2012-03-14 19:49:14 +00:00
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/* bigint.c */
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/*
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2014-02-22 17:00:36 +00:00
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This file is part of the AVR-Crypto-Lib.
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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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2012-03-14 19:49:14 +00:00
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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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#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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#include "bigint.h"
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#include <string.h>
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/*
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2014-02-22 17:00:36 +00:00
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#include "cli.h"
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#include "bigint_io.h"
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*/
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2012-03-14 19:49:14 +00:00
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#ifndef MAX
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2014-02-22 17:00:36 +00:00
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#define MAX(a,b) (((a)>(b))?(a):(b))
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2012-03-14 19:49:14 +00:00
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#endif
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#ifndef MIN
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2014-02-22 17:00:36 +00:00
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#define MIN(a,b) (((a)<(b))?(a):(b))
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2012-03-14 19:49:14 +00:00
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#endif
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#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
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#define GET_FBS(a) ((a)->info&BIGINT_FBS_MASK)
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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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#define XCHG(a,b) do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
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#define XCHG_PTR(a,b) do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
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b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
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a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
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#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
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/******************************************************************************/
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/*
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2014-02-22 17:00:36 +00:00
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void bigint_copy(bigint_t *dest, const bigint_t *src){
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memcpy(dest->wordv, src->wordv, src->length_W);
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dest->length_W = src->length_W;
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dest->info = src->info;
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}
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*/
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2012-03-14 19:49:14 +00:00
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/******************************************************************************/
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/* this should be implemented in assembly */
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/*
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2014-02-22 17:00:36 +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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uint16_t t=0, i;
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if(a->length_W < b->length_W){
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XCHG_PTR(a,b);
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}
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for(i=0; i<b->length_W; ++i){
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t = a->wordv[i] + b->wordv[i] + t;
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dest->wordv[i] = (uint8_t)t;
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t>>=8;
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}
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for(; i<a->length_W; ++i){
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t = a->wordv[i] + t;
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dest->wordv[i] = (uint8_t)t;
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t>>=8;
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}
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dest->wordv[i++] = t;
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dest->length_W = i;
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bigint_adjust(dest);
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}
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*/
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2012-03-14 19:49:14 +00:00
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/******************************************************************************/
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/* this should be implemented in assembly */
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/*
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2014-02-22 17:00:36 +00:00
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void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale){
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uint16_t i,j=0;
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uint16_t t=0;
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if(scale>dest->length_W)
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memset(dest->wordv+dest->length_W, 0, scale-dest->length_W);
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for(i=scale; i<a->length_W+scale; ++i,++j){
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t = a->wordv[j] + t;
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if(dest->length_W>i){
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t += dest->wordv[i];
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}
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dest->wordv[i] = (uint8_t)t;
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t>>=8;
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}
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while(t){
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if(dest->length_W>i){
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t = dest->wordv[i] + t;
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}
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dest->wordv[i] = (uint8_t)t;
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t>>=8;
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++i;
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}
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if(dest->length_W < i){
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dest->length_W = i;
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}
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bigint_adjust(dest);
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}
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*/
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2012-03-14 19:49:14 +00:00
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/******************************************************************************/
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/* this should be implemented in assembly */
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2014-02-22 17:00:36 +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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{
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int8_t borrow = 0;
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int8_t r;
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int16_t t;
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uint16_t i, min, max;
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min = MIN(a->length_W, b->length_W);
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max = MAX(a->length_W, b->length_W);
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r = bigint_cmp_u(a, b);
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if (r == 0) {
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dest->length_W = 0;
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dest->wordv[0] = 0;
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bigint_adjust(dest);
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return;
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}
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if (b->length_W == 0) {
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dest->length_W = a->length_W;
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memcpy(dest->wordv, a->wordv, a->length_W);
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dest->info = a->info;
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SET_POS(dest);
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return;
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}
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if (a->length_W == 0) {
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dest->length_W = b->length_W;
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memcpy(dest->wordv, b->wordv, b->length_W);
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dest->info = b->info;
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SET_NEG(dest);
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return;
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}
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if (r < 0) {
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bigint_sub_u(dest, b, a);
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SET_NEG(dest);
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} else {
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for (i = 0; i < min; ++i) {
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t = a->wordv[i] - b->wordv[i] - borrow;
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if (t < 0) {
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borrow = 1;
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dest->wordv[i] = (uint8_t) t;
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} else {
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borrow = 0;
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dest->wordv[i] = (uint8_t) t;
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}
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}
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for (; i < max; ++i) {
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t = a->wordv[i] - borrow;
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if (t < 0) {
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borrow = 1;
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dest->wordv[i] = (uint8_t) t;
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} else {
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borrow = 0;
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dest->wordv[i] = (uint8_t) t;
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}
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}
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SET_POS(dest);
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dest->length_W = i;
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bigint_adjust(dest);
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}
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b)
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{
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if (a->length_W > b->length_W) {
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return 1;
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}
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if (a->length_W < b->length_W) {
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return -1;
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}
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if (a->length_W == 0) {
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return 0;
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}
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uint16_t i;
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i = a->length_W - 1;
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do {
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if (a->wordv[i] != b->wordv[i]) {
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if (a->wordv[i] > b->wordv[i]) {
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return 1;
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} else {
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return -1;
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}
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}
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} while (i--);
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return 0;
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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void bigint_add_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
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{
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uint8_t s;
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s = GET_SIGN(a) ? 2 : 0;
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s |= GET_SIGN(b) ? 1 : 0;
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switch (s) {
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case 0: /* both positive */
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bigint_add_u(dest, a, b);
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SET_POS(dest);
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break;
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case 1: /* a positive, b negative */
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bigint_sub_u(dest, a, b);
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break;
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case 2: /* a negative, b positive */
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bigint_sub_u(dest, b, a);
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break;
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case 3: /* both negative */
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bigint_add_u(dest, a, b);
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SET_NEG(dest);
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break;
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default: /* how can this happen?*/
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break;
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}
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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void bigint_sub_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
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{
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uint8_t s;
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s = GET_SIGN(a) ? 2 : 0;
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s |= GET_SIGN(b) ? 1 : 0;
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switch (s) {
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case 0: /* both positive */
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bigint_sub_u(dest, a, b);
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break;
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case 1: /* a positive, b negative */
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bigint_add_u(dest, a, b);
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SET_POS(dest);
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break;
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case 2: /* a negative, b positive */
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bigint_add_u(dest, a, b);
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SET_NEG(dest);
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break;
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case 3: /* both negative */
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bigint_sub_u(dest, b, a);
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break;
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default: /* how can this happen?*/
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break;
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}
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b)
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{
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uint8_t s;
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if (a->length_W == 0 && b->length_W == 0) {
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return 0;
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}
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s = GET_SIGN(a) ? 2 : 0;
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s |= GET_SIGN(b) ? 1 : 0;
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switch (s) {
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case 0: /* both positive */
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return bigint_cmp_u(a, b);
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break;
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case 1: /* a positive, b negative */
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return 1;
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break;
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case 2: /* a negative, b positive */
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return -1;
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break;
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case 3: /* both negative */
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return bigint_cmp_u(b, a);
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break;
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default: /* how can this happen?*/
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break;
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}
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return 0; /* just to satisfy the compiler */
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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void bigint_shiftleft(bigint_t *a, uint16_t shift)
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{
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uint16_t byteshift;
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uint16_t i;
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uint8_t bitshift;
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uint16_t t = 0;
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byteshift = (shift + 3) / 8;
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bitshift = shift & 7;
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memmove(a->wordv + byteshift, a->wordv, a->length_W);
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memset(a->wordv, 0, byteshift);
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if (bitshift != 0) {
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if (bitshift <= 4) { /* shift to the left */
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for (i = byteshift; i < a->length_W + byteshift; ++i) {
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t |= (a->wordv[i]) << bitshift;
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a->wordv[i] = (uint8_t) t;
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t >>= 8;
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}
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a->wordv[i] = (uint8_t) t;
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byteshift++;
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} else { /* shift to the right */
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for (i = a->length_W + byteshift - 1; i > byteshift - 1; --i) {
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t |= (a->wordv[i]) << (bitshift);
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a->wordv[i] = (uint8_t) (t >> 8);
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t <<= 8;
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}
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t |= (a->wordv[i]) << (bitshift);
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a->wordv[i] = (uint8_t) (t >> 8);
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}
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}
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a->length_W += byteshift;
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bigint_adjust(a);
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2012-03-14 19:49:14 +00:00
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}
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/******************************************************************************/
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2014-02-22 17:00:36 +00:00
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void bigint_shiftright(bigint_t *a, uint16_t shift)
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{
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uint16_t byteshift;
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uint16_t i;
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uint8_t bitshift;
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uint16_t t = 0;
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byteshift = shift / 8;
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bitshift = shift & 7;
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if (byteshift >= a->length_W) { /* we would shift out more than we have */
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bigint_set_zero(a);
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return;
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}
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if (byteshift == a->length_W - 1 && bitshift > GET_FBS(a)) {
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bigint_set_zero(a);
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return;
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}
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if (byteshift) {
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memmove(a->wordv, a->wordv + byteshift, a->length_W - byteshift);
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memset(a->wordv + a->length_W - byteshift, 0, byteshift);
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}
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if (bitshift != 0) {
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/* shift to the right */
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|
|
|
for (i = a->length_W - byteshift - 1; i > 0; --i) {
|
|
|
|
t |= (a->wordv[i]) << (8 - bitshift);
|
|
|
|
a->wordv[i] = (uint8_t) (t >> 8);
|
|
|
|
t <<= 8;
|
|
|
|
}
|
|
|
|
t |= (a->wordv[0]) << (8 - bitshift);
|
|
|
|
a->wordv[0] = (uint8_t) (t >> 8);
|
|
|
|
}
|
|
|
|
a->length_W -= byteshift;
|
|
|
|
bigint_adjust(a);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_xor(bigint_t *dest, const bigint_t *a)
|
|
|
|
{
|
|
|
|
uint16_t i;
|
|
|
|
for (i = 0; i < a->length_W; ++i) {
|
|
|
|
dest->wordv[i] ^= a->wordv[i];
|
|
|
|
}
|
|
|
|
bigint_adjust(dest);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_set_zero(bigint_t *a)
|
|
|
|
{
|
|
|
|
a->length_W = 0;
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* using the Karatsuba-Algorithm */
|
|
|
|
/* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b)
|
|
|
|
{
|
|
|
|
if (a->length_W == 0 || b->length_W == 0) {
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if (dest == a || dest == b) {
|
|
|
|
bigint_t d;
|
|
|
|
uint8_t d_b[a->length_W + b->length_W];
|
|
|
|
d.wordv = d_b;
|
|
|
|
bigint_mul_u(&d, a, b);
|
|
|
|
bigint_copy(dest, &d);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if (a->length_W == 1 || b->length_W == 1) {
|
|
|
|
if (a->length_W != 1) {
|
|
|
|
XCHG_PTR(a, b);
|
|
|
|
}
|
|
|
|
uint16_t i, t = 0;
|
|
|
|
uint8_t x = a->wordv[0];
|
|
|
|
for (i = 0; i < b->length_W; ++i) {
|
|
|
|
t += b->wordv[i] * x;
|
|
|
|
dest->wordv[i] = (uint8_t) t;
|
|
|
|
t >>= 8;
|
|
|
|
}
|
|
|
|
dest->wordv[i] = (uint8_t) t;
|
|
|
|
dest->length_W = i + 1;
|
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if (a->length_W <= 4 && b->length_W <= 4) {
|
|
|
|
uint32_t p = 0, q = 0;
|
|
|
|
uint64_t r;
|
|
|
|
memcpy(&p, a->wordv, a->length_W);
|
|
|
|
memcpy(&q, b->wordv, b->length_W);
|
|
|
|
r = (uint64_t) p * (uint64_t) q;
|
|
|
|
memcpy(dest->wordv, &r, a->length_W + b->length_W);
|
|
|
|
dest->length_W = a->length_W + b->length_W;
|
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
bigint_set_zero(dest);
|
|
|
|
/* split a in xh & xl; split b in yh & yl */
|
|
|
|
uint16_t n;
|
|
|
|
n = (MAX(a->length_W, b->length_W) + 1) / 2;
|
|
|
|
bigint_t xl, xh, yl, yh;
|
|
|
|
xl.wordv = a->wordv;
|
|
|
|
yl.wordv = b->wordv;
|
|
|
|
if (a->length_W <= n) {
|
|
|
|
xh.info = 0;
|
|
|
|
xh.length_W = 0;
|
|
|
|
xl.length_W = a->length_W;
|
|
|
|
xl.info = 0;
|
|
|
|
} else {
|
|
|
|
xl.length_W = n;
|
|
|
|
xl.info = 0;
|
|
|
|
bigint_adjust(&xl);
|
|
|
|
xh.wordv = a->wordv + n;
|
|
|
|
xh.length_W = a->length_W - n;
|
|
|
|
xh.info = 0;
|
|
|
|
}
|
|
|
|
if (b->length_W <= n) {
|
|
|
|
yh.info = 0;
|
|
|
|
yh.length_W = 0;
|
|
|
|
yl.length_W = b->length_W;
|
|
|
|
yl.info = b->info;
|
|
|
|
} else {
|
|
|
|
yl.length_W = n;
|
|
|
|
yl.info = 0;
|
|
|
|
bigint_adjust(&yl);
|
|
|
|
yh.wordv = b->wordv + n;
|
|
|
|
yh.length_W = b->length_W - n;
|
|
|
|
yh.info = 0;
|
|
|
|
}
|
|
|
|
/* now we have split up a and b */
|
|
|
|
uint8_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); /* dest <= xl*yl */
|
|
|
|
bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */
|
|
|
|
bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */
|
|
|
|
bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp2*tmp */
|
|
|
|
bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */
|
|
|
|
bigint_sub_u(&m, &m, dest); /* m <= m-dest */
|
|
|
|
bigint_sub_u(&m, &m, &tmp); /* m <= m-h */
|
|
|
|
bigint_add_scale_u(dest, &m, n);
|
|
|
|
bigint_add_scale_u(dest, &tmp, 2 * n);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_mul_s(bigint_t *dest, const bigint_t *a, const bigint_t *b)
|
|
|
|
{
|
|
|
|
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;
|
|
|
|
}
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* square */
|
|
|
|
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_square(bigint_t *dest, const bigint_t *a)
|
|
|
|
{
|
|
|
|
if (a->length_W <= 4) {
|
|
|
|
uint64_t r = 0;
|
|
|
|
memcpy(&r, a->wordv, a->length_W);
|
|
|
|
r = r * r;
|
|
|
|
memcpy(dest->wordv, &r, 2 * a->length_W);
|
|
|
|
SET_POS(dest);
|
|
|
|
dest->length_W = 2 * a->length_W;
|
|
|
|
bigint_adjust(dest);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
if (dest == a) {
|
|
|
|
bigint_t d;
|
|
|
|
uint8_t d_b[a->length_W * 2];
|
|
|
|
d.wordv = d_b;
|
|
|
|
bigint_square(&d, a);
|
|
|
|
bigint_copy(dest, &d);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
uint16_t n;
|
|
|
|
n = (a->length_W + 1) / 2;
|
|
|
|
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
|
|
|
|
uint8_t buffer[2 * n + 1];
|
|
|
|
xl.wordv = a->wordv;
|
|
|
|
xl.length_W = n;
|
|
|
|
xh.wordv = a->wordv + n;
|
|
|
|
xh.length_W = a->length_W - n;
|
|
|
|
tmp.wordv = buffer;
|
|
|
|
bigint_square(dest, &xl);
|
|
|
|
bigint_square(&tmp, &xh);
|
|
|
|
bigint_add_scale_u(dest, &tmp, 2 * n);
|
|
|
|
bigint_mul_u(&tmp, &xl, &xh);
|
|
|
|
bigint_shiftleft(&tmp, 1);
|
|
|
|
bigint_add_scale_u(dest, &tmp, n);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale)
|
|
|
|
{
|
|
|
|
bigint_t tmp;
|
|
|
|
uint8_t tmp_b[b->length_W + 1];
|
|
|
|
uint16_t i, j, byteshift = bitscale / 8;
|
|
|
|
uint8_t borrow = 0;
|
|
|
|
int16_t t;
|
|
|
|
|
|
|
|
if (a->length_W < b->length_W + byteshift) {
|
|
|
|
bigint_set_zero(a);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
tmp.wordv = tmp_b;
|
|
|
|
bigint_copy(&tmp, b);
|
|
|
|
bigint_shiftleft(&tmp, bitscale & 7);
|
|
|
|
|
|
|
|
for (j = 0, i = byteshift; i < tmp.length_W + byteshift; ++i, ++j) {
|
|
|
|
t = a->wordv[i] - tmp.wordv[j] - borrow;
|
|
|
|
a->wordv[i] = (uint8_t) t;
|
|
|
|
if (t < 0) {
|
|
|
|
borrow = 1;
|
|
|
|
} else {
|
|
|
|
borrow = 0;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
while (borrow) {
|
|
|
|
if (i + 1 > a->length_W) {
|
|
|
|
bigint_set_zero(a);
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
a->wordv[i] -= borrow;
|
|
|
|
if (a->wordv[i] != 0xff) {
|
|
|
|
borrow = 0;
|
|
|
|
}
|
|
|
|
++i;
|
|
|
|
}
|
|
|
|
bigint_adjust(a);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_reduce(bigint_t *a, const bigint_t *r)
|
|
|
|
{
|
2012-03-14 19:49:14 +00:00
|
|
|
// bigint_adjust(r);
|
2014-02-22 17:00:36 +00:00
|
|
|
uint8_t rfbs = GET_FBS(r);
|
|
|
|
|
|
|
|
if (r->length_W == 0 || a->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
while (a->length_W > r->length_W) {
|
|
|
|
bigint_sub_u_bitscale(a, r, (a->length_W - r->length_W) * 8 + GET_FBS(a)
|
|
|
|
- rfbs - 1);
|
|
|
|
}
|
|
|
|
while ((GET_FBS(a) > rfbs + 1) && (a->length_W == r->length_W)) {
|
|
|
|
bigint_sub_u_bitscale(a, r, GET_FBS(a) - rfbs - 1);
|
|
|
|
}
|
|
|
|
while (bigint_cmp_u(a, r) >= 0) {
|
|
|
|
bigint_sub_u(a, a, r);
|
|
|
|
}
|
|
|
|
bigint_adjust(a);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
|
|
|
/* calculate dest = a**exp % r */
|
|
|
|
/* using square&multiply */
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp,
|
|
|
|
const bigint_t *r)
|
|
|
|
{
|
|
|
|
if (a->length_W == 0 || r->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
bigint_t res, base;
|
|
|
|
uint8_t base_b[MAX(a->length_W, r->length_W * 2)], res_b[r->length_W * 2];
|
|
|
|
uint16_t i;
|
|
|
|
uint8_t j, t;
|
|
|
|
res.wordv = res_b;
|
|
|
|
base.wordv = base_b;
|
|
|
|
bigint_copy(&base, a);
|
|
|
|
bigint_reduce(&base, r);
|
|
|
|
res.wordv[0] = 1;
|
|
|
|
res.length_W = 1;
|
|
|
|
res.info = 0;
|
|
|
|
bigint_adjust(&res);
|
|
|
|
for (i = 0; i + 1 < exp->length_W; ++i) {
|
|
|
|
t = exp->wordv[i];
|
|
|
|
for (j = 0; j < 8; ++j) {
|
|
|
|
if (t & 1) {
|
|
|
|
bigint_mul_u(&res, &res, &base);
|
|
|
|
bigint_reduce(&res, r);
|
|
|
|
}
|
|
|
|
bigint_square(&base, &base);
|
|
|
|
bigint_reduce(&base, r);
|
|
|
|
t >>= 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
t = exp->wordv[i];
|
|
|
|
while (t) {
|
|
|
|
if (t & 1) {
|
|
|
|
bigint_mul_u(&res, &res, &base);
|
|
|
|
bigint_reduce(&res, r);
|
|
|
|
}
|
|
|
|
bigint_square(&base, &base);
|
|
|
|
bigint_reduce(&base, r);
|
|
|
|
t >>= 1;
|
|
|
|
}
|
|
|
|
SET_POS(&res);
|
|
|
|
bigint_copy(dest, &res);
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
/* gcd <-- gcd(x,y) a*x+b*y=gcd */
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x,
|
|
|
|
const bigint_t *y)
|
|
|
|
{
|
|
|
|
bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
|
|
|
|
volatile uint16_t i = 0;
|
|
|
|
if (x->length_W == 0 || y->length_W == 0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
while (x->wordv[i] == 0 && y->wordv[i] == 0) {
|
|
|
|
++i;
|
|
|
|
}
|
|
|
|
uint8_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i];
|
|
|
|
uint8_t u_b[x->length_W - i], v_b[y->length_W - i];
|
|
|
|
uint8_t a_b[y->length_W + 2], c_b[y->length_W + 2];
|
|
|
|
uint8_t b_b[x->length_W + 2], d_b[x->length_W + 2];
|
|
|
|
|
|
|
|
g.wordv = g_b;
|
|
|
|
x_.wordv = x_b;
|
|
|
|
y_.wordv = y_b;
|
|
|
|
memset(g_b, 0, i);
|
|
|
|
g_b[i] = 1;
|
|
|
|
g.length_W = i + 1;
|
|
|
|
g.info = 0;
|
|
|
|
x_.info = y_.info = 0;
|
|
|
|
x_.length_W = x->length_W - i;
|
|
|
|
y_.length_W = y->length_W - i;
|
|
|
|
memcpy(x_.wordv, x->wordv + i, x_.length_W);
|
|
|
|
memcpy(y_.wordv, y->wordv + i, y_.length_W);
|
|
|
|
for (i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0;
|
|
|
|
++i) {
|
|
|
|
}
|
|
|
|
|
|
|
|
bigint_adjust(&x_);
|
|
|
|
bigint_adjust(&y_);
|
|
|
|
|
|
|
|
if (i) {
|
|
|
|
bigint_shiftleft(&g, i);
|
|
|
|
bigint_shiftright(&x_, i);
|
|
|
|
bigint_shiftright(&y_, i);
|
|
|
|
}
|
|
|
|
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;
|
|
|
|
a_.length_W = 1;
|
|
|
|
a_.info = 0;
|
|
|
|
d_.wordv[0] = 1;
|
|
|
|
d_.length_W = 1;
|
|
|
|
d_.info = 0;
|
|
|
|
bigint_set_zero(&b_);
|
|
|
|
bigint_set_zero(&c_);
|
|
|
|
do {
|
|
|
|
while ((u.wordv[0] & 1) == 0) {
|
|
|
|
bigint_shiftright(&u, 1);
|
|
|
|
if ((a_.wordv[0] & 1) || (b_.wordv[0] & 1)) {
|
|
|
|
bigint_add_s(&a_, &a_, &y_);
|
|
|
|
bigint_sub_s(&b_, &b_, &x_);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&a_, 1);
|
|
|
|
bigint_shiftright(&b_, 1);
|
|
|
|
}
|
|
|
|
while ((v.wordv[0] & 1) == 0) {
|
|
|
|
bigint_shiftright(&v, 1);
|
|
|
|
if ((c_.wordv[0] & 1) || (d_.wordv[0] & 1)) {
|
|
|
|
bigint_add_s(&c_, &c_, &y_);
|
|
|
|
bigint_sub_s(&d_, &d_, &x_);
|
|
|
|
}
|
|
|
|
bigint_shiftright(&c_, 1);
|
|
|
|
bigint_shiftright(&d_, 1);
|
|
|
|
|
|
|
|
}
|
|
|
|
if (bigint_cmp_u(&u, &v) >= 0) {
|
|
|
|
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_);
|
|
|
|
}
|
|
|
|
} while (u.length_W);
|
|
|
|
if (gcd) {
|
|
|
|
bigint_mul_s(gcd, &v, &g);
|
|
|
|
}
|
|
|
|
if (a) {
|
|
|
|
bigint_copy(a, &c_);
|
|
|
|
}
|
|
|
|
if (b) {
|
|
|
|
bigint_copy(b, &d_);
|
|
|
|
}
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m)
|
|
|
|
{
|
|
|
|
bigint_gcdext(NULL, dest, NULL, a, m);
|
|
|
|
while (dest->info & BIGINT_NEG_MASK) {
|
|
|
|
bigint_add_s(dest, dest, m);
|
|
|
|
}
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|
2014-02-22 17:00:36 +00:00
|
|
|
void bigint_changeendianess(bigint_t *a)
|
|
|
|
{
|
|
|
|
uint8_t t, *p, *q;
|
|
|
|
p = a->wordv;
|
|
|
|
q = p + a->length_W - 1;
|
|
|
|
while (p < q) {
|
|
|
|
t = *p;
|
|
|
|
*p = *q;
|
|
|
|
*q = t;
|
|
|
|
++p;
|
|
|
|
--q;
|
|
|
|
}
|
2012-03-14 19:49:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
/******************************************************************************/
|
|
|
|
|