/* bigint.c */
/*
- This file is part of the AVR-Crypto-Lib.
+ 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
#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
#define MIN(a,b) (((a)<(b))?(a):(b))
#endif
-#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
+#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_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--;
+ 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){
+ 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;
i--;
}
/******************************************************************************/
+uint16_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);
+}
+
+/******************************************************************************/
+
+uint16_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){
+ return (uint32_t)(-1);
+ }
+ return (a->length_W-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_W==0){
+ return (uint32_t)(-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){
- memcpy(dest->wordv, src->wordv, src->length_B);
- dest->length_B = src->length_B;
+ 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){
+ uint16_t i;
+ bigint_wordplus_t t = 0LL;
+ if(a->length_W < b->length_W){
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 = 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;
}
- for(; i<a->length_B; ++i){
- t = a->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+ if(t){
+ dest->wordv[i++] = (bigint_word_t)t;
}
- dest->wordv[i++] = t;
- dest->length_B = i;
+ 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_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];
+ if(a->length_W == 0){
+ return;
+ }
+ if(scale == 0){
+ bigint_add_u(dest, dest, a);
+ return;
+ }
+#if DEBUG_ADD_SCALE
+ cli_putstr_P(PSTR("\r\nDBG: bigint_add_scale("));
+ bigint_print_hex(dest);
+ cli_putc(',');
+ bigint_print_hex(dest);
+ cli_putc(',');
+ cli_hexdump_rev(&scale, 2);
+ cli_putc(')');
+#endif
+#if BIGINT_WORD_SIZE == 8
+ if(scale >= dest->length_W){
+#if DEBUG_ADD_SCALE
+ cli_putstr_P(PSTR("\r\n\tpath one"));
+#endif
+ memset(dest->wordv + dest->length_W, 0, scale - dest->length_W);
+ memcpy(dest->wordv + scale, a->wordv, a->length_W);
+ dest->info = a->info;
+ dest->length_W = a->length_W + scale;
+ return;
+ }
+ bigint_t x;
+#if DEBUG_ADD_SCALE
+ cli_putstr_P(PSTR("\r\n\tpath two"));
+#endif
+ x.length_W = dest->length_W - scale;
+ x.info = dest->info;
+ x.wordv = dest->wordv + scale;
+ bigint_add_u(&x, &x, a);
+ dest->length_W = x.length_W + 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_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
+
+
+/* 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_W*sizeof(bigint_word_t)){
+ memset(((uint8_t*)dest->wordv)+dest->length_W*sizeof(bigint_word_t), 0, scale-dest->length_W*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_W+scale_w; ++i,++j){
+ t += a->wordv[j];
+ if(dest->length_W>i){
+ t += dst[i];
}
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+ dst[i] = (bigint_word_t)t;
+ t>>=BIGINT_WORD_SIZE;
}
while(t){
- if(dest->length_B>i){
- t = dest->wordv[i] + t;
+ if(dest->length_W>i){
+ t += dst[i];
}
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+ dst[i] = (bigint_word_t)t;
+ t>>=BIGINT_WORD_SIZE;
++i;
}
- if(dest->length_B < i){
- dest->length_B = i;
+ if(dest->length_W < i){
+ dest->length_W = i;
}
bigint_adjust(dest);
+ */
}
/******************************************************************************/
void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
int8_t borrow=0;
int8_t r;
- int16_t t;
- uint16_t i, min, max;
- min = MIN(a->length_B, b->length_B);
- max = MAX(a->length_B, b->length_B);
+ bigint_wordplus_signed_t t=0LL;
+ uint16_t i;
r = bigint_cmp_u(a,b);
if(r==0){
- dest->length_B = 0;
- dest->wordv[0] = 0;
- bigint_adjust(dest);
+ bigint_set_zero(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;
+ 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){
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;
- }
+ return;
+ }
+ for(i=0; i < a->length_W; ++i){
+ t = a->wordv[i];
+ if(i < b->length_W){
+ t -= b->wordv[i];
}
- 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;
- }
-
+ 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);
}
+ 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){
+ 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;
+ 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;
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;
+ uint16_t byteshift, words_to_shift;
+ int16_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);
+ bigint_word_t *p;
+ bigint_wordplus_t t=0;
+ if(shift == 0){
+ return;
+ }
+ byteshift = shift / 8;
+ bitshift = shift & 7;
+ memset(&a->wordv[a->length_W], 0x00, byteshift);
+ 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){
+ p = (bigint_word_t*)((uint8_t*)a->wordv + byteshift / sizeof(bigint_word_t));
+ words_to_shift = a->length_W + ((byteshift % sizeof(bigint_word_t))?1:0);
+ /* XXX */
+ 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 += byteshift;
+ a->length_W += (shift + BIGINT_WORD_SIZE - 1) / BIGINT_WORD_SIZE;
bigint_adjust(a);
}
uint16_t byteshift;
uint16_t i;
uint8_t bitshift;
- uint16_t t=0;
+ bigint_wordplus_t t=0;
byteshift = shift/8;
bitshift = shift&7;
- if(byteshift >= a->length_B){ /* we would shift out more than we have */
+ 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_B-1 && bitshift>GET_FBS(a)){
+ if(byteshift == a->length_W * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){
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);
+ memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift);
+ memset((uint8_t*)a->wordv + a->length_W * sizeof(bigint_word_t) - byteshift, 0, byteshift);
}
- if(bitshift!=0){
+ byteshift /= sizeof(bigint_word_t);
+ a->length_W -= (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
+ if(bitshift != 0 && a->length_W){
/* 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);
+ i = a->length_W - 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--);
}
- 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){
+ 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;
+ 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){
+ 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_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;
+ uint16_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->wordv[i] = (uint8_t)t;
- dest->length_B=i+1;
+ dest->wordv[i] = (bigint_word_t)t;
+ dest->length_W = i+1;
+ dest->info = 0;
bigint_adjust(dest);
return;
}
- if(a->length_B<=4 && b->length_B<=4){
+ 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;
+ }
+#if BIGINT_WORD_SIZE == 8
+ if(a->length_W <= 4 || b->length_W <= 4){
+ if(a->length_W > 4){
+ XCHG_PTR(a,b);
+ }
+ uint32_t x = 0, y = 0;
+ uint16_t j = b->length_W / 4, idx = 0;
+ uint64_t r = 0;
+ memcpy(&x, a->wordv, a->length_W);
+ while(j){
+ r += (uint64_t)((uint32_t*)b->wordv)[idx] * (uint64_t)x;
+ ((uint32_t*)dest->wordv)[idx] = (uint32_t)r;
+ r >>= 32;
+ ++idx;
+ --j;
+ }
+ idx *= 4;
+ memcpy(&y, b->wordv + idx, b->length_W - idx);
+ r += (uint64_t)y * (uint64_t)x;
+ while(r){
+ dest->wordv[idx++] = (uint8_t)r;
+ r >>= 8;
+ }
+ dest->length_W = idx;
bigint_adjust(dest);
return;
}
- bigint_set_zero(dest);
+#endif
/* split a in xh & xl; split b in yh & yl */
- uint16_t n;
- n=(MAX(a->length_B, b->length_B)+1)/2;
+ const uint16_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;
+ if(a->length_W <= n){
+ bigint_set_zero(&xh);
+ xl.length_W = a->length_W;
+ xl.info = a->info;
}else{
- xl.length_B=n;
+ 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;
+ 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)];
- 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);
+ /* remember we want to do:
+ * x*y = (xh * b ** n + xl) * (yh * b ** n + 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
+ */
+ bigint_word_t tmp1_b[n*2+2];
+ bigint_t tmp1, tmp2;
+ tmp1.wordv = tmp1_b;
+ tmp2.wordv = &tmp1_b[n+1];
+
+ bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh + xl */
+ bigint_add_u(&tmp1, &yh, &yl); /* 3: tmp1 <= yh + yl */
+ bigint_mul_u(dest, &tmp2, &tmp1); /* 4: dest <= tmp2 * tmp1 */
+ bigint_mul_u(&tmp1, &xh, &yh); /* 5: tmp1 <= xh * yh */
+ bigint_sub_u(dest, dest, &tmp1); /* 7: dest <= dest - tmp1 */
+ bigint_word_t tmp3_b[2*n];
+ tmp2.wordv = tmp3_b;
+ bigint_mul_u(&tmp2, &xl, &yl); /* 1: tmp3 <= xl * yl */
+ bigint_sub_u(dest, dest, &tmp2); /* 6: dest <= dest - tmp3 */
+ bigint_shiftleft(dest, n * sizeof(bigint_word_t) * 8);
+ bigint_add_u(dest, dest, &tmp2); /* 8: dest <= tmp3 + dest ** n */
+ bigint_add_scale_u(dest, &tmp1, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest + tmp1 ** (2 * n) */
+
+#if 0
+ bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl * yl */
+ bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh + xl */
+ bigint_add_u(&tmp1, &yh, &yl); /* 3: tmp1 <= yh + yl */
+ bigint_mul_u(&tmp3, &tmp2, &tmp1); /* 4: tmp3 <= tmp2 * tmp1 */
+ bigint_mul_u(&tmp1, &xh, &yh); /* 5: h <= xh * yh */
+ bigint_sub_u(&tmp3, &tmp3, dest); /* 6: tmp3 <= tmp3 - dest */
+ bigint_sub_u(&tmp3, &tmp3, &tmp1); /* 7: tmp3 <= tmp3 - h */
+ bigint_add_scale_u(dest, &tmp3, n*sizeof(bigint_word_t)); /* 8: dest <= dest + tmp3 ** n */
+ bigint_add_scale_u(dest, &tmp1, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest + tmp1 ** (2 * n) */
+#endif
}
/******************************************************************************/
/* 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);
+ 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_B=2*a->length_B;
+ dest->length_W = 2 * a->length_W;
bigint_adjust(dest);
return;
}
if(dest==a){
bigint_t d;
- uint8_t d_b[a->length_B*2];
+ bigint_word_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_B+1)/2;
+ n = (a->length_W + 1) / 2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
- uint8_t buffer[2*n+1];
+ bigint_word_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;
+ xl.length_W = n;
+ xl.info = 0;
+ xh.wordv = &(a->wordv[n]);
+ xh.length_W = a->length_W - n;
+ xh.info = a->info;
+ bigint_adjust(&xl);
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);
- bigint_add_scale_u(dest, &tmp, 2*n);
+// 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);
- bigint_add_scale_u(dest, &tmp, n);
+// 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;
- uint8_t tmp_b[b->length_B+1];
- uint16_t i,j,byteshift=bitscale/8;
- uint8_t borrow=0;
- int16_t t;
+ bigint_t tmp, x;
+ bigint_word_t tmp_b[b->length_W + 1];
+ const uint16_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;
bigint_copy(&tmp, b);
- bigint_shiftleft(&tmp, bitscale&7);
+ bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
- 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;
- }
+// cli_putstr_P(PSTR("\r\nDBG: shifted value: ")); bigint_print_hex(&tmp);
+
+ x.info = a->info;
+ x.wordv = &(a->wordv[word_shift]);
+ x.length_W = a->length_W - word_shift;
+
+ bigint_sub_u(&x, &x, &tmp);
+ a->length_W = x.length_W + word_shift;
bigint_adjust(a);
+ return;
}
/******************************************************************************/
void bigint_reduce(bigint_t* a, const bigint_t* r){
-// bigint_adjust(r);
+// bigint_adjust((bigint_t*)r);
uint8_t rfbs = GET_FBS(r);
-
- if(r->length_B==0 || a->length_B==0){
+#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);
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);
+ 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+1) && (a->length_B == r->length_B)){
- bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
+ while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){
+ shift = GET_FBS(a)-rfbs-1;
+// cli_putstr("\r\nDBG: (2a) = "); bigint_print_hex(a);
+// cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
+ bigint_sub_u_bitscale(a, r, shift);
+// cli_putstr("\r\nDBG: (2b) = "); 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);
}
+// cli_putc(' ');
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){
+ if(a->length_W==0 || r->length_W==0){
return;
}
bigint_t res, base;
- uint8_t base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*2];
+ bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2];
uint16_t i;
- uint8_t j, t;
+ 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.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);
+ if(exp->length_W == 0){
+ bigint_copy(dest, &res);
+ return;
+ }
+ 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 & (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);
+ }
}
- bigint_square(&base, &base);
- bigint_reduce(&base, r);
- t>>=1;
+ 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;
- }
+
+// 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_;
- volatile uint16_t i=0;
- if(x->length_B==0 || y->length_B==0){
+ uint16_t i=0;
+ if(x->length_W==0 || y->length_W==0){
return;
}
+ if(x->length_W==1 && x->wordv[0]==1){
+ gcd->length_W = 1;
+ gcd->wordv[0] = 1;
+ if(a){
+ a->length_W = 1;
+ a->wordv[0] = 1;
+ SET_POS(a);
+ bigint_adjust(a);
+ }
+ if(b){
+ bigint_set_zero(b);
+ }
+ return;
+ }
+ if(y->length_W==1 && y->wordv[0]==1){
+ gcd->length_W = 1;
+ gcd->wordv[0] = 1;
+ 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];
+ bigint_word_t g_b[i+2], x_b[x->length_W-i], y_b[y->length_W-i];
+ bigint_word_t u_b[x->length_W-i], v_b[y->length_W-i];
+ bigint_word_t a_b[y->length_W+2], c_b[y->length_W+2];
+ bigint_word_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);
+ memset(g_b, 0, i*sizeof(bigint_word_t));
g_b[i]=1;
- g.length_B = 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);
+ 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]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
}
bigint_shiftright(&x_, i);
bigint_shiftright(&y_, i);
}
+
u.wordv = u_b;
v.wordv = v_b;
a_.wordv = a_b;
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{
+ 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_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(&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);
}
void bigint_changeendianess(bigint_t* a){
uint8_t t, *p, *q;
- p = a->wordv;
- q = p+a->length_B-1;
+ p = (uint8_t*)(a->wordv);
+ q = p + a->length_W * sizeof(bigint_word_t) - 1;
while(p<q){
t = *p;
*p = *q;
projects / avr-crypto-lib.git / blobdiff