--- /dev/null
+/* ecc.h */
+/*
+ This file is part of the AVR-Crypto-Lib.
+ Copyright (C) 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/>.
+*/
+
+#ifndef ECC_H_
+#define ECC_H_
+
+typedef struct {
+ bigint_t x;
+ bigint_t y;
+ bigint_t z1;
+ bigint_t z2;
+ bigint_t z3;
+} ecc_chudnovsky_point_t;
+
+typedef struct {
+ bigint_t x;
+ bigint_t y;
+} ecc_affine_point_t;
+
+typedef struct __attribute__((packed)){
+ ecc_affine_point_t affine;
+ ecc_chudnovsky_point_t chudnovsky;
+} ecc_combi_point_t;
+
+typedef struct {
+ bigint_t* p;
+ bigint_t* b;
+ int (*reduce_p)(bigint_t*);
+} ecc_curve_sp_t;
+
+void ecc_chudnovsky_point_print(const ecc_chudnovsky_point_t *p);
+
+
+uint8_t ecc_affine_to_chudnovsky_point(ecc_chudnovsky_point_t *dest,
+ const ecc_affine_point_t *src);
+uint8_t ecc_chudnovsky_to_affine_point(ecc_affine_point_t *dest,
+ const ecc_chudnovsky_point_t *src,
+ const ecc_curve_sp_t *curve);
+uint8_t ecc_chudnovsky_point_double_sp(ecc_chudnovsky_point_t *dest,
+ const ecc_chudnovsky_point_t *a,
+ const ecc_curve_sp_t *curve);
+void ecc_chudnovsky_point_copy(ecc_chudnovsky_point_t *dest,
+ const ecc_chudnovsky_point_t *src);
+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);
+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);
+uint8_t bigint_to_naf(uint8_t* dest, uint16_t *length, const bigint_t *src);
+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);
+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);
+
+#endif /* ECC_H_ */
--- /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);
+}
#include <stdlib.h>
#include <string.h>
+
#include "bigint.h"
+#include "ecc.h"
+#include "nist_p192.h"
+
+#include <stdio.h>
+#include <avr/pgmspace.h>
+#include "bigint_io.h"
+
+#define printf_P(...)
+#define bigint_print_hex(a)
+#undef putchar
+#define putchar(a)
/*
* p = 6277101735386680763835789423207666416083908700390324961279
* = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
*/
-static
uint8_t nist_curve_p192_p_w[] = {
- 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
- 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
- 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+ 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff
+};
+
+uint8_t nist_curve_p192_b_w[] = {
+ 0xb1, 0xb9, 0x46, 0xc1, 0xec, 0xde, 0xb8, 0xfe,
+ 0x49, 0x30, 0x24, 0x72, 0xab, 0xe9, 0xa7, 0x0f,
+ 0xe7, 0x80, 0x9c, 0xe5, 0x19, 0x05, 0x21, 0x64
+};
+
+uint8_t nist_curve_p192_gx_w[] = {
+ 0x12, 0x10, 0xff, 0x82, 0xfd, 0x0a, 0xff, 0xf4,
+ 0x00, 0x88, 0xa1, 0x43, 0xeb, 0x20, 0xbf, 0x7c,
+ 0xf6, 0x90, 0x30, 0xb0, 0x0e, 0xa8, 0x8d, 0x18
};
+uint8_t nist_curve_p192_gy_w[] = {
+ 0x11, 0x48, 0x79, 0x1e, 0xa1, 0x77, 0xf9, 0x73,
+ 0xd5, 0xcd, 0x24, 0x6b, 0xed, 0x11, 0x10, 0x63,
+ 0x78, 0xda, 0xc8, 0xff, 0x95, 0x2b, 0x19, 0x07
+};
+
+uint8_t nist_curve_p192_z1_w[192 / BIGINT_WORD_SIZE] = {
+ 1, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0 };
+
+uint8_t nist_curve_p192_z2_w[192 / BIGINT_WORD_SIZE] = {
+ 1, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0 };
+
+uint8_t nist_curve_p192_z3_w[192 / BIGINT_WORD_SIZE] = {
+ 1, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0 };
+
bigint_t nist_curve_p192_p = {
- .length_W = 192 / BIGINT_WORD_SIZE,
- .wordv = nist_curve_p192_p_w,
- .info = 7
+ .length_W = 192 / BIGINT_WORD_SIZE,
+ .wordv = nist_curve_p192_p_w,
+ .info = 7
+};
+
+bigint_t nist_curve_p192_b = {
+ .length_W = 192 / BIGINT_WORD_SIZE,
+ .wordv = nist_curve_p192_b_w,
+ .info = 6
};
+ecc_combi_point_t nist_curve_p192_basepoint = {
+ .chudnovsky = {
+ .x = {
+ .length_W = 192 / BIGINT_WORD_SIZE,
+ .wordv = nist_curve_p192_gx_w,
+ .info = 4
+ },
+ .y = {
+ .length_W = 192 / BIGINT_WORD_SIZE,
+ .wordv = nist_curve_p192_gy_w,
+ .info = 2
+ },
+ .z1 = {
+ .length_W = 1,
+ .wordv = nist_curve_p192_z1_w,
+ .info = 0
+ },
+ .z2 = {
+ .length_W = 1,
+ .wordv = nist_curve_p192_z2_w,
+ .info = 0
+ },
+ .z3 = {
+ .length_W = 1,
+ .wordv = nist_curve_p192_z3_w,
+ .info = 0
+ }
+ }
+};
+
+ecc_curve_sp_t nist_curve_p192 = {
+ .b = &nist_curve_p192_b,
+ .p = &nist_curve_p192_p,
+ .reduce_p = bigint_reduce_p192
+};
+
+
/*
* A = ( A5 || A4 || A3 || A2 || A1 || A0 ) ; An if 64-bit
* A mod p = B = T + S1 + S2 + S3 mod p
bigint_t s;
uint16_t o_length;
+ if(a->info & BIGINT_NEG_MASK){
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
+ /* negative value */
+ a->info &= ~BIGINT_NEG_MASK;
+ bigint_reduce_p192(a);
+ a->info |= BIGINT_NEG_MASK;
+ bigint_add_s(a, a, &nist_curve_p192_p);
+ return 0;
+ }
+
o_length = a->length_W;
if(o_length < 192 / BIGINT_WORD_SIZE){
if(o_length > 192 / BIGINT_WORD_SIZE){
s.wordv = s_w;
s.length_W = 2 * 64 / BIGINT_WORD_SIZE;
+ s.info = 0;
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
/*
* copy A3 twice in s
*/
if(o_length >= 4 * 64 / BIGINT_WORD_SIZE){
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memcpy(s.wordv, a->wordv + 3 * 64 / BIGINT_WORD_SIZE, 64 / 8);
}else{
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memset(s.wordv, 0, 8);
memcpy(s.wordv, a->wordv + 3 * 64 / BIGINT_WORD_SIZE,
o_length * BIGINT_WORD_SIZE / 8 - 3 * 64 / 8);
/*
* Set A3 to zero so we can use a as T
*/
- memset(a->wordv + 3 * 64 / BIGINT_WORD_SIZE, 0, BIGINT_WORD_SIZE / 8);
+ memset(a->wordv + 3 * 64 / BIGINT_WORD_SIZE, 0, sizeof(bigint_word_t));
a->length_W = 3 * 64 / BIGINT_WORD_SIZE;
bigint_adjust(a);
/*
* Add s (alias S1) to a (alias T)
*/
+
+ printf_P(PSTR("T: "));
+ bigint_print_hex(a);
+ putchar('\n');
+
+ printf_P(PSTR("s1: "));
+ bigint_print_hex(&s);
+ putchar('\n');
bigint_add_u(a, a, &s);
if(o_length > 4 * 64 / BIGINT_WORD_SIZE){
+ s.length_W = 2 * 64 / BIGINT_WORD_SIZE;
/*
* copy A4 twice in s
*/
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
if(o_length >= 5 * 64 / BIGINT_WORD_SIZE){
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memcpy(s.wordv, a->wordv + 4 * 64 / BIGINT_WORD_SIZE, 64 / 8);
}else{
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memset(s.wordv, 0, 8);
memcpy(s.wordv, a->wordv + 4 * 64 / BIGINT_WORD_SIZE,
o_length * BIGINT_WORD_SIZE / 8 - 4 * 64 / 8);
/*
* Add s (alias S2) to a (alias T + S1)
*/
+ printf_P(PSTR("s2: "));
+ bigint_print_hex(&s);
+ putchar('\n');
bigint_add_scale_u(a, &s, 8);
/*
* copy A5 three times in s
*/
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
if(o_length == 6 * 64 / BIGINT_WORD_SIZE){
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memcpy(s.wordv, a->wordv + 5 * 64 / BIGINT_WORD_SIZE, 64 / 8);
} else {
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
memset(s.wordv, 0, 8);
memcpy(s.wordv, a->wordv + 5 * 64 / BIGINT_WORD_SIZE,
o_length * BIGINT_WORD_SIZE / 8 - 5 * 64 / 8);
/*
* Add s (alias S2) to a (alias T + S1)
*/
+ printf_P(PSTR("s3: "));
+ bigint_print_hex(&s);
+ putchar('\n');
+
bigint_add_u(a, a, &s);
}
}
}
+ printf_P(PSTR("pre-result: "));
+ bigint_print_hex(a);
+ putchar('\n');
while(bigint_cmp_u(a, &nist_curve_p192_p) >= 0){
+ printf_P(PSTR("DBG: Line: %d\n"), __LINE__);
bigint_sub_u(a, a, &nist_curve_p192_p);
}
+ printf_P(PSTR("result: "));
+ bigint_print_hex(a);
+ putchar('\n');
return 0;
}
+
#define NIST_P192_H_
#include "bigint.h"
+#include "ecc.h"
extern bigint_t nist_curve_p192_p;
+
+extern bigint_t nist_curve_p192_b;
+
+extern ecc_combi_point_t nist_curve_p192_basepoint;
+
+extern ecc_curve_sp_t nist_curve_p192;
+
int bigint_reduce_p192(bigint_t *a);
#endif /* NIST_P192_H_ */
$(ALGO_NAME)_DIR := ecdsa/
$(ALGO_NAME)_INCDIR := memxor/ bigint/ sha1/ noekeon/ base64/ hfal/
-$(ALGO_NAME)_OBJ := bigint.o bigint_io.o sha1-asm.o nist_p192.o base64_enc.o
+$(ALGO_NAME)_OBJ := bigint.o bigint_io.o sha1-asm.o nist_p192.o ecc_chudnovsky.o base64_enc.o
$(ALGO_NAME)_TESTBIN := main-ecdsa-test.o $(CLI_STD) hfal_sha1.o $(HFAL_STD) \
noekeon_asm.o noekeon_prng.o memxor.o
* additional validation-functions *
*****************************************************************************/
-void testrun_performance_bigint(void){
- printf_P(PSTR("\n=== performance measurement ===\n"));
+void testrun_performance_invert_bigint(void){
+ printf_P(PSTR("\n=== performance measurement (invert) ===\n"));
+ unsigned i,j;
+ uint64_t time = 0;
+ bigint_t a, v;
+ bigint_word_t v_w[192 / BIGINT_WORD_SIZE];
+ bigint_word_t a_w[192 / BIGINT_WORD_SIZE];
+
+ a.wordv = a_w;
+ v.wordv = v_w;
+
+ for(j = 0; j < 32; ++j){
+ for(i = 0; i < 192 / BIGINT_WORD_SIZE; ++i){
+ ((uint8_t*)v_w)[i] = random();
+ }
+ v.length_W = 192 / BIGINT_WORD_SIZE;
+ v.info = 0;
+ bigint_adjust(&v);
+
+ for(i = 0; i < 16; ++i){
+ startTimer(1);
+ START_TIMER;
+ bigint_inverse(&a, &v, &nist_curve_p192_p);
+ STOP_TIMER;
+ time += stopTimer();
+ }
+ }
+
+ time >>= 8;
+ ++time;
+ time >>= 1;
+
+ printf_P(PSTR(" invert costs %"PRIu32" cycles\n"), (uint32_t)time);
+}
+
+void testrun_performance_multiply_bigint(void){
+ printf_P(PSTR("\n=== performance measurement (invert) ===\n"));
+ unsigned i,j;
+ uint64_t time_a = 0, time_b = 0;
+ uint32_t tmp;
+ bigint_t a, b, v;
+ bigint_word_t v_w[192 * 2 / BIGINT_WORD_SIZE];
+ bigint_word_t a_w[192 / BIGINT_WORD_SIZE];
+ bigint_word_t b_w[192 / BIGINT_WORD_SIZE];
+
+ a.wordv = a_w;
+ b.wordv = b_w;
+ v.wordv = v_w;
+
+ for(j = 0; j < 32; ++j){
+ for(i = 0; i < 192 / BIGINT_WORD_SIZE; ++i){
+ ((uint8_t*)a_w)[i] = random();
+ }
+ a.length_W = 192 / BIGINT_WORD_SIZE;
+ a.info = 0;
+ bigint_adjust(&a);
+
+ for(i = 0; i < 192 / BIGINT_WORD_SIZE; ++i){
+ ((uint8_t*)b_w)[i] = random();
+ }
+ b.length_W = 192 / BIGINT_WORD_SIZE;
+ b.info = 0;
+ bigint_adjust(&b);
+
+ for(i = 0; i < 16; ++i){
+ startTimer(1);
+ START_TIMER;
+ bigint_mul_u(&v,&a, &b);
+ STOP_TIMER;
+ tmp = stopTimer();
+ time_a += tmp;
+ time_b += tmp;
+
+ START_TIMER;
+ bigint_reduce_p192(&v);
+ STOP_TIMER;
+ tmp = stopTimer();
+ time_b += tmp;
+ }
+ }
+
+ time_a >>= 8;
+ ++time_a;
+ time_a >>= 1;
+
+ time_b >>= 8;
+ ++time_b;
+ time_b >>= 1;
+
+
+ printf_P(PSTR(" multiply costs %7"PRIu32" cycles\n"), (uint32_t)time_a);
+ printf_P(PSTR(" multiply + reduce costs %7"PRIu32" cycles\n"), (uint32_t)time_b);
+}
+
+void testrun_performance_reduce_bigint(void){
+ printf_P(PSTR("\n=== performance measurement (reduce) ===\n"));
unsigned i, j;
bigint_t a,b,v;
bigint_word_t v_w[192 * 2 / BIGINT_WORD_SIZE];
}
}
+uint8_t ecc_affine_point_alloc(ecc_affine_point_t *p, uint16_t length_b){
+ size_t len = (length_b + BIGINT_WORD_SIZE - 1)/ BIGINT_WORD_SIZE;
+ if (! (p->x.wordv = malloc(len))){
+ return 1;
+ }
+ if (! (p->y.wordv = malloc(len))){
+ free(p->x.wordv);
+ return 2;
+ }
+ return 0;
+}
+
+void ecc_affine_point_free(ecc_affine_point_t *p){
+ free(p->x.wordv);
+ free(p->y.wordv);
+}
+
+uint8_t ecc_chudnovsky_point_alloc(ecc_chudnovsky_point_t *p, uint16_t length_b){
+ size_t len = (length_b + BIGINT_WORD_SIZE - 1)/ BIGINT_WORD_SIZE;
+ if (! (p->x.wordv = malloc(len))){
+ return 1;
+ }
+ if (! (p->y.wordv = malloc(len))){
+ free(p->x.wordv);
+ return 2;
+ }
+ if (! (p->z1.wordv = malloc(len))){
+ free(p->x.wordv);
+ free(p->y.wordv);
+ return 3;
+ }
+ if (! (p->z2.wordv = malloc(len))){
+ free(p->x.wordv);
+ free(p->y.wordv);
+ free(p->z1.wordv);
+ return 4;
+ }
+ if (! (p->z3.wordv = malloc(len))){
+ free(p->x.wordv);
+ free(p->y.wordv);
+ free(p->z1.wordv);
+ free(p->z2.wordv);
+ return 5;
+ }
+ return 0;
+}
+
+void ecc_chudnovsky_point_free(ecc_chudnovsky_point_t *p){
+ free(p->x.wordv);
+ free(p->y.wordv);
+ free(p->z1.wordv);
+ free(p->z2.wordv);
+ free(p->z3.wordv);
+}
+
+void testrun_square(void){
+ bigint_word_t a_w[] = {
+ 0x82, 0x6f, 0x79, 0x39, 0x47, 0x06, 0x26, 0x9f,
+ 0x4b, 0xe2, 0x15, 0x61, 0x6f, 0xa1, 0xd4, 0x0c,
+ 0x1f, 0x24, 0x3a, 0xd4, 0xc2, 0x6d, 0xe8, 0xb6
+ };
+
+ bigint_word_t b_w[2 * 192 / BIGINT_WORD_SIZE];
+ bigint_t a, b;
+
+ a.wordv = a_w;
+ a.length_W = sizeof(a_w);
+ a.info = 7;
+
+ b.wordv = b_w;
+ b.info = 0;
+ b.length_W = 0;
+
+ printf_P(PSTR("\n a = "));
+ bigint_print_hex(&a);
+ bigint_square(&b, &a);
+ printf_P(PSTR("\n a^2 = "));
+ bigint_print_hex(&b);
+ bigint_reduce_p192(&b);
+ printf_P(PSTR("\n a^2 %% p = "));
+ bigint_print_hex(&b);
+ putchar('\n');
+
+
+}
+
+#if 1
+/*
+0: b3cfed2634516540528622e16c396c229e50bbdf773f8423
+1: b6e86dc2d43a241f0cd4a16f6115e24b9f26064739796f82
+2: 563f557e41731f268f82fe81c8fed959600dd46649ebeeee
+3: 5e45169bd87475db886b8a7833bb0845f5b011a7ce0c1766
+4: 4abf34c505a73308a804dcefacbd8f7b10b59fa6ac6421a
+*/
+uint8_t test_point_x_w[] = {
+ 0x23, 0x84, 0x3f, 0x77, 0xdf, 0xbb, 0x50, 0x9e,
+ 0x22, 0x6c, 0x39, 0x6c, 0xe1, 0x22, 0x86, 0x52,
+ 0x40, 0x65, 0x51, 0x34, 0x26, 0xed, 0xcf, 0xb3
+};
+
+uint8_t test_point_y_w[] = {
+ 0x82, 0x6f, 0x79, 0x39, 0x47, 0x06, 0x26, 0x9f,
+ 0x4b, 0xe2, 0x15, 0x61, 0x6f, 0xa1, 0xd4, 0x0c,
+ 0x1f, 0x24, 0x3a, 0xd4, 0xc2, 0x6d, 0xe8, 0xb6
+};
+
+uint8_t test_point_z1_w[] = {
+ 0xee, 0xee, 0xeb, 0x49, 0x66, 0xd4, 0x0d, 0x60,
+ 0x59, 0xd9, 0xfe, 0xc8, 0x81, 0xfe, 0x82, 0x8f,
+ 0x26, 0x1f, 0x73, 0x41, 0x7e, 0x55, 0x3f, 0x56
+};
+
+uint8_t test_point_z2_w[] = {
+ 0x66, 0x17, 0x0c, 0xce, 0xa7, 0x11, 0xb0, 0xf5,
+ 0x45, 0x08, 0xbb, 0x33, 0x78, 0x8a, 0x6b, 0x88,
+ 0xdb, 0x75, 0x74, 0xd8, 0x9b, 0x16, 0x45, 0x5e
+};
+
+uint8_t test_point_z3_w[] = {
+ 0x1a, 0x42, 0xc6, 0x6a, 0xfa, 0x59, 0x0b, 0xb1,
+ 0xf7, 0xd8, 0xcb, 0xfa, 0xce, 0x4d, 0x80, 0x8a,
+ 0x30, 0x73, 0x5a, 0x50, 0x4c, 0xf3, 0xab, 0x04
+};
+
+ecc_combi_point_t test_point = {
+ .chudnovsky = {
+ .x = {
+ .wordv = test_point_x_w,
+ .length_W = sizeof(test_point_x_w),
+ .info = 7
+ },
+ .y = {
+ .wordv = test_point_y_w,
+ .length_W = sizeof(test_point_y_w),
+ .info = 7
+ },
+ .z1 = {
+ .wordv = test_point_z1_w,
+ .length_W = sizeof(test_point_z1_w),
+ .info = 6
+ },
+ .z2 = {
+ .wordv = test_point_z2_w,
+ .length_W = sizeof(test_point_z2_w),
+ .info = 6
+ },
+ .z3 = {
+ .wordv = test_point_z3_w,
+ .length_W = sizeof(test_point_z3_w),
+ .info = 2
+ }
+ }
+};
+void testrun_genkey2(void){
+ ecc_chudnovsky_point_t q;
+ ecc_affine_point_t qa;
+
+ printf_P(PSTR("\n== testing key generation (2) ==\n"));
+
+ if(ecc_chudnovsky_point_alloc(&q, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+ if(ecc_affine_point_alloc(&qa, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+
+ ecc_chudnovsky_point_print(&test_point.chudnovsky);
+ ecc_chudnovsky_to_affine_point(&qa, &test_point.chudnovsky, &nist_curve_p192);
+ printf_P(PSTR("\n Qx: "));
+ bigint_print_hex(&qa.x);
+ printf_P(PSTR("\n Qy: "));
+ bigint_print_hex(&qa.y);
+ printf_P(PSTR("\n================\n"));
+ ecc_chudnovsky_point_double_sp(&q, &test_point.chudnovsky, &nist_curve_p192);
+ ecc_chudnovsky_point_print(&q);
+
+ ecc_chudnovsky_to_affine_point(&qa, &q, &nist_curve_p192);
+
+ printf_P(PSTR("\n Qx: "));
+ bigint_print_hex(&qa.x);
+ printf_P(PSTR("\n Qy: "));
+ bigint_print_hex(&qa.y);
+ puts("\n");
+
+}
+
+void testrun_genkey1(void){
+ ecc_chudnovsky_point_t q;
+ ecc_affine_point_t qa;
+
+ uint8_t k_w[] = {
+ // e5ce89a34adddf25ff3bf1ffe6803f57d0220de3118798ea
+ 0xea, 0x98, 0x87, 0x11, 0xe3, 0x0d, 0x22, 0xd0,
+ 0x57, 0x3f, 0x80, 0xe6, 0xff, 0xf1, 0x3b, 0xff,
+ 0x25, 0xdf, 0xdd, 0x4a, 0xa3, 0x89, 0xce, 0xe5
+ };
+
+ bigint_t k = {
+ .length_W = sizeof(k_w),
+ .wordv = k_w,
+ .info = 7
+ };
+
+ printf_P(PSTR("\n== testing key generation ==\n"));
+
+ if(ecc_chudnovsky_point_alloc(&q, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+ if(ecc_affine_point_alloc(&qa, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+
+ printf_P(PSTR(" k: "));
+ bigint_print_hex(&k);
+ ecc_chudnovsky_multiplication(&q, &k, &nist_curve_p192_basepoint.chudnovsky, &nist_curve_p192);
+ ecc_chudnovsky_to_affine_point(&qa, &q, &nist_curve_p192);
+
+ printf_P(PSTR("\n Qx: "));
+ bigint_print_hex(&qa.x);
+ printf_P(PSTR("\n Qy: "));
+ bigint_print_hex(&qa.y);
+ puts("\n");
+}
+
+void testrun_genkey3(void){
+ ecc_chudnovsky_point_t q;
+ ecc_affine_point_t qa;
+
+ uint8_t k_w[] = {
+ 0xb2, 0x51, 0x97, 0xc3, 0x7c, 0x61, 0xf8, 0x8f,
+ 0x19, 0x91, 0xcc, 0x67, 0xb5, 0x1c, 0x34, 0x23,
+ 0xff, 0x13, 0xad, 0x14, 0x57, 0x43, 0x14, 0x7d
+ };
+
+ bigint_t k = {
+ .length_W = sizeof(k_w),
+ .wordv = k_w,
+ .info = 6
+ };
+
+ printf_P(PSTR("\n== testing key generation ==\n"));
+
+ if(ecc_chudnovsky_point_alloc(&q, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+ if(ecc_affine_point_alloc(&qa, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+
+ printf_P(PSTR(" k: "));
+ bigint_print_hex(&k);
+ ecc_chudnovsky_double_and_add(&q, &k, &nist_curve_p192_basepoint.chudnovsky, &nist_curve_p192);
+ ecc_chudnovsky_to_affine_point(&qa, &q, &nist_curve_p192);
+
+ printf_P(PSTR("\n Qx: "));
+ bigint_print_hex(&qa.x);
+ printf_P(PSTR("\n Qy: "));
+ bigint_print_hex(&qa.y);
+ puts("\n");
+}
+
+void testrun_genkey(void){
+ ecc_chudnovsky_point_t q;
+ ecc_affine_point_t qa;
+
+ bigint_t k;
+
+ printf_P(PSTR("\n== testing key generation ==\n"));
+
+ printf_P(PSTR("enter secret key d: "));
+ bigint_read_hex_echo(&k);
+ putchar('\n');
+
+ if(ecc_chudnovsky_point_alloc(&q, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+ if(ecc_affine_point_alloc(&qa, 192)){
+ printf_P(PSTR("ERROR: OOM! <%s %s %d>\n"), __FILE__, __func__, __LINE__);
+ return;
+ }
+
+ printf_P(PSTR(" k: "));
+ bigint_print_hex(&k);
+ ecc_chudnovsky_multiplication(&q, &k, &nist_curve_p192_basepoint.chudnovsky, &nist_curve_p192);
+ ecc_chudnovsky_to_affine_point(&qa, &q, &nist_curve_p192);
+
+ printf_P(PSTR("\n Qx: "));
+ bigint_print_hex(&qa.x);
+ printf_P(PSTR("\n Qy: "));
+ bigint_print_hex(&qa.y);
+ puts("\n");
+}
+
+
+#endif
+
/*****************************************************************************
* main *
*****************************************************************************/
-const char echo_test_str[] PROGMEM = "echo-test";
-const char reset_prng_str[] PROGMEM = "reset-prng";
-const char quick_test_str[] PROGMEM = "quick-test";
-const char performance_str[] PROGMEM = "performance";
-const char echo_str[] PROGMEM = "echo";
+const char echo_test_str[] PROGMEM = "echo-test";
+const char reset_prng_str[] PROGMEM = "reset-prng";
+const char quick_test_str[] PROGMEM = "quick-test";
+const char performance_reduce_str[] PROGMEM = "performance_reduce";
+const char performance_invert_str[] PROGMEM = "performance_invert";
+const char performance_multiply_str[] PROGMEM = "performance_multiply";
+const char genkey1_str[] PROGMEM = "genkey1";
+const char genkey2_str[] PROGMEM = "genkey2";
+const char genkey3_str[] PROGMEM = "genkey3";
+const char genkey_str[] PROGMEM = "genkey";
+const char square_str[] PROGMEM = "square";
+const char echo_str[] PROGMEM = "echo";
const const cmdlist_entry_t cmdlist[] PROGMEM = {
-// { reset_prng_str, NULL, reset_prng },
-// { quick_test_str, NULL, quick_test },
- { performance_str, NULL, testrun_performance_bigint },
- { echo_str, (void*)1, (void_fpt)echo_ctrl },
- { NULL, NULL, NULL }
+// { reset_prng_str, NULL, reset_prng },
+// { quick_test_str, NULL, quick_test },
+ { square_str, NULL, testrun_square },
+ { genkey_str, NULL, testrun_genkey },
+ { genkey1_str, NULL, testrun_genkey1 },
+ { genkey2_str, NULL, testrun_genkey2 },
+ { genkey3_str, NULL, testrun_genkey3 },
+ { performance_reduce_str, NULL, testrun_performance_reduce_bigint },
+ { performance_invert_str, NULL, testrun_performance_invert_bigint },
+ { performance_multiply_str, NULL, testrun_performance_multiply_bigint },
+ { echo_str, (void*)1, (void_fpt)echo_ctrl },
+ { NULL, NULL, NULL }
};
int main (void){
projects / avr-crypto-lib.git / commitdiff