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/* bigint.c */
/*
This file is part of the AVR-Crypto-Lib.
Copyright (C) 2006-2015 Daniel Otte (bg@nerilex.org)
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_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);
}
*/
/******************************************************************************/
/* 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);
}
*/
/******************************************************************************/
/* 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);
}
}
/******************************************************************************/
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_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 */
}
/******************************************************************************/
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_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;
}
/******************************************************************************/
/* 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_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_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)
{
// 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);
}
/******************************************************************************/
/* 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);
}
/******************************************************************************/
/* 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_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;
}
}
/******************************************************************************/
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