/* bigint.c */
/*
- This file is part of the AVR-Crypto-Lib.
- Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de)
+ This file is part of the ARM-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
#include "bigint.h"
#include <string.h>
-/*
+#include <stdio.h>
+
+#define PREFERE_HEAP_SPACE 1
+
+#if PREFERE_HEAP_SPACE
+#include <stdlib.h>
+
+#define ALLOC_BIGINT_WORDS(var,words) \
+ bigint_word_t *(var) = malloc((words) * sizeof(bigint_word_t)); \
+ if (!(var)) { \
+ puts_P(PSTR("\n\nDBG: OOM ERROR (in arithmeics)!\n")); \
+ uart0_flush(); \
+ for(;;) \
+ ; \
+ }
+
+#define FREE(x) free(x)
+
+#else
+
+#define ALLOC_BIGINT_WORDS(var,words) bigint_word_t var[words]
+#define FREE(x)
+
+#endif
+
+#define DEBUG 1
+
+#if DEBUG
#include "cli.h"
+#include "uart_i.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))
+ #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_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*)(((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 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)
+#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--;
+void bigint_adjust(bigint_t *a){
+ while (a->length_W != 0 && a->wordv[a->length_W - 1] == 0) {
+ a->length_W--;
}
- if(a->length_B==0){
+ if (a->length_W == 0) {
a->info=0;
return;
}
- uint8_t t;
- uint8_t i = 0x07;
- t = a->wordv[a->length_B-1];
- while((t&0x80)==0 && i){
- t<<=1;
+ bigint_word_t t;
+ 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);
/******************************************************************************/
-void bigint_copy(bigint_t* dest, const bigint_t* src){
- memcpy(dest->wordv, src->wordv, src->length_B);
- dest->length_B = src->length_B;
+bigint_length_t bigint_length_b(const bigint_t *a){
+ if(!a->length_W || a->length_W==0){
+ return 0;
+ }
+ return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a);
+}
+
+/******************************************************************************/
+
+bigint_length_t bigint_length_B(const bigint_t *a){
+ return a->length_W * sizeof(bigint_word_t);
+}
+
+/******************************************************************************/
+
+int32_t bigint_get_first_set_bit(const bigint_t *a){
+ if(a->length_W == 0) {
+ return -1;
+ }
+ return (a->length_W-1) * sizeof(bigint_word_t) * CHAR_BIT + GET_FBS(a);
+}
+
+
+/******************************************************************************/
+
+int32_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_W == 0) {
+ return -1;
+ }
+ while (a->wordv[r] == 0 && r < a->length_W) {
+ ++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){
+ if(dest->wordv != src->wordv){
+ memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t));
+ }
+ 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_B < b->length_B){
- XCHG_PTR(a,b);
- }
- for(i=0; i<b->length_B; ++i){
- t = a->wordv[i] + b->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- for(; i<a->length_B; ++i){
- t = a->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- }
- dest->wordv[i++] = t;
- dest->length_B = i;
+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);
+ }
+ 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){
+ 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_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){
- uint16_t i,j=0;
- uint16_t t=0;
- if(scale>dest->length_B)
- memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
- for(i=scale; i<a->length_B+scale; ++i,++j){
- t = a->wordv[j] + t;
- if(dest->length_B>i){
- t += dest->wordv[i];
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){
+ if(a->length_W == 0){
+ return;
}
- while(t){
- if(dest->length_B>i){
- t = dest->wordv[i] + t;
- }
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
- ++i;
+ if(scale == 0){
+ bigint_add_u(dest, dest, a);
+ return;
}
- if(dest->length_B < i){
- dest->length_B = i;
+ bigint_t x;
+#if BIGINT_WORD_SIZE == 8
+ memset(dest->wordv + dest->length_W, 0, MAX(dest->length_W, a->length_W + scale) - dest->length_W);
+ x.wordv = dest->wordv + scale;
+ x.length_W = dest->length_W - scale;
+ if((int16_t)x.length_W < 0){
+ x.length_W = 0;
+ x.info = 0;
+ } else {
+ x.info = dest->info;
}
+ bigint_add_u(&x, &x, a);
+ dest->length_W = x.length_W + scale;
+ dest->info = 0;
bigint_adjust(dest);
+#else
+ bigint_t s;
+ 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;
+ memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_W * sizeof(bigint_word_t));
+ s.length_W = a->length_W + 1;
+ bigint_adjust(&s);
+ memset(dest->wordv + dest->length_W, 0, (MAX(dest->length_W, s.length_W + word_shift) - dest->length_W) * sizeof(bigint_word_t));
+ x.wordv = dest->wordv + word_shift;
+ x.length_W = dest->length_W - word_shift;
+ if((int16_t)x.length_W < 0){
+ x.length_W = 0;
+ x.info = 0;
+ }else{
+ x.info = dest->info;
+ }
+ bigint_add_u(&x, &x, &s);
+ dest->length_W = x.length_W + word_shift;
+ dest->info = 0;
+ bigint_adjust(dest);
+#endif
}
/******************************************************************************/
/* 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;
- int16_t t;
- uint16_t i, min, max;
- min = MIN(a->length_B, b->length_B);
- max = MAX(a->length_B, b->length_B);
- r = bigint_cmp_u(a,b);
- if(r==0){
- dest->length_B = 0;
- dest->wordv[0] = 0;
- bigint_adjust(dest);
- return;
- }
- if(b->length_B==0){
- dest->length_B = a->length_B;
- memcpy(dest->wordv, a->wordv, a->length_B);
- dest->info = a->info;
+ bigint_wordplus_signed_t t = 0;
+ bigint_length_t i;
+ if(b->length_W == 0){
+ bigint_copy(dest, a);
SET_POS(dest);
return;
}
- if(a->length_B==0){
- dest->length_B = b->length_B;
- memcpy(dest->wordv, b->wordv, b->length_B);
- dest->info = b->info;
- SET_NEG(dest);
- return;
+ if(a->length_W == 0){
+ bigint_copy(dest, b);
+ SET_NEG(dest);
+ return;
}
- if(r<0){
+ r = bigint_cmp_u(a,b);
+ if(r == 0){
+ bigint_set_zero(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;
- }
-
+ return;
+ }
+ for(i = 0; i < a->length_W; ++i){
+ t = a->wordv[i];
+ if(i < b->length_W){
+ t -= b->wordv[i];
}
- SET_POS(dest);
- dest->length_B = i;
- bigint_adjust(dest);
+ t -= borrow;
+ dest->wordv[i] = (bigint_word_t)t;
+ borrow = t < 0 ? 1 : 0;
}
+ 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_B > b->length_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_B < b->length_B){
+ if(a->length_W < b->length_W){
return -1;
}
- if(a->length_B==0){
+ if(a->length_W == 0){
return 0;
}
- uint16_t i;
- i = a->length_B-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]){
+ if(a->wordv[i] != b->wordv[i]){
+ if(a->wordv[i] > b->wordv[i]){
return 1;
}else{
return -1;
/******************************************************************************/
-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_B==0 && b->length_B==0){
+ if(a->length_W==0 && b->length_W==0){
return 0;
}
s = GET_SIGN(a)?2:0;
/******************************************************************************/
-void bigint_shiftleft(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
- uint8_t bitshift;
- uint16_t t=0;
- byteshift = (shift+3)/8;
- bitshift = shift&7;
- memmove(a->wordv+byteshift, a->wordv, a->length_B);
- memset(a->wordv, 0, byteshift);
- if(bitshift!=0){
- if(bitshift<=4){ /* shift to the left */
- for(i=byteshift; i<a->length_B+byteshift; ++i){
- t |= (a->wordv[i])<<bitshift;
- a->wordv[i] = (uint8_t)t;
- t >>= 8;
- }
- a->wordv[i] = (uint8_t)t;
- byteshift++;
- }else{ /* shift to the right */
- for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
- t |= (a->wordv[i])<<(bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- t <<= 8;
- }
- t |= (a->wordv[i])<<(bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- }
- }
- a->length_B += byteshift;
- bigint_adjust(a);
+void bigint_shiftleft_bits(bigint_t *a, uint8_t shift) {
+ bigint_length_t i;
+ bigint_wordplus_t t = 0;
+
+ for (i = 0; i < a->length_W; ++i) {
+ t |= ((bigint_wordplus_t)a->wordv[i]) << shift;
+ a->wordv[i] = (bigint_word_t)t;
+ t >>= BIGINT_WORD_SIZE;
+ }
+ if (t) {
+ a->wordv[a->length_W++] = (bigint_word_t)t;
+ }
+ bigint_adjust(a);
}
/******************************************************************************/
-void bigint_shiftright(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
+void bigint_shiftleft(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift;
uint8_t bitshift;
- uint16_t t=0;
- byteshift = shift/8;
- bitshift = shift&7;
- if(byteshift >= a->length_B){ /* we would shift out more than we have */
- bigint_set_zero(a);
+
+ if (a->length_W == 0 || shift == 0) {
return;
}
- if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
+ byteshift = shift / 8;
+ bitshift = shift & 7;
+ 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);
+ a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
+ }
+
+ if (bitshift == 0) {
+ bigint_adjust(a);
+ } else {
+ bigint_shiftleft_bits(a, bitshift);
+ }
+}
+
+/******************************************************************************/
+
+void bigint_shiftright_bits(bigint_t *a, uint8_t shift){
+ bigint_length_t i;
+ bigint_wordplus_t t = 0;
+
+ i = a->length_W;
+ while (i--) {
+ t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - shift);
+ a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE);
+ t <<= BIGINT_WORD_SIZE;
+ }
+
+ bigint_adjust(a);
+}
+
+/******************************************************************************/
+
+void bigint_shiftright_1bit(bigint_t *a){
+ bigint_length_t i;
+ bigint_word_t t1 = 0, t2;
+
+ i = a->length_W;
+ while (i--) {
+ t2 = a->wordv[i] & 1;
+ a->wordv[i] >>= 1;
+ a->wordv[i] |= t1;
+ t1 = t2 << (BIGINT_WORD_SIZE - 1);
+ }
+ bigint_adjust(a);
+}
+
+/******************************************************************************/
+
+void bigint_shiftright_1word(bigint_t *a){
+ if (a->length_W == 0) {
+ return;
+ }
+ memmove(a->wordv, &a->wordv[1], (a->length_W - 1) * sizeof(bigint_word_t));
+ a->length_W--;
+}
+
+/******************************************************************************/
+
+void bigint_shiftright(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift = shift / 8;
+ uint8_t bitshift = shift & 7;
+
+ if (a->length_W == 0) {
+ return;
+ }
+
+ 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, a->wordv+byteshift, a->length_B-byteshift);
- memset(a->wordv+a->length_B-byteshift, 0, byteshift);
- }
- if(bitshift!=0){
- /* shift to the right */
- for(i=a->length_B-byteshift-1; i>0; --i){
- t |= (a->wordv[i])<<(8-bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- t <<= 8;
- }
- t |= (a->wordv[0])<<(8-bitshift);
- a->wordv[0] = (uint8_t)(t>>8);
+ 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);
+ a->length_W -= byteshift / sizeof(bigint_word_t);
+ bigint_adjust(a);
+ }
+
+ if(bitshift != 0){
+ bigint_shiftright_bits(a, bitshift);
}
- a->length_B -= byteshift;
- bigint_adjust(a);
}
/******************************************************************************/
-void bigint_xor(bigint_t* dest, const bigint_t* a){
- uint16_t i;
- for(i=0; i<a->length_B; ++i){
+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];
}
bigint_adjust(dest);
/******************************************************************************/
-void bigint_set_zero(bigint_t* a){
- a->length_B=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_B==0 || b->length_B==0){
+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){
+ if (dest == a || dest == b) {
bigint_t d;
- uint8_t d_b[a->length_B+b->length_B];
+ bigint_word_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_B==1 || b->length_B==1){
- if(a->length_B!=1){
+ 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_B; ++i){
- t += b->wordv[i]*x;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+ bigint_wordplus_t t = 0;
+ 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);
+ dest->wordv[i] = (bigint_word_t)t;
+ t >>= BIGINT_WORD_SIZE;
+ }
+ dest->length_W = i;
+ if (t) {
+ dest->wordv[i] = (bigint_word_t)t;
+ dest->length_W += 1;
}
- dest->wordv[i] = (uint8_t)t;
- dest->length_B=i+1;
+ dest->info = 0;
bigint_adjust(dest);
return;
}
- if(a->length_B<=4 && b->length_B<=4){
- uint32_t p=0, q=0;
+ if (a->length_W * sizeof(bigint_word_t) <= 4 && b->length_W * sizeof(bigint_word_t) <= 4) {
+ uint32_t p = 0, q = 0;
uint64_t r;
- memcpy(&p, a->wordv, a->length_B);
- memcpy(&q, b->wordv, b->length_B);
- r = (uint64_t)p*(uint64_t)q;
- memcpy(dest->wordv, &r, a->length_B+b->length_B);
- dest->length_B = a->length_B+b->length_B;
+ memcpy(&p, a->wordv, a->length_W * sizeof(bigint_word_t));
+ memcpy(&q, b->wordv, b->length_W * sizeof(bigint_word_t));
+ r = (uint64_t)p * (uint64_t)q;
+ memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W) * sizeof(bigint_word_t));
bigint_adjust(dest);
return;
}
- bigint_set_zero(dest);
/* split a in xh & xl; split b in yh & yl */
- uint16_t n;
- n=(MAX(a->length_B, b->length_B)+1)/2;
+ 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;
- if(a->length_B<=n){
- xh.info=0;
- xh.length_B = 0;
- xl.length_B = a->length_B;
- xl.info = 0;
- }else{
- xl.length_B=n;
+ if (a->length_W <= n) {
+ bigint_set_zero(&xh);
+ xl.length_W = a->length_W;
+ xl.info = a->info;
+ } else {
+ xl.length_W = n;
xl.info = 0;
bigint_adjust(&xl);
- xh.wordv = a->wordv+n;
- xh.length_B = a->length_B-n;
- xh.info = 0;
- }
- if(b->length_B<=n){
- yh.info=0;
- yh.length_B = 0;
- yl.length_B = b->length_B;
+ xh.wordv = &(a->wordv[n]);
+ xh.length_W = a->length_W-n;
+ xh.info = a->info;
+ }
+ if (b->length_W <= n) {
+ bigint_set_zero(&yh);
+ yl.length_W = b->length_W;
yl.info = b->info;
- }else{
- yl.length_B=n;
+ } else {
+ yl.length_W = n;
yl.info = 0;
bigint_adjust(&yl);
- yh.wordv = b->wordv+n;
- yh.length_B = b->length_B-n;
- yh.info = 0;
+ yh.wordv = &(b->wordv[n]);
+ yh.length_W = b->length_W-n;
+ yh.info = b->info;
}
/* now we have split up a and b */
- uint8_t tmp_b[2*n+2], m_b[2*(n+1)];
+ /* remember we want to do:
+ * x*y = (xh * b**n + xl) * (yh * b**n + yl)
+ * = (xh * yh) * b**2n + xh * b**n * yl + yh * b**n * xl + xl * yl
+ * = (xh * yh) * b**2n + (xh * yl + yh * xl) * b**n + xl *yl
+ * // xh * yl + yh * xl = (xh + yh) * (xl + yl) - xh * yh - xl * yl
+ * x*y = (xh * yh) * b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + xl*yl
+ * 5 9 2 4 3 7 5 6 1 8 1
+ */
+ ALLOC_BIGINT_WORDS(tmp_w, 2 * n + 2);
+ ALLOC_BIGINT_WORDS(m_w, 2 * n + 2);
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);
+ tmp.wordv = tmp_w;
+ tmp2.wordv = &(tmp_w[n + 1]);
+ m.wordv = m_w;
+
+ 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: tmp <= xh*yh */
+ bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */
+ bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-tmp */
+ 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) */
+ FREE(m_w);
+ FREE(tmp_w);
}
/******************************************************************************/
-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;
/******************************************************************************/
-/* square */
-/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
-void bigint_square(bigint_t* dest, const bigint_t* a){
- if(a->length_B<=4){
- uint64_t r=0;
- memcpy(&r, a->wordv, a->length_B);
- r = r*r;
- memcpy(dest->wordv, &r, 2*a->length_B);
- SET_POS(dest);
- dest->length_B=2*a->length_B;
- bigint_adjust(dest);
- return;
- }
- if(dest==a){
- bigint_t d;
- uint8_t d_b[a->length_B*2];
- d.wordv = d_b;
- bigint_square(&d, a);
- bigint_copy(dest, &d);
- return;
- }
- uint16_t n;
- n=(a->length_B+1)/2;
- bigint_t xh, xl, tmp; /* x-high, x-low, temp */
- uint8_t buffer[2*n+1];
- xl.wordv = a->wordv;
- xl.length_B = n;
- xh.wordv = a->wordv+n;
- xh.length_B = a->length_B-n;
- tmp.wordv = buffer;
- bigint_square(dest, &xl);
- bigint_square(&tmp, &xh);
- bigint_add_scale_u(dest, &tmp, 2*n);
- bigint_mul_u(&tmp, &xl, &xh);
- bigint_shiftleft(&tmp, 1);
- bigint_add_scale_u(dest, &tmp, n);
+void bigint_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;
+ ALLOC_BIGINT_WORDS(d_w, a->length_W * 2);
+ d.wordv = d_w;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ FREE(d_w);
+ 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, uint16_t bitscale){
- bigint_t tmp;
- uint8_t tmp_b[b->length_B+1];
- uint16_t i,j,byteshift=bitscale/8;
- uint8_t borrow=0;
- int16_t t;
+void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){
+ bigint_t tmp, x;
+ const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE;
- if(a->length_B < b->length_B+byteshift){
+ if (a->length_W < b->length_W + word_shift) {
+#if DEBUG
+ cli_putstr("\r\nDBG: *bang*\r\n");
+#endif
bigint_set_zero(a);
return;
}
-
- tmp.wordv = tmp_b;
+ ALLOC_BIGINT_WORDS(tmp_w, b->length_W + 1);
+ tmp.wordv = tmp_w;
bigint_copy(&tmp, b);
- bigint_shiftleft(&tmp, bitscale&7);
-
- for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
- t = a->wordv[i] - tmp.wordv[j] - borrow;
- a->wordv[i] = (uint8_t)t;
- if(t<0){
- borrow = 1;
- }else{
- borrow = 0;
- }
- }
- while(borrow){
- if(i+1 > a->length_B){
- bigint_set_zero(a);
- return;
- }
- a->wordv[i] -= borrow;
- if(a->wordv[i]!=0xff){
- borrow=0;
- }
- ++i;
- }
+ bigint_shiftleft_bits(&tmp, bitscale % BIGINT_WORD_SIZE);
+
+ x.info = a->info;
+ x.wordv = &(a->wordv[word_shift]);
+ x.length_W = a->length_W - word_shift;
+
+ bigint_sub_u(&x, &x, &tmp);
+ FREE(tmp_w);
bigint_adjust(a);
+ return;
}
/******************************************************************************/
-void bigint_reduce(bigint_t* a, const bigint_t* r){
-// bigint_adjust(r);
+void bigint_reduce(bigint_t *a, const bigint_t *r){
uint8_t rfbs = GET_FBS(r);
-
- if(r->length_B==0 || a->length_B==0){
+ if (r->length_W == 0 || a->length_W == 0) {
return;
}
- while(a->length_B > r->length_B){
- bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
- }
- while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
- bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
+
+ 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);
+ while (bigint_cmp_u(a, r) >= 0) {
+ bigint_sub_u(a, a, r);
}
bigint_adjust(a);
}
/* calculate dest = a**exp % r */
/* using square&multiply */
-void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
- if(a->length_B==0 || r->length_B==0){
+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;
- uint8_t base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*2];
- uint16_t i;
- uint8_t j, t;
- res.wordv = res_b;
- base.wordv = base_b;
+ if(exp->length_W == 0){
+ dest->info = 0;
+ dest->length_W = 1;
+ dest->wordv[0] = 1;
+ return;
+ }
+
+ bigint_t res, base;
+ bigint_word_t t;
+ bigint_length_t i;
+ uint8_t j;
+
+ ALLOC_BIGINT_WORDS(base_w, MAX(a->length_W, r->length_W));
+ ALLOC_BIGINT_WORDS(res_w, r->length_W * 2);
+
+ res.wordv = res_w;
+ base.wordv = base_w;
bigint_copy(&base, a);
bigint_reduce(&base, r);
- res.wordv[0]=1;
- res.length_B=1;
+ res.wordv[0] = 1;
+ res.length_W = 1;
res.info = 0;
bigint_adjust(&res);
- for(i=0; i+1<exp->length_B; ++i){
- t=exp->wordv[i];
- for(j=0; j<8; ++j){
- if(t&1){
- bigint_mul_u(&res, &res, &base);
+ bigint_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[i - 1];
+ for (j = BIGINT_WORD_SIZE; j > 0; --j) {
+ if (!flag) {
+ if (t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) {
+ flag = 1;
+ }
+ } else {
+ bigint_square(&res, &res);
bigint_reduce(&res, r);
+ if(t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 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);
+ t <<= 1;
}
- bigint_square(&base, &base);
- bigint_reduce(&base, r);
- t>>=1;
}
+
SET_POS(&res);
bigint_copy(dest, &res);
+ FREE(res_w);
+ FREE(base_w);
}
/******************************************************************************/
/* gcd <-- gcd(x,y) a*x+b*y=gcd */
-void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
- bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
- volatile uint16_t i=0;
- if(x->length_B==0 || y->length_B==0){
+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){
+ if(gcd){
+ bigint_set_zero(gcd);
+ }
+ if(a){
+ bigint_set_zero(a);
+ }
+ if(b){
+ bigint_set_zero(b);
+ }
+ return;
+ }
+ if(x->length_W == 1 && x->wordv[0] == 1){
+ if(gcd){
+ gcd->length_W = 1;
+ gcd->wordv[0] = 1;
+ gcd->info = 0;
+ }
+ if(a){
+ a->length_W = 1;
+ a->wordv[0] = 1;
+ SET_POS(a);
+ bigint_adjust(a);
+ }
+ if(b){
+ bigint_set_zero(b);
+ }
return;
}
- while(x->wordv[i]==0 && y->wordv[i]==0){
+ if(y->length_W == 1 && y->wordv[0] == 1){
+ if(gcd){
+ gcd->length_W = 1;
+ gcd->wordv[0] = 1;
+ gcd->info = 0;
+ }
+ if(b){
+ b->length_W = 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;
}
- uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
- uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
- uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
- uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
-
- g.wordv = g_b;
- x_.wordv = x_b;
- y_.wordv = y_b;
- memset(g_b, 0, i);
- g_b[i]=1;
- g.length_B = i+1;
- g.info=0;
+
+ ALLOC_BIGINT_WORDS(g_w, i + 2);
+ ALLOC_BIGINT_WORDS(x_w, x->length_W - i);
+ ALLOC_BIGINT_WORDS(y_w, y->length_W - i);
+ ALLOC_BIGINT_WORDS(u_w, x->length_W - i);
+ ALLOC_BIGINT_WORDS(v_w, y->length_W - i);
+ ALLOC_BIGINT_WORDS(a_w, y->length_W + 2);
+ ALLOC_BIGINT_WORDS(c_w, y->length_W + 2);
+ ALLOC_BIGINT_WORDS(b_w, x->length_W + 2);
+ ALLOC_BIGINT_WORDS(d_w, x->length_W + 2);
+
+ bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
+
+ g.wordv = g_w;
+ x_.wordv = x_w;
+ y_.wordv = y_w;
+ memset(g_w, 0, i * sizeof(bigint_word_t));
+ g_w[i] = 1;
+ g.length_W = i + 1;
+ g.info = 0;
x_.info = y_.info = 0;
- x_.length_B = x->length_B-i;
- y_.length_B = y->length_B-i;
- memcpy(x_.wordv, x->wordv+i, x_.length_B);
- memcpy(y_.wordv, y->wordv+i, y_.length_B);
- for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
- }
+ x_.length_W = x->length_W - i;
+ y_.length_W = y->length_W - i;
+ memcpy(x_.wordv, x->wordv + i, x_.length_W * sizeof(bigint_word_t));
+ memcpy(y_.wordv, y->wordv + i, y_.length_W * sizeof(bigint_word_t));
+
+ for(i = 0; (x_.wordv[0] & ((bigint_word_t)1 << i)) == 0 && (y_.wordv[0] & ((bigint_word_t)1 << i)) == 0; ++i)
+ ;
bigint_adjust(&x_);
bigint_adjust(&y_);
if(i){
- bigint_shiftleft(&g, i);
- bigint_shiftright(&x_, i);
- bigint_shiftright(&y_, i);
+ bigint_shiftleft_bits(&g, i);
+ bigint_shiftright_bits(&x_, i);
+ bigint_shiftright_bits(&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;
+
+ u.wordv = u_w;
+ v.wordv = v_w;
+ a_.wordv = a_w;
+ b_.wordv = b_w;
+ c_.wordv = c_w;
+ d_.wordv = d_w;
bigint_copy(&u, &x_);
bigint_copy(&v, &y_);
a_.wordv[0] = 1;
- a_.length_B = 1;
+ a_.length_W = 1;
a_.info = 0;
d_.wordv[0] = 1;
- d_.length_B = 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)){
+ do {
+ while ((u.wordv[0] & 1) == 0) {
+ bigint_shiftright_1bit(&u);
+ 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);
+ bigint_shiftright_1bit(&a_);
+ bigint_shiftright_1bit(&b_);
}
- while((v.wordv[0]&1)==0){
- bigint_shiftright(&v, 1);
- if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
+ while ((v.wordv[0] & 1) == 0) {
+ bigint_shiftright_1bit(&v);
+ 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);
-
+ bigint_shiftright_1bit(&c_);
+ bigint_shiftright_1bit(&d_);
}
- if(bigint_cmp_u(&u, &v)>=0){
+ 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_);
bigint_sub_s(&c_, &c_, &a_);
bigint_sub_s(&d_, &d_, &b_);
}
- }while(u.length_B);
+ } while(u.length_W);
if(gcd){
bigint_mul_s(gcd, &v, &g);
}
if(b){
bigint_copy(b, &d_);
}
+
+ FREE(d_w);
+ FREE(b_w);
+ FREE(c_w);
+ FREE(a_w);
+ FREE(v_w);
+ FREE(u_w);
+ FREE(y_w);
+ FREE(x_w);
+ FREE(g_w);
}
/******************************************************************************/
-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 = a->wordv;
- q = p+a->length_B-1;
- while(p<q){
+ p = (uint8_t*)a->wordv;
+ q = p + a->length_W * sizeof(bigint_word_t) - 1;
+ while(p < q){
t = *p;
*p = *q;
*q = t;
/******************************************************************************/
+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);
+}
+/******************************************************************************/
+
+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_length_t i;
+
+ if (a->length_W == 0 || b->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ ALLOC_BIGINT_WORDS(u_w, s + 2);
+ ALLOC_BIGINT_WORDS(t_w, s + 2);
+ 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_1word(&u);
+ }
+ 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_1word(&u);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+ FREE(t_w);
+ FREE(u_w);
+}
+/******************************************************************************/
+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, MAX(m->length_W, m_->length_W));
+
+ if (a->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+
+ ALLOC_BIGINT_WORDS(u_w, s + 2);
+ ALLOC_BIGINT_WORDS(t_w, s + 2);
+ t.wordv = t_w;
+ u.wordv = u_w;
+ 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_1word(&u);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+ FREE(t_w);
+ FREE(u_w);
+}
+/******************************************************************************/
+/*
+ * 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 (m->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ if ((m->wordv[0] & 1) == 0) {
+#if DEBUG
+ printf_P(PSTR("ERROR: m must not be even, m = "));
+ bigint_print_hex(m);
+ putchar('\n');
+ uart0_flush();
+#endif
+ 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);
+ bigint_inverse(dest, &m_0, &x);
+ bigint_sub_s(&x, &x, dest);
+ 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;
+
+ ALLOC_BIGINT_WORDS(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);
+ FREE(t_w);
+}
+
+/******************************************************************************/
+
+/* 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_t res, ax;
+ bigint_word_t t;
+ bigint_length_t i;
+ uint8_t j;
+
+ if (exp->length_W == 0) {
+ dest->length_W = 1;
+ dest->info = 0;
+ dest->wordv[0] = 1;
+ return;
+ }
+
+ ALLOC_BIGINT_WORDS(res_w, r->length_W * 2);
+ ALLOC_BIGINT_WORDS(ax_w, MAX(r->length_W, a->length_W));
+
+ res.wordv = res_w;
+ ax.wordv = ax_w;
+
+ res.wordv[0] = 1;
+ res.length_W = 1;
+ res.info = 0;
+
+ 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_word_t)1) << (BIGINT_WORD_SIZE - 1))){
+ flag = 1;
+ }
+ }
+ if (flag) {
+ bigint_square(&res, &res);
+ bigint_mont_red(&res, &res, r, m_);
+ if (t & (((bigint_word_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_);
+ FREE(ax_w);
+ FREE(res_w);
+}
+
+/******************************************************************************/
+
+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_);
+}
+
+/******************************************************************************/
+
+void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
+#if 0
+ printf("\nDBG: expmod_u (a ** e %% m) <%s %s %d>\n\ta: ", __FILE__, __func__, __LINE__);
+ bigint_print_hex(a);
+ printf("\n\te: ");
+ bigint_print_hex(exp);
+ printf("\n\tm: ");
+ bigint_print_hex(r);
+#endif
+ 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