574 lines
13 KiB
C
574 lines
13 KiB
C
/* bigint.c */
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/*
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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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/**
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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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#include "bigint.h"
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#include <string.h>
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#include "bigint_io.h"
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#include "cli.h"
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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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#define MIN(a,b) (((a)<(b))?(a):(b))
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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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void bigint_adjust(bigint_t* a){
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while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
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a->length_B--;
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}
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if(a->length_B==0){
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a->info=0;
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return;
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}
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uint8_t t;
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uint8_t i = 0x07;
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t = a->wordv[a->length_B-1];
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while((t&0x80)==0 && i){
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t<<=1;
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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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void bigint_copy(bigint_t* dest, const bigint_t* src){
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memcpy(dest->wordv, src->wordv, src->length_B);
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dest->length_B = src->length_B;
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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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/*
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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_B < b->length_B){
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XCHG_PTR(a,b);
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}
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for(i=0; i<b->length_B; ++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_B; ++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_B = i;
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bigint_adjust(dest);
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}
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*/
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/******************************************************************************/
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/* this should be implemented in assembly */
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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_B)
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memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
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for(i=scale; i<a->length_B+scale; ++i,++j){
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t = a->wordv[j] + t;
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if(dest->length_B>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_B>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_B < i){
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dest->length_B = i;
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}
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bigint_adjust(dest);
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}
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/******************************************************************************/
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/* this should be implemented in assembly */
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void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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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_B, b->length_B);
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max = MAX(a->length_B, b->length_B);
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r = bigint_cmp_u(a,b);
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if(r==0){
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dest->length_B = 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_B==0){
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dest->length_B = a->length_B;
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memcpy(dest->wordv, a->wordv, a->length_B);
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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_B==0){
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dest->length_B = b->length_B;
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memcpy(dest->wordv, b->wordv, b->length_B);
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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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for(i=0; i<min; ++i){
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t = a->wordv[i] - b->wordv[i] - borrow;
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if(t<1){
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borrow = 0;
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dest->wordv[i]=(uint8_t)(-t);
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}else{
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borrow = -1;
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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 = b->wordv[i] + borrow;
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if(t<1){
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borrow = 0;
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dest->wordv[i]=(uint8_t)t;
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}else{
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borrow = -1;
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dest->wordv[i]=(uint8_t)t;
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}
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}
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SET_NEG(dest);
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dest->length_B = i;
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bigint_adjust(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_B = i;
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bigint_adjust(dest);
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}
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}
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/******************************************************************************/
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int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
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if(a->length_B > b->length_B){
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return 1;
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}
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if(a->length_B < b->length_B){
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return -1;
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}
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if(GET_FBS(a) > GET_FBS(b)){
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return 1;
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}
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if(GET_FBS(a) < GET_FBS(b)){
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return -1;
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}
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if(a->length_B==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_B-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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}
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/******************************************************************************/
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void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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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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}
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/******************************************************************************/
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void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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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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}
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/******************************************************************************/
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int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
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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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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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}
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/******************************************************************************/
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void bigint_shiftleft(bigint_t* a, uint16_t shift){
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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_B);
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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_B+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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}else{ /* shift to the right */
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bitshift = 8 - bitshift;
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for(i=a->length_B+byteshift-1; i>byteshift; --i){
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t |= (a->wordv[i])<<(8-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])<<(8-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_B += byteshift+1;
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bigint_adjust(a);
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}
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/******************************************************************************/
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void bigint_shiftright(bigint_t* a, uint16_t shift){
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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_B){ /* we would shift out more than we have */
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a->length_B=0;
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a->wordv[0] = 0;
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SET_FBS(a, 0);
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return;
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}
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if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
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a->length_B=0;
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a->wordv[0] = 0;
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SET_FBS(a, 0);
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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_B-byteshift);
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memset(a->wordv+a->length_B-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_B-byteshift-1; i>0; --i){
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t |= (a->wordv[i])<<(8-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[0])<<(8-bitshift);
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a->wordv[0] = (uint8_t)(t>>8);
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}
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a->length_B -= byteshift;
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bigint_adjust(a);
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}
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/******************************************************************************/
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void bigint_xor(bigint_t* dest, const bigint_t* a){
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uint16_t i;
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for(i=0; i<a->length_B; ++i){
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dest->wordv[i] ^= a->wordv[i];
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}
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bigint_adjust(dest);
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}
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/******************************************************************************/
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void bigint_set_zero(bigint_t* a){
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a->length_B=0;
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}
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/******************************************************************************/
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/* using the Karatsuba-Algorithm */
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/* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
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void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
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if(a->length_B==0 || b->length_B==0){
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bigint_set_zero(dest);
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depth -= 1;
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return;
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}
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if(a->length_B==1 || b->length_B==1){
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if(a->length_B!=1){
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XCHG_PTR(a,b);
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}
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uint16_t i, t=0;
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uint8_t x = a->wordv[0];
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for(i=0; i<b->length_B; ++i){
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t += b->wordv[i]*x;
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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] = (uint8_t)t;
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dest->length_B=i+1;
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bigint_adjust(dest);
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return;
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}
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if(a->length_B<=4 && b->length_B<=4){
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uint32_t p=0, q=0;
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uint64_t r;
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memcpy(&p, a->wordv, a->length_B);
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memcpy(&q, b->wordv, b->length_B);
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r = (uint64_t)p*(uint64_t)q;
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memcpy(dest->wordv, &r, a->length_B+b->length_B);
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dest->length_B = a->length_B+b->length_B;
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bigint_adjust(dest);
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return;
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}
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bigint_set_zero(dest);
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/* split a in xh & xl; split b in yh & yl */
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uint16_t n;
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n=(MAX(a->length_B, b->length_B)+1)/2;
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bigint_t xl, xh, yl, yh;
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xl.wordv = a->wordv;
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yl.wordv = b->wordv;
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if(a->length_B<=n){
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xh.info=0;
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xh.length_B = 0;
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xl.length_B = a->length_B;
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xl.info = 0;
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}else{
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xl.length_B=n;
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xl.info = 0;
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bigint_adjust(&xl);
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xh.wordv = a->wordv+n;
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xh.length_B = a->length_B-n;
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xh.info = 0;
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}
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if(b->length_B<=n){
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yh.info=0;
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yh.length_B = 0;
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yl.length_B = b->length_B;
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yl.info = b->info;
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}else{
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yl.length_B=n;
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yl.info = 0;
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bigint_adjust(&yl);
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yh.wordv = b->wordv+n;
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yh.length_B = b->length_B-n;
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yh.info = 0;
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}
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/* now we have split up a and b */
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uint8_t tmp_b[2*n+2], m_b[2*(n+1)];
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bigint_t tmp, tmp2, m;
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/* calculate h=xh*yh; l=xl*yl; sx=xh+xl; sy=yh+yl */
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tmp.wordv = tmp_b;
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tmp2.wordv = tmp_b+n+1;
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m.wordv = m_b;
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bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl */
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bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */
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bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */
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bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp*tmp */
|
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bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */
|
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bigint_sub_u(&m, &m, dest); /* m <= m-dest */
|
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bigint_sub_u(&m, &m, &tmp); /* m <= m-h */
|
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bigint_add_scale_u(dest, &m, n);
|
|
bigint_add_scale_u(dest, &tmp, 2*n);
|
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}
|
|
|
|
/******************************************************************************/
|
|
|
|
void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
|
|
uint8_t s;
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s = GET_SIGN(a)?2:0;
|
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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;
|
|
}
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
/* square */
|
|
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
|
|
void bigint_square(bigint_t* dest, const bigint_t* a){
|
|
if(a->length_B<=4){
|
|
uint64_t r=0;
|
|
memcpy(&r, a->wordv, a->length_B);
|
|
r = r*r;
|
|
memcpy(dest->wordv, &r, 2*a->length_B);
|
|
SET_POS(dest);
|
|
dest->length_B=2*a->length_B;
|
|
bigint_adjust(dest);
|
|
return;
|
|
}
|
|
uint16_t n;
|
|
n=(a->length_B+1)/2;
|
|
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
|
|
uint8_t buffer[2*n+1];
|
|
xl.wordv = a->wordv;
|
|
xl.length_B = n;
|
|
xh.wordv = a->wordv+n;
|
|
xh.length_B = a->length_B-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);
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
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|