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(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;
}
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){
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);
+ 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);
+ bigint_set_zero(a);
return;
}
if(byteshift){
/* 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(dest==a || dest==b){
+ bigint_t d;
+ uint8_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==0 || b->length_B==0){
bigint_set_zero(dest);
return;
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(&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_adjust(dest);
return;
}
+ if(dest==a){
+ bigint_t d;
+ uint8_t d_b[a->length_B*2];
+ d.wordv = d_b;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ return;
+ }
uint16_t n;
n=(a->length_B+1)/2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
void bigint_reduce(bigint_t* a, const bigint_t* r){
uint8_t rfbs = GET_FBS(r);
+/*
+ cli_putstr_P(PSTR("\r\nreduce "));
+ bigint_print_hex(a);
+ cli_putstr_P(PSTR(" % "));
+ bigint_print_hex(r);
+ cli_putstr_P(PSTR("\r\n"));
+*/
+
if(r->length_B==0){
return;
}
while(a->length_B > r->length_B){
bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
}
- while(GET_FBS(a) > rfbs+1){
+
+ while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
}
+
while(bigint_cmp_u(a,r)>=0){
bigint_sub_u(a,a,r);
}
bigint_adjust(a);
}
+
+/******************************************************************************/
+
+/* calculate dest = a**exp % r */
+/* using square&multiply */
+void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
+ bigint_t tmp, tmp2, x;
+ uint8_t x_b[MAX(r->length_B, a->length_B)], tmp_b[r->length_B*2], tmp2_b[r->length_B*2];
+ int16_t i;
+ uint8_t j;
+ x.wordv = x_b;
+ tmp.wordv = tmp_b;
+ tmp2.wordv = tmp2_b;
+ bigint_copy(&x, a);
+ bigint_reduce(&x, r);
+ bigint_copy(&tmp, &x);
+ if(a->length_B==0 || exp->length_B==0 || r->length_B==0){
+ return;
+ }
+ i=exp->length_B-1;
+ if(exp->wordv[i]!=1){
+ for(j=1<<(GET_FBS(exp)-1); j>0; j>>=1){
+ // cli_putc('Q');
+ bigint_square(&tmp2, &tmp);
+ bigint_reduce(&tmp2, r);
+ if(exp->wordv[i]&j){
+ // cli_putc('M');
+ bigint_mul_u(&tmp, &tmp2, &x);
+ bigint_reduce(&tmp, r);
+ }else{
+ bigint_copy(&tmp, &tmp2);
+ }
+ }
+ }
+ for(--i; i>=0; --i){
+ for(j=0x80; j>0; j>>=1){
+// cli_putc('q');
+ bigint_square(&tmp2, &tmp);
+ bigint_reduce(&tmp2, r);
+ if(exp->wordv[i]&j){
+// cli_putc('m');
+ bigint_mul_u(&tmp, &tmp2, &x);
+ bigint_reduce(&tmp, r);
+ }else{
+ bigint_copy(&tmp, &tmp2);
+ }
+ }
+ }
+// cli_putstr_P(PSTR("\r\n"));
+ bigint_copy(dest, &tmp);
+}
+#define DEBUG 0
+/******************************************************************************/
+/* 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){
+ return;
+ }
+ while(x->wordv[i]==0 && y->wordv[i]==0){
+ ++i;
+ }
+ uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
+ uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
+ uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
+ uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
+
+ g.wordv = g_b;
+ x_.wordv = x_b;
+ y_.wordv = y_b;
+ memset(g_b, 0, i);
+ g_b[i]=1;
+ g.length_B = i+1;
+ g.info=0;
+ x_.info = y_.info = 0;
+ x_.length_B = x->length_B-i;
+ y_.length_B = y->length_B-i;
+ memcpy(x_.wordv, x->wordv+i, x_.length_B);
+ memcpy(y_.wordv, y->wordv+i, y_.length_B);
+ for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
+ }
+
+#if DEBUG
+ cli_putstr_P(PSTR("\r\nDBG: initshift = "));
+ cli_hexdump_rev(&i, 2);
+#endif
+ bigint_adjust(&x_);
+ bigint_adjust(&y_);
+
+ if(i){
+ bigint_shiftleft(&g, i);
+#if DEBUG
+ cli_putstr_P(PSTR("\r\nDBG: initshift (2) = "));
+ cli_hexdump_rev(&i, 2);
+ cli_putstr_P(PSTR("\r\n x' = "));
+ bigint_print_hex(&x_);
+ cli_putstr_P(PSTR("\r\n y' = "));
+ bigint_print_hex(&y_);
+#endif
+ bigint_shiftright(&x_, i);
+ bigint_shiftright(&y_, i);
+#if DEBUG
+ cli_putstr_P(PSTR("\r\n x' = "));
+ bigint_print_hex(&x_);
+ cli_putstr_P(PSTR("\r\n y' = "));
+ bigint_print_hex(&y_);
+#endif
+ }
+ 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{
+#if DEBUG
+ cli_putstr_P(PSTR("\r\n while u%2==0; u = "));
+ bigint_print_hex(&u);
+ cli_putstr_P(PSTR("\r\nDBG: (10) a = "));
+ bigint_print_hex(&a_);
+ cli_putstr_P(PSTR("\r\nDBG: (10) b = "));
+ bigint_print_hex(&b_);
+ cli_putstr_P(PSTR("\r\nDBG: (10) c = "));
+ bigint_print_hex(&c_);
+ cli_putstr_P(PSTR("\r\nDBG: (10) d = "));
+ bigint_print_hex(&d_);
+#endif
+ while((u.wordv[0]&1)==0){
+ 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);
+ }
+#if DEBUG
+ cli_putstr_P(PSTR("\r\n while v%2==0; v = "));
+ bigint_print_hex(&v);
+ cli_putstr_P(PSTR("\r\nDBG: (20) a = "));
+ bigint_print_hex(&a_);
+ cli_putstr_P(PSTR("\r\nDBG: (20) b = "));
+ bigint_print_hex(&b_);
+ cli_putstr_P(PSTR("\r\nDBG: (20) c = "));
+ bigint_print_hex(&c_);
+ cli_putstr_P(PSTR("\r\nDBG: (20) d = "));
+ bigint_print_hex(&d_);
+#endif
+ while((v.wordv[0]&1)==0){
+ 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 DEBUG
+ cli_putstr_P(PSTR("\r\n if u>=v ..."));
+ cli_putstr_P(PSTR("\r\nDBG: (30) a = "));
+ bigint_print_hex(&a_);
+ cli_putstr_P(PSTR("\r\nDBG: (30) b = "));
+ bigint_print_hex(&b_);
+ cli_putstr_P(PSTR("\r\nDBG: (30) c = "));
+ bigint_print_hex(&c_);
+ cli_putstr_P(PSTR("\r\nDBG: (30) d = "));
+ bigint_print_hex(&d_);
+#endif
+ 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_);
+ }
+#if DEBUG
+ if(GET_SIGN(&u)){
+ cli_putstr_P(PSTR("\r\nDBG: u negative! u = "));
+ bigint_print_hex(&u);
+ }
+ if(GET_SIGN(&v)){
+ cli_putstr_P(PSTR("\r\nDBG: v negative! v = "));
+ bigint_print_hex(&v);
+ }
+#endif
+/*
+ cli_putstr_P(PSTR("\r\nDBG: (2) a = "));
+ bigint_print_hex(&a_);
+ cli_putstr_P(PSTR("\r\nDBG: (2) b = "));
+ bigint_print_hex(&b_);
+ cli_putstr_P(PSTR("\r\nDBG: (2) c = "));
+ bigint_print_hex(&c_);
+ cli_putstr_P(PSTR("\r\nDBG: (2) d = "));
+ bigint_print_hex(&d_);
+*/
+ }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, bigint_t* a, bigint_t* m){
+ bigint_gcdext(NULL, dest, NULL, a, m);
+ while(dest->info&BIGINT_NEG_MASK){
+ bigint_add_s(dest, dest, m);
+ }
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
projects / avr-crypto-lib.git / blobdiff