/* 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
*/
+#define STRING2(x) #x
+#define STRING(x) STRING2(x)
+#define STR_LINE STRING(__LINE__)
+
#include "bigint.h"
#include <string.h>
-#include "bigint_io.h"
+#define DEBUG 0
+
+#if DEBUG
#include "cli.h"
+#include "bigint_io.h"
+#endif
#ifndef MAX
#define MAX(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 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*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b))); \
+ b = (void*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b))); \
+ a = (void*)(((bigint_ptr_int_t)(a)) ^ ((bigint_ptr_int_t)(b)));}while(0)
#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
a->info=0;
return;
}
- uint8_t t;
- uint8_t i = 0x07;
+ bigint_word_t t;
+ uint8_t i = BIGINT_WORD_SIZE-1;
t = a->wordv[a->length_B-1];
- while((t&0x80)==0 && i){
+ while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
t<<=1;
i--;
}
/******************************************************************************/
+uint16_t bigint_length_b(bigint_t* a){
+ if(!a->length_B || a->length_B==0){
+ return 0;
+ }
+ return (a->length_B-1) * BIGINT_WORD_SIZE + GET_FBS(a);
+}
+
+/******************************************************************************/
+
+uint16_t bigint_length_B(bigint_t* a){
+ return a->length_B * sizeof(bigint_word_t);
+}
+
+/******************************************************************************/
+
+uint32_t bigint_get_first_set_bit(bigint_t* a){
+ if(a->length_B==0){
+ return (uint32_t)(-1);
+ }
+ return (a->length_B-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
+}
+
+
+/******************************************************************************/
+
+uint32_t bigint_get_last_set_bit(bigint_t* a){
+ uint32_t r=0;
+ uint8_t b=0;
+ bigint_word_t x=1;
+ if(a->length_B==0){
+ return (uint32_t)(-1);
+ }
+ while(a->wordv[r]==0 && r<a->length_B){
+ ++r;
+ }
+ if(a->wordv[r] == 0){
+ return (uint32_t)(-1);
+ }
+ while((x&a->wordv[r])==0){
+ ++b;
+ x <<= 1;
+ }
+ return r*BIGINT_WORD_SIZE+b;
+}
+
+/******************************************************************************/
+
void bigint_copy(bigint_t* dest, const bigint_t* src){
- memcpy(dest->wordv, src->wordv, src->length_B);
+ memcpy(dest->wordv, src->wordv, src->length_B*sizeof(bigint_word_t));
dest->length_B = src->length_B;
dest->info = src->info;
}
/******************************************************************************/
/* this should be implemented in assembly */
-/*
void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
- uint16_t t=0, i;
+ uint16_t i;
+ bigint_wordplus_t t=0LL;
if(a->length_B < b->length_B){
XCHG_PTR(a,b);
}
for(i=0; i<b->length_B; ++i){
- t = a->wordv[i] + b->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
+ t += a->wordv[i];
+ t += b->wordv[i];
+ dest->wordv[i] = (bigint_word_t)t;
+ t>>=BIGINT_WORD_SIZE;
}
for(; i<a->length_B; ++i){
- t = a->wordv[i] + t;
- dest->wordv[i] = (uint8_t)t;
- t>>=8;
+ t += a->wordv[i];
+ dest->wordv[i] = (bigint_word_t)t;
+ t>>=BIGINT_WORD_SIZE;
}
- dest->wordv[i++] = t;
+ dest->wordv[i++] = (bigint_word_t)t;
dest->length_B = i;
bigint_adjust(dest);
}
-*/
+
/******************************************************************************/
/* this should be implemented in assembly */
void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
- 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;
+ bigint_t x;
+#if BIGINT_WORD_SIZE == 8
+ memset(dest->wordv + dest->length_B, 0, MAX(dest->length_B, a->length_B + scale) - dest->length_B);
+ x.wordv = dest->wordv + scale;
+ x.length_B = dest->length_B - scale;
+ if((int16_t)x.length_B < 0)
+ x.length_B = 0;
+ x.info = dest->info;
+ bigint_add_u(&x, &x, a);
+ dest->length_B = x.length_B + scale;
+ dest->info = 0;
+ bigint_adjust(dest);
+#else
+#error unimplemented!
+#endif
+
+
+/* uint16_t i,j=0;
+ uint16_t scale_w;
+ bigint_word_t *dst;
+ bigint_wordplus_t t=0;
+ scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
+ if(scale>dest->length_B*sizeof(bigint_word_t)){
+ memset(((uint8_t*)dest->wordv)+dest->length_B*sizeof(bigint_word_t), 0, scale-dest->length_B*sizeof(bigint_word_t));
+ }
+ // a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3));
+ dst = dest->wordv + (scale&(sizeof(bigint_word_t)-1));
+ for(i=scale/sizeof(bigint_word_t); i<a->length_B+scale_w; ++i,++j){
+ t += a->wordv[j];
if(dest->length_B>i){
- t += dest->wordv[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;
+ 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;
}
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;
+ bigint_wordplus_signed_t t=0LL;
uint16_t i, min, max;
min = MIN(a->length_B, b->length_B);
max = MAX(a->length_B, b->length_B);
r = bigint_cmp_u(a,b);
if(r==0){
- 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;
+ 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;
+ bigint_copy(dest, b);
+ SET_NEG(dest);
+ return;
}
if(r<0){
- for(i=0; i<min; ++i){
- t = a->wordv[i] - b->wordv[i] - borrow;
- if(t<1){
- borrow = 0;
- dest->wordv[i]=(uint8_t)(-t);
- }else{
- borrow = -1;
- dest->wordv[i]=(uint8_t)(-t);
- }
- }
- for(;i<max; ++i){
- t = b->wordv[i] + borrow;
- if(t<1){
- borrow = 0;
- dest->wordv[i]=(uint8_t)t;
- }else{
- borrow = -1;
- dest->wordv[i]=(uint8_t)t;
- }
- }
+ bigint_sub_u(dest, b, a);
SET_NEG(dest);
- dest->length_B = i;
- bigint_adjust(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<max; ++i){
+ t = a->wordv[i];
+ if(i<min){
+ 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_B = i;
+ bigint_adjust(dest);
}
/******************************************************************************/
if(a->length_B < b->length_B){
return -1;
}
- if(GET_FBS(a) > GET_FBS(b)){
- return 1;
- }
- if(GET_FBS(a) < GET_FBS(b)){
- return -1;
- }
if(a->length_B==0){
return 0;
}
uint16_t i;
i = a->length_B-1;
do{
- if(a->wordv[i]!=b->wordv[i]){
- if(a->wordv[i]>b->wordv[i]){
+ 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){
+ return 0;
+ }
s = GET_SIGN(a)?2:0;
s |= GET_SIGN(b)?1:0;
switch(s){
/******************************************************************************/
void bigint_shiftleft(bigint_t* a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
+ uint16_t byteshift, word_alloc;
+ int16_t i;
uint8_t bitshift;
- uint16_t t=0;
- byteshift = (shift+3)/8;
+ bigint_word_t *p;
+ bigint_wordplus_t t=0;
+ if(shift==0){
+ return;
+ }
+ byteshift = shift/8;
bitshift = shift&7;
- memmove(a->wordv+byteshift, a->wordv, a->length_B);
- memset(a->wordv, 0, byteshift);
+ for(i=0;i<=byteshift/sizeof(bigint_word_t); ++i){
+ a->wordv[a->length_B+i] = 0;
+ }
+ if(byteshift){
+ memmove(((uint8_t*)a->wordv)+byteshift, a->wordv, a->length_B*sizeof(bigint_word_t));
+ memset(a->wordv, 0, byteshift);
+ }
+ p = (bigint_word_t*)(((uint8_t*)a->wordv)+byteshift);
+ word_alloc = a->length_B+(byteshift+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t)+1;
+ a->wordv[word_alloc-1]=0;
if(bitshift!=0){
- 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;
- }else{ /* shift to the right */
- bitshift = 8 - bitshift;
- for(i=a->length_B+byteshift-1; i>byteshift; --i){
- t |= (a->wordv[i])<<(8-bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
- t <<= 8;
- }
- t |= (a->wordv[i])<<(8-bitshift);
- a->wordv[i] = (uint8_t)(t>>8);
+ for(i=0; i<a->length_B; ++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+1;
+ a->length_B = word_alloc;
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 */
- a->length_B=0;
- a->wordv[0] = 0;
- SET_FBS(a, 0);
+ if(byteshift >= a->length_B*sizeof(bigint_word_t)){ /* we would shift out more than we have */
+ bigint_set_zero(a);
return;
}
- if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
- a->length_B=0;
- a->wordv[0] = 0;
- SET_FBS(a, 0);
+ if(byteshift == a->length_B*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_B-byteshift);
+ memset((uint8_t*)a->wordv+a->length_B-byteshift, 0, byteshift);
}
+ byteshift /= sizeof(bigint_word_t);
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 |= ((bigint_wordplus_t)(a->wordv[i]))<<(BIGINT_WORD_SIZE-bitshift);
+ a->wordv[i] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
+ t <<= BIGINT_WORD_SIZE;
}
- t |= (a->wordv[0])<<(8-bitshift);
- a->wordv[0] = (uint8_t)(t>>8);
+ t |= ((bigint_wordplus_t)(a->wordv[0]))<<(BIGINT_WORD_SIZE-bitshift);
+ a->wordv[0] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
}
- a->length_B -= byteshift;
+ a->length_B -= ((shift/8)+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
bigint_adjust(a);
}
void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
if(a->length_B==0 || b->length_B==0){
bigint_set_zero(dest);
- depth -= 1;
+ return;
+ }
+ if(dest==a || dest==b){
+ bigint_t d;
+ bigint_word_t d_b[a->length_B+b->length_B];
+ d.wordv = d_b;
+ bigint_mul_u(&d, a, b);
+ bigint_copy(dest, &d);
return;
}
if(a->length_B==1 || b->length_B==1){
if(a->length_B!=1){
XCHG_PTR(a,b);
}
- 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_B; ++i){
+ t += ((bigint_wordplus_t)b->wordv[i])*((bigint_wordplus_t)x);
+ dest->wordv[i] = (bigint_word_t)t;
+ t>>=BIGINT_WORD_SIZE;
}
- dest->wordv[i] = (uint8_t)t;
- dest->length_B=i+1;
+ dest->wordv[i] = (bigint_word_t)t;
+ dest->length_B = i+1;
+ dest->info = 0;
bigint_adjust(dest);
return;
}
- if(a->length_B<=4 && b->length_B<=4){
+ if(a->length_B * sizeof(bigint_word_t) <= 4 && b->length_B * sizeof(bigint_word_t) <= 4){
uint32_t p=0, q=0;
uint64_t r;
- memcpy(&p, a->wordv, a->length_B);
- 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_B*sizeof(bigint_word_t));
+ memcpy(&q, b->wordv, b->length_B*sizeof(bigint_word_t));
+ r = (uint64_t)p * (uint64_t)q;
+ memcpy(dest->wordv, &r, (dest->length_B = a->length_B + b->length_B)*sizeof(bigint_word_t));
bigint_adjust(dest);
return;
}
bigint_set_zero(dest);
/* split a in xh & xl; split b in yh & yl */
- uint16_t n;
- n=(MAX(a->length_B, b->length_B)+1)/2;
+ const uint16_t n = (MAX(a->length_B, b->length_B)+1)/2;
bigint_t xl, xh, yl, yh;
xl.wordv = a->wordv;
yl.wordv = b->wordv;
if(a->length_B<=n){
- xh.info=0;
- xh.length_B = 0;
+ bigint_set_zero(&xh);
xl.length_B = a->length_B;
- xl.info = 0;
+ xl.info = a->info;
}else{
xl.length_B=n;
xl.info = 0;
bigint_adjust(&xl);
- xh.wordv = a->wordv+n;
+ xh.wordv = &(a->wordv[n]);
xh.length_B = a->length_B-n;
- xh.info = 0;
+ xh.info = a->info;
}
if(b->length_B<=n){
- yh.info=0;
- yh.length_B = 0;
+ bigint_set_zero(&yh);
yl.length_B = b->length_B;
yl.info = b->info;
}else{
yl.length_B=n;
yl.info = 0;
bigint_adjust(&yl);
- yh.wordv = b->wordv+n;
+ yh.wordv = &(b->wordv[n]);
yh.length_B = b->length_B-n;
- yh.info = 0;
+ 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*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl
+ * 5 9 2 4 3 7 5 6 1 8 1
+ */
+ bigint_word_t tmp_b[2*n+2], m_b[2*(n+1)];
bigint_t tmp, tmp2, m;
- /* calculate h=xh*yh; l=xl*yl; sx=xh+xl; sy=yh+yl */
tmp.wordv = tmp_b;
- tmp2.wordv = tmp_b+n+1;
+ 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 <= tmp*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);
+ bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl*yl */
+ bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl */
+ bigint_add_u(&tmp, &yh, &yl); /* 3: tmp <= yh+yl */
+ bigint_mul_u(&m, &tmp2, &tmp); /* 4: m <= tmp2*tmp */
+ bigint_mul_u(&tmp, &xh, &yh); /* 5: h <= xh*yh */
+ bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */
+ bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-h */
+ bigint_add_scale_u(dest, &m, n*sizeof(bigint_word_t)); /* 8: dest <= dest+m**n*/
+ bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */
}
/******************************************************************************/
/* 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){
+ if(a->length_B*sizeof(bigint_word_t)<=4){
uint64_t r=0;
- memcpy(&r, a->wordv, a->length_B);
+ memcpy(&r, a->wordv, a->length_B*sizeof(bigint_word_t));
r = r*r;
- memcpy(dest->wordv, &r, 2*a->length_B);
+ memcpy(dest->wordv, &r, 2*a->length_B*sizeof(bigint_word_t));
SET_POS(dest);
dest->length_B=2*a->length_B;
bigint_adjust(dest);
return;
}
+ if(dest==a){
+ bigint_t d;
+ bigint_word_t d_b[a->length_B*2];
+ d.wordv = d_b;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ return;
+ }
uint16_t n;
n=(a->length_B+1)/2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
- 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;
+ xl.info = 0;
+ xh.wordv = &(a->wordv[n]);
xh.length_B = a->length_B-n;
+ xh.info = 0;
+ bigint_adjust(&xl);
+ bigint_adjust(&xh);
tmp.wordv = buffer;
+/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
+
+// cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
+// cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
bigint_square(dest, &xl);
+// cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
bigint_square(&tmp, &xh);
- 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, x;
+ bigint_word_t tmp_b[b->length_B + 1];
+ const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
+
+ if(a->length_B < b->length_B + word_shift){
+#if DEBUG
+ cli_putstr("\r\nDBG: *bang*\r\n");
+#endif
+ bigint_set_zero(a);
+ return;
+ }
+ tmp.wordv = tmp_b;
+ bigint_copy(&tmp, b);
+ bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
+
+ x.info = a->info;
+ x.wordv = &(a->wordv[word_shift]);
+ x.length_B = a->length_B - word_shift;
+
+ bigint_sub_u(&x, &x, &tmp);
+ bigint_adjust(a);
+ return;
+}
+
+/******************************************************************************/
+void bigint_reduce(bigint_t* a, const bigint_t* r){
+// bigint_adjust((bigint_t*)r);
+ uint8_t rfbs = GET_FBS(r);
+#if DEBUG
+ cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+#endif
+ if(r->length_B==0 || a->length_B==0){
+ return;
+ }
+ if((r->length_B*sizeof(bigint_word_t)<=4) && (a->length_B*sizeof(bigint_word_t)<=4)){
+ uint32_t p=0, q=0;
+ memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
+ memcpy(&q, r->wordv, r->length_B*sizeof(bigint_word_t));
+ p %= q;
+ memcpy(a->wordv, &p, a->length_B*sizeof(bigint_word_t));
+ bigint_adjust(a);
+// cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
+ return;
+ }
+ uint16_t shift;
+ while(a->length_B > r->length_B){
+ shift = (a->length_B - r->length_B) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
+ /*
+ if((a->wordv[a->length_B-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_B-1]){
+ // cli_putc('~');
+ cli_putstr("\r\n ~ [a] = ");
+ cli_hexdump_rev(&a->wordv[a->length_B-1], 4);
+ cli_putstr(" [r] = ");
+ cli_hexdump_rev(&r->wordv[r->length_B-1], 4);
+ shift += 1;
+ }
+ */
+// cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
+// cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_B, 2);
+// cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_B, 2);
+// uart_flush(0);
+ bigint_sub_u_bitscale(a, r, shift);
+// cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
+ }
+ while((GET_FBS(a) > rfbs) && (a->length_B == r->length_B)){
+ shift = GET_FBS(a)-rfbs-1;
+// cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
+ bigint_sub_u_bitscale(a, r, shift);
+// cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
+ }
+ while(bigint_cmp_u(a,r)>=0){
+ bigint_sub_u(a,a,r);
+// cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
+ }
+ bigint_adjust(a);
+// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+// cli_putstr("\r\n");
}
+/******************************************************************************/
+
+/* calculate dest = a**exp % r */
+/* using square&multiply */
+void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
+ if(a->length_B==0 || r->length_B==0){
+ return;
+ }
+
+ bigint_t res, base;
+ bigint_word_t t, base_b[MAX(a->length_B,r->length_B)], res_b[r->length_B*2];
+ uint16_t i;
+ uint8_t j;
+// uint16_t *xaddr = &i;
+// cli_putstr("\r\npre-alloc (");
+// cli_hexdump_rev(&xaddr, 4);
+// cli_putstr(") ...");
+ res.wordv = res_b;
+ base.wordv = base_b;
+ bigint_copy(&base, a);
+// cli_putstr("\r\npost-copy");
+ bigint_reduce(&base, r);
+ res.wordv[0]=1;
+ res.length_B=1;
+ res.info = 0;
+ bigint_adjust(&res);
+ if(exp->length_B == 0){
+ bigint_copy(dest, &res);
+ return;
+ }
+ uint8_t flag = 0;
+ t=exp->wordv[exp->length_B - 1];
+ for(i=exp->length_B; i > 0; --i){
+ t = exp->wordv[i - 1];
+ for(j=BIGINT_WORD_SIZE; j > 0; --j){
+ if(!flag){
+ if(t & (1<<(BIGINT_WORD_SIZE-1))){
+ flag = 1;
+ }
+ }
+ if(flag){
+ bigint_square(&res, &res);
+ bigint_reduce(&res, r);
+ if(t & (1<<(BIGINT_WORD_SIZE-1))){
+ bigint_mul_u(&res, &res, &base);
+ bigint_reduce(&res, r);
+ }
+ }
+ t<<=1;
+ }
+ }
+
+// cli_putc('+');
+ SET_POS(&res);
+ bigint_copy(dest, &res);
+}
+
+/******************************************************************************/
+
+#define cli_putstr(a)
+#define bigint_print_hex(a)
+#define cli_hexdump_rev(a,b)
+#define uart_flush(a)
+
+/* gcd <-- gcd(x,y) a*x+b*y=gcd */
+void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
+ bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
+ uint16_t i=0;
+ if(x->length_B==0 || y->length_B==0){
+ return;
+ }
+ if(x->length_B==1 && x->wordv[0]==1){
+ gcd->length_B = 1;
+ gcd->wordv[0] = 1;
+ if(a){
+ a->length_B = 1;
+ a->wordv[0] = 1;
+ SET_POS(a);
+ bigint_adjust(a);
+ }
+ if(b){
+ bigint_set_zero(b);
+ }
+ return;
+ }
+ if(y->length_B==1 && y->wordv[0]==1){
+ gcd->length_B = 1;
+ gcd->wordv[0] = 1;
+ if(b){
+ b->length_B = 1;
+ b->wordv[0] = 1;
+ SET_POS(b);
+ bigint_adjust(b);
+ }
+ if(a){
+ bigint_set_zero(a);
+ }
+ return;
+ }
+
+ while(x->wordv[i]==0 && y->wordv[i]==0){
+ ++i;
+ }
+ bigint_word_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
+ bigint_word_t u_b[x->length_B-i], v_b[y->length_B-i];
+ bigint_word_t a_b[y->length_B+2], c_b[y->length_B+2];
+ bigint_word_t b_b[x->length_B+2], d_b[x->length_B+2];
+
+ g.wordv = g_b;
+ x_.wordv = x_b;
+ y_.wordv = y_b;
+ memset(g_b, 0, i*sizeof(bigint_word_t));
+ g_b[i]=1;
+ g.length_B = i+1;
+ g.info=0;
+ x_.info = y_.info = 0;
+ x_.length_B = x->length_B-i;
+ y_.length_B = y->length_B-i;
+ memcpy(x_.wordv, x->wordv+i, x_.length_B*sizeof(bigint_word_t));
+ memcpy(y_.wordv, y->wordv+i, y_.length_B*sizeof(bigint_word_t));
+ for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
+ }
+
+ bigint_adjust(&x_);
+ bigint_adjust(&y_);
+
+ if(i){
+ bigint_shiftleft(&g, i);
+ bigint_shiftright(&x_, i);
+ bigint_shiftright(&y_, i);
+ }
+
+ u.wordv = u_b;
+ v.wordv = v_b;
+ a_.wordv = a_b;
+ b_.wordv = b_b;
+ c_.wordv = c_b;
+ d_.wordv = d_b;
+
+ bigint_copy(&u, &x_);
+ bigint_copy(&v, &y_);
+ a_.wordv[0] = 1;
+ a_.length_B = 1;
+ a_.info = 0;
+ d_.wordv[0] = 1;
+ d_.length_B = 1;
+ d_.info = 0;
+ bigint_set_zero(&b_);
+ bigint_set_zero(&c_);
+ do{
+ cli_putstr("\r\nDBG (gcdext) 0");
+ while((u.wordv[0]&1)==0){
+ cli_putstr("\r\nDBG (gcdext) 0.1");
+ bigint_shiftright(&u, 1);
+ if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
+ bigint_add_s(&a_, &a_, &y_);
+ bigint_sub_s(&b_, &b_, &x_);
+ }
+ bigint_shiftright(&a_, 1);
+ bigint_shiftright(&b_, 1);
+ }
+ while((v.wordv[0]&1)==0){
+ cli_putstr("\r\nDBG (gcdext) 0.2");
+ bigint_shiftright(&v, 1);
+ if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
+ bigint_add_s(&c_, &c_, &y_);
+ bigint_sub_s(&d_, &d_, &x_);
+ }
+ bigint_shiftright(&c_, 1);
+ bigint_shiftright(&d_, 1);
+
+ }
+ if(bigint_cmp_u(&u, &v)>=0){
+ bigint_sub_u(&u, &u, &v);
+ bigint_sub_s(&a_, &a_, &c_);
+ bigint_sub_s(&b_, &b_, &d_);
+ }else{
+ bigint_sub_u(&v, &v, &u);
+ bigint_sub_s(&c_, &c_, &a_);
+ bigint_sub_s(&d_, &d_, &b_);
+ }
+ }while(u.length_B);
+ if(gcd){
+ bigint_mul_s(gcd, &v, &g);
+ }
+ if(a){
+ bigint_copy(a, &c_);
+ }
+ if(b){
+ bigint_copy(b, &d_);
+ }
+}
+
+/******************************************************************************/
+
+void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
+ bigint_gcdext(NULL, dest, NULL, a, m);
+ while(dest->info&BIGINT_NEG_MASK){
+ bigint_add_s(dest, dest, m);
+ }
+}
+
+/******************************************************************************/
+
+void bigint_changeendianess(bigint_t* a){
+ uint8_t t, *p, *q;
+ p = (uint8_t*)(a->wordv);
+ q = ((uint8_t*)p)+a->length_B*sizeof(bigint_word_t)-1;
+ while(p<q){
+ t = *p;
+ *p = *q;
+ *q = t;
+ ++p; --q;
+ }
+}
+
+/******************************************************************************/
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
projects / avr-crypto-lib.git / blobdiff