET_POS(dest);
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return;
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}
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2012-09-29 13:59:59 +00:00
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if(a->length_W == 0){
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2012-03-28 02:25:11 +00:00
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bigint_copy(dest, b);
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SET_NEG(dest);
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return;
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2010-03-03 19:20:03 +00:00
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}
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2012-09-29 13:59:59 +00:00
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r = bigint_cmp_u(a,b);
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if(r == 0){
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bigint_set_zero(dest);
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return;
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}
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if(r < 0){
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2010-03-06 20:54:30 +00:00
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bigint_sub_u(dest, b, a);
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2010-03-03 19:20:03 +00:00
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SET_NEG(dest);
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2012-03-28 02:25:11 +00:00
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return;
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}
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2012-09-29 13:59:59 +00:00
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for(i = 0; i < a->length_W; ++i){
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2012-03-28 02:25:11 +00:00
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t = a->wordv[i];
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2012-09-07 21:34:12 +00:00
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if(i < b->length_W){
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2012-03-28 02:25:11 +00:00
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t -= b->wordv[i];
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2010-03-03 19:20:03 +00:00
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}
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2012-03-28 02:25:11 +00:00
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t -= borrow;
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2013-09-19 23:57:40 +00:00
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dest->wordv[i] = (bigint_word_t)t;
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2014-02-14 22:10:30 +00:00
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borrow = t < 0 ? 1 : 0;
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2010-03-03 19:20:03 +00:00
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}
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2012-03-28 02:25:11 +00:00
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SET_POS(dest);
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2012-09-07 21:34:12 +00:00
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dest->length_W = i;
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2012-03-28 02:25:11 +00:00
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bigint_adjust(dest);
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2010-03-03 19:20:03 +00:00
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}
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/******************************************************************************/
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2013-02-17 09:44:36 +00:00
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int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b){
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2012-09-07 21:34:12 +00:00
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if(a->length_W > b->length_W){
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2010-03-03 19:20:03 +00:00
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return 1;
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}
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2012-09-07 21:34:12 +00:00
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if(a->length_W < b->length_W){
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2010-03-03 19:20:03 +00:00
|
|
|
return -1;
|
|
|
|
}
|
2013-09-19 23:57:40 +00:00
|
|
|
if(a->length_W == 0){
|
2010-03-03 19:20:03 +00:00
|
|
|
return 0;
|
|
|
|
}
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i;
|
|
|
|
i = a->length_W - 1;
|
2010-03-03 19:20:03 +00:00
|
|
|
do{
|
2012-03-28 02:25:11 +00:00
|
|
|
if(a->wordv[i] != b->wordv[i]){
|
|
|
|
if(a->wordv[i] > b->wordv[i]){
|
2010-03-03 19:20:03 +00:00
|
|
|
return 1;
|
|
|
|
}else{
|
|
|
|
return -1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}while(i--);
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_add_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t s;
|
|
|
|
s = GET_SIGN(a)?2:0;
|
|
|
|
s |= GET_SIGN(b)?1:0;
|
|
|
|
switch(s){
|
|
|
|
case 0: /* both positive */
|
|
|
|
bigint_add_u(dest, a,b);
|
2012-06-20 21:58:55 +00:00
|
|
|
SET_POS(dest);
|
2010-03-03 19:20:03 +00:00
|
|
|
break;
|
|
|
|
case 1: /* a positive, b negative */
|
|
|
|
bigint_sub_u(dest, a, b);
|
|
|
|
break;
|
|
|
|
case 2: /* a negative, b positive */
|
|
|
|
bigint_sub_u(dest, b, a);
|
|
|
|
break;
|
|
|
|
case 3: /* both negative */
|
|
|
|
bigint_add_u(dest, a, b);
|
2012-06-20 21:58:55 +00:00
|
|
|
SET_NEG(dest);
|
2010-03-03 19:20:03 +00:00
|
|
|
break;
|
|
|
|
default: /* how can this happen?*/
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_sub_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t s;
|
|
|
|
s = GET_SIGN(a)?2:0;
|
|
|
|
s |= GET_SIGN(b)?1:0;
|
|
|
|
switch(s){
|
|
|
|
case 0: /* both positive */
|
|
|
|
bigint_sub_u(dest, a,b);
|
|
|
|
break;
|
|
|
|
case 1: /* a positive, b negative */
|
|
|
|
bigint_add_u(dest, a, b);
|
|
|
|
SET_POS(dest);
|
|
|
|
break;
|
|
|
|
case 2: /* a negative, b positive */
|
|
|
|
bigint_add_u(dest, a, b);
|
|
|
|
SET_NEG(dest);
|
|
|
|
break;
|
|
|
|
case 3: /* both negative */
|
|
|
|
bigint_sub_u(dest, b, a);
|
|
|
|
break;
|
|
|
|
default: /* how can this happen?*/
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b){
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t s;
|
2012-09-07 21:34:12 +00:00
|
|
|
if(a->length_W==0 && b->length_W==0){
|
2010-03-06 20:54:30 +00:00
|
|
|
return 0;
|
|
|
|
}
|
2010-03-03 19:20:03 +00:00
|
|
|
s = GET_SIGN(a)?2:0;
|
|
|
|
s |= GET_SIGN(b)?1:0;
|
|
|
|
switch(s){
|
|
|
|
case 0: /* both positive */
|
|
|
|
return bigint_cmp_u(a, b);
|
|
|
|
break;
|
|
|
|
case 1: /* a positive, b negative */
|
|
|
|
return 1;
|
|
|
|
break;
|
|
|
|
case 2: /* a negative, b positive */
|
|
|
|
return -1;
|
|
|
|
break;
|
|
|
|
case 3: /* both negative */
|
|
|
|
return bigint_cmp_u(b, a);
|
|
|
|
break;
|
|
|
|
default: /* how can this happen?*/
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
return 0; /* just to satisfy the compiler */
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
void bigint_shiftleft(bigint_t *a, bigint_length_t shift){
|
|
|
|
bigint_length_t byteshift, words_to_shift;
|
2012-03-28 02:25:11 +00:00
|
|
|
int16_t i;
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t bitshift;
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_word_t *p;
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_wordplus_t t = 0;
|
2014-02-14 22:10:30 +00:00
|
|
|
|
2014-02-15 00:23:43 +00:00
|
|
|
if (a->length_W == 0 || shift == 0) {
|
2012-03-28 02:25:11 +00:00
|
|
|
return;
|
|
|
|
}
|
2012-06-20 21:58:55 +00:00
|
|
|
byteshift = shift / 8;
|
|
|
|
bitshift = shift & 7;
|
2014-02-14 22:10:30 +00:00
|
|
|
if (byteshift % sizeof(bigint_word_t)) {
|
|
|
|
a->wordv[a->length_W + byteshift / sizeof(bigint_t)] = 0;
|
|
|
|
}
|
|
|
|
if (byteshift) {
|
2012-09-29 13:59:59 +00:00
|
|
|
memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t));
|
2012-03-28 02:25:11 +00:00
|
|
|
memset(a->wordv, 0, byteshift);
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
if (bitshift == 0) {
|
2012-09-29 13:59:59 +00:00
|
|
|
a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
|
|
|
|
bigint_adjust(a);
|
|
|
|
return;
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
p = &a->wordv[byteshift / sizeof(bigint_word_t)];
|
|
|
|
words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t) ? 1 : 0);
|
|
|
|
for (i = 0; i < words_to_shift; ++i) {
|
2012-09-29 13:59:59 +00:00
|
|
|
t |= ((bigint_wordplus_t)p[i]) << bitshift;
|
|
|
|
p[i] = (bigint_word_t)t;
|
|
|
|
t >>= BIGINT_WORD_SIZE;
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
if (t) {
|
2012-09-29 13:59:59 +00:00
|
|
|
p[i] = (bigint_word_t)t;
|
|
|
|
a->length_W += 1;
|
|
|
|
}
|
|
|
|
a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_adjust(a);
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
void bigint_shiftright(bigint_t *a, bigint_length_t shift){
|
|
|
|
bigint_length_t byteshift;
|
|
|
|
bigint_length_t i;
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t bitshift;
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_wordplus_t t = 0;
|
|
|
|
byteshift = shift / 8;
|
|
|
|
bitshift = shift & 7;
|
|
|
|
|
2014-02-15 00:23:43 +00:00
|
|
|
if (a->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
2014-02-14 22:10:30 +00:00
|
|
|
if(bigint_get_first_set_bit(a) < shift){ /* we would shift out more than we have */
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_set_zero(a);
|
2010-03-03 19:20:03 +00:00
|
|
|
return;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
|
2010-03-03 19:20:03 +00:00
|
|
|
if(byteshift){
|
2012-09-07 21:34:12 +00:00
|
|
|
memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift);
|
2014-02-14 22:10:30 +00:00
|
|
|
memset((uint8_t*)&a->wordv[a->length_W] - byteshift, 0, byteshift);
|
2014-02-15 00:23:43 +00:00
|
|
|
a->length_W -= byteshift / sizeof(bigint_word_t);
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
|
2014-02-14 22:10:30 +00:00
|
|
|
|
|
|
|
if(bitshift != 0 && a->length_W){
|
2010-03-03 19:20:03 +00:00
|
|
|
/* shift to the right */
|
2012-09-07 21:34:12 +00:00
|
|
|
i = a->length_W - 1;
|
2012-06-20 21:58:55 +00:00
|
|
|
do{
|
|
|
|
t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - bitshift);
|
|
|
|
a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE);
|
2012-03-28 02:25:11 +00:00
|
|
|
t <<= BIGINT_WORD_SIZE;
|
2012-06-20 21:58:55 +00:00
|
|
|
}while(i--);
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
bigint_adjust(a);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_xor(bigint_t *dest, const bigint_t *a){
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i;
|
2012-09-07 21:34:12 +00:00
|
|
|
for(i=0; i<a->length_W; ++i){
|
2010-03-03 19:20:03 +00:00
|
|
|
dest->wordv[i] ^= a->wordv[i];
|
|
|
|
}
|
|
|
|
bigint_adjust(dest);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_set_zero(bigint_t *a){
|
2012-09-07 21:34:12 +00:00
|
|
|
a->length_W=0;
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* using the Karatsuba-Algorithm */
|
|
|
|
/* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
|
2012-09-29 13:59:59 +00:00
|
|
|
if(a->length_W == 0 || b->length_W == 0){
|
2010-03-18 18:53:47 +00:00
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(dest == a || dest == b){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_t d;
|
2012-09-07 21:34:12 +00:00
|
|
|
bigint_word_t d_b[a->length_W + b->length_W];
|
2010-03-06 20:54:30 +00:00
|
|
|
d.wordv = d_b;
|
|
|
|
bigint_mul_u(&d, a, b);
|
|
|
|
bigint_copy(dest, &d);
|
|
|
|
return;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(a->length_W == 1 || b->length_W == 1){
|
2012-09-07 21:34:12 +00:00
|
|
|
if(a->length_W != 1){
|
2010-03-03 19:20:03 +00:00
|
|
|
XCHG_PTR(a,b);
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_wordplus_t t = 0;
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i;
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_word_t x = a->wordv[0];
|
2012-09-07 21:34:12 +00:00
|
|
|
for(i=0; i < b->length_W; ++i){
|
2012-06-20 21:58:55 +00:00
|
|
|
t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x);
|
2012-03-28 02:25:11 +00:00
|
|
|
dest->wordv[i] = (bigint_word_t)t;
|
2012-09-29 13:59:59 +00:00
|
|
|
t >>= BIGINT_WORD_SIZE;
|
|
|
|
}
|
|
|
|
dest->length_W = i;
|
|
|
|
if(t){
|
|
|
|
dest->wordv[i] = (bigint_word_t)t;
|
|
|
|
dest->length_W += 1;
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
dest->info = 0;
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
2012-09-07 21:34:12 +00:00
|
|
|
if(a->length_W * sizeof(bigint_word_t) <= 4 && b->length_W * sizeof(bigint_word_t) <= 4){
|
2010-03-03 19:20:03 +00:00
|
|
|
uint32_t p=0, q=0;
|
|
|
|
uint64_t r;
|
2012-09-07 21:34:12 +00:00
|
|
|
memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t));
|
|
|
|
memcpy(&q, b->wordv, b->length_W*sizeof(bigint_word_t));
|
2012-03-28 02:25:11 +00:00
|
|
|
r = (uint64_t)p * (uint64_t)q;
|
2012-09-07 21:34:12 +00:00
|
|
|
memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W)*sizeof(bigint_word_t));
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
/* split a in xh & xl; split b in yh & yl */
|
2013-09-19 23:57:40 +00:00
|
|
|
const bigint_length_t n = (MAX(a->length_W, b->length_W)+1)/2;
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_t xl, xh, yl, yh;
|
|
|
|
xl.wordv = a->wordv;
|
|
|
|
yl.wordv = b->wordv;
|
2012-09-29 13:59:59 +00:00
|
|
|
if(a->length_W<=n){
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_set_zero(&xh);
|
2012-09-07 21:34:12 +00:00
|
|
|
xl.length_W = a->length_W;
|
2012-03-28 02:25:11 +00:00
|
|
|
xl.info = a->info;
|
2010-03-03 19:20:03 +00:00
|
|
|
}else{
|
2012-09-29 13:59:59 +00:00
|
|
|
xl.length_W=n;
|
2010-03-03 19:20:03 +00:00
|
|
|
xl.info = 0;
|
|
|
|
bigint_adjust(&xl);
|
2012-03-28 02:25:11 +00:00
|
|
|
xh.wordv = &(a->wordv[n]);
|
2012-09-07 21:34:12 +00:00
|
|
|
xh.length_W = a->length_W-n;
|
2012-03-28 02:25:11 +00:00
|
|
|
xh.info = a->info;
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(b->length_W<=n){
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_set_zero(&yh);
|
2012-09-07 21:34:12 +00:00
|
|
|
yl.length_W = b->length_W;
|
2010-03-03 19:20:03 +00:00
|
|
|
yl.info = b->info;
|
|
|
|
}else{
|
2012-09-29 13:59:59 +00:00
|
|
|
yl.length_W=n;
|
2010-03-03 19:20:03 +00:00
|
|
|
yl.info = 0;
|
|
|
|
bigint_adjust(&yl);
|
2012-03-28 02:25:11 +00:00
|
|
|
yh.wordv = &(b->wordv[n]);
|
2012-09-07 21:34:12 +00:00
|
|
|
yh.length_W = b->length_W-n;
|
2012-03-28 02:25:11 +00:00
|
|
|
yh.info = b->info;
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
/* now we have split up a and b */
|
2012-03-28 02:25:11 +00:00
|
|
|
/* remember we want to do:
|
2012-09-29 13:59:59 +00:00
|
|
|
* x*y = (xh * b**n + xl) * (yh * b**n + yl)
|
|
|
|
* = (xh * yh) * b**2n + xh * b**n * yl + yh * b**n * xl + xl * yl
|
|
|
|
* = (xh * yh) * b**2n + (xh * yl + yh * xl) * b**n + xl *yl
|
|
|
|
* // xh * yl + yh * xl = (xh + yh) * (xl + yl) - xh * yh - xl * yl
|
|
|
|
* x*y = (xh * yh) * b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + xl*yl
|
|
|
|
* 5 9 2 4 3 7 5 6 1 8 1
|
2012-03-28 02:25:11 +00:00
|
|
|
*/
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_word_t tmp_b[2 * n + 2], m_b[2 * (n + 1)];
|
|
|
|
bigint_t tmp, tmp2, m;
|
|
|
|
tmp.wordv = tmp_b;
|
|
|
|
tmp2.wordv = &(tmp_b[n + 1]);
|
|
|
|
m.wordv = m_b;
|
|
|
|
|
|
|
|
bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl*yl */
|
|
|
|
bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl */
|
|
|
|
bigint_add_u(&tmp, &yh, &yl); /* 3: tmp <= yh+yl */
|
|
|
|
bigint_mul_u(&m, &tmp2, &tmp); /* 4: m <= tmp2*tmp */
|
|
|
|
bigint_mul_u(&tmp, &xh, &yh); /* 5: tmp <= xh*yh */
|
|
|
|
bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */
|
|
|
|
bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-tmp */
|
|
|
|
bigint_add_scale_u(dest, &m, n * sizeof(bigint_word_t)); /* 8: dest <= dest+m**n*/
|
|
|
|
bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_mul_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){
|
2010-03-03 19:20:03 +00:00
|
|
|
uint8_t s;
|
|
|
|
s = GET_SIGN(a)?2:0;
|
|
|
|
s |= GET_SIGN(b)?1:0;
|
|
|
|
switch(s){
|
|
|
|
case 0: /* both positive */
|
|
|
|
bigint_mul_u(dest, a,b);
|
|
|
|
SET_POS(dest);
|
|
|
|
break;
|
|
|
|
case 1: /* a positive, b negative */
|
|
|
|
bigint_mul_u(dest, a,b);
|
|
|
|
SET_NEG(dest);
|
|
|
|
break;
|
|
|
|
case 2: /* a negative, b positive */
|
|
|
|
bigint_mul_u(dest, a,b);
|
|
|
|
SET_NEG(dest);
|
|
|
|
break;
|
|
|
|
case 3: /* both negative */
|
|
|
|
bigint_mul_u(dest, a,b);
|
|
|
|
SET_POS(dest);
|
|
|
|
break;
|
|
|
|
default: /* how can this happen?*/
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
2013-09-19 23:57:40 +00:00
|
|
|
#if OLD_SQUARE
|
2012-09-29 13:59:59 +00:00
|
|
|
|
|
|
|
#if DEBUG_SQUARE
|
|
|
|
unsigned square_depth = 0;
|
|
|
|
#endif
|
|
|
|
|
2010-03-03 19:20:03 +00:00
|
|
|
/* square */
|
|
|
|
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_square(bigint_t *dest, const bigint_t *a){
|
2013-09-19 23:57:40 +00:00
|
|
|
if(a->length_W * sizeof(bigint_word_t) <= 4){
|
2012-06-20 21:58:55 +00:00
|
|
|
uint64_t r = 0;
|
2012-09-07 21:34:12 +00:00
|
|
|
memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
|
2012-06-20 21:58:55 +00:00
|
|
|
r = r * r;
|
2012-09-29 13:59:59 +00:00
|
|
|
memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t));
|
2010-03-03 19:20:03 +00:00
|
|
|
SET_POS(dest);
|
2012-09-07 21:34:12 +00:00
|
|
|
dest->length_W = 2 * a->length_W;
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
2013-09-19 23:57:40 +00:00
|
|
|
|
2012-09-29 13:59:59 +00:00
|
|
|
if(dest->wordv == a->wordv){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_t d;
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_word_t d_b[a->length_W*2];
|
2010-03-06 20:54:30 +00:00
|
|
|
d.wordv = d_b;
|
|
|
|
bigint_square(&d, a);
|
|
|
|
bigint_copy(dest, &d);
|
|
|
|
return;
|
|
|
|
}
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_fast_square(dest, a);
|
|
|
|
return;
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
square_depth += 1;
|
|
|
|
#endif
|
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t n;
|
2012-09-29 13:59:59 +00:00
|
|
|
n=(a->length_W+1)/2;
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_word_t buffer[2*n+1];
|
2010-03-03 19:20:03 +00:00
|
|
|
xl.wordv = a->wordv;
|
2012-09-07 21:34:12 +00:00
|
|
|
xl.length_W = n;
|
2012-03-28 02:25:11 +00:00
|
|
|
xl.info = 0;
|
|
|
|
xh.wordv = &(a->wordv[n]);
|
2012-09-29 13:59:59 +00:00
|
|
|
xh.length_W = a->length_W-n;
|
2012-06-20 21:58:55 +00:00
|
|
|
xh.info = a->info;
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_adjust(&xl);
|
2010-03-03 19:20:03 +00:00
|
|
|
tmp.wordv = buffer;
|
2012-03-28 02:25:11 +00:00
|
|
|
/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
|
|
|
|
cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
|
|
|
|
}
|
|
|
|
#endif
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_square(dest, &xl);
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
bigint_square(&tmp, &xh);
|
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
|
|
|
|
}
|
|
|
|
#endif
|
2012-06-20 21:58:55 +00:00
|
|
|
bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t));
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
|
|
|
|
}
|
|
|
|
#endif
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_mul_u(&tmp, &xl, &xh);
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
|
|
|
|
}
|
|
|
|
#endif
|
2010-03-03 19:20:03 +00:00
|
|
|
bigint_shiftleft(&tmp, 1);
|
2012-09-29 13:59:59 +00:00
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
bigint_add_scale_u(dest, &tmp, n * sizeof(bigint_word_t));
|
|
|
|
#if DEBUG_SQUARE
|
|
|
|
if(square_depth == 1){
|
|
|
|
cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
|
|
|
|
cli_putstr("\r\n");
|
|
|
|
}
|
|
|
|
square_depth -= 1;
|
|
|
|
#endif
|
2010-03-03 19:20:03 +00:00
|
|
|
}
|
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
#endif
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
void bigint_square(bigint_t *dest, const bigint_t *a) {
|
2014-02-14 22:10:30 +00:00
|
|
|
union __attribute__((packed)) {
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_word_t u[2];
|
|
|
|
bigint_wordplus_t uv;
|
|
|
|
} acc;
|
|
|
|
bigint_word_t q, c1, c2;
|
|
|
|
bigint_length_t i, j;
|
|
|
|
|
|
|
|
if(a->length_W * sizeof(bigint_word_t) <= 4){
|
|
|
|
uint64_t r = 0;
|
|
|
|
memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
|
|
|
|
r = r * r;
|
|
|
|
memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t));
|
|
|
|
SET_POS(dest);
|
|
|
|
dest->length_W = 2 * a->length_W;
|
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
if(dest->wordv == a->wordv){
|
|
|
|
bigint_t d;
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_word_t d_b[a->length_W * 2];
|
2013-09-19 23:57:40 +00:00
|
|
|
d.wordv = d_b;
|
|
|
|
bigint_square(&d, a);
|
|
|
|
bigint_copy(dest, &d);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
memset(dest->wordv, 0, a->length_W * 2 * sizeof(bigint_word_t));
|
|
|
|
|
|
|
|
for (i = 0; i < a->length_W; ++i) {
|
2014-02-14 22:10:30 +00:00
|
|
|
acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[i] + (bigint_wordplus_t)dest->wordv[2 * i];
|
2013-09-19 23:57:40 +00:00
|
|
|
dest->wordv[2 * i] = acc.u[0];
|
|
|
|
c1 = acc.u[1];
|
|
|
|
c2 = 0;
|
|
|
|
for (j = i + 1; j < a->length_W; ++j) {
|
2014-02-14 22:10:30 +00:00
|
|
|
acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[j];
|
2013-09-19 23:57:40 +00:00
|
|
|
q = acc.u[1] >> (BIGINT_WORD_SIZE - 1);
|
|
|
|
acc.uv <<= 1;
|
|
|
|
acc.uv += dest->wordv[i + j];
|
|
|
|
q += (acc.uv < dest->wordv[i + j]);
|
|
|
|
acc.uv += c1;
|
|
|
|
q += (acc.uv < c1);
|
|
|
|
dest->wordv[i + j] = acc.u[0];
|
2014-02-14 22:10:30 +00:00
|
|
|
c1 = (bigint_wordplus_t)acc.u[1] + c2;
|
2013-09-19 23:57:40 +00:00
|
|
|
c2 = q + (c1 < c2);
|
|
|
|
}
|
|
|
|
dest->wordv[i + a->length_W] += c1;
|
2014-02-14 22:10:30 +00:00
|
|
|
if (i < a->length_W - 1) {
|
|
|
|
dest->wordv[i + a->length_W + 1] = c2 + (dest->wordv[i + a->length_W] < c1);
|
|
|
|
}
|
2013-09-19 23:57:40 +00:00
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
dest->info = 0;
|
2013-09-19 23:57:40 +00:00
|
|
|
dest->length_W = 2 * a->length_W;
|
|
|
|
bigint_adjust(dest);
|
|
|
|
}
|
|
|
|
|
2010-03-04 18:34:50 +00:00
|
|
|
/******************************************************************************/
|
2013-02-17 09:35:16 +00:00
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_t tmp, x;
|
2012-09-07 21:34:12 +00:00
|
|
|
bigint_word_t tmp_b[b->length_W + 1];
|
2013-09-19 23:57:40 +00:00
|
|
|
const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE;
|
2010-03-03 19:20:03 +00:00
|
|
|
|
2014-02-14 22:10:30 +00:00
|
|
|
if (a->length_W < b->length_W + word_shift) {
|
2012-03-28 02:25:11 +00:00
|
|
|
#if DEBUG
|
|
|
|
cli_putstr("\r\nDBG: *bang*\r\n");
|
|
|
|
#endif
|
2010-03-04 18:34:50 +00:00
|
|
|
bigint_set_zero(a);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
tmp.wordv = tmp_b;
|
|
|
|
bigint_copy(&tmp, b);
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
|
2010-03-04 18:34:50 +00:00
|
|
|
|
2012-03-28 02:25:11 +00:00
|
|
|
x.info = a->info;
|
|
|
|
x.wordv = &(a->wordv[word_shift]);
|
2012-09-07 21:34:12 +00:00
|
|
|
x.length_W = a->length_W - word_shift;
|
2012-03-28 02:25:11 +00:00
|
|
|
|
|
|
|
bigint_sub_u(&x, &x, &tmp);
|
2010-03-04 18:34:50 +00:00
|
|
|
bigint_adjust(a);
|
2012-03-28 02:25:11 +00:00
|
|
|
return;
|
2010-03-04 18:34:50 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_reduce(bigint_t *a, const bigint_t *r){
|
2010-03-04 18:34:50 +00:00
|
|
|
uint8_t rfbs = GET_FBS(r);
|
2014-02-14 22:10:30 +00:00
|
|
|
if (r->length_W == 0 || a->length_W == 0) {
|
2010-03-04 18:34:50 +00:00
|
|
|
return;
|
|
|
|
}
|
2013-02-17 09:35:16 +00:00
|
|
|
|
2014-02-14 22:10:30 +00:00
|
|
|
if (bigint_length_b(a) + 3 > bigint_length_b(r)) {
|
|
|
|
if ((r->length_W * sizeof(bigint_word_t) <= 4) && (a->length_W * sizeof(bigint_word_t) <= 4)) {
|
|
|
|
uint32_t p = 0, q = 0;
|
|
|
|
memcpy(&p, a->wordv, a->length_W * sizeof(bigint_word_t));
|
|
|
|
memcpy(&q, r->wordv, r->length_W * sizeof(bigint_word_t));
|
2013-02-17 09:35:16 +00:00
|
|
|
p %= q;
|
2014-02-14 22:10:30 +00:00
|
|
|
memcpy(a->wordv, &p, a->length_W * sizeof(bigint_word_t));
|
|
|
|
a->length_W = r->length_W;
|
2013-02-17 09:35:16 +00:00
|
|
|
bigint_adjust(a);
|
|
|
|
return;
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
unsigned shift;
|
|
|
|
while (a->length_W > r->length_W) {
|
|
|
|
shift = (a->length_W - r->length_W) * CHAR_BIT * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
|
2013-02-17 09:35:16 +00:00
|
|
|
bigint_sub_u_bitscale(a, r, shift);
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
while ((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)) {
|
|
|
|
shift = GET_FBS(a) - rfbs - 1;
|
2013-02-17 09:35:16 +00:00
|
|
|
bigint_sub_u_bitscale(a, r, shift);
|
|
|
|
}
|
2010-03-04 18:34:50 +00:00
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
while (bigint_cmp_u(a, r) >= 0) {
|
|
|
|
bigint_sub_u(a, a, r);
|
2010-03-04 18:34:50 +00:00
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_adjust(a);
|
2010-03-04 18:34:50 +00:00
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* calculate dest = a**exp % r */
|
|
|
|
/* using square&multiply */
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
|
2013-09-19 23:57:40 +00:00
|
|
|
if(a->length_W == 0){
|
|
|
|
bigint_set_zero(dest);
|
2010-03-06 20:54:30 +00:00
|
|
|
return;
|
|
|
|
}
|
2010-03-18 18:53:47 +00:00
|
|
|
|
|
|
|
bigint_t res, base;
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_word_t t, base_w[MAX(a->length_W, r->length_W)], res_w[r->length_W * 2];
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i;
|
2012-03-28 02:25:11 +00:00
|
|
|
uint8_t j;
|
2013-09-19 23:57:40 +00:00
|
|
|
res.wordv = res_w;
|
|
|
|
base.wordv = base_w;
|
2010-03-18 18:53:47 +00:00
|
|
|
bigint_copy(&base, a);
|
|
|
|
bigint_reduce(&base, r);
|
2013-09-19 23:57:40 +00:00
|
|
|
res.wordv[0] = 1;
|
|
|
|
res.length_W = 1;
|
2010-03-18 18:53:47 +00:00
|
|
|
res.info = 0;
|
|
|
|
bigint_adjust(&res);
|
2012-09-07 21:34:12 +00:00
|
|
|
if(exp->length_W == 0){
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_copy(dest, &res);
|
|
|
|
return;
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_copy(&res, &base);
|
2012-03-28 02:25:11 +00:00
|
|
|
uint8_t flag = 0;
|
2014-02-14 22:10:30 +00:00
|
|
|
t = exp->wordv[exp->length_W - 1];
|
|
|
|
for (i = exp->length_W; i > 0; --i) {
|
2012-03-28 02:25:11 +00:00
|
|
|
t = exp->wordv[i - 1];
|
2014-02-14 22:10:30 +00:00
|
|
|
for (j = BIGINT_WORD_SIZE; j > 0; --j) {
|
|
|
|
if (!flag) {
|
|
|
|
if (t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) {
|
2012-03-28 02:25:11 +00:00
|
|
|
flag = 1;
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
} else {
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_square(&res, &res);
|
2010-03-18 18:53:47 +00:00
|
|
|
bigint_reduce(&res, r);
|
2014-02-14 22:10:30 +00:00
|
|
|
if(t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))){
|
2012-03-28 02:25:11 +00:00
|
|
|
bigint_mul_u(&res, &res, &base);
|
|
|
|
bigint_reduce(&res, r);
|
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
t <<= 1;
|
2010-03-06 20:54:30 +00:00
|
|
|
}
|
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
|
2010-03-18 18:53:47 +00:00
|
|
|
SET_POS(&res);
|
|
|
|
bigint_copy(dest, &res);
|
2010-03-06 20:54:30 +00:00
|
|
|
}
|
2010-03-06 22:46:52 +00:00
|
|
|
|
2010-03-06 20:54:30 +00:00
|
|
|
/******************************************************************************/
|
|
|
|
/* gcd <-- gcd(x,y) a*x+b*y=gcd */
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, const bigint_t *y){
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i = 0;
|
2012-09-29 13:59:59 +00:00
|
|
|
if(x->length_W == 0 || y->length_W == 0){
|
|
|
|
if(gcd){
|
|
|
|
bigint_set_zero(gcd);
|
|
|
|
}
|
|
|
|
if(a){
|
|
|
|
bigint_set_zero(a);
|
|
|
|
}
|
|
|
|
if(b){
|
|
|
|
bigint_set_zero(b);
|
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
return;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(x->length_W == 1 && x->wordv[0] == 1){
|
|
|
|
if(gcd){
|
|
|
|
gcd->length_W = 1;
|
|
|
|
gcd->wordv[0] = 1;
|
|
|
|
gcd->info = 0;
|
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
if(a){
|
2012-09-07 21:34:12 +00:00
|
|
|
a->length_W = 1;
|
2012-03-28 02:25:11 +00:00
|
|
|
a->wordv[0] = 1;
|
|
|
|
SET_POS(a);
|
|
|
|
bigint_adjust(a);
|
|
|
|
}
|
|
|
|
if(b){
|
|
|
|
bigint_set_zero(b);
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(y->length_W == 1 && y->wordv[0] == 1){
|
|
|
|
if(gcd){
|
|
|
|
gcd->length_W = 1;
|
|
|
|
gcd->wordv[0] = 1;
|
|
|
|
gcd->info = 0;
|
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
if(b){
|
2012-09-07 21:34:12 +00:00
|
|
|
b->length_W = 1;
|
2012-03-28 02:25:11 +00:00
|
|
|
b->wordv[0] = 1;
|
|
|
|
SET_POS(b);
|
|
|
|
bigint_adjust(b);
|
|
|
|
}
|
|
|
|
if(a){
|
|
|
|
bigint_set_zero(a);
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
2012-09-29 13:59:59 +00:00
|
|
|
while(x->wordv[i] == 0 && y->wordv[i] == 0){
|
2010-03-06 20:54:30 +00:00
|
|
|
++i;
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
bigint_word_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i];
|
|
|
|
bigint_word_t u_b[x->length_W - i], v_b[y->length_W - i];
|
|
|
|
bigint_word_t a_b[y->length_W + 2], c_b[y->length_W + 2];
|
|
|
|
bigint_word_t b_b[x->length_W + 2], d_b[x->length_W + 2];
|
|
|
|
bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
|
2010-03-06 20:54:30 +00:00
|
|
|
|
|
|
|
g.wordv = g_b;
|
|
|
|
x_.wordv = x_b;
|
|
|
|
y_.wordv = y_b;
|
2012-09-29 13:59:59 +00:00
|
|
|
memset(g_b, 0, i * sizeof(bigint_word_t));
|
|
|
|
g_b[i] = 1;
|
|
|
|
g.length_W = i + 1;
|
|
|
|
g.info = 0;
|
2010-03-06 20:54:30 +00:00
|
|
|
x_.info = y_.info = 0;
|
2012-09-29 13:59:59 +00:00
|
|
|
x_.length_W = x->length_W - i;
|
|
|
|
y_.length_W = y->length_W - i;
|
|
|
|
memcpy(x_.wordv, x->wordv + i, x_.length_W * sizeof(bigint_word_t));
|
|
|
|
memcpy(y_.wordv, y->wordv + i, y_.length_W * sizeof(bigint_word_t));
|
|
|
|
for(i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0; ++i){
|
2010-03-06 20:54:30 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
bigint_adjust(&x_);
|
|
|
|
bigint_adjust(&y_);
|
|
|
|
|
|
|
|
if(i){
|
|
|
|
bigint_shiftleft(&g, i);
|
2010-03-06 22:46:52 +00:00
|
|
|
bigint_shiftright(&x_, i);
|
|
|
|
bigint_shiftright(&y_, i);
|
2010-03-06 20:54:30 +00:00
|
|
|
}
|
2012-03-28 02:25:11 +00:00
|
|
|
|
2010-03-06 20:54:30 +00:00
|
|
|
u.wordv = u_b;
|
|
|
|
v.wordv = v_b;
|
|
|
|
a_.wordv = a_b;
|
|
|
|
b_.wordv = b_b;
|
|
|
|
c_.wordv = c_b;
|
|
|
|
d_.wordv = d_b;
|
|
|
|
|
|
|
|
bigint_copy(&u, &x_);
|
|
|
|
bigint_copy(&v, &y_);
|
|
|
|
a_.wordv[0] = 1;
|
2012-09-07 21:34:12 +00:00
|
|
|
a_.length_W = 1;
|
2010-03-06 20:54:30 +00:00
|
|
|
a_.info = 0;
|
|
|
|
d_.wordv[0] = 1;
|
2012-09-07 21:34:12 +00:00
|
|
|
d_.length_W = 1;
|
2010-03-06 20:54:30 +00:00
|
|
|
d_.info = 0;
|
|
|
|
bigint_set_zero(&b_);
|
|
|
|
bigint_set_zero(&c_);
|
2014-02-14 22:10:30 +00:00
|
|
|
do {
|
|
|
|
while ((u.wordv[0] & 1) == 0) {
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_shiftright(&u, 1);
|
2012-09-29 13:59:59 +00:00
|
|
|
if((a_.wordv[0] & 1) || (b_.wordv[0] & 1)){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_add_s(&a_, &a_, &y_);
|
|
|
|
bigint_sub_s(&b_, &b_, &x_);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&a_, 1);
|
|
|
|
bigint_shiftright(&b_, 1);
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
while ((v.wordv[0] & 1) == 0) {
|
|
|
|
bigint_shiftright(&v, 1);
|
2012-09-29 13:59:59 +00:00
|
|
|
if((c_.wordv[0] & 1) || (d_.wordv[0] & 1)){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_add_s(&c_, &c_, &y_);
|
|
|
|
bigint_sub_s(&d_, &d_, &x_);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&c_, 1);
|
|
|
|
bigint_shiftright(&d_, 1);
|
|
|
|
}
|
2012-09-29 13:59:59 +00:00
|
|
|
if(bigint_cmp_u(&u, &v) >= 0){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_sub_u(&u, &u, &v);
|
|
|
|
bigint_sub_s(&a_, &a_, &c_);
|
|
|
|
bigint_sub_s(&b_, &b_, &d_);
|
|
|
|
}else{
|
|
|
|
bigint_sub_u(&v, &v, &u);
|
|
|
|
bigint_sub_s(&c_, &c_, &a_);
|
|
|
|
bigint_sub_s(&d_, &d_, &b_);
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
} while(u.length_W);
|
2010-03-06 20:54:30 +00:00
|
|
|
if(gcd){
|
|
|
|
bigint_mul_s(gcd, &v, &g);
|
|
|
|
}
|
|
|
|
if(a){
|
|
|
|
bigint_copy(a, &c_);
|
|
|
|
}
|
|
|
|
if(b){
|
|
|
|
bigint_copy(b, &d_);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m){
|
2010-03-06 20:54:30 +00:00
|
|
|
bigint_gcdext(NULL, dest, NULL, a, m);
|
|
|
|
while(dest->info&BIGINT_NEG_MASK){
|
|
|
|
bigint_add_s(dest, dest, m);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2010-03-18 18:53:47 +00:00
|
|
|
/******************************************************************************/
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_changeendianess(bigint_t *a){
|
2010-03-18 18:53:47 +00:00
|
|
|
uint8_t t, *p, *q;
|
2012-03-28 02:25:11 +00:00
|
|
|
p = (uint8_t*)(a->wordv);
|
2012-09-07 21:34:12 +00:00
|
|
|
q = p + a->length_W * sizeof(bigint_word_t) - 1;
|
2010-03-18 18:53:47 +00:00
|
|
|
while(p<q){
|
|
|
|
t = *p;
|
|
|
|
*p = *q;
|
|
|
|
*q = t;
|
|
|
|
++p; --q;
|
|
|
|
}
|
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
|
2010-03-18 18:53:47 +00:00
|
|
|
/******************************************************************************/
|
2010-03-06 20:54:30 +00:00
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
void bigint_mul_word_u(bigint_t *a, bigint_word_t b){
|
|
|
|
bigint_wordplus_t c0 = 0, c1 = 0;
|
|
|
|
bigint_length_t i;
|
|
|
|
|
|
|
|
if(b == 0){
|
|
|
|
bigint_set_zero(a);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
for(i = 0; i < a->length_W; ++i){
|
|
|
|
c1 = ((bigint_wordplus_t)(a->wordv[i])) * ((bigint_wordplus_t)b);
|
|
|
|
c1 += c0;
|
|
|
|
a->wordv[i] = (bigint_word_t)c1;
|
|
|
|
c0 = c1 >> BIGINT_WORD_SIZE;
|
|
|
|
}
|
|
|
|
if(c0){
|
|
|
|
a->wordv[a->length_W] = (bigint_word_t)c0;
|
|
|
|
a->length_W += 1;
|
|
|
|
}
|
|
|
|
bigint_adjust(a);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
#if 1
|
|
|
|
|
|
|
|
void bigint_clip(bigint_t *dest, bigint_length_t length_W){
|
|
|
|
if(dest->length_W > length_W){
|
|
|
|
dest->length_W = length_W;
|
|
|
|
}
|
|
|
|
bigint_adjust(dest);
|
|
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/*
|
|
|
|
* m_ = m * m'[0]
|
2014-02-14 22:10:30 +00:00
|
|
|
* dest = (a * b) % m (?)
|
2013-09-19 23:57:40 +00:00
|
|
|
*/
|
|
|
|
|
|
|
|
void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_){
|
|
|
|
const bigint_length_t s = MAX(MAX(a->length_W, b->length_W), m->length_W);
|
|
|
|
bigint_t u, t;
|
|
|
|
bigint_word_t u_w[s + 2], t_w[s + 2];
|
|
|
|
bigint_length_t i;
|
|
|
|
|
|
|
|
if (a->length_W == 0 || b->length_W == 0) {
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
u.wordv = u_w;
|
|
|
|
u.info = 0;
|
|
|
|
u.length_W = 0;
|
|
|
|
t.wordv = t_w;
|
|
|
|
for (i = 0; i < a->length_W; ++i) {
|
|
|
|
bigint_copy(&t, b);
|
|
|
|
bigint_mul_word_u(&t, a->wordv[i]);
|
|
|
|
bigint_add_u(&u, &u, &t);
|
|
|
|
bigint_copy(&t, m_);
|
|
|
|
if (u.length_W != 0) {
|
|
|
|
bigint_mul_word_u(&t, u.wordv[0]);
|
|
|
|
bigint_add_u(&u, &u, &t);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&u, BIGINT_WORD_SIZE);
|
|
|
|
}
|
|
|
|
for (; i < s; ++i) {
|
|
|
|
bigint_copy(&t, m_);
|
|
|
|
if (u.length_W != 0) {
|
|
|
|
bigint_mul_word_u(&t, u.wordv[0]);
|
|
|
|
bigint_add_u(&u, &u, &t);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&u, BIGINT_WORD_SIZE);
|
|
|
|
}
|
|
|
|
bigint_reduce(&u, m);
|
|
|
|
bigint_copy(dest, &u);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_){
|
|
|
|
bigint_t u, t;
|
|
|
|
bigint_length_t i, s = MAX(a->length_W, m->length_W);
|
|
|
|
bigint_word_t u_w[s + 2], t_w[s + 2];
|
2010-03-06 20:54:30 +00:00
|
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|
|
2013-09-19 23:57:40 +00:00
|
|
|
t.wordv = t_w;
|
|
|
|
u.wordv = u_w;
|
|
|
|
if (a->length_W == 0) {
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
bigint_copy(&u, a);
|
|
|
|
for (i = 0; i < m->length_W; ++i) {
|
|
|
|
bigint_copy(&t, m_);
|
|
|
|
if (u.length_W != 0) {
|
|
|
|
bigint_mul_word_u(&t, u.wordv[0]);
|
|
|
|
bigint_add_u(&u, &u, &t);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&u, BIGINT_WORD_SIZE);
|
|
|
|
}
|
|
|
|
bigint_reduce(&u, m);
|
|
|
|
bigint_copy(dest, &u);
|
|
|
|
}
|
2010-03-06 20:54:30 +00:00
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|
2013-09-19 23:57:40 +00:00
|
|
|
/******************************************************************************/
|
|
|
|
/*
|
|
|
|
* m_ = m * (- m0^-1 (mod 2^W))
|
|
|
|
*/
|
|
|
|
void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m){
|
|
|
|
bigint_word_t x_w[2], m_w_0[1];
|
|
|
|
bigint_t x, m_0;
|
2014-02-14 22:10:30 +00:00
|
|
|
#if 0
|
|
|
|
printf("\nm = ");
|
|
|
|
bigint_print_hex(m);
|
|
|
|
uart0_flush();
|
|
|
|
#endif
|
2013-09-19 23:57:40 +00:00
|
|
|
if (m->length_W == 0) {
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if ((m->wordv[0] & 1) == 0) {
|
|
|
|
printf_P(PSTR("ERROR: m must not be even, m = "));
|
|
|
|
bigint_print_hex(m);
|
|
|
|
putchar('\n');
|
|
|
|
uart0_flush();
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
x.wordv = x_w;
|
|
|
|
x.info = 0;
|
|
|
|
x.length_W = 2;
|
|
|
|
x_w[0] = 0;
|
|
|
|
x_w[1] = 1;
|
|
|
|
m_0.wordv = m_w_0;
|
|
|
|
m_0.info = 0;
|
|
|
|
m_0.length_W = 1;
|
|
|
|
m_0.wordv[0] = m->wordv[0];
|
|
|
|
bigint_adjust(&x);
|
|
|
|
bigint_adjust(&m_0);
|
2014-02-14 22:10:30 +00:00
|
|
|
#if 0
|
|
|
|
printf("\nm0 = ");
|
|
|
|
bigint_print_hex(&m_0);
|
|
|
|
printf("\nx = ");
|
|
|
|
bigint_print_hex(&x);
|
|
|
|
uart0_flush();
|
|
|
|
#endif
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_inverse(dest, &m_0, &x);
|
2014-02-14 22:10:30 +00:00
|
|
|
#if 0
|
|
|
|
printf("\nm0^-1 = ");
|
|
|
|
bigint_print_hex(dest);
|
|
|
|
uart0_flush();
|
|
|
|
#endif
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_sub_s(&x, &x, dest);
|
2014-02-14 22:10:30 +00:00
|
|
|
#if 0
|
|
|
|
printf("\n-m0^-1 = ");
|
|
|
|
bigint_print_hex(&x);
|
|
|
|
uart0_flush();
|
|
|
|
#endif
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_copy(dest, m);
|
|
|
|
bigint_mul_word_u(dest, x.wordv[0]);
|
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
|
2013-02-17 09:35:16 +00:00
|
|
|
/******************************************************************************/
|
2010-03-06 20:54:30 +00:00
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
/*
|
|
|
|
* dest = a * R mod m
|
|
|
|
*/
|
|
|
|
void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m){
|
|
|
|
bigint_t t;
|
|
|
|
bigint_word_t t_w[a->length_W + m->length_W];
|
|
|
|
|
|
|
|
t.wordv = t_w;
|
|
|
|
memset(t_w, 0, m->length_W * sizeof(bigint_word_t));
|
2014-02-14 22:10:30 +00:00
|
|
|
memcpy(&t_w[m->length_W], a->wordv, a->length_W * sizeof(bigint_word_t));
|
2013-09-19 23:57:40 +00:00
|
|
|
t.info = a->info;
|
|
|
|
t.length_W = a->length_W + m->length_W;
|
|
|
|
bigint_reduce(&t, m);
|
|
|
|
bigint_copy(dest, &t);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* calculate dest = a**exp % r */
|
|
|
|
/* using square&multiply */
|
2014-02-14 22:10:30 +00:00
|
|
|
void bigint_expmod_u_mont_accel(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r, const bigint_t *m_){
|
2013-09-19 23:57:40 +00:00
|
|
|
if(r->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
2014-02-14 22:10:30 +00:00
|
|
|
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t s = r->length_W;
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_t res, ax;
|
|
|
|
bigint_word_t t, res_w[r->length_W * 2], ax_w[MAX(s, a->length_W)];
|
2013-09-19 23:57:40 +00:00
|
|
|
bigint_length_t i;
|
|
|
|
uint8_t j;
|
|
|
|
|
|
|
|
res.wordv = res_w;
|
|
|
|
ax.wordv = ax_w;
|
|
|
|
|
|
|
|
res.wordv[0] = 1;
|
|
|
|
res.length_W = 1;
|
|
|
|
res.info = 0;
|
|
|
|
bigint_adjust(&res);
|
|
|
|
if (exp->length_W == 0) {
|
|
|
|
bigint_copy(dest, &res);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
bigint_copy(&ax, a);
|
|
|
|
bigint_reduce(&ax, r);
|
|
|
|
bigint_mont_trans(&ax, &ax, r);
|
|
|
|
bigint_mont_trans(&res, &res, r);
|
|
|
|
uint8_t flag = 0;
|
|
|
|
t = exp->wordv[exp->length_W - 1];
|
|
|
|
for (i = exp->length_W; i > 0; --i) {
|
|
|
|
t = exp->wordv[i - 1];
|
|
|
|
for(j = BIGINT_WORD_SIZE; j > 0; --j){
|
|
|
|
if (!flag) {
|
2014-02-14 22:10:30 +00:00
|
|
|
if(t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))){
|
2013-09-19 23:57:40 +00:00
|
|
|
flag = 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (flag) {
|
|
|
|
bigint_square(&res, &res);
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_mont_red(&res, &res, r, m_);
|
|
|
|
if (t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))) {
|
|
|
|
bigint_mont_mul(&res, &res, &ax, r, m_);
|
2013-09-19 23:57:40 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
t <<= 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
SET_POS(&res);
|
2014-02-14 22:10:30 +00:00
|
|
|
bigint_mont_red(dest, &res, r, m_);
|
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
|
|
|
|
if(r->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if(a->length_W == 0) {
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
bigint_t m_;
|
|
|
|
bigint_word_t m_w_[r->length_W + 1];
|
|
|
|
m_.wordv = m_w_;
|
|
|
|
bigint_mont_gen_m_(&m_, r);
|
|
|
|
bigint_expmod_u_mont_accel(dest, a, exp, r,&m_);
|
2013-09-19 23:57:40 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
2013-02-17 09:44:36 +00:00
|
|
|
void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
|
2013-09-19 23:57:40 +00:00
|
|
|
if (r->wordv[0] & 1) {
|
|
|
|
bigint_expmod_u_mont_sam(dest, a, exp, r);
|
|
|
|
} else {
|
|
|
|
bigint_expmod_u_sam(dest, a, exp, r);
|
|
|
|
}
|
2013-02-17 09:35:16 +00:00
|
|
|
}
|
2010-03-06 20:54:30 +00:00
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2010-03-03 19:20:03 +00:00
|
|
|
|
|
|
|
|
|
|
|
|