#include "bigint.h"
#include <string.h>
-#define DEBUG 1
+#define DEBUG 0
#if DEBUG
#include "cli.h"
-#include "uart_lowlevel.h"
#include "bigint_io.h"
#endif
#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*)(((uint32_t)(a)) ^ ((uint32_t)(b))); \
- b = (void*)(((uint32_t)(a)) ^ ((uint32_t)(b))); \
- a = (void*)(((uint32_t)(a)) ^ ((uint32_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)
bigint_word_t t;
uint8_t i = BIGINT_WORD_SIZE-1;
t = a->wordv[a->length_B-1];
- while((t&(1<<(BIGINT_WORD_SIZE-1)))==0 && i){
+ while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
t<<=1;
i--;
}
dest->wordv[i] = (bigint_word_t)t;
t>>=BIGINT_WORD_SIZE;
}
- dest->wordv[i++] = (bigint_word_t)t;
+ if(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;
+ if(a->length_B == 0){
+ return;
+ }
+ if(scale == 0){
+ bigint_add_u(dest, dest, a);
+ return;
+ }
+ 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 = 0;
+ } else {
+ x.info = dest->info;
+ }
+ bigint_add_u(&x, &x, a);
+ dest->length_B = x.length_B + 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_B + 1];
+ s.wordv = bv;
+ bv[0] = bv[a->length_B] = 0;
+ memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_B * sizeof(bigint_word_t));
+ s.length_B = a->length_B + 1;
+ bigint_adjust(&s);
+ memset(dest->wordv + dest->length_B, 0, (MAX(dest->length_B, s.length_B + word_shift) - dest->length_B) * sizeof(bigint_word_t));
+ x.wordv = dest->wordv + word_shift;
+ x.length_B = dest->length_B - word_shift;
+ if((int16_t)x.length_B < 0){
+ x.length_B = 0;
+ x.info = 0;
+ }else{
+ x.info = dest->info;
+ }
+ bigint_add_u(&x, &x, &s);
+ dest->length_B = x.length_B + word_shift;
+ dest->info = 0;
+ bigint_adjust(dest);
+#endif
+
+
+/* uint16_t i,j=0;
uint16_t scale_w;
- uint32_t *dst;
+ 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)){
dest->length_B = i;
}
bigint_adjust(dest);
+ */
}
/******************************************************************************/
if(r<0){
bigint_sub_u(dest, b, a);
SET_NEG(dest);
- }else{
- for(i=0; i<min; ++i){
- t = a->wordv[i];
+ return;
+ }
+ for(i=0; i<max; ++i){
+ t = a->wordv[i];
+ if(i<min){
t -= b->wordv[i];
- t -= borrow;
- if(t<0){
- borrow = 1;
- dest->wordv[i]=(bigint_word_t)t;
- }else{
- borrow = 0;
- dest->wordv[i]=(bigint_word_t)t;
- }
}
- for(;i<max; ++i){
- t = a->wordv[i] - borrow;
- if(t<0){
- borrow = 1;
- dest->wordv[i]=(bigint_word_t)t;
- }else{
- borrow = 0;
- dest->wordv[i]=(bigint_word_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);
}
/******************************************************************************/
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;
if(a->length_B!=1){
XCHG_PTR(a,b);
}
- bigint_wordplus_t i, t=0;
+ bigint_wordplus_t t=0;
+ uint16_t i;
bigint_word_t x = a->wordv[0];
- for(i=0; i<b->length_B; ++i){
+ 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] = (bigint_word_t)t;
- dest->length_B=i+1;
+ dest->length_B = i+1;
+ dest->info = 0;
bigint_adjust(dest);
return;
}
- if(a->length_B<=4/sizeof(bigint_word_t) && b->length_B<=4/sizeof(bigint_word_t)){
+ 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*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, (a->length_B+b->length_B)*sizeof(bigint_word_t));
- dest->length_B = a->length_B+b->length_B;
+ 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 */
+ /* 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;
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 <= 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*sizeof(bigint_word_t));
- bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t));
+ 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) */
}
/******************************************************************************/
bigint_word_t buffer[2*n+1];
xl.wordv = a->wordv;
xl.length_B = 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);
/******************************************************************************/
void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
- bigint_t tmp;
- bigint_word_t tmp_b[b->length_B+4];
- uint16_t i,j,word_shift=bitscale/(8*sizeof(bigint_word_t));
- uint8_t borrow=0;
- bigint_wordplus_signed_t t;
+ 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(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-1));
-// cli_putstr("\r\nDBG(sub_ub.0) tmp_shift = "); bigint_print_hex(&tmp);
- for(j=0,i=word_shift; i<tmp.length_B+word_shift; ++i, ++j){
- t = a->wordv[i];
- t -= tmp.wordv[j];
- t -= borrow;
- a->wordv[i] = (bigint_word_t)t;
- if(t<0){
- borrow = 1;
- }else{
- borrow = 0;
- }
- }
- while(borrow){
- if(i+1 > a->length_B){
- // char str[16];
- cli_putstr("\r\nDBG: *boom* a->length_B = ");
- cli_hexdump_rev(&a->length_B, 2);
- cli_putstr(" b->length_B = ");
- cli_hexdump_rev(&b->length_B, 2);
- cli_putstr(" bitscale = ");
- cli_hexdump_rev(&bitscale, 2);
- bigint_set_zero(a);
- return;
- }
- a->wordv[i] -= borrow;
- if(a->wordv[i] != (1LL<<BIGINT_WORD_SIZE) - 1){
- borrow=0;
- }
- ++i;
- }
+ 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);
-
-// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+#if DEBUG
+ cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
+#endif
if(r->length_B==0 || a->length_B==0){
return;
}
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)){
+ 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, GET_FBS(a)-rfbs-1);
+ bigint_sub_u_bitscale(a, r, shift);
// cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
}
while(bigint_cmp_u(a,r)>=0){
}
bigint_t res, base;
- bigint_word_t 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_B,r->length_B)], res_b[r->length_B*2];
uint16_t i;
uint8_t j;
// uint16_t *xaddr = &i;
res.wordv[0]=1;
res.length_B=1;
res.info = 0;
-// cli_putstr("\r\nadjust ");
bigint_adjust(&res);
-// cli_putstr("\r\nexpmod ");
- for(i=0; i+1<exp->length_B; ++i){
- t=exp->wordv[i];
- for(j=0; j<BIGINT_WORD_SIZE; ++j){
- if(t&1){
- bigint_mul_u(&res, &res, &base);
+ 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);
+ }
}
- bigint_square(&base, &base);
- bigint_reduce(&base, r);
- t>>=1;
+ t<<=1;
}
}
- t=exp->wordv[i];
// cli_putc('+');
- 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;
- }
SET_POS(&res);
bigint_copy(dest, &res);
}
projects / arm-crypto-lib.git / blobdiff