/* bigint.c */
/*
- This file is part of the AVR-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/>.
-*/
+ This file is part of the AVR-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
* \license GPLv3 or later
*
*/
-
#define STRING2(x) #x
#define STRING(x) STRING2(x)
#include "bigint.h"
#include <string.h>
/*
-#include "cli.h"
-#include "bigint_io.h"
-*/
+ #include "cli.h"
+ #include "bigint_io.h"
+ */
#ifndef MAX
- #define MAX(a,b) (((a)>(b))?(a):(b))
+#define MAX(a,b) (((a)>(b))?(a):(b))
#endif
#ifndef MIN
- #define MIN(a,b) (((a)<(b))?(a):(b))
+#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_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
-
/******************************************************************************/
/*
-void bigint_copy(bigint_t *dest, const bigint_t *src){
- memcpy(dest->wordv, src->wordv, src->length_W);
- dest->length_W = src->length_W;
- dest->info = src->info;
-}
-*/
+ void bigint_copy(bigint_t *dest, const bigint_t *src){
+ memcpy(dest->wordv, src->wordv, src->length_W);
+ dest->length_W = src->length_W;
+ 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_W < b->length_W){
- XCHG_PTR(a,b);
- }
- for(i=0; i<b->length_W; ++i){
- t = a->wordv[i] + b->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
-
for(; i<a->length_W; ++i){
- t = a->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- dest->wordv[i++] = t;
- dest->length_W = i;
- bigint_adjust(dest);
-}
-*/
+ void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
+ uint16_t t=0, i;
+ if(a->length_W < b->length_W){
+ XCHG_PTR(a,b);
+ }
+ for(i=0; i<b->length_W; ++i){
+ t = a->wordv[i] + b->wordv[i] + t;
+ dest->wordv[i] = (uint8_t)t;
+ t>>=8;
+ }
+ for(; i<a->length_W; ++i){
+ t = a->wordv[i] + t;
+ dest->wordv[i] = (uint8_t)t;
+ t>>=8;
+ }
+ dest->wordv[i++] = t;
+ dest->length_W = 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_W)
- memset(dest->wordv+dest->length_W, 0, scale-dest->length_W);
-
for(i=scale; i<a->length_W+scale; ++i,++j){
- t = a->wordv[j] + t;
- if(dest->length_W>i){
- t += dest->wordv[i];
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- while(t){
- if(dest->length_W>i){
- t = dest->wordv[i] + t;
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- ++i;
- }
- if(dest->length_W < i){
- dest->length_W = i;
- }
- bigint_adjust(dest);
-}
-*/
+ 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_W)
+ memset(dest->wordv+dest->length_W, 0, scale-dest->length_W);
+ for(i=scale; i<a->length_W+scale; ++i,++j){
+ t = a->wordv[j] + t;
+ if(dest->length_W>i){
+ t += dest->wordv[i];
+ }
+ dest->wordv[i] = (uint8_t)t;
+ t>>=8;
+ }
+ while(t){
+ if(dest->length_W>i){
+ t = dest->wordv[i] + t;
+ }
+ dest->wordv[i] = (uint8_t)t;
+ t>>=8;
+ ++i;
+ }
+ if(dest->length_W < i){
+ dest->length_W = 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_W, b->length_W);
- max = MAX(a->length_W, b->length_W);
- r = bigint_cmp_u(a,b);
- if(r==0){
- dest->length_W = 0;
- dest->wordv[0] = 0;
- bigint_adjust(dest);
- return;
- }
- if(b->length_W==0){
- dest->length_W = a->length_W;
- memcpy(dest->wordv, a->wordv, a->length_W);
- dest->info = a->info;
- SET_POS(dest);
- return;
- }
- if(a->length_W==0){
- dest->length_W = b->length_W;
- memcpy(dest->wordv, b->wordv, b->length_W);
- 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_W = i;
- bigint_adjust(dest);
- }
+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_W, b->length_W);
+ max = MAX(a->length_W, b->length_W);
+ r = bigint_cmp_u(a, b);
+ if (r == 0) {
+ dest->length_W = 0;
+ dest->wordv[0] = 0;
+ bigint_adjust(dest);
+ return;
+ }
+ if (b->length_W == 0) {
+ dest->length_W = a->length_W;
+ memcpy(dest->wordv, a->wordv, a->length_W);
+ dest->info = a->info;
+ SET_POS(dest);
+ return;
+ }
+ if (a->length_W == 0) {
+ dest->length_W = b->length_W;
+ memcpy(dest->wordv, b->wordv, b->length_W);
+ 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_W = i;
+ bigint_adjust(dest);
+ }
}
/******************************************************************************/
-int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b){
- if(a->length_W > b->length_W){
- return 1;
- }
- if(a->length_W < b->length_W){
- return -1;
- }
- if(a->length_W==0){
- return 0;
- }
- uint16_t i;
- i = a->length_W-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;
+int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b)
+{
+ if (a->length_W > b->length_W) {
+ return 1;
+ }
+ if (a->length_W < b->length_W) {
+ return -1;
+ }
+ if (a->length_W == 0) {
+ return 0;
+ }
+ uint16_t i;
+ i = a->length_W - 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_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;
- }
+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_W==0 && b->length_W==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 */
+int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b)
+{
+ uint8_t s;
+ if (a->length_W == 0 && b->length_W == 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_W);
- memset(a->wordv, 0, byteshift);
- if(bitshift!=0){
- if(bitshift<=4){ /* shift to the left */
- for(i=byteshift; i<a->length_W+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_W+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_W += byteshift;
- bigint_adjust(a);
+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_W);
+ memset(a->wordv, 0, byteshift);
+ if (bitshift != 0) {
+ if (bitshift <= 4) { /* shift to the left */
+ for (i = byteshift; i < a->length_W + 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_W + 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_W += 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_W){ /* we would shift out more than we have */
- bigint_set_zero(a);
- return;
- }
- if(byteshift == a->length_W-1 && bitshift>GET_FBS(a)){
- bigint_set_zero(a);
- return;
- }
- if(byteshift){
- memmove(a->wordv, a->wordv+byteshift, a->length_W-byteshift);
- memset(a->wordv+a->length_W-byteshift, 0, byteshift);
- }
- if(bitshift!=0){
- /* shift to the right */
- for(i=a->length_W-byteshift-1; i>0; --i){
- t |= (a->wordv[i])<<(8-bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- t <<= 8;
- }
- t |= (a->wordv[0])<<(8-bitshift);
- a->wordv[0] = (uint8_t)(t>>8);
- }
- a->length_W -= byteshift;
- bigint_adjust(a);
+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_W) { /* we would shift out more than we have */
+ bigint_set_zero(a);
+ return;
+ }
+ if (byteshift == a->length_W - 1 && bitshift > GET_FBS(a)) {
+ bigint_set_zero(a);
+ return;
+ }
+ if (byteshift) {
+ memmove(a->wordv, a->wordv + byteshift, a->length_W - byteshift);
+ memset(a->wordv + a->length_W - byteshift, 0, byteshift);
+ }
+ if (bitshift != 0) {
+ /* shift to the right */
+ for (i = a->length_W - byteshift - 1; i > 0; --i) {
+ t |= (a->wordv[i]) << (8 - bitshift);
+ a->wordv[i] = (uint8_t) (t >> 8);
+ t <<= 8;
+ }
+ t |= (a->wordv[0]) << (8 - bitshift);
+ a->wordv[0] = (uint8_t) (t >> 8);
+ }
+ a->length_W -= byteshift;
+ bigint_adjust(a);
}
/******************************************************************************/
-void bigint_xor(bigint_t *dest, const bigint_t *a){
- uint16_t i;
- for(i=0; i<a->length_W; ++i){
- dest->wordv[i] ^= a->wordv[i];
- }
- bigint_adjust(dest);
+void bigint_xor(bigint_t *dest, const bigint_t *a)
+{
+ uint16_t i;
+ for (i = 0; i < a->length_W; ++i) {
+ dest->wordv[i] ^= a->wordv[i];
+ }
+ bigint_adjust(dest);
}
/******************************************************************************/
-void bigint_set_zero(bigint_t *a){
- a->length_W=0;
+void bigint_set_zero(bigint_t *a)
+{
+ a->length_W = 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_W==0 || b->length_W==0){
- bigint_set_zero(dest);
- return;
- }
- if(dest==a || dest==b){
- bigint_t d;
- uint8_t d_b[a->length_W+b->length_W];
- d.wordv = d_b;
- bigint_mul_u(&d, a, b);
- bigint_copy(dest, &d);
- return;
- }
- if(a->length_W==1 || b->length_W==1){
- if(a->length_W!=1){
- XCHG_PTR(a,b);
- }
- uint16_t i, t=0;
- uint8_t x = a->wordv[0];
- for(i=0; i<b->length_W; ++i){
- t += b->wordv[i]*x;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- dest->wordv[i] = (uint8_t)t;
- dest->length_W=i+1;
- bigint_adjust(dest);
- return;
- }
- if(a->length_W<=4 && b->length_W<=4){
- uint32_t p=0, q=0;
- uint64_t r;
- memcpy(&p, a->wordv, a->length_W);
- memcpy(&q, b->wordv, b->length_W);
- r = (uint64_t)p*(uint64_t)q;
- memcpy(dest->wordv, &r, a->length_W+b->length_W);
- dest->length_W = a->length_W+b->length_W;
- bigint_adjust(dest);
- return;
- }
- bigint_set_zero(dest);
- /* split a in xh & xl; split b in yh & yl */
- uint16_t n;
- n=(MAX(a->length_W, b->length_W)+1)/2;
- bigint_t xl, xh, yl, yh;
- xl.wordv = a->wordv;
- yl.wordv = b->wordv;
- if(a->length_W<=n){
- xh.info=0;
- xh.length_W = 0;
- xl.length_W = a->length_W;
- xl.info = 0;
- }else{
- xl.length_W=n;
- xl.info = 0;
- bigint_adjust(&xl);
- xh.wordv = a->wordv+n;
- xh.length_W = a->length_W-n;
- xh.info = 0;
- }
- if(b->length_W<=n){
- yh.info=0;
- yh.length_W = 0;
- yl.length_W = b->length_W;
- yl.info = b->info;
- }else{
- yl.length_W=n;
- yl.info = 0;
- bigint_adjust(&yl);
- yh.wordv = b->wordv+n;
- yh.length_W = b->length_W-n;
- yh.info = 0;
- }
- /* now we have split up a and b */
- uint8_t tmp_b[2*n+2], m_b[2*(n+1)];
- bigint_t tmp, tmp2, m;
- tmp.wordv = tmp_b;
- tmp2.wordv = tmp_b+n+1;
- m.wordv = m_b;
-
- bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl */
- bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */
- bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */
- bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp2*tmp */
- bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */
- bigint_sub_u(&m, &m, dest); /* m <= m-dest */
- bigint_sub_u(&m, &m, &tmp); /* m <= m-h */
- bigint_add_scale_u(dest, &m, n);
- bigint_add_scale_u(dest, &tmp, 2*n);
+void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b)
+{
+ if (a->length_W == 0 || b->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ if (dest == a || dest == b) {
+ bigint_t d;
+ uint8_t d_b[a->length_W + b->length_W];
+ d.wordv = d_b;
+ bigint_mul_u(&d, a, b);
+ bigint_copy(dest, &d);
+ return;
+ }
+ if (a->length_W == 1 || b->length_W == 1) {
+ if (a->length_W != 1) {
+ XCHG_PTR(a, b);
+ }
+ uint16_t i, t = 0;
+ uint8_t x = a->wordv[0];
+ for (i = 0; i < b->length_W; ++i) {
+ t += b->wordv[i] * x;
+ dest->wordv[i] = (uint8_t) t;
+ t >>= 8;
+ }
+ dest->wordv[i] = (uint8_t) t;
+ dest->length_W = i + 1;
+ bigint_adjust(dest);
+ return;
+ }
+ if (a->length_W <= 4 && b->length_W <= 4) {
+ uint32_t p = 0, q = 0;
+ uint64_t r;
+ memcpy(&p, a->wordv, a->length_W);
+ memcpy(&q, b->wordv, b->length_W);
+ r = (uint64_t) p * (uint64_t) q;
+ memcpy(dest->wordv, &r, a->length_W + b->length_W);
+ dest->length_W = a->length_W + b->length_W;
+ bigint_adjust(dest);
+ return;
+ }
+ bigint_set_zero(dest);
+ /* split a in xh & xl; split b in yh & yl */
+ uint16_t n;
+ n = (MAX(a->length_W, b->length_W) + 1) / 2;
+ bigint_t xl, xh, yl, yh;
+ xl.wordv = a->wordv;
+ yl.wordv = b->wordv;
+ if (a->length_W <= n) {
+ xh.info = 0;
+ xh.length_W = 0;
+ xl.length_W = a->length_W;
+ xl.info = 0;
+ } else {
+ xl.length_W = n;
+ xl.info = 0;
+ bigint_adjust(&xl);
+ xh.wordv = a->wordv + n;
+ xh.length_W = a->length_W - n;
+ xh.info = 0;
+ }
+ if (b->length_W <= n) {
+ yh.info = 0;
+ yh.length_W = 0;
+ yl.length_W = b->length_W;
+ yl.info = b->info;
+ } else {
+ yl.length_W = n;
+ yl.info = 0;
+ bigint_adjust(&yl);
+ yh.wordv = b->wordv + n;
+ yh.length_W = b->length_W - n;
+ yh.info = 0;
+ }
+ /* now we have split up a and b */
+ uint8_t tmp_b[2 * n + 2], m_b[2 * (n + 1)];
+ bigint_t tmp, tmp2, m;
+ tmp.wordv = tmp_b;
+ tmp2.wordv = tmp_b + n + 1;
+ m.wordv = m_b;
+
+ bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl */
+ bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */
+ bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */
+ bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp2*tmp */
+ bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */
+ bigint_sub_u(&m, &m, dest); /* m <= m-dest */
+ bigint_sub_u(&m, &m, &tmp); /* m <= m-h */
+ bigint_add_scale_u(dest, &m, n);
+ bigint_add_scale_u(dest, &tmp, 2 * n);
}
/******************************************************************************/
-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;
- }
+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<=4){
- uint64_t r=0;
- memcpy(&r, a->wordv, a->length_W);
- r = r*r;
- memcpy(dest->wordv, &r, 2*a->length_W);
- SET_POS(dest);
- dest->length_W=2*a->length_W;
- bigint_adjust(dest);
- return;
- }
- if(dest==a){
- bigint_t d;
- uint8_t d_b[a->length_W*2];
- d.wordv = d_b;
- bigint_square(&d, a);
- bigint_copy(dest, &d);
- return;
- }
- uint16_t n;
- n=(a->length_W+1)/2;
- bigint_t xh, xl, tmp; /* x-high, x-low, temp */
- uint8_t buffer[2*n+1];
- xl.wordv = a->wordv;
- xl.length_W = n;
- xh.wordv = a->wordv+n;
- xh.length_W = a->length_W-n;
- tmp.wordv = buffer;
- bigint_square(dest, &xl);
- bigint_square(&tmp, &xh);
- bigint_add_scale_u(dest, &tmp, 2*n);
- bigint_mul_u(&tmp, &xl, &xh);
- bigint_shiftleft(&tmp, 1);
- bigint_add_scale_u(dest, &tmp, n);
+void bigint_square(bigint_t *dest, const bigint_t *a)
+{
+ if (a->length_W <= 4) {
+ uint64_t r = 0;
+ memcpy(&r, a->wordv, a->length_W);
+ r = r * r;
+ memcpy(dest->wordv, &r, 2 * a->length_W);
+ SET_POS(dest);
+ dest->length_W = 2 * a->length_W;
+ bigint_adjust(dest);
+ return;
+ }
+ if (dest == a) {
+ bigint_t d;
+ uint8_t d_b[a->length_W * 2];
+ d.wordv = d_b;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ return;
+ }
+ uint16_t n;
+ n = (a->length_W + 1) / 2;
+ bigint_t xh, xl, tmp; /* x-high, x-low, temp */
+ uint8_t buffer[2 * n + 1];
+ xl.wordv = a->wordv;
+ xl.length_W = n;
+ xh.wordv = a->wordv + n;
+ xh.length_W = a->length_W - n;
+ tmp.wordv = buffer;
+ bigint_square(dest, &xl);
+ bigint_square(&tmp, &xh);
+ bigint_add_scale_u(dest, &tmp, 2 * n);
+ bigint_mul_u(&tmp, &xl, &xh);
+ bigint_shiftleft(&tmp, 1);
+ bigint_add_scale_u(dest, &tmp, n);
}
/******************************************************************************/
-void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale){
- bigint_t tmp;
- uint8_t tmp_b[b->length_W+1];
- uint16_t i,j,byteshift=bitscale/8;
- uint8_t borrow=0;
- int16_t t;
-
- if(a->length_W < b->length_W+byteshift){
- bigint_set_zero(a);
- return;
- }
-
- tmp.wordv = tmp_b;
- bigint_copy(&tmp, b);
- bigint_shiftleft(&tmp, bitscale&7);
-
- for(j=0,i=byteshift; i<tmp.length_W+byteshift; ++i, ++j){
- t = a->wordv[i] - tmp.wordv[j] - borrow;
- a->wordv[i] = (uint8_t)t;
- if(t<0){
- borrow = 1;
- }else{
- borrow = 0;
- }
- }
- while(borrow){
- if(i+1 > a->length_W){
- bigint_set_zero(a);
- return;
- }
- a->wordv[i] -= borrow;
- if(a->wordv[i]!=0xff){
- borrow=0;
- }
- ++i;
- }
- bigint_adjust(a);
+void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale)
+{
+ bigint_t tmp;
+ uint8_t tmp_b[b->length_W + 1];
+ uint16_t i, j, byteshift = bitscale / 8;
+ uint8_t borrow = 0;
+ int16_t t;
+
+ if (a->length_W < b->length_W + byteshift) {
+ bigint_set_zero(a);
+ return;
+ }
+
+ tmp.wordv = tmp_b;
+ bigint_copy(&tmp, b);
+ bigint_shiftleft(&tmp, bitscale & 7);
+
+ for (j = 0, i = byteshift; i < tmp.length_W + byteshift; ++i, ++j) {
+ t = a->wordv[i] - tmp.wordv[j] - borrow;
+ a->wordv[i] = (uint8_t) t;
+ if (t < 0) {
+ borrow = 1;
+ } else {
+ borrow = 0;
+ }
+ }
+ while (borrow) {
+ if (i + 1 > a->length_W) {
+ bigint_set_zero(a);
+ return;
+ }
+ a->wordv[i] -= borrow;
+ if (a->wordv[i] != 0xff) {
+ borrow = 0;
+ }
+ ++i;
+ }
+ bigint_adjust(a);
}
/******************************************************************************/
-void bigint_reduce(bigint_t *a, const bigint_t *r){
+void bigint_reduce(bigint_t *a, const bigint_t *r)
+{
// bigint_adjust(r);
- uint8_t rfbs = GET_FBS(r);
-
- if(r->length_W==0 || a->length_W==0){
- return;
- }
- while(a->length_W > r->length_W){
- bigint_sub_u_bitscale(a, r, (a->length_W-r->length_W)*8+GET_FBS(a)-rfbs-1);
- }
- while((GET_FBS(a) > rfbs+1) && (a->length_W == r->length_W)){
- bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
- }
- while(bigint_cmp_u(a,r)>=0){
- bigint_sub_u(a,a,r);
- }
- bigint_adjust(a);
+ uint8_t rfbs = GET_FBS(r);
+
+ if (r->length_W == 0 || a->length_W == 0) {
+ return;
+ }
+ while (a->length_W > r->length_W) {
+ bigint_sub_u_bitscale(a, r, (a->length_W - r->length_W) * 8 + GET_FBS(a)
+ - rfbs - 1);
+ }
+ while ((GET_FBS(a) > rfbs + 1) && (a->length_W == r->length_W)) {
+ bigint_sub_u_bitscale(a, r, GET_FBS(a) - rfbs - 1);
+ }
+ while (bigint_cmp_u(a, r) >= 0) {
+ bigint_sub_u(a, a, r);
+ }
+ bigint_adjust(a);
}
/******************************************************************************/
/* 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;
- uint8_t base_b[MAX(a->length_W,r->length_W*2)], res_b[r->length_W*2];
- uint16_t i;
- uint8_t j, t;
- res.wordv = res_b;
- base.wordv = base_b;
- bigint_copy(&base, a);
- bigint_reduce(&base, r);
- res.wordv[0]=1;
- res.length_W=1;
- res.info = 0;
- bigint_adjust(&res);
- for(i=0; i+1<exp->length_W; ++i){
- t=exp->wordv[i];
- for(j=0; j<8; ++j){
- if(t&1){
- bigint_mul_u(&res, &res, &base);
- bigint_reduce(&res, r);
- }
- bigint_square(&base, &base);
- bigint_reduce(&base, r);
- t>>=1;
- }
- }
- t=exp->wordv[i];
- while(t){
- if(t&1){
- bigint_mul_u(&res, &res, &base);
- bigint_reduce(&res, r);
- }
- bigint_square(&base, &base);
- bigint_reduce(&base, r);
- t>>=1;
- }
- SET_POS(&res);
- bigint_copy(dest, &res);
+void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp,
+ const bigint_t *r)
+{
+ if (a->length_W == 0 || r->length_W == 0) {
+ return;
+ }
+
+ bigint_t res, base;
+ uint8_t base_b[MAX(a->length_W, r->length_W * 2)], res_b[r->length_W * 2];
+ uint16_t i;
+ uint8_t j, t;
+ res.wordv = res_b;
+ base.wordv = base_b;
+ bigint_copy(&base, a);
+ bigint_reduce(&base, r);
+ res.wordv[0] = 1;
+ res.length_W = 1;
+ res.info = 0;
+ bigint_adjust(&res);
+ for (i = 0; i + 1 < exp->length_W; ++i) {
+ t = exp->wordv[i];
+ for (j = 0; j < 8; ++j) {
+ if (t & 1) {
+ bigint_mul_u(&res, &res, &base);
+ bigint_reduce(&res, r);
+ }
+ bigint_square(&base, &base);
+ bigint_reduce(&base, r);
+ t >>= 1;
+ }
+ }
+ t = exp->wordv[i];
+ while (t) {
+ if (t & 1) {
+ bigint_mul_u(&res, &res, &base);
+ bigint_reduce(&res, r);
+ }
+ bigint_square(&base, &base);
+ bigint_reduce(&base, r);
+ t >>= 1;
+ }
+ SET_POS(&res);
+ bigint_copy(dest, &res);
}
/******************************************************************************/
/* 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_W==0 || y->length_W==0){
- return;
- }
- while(x->wordv[i]==0 && y->wordv[i]==0){
- ++i;
- }
- uint8_t g_b[i+2], x_b[x->length_W-i], y_b[y->length_W-i];
- uint8_t u_b[x->length_W-i], v_b[y->length_W-i];
- uint8_t a_b[y->length_W+2], c_b[y->length_W+2];
- uint8_t b_b[x->length_W+2], d_b[x->length_W+2];
-
- g.wordv = g_b;
- x_.wordv = x_b;
- y_.wordv = y_b;
- memset(g_b, 0, i);
- g_b[i]=1;
- g.length_W = i+1;
- g.info=0;
- x_.info = y_.info = 0;
- x_.length_W = x->length_W-i;
- y_.length_W = y->length_W-i;
- memcpy(x_.wordv, x->wordv+i, x_.length_W);
- memcpy(y_.wordv, y->wordv+i, y_.length_W);
- for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
- }
-
- bigint_adjust(&x_);
- bigint_adjust(&y_);
-
- if(i){
- bigint_shiftleft(&g, i);
- bigint_shiftright(&x_, i);
- bigint_shiftright(&y_, i);
- }
- u.wordv = u_b;
- v.wordv = v_b;
- a_.wordv = a_b;
- b_.wordv = b_b;
- c_.wordv = c_b;
- d_.wordv = d_b;
-
- bigint_copy(&u, &x_);
- bigint_copy(&v, &y_);
- a_.wordv[0] = 1;
- a_.length_W = 1;
- a_.info = 0;
- d_.wordv[0] = 1;
- d_.length_W = 1;
- d_.info = 0;
- bigint_set_zero(&b_);
- bigint_set_zero(&c_);
- do{
- while((u.wordv[0]&1)==0){
- bigint_shiftright(&u, 1);
- if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
- bigint_add_s(&a_, &a_, &y_);
- bigint_sub_s(&b_, &b_, &x_);
- }
- bigint_shiftright(&a_, 1);
- bigint_shiftright(&b_, 1);
- }
- while((v.wordv[0]&1)==0){
- bigint_shiftright(&v, 1);
- if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
- bigint_add_s(&c_, &c_, &y_);
- bigint_sub_s(&d_, &d_, &x_);
- }
- bigint_shiftright(&c_, 1);
- bigint_shiftright(&d_, 1);
-
- }
- if(bigint_cmp_u(&u, &v)>=0){
- bigint_sub_u(&u, &u, &v);
- bigint_sub_s(&a_, &a_, &c_);
- bigint_sub_s(&b_, &b_, &d_);
- }else{
- bigint_sub_u(&v, &v, &u);
- bigint_sub_s(&c_, &c_, &a_);
- bigint_sub_s(&d_, &d_, &b_);
- }
- }while(u.length_W);
- if(gcd){
- bigint_mul_s(gcd, &v, &g);
- }
- if(a){
- bigint_copy(a, &c_);
- }
- if(b){
- bigint_copy(b, &d_);
- }
+void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x,
+ const bigint_t *y)
+{
+ bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
+ volatile uint16_t i = 0;
+ if (x->length_W == 0 || y->length_W == 0) {
+ return;
+ }
+ while (x->wordv[i] == 0 && y->wordv[i] == 0) {
+ ++i;
+ }
+ uint8_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i];
+ uint8_t u_b[x->length_W - i], v_b[y->length_W - i];
+ uint8_t a_b[y->length_W + 2], c_b[y->length_W + 2];
+ uint8_t b_b[x->length_W + 2], d_b[x->length_W + 2];
+
+ g.wordv = g_b;
+ x_.wordv = x_b;
+ y_.wordv = y_b;
+ memset(g_b, 0, i);
+ g_b[i] = 1;
+ g.length_W = i + 1;
+ g.info = 0;
+ x_.info = y_.info = 0;
+ x_.length_W = x->length_W - i;
+ y_.length_W = y->length_W - i;
+ memcpy(x_.wordv, x->wordv + i, x_.length_W);
+ memcpy(y_.wordv, y->wordv + i, y_.length_W);
+ for (i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0;
+ ++i) {
+ }
+
+ bigint_adjust(&x_);
+ bigint_adjust(&y_);
+
+ if (i) {
+ bigint_shiftleft(&g, i);
+ bigint_shiftright(&x_, i);
+ bigint_shiftright(&y_, i);
+ }
+ u.wordv = u_b;
+ v.wordv = v_b;
+ a_.wordv = a_b;
+ b_.wordv = b_b;
+ c_.wordv = c_b;
+ d_.wordv = d_b;
+
+ bigint_copy(&u, &x_);
+ bigint_copy(&v, &y_);
+ a_.wordv[0] = 1;
+ a_.length_W = 1;
+ a_.info = 0;
+ d_.wordv[0] = 1;
+ d_.length_W = 1;
+ d_.info = 0;
+ bigint_set_zero(&b_);
+ bigint_set_zero(&c_);
+ do {
+ while ((u.wordv[0] & 1) == 0) {
+ bigint_shiftright(&u, 1);
+ if ((a_.wordv[0] & 1) || (b_.wordv[0] & 1)) {
+ bigint_add_s(&a_, &a_, &y_);
+ bigint_sub_s(&b_, &b_, &x_);
+ }
+ bigint_shiftright(&a_, 1);
+ bigint_shiftright(&b_, 1);
+ }
+ while ((v.wordv[0] & 1) == 0) {
+ bigint_shiftright(&v, 1);
+ if ((c_.wordv[0] & 1) || (d_.wordv[0] & 1)) {
+ bigint_add_s(&c_, &c_, &y_);
+ bigint_sub_s(&d_, &d_, &x_);
+ }
+ bigint_shiftright(&c_, 1);
+ bigint_shiftright(&d_, 1);
+
+ }
+ if (bigint_cmp_u(&u, &v) >= 0) {
+ bigint_sub_u(&u, &u, &v);
+ bigint_sub_s(&a_, &a_, &c_);
+ bigint_sub_s(&b_, &b_, &d_);
+ } else {
+ bigint_sub_u(&v, &v, &u);
+ bigint_sub_s(&c_, &c_, &a_);
+ bigint_sub_s(&d_, &d_, &b_);
+ }
+ } while (u.length_W);
+ if (gcd) {
+ bigint_mul_s(gcd, &v, &g);
+ }
+ if (a) {
+ bigint_copy(a, &c_);
+ }
+ if (b) {
+ bigint_copy(b, &d_);
+ }
}
/******************************************************************************/
-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_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_W-1;
- while(p<q){
- t = *p;
- *p = *q;
- *q = t;
- ++p; --q;
- }
+void bigint_changeendianess(bigint_t *a)
+{
+ uint8_t t, *p, *q;
+ p = a->wordv;
+ q = p + a->length_W - 1;
+ while (p < q) {
+ t = *p;
+ *p = *q;
+ *q = t;
+ ++p;
+ --q;
+ }
}
/******************************************************************************/
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projects / avr-crypto-lib.git / blobdiff