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arm-crypto-lib/bigint/bigint.c

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/* 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>
#define DEBUG 0
#if DEBUG
#include "cli.h"
#include "bigint_io.h"
#endif
#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 &=~BIGINT_FBS_MASK; (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*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
b = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));}while(0)
#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
/******************************************************************************/
void bigint_adjust(bigint_t* a){
while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
a->length_B--;
}
if(a->length_B==0){
a->info=0;
return;
}
bigint_word_t t;
uint8_t i = BIGINT_WORD_SIZE-1;
t = a->wordv[a->length_B-1];
while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
t<<=1;
i--;
}
SET_FBS(a, i);
}
/******************************************************************************/
uint16_t bigint_length_b(const bigint_t* a){
if(!a->length_B || a->length_B==0){
return 0;
}
return (a->length_B-1) * BIGINT_WORD_SIZE + GET_FBS(a);
}
/******************************************************************************/
uint16_t bigint_length_B(const bigint_t* a){
return a->length_B * sizeof(bigint_word_t);
}
/******************************************************************************/
uint32_t bigint_get_first_set_bit(const bigint_t* a){
if(a->length_B==0){
return (uint32_t)(-1);
}
return (a->length_B-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
}
/******************************************************************************/
uint32_t bigint_get_last_set_bit(const bigint_t* a){
uint32_t r=0;
uint8_t b=0;
bigint_word_t x=1;
if(a->length_B==0){
return (uint32_t)(-1);
}
while(a->wordv[r]==0 && r<a->length_B){
++r;
}
if(a->wordv[r] == 0){
return (uint32_t)(-1);
}
while((x&a->wordv[r])==0){
++b;
x <<= 1;
}
return r*BIGINT_WORD_SIZE+b;
}
/******************************************************************************/
void bigint_copy(bigint_t* dest, const bigint_t* src){
memcpy(dest->wordv, src->wordv, src->length_B*sizeof(bigint_word_t));
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 i;
bigint_wordplus_t t=0LL;
if(a->length_B < b->length_B){
XCHG_PTR(a,b);
}
for(i=0; i<b->length_B; ++i){
// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
t += a->wordv[i];
t += b->wordv[i];
dest->wordv[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
}
for(; i<a->length_B; ++i){
t += a->wordv[i];
dest->wordv[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
}
if(t){
dest->wordv[i++] = (bigint_word_t)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){
if(a->length_B == 0){
return;
}
if(scale == 0){
bigint_add_u(dest, dest, a);
return;
}
bigint_t x;
#if BIGINT_WORD_SIZE == 8
memset(dest->wordv + dest->length_B, 0, MAX(dest->length_B, a->length_B + scale) - dest->length_B);
x.wordv = dest->wordv + scale;
x.length_B = dest->length_B - scale;
if((int16_t)x.length_B < 0){
x.length_B = 0;
x.info = 0;
} else {
x.info = dest->info;
}
bigint_add_u(&x, &x, a);
dest->length_B = x.length_B + scale;
dest->info = 0;
bigint_adjust(dest);
#else
bigint_t s;
uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
bigint_word_t bv[a->length_B + 1];
s.wordv = bv;
bv[0] = bv[a->length_B] = 0;
memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_B * sizeof(bigint_word_t));
s.length_B = a->length_B + 1;
bigint_adjust(&s);
memset(dest->wordv + dest->length_B, 0, (MAX(dest->length_B, s.length_B + word_shift) - dest->length_B) * sizeof(bigint_word_t));
x.wordv = dest->wordv + word_shift;
x.length_B = dest->length_B - word_shift;
if((int16_t)x.length_B < 0){
x.length_B = 0;
x.info = 0;
}else{
x.info = dest->info;
}
bigint_add_u(&x, &x, &s);
dest->length_B = x.length_B + word_shift;
dest->info = 0;
bigint_adjust(dest);
#endif
/* uint16_t i,j=0;
uint16_t scale_w;
bigint_word_t *dst;
bigint_wordplus_t t=0;
scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
if(scale>dest->length_B*sizeof(bigint_word_t)){
memset(((uint8_t*)dest->wordv)+dest->length_B*sizeof(bigint_word_t), 0, scale-dest->length_B*sizeof(bigint_word_t));
}
// a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3));
dst = dest->wordv + (scale&(sizeof(bigint_word_t)-1));
for(i=scale/sizeof(bigint_word_t); i<a->length_B+scale_w; ++i,++j){
t += a->wordv[j];
if(dest->length_B>i){
t += dst[i];
}
dst[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
}
while(t){
if(dest->length_B>i){
t += dst[i];
}
dst[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
++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;
bigint_wordplus_signed_t t=0LL;
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){
bigint_set_zero(dest);
return;
}
if(b->length_B==0){
bigint_copy(dest, a);
SET_POS(dest);
return;
}
if(a->length_B==0){
bigint_copy(dest, b);
SET_NEG(dest);
return;
}
if(r<0){
bigint_sub_u(dest, b, a);
SET_NEG(dest);
return;
}
for(i=0; i<max; ++i){
t = a->wordv[i];
if(i<min){
t -= b->wordv[i];
}
t -= borrow;
dest->wordv[i]=(bigint_word_t)t;
if(t<0){
borrow = 1;
}else{
borrow = 0;
}
}
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, word_alloc, words_to_shift;
int16_t i;
uint8_t bitshift;
bigint_word_t *p;
bigint_wordplus_t t=0;
if(shift==0){
return;
}
byteshift = shift/8;
bitshift = shift&7;
for(i=0;i<=byteshift/sizeof(bigint_word_t); ++i){
a->wordv[a->length_B+i] = 0;
}
if(byteshift){
memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_B * sizeof(bigint_word_t));
memset(a->wordv, 0, byteshift);
}
p = a->wordv + byteshift / sizeof(bigint_word_t);
words_to_shift = a->length_B + (byteshift % sizeof(bigint_word_t)?1:0);
word_alloc = a->length_B + (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t) + 1;
a->wordv[word_alloc-1]=0;
if(bitshift!=0){
for(i=0; i < words_to_shift; ++i){
t |= ((bigint_wordplus_t)p[i])<<bitshift;
p[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE;
}
p[i] = (bigint_word_t)t;
}
a->length_B = word_alloc;
bigint_adjust(a);
}
/******************************************************************************/
void bigint_shiftright(bigint_t* a, uint16_t shift){
uint16_t byteshift;
uint16_t i;
uint8_t bitshift;
bigint_wordplus_t t=0;
byteshift = shift/8;
bitshift = shift&7;
if(byteshift >= a->length_B * sizeof(bigint_word_t)){ /* we would shift out more than we have */
bigint_set_zero(a);
return;
}
if(byteshift == a->length_B * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){
bigint_set_zero(a);
return;
}
if(byteshift){
memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_B * sizeof(bigint_word_t) - byteshift);
memset((uint8_t*)a->wordv + a->length_B * sizeof(bigint_word_t) - byteshift, 0, byteshift);
}
byteshift /= sizeof(bigint_word_t);
a->length_B -= (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
if(bitshift != 0 && a->length_B){
/* shift to the right */
i = a->length_B - 1;
do{
t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - bitshift);
a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE);
t <<= BIGINT_WORD_SIZE;
}while(i--);
}
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;
bigint_word_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);
}
bigint_wordplus_t t=0;
uint16_t i;
bigint_word_t x = a->wordv[0];
for(i=0; i < b->length_B; ++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_B = i+1;
dest->info = 0;
bigint_adjust(dest);
return;
}
if(a->length_B * sizeof(bigint_word_t) <= 4 && b->length_B * sizeof(bigint_word_t) <= 4){
uint32_t p=0, q=0;
uint64_t r;
memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
memcpy(&q, b->wordv, b->length_B*sizeof(bigint_word_t));
r = (uint64_t)p * (uint64_t)q;
memcpy(dest->wordv, &r, (dest->length_B = a->length_B + b->length_B)*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_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){
bigint_set_zero(&xh);
xl.length_B = a->length_B;
xl.info = a->info;
}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 = a->info;
}
if(b->length_B<=n){
bigint_set_zero(&yh);
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 = 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_B*sizeof(bigint_word_t)<=4){
uint64_t r=0;
memcpy(&r, a->wordv, a->length_B*sizeof(bigint_word_t));
r = r*r;
memcpy(dest->wordv, &r, 2*a->length_B*sizeof(bigint_word_t));
SET_POS(dest);
dest->length_B=2*a->length_B;
bigint_adjust(dest);
return;
}
if(dest==a){
bigint_t d;
bigint_word_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 */
bigint_word_t buffer[2*n+1];
xl.wordv = a->wordv;
xl.length_B = n;
xl.info = 0;
xh.wordv = &(a->wordv[n]);
xh.length_B = a->length_B-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_B + 1];
const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
if(a->length_B < b->length_B + 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_B = a->length_B - 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_B==0 || a->length_B==0){
return;
}
if((r->length_B*sizeof(bigint_word_t)<=4) && (a->length_B*sizeof(bigint_word_t)<=4)){
uint32_t p=0, q=0;
memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
memcpy(&q, r->wordv, r->length_B*sizeof(bigint_word_t));
p %= q;
memcpy(a->wordv, &p, a->length_B*sizeof(bigint_word_t));
bigint_adjust(a);
// cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
return;
}
uint16_t shift;
while(a->length_B > r->length_B){
shift = (a->length_B - r->length_B) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
/*
if((a->wordv[a->length_B-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_B-1]){
// cli_putc('~');
cli_putstr("\r\n ~ [a] = ");
cli_hexdump_rev(&a->wordv[a->length_B-1], 4);
cli_putstr(" [r] = ");
cli_hexdump_rev(&r->wordv[r->length_B-1], 4);
shift += 1;
}
*/
// cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
// cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_B, 2);
// cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_B, 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_B == r->length_B)){
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_B==0 || r->length_B==0){
return;
}
bigint_t res, base;
bigint_word_t t, base_b[MAX(a->length_B,r->length_B)], res_b[r->length_B*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_B=1;
res.info = 0;
bigint_adjust(&res);
if(exp->length_B == 0){
bigint_copy(dest, &res);
return;
}
uint8_t flag = 0;
t=exp->wordv[exp->length_B - 1];
for(i=exp->length_B; 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_B==0 || y->length_B==0){
return;
}
if(x->length_B==1 && x->wordv[0]==1){
gcd->length_B = 1;
gcd->wordv[0] = 1;
if(a){
a->length_B = 1;
a->wordv[0] = 1;
SET_POS(a);
bigint_adjust(a);
}
if(b){
bigint_set_zero(b);
}
return;
}
if(y->length_B==1 && y->wordv[0]==1){
gcd->length_B = 1;
gcd->wordv[0] = 1;
if(b){
b->length_B = 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_B-i], y_b[y->length_B-i];
bigint_word_t u_b[x->length_B-i], v_b[y->length_B-i];
bigint_word_t a_b[y->length_B+2], c_b[y->length_B+2];
bigint_word_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*sizeof(bigint_word_t));
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*sizeof(bigint_word_t));
memcpy(y_.wordv, y->wordv+i, y_.length_B*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_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{
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);
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 = (uint8_t*)(a->wordv);
q = p + a->length_B * sizeof(bigint_word_t) - 1;
while(p<q){
t = *p;
*p = *q;
*q = t;
++p; --q;
}
}
/******************************************************************************/
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