--- /dev/null
+/* ecc_chudnovsky.c */
+/*
+ This file is part of the ARM-Crypto-Lib.
+ Copyright (C) 2006-2012 Daniel Otte (daniel.otte@rub.de)
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#include <stdlib.h>
+#include <string.h>
+#include "bigint.h"
+#include "ecc.h"
+#include <stdlib.h>
+#include <string.h>
+
+#if 1
+#include <stdio.h>
+#include "bigint_io.h"
+#include "uart_i.h"
+#include <avr/pgmspace.h>
+#endif
+
+#if 0
+#define printf_P(...)
+#define bigint_print_hex(a)
+#undef putchar
+#define putchar(a)
+#endif
+
+/*
+ * if (Y == 0)
+ * return POINT_AT_INFINITY
+ * S = 4*X*Y^2
+ * M = 3*(X + Z^2)*(X - Z^2)
+ * X' = M^2 - 2*S
+ * Y' = M*(S - X') - 8*Y^4
+ * Z' = 2*Y*Z
+ * Z'^2 = Z'^2
+ * Z'^3 = Z'^2 * Z'
+ * return (X', Y', Z', Z'^2, Z'^3)
+ */
+
+uint8_t ecc_affine_to_chudnovsky_point(ecc_chudnovsky_point_t *dest,
+ const ecc_affine_point_t *src){
+ if(src->y.length_W == 0){
+ /* point at infinity */
+ bigint_set_zero(&dest->y);
+ return 0;
+ }
+ bigint_copy(&dest->x, &src->x);
+ bigint_copy(&dest->y, &src->y);
+ dest->z1.wordv[0] = 1;
+ dest->z2.wordv[0] = 1;
+ dest->z3.wordv[0] = 1;
+ dest->z1.length_W = 1;
+ dest->z2.length_W = 1;
+ dest->z3.length_W = 1;
+ dest->z1.info = 0;
+ dest->z2.info = 0;
+ dest->z3.info = 0;
+ bigint_adjust(&dest->z1);
+ bigint_adjust(&dest->z2);
+ bigint_adjust(&dest->z3);
+ return 0;
+}
+
+uint8_t ecc_chudnovsky_to_affine_point(ecc_affine_point_t *dest,
+ const ecc_chudnovsky_point_t *src,
+ const ecc_curve_sp_t *curve){
+ if(src->y.length_W == 0){
+ /* point at infinity */
+ bigint_set_zero(&dest->y);
+ return 0;
+ }
+ bigint_word_t t_w[curve->p->length_W * 2];
+ bigint_word_t z1_w[curve->p->length_W * 2];
+ bigint_word_t z2_w[curve->p->length_W];
+ bigint_t t, z1, z2;
+ t.wordv = t_w;
+ z1.wordv = z1_w;
+ z2.wordv = z2_w;
+
+ bigint_inverse(&z1, &src->z1, curve->p);
+ bigint_square(&t, &z1);
+ curve->reduce_p(&t);
+ bigint_copy(&z2, &t);
+ bigint_mul_u(&t, &src->x, &z2);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->x, &t);
+ bigint_mul_u(&t, &z1, &z2);
+ curve->reduce_p(&t);
+ bigint_mul_u(&t, &t, &src->y);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->y, &t);
+
+ return 0;
+}
+
+void ecc_chudnovsky_point_print(const ecc_chudnovsky_point_t *p){
+ if(p->y.length_W == 0){
+ printf_P(PSTR(" ECC point = point-at-infinity\n"));
+ return;
+ }
+ printf_P(PSTR(" ECC point x = "));
+ bigint_print_hex(&p->x);
+ printf_P(PSTR("\n ECC point y = "));
+ bigint_print_hex(&p->y);
+ printf_P(PSTR("\n ECC point z1 = "));
+ bigint_print_hex(&p->z1);
+ printf_P(PSTR("\n ECC point z2 = "));
+ bigint_print_hex(&p->z2);
+ printf_P(PSTR("\n ECC point z3 = "));
+ bigint_print_hex(&p->z3);
+ putchar('\n');
+}
+
+uint8_t ecc_chudnovsky_point_double_sp(ecc_chudnovsky_point_t *dest,
+ const ecc_chudnovsky_point_t *a,
+ const ecc_curve_sp_t *curve){
+ if(a->y.length_W == 0){
+ /* point at infinity */
+ bigint_set_zero(&dest->y);
+ return 0;
+ }
+ bigint_word_t s_w[curve->p->length_W * 2];
+ bigint_word_t m_w[curve->p->length_W * 2];
+ bigint_word_t t_w[curve->p->length_W * 2];
+ bigint_t s, m, t;
+
+ s.wordv = s_w;
+ m.wordv = m_w;
+ t.wordv = t_w;
+
+ /* compute s*/
+ bigint_square(&t, &a->y);
+ curve->reduce_p(&t);
+ bigint_mul_u(&s, &t, &a->x);
+ curve->reduce_p(&s);
+ bigint_shiftleft(&s, 2);
+ curve->reduce_p(&s);
+
+ /* compute m */
+ bigint_sub_u(&t, &a->x, &a->z2);
+// /**/curve->reduce_p(&t);
+ bigint_add_u(&m, &a->x, &a->z2);
+// /**/curve->reduce_p(&m);
+ bigint_mul_s(&m, &m, &t);
+ curve->reduce_p(&m);
+ bigint_copy(&t, &m);
+ bigint_shiftleft(&t, 1);
+ bigint_add_s(&m, &m, &t);
+ curve->reduce_p(&m);
+
+ /* compute new z1 */
+ bigint_mul_u(&t, &a->z1, &a->y);
+ curve->reduce_p(&t);
+ bigint_shiftleft(&t, 1);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->z1, &t);
+
+ /* compute new x */
+ bigint_square(&t, &m);
+ curve->reduce_p(&t);
+ bigint_sub_s(&t, &t, &s);
+ bigint_sub_s(&t, &t, &s);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->x, &t);
+
+ /* compute new y */
+ bigint_sub_s(&s, &s, &t);
+ curve->reduce_p(&s);
+ bigint_mul_s(&s, &s, &m);
+ curve->reduce_p(&s);
+ bigint_square(&t, &a->y);
+ curve->reduce_p(&t);
+ bigint_square(&t, &t);
+ curve->reduce_p(&t);
+ bigint_shiftleft(&t, 3);
+ curve->reduce_p(&t);
+ bigint_sub_s(&s, &s, &t);
+ curve->reduce_p(&s);
+ bigint_copy(&dest->y, &s);
+
+ /* compute new z2 */
+ bigint_square(&t, &dest->z1);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->z2, &t);
+
+ /* compute new z3 */
+ bigint_mul_u(&t, &t, &dest->z1);
+ curve->reduce_p(&t);
+ bigint_copy(&dest->z3, &t);
+
+ return 0;
+}
+
+void ecc_chudnovsky_point_copy(ecc_chudnovsky_point_t *dest,
+ const ecc_chudnovsky_point_t *src){
+ bigint_copy(&dest->x, &src->x);
+ bigint_copy(&dest->y, &src->y);
+ bigint_copy(&dest->z1, &src->z1);
+ bigint_copy(&dest->z2, &src->z2);
+ bigint_copy(&dest->z3, &src->z3);
+}
+
+uint8_t ecc_chudnovsky_point_add_sp(ecc_chudnovsky_point_t *dest,
+ const ecc_chudnovsky_point_t *a,
+ const ecc_chudnovsky_point_t *b,
+ const ecc_curve_sp_t *curve){
+ if(a->y.length_W == 0){
+ ecc_chudnovsky_point_copy(dest, b);
+ return 0;
+ }
+ if(b->y.length_W == 0){
+ ecc_chudnovsky_point_copy(dest, a);
+ return 0;
+ }
+ bigint_word_t u1_w[curve->p->length_W * 2];
+ bigint_word_t u2_w[curve->p->length_W * 2];
+ bigint_word_t s1_w[curve->p->length_W * 2];
+ bigint_word_t s2_w[curve->p->length_W * 2];
+ bigint_t u1, u2, s1, s2;
+
+ u1.wordv = u1_w;
+ u2.wordv = u2_w;
+ s1.wordv = s1_w;
+ s2.wordv = s2_w;
+
+ /* compute u1 */
+ bigint_mul_u(&u1, &a->x, &b->z2);
+ curve->reduce_p(&u1);
+
+ /* compute u2 */
+ bigint_mul_u(&u2, &b->x, &a->z2);
+ curve->reduce_p(&u2);
+
+ /* compute s1 */
+ bigint_mul_u(&s1, &a->y, &b->z3);
+ curve->reduce_p(&s1);
+
+ /* compute s2 */
+ bigint_mul_u(&s2, &b->y, &a->z3);
+ curve->reduce_p(&s2);
+
+ if(bigint_cmp_u(&u1, &u2) == 0){
+ if(bigint_cmp_u(&s1, &s2)){
+ /* point at infinity */
+ bigint_set_zero(&dest->y);
+ return 0;
+ }else{
+ /* a == b --> dest = 2*a */
+ ecc_chudnovsky_point_double_sp(dest, a, curve);
+ }
+ }
+
+ bigint_word_t h_w[curve->p->length_W * 2];
+ bigint_word_t r_w[curve->p->length_W * 2];
+ bigint_t h, r;
+
+ h.wordv = h_w;
+ r.wordv = r_w;
+ /* compute h */
+ bigint_sub_s(&h, &u2, &u1);
+ /**/curve->reduce_p(&h);
+
+ /* compute r */
+ bigint_sub_s(&r, &s2, &s1);
+// /**/curve->reduce_p(&r);
+
+ /* compute new z */
+ bigint_mul_u(&s2, &a->z1, &b->z1);
+ curve->reduce_p(&s2);
+ bigint_mul_s(&s2, &s2, &h);
+ curve->reduce_p(&s2);
+ bigint_copy(&dest->z1, &s2);
+
+ /* compute u1*h^2 and h^3 */
+ bigint_square(&s2, &h);
+ curve->reduce_p(&s2);
+ bigint_mul_s(&h, &s2, &h);
+ curve->reduce_p(&h);
+ bigint_mul_s(&u1, &s2, &u1);
+ curve->reduce_p(&u1);
+
+ /* compute new x */
+ bigint_square(&u2, &r);
+ curve->reduce_p(&u2);
+ bigint_sub_s(&u2, &u2, &h);
+ curve->reduce_p(&u2);
+ bigint_sub_s(&u2, &u2, &u1);
+ bigint_sub_s(&u2, &u2, &u1);
+ curve->reduce_p(&u2);
+ bigint_copy(&dest->x, &u2);
+
+ /* compute new y */
+ bigint_sub_s(&u1, &u1, &u2);
+ curve->reduce_p(&u1);
+ bigint_mul_s(&s2, &u1, &r);
+ curve->reduce_p(&s2);
+ bigint_mul_s(&s1, &s1, &h);
+ curve->reduce_p(&s1);
+ bigint_sub_s(&s2, &s2, &s1);
+ curve->reduce_p(&s2);
+ bigint_copy(&dest->y, &s2);
+
+
+ /* compute new z2 */
+ bigint_square(&s1, &dest->z1);
+ curve->reduce_p(&s1);
+ bigint_copy(&dest->z2, &s1);
+
+ /* compute new z2 */
+ bigint_mul_u(&s1, &s1, &dest->z1);
+ curve->reduce_p(&s1);
+ bigint_copy(&dest->z3, &s1);
+
+ return 0;
+}
+
+uint8_t ecc_chudnovsky_double_and_add(ecc_chudnovsky_point_t *dest,
+ const bigint_t *k,
+ const ecc_chudnovsky_point_t *p,
+ const ecc_curve_sp_t* curve){
+ uint16_t i;
+ uint8_t s = 0;
+ bigint_word_t v, t;
+
+ for(i = k->length_W; i > 0; --i){
+ v = 1 << (BIGINT_WORD_SIZE - 1);
+ t = k->wordv[i - 1];
+ do{
+ if(s){
+ ecc_chudnovsky_point_double_sp(dest, dest, curve);
+ if(v & t){
+ ecc_chudnovsky_point_add_sp(dest, dest, p, curve);
+ }
+ }else{
+ if(v & t){
+ s = 1;
+ ecc_chudnovsky_point_copy(dest, p);
+ }
+ }
+ v >>= 1;
+ }while(v);
+ }
+ return 0;
+}
+
+uint8_t bigint_to_naf(uint8_t* dest, uint16_t *length, const bigint_t *src){
+ if(src->length_W == 0){
+ *dest = 0;
+ *length = 2;
+ return 0;
+ }
+
+ memset(dest, 0, src->length_W * sizeof(bigint_word_t));
+
+ uint16_t i = 0;
+ uint8_t t; /* 3 -> -1 ; 1 -> 1; 0 -> 0 (2 should not happen) */
+ bigint_t k, p;
+ bigint_word_t k_w[src->length_W];
+ bigint_word_t p_w = 1;
+ p.wordv = &p_w;
+ p.info = 0;
+ p.length_W = 1;
+ k.wordv = k_w;
+ bigint_copy(&k, src);
+
+ while(k.length_W >= 1){
+ if(k.wordv[0] & 1){
+ t = k.wordv[0] & 3;
+ if(t == 1){
+ bigint_sub_u(&k, &k, &p);
+ }else{
+ bigint_add_u(&k, &k, &p);
+ }
+ }else{
+ t = 0;
+ }
+ dest[(i * 2) / 8] |= t << ((2 * i) & 7);
+ bigint_shiftright(&k, 1);
+ i += 1;
+ }
+ *length = i;
+ return 0;
+}
+
+void print_naf(uint8_t* naf, uint16_t length){
+ if(!length){
+ return;
+ }
+ --length;
+ int8_t t;
+ do{
+ t = (naf[(length * 2) / 8] >> ((length * 2) & 7)) & 3;
+ switch(t & 3){
+ case 0: putchar('0'); break;
+ case 1: putchar('1'); break;
+ case 3: putchar('-'); putchar('1'); break;
+ default: putchar('E');
+ }
+ if(length){
+ putchar(' ');
+ }
+ }while(length--);
+}
+
+uint8_t ecc_chudnovsky_naf_multiplication(ecc_chudnovsky_point_t *dest,
+ const bigint_t *k,
+ const ecc_chudnovsky_point_t *p,
+ const ecc_curve_sp_t* curve){
+ if(k->length_W == 0 || p->y.length_W == 0){
+ bigint_set_zero(&dest->y);
+ return 0;
+ }
+
+ uint8_t *t, q;
+ uint16_t i;
+ ecc_chudnovsky_point_t p_;
+ bigint_word_t y_[curve->p->length_W];
+
+ /* p_ = -p*/
+
+ memcpy(&p_, p, sizeof(p_));
+ p_.y.wordv = y_;
+ bigint_copy(&p_.y, &p->y);
+ p_.y.info |= BIGINT_NEG_MASK;
+ bigint_add_s(&p_.y, &p_.y, curve->p);
+
+
+ if(!(t = malloc(k->length_W * sizeof(bigint_word_t) * 2))){
+ return 1;
+ }
+ bigint_to_naf(t, &i, k);
+
+ --i;
+ dest->y.length_W = 0;
+ do{
+ q = (t[(i * 2) / 8] >> ((i * 2) & 7)) & 3;
+ ecc_chudnovsky_point_double_sp(dest, dest, curve);
+ if(q == 1){
+ ecc_chudnovsky_point_add_sp(dest, dest, p, curve);
+ }
+ if(q == 3){
+ ecc_chudnovsky_point_add_sp(dest, dest, &p_, curve);
+ }
+ }while(i--);
+
+ free(t);
+
+ return 0;
+}
+
+uint8_t ecc_chudnovsky_multiplication(ecc_chudnovsky_point_t *dest,
+ const bigint_t *k,
+ const ecc_chudnovsky_point_t *p,
+ const ecc_curve_sp_t* curve){
+ return ecc_chudnovsky_naf_multiplication(dest, k, p, curve);
+}
projects / avr-crypto-lib.git / blobdiff