992 lines
25 KiB
C
992 lines
25 KiB
C
/* bigint.c */
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/*
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This file is part of the ARM-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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#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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#define DEBUG 0
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#if DEBUG
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#include "cli.h"
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#include "bigint_io.h"
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#endif
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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 &=~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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#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*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
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b = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
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a = (void*)(((intptr_t)(a)) ^ ((intptr_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_W!=0 && a->wordv[a->length_W-1]==0){
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a->length_W--;
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}
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if(a->length_W==0){
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a->info=0;
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return;
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}
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bigint_word_t t;
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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&(1L<<(BIGINT_WORD_SIZE-1)))==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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uint16_t bigint_length_b(const bigint_t* a){
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if(!a->length_W || a->length_W==0){
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return 0;
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}
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return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a);
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}
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/******************************************************************************/
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uint16_t bigint_length_B(const bigint_t* a){
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return a->length_W * sizeof(bigint_word_t);
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}
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/******************************************************************************/
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uint32_t bigint_get_first_set_bit(const bigint_t* a){
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if(a->length_W==0){
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return (uint32_t)(-1);
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}
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return (a->length_W-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
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}
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/******************************************************************************/
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uint32_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 (uint32_t)(-1);
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}
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while(a->wordv[r]==0 && r<a->length_W){
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++r;
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}
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if(a->wordv[r] == 0){
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return (uint32_t)(-1);
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}
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while((x&a->wordv[r])==0){
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++b;
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x <<= 1;
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}
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return r*BIGINT_WORD_SIZE+b;
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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_W*sizeof(bigint_word_t));
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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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/* this should be implemented in assembly */
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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 i;
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bigint_wordplus_t t=0LL;
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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 = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
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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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t>>=BIGINT_WORD_SIZE;
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}
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for(; i<a->length_W; ++i){
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t += a->wordv[i];
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dest->wordv[i] = (bigint_word_t)t;
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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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}
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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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/* 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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if(a->length_W == 0){
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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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#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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x.wordv = dest->wordv + scale;
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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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bigint_add_u(&x, &x, a);
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dest->length_W = x.length_W + scale;
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dest->info = 0;
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bigint_adjust(dest);
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#else
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bigint_t s;
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uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
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bigint_word_t bv[a->length_W + 1];
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s.wordv = bv;
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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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bigint_adjust(&s);
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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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x.wordv = dest->wordv + word_shift;
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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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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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dest->length_W = x.length_W + word_shift;
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dest->info = 0;
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bigint_adjust(dest);
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#endif
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/* uint16_t i,j=0;
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uint16_t scale_w;
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bigint_word_t *dst;
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bigint_wordplus_t t=0;
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scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
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if(scale>dest->length_W*sizeof(bigint_word_t)){
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memset(((uint8_t*)dest->wordv)+dest->length_W*sizeof(bigint_word_t), 0, scale-dest->length_W*sizeof(bigint_word_t));
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}
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// a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3));
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dst = dest->wordv + (scale&(sizeof(bigint_word_t)-1));
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for(i=scale/sizeof(bigint_word_t); i<a->length_W+scale_w; ++i,++j){
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t += a->wordv[j];
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if(dest->length_W>i){
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t += dst[i];
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}
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dst[i] = (bigint_word_t)t;
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t>>=BIGINT_WORD_SIZE;
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}
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while(t){
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if(dest->length_W>i){
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t += dst[i];
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}
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dst[i] = (bigint_word_t)t;
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t>>=BIGINT_WORD_SIZE;
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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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/******************************************************************************/
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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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bigint_wordplus_signed_t t=0LL;
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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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bigint_set_zero(dest);
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return;
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}
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if(b->length_W==0){
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bigint_copy(dest, a);
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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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bigint_copy(dest, b);
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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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return;
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}
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for(i=0; i<max; ++i){
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t = a->wordv[i];
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if(i<min){
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t -= b->wordv[i];
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}
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t -= borrow;
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dest->wordv[i]=(bigint_word_t)t;
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if(t<0){
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borrow = 1;
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}else{
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borrow = 0;
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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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/******************************************************************************/
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int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
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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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}
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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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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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}
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/******************************************************************************/
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void bigint_shiftleft(bigint_t* a, uint16_t shift){
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uint16_t byteshift, word_alloc, words_to_shift;
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int16_t i;
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uint8_t bitshift;
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bigint_word_t *p;
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bigint_wordplus_t t=0;
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if(shift==0){
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return;
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}
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byteshift = shift/8;
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bitshift = shift&7;
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for(i=0;i<=byteshift/sizeof(bigint_word_t); ++i){
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a->wordv[a->length_W+i] = 0;
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}
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if(byteshift){
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memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t));
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memset(a->wordv, 0, byteshift);
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}
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p = a->wordv + byteshift / sizeof(bigint_word_t);
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words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t)?1:0);
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word_alloc = a->length_W + (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t) + 1;
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a->wordv[word_alloc-1]=0;
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if(bitshift!=0){
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for(i=0; i < words_to_shift; ++i){
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t |= ((bigint_wordplus_t)p[i])<<bitshift;
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p[i] = (bigint_word_t)t;
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t >>= BIGINT_WORD_SIZE;
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}
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p[i] = (bigint_word_t)t;
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}
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a->length_W = word_alloc;
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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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bigint_wordplus_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 * sizeof(bigint_word_t)){ /* 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 * sizeof(bigint_word_t) - 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, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift);
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memset((uint8_t*)a->wordv + a->length_W * sizeof(bigint_word_t) - byteshift, 0, byteshift);
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}
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byteshift /= sizeof(bigint_word_t);
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a->length_W -= (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
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if(bitshift != 0 && a->length_W){
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/* shift to the right */
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i = a->length_W - 1;
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do{
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t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - bitshift);
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a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE);
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t <<= BIGINT_WORD_SIZE;
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}while(i--);
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}
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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_W; ++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_W=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 */
|
|
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;
|
|
bigint_word_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);
|
|
}
|
|
bigint_wordplus_t t=0;
|
|
uint16_t i;
|
|
bigint_word_t x = a->wordv[0];
|
|
for(i=0; i < b->length_W; ++i){
|
|
t += ((bigint_wordplus_t)b->wordv[i])*((bigint_wordplus_t)x);
|
|
dest->wordv[i] = (bigint_word_t)t;
|
|
t>>=BIGINT_WORD_SIZE;
|
|
}
|
|
dest->wordv[i] = (bigint_word_t)t;
|
|
dest->length_W = i+1;
|
|
dest->info = 0;
|
|
bigint_adjust(dest);
|
|
return;
|
|
}
|
|
if(a->length_W * sizeof(bigint_word_t) <= 4 && b->length_W * sizeof(bigint_word_t) <= 4){
|
|
uint32_t p=0, q=0;
|
|
uint64_t r;
|
|
memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t));
|
|
memcpy(&q, b->wordv, b->length_W*sizeof(bigint_word_t));
|
|
r = (uint64_t)p * (uint64_t)q;
|
|
memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W)*sizeof(bigint_word_t));
|
|
bigint_adjust(dest);
|
|
return;
|
|
}
|
|
bigint_set_zero(dest);
|
|
/* split a in xh & xl; split b in yh & yl */
|
|
const uint16_t 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){
|
|
bigint_set_zero(&xh);
|
|
xl.length_W = a->length_W;
|
|
xl.info = a->info;
|
|
}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 = a->info;
|
|
}
|
|
if(b->length_W<=n){
|
|
bigint_set_zero(&yh);
|
|
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 = b->info;
|
|
}
|
|
/* now we have split up a and b */
|
|
/* remember we want to do:
|
|
* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl
|
|
* 5 9 2 4 3 7 5 6 1 8 1
|
|
*/
|
|
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: h <= xh*yh */
|
|
bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */
|
|
bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-h */
|
|
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) */
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
/* 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_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==a){
|
|
bigint_t d;
|
|
bigint_word_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 */
|
|
bigint_word_t buffer[2*n+1];
|
|
xl.wordv = a->wordv;
|
|
xl.length_W = n;
|
|
xl.info = 0;
|
|
xh.wordv = &(a->wordv[n]);
|
|
xh.length_W = a->length_W-n;
|
|
xh.info = 0;
|
|
bigint_adjust(&xl);
|
|
bigint_adjust(&xh);
|
|
tmp.wordv = buffer;
|
|
/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
|
|
|
|
// cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
|
|
// cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
|
|
bigint_square(dest, &xl);
|
|
// cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
|
|
bigint_square(&tmp, &xh);
|
|
// cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
|
|
bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t));
|
|
// cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
|
|
bigint_mul_u(&tmp, &xl, &xh);
|
|
// cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
|
|
bigint_shiftleft(&tmp, 1);
|
|
// cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
|
|
bigint_add_scale_u(dest, &tmp, n*sizeof(bigint_word_t));
|
|
// cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
|
|
// cli_putstr("\r\n");
|
|
}
|
|
|
|
/******************************************************************************/
|
|
void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
|
|
bigint_t tmp, x;
|
|
bigint_word_t tmp_b[b->length_W + 1];
|
|
const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
|
|
|
|
if(a->length_W < b->length_W + word_shift){
|
|
#if DEBUG
|
|
cli_putstr("\r\nDBG: *bang*\r\n");
|
|
#endif
|
|
bigint_set_zero(a);
|
|
return;
|
|
}
|
|
tmp.wordv = tmp_b;
|
|
bigint_copy(&tmp, b);
|
|
bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
|
|
|
|
x.info = a->info;
|
|
x.wordv = &(a->wordv[word_shift]);
|
|
x.length_W = a->length_W - word_shift;
|
|
|
|
bigint_sub_u(&x, &x, &tmp);
|
|
bigint_adjust(a);
|
|
return;
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
void bigint_reduce(bigint_t* a, const bigint_t* r){
|
|
// bigint_adjust((bigint_t*)r);
|
|
uint8_t rfbs = GET_FBS(r);
|
|
#if DEBUG
|
|
cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
|
|
#endif
|
|
if(r->length_W==0 || a->length_W==0){
|
|
return;
|
|
}
|
|
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));
|
|
p %= q;
|
|
memcpy(a->wordv, &p, a->length_W*sizeof(bigint_word_t));
|
|
bigint_adjust(a);
|
|
// cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
|
|
return;
|
|
}
|
|
uint16_t shift;
|
|
while(a->length_W > r->length_W){
|
|
shift = (a->length_W - r->length_W) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
|
|
/*
|
|
if((a->wordv[a->length_W-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_W-1]){
|
|
// cli_putc('~');
|
|
cli_putstr("\r\n ~ [a] = ");
|
|
cli_hexdump_rev(&a->wordv[a->length_W-1], 4);
|
|
cli_putstr(" [r] = ");
|
|
cli_hexdump_rev(&r->wordv[r->length_W-1], 4);
|
|
shift += 1;
|
|
}
|
|
*/
|
|
// cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
|
|
// cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_W, 2);
|
|
// cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_W, 2);
|
|
// uart_flush(0);
|
|
bigint_sub_u_bitscale(a, r, shift);
|
|
// cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
|
|
}
|
|
while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){
|
|
shift = GET_FBS(a)-rfbs-1;
|
|
// cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
|
|
bigint_sub_u_bitscale(a, r, shift);
|
|
// cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
|
|
}
|
|
while(bigint_cmp_u(a,r)>=0){
|
|
bigint_sub_u(a,a,r);
|
|
// cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
|
|
}
|
|
bigint_adjust(a);
|
|
// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
|
|
// cli_putstr("\r\n");
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
/* calculate dest = a**exp % r */
|
|
/* using square&multiply */
|
|
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;
|
|
bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2];
|
|
uint16_t i;
|
|
uint8_t j;
|
|
// uint16_t *xaddr = &i;
|
|
// cli_putstr("\r\npre-alloc (");
|
|
// cli_hexdump_rev(&xaddr, 4);
|
|
// cli_putstr(") ...");
|
|
res.wordv = res_b;
|
|
base.wordv = base_b;
|
|
bigint_copy(&base, a);
|
|
// cli_putstr("\r\npost-copy");
|
|
bigint_reduce(&base, r);
|
|
res.wordv[0]=1;
|
|
res.length_W=1;
|
|
res.info = 0;
|
|
bigint_adjust(&res);
|
|
if(exp->length_W == 0){
|
|
bigint_copy(dest, &res);
|
|
return;
|
|
}
|
|
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){
|
|
if(t & (1<<(BIGINT_WORD_SIZE-1))){
|
|
flag = 1;
|
|
}
|
|
}
|
|
if(flag){
|
|
bigint_square(&res, &res);
|
|
bigint_reduce(&res, r);
|
|
if(t & (1 << (BIGINT_WORD_SIZE - 1))){
|
|
bigint_mul_u(&res, &res, &base);
|
|
bigint_reduce(&res, r);
|
|
}
|
|
}
|
|
t <<= 1;
|
|
}
|
|
}
|
|
|
|
// cli_putc('+');
|
|
SET_POS(&res);
|
|
bigint_copy(dest, &res);
|
|
}
|
|
|
|
/******************************************************************************/
|
|
|
|
#define cli_putstr(a)
|
|
#define bigint_print_hex(a)
|
|
#define cli_hexdump_rev(a,b)
|
|
#define uart_flush(a)
|
|
|
|
/* gcd <-- gcd(x,y) a*x+b*y=gcd */
|
|
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_;
|
|
uint16_t i=0;
|
|
if(x->length_W==0 || y->length_W==0){
|
|
return;
|
|
}
|
|
if(x->length_W==1 && x->wordv[0]==1){
|
|
gcd->length_W = 1;
|
|
gcd->wordv[0] = 1;
|
|
if(a){
|
|
a->length_W = 1;
|
|
a->wordv[0] = 1;
|
|
SET_POS(a);
|
|
bigint_adjust(a);
|
|
}
|
|
if(b){
|
|
bigint_set_zero(b);
|
|
}
|
|
return;
|
|
}
|
|
if(y->length_W==1 && y->wordv[0]==1){
|
|
gcd->length_W = 1;
|
|
gcd->wordv[0] = 1;
|
|
if(b){
|
|
b->length_W = 1;
|
|
b->wordv[0] = 1;
|
|
SET_POS(b);
|
|
bigint_adjust(b);
|
|
}
|
|
if(a){
|
|
bigint_set_zero(a);
|
|
}
|
|
return;
|
|
}
|
|
|
|
while(x->wordv[i]==0 && y->wordv[i]==0){
|
|
++i;
|
|
}
|
|
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];
|
|
|
|
g.wordv = g_b;
|
|
x_.wordv = x_b;
|
|
y_.wordv = y_b;
|
|
memset(g_b, 0, i*sizeof(bigint_word_t));
|
|
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*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){
|
|
}
|
|
|
|
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{
|
|
cli_putstr("\r\nDBG (gcdext) 0");
|
|
while((u.wordv[0]&1)==0){
|
|
cli_putstr("\r\nDBG (gcdext) 0.1");
|
|
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){
|
|
cli_putstr("\r\nDBG (gcdext) 0.2");
|
|
bigint_shiftright(&v, 1);
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if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
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bigint_add_s(&c_, &c_, &y_);
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bigint_sub_s(&d_, &d_, &x_);
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}
|
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bigint_shiftright(&c_, 1);
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bigint_shiftright(&d_, 1);
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}
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if(bigint_cmp_u(&u, &v)>=0){
|
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bigint_sub_u(&u, &u, &v);
|
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bigint_sub_s(&a_, &a_, &c_);
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bigint_sub_s(&b_, &b_, &d_);
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}else{
|
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bigint_sub_u(&v, &v, &u);
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bigint_sub_s(&c_, &c_, &a_);
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bigint_sub_s(&d_, &d_, &b_);
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}
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}while(u.length_W);
|
|
if(gcd){
|
|
bigint_mul_s(gcd, &v, &g);
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}
|
|
if(a){
|
|
bigint_copy(a, &c_);
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}
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if(b){
|
|
bigint_copy(b, &d_);
|
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}
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}
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/******************************************************************************/
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void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
|
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bigint_gcdext(NULL, dest, NULL, a, m);
|
|
while(dest->info&BIGINT_NEG_MASK){
|
|
bigint_add_s(dest, dest, m);
|
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}
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}
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/******************************************************************************/
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void bigint_changeendianess(bigint_t* a){
|
|
uint8_t t, *p, *q;
|
|
p = (uint8_t*)(a->wordv);
|
|
q = p + a->length_W * sizeof(bigint_word_t) - 1;
|
|
while(p<q){
|
|
t = *p;
|
|
*p = *q;
|
|
*q = t;
|
|
++p; --q;
|
|
}
|
|
}
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/******************************************************************************/
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