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fixing bigint

This commit is contained in:
bg 2012-09-29 15:59:59 +02:00
parent 45d15fcc09
commit d3b4df851c
4 changed files with 235 additions and 223 deletions
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449
bigint/bigint.c
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@ -35,9 +35,10 @@
#define DEBUG 0 #define DEBUG 0
#if DEBUG #if DEBUG || 1
#include "cli.h" #include "cli.h"
#include "bigint_io.h" #include "bigint_io.h"
#include <stdio.h>
#endif #endif
#ifndef MAX #ifndef MAX
@ -128,8 +129,10 @@ uint32_t bigint_get_last_set_bit(const bigint_t* a){
/******************************************************************************/ /******************************************************************************/
void bigint_copy(bigint_t* dest, const bigint_t* src){ void bigint_copy(bigint_t* dest, const bigint_t* src){
memcpy(dest->wordv, src->wordv, src->length_W*sizeof(bigint_word_t)); if(dest->wordv != src->wordv){
dest->length_W = src->length_W; memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t));
}
dest->length_W = src->length_W;
dest->info = src->info; dest->info = src->info;
} }
@ -143,12 +146,13 @@ void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
XCHG_PTR(a,b); XCHG_PTR(a,b);
} }
for(i = 0; i < b->length_W; ++i){ for(i = 0; i < b->length_W; ++i){
// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
t += a->wordv[i]; t += a->wordv[i];
t += b->wordv[i]; t += b->wordv[i];
dest->wordv[i] = (bigint_word_t)t; dest->wordv[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE; t >>= BIGINT_WORD_SIZE;
} }
for(; i < a->length_W; ++i){ for(; i<a->length_W; ++i){
t += a->wordv[i]; t += a->wordv[i];
dest->wordv[i] = (bigint_word_t)t; dest->wordv[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE; t >>= BIGINT_WORD_SIZE;
@ -171,33 +175,17 @@ void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
bigint_add_u(dest, dest, a); bigint_add_u(dest, dest, a);
return; 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; bigint_t x;
#if DEBUG_ADD_SCALE #if BIGINT_WORD_SIZE == 8
cli_putstr_P(PSTR("\r\n\tpath two")); memset(dest->wordv + dest->length_W, 0, MAX(dest->length_W, a->length_W + scale) - dest->length_W);
#endif
x.length_W = dest->length_W - scale;
x.info = dest->info;
x.wordv = dest->wordv + scale; 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); bigint_add_u(&x, &x, a);
dest->length_W = x.length_W + scale; dest->length_W = x.length_W + scale;
dest->info = 0; dest->info = 0;
@ -225,39 +213,6 @@ void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
dest->info = 0; dest->info = 0;
bigint_adjust(dest); bigint_adjust(dest);
#endif #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];
}
dst[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
}
while(t){
if(dest->length_W>i){
t += dst[i];
}
dst[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
++i;
}
if(dest->length_W < i){
dest->length_W = i;
}
bigint_adjust(dest);
*/
} }
/******************************************************************************/ /******************************************************************************/
@ -268,27 +223,27 @@ void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
int8_t r; int8_t r;
bigint_wordplus_signed_t t=0LL; bigint_wordplus_signed_t t=0LL;
uint16_t i; uint16_t i;
r = bigint_cmp_u(a,b); if(b->length_W == 0){
if(r==0){
bigint_set_zero(dest);
return;
}
if(b->length_W==0){
bigint_copy(dest, a); bigint_copy(dest, a);
SET_POS(dest); SET_POS(dest);
return; return;
} }
if(a->length_W==0){ if(a->length_W == 0){
bigint_copy(dest, b); bigint_copy(dest, b);
SET_NEG(dest); SET_NEG(dest);
return; 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); bigint_sub_u(dest, b, a);
SET_NEG(dest); SET_NEG(dest);
return; return;
} }
for(i=0; i < a->length_W; ++i){ for(i = 0; i < a->length_W; ++i){
t = a->wordv[i]; t = a->wordv[i];
if(i < b->length_W){ if(i < b->length_W){
t -= b->wordv[i]; t -= b->wordv[i];
@ -315,7 +270,7 @@ int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
if(a->length_W < b->length_W){ if(a->length_W < b->length_W){
return -1; return -1;
} }
if(a->length_W == 0){ if(a->length_W==0){
return 0; return 0;
} }
uint16_t i; uint16_t i;
@ -420,29 +375,34 @@ void bigint_shiftleft(bigint_t* a, uint16_t shift){
int16_t i; int16_t i;
uint8_t bitshift; uint8_t bitshift;
bigint_word_t *p; bigint_word_t *p;
bigint_wordplus_t t=0; bigint_wordplus_t t = 0;
if(shift == 0){ if(shift == 0){
return; return;
} }
byteshift = shift / 8; byteshift = shift / 8;
bitshift = shift & 7; bitshift = shift & 7;
memset(&a->wordv[a->length_W], 0x00, byteshift);
if(byteshift){ if(byteshift){
memmove(((uint8_t*)a->wordv)+byteshift, a->wordv, a->length_W * sizeof(bigint_word_t)); memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t));
memset(a->wordv, 0, byteshift); memset(a->wordv, 0, byteshift);
} }
if(bitshift != 0){ if(bitshift == 0){
p = (bigint_word_t*)((uint8_t*)a->wordv + byteshift / sizeof(bigint_word_t)); a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
words_to_shift = a->length_W + ((byteshift % sizeof(bigint_word_t))?1:0); bigint_adjust(a);
/* XXX */ return;
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_W += (shift + BIGINT_WORD_SIZE - 1) / BIGINT_WORD_SIZE; p = a->wordv + byteshift / sizeof(bigint_word_t);
words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t)?1:0);
for(i=0; i < words_to_shift; ++i){
t |= ((bigint_wordplus_t)p[i]) << bitshift;
p[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE;
}
if(t){
p[i] = (bigint_word_t)t;
a->length_W += 1;
}
a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
bigint_adjust(a); bigint_adjust(a);
} }
@ -452,9 +412,10 @@ void bigint_shiftright(bigint_t* a, uint16_t shift){
uint16_t byteshift; uint16_t byteshift;
uint16_t i; uint16_t i;
uint8_t bitshift; uint8_t bitshift;
bigint_wordplus_t t=0; bigint_wordplus_t t = 0;
byteshift = shift/8; byteshift = shift / 8;
bitshift = shift&7; bitshift = shift & 7;
if(byteshift >= a->length_W * sizeof(bigint_word_t)){ /* 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); bigint_set_zero(a);
return; return;
@ -463,12 +424,13 @@ void bigint_shiftright(bigint_t* a, uint16_t shift){
bigint_set_zero(a); bigint_set_zero(a);
return; return;
} }
if(byteshift){ if(byteshift){
memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - 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);
} }
byteshift /= sizeof(bigint_word_t);
a->length_W -= (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); byteshift /= sizeof(bigint_word_t); /* byteshift is now wordshift */
a->length_W -= byteshift;
if(bitshift != 0 && a->length_W){ if(bitshift != 0 && a->length_W){
/* shift to the right */ /* shift to the right */
i = a->length_W - 1; i = a->length_W - 1;
@ -502,11 +464,11 @@ void bigint_set_zero(bigint_t* a){
/* using the Karatsuba-Algorithm */ /* using the Karatsuba-Algorithm */
/* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */ /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
if(a->length_W==0 || b->length_W==0){ if(a->length_W == 0 || b->length_W == 0){
bigint_set_zero(dest); bigint_set_zero(dest);
return; return;
} }
if(dest==a || dest==b){ if(dest == a || dest == b){
bigint_t d; bigint_t d;
bigint_word_t d_b[a->length_W + b->length_W]; bigint_word_t d_b[a->length_W + b->length_W];
d.wordv = d_b; d.wordv = d_b;
@ -514,20 +476,23 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
bigint_copy(dest, &d); bigint_copy(dest, &d);
return; return;
} }
if(a->length_W==1 || b->length_W==1){ if(a->length_W == 1 || b->length_W == 1){
if(a->length_W != 1){ if(a->length_W != 1){
XCHG_PTR(a,b); XCHG_PTR(a,b);
} }
bigint_wordplus_t t=0; bigint_wordplus_t t = 0;
uint16_t i; uint16_t i;
bigint_word_t x = a->wordv[0]; bigint_word_t x = a->wordv[0];
for(i=0; i < b->length_W; ++i){ for(i=0; i < b->length_W; ++i){
t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x); t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x);
dest->wordv[i] = (bigint_word_t)t; dest->wordv[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE; t >>= BIGINT_WORD_SIZE;
}
dest->length_W = i;
if(t){
dest->wordv[i] = (bigint_word_t)t;
dest->length_W += 1;
} }
dest->wordv[i] = (bigint_word_t)t;
dest->length_W = i+1;
dest->info = 0; dest->info = 0;
bigint_adjust(dest); bigint_adjust(dest);
return; return;
@ -542,57 +507,29 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
bigint_adjust(dest); bigint_adjust(dest);
return; 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;
}
#endif
/* split a in xh & xl; split b in yh & yl */ /* split a in xh & xl; split b in yh & yl */
const uint16_t n = (MAX(a->length_W, b->length_W)+1)/2; const uint16_t n = (MAX(a->length_W, b->length_W)+1)/2;
bigint_t xl, xh, yl, yh; bigint_t xl, xh, yl, yh;
xl.wordv = a->wordv; xl.wordv = a->wordv;
yl.wordv = b->wordv; yl.wordv = b->wordv;
if(a->length_W <= n){ if(a->length_W<=n){
bigint_set_zero(&xh); bigint_set_zero(&xh);
xl.length_W = a->length_W; xl.length_W = a->length_W;
xl.info = a->info; xl.info = a->info;
}else{ }else{
xl.length_W = n; xl.length_W=n;
xl.info = 0; xl.info = 0;
bigint_adjust(&xl); bigint_adjust(&xl);
xh.wordv = &(a->wordv[n]); xh.wordv = &(a->wordv[n]);
xh.length_W = a->length_W-n; xh.length_W = a->length_W-n;
xh.info = a->info; xh.info = a->info;
} }
if(b->length_W <= n){ if(b->length_W<=n){
bigint_set_zero(&yh); bigint_set_zero(&yh);
yl.length_W = b->length_W; yl.length_W = b->length_W;
yl.info = b->info; yl.info = b->info;
}else{ }else{
yl.length_W = n; yl.length_W=n;
yl.info = 0; yl.info = 0;
bigint_adjust(&yl); bigint_adjust(&yl);
yh.wordv = &(b->wordv[n]); yh.wordv = &(b->wordv[n]);
@ -601,39 +538,28 @@ void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
} }
/* now we have split up a and b */ /* now we have split up a and b */
/* remember we want to do: /* remember we want to do:
* x*y = (xh * b ** n + xl) * (yh * b ** n + yl) * 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 * = (xh * yh) * b**2n + xh * b**n * yl + yh * b**n * xl + xl * yl
* 5 9 2 4 3 7 5 6 1 8 1 * = (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
*/ */
bigint_word_t tmp1_b[n*2+2]; bigint_word_t tmp_b[2 * n + 2], m_b[2 * (n + 1)];
bigint_t tmp1, tmp2; bigint_t tmp, tmp2, m;
tmp1.wordv = tmp1_b; tmp.wordv = tmp_b;
tmp2.wordv = &tmp1_b[n+1]; tmp2.wordv = &(tmp_b[n + 1]);
m.wordv = m_b;
bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh + xl */ bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl*yl */
bigint_add_u(&tmp1, &yh, &yl); /* 3: tmp1 <= yh + yl */ bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl */
bigint_mul_u(dest, &tmp2, &tmp1); /* 4: dest <= tmp2 * tmp1 */ bigint_add_u(&tmp, &yh, &yl); /* 3: tmp <= yh+yl */
bigint_mul_u(&tmp1, &xh, &yh); /* 5: tmp1 <= xh * yh */ bigint_mul_u(&m, &tmp2, &tmp); /* 4: m <= tmp2*tmp */
bigint_sub_u(dest, dest, &tmp1); /* 7: dest <= dest - tmp1 */ bigint_mul_u(&tmp, &xh, &yh); /* 5: tmp <= xh*yh */
bigint_word_t tmp3_b[2*n]; bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */
tmp2.wordv = tmp3_b; bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-tmp */
bigint_mul_u(&tmp2, &xl, &yl); /* 1: tmp3 <= xl * yl */ bigint_add_scale_u(dest, &m, n * sizeof(bigint_word_t)); /* 8: dest <= dest+m**n*/
bigint_sub_u(dest, dest, &tmp2); /* 6: dest <= dest - tmp3 */ bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */
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
} }
/******************************************************************************/ /******************************************************************************/
@ -666,6 +592,11 @@ void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
/******************************************************************************/ /******************************************************************************/
#if DEBUG_SQUARE
unsigned square_depth = 0;
#endif
/* square */ /* square */
/* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */ /* (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){ void bigint_square(bigint_t* dest, const bigint_t* a){
@ -673,49 +604,82 @@ void bigint_square(bigint_t* dest, const bigint_t* a){
uint64_t r = 0; uint64_t r = 0;
memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t)); memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
r = r * r; r = r * r;
memcpy(dest->wordv, &r, 2 * a->length_W*sizeof(bigint_word_t)); memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t));
SET_POS(dest); SET_POS(dest);
dest->length_W = 2 * a->length_W; dest->length_W = 2 * a->length_W;
bigint_adjust(dest); bigint_adjust(dest);
return; return;
} }
if(dest==a){ if(dest->wordv == a->wordv){
bigint_t d; bigint_t d;
bigint_word_t d_b[a->length_W * 2]; bigint_word_t d_b[a->length_W*2];
d.wordv = d_b; d.wordv = d_b;
bigint_square(&d, a); bigint_square(&d, a);
bigint_copy(dest, &d); bigint_copy(dest, &d);
return; return;
} }
#if DEBUG_SQUARE
square_depth += 1;
#endif
uint16_t n; uint16_t n;
n = (a->length_W + 1) / 2; n=(a->length_W+1)/2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */ bigint_t xh, xl, tmp; /* x-high, x-low, temp */
bigint_word_t buffer[2 * n + 1]; bigint_word_t buffer[2*n+1];
xl.wordv = a->wordv; xl.wordv = a->wordv;
xl.length_W = n; xl.length_W = n;
xl.info = 0; xl.info = 0;
xh.wordv = &(a->wordv[n]); xh.wordv = &(a->wordv[n]);
xh.length_W = a->length_W - n; xh.length_W = a->length_W-n;
xh.info = a->info; xh.info = a->info;
bigint_adjust(&xl); bigint_adjust(&xl);
tmp.wordv = buffer; tmp.wordv = buffer;
/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */ /* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
#if DEBUG_SQUARE
// cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl); if(square_depth == 1){
// cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh); cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
}
#endif
bigint_square(dest, &xl); bigint_square(dest, &xl);
// cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest); #if DEBUG_SQUARE
bigint_square(&tmp, &xh); if(square_depth == 1){
// cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp); cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
}
#endif
bigint_square(&tmp, &xh);
#if DEBUG_SQUARE
if(square_depth == 1){
cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
}
#endif
bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); 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); #if DEBUG_SQUARE
if(square_depth == 1){
cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
}
#endif
bigint_mul_u(&tmp, &xl, &xh); bigint_mul_u(&tmp, &xl, &xh);
// cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp); #if DEBUG_SQUARE
if(square_depth == 1){
cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
}
#endif
bigint_shiftleft(&tmp, 1); bigint_shiftleft(&tmp, 1);
// cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp); #if DEBUG_SQUARE
bigint_add_scale_u(dest, &tmp, n*sizeof(bigint_word_t)); if(square_depth == 1){
// cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest); cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
// cli_putstr("\r\n"); }
#endif
bigint_add_scale_u(dest, &tmp, n * sizeof(bigint_word_t));
#if DEBUG_SQUARE
if(square_depth == 1){
cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
cli_putstr("\r\n");
}
square_depth -= 1;
#endif
} }
/******************************************************************************/ /******************************************************************************/
@ -735,14 +699,11 @@ void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
bigint_copy(&tmp, b); bigint_copy(&tmp, b);
bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE); bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
// cli_putstr_P(PSTR("\r\nDBG: shifted value: ")); bigint_print_hex(&tmp);
x.info = a->info; x.info = a->info;
x.wordv = &(a->wordv[word_shift]); x.wordv = &(a->wordv[word_shift]);
x.length_W = a->length_W - word_shift; x.length_W = a->length_W - word_shift;
bigint_sub_u(&x, &x, &tmp); bigint_sub_u(&x, &x, &tmp);
a->length_W = x.length_W + word_shift;
bigint_adjust(a); bigint_adjust(a);
return; return;
} }
@ -790,16 +751,14 @@ void bigint_reduce(bigint_t* a, const bigint_t* r){
} }
while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){ while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){
shift = GET_FBS(a)-rfbs-1; 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); // cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
bigint_sub_u_bitscale(a, r, shift); bigint_sub_u_bitscale(a, r, shift);
// cli_putstr("\r\nDBG: (2b) = "); bigint_print_hex(a); // cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
} }
while(bigint_cmp_u(a,r)>=0){ while(bigint_cmp_u(a,r)>=0){
bigint_sub_u(a,a,r); bigint_sub_u(a,a,r);
// cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a); // cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
} }
// cli_putc(' ');
bigint_adjust(a); bigint_adjust(a);
// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); // cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
// cli_putstr("\r\n"); // cli_putstr("\r\n");
@ -848,12 +807,12 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con
if(flag){ if(flag){
bigint_square(&res, &res); bigint_square(&res, &res);
bigint_reduce(&res, r); bigint_reduce(&res, r);
if(t & (1<<(BIGINT_WORD_SIZE-1))){ if(t & (1 << (BIGINT_WORD_SIZE - 1))){
bigint_mul_u(&res, &res, &base); bigint_mul_u(&res, &res, &base);
bigint_reduce(&res, r); bigint_reduce(&res, r);
} }
} }
t<<=1; t <<= 1;
} }
} }
@ -863,22 +822,41 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con
} }
/******************************************************************************/ /******************************************************************************/
#if 1
#define cli_putstr(a) #define cli_putstr(a)
#define cli_putstr_P(a)
#define bigint_print_hex(a) #define bigint_print_hex(a)
#define cli_hexdump_rev(a,b) #define cli_hexdump_rev(a,b)
#define uart_flush(a) #define uart_flush(a)
#define printf_P(...)
#endif
/* gcd <-- gcd(x,y) a*x+b*y=gcd */ /* 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){ 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;
uint16_t i=0; printf_P(PSTR("\nDBG: gcdext( "));
if(x->length_W==0 || y->length_W==0){ bigint_print_hex(x);
printf_P(PSTR(", "));
bigint_print_hex(y);
printf_P(PSTR(")\n"));
if(x->length_W == 0 || y->length_W == 0){
printf_P(PSTR("\nDBG: got zero in gcd <%s %s %d>\n"), __FILE__, __func__, __LINE__);
if(gcd){
bigint_set_zero(gcd);
}
if(a){
bigint_set_zero(a);
}
if(b){
bigint_set_zero(b);
}
return; return;
} }
if(x->length_W==1 && x->wordv[0]==1){ if(x->length_W == 1 && x->wordv[0] == 1){
gcd->length_W = 1; if(gcd){
gcd->wordv[0] = 1; gcd->length_W = 1;
gcd->wordv[0] = 1;
gcd->info = 0;
}
if(a){ if(a){
a->length_W = 1; a->length_W = 1;
a->wordv[0] = 1; a->wordv[0] = 1;
@ -890,9 +868,12 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
} }
return; return;
} }
if(y->length_W==1 && y->wordv[0]==1){ if(y->length_W == 1 && y->wordv[0] == 1){
gcd->length_W = 1; if(gcd){
gcd->wordv[0] = 1; gcd->length_W = 1;
gcd->wordv[0] = 1;
gcd->info = 0;
}
if(b){ if(b){
b->length_W = 1; b->length_W = 1;
b->wordv[0] = 1; b->wordv[0] = 1;
@ -905,27 +886,28 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
return; return;
} }
while(x->wordv[i]==0 && y->wordv[i]==0){ while(x->wordv[i] == 0 && y->wordv[i] == 0){
++i; ++i;
} }
bigint_word_t g_b[i+2], x_b[x->length_W-i], y_b[y->length_W-i]; 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 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 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]; bigint_word_t b_b[x->length_W + 2], d_b[x->length_W + 2];
bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
g.wordv = g_b; g.wordv = g_b;
x_.wordv = x_b; x_.wordv = x_b;
y_.wordv = y_b; y_.wordv = y_b;
memset(g_b, 0, i*sizeof(bigint_word_t)); memset(g_b, 0, i * sizeof(bigint_word_t));
g_b[i]=1; g_b[i] = 1;
g.length_W = i+1; g.length_W = i + 1;
g.info=0; g.info = 0;
x_.info = y_.info = 0; x_.info = y_.info = 0;
x_.length_W = x->length_W-i; x_.length_W = x->length_W - i;
y_.length_W = y->length_W-i; y_.length_W = y->length_W - i;
memcpy(x_.wordv, x->wordv+i, x_.length_W*sizeof(bigint_word_t)); 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)); 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){ for(i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0; ++i){
} }
bigint_adjust(&x_); bigint_adjust(&x_);
@ -954,37 +936,60 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c
d_.info = 0; d_.info = 0;
bigint_set_zero(&b_); bigint_set_zero(&b_);
bigint_set_zero(&c_); bigint_set_zero(&c_);
printf_P(PSTR("\nloop: x_ = "));
bigint_print_hex(&x_);
printf_P(PSTR("; y_ = "));
bigint_print_hex(&y_);
do{ do{
cli_putstr("\r\nDBG (gcdext) 0"); printf_P(PSTR("\nDBG (gcdext) 0"));
while((u.wordv[0]&1)==0){ while((u.wordv[0] & 1) == 0){
cli_putstr("\r\nDBG (gcdext) 0.1"); printf_P(PSTR("\nDBG (gcdext) 0.1"));
bigint_shiftright(&u, 1); bigint_shiftright(&u, 1);
if((a_.wordv[0]&1) || (b_.wordv[0]&1)){ if((a_.wordv[0] & 1) || (b_.wordv[0] & 1)){
bigint_add_s(&a_, &a_, &y_); bigint_add_s(&a_, &a_, &y_);
bigint_sub_s(&b_, &b_, &x_); bigint_sub_s(&b_, &b_, &x_);
} }
bigint_shiftright(&a_, 1); bigint_shiftright(&a_, 1);
bigint_shiftright(&b_, 1); bigint_shiftright(&b_, 1);
printf_P(PSTR(" a_ = "));
bigint_print_hex(&a_);
printf_P(PSTR("; b_ = "));
bigint_print_hex(&b_);
} }
while((v.wordv[0]&1)==0){ while((v.wordv[0] & 1) == 0){
cli_putstr("\r\nDBG (gcdext) 0.2"); printf_P(PSTR("\nDBG (gcdext) 0.2"));
bigint_shiftright(&v, 1); bigint_shiftright(&v, 1);
if((c_.wordv[0]&1) || (d_.wordv[0]&1)){ if((c_.wordv[0] & 1) || (d_.wordv[0] & 1)){
bigint_add_s(&c_, &c_, &y_); bigint_add_s(&c_, &c_, &y_);
bigint_sub_s(&d_, &d_, &x_); bigint_sub_s(&d_, &d_, &x_);
} }
printf_P(PSTR(" c* = "));
bigint_print_hex(&c_);
bigint_shiftright(&c_, 1); bigint_shiftright(&c_, 1);
bigint_shiftright(&d_, 1); bigint_shiftright(&d_, 1);
printf_P(PSTR(" c_ = "));
bigint_print_hex(&c_);
printf_P(PSTR("; d_ = "));
bigint_print_hex(&d_);
} }
if(bigint_cmp_u(&u, &v)>=0){ if(bigint_cmp_u(&u, &v) >= 0){
printf_P(PSTR("\nDBG (gcdext) 0.3"));
bigint_sub_u(&u, &u, &v); bigint_sub_u(&u, &u, &v);
bigint_sub_s(&a_, &a_, &c_); bigint_sub_s(&a_, &a_, &c_);
bigint_sub_s(&b_, &b_, &d_); bigint_sub_s(&b_, &b_, &d_);
printf_P(PSTR(" a_ = "));
bigint_print_hex(&a_);
printf_P(PSTR("; b_ = "));
bigint_print_hex(&b_);
}else{ }else{
printf_P(PSTR("\nDBG (gcdext) 0.4"));
bigint_sub_u(&v, &v, &u); bigint_sub_u(&v, &v, &u);
bigint_sub_s(&c_, &c_, &a_); bigint_sub_s(&c_, &c_, &a_);
bigint_sub_s(&d_, &d_, &b_); bigint_sub_s(&d_, &d_, &b_);
printf_P(PSTR(" c_ = "));
bigint_print_hex(&c_);
printf_P(PSTR("; d_ = "));
bigint_print_hex(&d_);
} }
}while(u.length_W); }while(u.length_W);
if(gcd){ if(gcd){

4
bigint/bigint_io.c
View File

@ -153,5 +153,9 @@ uint8_t bigint_read_hex_echo(bigint_t* a){
if(shift4){ if(shift4){
bigint_shiftright(a, 4); bigint_shiftright(a, 4);
} }
if(a->length_W == 1 && a->wordv[0] == 0){
a->length_W = 0;
a->info = 0;
}
return 0; return 0;
} }

2
host/bigint_test.rb
View File

@ -80,6 +80,7 @@ end
################################################################################ ################################################################################
def gcdext(x,y) def gcdext(x,y)
return [0, 0, 0] if(x == 0 || y == 0)
g=1 g=1
while(x&1==0 && y&1==0) do while(x&1==0 && y&1==0) do
x>>=1 x>>=1
@ -474,6 +475,7 @@ end
################################################################################ ################################################################################
def gcdext_test(a,b) def gcdext_test(a,b)
$logfile.printf("[testing] gcdext(%s, %s)\n", a.to_s(16), b.to_s(16))
begin begin
line = $sp.gets() line = $sp.gets()
line = "" if line==nil line = "" if line==nil

3
mkfiles/bigint.mk
View File

@ -6,7 +6,8 @@ AUX += $(ALGO_NAME)
$(ALGO_NAME)_DIR := bigint/ $(ALGO_NAME)_DIR := bigint/
$(ALGO_NAME)_INCDIR := memxor/ noekeon/ $(ALGO_NAME)_INCDIR := memxor/ noekeon/
$(ALGO_NAME)_OBJ := bigint-stub.o bigint_io.o bigint_asm.o #$(ALGO_NAME)_OBJ := bigint-stub.o bigint_io.o bigint_asm.o
$(ALGO_NAME)_OBJ := bigint.o bigint_io.o
$(ALGO_NAME)_TESTBIN := main-bigint-test.o $(CLI_STD) \ $(ALGO_NAME)_TESTBIN := main-bigint-test.o $(CLI_STD) \
performance_test.o noekeon_asm.o noekeon_prng.o memxor.o performance_test.o noekeon_asm.o noekeon_prng.o memxor.o