+++ /dev/null
-/* bigint.c */
-/*
- This file is part of the ARM-Crypto-Lib.
- Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de)
-
- This program is free software: you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation, either version 3 of the License, or
- (at your option) any later version.
-
- This program is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with this program. If not, see <http://www.gnu.org/licenses/>.
-*/
-/**
- * \file bigint.c
- * \author Daniel Otte
- * \date 2010-02-22
- *
- * \license GPLv3 or later
- *
- */
-
-
-#define STRING2(x) #x
-#define STRING(x) STRING2(x)
-#define STR_LINE STRING(__LINE__)
-
-#include "bigint.h"
-#include <string.h>
-/*
-#include "cli.h"
-#include "bigint_io.h"
-*/
-#ifndef MAX
- #define MAX(a,b) (((a)>(b))?(a):(b))
-#endif
-
-#ifndef MIN
- #define MIN(a,b) (((a)<(b))?(a):(b))
-#endif
-
-#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
-#define GET_FBS(a) ((a)->info&BIGINT_FBS_MASK)
-#define SET_NEG(a) (a)->info |= BIGINT_NEG_MASK
-#define SET_POS(a) (a)->info &= ~BIGINT_NEG_MASK
-#define XCHG(a,b) do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
-#define XCHG_PTR(a,b) do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
- b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
- a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
-
-#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
-
-
-/******************************************************************************/
-/*
-void bigint_copy(bigint_t* dest, const bigint_t* src){
- memcpy(dest->wordv, src->wordv, src->length_B);
- dest->length_B = src->length_B;
- dest->info = src->info;
-}
-*/
-/******************************************************************************/
-
-/* this should be implemented in assembly */
-/*
-void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
- uint16_t t=0, i;
- if(a->length_B < b->length_B){
- XCHG_PTR(a,b);
- }
- for(i=0; i<b->length_B; ++i){
- t = a->wordv[i] + b->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- for(; i<a->length_B; ++i){
- t = a->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- dest->wordv[i++] = t;
- dest->length_B = i;
- bigint_adjust(dest);
-}
-*/
-/******************************************************************************/
-
-/* this should be implemented in assembly */
-void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
- uint16_t i,j=0;
- uint16_t t=0;
- if(scale>dest->length_B)
- memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
- for(i=scale; i<a->length_B+scale; ++i,++j){
- t = a->wordv[j] + t;
- if(dest->length_B>i){
- t += dest->wordv[i];
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- while(t){
- if(dest->length_B>i){
- t = dest->wordv[i] + t;
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- ++i;
- }
- if(dest->length_B < i){
- dest->length_B = i;
- }
- bigint_adjust(dest);
-}
-
-/******************************************************************************/
-
-/* this should be implemented in assembly */
-void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
- int8_t borrow=0;
- int8_t r;
- int16_t t;
- uint16_t i, min, max;
- min = MIN(a->length_B, b->length_B);
- max = MAX(a->length_B, b->length_B);
- r = bigint_cmp_u(a,b);
- if(r==0){
- dest->length_B = 0;
- dest->wordv[0] = 0;
- bigint_adjust(dest);
- return;
- }
- if(b->length_B==0){
- dest->length_B = a->length_B;
- memcpy(dest->wordv, a->wordv, a->length_B);
- dest->info = a->info;
- SET_POS(dest);
- return;
- }
- if(a->length_B==0){
- dest->length_B = b->length_B;
- memcpy(dest->wordv, b->wordv, b->length_B);
- dest->info = b->info;
- SET_NEG(dest);
- return;
- }
- if(r<0){
- bigint_sub_u(dest, b, a);
- SET_NEG(dest);
- }else{
- for(i=0; i<min; ++i){
- t = a->wordv[i] - b->wordv[i] - borrow;
- if(t<0){
- borrow = 1;
- dest->wordv[i]=(uint8_t)t;
- }else{
- borrow = 0;
- dest->wordv[i]=(uint8_t)t;
- }
- }
- for(;i<max; ++i){
- t = a->wordv[i] - borrow;
- if(t<0){
- borrow = 1;
- dest->wordv[i]=(uint8_t)t;
- }else{
- borrow = 0;
- dest->wordv[i]=(uint8_t)t;
- }
-
- }
- SET_POS(dest);
- dest->length_B = i;
- bigint_adjust(dest);
- }
-}
-
-/******************************************************************************/
-
-int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
- if(a->length_B > b->length_B){
- return 1;
- }
- if(a->length_B < b->length_B){
- return -1;
- }
- if(a->length_B==0){
- return 0;
- }
- uint16_t i;
- i = a->length_B-1;
- do{
- if(a->wordv[i]!=b->wordv[i]){
- if(a->wordv[i]>b->wordv[i]){
- return 1;
- }else{
- return -1;
- }
- }
- }while(i--);
- return 0;
-}
-
-/******************************************************************************/
-
-void bigint_add_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_add_u(dest, a,b);
- SET_POS(dest);
- break;
- case 1: /* a positive, b negative */
- bigint_sub_u(dest, a, b);
- break;
- case 2: /* a negative, b positive */
- bigint_sub_u(dest, b, a);
- break;
- case 3: /* both negative */
- bigint_add_u(dest, a, b);
- SET_NEG(dest);
- break;
- default: /* how can this happen?*/
- break;
- }
-}
-
-/******************************************************************************/
-
-void bigint_sub_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_sub_u(dest, a,b);
- break;
- case 1: /* a positive, b negative */
- bigint_add_u(dest, a, b);
- SET_POS(dest);
- break;
- case 2: /* a negative, b positive */
- bigint_add_u(dest, a, b);
- SET_NEG(dest);
- break;
- case 3: /* both negative */
- bigint_sub_u(dest, b, a);
- break;
- default: /* how can this happen?*/
- break;
- }
-
-}
-
-/******************************************************************************/
-
-int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
- uint8_t s;
- if(a->length_B==0 && b->length_B==0){
- return 0;
- }
- s = GET_SIGN(a)?2:0;
- s |= GET_SIGN(b)?1:0;
- switch(s){
- case 0: /* both positive */
- return bigint_cmp_u(a, b);
- break;
- case 1: /* a positive, b negative */
- return 1;
- break;
- case 2: /* a negative, b positive */
- return -1;
- break;
- case 3: /* both negative */
- return bigint_cmp_u(b, a);
- break;
- default: /* how can this happen?*/
- break;
- }
- return 0; /* just to satisfy the compiler */
-}
-
-/******************************************************************************/
-
-void bigint_shiftleft(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
- uint8_t bitshift;
- uint16_t t=0;
- byteshift = (shift+3)/8;
- bitshift = shift&7;
- memmove(a->wordv+byteshift, a->wordv, a->length_B);
- memset(a->wordv, 0, byteshift);
- if(bitshift!=0){
- if(bitshift<=4){ /* shift to the left */
- for(i=byteshift; i<a->length_B+byteshift; ++i){
- t |= (a->wordv[i])<<bitshift;
- a->wordv[i] = (uint8_t)t;
- t >>= 8;
- }
- a->wordv[i] = (uint8_t)t;
- byteshift++;
- }else{ /* shift to the right */
- for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
- t |= (a->wordv[i])<<(bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- t <<= 8;
- }
- t |= (a->wordv[i])<<(bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- }
- }
- a->length_B += byteshift;
- bigint_adjust(a);
-}
-
-/******************************************************************************/
-
-void bigint_shiftright(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
- uint8_t bitshift;
- uint16_t t=0;
- byteshift = shift/8;
- bitshift = shift&7;
- if(byteshift >= a->length_B){ /* we would shift out more than we have */
- bigint_set_zero(a);
- return;
- }
- if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
- bigint_set_zero(a);
- return;
- }
- if(byteshift){
- memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift);
- memset(a->wordv+a->length_B-byteshift, 0, byteshift);
- }
- if(bitshift!=0){
- /* shift to the right */
- for(i=a->length_B-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_B -= byteshift;
- bigint_adjust(a);
-}
-
-/******************************************************************************/
-
-void bigint_xor(bigint_t* dest, const bigint_t* a){
- uint16_t i;
- for(i=0; i<a->length_B; ++i){
- dest->wordv[i] ^= a->wordv[i];
- }
- bigint_adjust(dest);
-}
-
-/******************************************************************************/
-
-void bigint_set_zero(bigint_t* a){
- a->length_B=0;
-}
-
-/******************************************************************************/
-
-/* using the Karatsuba-Algorithm */
-/* 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_B==0 || b->length_B==0){
- bigint_set_zero(dest);
- return;
- }
- if(dest==a || dest==b){
- bigint_t d;
- uint8_t d_b[a->length_B+b->length_B];
- d.wordv = d_b;
- bigint_mul_u(&d, a, b);
- bigint_copy(dest, &d);
- return;
- }
- if(a->length_B==1 || b->length_B==1){
- if(a->length_B!=1){
- XCHG_PTR(a,b);
- }
- uint16_t i, t=0;
- uint8_t x = a->wordv[0];
- for(i=0; i<b->length_B; ++i){
- t += b->wordv[i]*x;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- dest->wordv[i] = (uint8_t)t;
- dest->length_B=i+1;
- bigint_adjust(dest);
- return;
- }
- if(a->length_B<=4 && b->length_B<=4){
- uint32_t p=0, q=0;
- uint64_t r;
- memcpy(&p, a->wordv, a->length_B);
- memcpy(&q, b->wordv, b->length_B);
- r = (uint64_t)p*(uint64_t)q;
- memcpy(dest->wordv, &r, a->length_B+b->length_B);
- dest->length_B = a->length_B+b->length_B;
- 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_B, b->length_B)+1)/2;
- bigint_t xl, xh, yl, yh;
- xl.wordv = a->wordv;
- yl.wordv = b->wordv;
- if(a->length_B<=n){
- xh.info=0;
- xh.length_B = 0;
- xl.length_B = a->length_B;
- xl.info = 0;
- }else{
- xl.length_B=n;
- xl.info = 0;
- bigint_adjust(&xl);
- xh.wordv = a->wordv+n;
- xh.length_B = a->length_B-n;
- xh.info = 0;
- }
- if(b->length_B<=n){
- yh.info=0;
- yh.length_B = 0;
- yl.length_B = b->length_B;
- yl.info = b->info;
- }else{
- yl.length_B=n;
- yl.info = 0;
- bigint_adjust(&yl);
- yh.wordv = b->wordv+n;
- yh.length_B = b->length_B-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);
-}
-
-/******************************************************************************/
-
-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_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;
- }
- if(dest==a){
- bigint_t d;
- uint8_t d_b[a->length_B*2];
- d.wordv = d_b;
- bigint_square(&d, a);
- bigint_copy(dest, &d);
- 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);
-}
-
-/******************************************************************************/
-
-void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
- bigint_t tmp;
- uint8_t tmp_b[b->length_B+1];
- uint16_t i,j,byteshift=bitscale/8;
- uint8_t borrow=0;
- int16_t t;
-
- if(a->length_B < b->length_B+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_B+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_B){
- bigint_set_zero(a);
- return;
- }
- a->wordv[i] -= borrow;
- if(a->wordv[i]!=0xff){
- borrow=0;
- }
- ++i;
- }
- bigint_adjust(a);
-}
-
-/******************************************************************************/
-
-void bigint_reduce(bigint_t* a, const bigint_t* r){
-// bigint_adjust(r);
- uint8_t rfbs = GET_FBS(r);
-
- if(r->length_B==0 || a->length_B==0){
- return;
- }
- while(a->length_B > r->length_B){
- bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
- }
- while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
- 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);
-}
-
-/******************************************************************************/
-
-/* 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_B==0 || r->length_B==0){
- return;
- }
-
- bigint_t res, base;
- uint8_t base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*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_B=1;
- res.info = 0;
- bigint_adjust(&res);
- for(i=0; i+1<exp->length_B; ++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);
-}
-
-/******************************************************************************/
-/* 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_;
- volatile uint16_t i=0;
- if(x->length_B==0 || y->length_B==0){
- return;
- }
- while(x->wordv[i]==0 && y->wordv[i]==0){
- ++i;
- }
- uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
- uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
- uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
- uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
-
- g.wordv = g_b;
- x_.wordv = x_b;
- y_.wordv = y_b;
- memset(g_b, 0, i);
- g_b[i]=1;
- g.length_B = i+1;
- g.info=0;
- x_.info = y_.info = 0;
- x_.length_B = x->length_B-i;
- y_.length_B = y->length_B-i;
- memcpy(x_.wordv, x->wordv+i, x_.length_B);
- memcpy(y_.wordv, y->wordv+i, y_.length_B);
- 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_B = 1;
- a_.info = 0;
- d_.wordv[0] = 1;
- d_.length_B = 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_B);
- if(gcd){
- bigint_mul_s(gcd, &v, &g);
- }
- if(a){
- bigint_copy(a, &c_);
- }
- if(b){
- bigint_copy(b, &d_);
- }
-}
-
-/******************************************************************************/
-
-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);
- }
-}
-
-/******************************************************************************/
-
-void bigint_changeendianess(bigint_t* a){
- uint8_t t, *p, *q;
- p = a->wordv;
- q = p+a->length_B-1;
- while(p<q){
- t = *p;
- *p = *q;
- *q = t;
- ++p; --q;
- }
-}
-
-/******************************************************************************/
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projects / arm-crypto-lib.git / blobdiff