#include "bigint.h"
#include <string.h>
-#define DEBUG 0
+#define DEBUG 1
#if DEBUG || 1
#include "cli.h"
+#include "uart_i.h"
#include "bigint_io.h"
#include <stdio.h>
#endif
#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 &=~BIGINT_FBS_MASK; (a)->info |= (v);}while(0)
-#define GET_FBS(a) ((a)->info&BIGINT_FBS_MASK)
+#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(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)
+ a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));} while(0)
-#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
+#define GET_SIGN(a) ((a)->info & BIGINT_NEG_MASK)
/******************************************************************************/
-void bigint_adjust(bigint_t* a){
- while(a->length_W!=0 && a->wordv[a->length_W-1]==0){
+void bigint_adjust(bigint_t *a){
+ while (a->length_W != 0 && a->wordv[a->length_W - 1] == 0) {
a->length_W--;
}
- if(a->length_W==0){
+ if (a->length_W == 0) {
a->info=0;
return;
}
bigint_word_t t;
- uint8_t i = BIGINT_WORD_SIZE-1;
- t = a->wordv[a->length_W-1];
- while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
- t<<=1;
+ uint8_t i = BIGINT_WORD_SIZE - 1;
+ t = a->wordv[a->length_W - 1];
+ while ((t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) == 0 && i) {
+ t <<= 1;
i--;
}
SET_FBS(a, i);
/******************************************************************************/
-uint16_t bigint_length_b(const bigint_t* a){
+bigint_length_t bigint_length_b(const bigint_t *a){
if(!a->length_W || a->length_W==0){
return 0;
}
/******************************************************************************/
-uint16_t bigint_length_B(const bigint_t* a){
+bigint_length_t bigint_length_B(const bigint_t *a){
return a->length_W * sizeof(bigint_word_t);
}
/******************************************************************************/
-uint32_t bigint_get_first_set_bit(const bigint_t* a){
- if(a->length_W==0){
+uint32_t bigint_get_first_set_bit(const bigint_t *a){
+ if(a->length_W == 0) {
return (uint32_t)(-1);
}
- return (a->length_W-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
+ return (a->length_W-1) * sizeof(bigint_word_t) * CHAR_BIT + GET_FBS(a);
}
/******************************************************************************/
-uint32_t bigint_get_last_set_bit(const bigint_t* 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;
/******************************************************************************/
-void bigint_copy(bigint_t* dest, const bigint_t* src){
+void bigint_copy(bigint_t *dest, const bigint_t *src){
if(dest->wordv != src->wordv){
memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t));
}
/******************************************************************************/
/* this should be implemented in assembly */
-void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
- uint16_t i;
+void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
+ bigint_length_t i;
bigint_wordplus_t t = 0LL;
- if(a->length_W < b->length_W){
- XCHG_PTR(a,b);
+ if (a->length_W < b->length_W) {
+ XCHG_PTR(a, b);
}
- for(i = 0; i < b->length_W; ++i){
-// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
+ for(i = 0; i < b->length_W; ++i) {
t += a->wordv[i];
t += b->wordv[i];
dest->wordv[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE;
}
- for(; i<a->length_W; ++i){
+ for(; i < a->length_W; ++i){
t += a->wordv[i];
dest->wordv[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE;
dest->wordv[i++] = (bigint_word_t)t;
}
dest->length_W = i;
+ SET_POS(dest);
bigint_adjust(dest);
}
/******************************************************************************/
/* this should be implemented in assembly */
-void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
+void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){
if(a->length_W == 0){
return;
}
bigint_adjust(dest);
#else
bigint_t s;
- uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
+ bigint_length_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
bigint_word_t bv[a->length_W + 1];
s.wordv = bv;
bv[0] = bv[a->length_W] = 0;
/******************************************************************************/
/* 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;
+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;
+ bigint_wordplus_signed_t t = 0;
+ bigint_length_t i;
if(b->length_W == 0){
bigint_copy(dest, a);
SET_POS(dest);
t -= b->wordv[i];
}
t -= borrow;
- dest->wordv[i]=(bigint_word_t)t;
- if(t<0){
- borrow = 1;
- }else{
- borrow = 0;
- }
+ dest->wordv[i] = (bigint_word_t)t;
+ borrow = t < 0 ? 1 : 0;
}
SET_POS(dest);
dest->length_W = i;
/******************************************************************************/
-int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
+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){
+ if(a->length_W == 0){
return 0;
}
- uint16_t i;
- i = a->length_W-1;
+ bigint_length_t i;
+ i = a->length_W - 1;
do{
if(a->wordv[i] != b->wordv[i]){
if(a->wordv[i] > b->wordv[i]){
/******************************************************************************/
-void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
+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;
/******************************************************************************/
-void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
+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;
/******************************************************************************/
-int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
+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;
/******************************************************************************/
-void bigint_shiftleft(bigint_t* a, uint16_t shift){
- uint16_t byteshift, words_to_shift;
+void bigint_shiftleft(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift, words_to_shift;
int16_t i;
uint8_t bitshift;
bigint_word_t *p;
bigint_wordplus_t t = 0;
- if(shift == 0){
+
+ if (shift == 0) {
return;
}
byteshift = shift / 8;
bitshift = shift & 7;
-
- if(byteshift){
+ if (byteshift % sizeof(bigint_word_t)) {
+ a->wordv[a->length_W + byteshift / sizeof(bigint_t)] = 0;
+ }
+ if (byteshift) {
memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t));
memset(a->wordv, 0, byteshift);
}
- if(bitshift == 0){
+ if (bitshift == 0) {
a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
bigint_adjust(a);
return;
}
- p = a->wordv + byteshift / sizeof(bigint_word_t);
- words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t)?1:0);
- for(i=0; i < words_to_shift; ++i){
+ p = &a->wordv[byteshift / sizeof(bigint_word_t)];
+ words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t) ? 1 : 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;
}
- if(t){
+ if (t) {
p[i] = (bigint_word_t)t;
a->length_W += 1;
}
a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
- bigint_adjust(a);
+ bigint_adjust(a);
}
/******************************************************************************/
-void bigint_shiftright(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
+void bigint_shiftright(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift;
+ bigint_length_t i;
uint8_t bitshift;
bigint_wordplus_t t = 0;
byteshift = shift / 8;
bitshift = shift & 7;
- if(byteshift >= a->length_W * sizeof(bigint_word_t)){ /* we would shift out more than we have */
- bigint_set_zero(a);
- return;
- }
- if(byteshift == a->length_W * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){
+ if(bigint_get_first_set_bit(a) < shift){ /* we would shift out more than we have */
bigint_set_zero(a);
return;
}
if(byteshift){
memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift);
+ memset((uint8_t*)&a->wordv[a->length_W] - byteshift, 0, byteshift);
}
- byteshift /= sizeof(bigint_word_t); /* byteshift is now wordshift */
- a->length_W -= byteshift;
- if(bitshift != 0 && a->length_W){
+ a->length_W -= byteshift / sizeof(bigint_word_t);
+
+ if(bitshift != 0 && a->length_W){
/* shift to the right */
i = a->length_W - 1;
do{
/******************************************************************************/
-void bigint_xor(bigint_t* dest, const bigint_t* a){
- uint16_t i;
+void bigint_xor(bigint_t *dest, const bigint_t *a){
+ bigint_length_t i;
for(i=0; i<a->length_W; ++i){
dest->wordv[i] ^= a->wordv[i];
}
/******************************************************************************/
-void bigint_set_zero(bigint_t* a){
+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){
+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;
XCHG_PTR(a,b);
}
bigint_wordplus_t t = 0;
- uint16_t i;
+ bigint_length_t i;
bigint_word_t x = a->wordv[0];
for(i=0; i < b->length_W; ++i){
t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x);
return;
}
/* split a in xh & xl; split b in yh & yl */
- const uint16_t n = (MAX(a->length_W, b->length_W)+1)/2;
+ const bigint_length_t n = (MAX(a->length_W, b->length_W)+1)/2;
bigint_t xl, xh, yl, yh;
xl.wordv = a->wordv;
yl.wordv = b->wordv;
/******************************************************************************/
-void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
+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;
}
/******************************************************************************/
-
+#if OLD_SQUARE
#if DEBUG_SQUARE
unsigned square_depth = 0;
/* square */
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
-void bigint_square(bigint_t* dest, const bigint_t* a){
- if(a->length_W * sizeof(bigint_word_t) <= 4){
+void bigint_square(bigint_t *dest, const bigint_t *a){
+ if(a->length_W * sizeof(bigint_word_t) <= 4){
uint64_t r = 0;
memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
r = r * r;
bigint_adjust(dest);
return;
}
+
if(dest->wordv == a->wordv){
bigint_t d;
bigint_word_t d_b[a->length_W*2];
bigint_copy(dest, &d);
return;
}
-
+ bigint_fast_square(dest, a);
+ return;
#if DEBUG_SQUARE
square_depth += 1;
#endif
- uint16_t n;
+ bigint_length_t n;
n=(a->length_W+1)/2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
bigint_word_t buffer[2*n+1];
#endif
}
+#endif
+
/******************************************************************************/
-void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
+
+void bigint_square(bigint_t *dest, const bigint_t *a) {
+ union __attribute__((packed)) {
+ bigint_word_t u[2];
+ bigint_wordplus_t uv;
+ } acc;
+ bigint_word_t q, c1, c2;
+ bigint_length_t i, j;
+
+ if(a->length_W * sizeof(bigint_word_t) <= 4){
+ uint64_t r = 0;
+ memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
+ r = r * r;
+ memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t));
+ SET_POS(dest);
+ dest->length_W = 2 * a->length_W;
+ bigint_adjust(dest);
+ return;
+ }
+
+ if(dest->wordv == a->wordv){
+ bigint_t d;
+ bigint_word_t d_b[a->length_W * 2];
+ d.wordv = d_b;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ return;
+ }
+
+ memset(dest->wordv, 0, a->length_W * 2 * sizeof(bigint_word_t));
+
+ for (i = 0; i < a->length_W; ++i) {
+ acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[i] + (bigint_wordplus_t)dest->wordv[2 * i];
+ dest->wordv[2 * i] = acc.u[0];
+ c1 = acc.u[1];
+ c2 = 0;
+ for (j = i + 1; j < a->length_W; ++j) {
+ acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[j];
+ q = acc.u[1] >> (BIGINT_WORD_SIZE - 1);
+ acc.uv <<= 1;
+ acc.uv += dest->wordv[i + j];
+ q += (acc.uv < dest->wordv[i + j]);
+ acc.uv += c1;
+ q += (acc.uv < c1);
+ dest->wordv[i + j] = acc.u[0];
+ c1 = (bigint_wordplus_t)acc.u[1] + c2;
+ c2 = q + (c1 < c2);
+ }
+ dest->wordv[i + a->length_W] += c1;
+ if (i < a->length_W - 1) {
+ dest->wordv[i + a->length_W + 1] = c2 + (dest->wordv[i + a->length_W] < c1);
+ }
+ }
+ dest->info = 0;
+ dest->length_W = 2 * a->length_W;
+ bigint_adjust(dest);
+}
+
+/******************************************************************************/
+
+void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){
bigint_t tmp, x;
bigint_word_t tmp_b[b->length_W + 1];
- const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
+ const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE;
- if(a->length_W < b->length_W + word_shift){
+ if (a->length_W < b->length_W + word_shift) {
#if DEBUG
cli_putstr("\r\nDBG: *bang*\r\n");
#endif
/******************************************************************************/
-void bigint_reduce(bigint_t* a, const bigint_t* r){
-// bigint_adjust((bigint_t*)r);
+void bigint_reduce(bigint_t *a, const bigint_t *r){
uint8_t rfbs = GET_FBS(r);
-#if DEBUG
- cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
-#endif
- if(r->length_W==0 || a->length_W==0){
- return;
- }
- if((r->length_W*sizeof(bigint_word_t)<=4) && (a->length_W*sizeof(bigint_word_t)<=4)){
- uint32_t p=0, q=0;
- memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t));
- memcpy(&q, r->wordv, r->length_W*sizeof(bigint_word_t));
- p %= q;
- memcpy(a->wordv, &p, a->length_W*sizeof(bigint_word_t));
- bigint_adjust(a);
-// cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
+ if (r->length_W == 0 || a->length_W == 0) {
return;
}
- uint16_t shift;
- while(a->length_W > r->length_W){
- shift = (a->length_W - r->length_W) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
- /*
- if((a->wordv[a->length_W-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_W-1]){
- // cli_putc('~');
- cli_putstr("\r\n ~ [a] = ");
- cli_hexdump_rev(&a->wordv[a->length_W-1], 4);
- cli_putstr(" [r] = ");
- cli_hexdump_rev(&r->wordv[r->length_W-1], 4);
- shift += 1;
- }
- */
-// cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
-// cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_W, 2);
-// cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_W, 2);
-// uart_flush(0);
- bigint_sub_u_bitscale(a, r, shift);
-// cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
- }
- while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){
- shift = GET_FBS(a)-rfbs-1;
-// cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
- bigint_sub_u_bitscale(a, r, shift);
-// cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
+
+ if (bigint_length_b(a) + 3 > bigint_length_b(r)) {
+ if ((r->length_W * sizeof(bigint_word_t) <= 4) && (a->length_W * sizeof(bigint_word_t) <= 4)) {
+ uint32_t p = 0, q = 0;
+ memcpy(&p, a->wordv, a->length_W * sizeof(bigint_word_t));
+ memcpy(&q, r->wordv, r->length_W * sizeof(bigint_word_t));
+ p %= q;
+ memcpy(a->wordv, &p, a->length_W * sizeof(bigint_word_t));
+ a->length_W = r->length_W;
+ bigint_adjust(a);
+ return;
+ }
+ unsigned shift;
+ while (a->length_W > r->length_W) {
+ shift = (a->length_W - r->length_W) * CHAR_BIT * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
+ bigint_sub_u_bitscale(a, r, shift);
+ }
+ while ((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)) {
+ shift = GET_FBS(a) - rfbs - 1;
+ bigint_sub_u_bitscale(a, r, shift);
+ }
}
- while(bigint_cmp_u(a,r)>=0){
- bigint_sub_u(a,a,r);
-// cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
+ while (bigint_cmp_u(a, r) >= 0) {
+ bigint_sub_u(a, a, r);
}
bigint_adjust(a);
-// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
-// cli_putstr("\r\n");
}
/******************************************************************************/
/* calculate dest = a**exp % r */
/* using square&multiply */
-void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
- if(a->length_W==0 || r->length_W==0){
+void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
+ if(a->length_W == 0){
+ bigint_set_zero(dest);
return;
}
bigint_t res, base;
- bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2];
- uint16_t i;
+ bigint_word_t t, base_w[MAX(a->length_W, r->length_W)], res_w[r->length_W * 2];
+ bigint_length_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;
+ res.wordv = res_w;
+ base.wordv = base_w;
bigint_copy(&base, a);
-// cli_putstr("\r\npost-copy");
bigint_reduce(&base, r);
- res.wordv[0]=1;
- res.length_W=1;
+ res.wordv[0] = 1;
+ res.length_W = 1;
res.info = 0;
bigint_adjust(&res);
if(exp->length_W == 0){
bigint_copy(dest, &res);
return;
}
+ bigint_copy(&res, &base);
uint8_t flag = 0;
- t=exp->wordv[exp->length_W - 1];
- for(i=exp->length_W; i > 0; --i){
+ t = exp->wordv[exp->length_W - 1];
+ for (i = exp->length_W; i > 0; --i) {
t = exp->wordv[i - 1];
- for(j=BIGINT_WORD_SIZE; j > 0; --j){
- if(!flag){
- if(t & (1<<(BIGINT_WORD_SIZE-1))){
+ for (j = BIGINT_WORD_SIZE; j > 0; --j) {
+ if (!flag) {
+ if (t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) {
flag = 1;
}
- }
- if(flag){
+ } else {
bigint_square(&res, &res);
bigint_reduce(&res, r);
- if(t & (1 << (BIGINT_WORD_SIZE - 1))){
+ if(t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))){
bigint_mul_u(&res, &res, &base);
bigint_reduce(&res, r);
}
}
}
-// cli_putc('+');
SET_POS(&res);
bigint_copy(dest, &res);
}
/******************************************************************************/
-#if 1
-#define cli_putstr(a)
-#define cli_putstr_P(a)
-#define bigint_print_hex(a)
-#define cli_hexdump_rev(a,b)
-#define uart_flush(a)
-#define printf_P(...)
-#endif
/* 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){
- uint16_t i = 0;
- printf_P(PSTR("\nDBG: gcdext( "));
- bigint_print_hex(x);
- printf_P(PSTR(", "));
- bigint_print_hex(y);
- printf_P(PSTR(")\n"));
+void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, const bigint_t *y){
+ bigint_length_t i = 0;
if(x->length_W == 0 || y->length_W == 0){
- printf_P(PSTR("\nDBG: got zero in gcd <%s %s %d>\n"), __FILE__, __func__, __LINE__);
if(gcd){
bigint_set_zero(gcd);
}
d_.info = 0;
bigint_set_zero(&b_);
bigint_set_zero(&c_);
- printf_P(PSTR("\nloop: x_ = "));
- bigint_print_hex(&x_);
- printf_P(PSTR("; y_ = "));
- bigint_print_hex(&y_);
- do{
- printf_P(PSTR("\nDBG (gcdext) 0"));
- while((u.wordv[0] & 1) == 0){
- printf_P(PSTR("\nDBG (gcdext) 0.1"));
+ 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_shiftright(&a_, 1);
bigint_shiftright(&b_, 1);
- printf_P(PSTR(" a_ = "));
- bigint_print_hex(&a_);
- printf_P(PSTR("; b_ = "));
- bigint_print_hex(&b_);
}
- while((v.wordv[0] & 1) == 0){
- printf_P(PSTR("\nDBG (gcdext) 0.2"));
- bigint_shiftright(&v, 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_);
}
- printf_P(PSTR(" c* = "));
- bigint_print_hex(&c_);
bigint_shiftright(&c_, 1);
bigint_shiftright(&d_, 1);
- printf_P(PSTR(" c_ = "));
- bigint_print_hex(&c_);
- printf_P(PSTR("; d_ = "));
- bigint_print_hex(&d_);
}
if(bigint_cmp_u(&u, &v) >= 0){
- printf_P(PSTR("\nDBG (gcdext) 0.3"));
bigint_sub_u(&u, &u, &v);
bigint_sub_s(&a_, &a_, &c_);
bigint_sub_s(&b_, &b_, &d_);
- printf_P(PSTR(" a_ = "));
- bigint_print_hex(&a_);
- printf_P(PSTR("; b_ = "));
- bigint_print_hex(&b_);
}else{
- printf_P(PSTR("\nDBG (gcdext) 0.4"));
bigint_sub_u(&v, &v, &u);
bigint_sub_s(&c_, &c_, &a_);
bigint_sub_s(&d_, &d_, &b_);
- printf_P(PSTR(" c_ = "));
- bigint_print_hex(&c_);
- printf_P(PSTR("; d_ = "));
- bigint_print_hex(&d_);
}
- }while(u.length_W);
+ } while(u.length_W);
if(gcd){
bigint_mul_s(gcd, &v, &g);
}
/******************************************************************************/
-void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* 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){
+void bigint_changeendianess(bigint_t *a){
uint8_t t, *p, *q;
p = (uint8_t*)(a->wordv);
q = p + a->length_W * sizeof(bigint_word_t) - 1;
/******************************************************************************/
+void bigint_mul_word_u(bigint_t *a, bigint_word_t b){
+ bigint_wordplus_t c0 = 0, c1 = 0;
+ bigint_length_t i;
+ if(b == 0){
+ bigint_set_zero(a);
+ return;
+ }
+ for(i = 0; i < a->length_W; ++i){
+ c1 = ((bigint_wordplus_t)(a->wordv[i])) * ((bigint_wordplus_t)b);
+ c1 += c0;
+ a->wordv[i] = (bigint_word_t)c1;
+ c0 = c1 >> BIGINT_WORD_SIZE;
+ }
+ if(c0){
+ a->wordv[a->length_W] = (bigint_word_t)c0;
+ a->length_W += 1;
+ }
+ bigint_adjust(a);
+}
+/******************************************************************************/
+#if 1
+void bigint_clip(bigint_t *dest, bigint_length_t length_W){
+ if(dest->length_W > length_W){
+ dest->length_W = length_W;
+ }
+ bigint_adjust(dest);
+}
+/******************************************************************************/
+/*
+ * m_ = m * m'[0]
+ * dest = (a * b) % m (?)
+ */
+
+void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_){
+ const bigint_length_t s = MAX(MAX(a->length_W, b->length_W), m->length_W);
+ bigint_t u, t;
+ bigint_word_t u_w[s + 2], t_w[s + 2];
+ bigint_length_t i;
+ if (a->length_W == 0 || b->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ u.wordv = u_w;
+ u.info = 0;
+ u.length_W = 0;
+ t.wordv = t_w;
+ for (i = 0; i < a->length_W; ++i) {
+ bigint_copy(&t, b);
+ bigint_mul_word_u(&t, a->wordv[i]);
+ bigint_add_u(&u, &u, &t);
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ for (; i < s; ++i) {
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+}
+
+/******************************************************************************/
+
+void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_){
+ bigint_t u, t;
+ bigint_length_t i, s = MAX(a->length_W, m->length_W);
+ bigint_word_t u_w[s + 2], t_w[s + 2];
+
+ t.wordv = t_w;
+ u.wordv = u_w;
+ if (a->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ bigint_copy(&u, a);
+ for (i = 0; i < m->length_W; ++i) {
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+}
+
+/******************************************************************************/
+/*
+ * m_ = m * (- m0^-1 (mod 2^W))
+ */
+void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m){
+ bigint_word_t x_w[2], m_w_0[1];
+ bigint_t x, m_0;
+#if 0
+ printf("\nm = ");
+ bigint_print_hex(m);
+ uart0_flush();
+#endif
+ if (m->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ if ((m->wordv[0] & 1) == 0) {
+ printf_P(PSTR("ERROR: m must not be even, m = "));
+ bigint_print_hex(m);
+ putchar('\n');
+ uart0_flush();
+ return;
+ }
+ x.wordv = x_w;
+ x.info = 0;
+ x.length_W = 2;
+ x_w[0] = 0;
+ x_w[1] = 1;
+ m_0.wordv = m_w_0;
+ m_0.info = 0;
+ m_0.length_W = 1;
+ m_0.wordv[0] = m->wordv[0];
+ bigint_adjust(&x);
+ bigint_adjust(&m_0);
+#if 0
+ printf("\nm0 = ");
+ bigint_print_hex(&m_0);
+ printf("\nx = ");
+ bigint_print_hex(&x);
+ uart0_flush();
+#endif
+ bigint_inverse(dest, &m_0, &x);
+#if 0
+ printf("\nm0^-1 = ");
+ bigint_print_hex(dest);
+ uart0_flush();
+#endif
+ bigint_sub_s(&x, &x, dest);
+#if 0
+ printf("\n-m0^-1 = ");
+ bigint_print_hex(&x);
+ uart0_flush();
+#endif
+ bigint_copy(dest, m);
+ bigint_mul_word_u(dest, x.wordv[0]);
+}
+
+/******************************************************************************/
+
+/*
+ * dest = a * R mod m
+ */
+void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m){
+ bigint_t t;
+ bigint_word_t t_w[a->length_W + m->length_W];
+
+ t.wordv = t_w;
+ memset(t_w, 0, m->length_W * sizeof(bigint_word_t));
+ memcpy(&t_w[m->length_W], a->wordv, a->length_W * sizeof(bigint_word_t));
+ t.info = a->info;
+ t.length_W = a->length_W + m->length_W;
+ bigint_reduce(&t, m);
+ bigint_copy(dest, &t);
+}
+
+/******************************************************************************/
+
+/* calculate dest = a**exp % r */
+/* using square&multiply */
+void bigint_expmod_u_mont_accel(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r, const bigint_t *m_){
+ if(r->length_W == 0) {
+ return;
+ }
+
+ bigint_length_t s = r->length_W;
+ bigint_t res, ax;
+ bigint_word_t t, res_w[r->length_W * 2], ax_w[MAX(s, a->length_W)];
+ bigint_length_t i;
+ uint8_t j;
+
+ res.wordv = res_w;
+ ax.wordv = ax_w;
+
+ res.wordv[0] = 1;
+ res.length_W = 1;
+ res.info = 0;
+ bigint_adjust(&res);
+ if (exp->length_W == 0) {
+ bigint_copy(dest, &res);
+ return;
+ }
+ bigint_copy(&ax, a);
+ bigint_reduce(&ax, r);
+ bigint_mont_trans(&ax, &ax, r);
+ bigint_mont_trans(&res, &res, r);
+ uint8_t flag = 0;
+ t = exp->wordv[exp->length_W - 1];
+ for (i = exp->length_W; i > 0; --i) {
+ t = exp->wordv[i - 1];
+ for(j = BIGINT_WORD_SIZE; j > 0; --j){
+ if (!flag) {
+ if(t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))){
+ flag = 1;
+ }
+ }
+ if (flag) {
+ bigint_square(&res, &res);
+ bigint_mont_red(&res, &res, r, m_);
+ if (t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))) {
+ bigint_mont_mul(&res, &res, &ax, r, m_);
+ }
+ }
+ t <<= 1;
+ }
+ }
+ SET_POS(&res);
+ bigint_mont_red(dest, &res, r, m_);
+}
+
+/******************************************************************************/
+
+void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
+ if(r->length_W == 0) {
+ return;
+ }
+ if(a->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ bigint_t m_;
+ bigint_word_t m_w_[r->length_W + 1];
+ m_.wordv = m_w_;
+ bigint_mont_gen_m_(&m_, r);
+ bigint_expmod_u_mont_accel(dest, a, exp, r,&m_);
+}
+
+/******************************************************************************/
+
+#endif
+
+void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
+ if (r->wordv[0] & 1) {
+ bigint_expmod_u_mont_sam(dest, a, exp, r);
+ } else {
+ bigint_expmod_u_sam(dest, a, exp, r);
+ }
+}
projects / avr-crypto-lib.git / blobdiff