#include "bigint.h"
#include <string.h>
-#define DEBUG 0
+#define DEBUG 1
#if DEBUG || 1
#include "cli.h"
+#include "uart_i.h"
#include "bigint_io.h"
#include <stdio.h>
#endif
#endif
#ifndef MIN
- #define MIN(a,b) (((a)<(b))?(a):(b))
+ #define MIN(a,b) (((a) < (b)) ? (a) : (b))
#endif
-#define SET_FBS(a, v) do{(a)->info &=~BIGINT_FBS_MASK; (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(a,b) do{(a) ^= (b); (b) ^= (a); (a) ^= (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)
+ a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));} while(0)
-#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
+#define GET_SIGN(a) ((a)->info & BIGINT_NEG_MASK)
/******************************************************************************/
void bigint_adjust(bigint_t *a){
/******************************************************************************/
-uint16_t bigint_length_b(const bigint_t *a){
+bigint_length_t bigint_length_b(const bigint_t *a){
if(!a->length_W || a->length_W==0){
return 0;
}
/******************************************************************************/
-uint16_t bigint_length_B(const bigint_t *a){
+bigint_length_t bigint_length_B(const bigint_t *a){
return a->length_W * sizeof(bigint_word_t);
}
/* this should be implemented in assembly */
void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
- uint16_t i;
+ bigint_length_t i;
bigint_wordplus_t t = 0LL;
- if(a->length_W < b->length_W){
- XCHG_PTR(a,b);
+ if (a->length_W < b->length_W) {
+ XCHG_PTR(a, b);
}
- for(i = 0; i < b->length_W; ++i){
-// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
+ 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){
+ for(; i < a->length_W; ++i){
t += a->wordv[i];
dest->wordv[i] = (bigint_word_t)t;
t >>= BIGINT_WORD_SIZE;
dest->wordv[i++] = (bigint_word_t)t;
}
dest->length_W = i;
+ SET_POS(dest);
bigint_adjust(dest);
}
/******************************************************************************/
/* this should be implemented in assembly */
-void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale){
+void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){
if(a->length_W == 0){
return;
}
bigint_adjust(dest);
#else
bigint_t s;
- uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
+ bigint_length_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;
/* this should be implemented in assembly */
void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){
- int8_t borrow=0;
+ int8_t borrow = 0;
int8_t r;
- bigint_wordplus_signed_t t=0LL;
- uint16_t i;
+ bigint_wordplus_signed_t t = 0LL;
+ bigint_length_t i;
if(b->length_W == 0){
bigint_copy(dest, a);
SET_POS(dest);
t -= b->wordv[i];
}
t -= borrow;
- dest->wordv[i]=(bigint_word_t)t;
+ dest->wordv[i] = (bigint_word_t)t;
if(t<0){
borrow = 1;
}else{
if(a->length_W < b->length_W){
return -1;
}
- if(a->length_W==0){
+ if(a->length_W == 0){
return 0;
}
- uint16_t i;
- i = a->length_W-1;
+ bigint_length_t i;
+ i = a->length_W - 1;
do{
if(a->wordv[i] != b->wordv[i]){
if(a->wordv[i] > b->wordv[i]){
/******************************************************************************/
-void bigint_shiftleft(bigint_t *a, uint16_t shift){
- uint16_t byteshift, words_to_shift;
+void bigint_shiftleft(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift, words_to_shift;
int16_t i;
uint8_t bitshift;
bigint_word_t *p;
/******************************************************************************/
-void bigint_shiftright(bigint_t *a, uint16_t shift){
- uint16_t byteshift;
- uint16_t i;
+void bigint_shiftright(bigint_t *a, bigint_length_t shift){
+ bigint_length_t byteshift;
+ bigint_length_t i;
uint8_t bitshift;
bigint_wordplus_t t = 0;
byteshift = shift / 8;
/******************************************************************************/
void bigint_xor(bigint_t *dest, const bigint_t *a){
- uint16_t i;
+ bigint_length_t i;
for(i=0; i<a->length_W; ++i){
dest->wordv[i] ^= a->wordv[i];
}
XCHG_PTR(a,b);
}
bigint_wordplus_t t = 0;
- uint16_t i;
+ bigint_length_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);
return;
}
/* split a in xh & xl; split b in yh & yl */
- const uint16_t n = (MAX(a->length_W, b->length_W)+1)/2;
+ const bigint_length_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 OLD_SQUARE
#if DEBUG_SQUARE
unsigned square_depth = 0;
/* 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_W * sizeof(bigint_word_t) <= 4){
+ 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;
bigint_adjust(dest);
return;
}
+
if(dest->wordv == a->wordv){
bigint_t d;
bigint_word_t d_b[a->length_W*2];
bigint_copy(dest, &d);
return;
}
-
+ bigint_fast_square(dest, a);
+ return;
#if DEBUG_SQUARE
square_depth += 1;
#endif
- uint16_t n;
+ bigint_length_t n;
n=(a->length_W+1)/2;
bigint_t xh, xl, tmp; /* x-high, x-low, temp */
bigint_word_t buffer[2*n+1];
#endif
}
+#endif
+
+/******************************************************************************/
+
+void bigint_square(bigint_t *dest, const bigint_t *a) {
+ union {
+ bigint_word_t u[2];
+ bigint_wordplus_t uv;
+ } acc;
+ bigint_word_t q, c1, c2;
+ bigint_length_t i, j;
+
+ 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_W = 2 * a->length_W;
+ bigint_adjust(dest);
+ return;
+ }
+
+ if(dest->wordv == a->wordv){
+ bigint_t d;
+ bigint_word_t d_b[a->length_W*2];
+ d.wordv = d_b;
+ bigint_square(&d, a);
+ bigint_copy(dest, &d);
+ return;
+ }
+
+ memset(dest->wordv, 0, a->length_W * 2 * sizeof(bigint_word_t));
+
+ for (i = 0; i < a->length_W; ++i) {
+ acc.uv = a->wordv[i] * a->wordv[i] + dest->wordv[2 * i];
+ dest->wordv[2 * i] = acc.u[0];
+ c1 = acc.u[1];
+ c2 = 0;
+ for (j = i + 1; j < a->length_W; ++j) {
+ acc.uv = a->wordv[i] * a->wordv[j];
+ q = acc.u[1] >> (BIGINT_WORD_SIZE - 1);
+ acc.uv <<= 1;
+ acc.uv += dest->wordv[i + j];
+ q += (acc.uv < dest->wordv[i + j]);
+ acc.uv += c1;
+ q += (acc.uv < c1);
+ dest->wordv[i + j] = acc.u[0];
+ c1 = acc.u[1] + c2;
+ c2 = q + (c1 < c2);
+ }
+ dest->wordv[i + a->length_W] += c1;
+ dest->wordv[i + a->length_W + 1] = c2 + (dest->wordv[i + a->length_W] < c1);
+ }
+ SET_POS(dest);
+ dest->length_W = 2 * a->length_W;
+ bigint_adjust(dest);
+}
+
/******************************************************************************/
-void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale){
+void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){
bigint_t tmp, x;
bigint_word_t tmp_b[b->length_W + 1];
- const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
+ const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE;
if(a->length_W < b->length_W + word_shift){
#if DEBUG
/******************************************************************************/
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_W==0 || a->length_W==0){
return;
}
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;
}
- uint16_t shift;
+ bigint_length_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) && (a->length_W == r->length_W)){
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_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
- if(a->length_W==0 || r->length_W==0){
+ if(a->length_W == 0){
+ bigint_set_zero(dest);
return;
}
bigint_t res, base;
- bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2];
- uint16_t i;
+ bigint_word_t t, base_w[MAX(a->length_W,r->length_W)], res_w[r->length_W*2];
+ bigint_length_t i;
uint8_t j;
-// uint16_t *xaddr = &i;
+// bigint_length_t *xaddr = &i;
// cli_putstr("\r\npre-alloc (");
// cli_hexdump_rev(&xaddr, 4);
// cli_putstr(") ...");
- res.wordv = res_b;
- base.wordv = base_b;
+ res.wordv = res_w;
+ base.wordv = base_w;
bigint_copy(&base, a);
// cli_putstr("\r\npost-copy");
bigint_reduce(&base, r);
- res.wordv[0]=1;
- res.length_W=1;
+ res.wordv[0] = 1;
+ res.length_W = 1;
res.info = 0;
bigint_adjust(&res);
if(exp->length_W == 0){
}
uint8_t flag = 0;
t=exp->wordv[exp->length_W - 1];
- for(i=exp->length_W; i > 0; --i){
+ for(i = exp->length_W; i > 0; --i){
t = exp->wordv[i - 1];
- for(j=BIGINT_WORD_SIZE; j > 0; --j){
+ for(j = BIGINT_WORD_SIZE; j > 0; --j){
if(!flag){
- if(t & (1<<(BIGINT_WORD_SIZE-1))){
+ if(t & (1 << (BIGINT_WORD_SIZE - 1))){
flag = 1;
}
}
}
/******************************************************************************/
-#if 1
-#define cli_putstr(a)
-#define cli_putstr_P(a)
-#define bigint_print_hex(a)
-#define cli_hexdump_rev(a,b)
-#define uart_flush(a)
-#define printf_P(...)
-#endif
/* 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){
- uint16_t i = 0;
- printf_P(PSTR("\nDBG: gcdext( "));
- bigint_print_hex(x);
- printf_P(PSTR(", "));
- bigint_print_hex(y);
- printf_P(PSTR(")\n"));
+ bigint_length_t i = 0;
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);
}
d_.info = 0;
bigint_set_zero(&b_);
bigint_set_zero(&c_);
- printf_P(PSTR("\nloop: x_ = "));
- bigint_print_hex(&x_);
- printf_P(PSTR("; y_ = "));
- bigint_print_hex(&y_);
do{
- printf_P(PSTR("\nDBG (gcdext) 0"));
while((u.wordv[0] & 1) == 0){
- printf_P(PSTR("\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(&a_, 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){
- printf_P(PSTR("\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_);
}
- printf_P(PSTR(" c* = "));
- bigint_print_hex(&c_);
bigint_shiftright(&c_, 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){
- printf_P(PSTR("\nDBG (gcdext) 0.3"));
bigint_sub_u(&u, &u, &v);
bigint_sub_s(&a_, &a_, &c_);
bigint_sub_s(&b_, &b_, &d_);
- printf_P(PSTR(" a_ = "));
- bigint_print_hex(&a_);
- printf_P(PSTR("; b_ = "));
- bigint_print_hex(&b_);
}else{
- printf_P(PSTR("\nDBG (gcdext) 0.4"));
bigint_sub_u(&v, &v, &u);
bigint_sub_s(&c_, &c_, &a_);
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);
if(gcd){
/******************************************************************************/
+void bigint_mul_word_u(bigint_t *a, bigint_word_t b){
+ bigint_wordplus_t c0 = 0, c1 = 0;
+ bigint_length_t i;
+
+ if(b == 0){
+ bigint_set_zero(a);
+ return;
+ }
+
+ for(i = 0; i < a->length_W; ++i){
+ c1 = ((bigint_wordplus_t)(a->wordv[i])) * ((bigint_wordplus_t)b);
+ c1 += c0;
+ a->wordv[i] = (bigint_word_t)c1;
+ c0 = c1 >> BIGINT_WORD_SIZE;
+ }
+ if(c0){
+ a->wordv[a->length_W] = (bigint_word_t)c0;
+ a->length_W += 1;
+ }
+ bigint_adjust(a);
+}
+
+/******************************************************************************/
+#if 1
+
+void bigint_clip(bigint_t *dest, bigint_length_t length_W){
+ if(dest->length_W > length_W){
+ dest->length_W = length_W;
+ }
+ bigint_adjust(dest);
+}
+/******************************************************************************/
+
+/*
+ * m_ = m * m'[0]
+ */
+
+void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_){
+ const bigint_length_t s = MAX(MAX(a->length_W, b->length_W), m->length_W);
+ bigint_t u, t;
+ bigint_word_t u_w[s + 2], t_w[s + 2];
+ bigint_length_t i;
+
+ if (a->length_W == 0 || b->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ u.wordv = u_w;
+ u.info = 0;
+ u.length_W = 0;
+ t.wordv = t_w;
+ for (i = 0; i < a->length_W; ++i) {
+ bigint_copy(&t, b);
+ bigint_mul_word_u(&t, a->wordv[i]);
+ bigint_add_u(&u, &u, &t);
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ for (; i < s; ++i) {
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+}
+
+/******************************************************************************/
+
+void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_){
+ bigint_t u, t;
+ bigint_length_t i, s = MAX(a->length_W, m->length_W);
+ bigint_word_t u_w[s + 2], t_w[s + 2];
+ t.wordv = t_w;
+ u.wordv = u_w;
+ if (a->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ bigint_copy(&u, a);
+ for (i = 0; i < m->length_W; ++i) {
+ bigint_copy(&t, m_);
+ if (u.length_W != 0) {
+ bigint_mul_word_u(&t, u.wordv[0]);
+ bigint_add_u(&u, &u, &t);
+ }
+ bigint_shiftright(&u, BIGINT_WORD_SIZE);
+ }
+ bigint_reduce(&u, m);
+ bigint_copy(dest, &u);
+}
+/******************************************************************************/
+/*
+ * m_ = m * (- m0^-1 (mod 2^W))
+ */
+void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m){
+ bigint_word_t x_w[2], m_w_0[1];
+ bigint_t x, m_0;
+ if (m->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ if ((m->wordv[0] & 1) == 0) {
+ printf_P(PSTR("ERROR: m must not be even, m = "));
+ bigint_print_hex(m);
+ putchar('\n');
+ uart0_flush();
+ return;
+ }
+ x.wordv = x_w;
+ x.info = 0;
+ x.length_W = 2;
+ x_w[0] = 0;
+ x_w[1] = 1;
+ m_0.wordv = m_w_0;
+ m_0.info = 0;
+ m_0.length_W = 1;
+ m_0.wordv[0] = m->wordv[0];
+ bigint_adjust(&x);
+ bigint_adjust(&m_0);
+ bigint_inverse(dest, &m_0, &x);
+ bigint_sub_s(&x, &x, dest);
+ bigint_copy(dest, m);
+ bigint_mul_word_u(dest, x.wordv[0]);
+}
/******************************************************************************/
+/*
+ * dest = a * R mod m
+ */
+void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m){
+ bigint_t t;
+ bigint_word_t t_w[a->length_W + m->length_W];
+
+ t.wordv = t_w;
+ memset(t_w, 0, m->length_W * sizeof(bigint_word_t));
+ memcpy(t_w + m->length_W * sizeof(bigint_word_t), a->wordv, a->length_W * sizeof(bigint_word_t));
+ t.info = a->info;
+ t.length_W = a->length_W + m->length_W;
+ bigint_reduce(&t, m);
+ bigint_copy(dest, &t);
+}
+
+/******************************************************************************/
+
+/* calculate dest = a**exp % r */
+/* using square&multiply */
+void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
+ if(r->length_W == 0) {
+ return;
+ }
+ if(a->length_W == 0) {
+ bigint_set_zero(dest);
+ return;
+ }
+ bigint_length_t s = r->length_W;
+ bigint_t res, m_, ax;
+ bigint_word_t t, res_w[r->length_W*2], ax_w[MAX(s, a->length_W)];
+ bigint_word_t m_w_[s + 1];
+ bigint_length_t i;
+ uint8_t j;
+
+ res.wordv = res_w;
+ m_.wordv = m_w_;
+ ax.wordv = ax_w;
+
+ res.wordv[0] = 1;
+ res.length_W = 1;
+ res.info = 0;
+ bigint_adjust(&res);
+ if (exp->length_W == 0) {
+ bigint_copy(dest, &res);
+ return;
+ }
+ bigint_copy(&ax, a);
+ bigint_reduce(&ax, r);
+ bigint_mont_trans(&ax, &ax, r);
+ bigint_mont_trans(&res, &res, r);
+ bigint_mont_gen_m_(&m_, r);
+ 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_mont_red(&res, &res, r, &m_);
+ if (t & (1 << (BIGINT_WORD_SIZE - 1))) {
+ bigint_mont_mul(&res, &res, &ax, r, &m_);
+ }
+ }
+ t <<= 1;
+ }
+ }
+ SET_POS(&res);
+ bigint_mont_red(dest, &res, r, &m_);
+}
+
+/******************************************************************************/
+
+#endif
+
void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){
- bigint_expmod_u_sam(dest, a, exp, r);
+ if (r->wordv[0] & 1) {
+ bigint_expmod_u_mont_sam(dest, a, exp, r);
+ } else {
+ bigint_expmod_u_sam(dest, a, exp, r);
+ }
}
#ifndef BIGINT_H_
#define BIGINT_H_
+#include <stddef.h>
#include <stdint.h>
-typedef uint8_t bigint_word_t;
+typedef uint8_t bigint_word_t;
typedef uint16_t bigint_wordplus_t;
typedef int16_t bigint_wordplus_signed_t;
#define BIGINT_WORD_SIZE 8
#define BIGINT_FBS_MASK (BIGINT_WORD_SIZE-1) /* the last five bits indicate which is the first bit set */
#define BIGINT_NEG_MASK 0x80 /* this bit indicates a negative value */
+
+typedef size_t bigint_length_t;
+typedef uint_fast8_t bigint_info_t;
+
typedef struct{
- uint16_t length_W;
- uint8_t info;
- bigint_word_t *wordv; /* word vector, pointing to the LSB */
+ bigint_length_t length_W;
+ bigint_info_t info;
+ bigint_word_t *wordv; /* word vector, pointing to the LSB */
}bigint_t;
void bigint_adjust(bigint_t *a);
uint32_t bigint_get_first_set_bit(const bigint_t *a);
uint32_t bigint_get_last_set_bit(const bigint_t *a);
-uint16_t bigint_length_b(const bigint_t *a);
-uint16_t bigint_length_B(const bigint_t *a);
+bigint_length_t bigint_length_b(const bigint_t *a);
+bigint_length_t bigint_length_B(const bigint_t *a);
void bigint_copy(bigint_t *dest, const bigint_t *src);
void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b);
-void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale);
+void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale);
void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b);
int8_t bigint_cmp_u(const bigint_t * a, const bigint_t * b);
void bigint_add_s(bigint_t *dest, const bigint_t *a, const bigint_t *b);
void bigint_sub_s(bigint_t *dest, const bigint_t *a, const bigint_t *b);
int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b);
-void bigint_shiftleft(bigint_t *a, uint16_t shift);
-void bigint_shiftright(bigint_t *a, uint16_t shift);
+void bigint_shiftleft(bigint_t *a, bigint_length_t shift);
+void bigint_shiftright(bigint_t *a, bigint_length_t shift);
void bigint_xor(bigint_t *dest, const bigint_t *a);
void bigint_set_zero(bigint_t *a);
void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b);
void bigint_mul_s(bigint_t *dest, const bigint_t *a, const bigint_t *b);
void bigint_square(bigint_t *dest, const bigint_t *a);
-void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale);
+void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale);
void bigint_reduce(bigint_t *a, const bigint_t *r);
-void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r);
+void bigint_mul_word_u(bigint_t *a, bigint_word_t b);
void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, const bigint_t *y);
void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m);
void bigint_changeendianess(bigint_t *a);
-/******************************************************************************/
+void bigint_clip(bigint_t *dest, bigint_length_t s);
+void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_);
+void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_);
+void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m);
+void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m);
+
+void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r);
+void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r);
+void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r);
+
#endif /*BIGINT_H_*/
}
}
+void test_mul_mont_bigint(void){
+ bigint_t a, b, c, a_, b_, m_, res;
+ bigint_length_t s;
+ cli_putstr_P(PSTR("\r\nmul-mont test ( (a * b) % c )\r\n"));
+ for(;;){
+ cli_putstr_P(PSTR("\r\nenter a:"));
+ if(bigint_read_hex_echo(&a)){
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\nenter b:"));
+ if(bigint_read_hex_echo(&b)){
+ free(a.wordv);
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\nenter c:"));
+ if(bigint_read_hex_echo(&c)){
+ free(a.wordv);
+ free(b.wordv);
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ return;
+ }
+ s = c.length_W;
+ cli_putstr_P(PSTR("\r\n ("));
+ bigint_print_hex(&a);
+ cli_putstr_P(PSTR(" * "));
+ bigint_print_hex(&b);
+ cli_putstr_P(PSTR(") % "));
+ bigint_print_hex(&c);
+ cli_putstr_P(PSTR(" = "));
+ bigint_word_t res_w[s], a_w_[s], b_w_[s], m_w_[s + 1];
+ res.wordv = res_w;
+ a_.wordv = a_w_;
+ b_.wordv = b_w_;
+ m_.wordv = m_w_;
+ bigint_mont_gen_m_(&m_, &c);
+ bigint_mont_trans(&a_, &a, &c);
+ bigint_mont_trans(&b_, &b, &c);
+ bigint_mont_mul(&res, &a_, &b_, &c, &m_);
+ bigint_mont_red(&res, &res, &c, &m_);
+ bigint_print_hex(&res);
+ putchar('\n');
+ free(a.wordv);
+ free(b.wordv);
+ free(c.wordv);
+ }
+}
+
+void test_mul_word_bigint(void){
+ bigint_t a, b;
+ bigint_word_t *t;
+ cli_putstr_P(PSTR("\r\nmul test\r\n"));
+ for(;;){
+ cli_putstr_P(PSTR("\r\nenter a:"));
+ if(bigint_read_hex_echo(&a)){
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\nenter b:"));
+ if(bigint_read_hex_echo(&b)){
+ free(a.wordv);
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\n "));
+ bigint_print_hex(&a);
+ cli_putstr_P(PSTR(" * "));
+ bigint_print_hex(&b);
+ cli_putstr_P(PSTR(" = "));
+
+ if(b.length_W > 1){
+ free(a.wordv);
+ free(b.wordv);
+ cli_putstr_P(PSTR("\r\n end mul test"));
+ }
+
+ t = realloc(a.wordv, a.length_W + 3);
+ if(t == NULL){
+ cli_putstr_P(PSTR("\n\rERROR: Out of memory!"));
+ free(a.wordv);
+ free(b.wordv);
+ continue;
+ }
+ a.wordv = t;
+ bigint_mul_word_u(&a, b.wordv[0]);
+ bigint_print_hex(&a);
+ cli_putstr_P(PSTR("\r\n"));
+ free(a.wordv);
+ free(b.wordv);
+ }
+}
+
void test_square_bigint(void){
bigint_t a, c;
cli_putstr_P(PSTR("\r\nsquare test\r\n"));
void test_expmod_bigint(void){
bigint_t a, b, c, d;
uint8_t *d_b;
- cli_putstr_P(PSTR("\r\nreduce test\r\n"));
+ cli_putstr_P(PSTR("\r\nexpnonentiation-modulo test\r\n"));
for(;;){
cli_putstr_P(PSTR("\r\nenter a:"));
if(bigint_read_hex_echo(&a)){
}
}
+/* d = a**b % c */
+void test_expmod_mont_bigint(void){
+ bigint_t a, b, c, d;
+ uint8_t *d_b;
+ cli_putstr_P(PSTR("\r\nexpnonentiation-modulo-montgomory test\r\n"));
+ for(;;){
+ cli_putstr_P(PSTR("\r\nenter a:"));
+ if(bigint_read_hex_echo(&a)){
+ cli_putstr_P(PSTR("\r\n end expmod test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\nenter b:"));
+ if(bigint_read_hex_echo(&b)){
+ free(a.wordv);
+ cli_putstr_P(PSTR("\r\n end expmod test"));
+ return;
+ }
+ cli_putstr_P(PSTR("\r\nenter c:"));
+ if(bigint_read_hex_echo(&c)){
+ free(a.wordv);
+ free(b.wordv);
+ cli_putstr_P(PSTR("\r\n end expmod test"));
+ return;
+ }
+ d_b = malloc(c.length_W);
+ if(d_b==NULL){
+ cli_putstr_P(PSTR("\n\rERROR: Out of memory!"));
+ free(a.wordv);
+ free(b.wordv);
+ free(c.wordv);
+ continue;
+ }
+ d.wordv = d_b;
+ cli_putstr_P(PSTR("\r\n "));
+ bigint_print_hex(&a);
+ cli_putstr_P(PSTR("**"));
+ bigint_print_hex(&b);
+ cli_putstr_P(PSTR(" % "));
+ bigint_print_hex(&c);
+ cli_putstr_P(PSTR(" = "));
+ bigint_expmod_u_mont_sam(&d, &a, &b, &c);
+ bigint_print_hex(&d);
+ cli_putstr_P(PSTR("\r\n"));
+ free(a.wordv);
+ free(b.wordv);
+ free(c.wordv);
+ free(d.wordv);
+
+ }
+}
+
void test_gcdext_bigint(void){
bigint_t a, b, c, d, e;
cli_putstr_P(PSTR("\r\ngcdext test\r\n"));
const char add_test_str[] PROGMEM = "add-test";
const char add_scale_test_str[] PROGMEM = "add-scale-test";
const char mul_test_str[] PROGMEM = "mul-test";
+const char mul_mont_test_str[] PROGMEM = "mul-mont-test";
+const char mul_word_test_str[] PROGMEM = "mul-word-test";
const char square_test_str[] PROGMEM = "square-test";
const char reduce_test_str[] PROGMEM = "reduce-test";
const char expmod_test_str[] PROGMEM = "expmod-test";
+const char expmod_mont_test_str[] PROGMEM = "expmod-mont-test";
const char gcdext_test_str[] PROGMEM = "gcdext-test";
const char quick_test_str[] PROGMEM = "quick-test";
const char performance_str[] PROGMEM = "performance";
{ add_test_str, NULL, test_add_bigint },
{ add_scale_test_str, NULL, test_add_scale_bigint },
{ mul_test_str, NULL, test_mul_bigint },
+ { mul_mont_test_str, NULL, test_mul_mont_bigint },
+ { mul_word_test_str, NULL, test_mul_word_bigint },
{ square_test_str, NULL, test_square_bigint },
{ reduce_test_str, NULL, test_reduce_bigint },
- { expmod_test_str, NULL, test_expmod_bigint },
+ { expmod_test_str, NULL, test_expmod_bigint },
+ { expmod_mont_test_str, NULL, test_expmod_mont_bigint },
{ gcdext_test_str, NULL, test_gcdext_bigint },
{ quick_test_str, NULL, test_gcdext_simple },
{ echo_test_str, NULL, test_echo_bigint },
projects / avr-crypto-lib.git / commitdiff