tomcrypt/src/pk/ecc/ecc.c
2010-06-16 12:38:41 +02:00

1216 lines
40 KiB
C

/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.org
*/
/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
*
* All curves taken from NIST recommendation paper of July 1999
* Available at http://csrc.nist.gov/cryptval/dss.htm
*/
#include "tomcrypt.h"
/**
@file ecc.c
ECC Crypto, Tom St Denis
*/
#ifdef MECC
/* size of our temp buffers for exported keys */
#define ECC_BUF_SIZE 256
/* max private key size */
#define ECC_MAXSIZE 66
/* This holds the key settings. ***MUST*** be organized by size from smallest to largest. */
const ltc_ecc_set_type ltc_ecc_sets[] = {
#ifdef ECC192
{
24,
"ECC-192",
/* prime */
"/////////////////////l//////////",
/* B */
"P2456UMSWESFf+chSYGmIVwutkp1Hhcn",
/* order */
"////////////////cTxuDXHhoR6qqYWn",
/* Gx */
"68se3h0maFPylo3hGw680FJ/2ls2/n0I",
/* Gy */
"1nahbV/8sdXZ417jQoJDrNFvTw4UUKWH"
},
#endif
#ifdef ECC224
{
28,
"ECC-224",
/* prime */
"3/////////////////////0000000000000001",
/* B */
"2q1Gg530Ipg/L1CbPGHB2trx/OkYSBEKCZLV+q",
/* order */
"3//////////////////nQYuBZmFXFTAKLSN2ez",
/* Gx */
"2t3WozQxI/Vp8JaBbA0y7JLi8H8ZGoWDOHN1qX",
/* Gy */
"2zDsE8jVSZ+qmYt+RDGtMWMWT7P4JLWPc507uq",
},
#endif
#ifdef ECC256
{
32,
"ECC-256",
/* Prime */
"F////y000010000000000000000////////////////",
/* B */
"5h6DTYgEfFdi+kzLNQOXhnb7GQmp5EmzZlEF3udqc1B",
/* Order */
"F////y00000//////////+yvlgjfnUUXFEvoiByOoLH",
/* Gx */
"6iNqVBXB497+BpcvMEaGF9t0ts1BUipeFIXEKNOcCAM",
/* Gy */
"4/ZGkB+6d+RZkVhIdmFdXOhpZDNQp5UpiksG6Wtlr7r"
},
#endif
#ifdef ECC384
{
48,
"ECC-384",
/* prime */
"//////////////////////////////////////////x/////00000000003/"
"////",
/* B */
"ip4lf+8+v+IOZWLhu/Wj6HWTd6x+WK4I0nG8Zr0JXrh6LZcDYYxHdIg5oEtJ"
"x2hl",
/* Order */
"////////////////////////////////nsDDWVGtBTzO6WsoIB2dUkpi6MhC"
"nIbp",
/* Gx and Gy */
"geVA8hwB1JUEiSSUyo2jT6uTEsABfvkOMVT1u89KAZXL0l9TlrKfR3fKNZXo"
"TWgt",
"DXVUIfOcB6zTdfY/afBSAVZq7RqecXHywTen4xNmkC0AOB7E7Nw1dNf37NoG"
"wWvV"
},
#endif
#ifdef ECC521
{
65,
"ECC-521",
/* prime */
"V///////////////////////////////////////////////////////////"
"///////////////////////////",
/* B */
"56LFhbXZXoQ7vAQ8Q2sXK3kejfoMvcp5VEuj8cHZl49uLOPEL7iVfDx5bB0l"
"JknlmSrSz+8FImqyUz57zHhK3y0",
/* Order */
"V//////////////////////////////////////////+b66XuE/BvPhVym1I"
"FS9fT0xjScuYPn7hhjljnwHE6G9",
/* Gx and Gy */
"CQ5ZWQt10JfpPu+osOZbRH2d6I1EGK/jI7uAAzWQqqzkg5BNdVlvrae/Xt19"
"wB/gDupIBF1XMf2c/b+VZ72vRrc",
"HWvAMfucZl015oANxGiVHlPcFL4ILURH6WNhxqN9pvcB9VkSfbUz2P0nL2v0"
"J+j1s4rF726edB2G8Y+b7QVqMPG",
},
#endif
{
0,
NULL, NULL, NULL, NULL, NULL, NULL
}
};
static int is_valid_idx(int n)
{
int x;
for (x = 0; ltc_ecc_sets[x].size != 0; x++);
if ((n < 0) || (n >= x)) {
return 0;
}
return 1;
}
/**
Allocate a new ECC point
@return A newly allocated point or NULL on error
*/
ecc_point *ltc_ecc_new_point(void)
{
ecc_point *p;
p = XMALLOC(sizeof(ecc_point));
if (p == NULL) {
return NULL;
}
if (mp_init_multi(&p->x, &p->y, &p->z, NULL) != CRYPT_OK) {
XFREE(p);
return NULL;
}
return p;
}
/** Free an ECC point from memory
@param p The point to free
*/
void ltc_ecc_del_point(ecc_point *p)
{
/* prevents free'ing null arguments */
if (p != NULL) {
mp_clear_multi(p->x, p->y, p->z, NULL);
XFREE(p);
}
}
/**
Map a projective jacbobian point back to affine space
@param P [in/out] The point to map
@param modulus The modulus of the field the ECC curve is in
@param mp The "b" value from montgomery_setup()
@return CRYPT_OK on success
*/
int ltc_ecc_map(ecc_point *P, void *modulus, void *mp)
{
void *t1, *t2;
int err;
LTC_ARGCHK(P != NULL);
LTC_ARGCHK(modulus != NULL);
LTC_ARGCHK(mp != NULL);
if ((err = mp_init_multi(&t1, &t2, NULL)) != CRYPT_OK) {
return CRYPT_MEM;
}
/* first map z back to normal */
if ((err = mp_montgomery_reduce(P->z, modulus, mp)) != CRYPT_OK) { goto done; }
/* get 1/z */
if ((err = mp_invmod(P->z, modulus, t1)) != CRYPT_OK) { goto done; }
/* get 1/z^2 and 1/z^3 */
if ((err = mp_sqr(t1, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_mod(t2, modulus, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_mul(t1, t2, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_mod(t1, modulus, t1)) != CRYPT_OK) { goto done; }
/* multiply against x/y */
if ((err = mp_mul(P->x, t2, P->x)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(P->x, modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = mp_mul(P->y, t1, P->y)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(P->y, modulus, mp)) != CRYPT_OK) { goto done; }
mp_set(P->z, 1);
err = CRYPT_OK;
goto done;
done:
mp_clear_multi(t1, t2, NULL);
return err;
}
/**
Double an ECC point
@param P The point to double
@param R [out] The destination of the double
@param modulus The modulus of the field the ECC curve is in
@param mp The "b" value from montgomery_setup()
@return CRYPT_OK on success
*/
int ltc_ecc_dbl_point(ecc_point *P, ecc_point *R, void *modulus, void *mp)
{
void *t1, *t2;
int err;
LTC_ARGCHK(P != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
LTC_ARGCHK(mp != NULL);
if ((err = mp_init_multi(&t1, &t2, NULL)) != CRYPT_OK) {
return err;
}
if ((err = mp_copy(P->x, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(P->y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(P->z, R->z)) != CRYPT_OK) { goto done; }
/* t1 = Z * Z */
if ((err = mp_sqr(R->z, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* Z = Y * Z */
if ((err = mp_mul(R->z, R->y, R->z)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(R->z, modulus, mp)) != CRYPT_OK) { goto done; }
/* Z = 2Z */
if ((err = mp_add(R->z, R->z, R->z)) != CRYPT_OK) { goto done; }
if (mp_cmp(R->z, modulus) != LTC_MP_LT) {
if ((err = mp_sub(R->z, modulus, R->z)) != CRYPT_OK) { goto done; }
}
/* T2 = X - T1 */
if ((err = mp_sub(R->x, t1, t2)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
/* T1 = X + T1 */
if ((err = mp_add(t1, R->x, t1)) != CRYPT_OK) { goto done; }
if (mp_cmp(t1, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
}
/* T2 = T1 * T2 */
if ((err = mp_mul(t1, t2, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = 2T2 */
if ((err = mp_add(t2, t2, t1)) != CRYPT_OK) { goto done; }
if (mp_cmp(t1, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
}
/* T1 = T1 + T2 */
if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto done; }
if (mp_cmp(t1, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
}
/* Y = 2Y */
if ((err = mp_add(R->y, R->y, R->y)) != CRYPT_OK) { goto done; }
if (mp_cmp(R->y, modulus) != LTC_MP_LT) {
if ((err = mp_sub(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
}
/* Y = Y * Y */
if ((err = mp_sqr(R->y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
/* T2 = Y * Y */
if ((err = mp_sqr(R->y, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
/* T2 = T2/2 */
if (mp_isodd(t2)) {
if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
if ((err = mp_div_2(t2, t2)) != CRYPT_OK) { goto done; }
/* Y = Y * X */
if ((err = mp_mul(R->y, R->x, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = T1 * T1 */
if ((err = mp_sqr(t1, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(R->x, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = X - Y */
if ((err = mp_sub(R->x, R->y, R->x)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(R->x, 0) == LTC_MP_LT) {
if ((err = mp_add(R->x, modulus, R->x)) != CRYPT_OK) { goto done; }
}
/* X = X - Y */
if ((err = mp_sub(R->x, R->y, R->x)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(R->x, 0) == LTC_MP_LT) {
if ((err = mp_add(R->x, modulus, R->x)) != CRYPT_OK) { goto done; }
}
/* Y = Y - X */
if ((err = mp_sub(R->y, R->x, R->y)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(R->y, 0) == LTC_MP_LT) {
if ((err = mp_add(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
}
/* Y = Y * T1 */
if ((err = mp_mul(R->y, t1, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
/* Y = Y - T2 */
if ((err = mp_sub(R->y, t2, R->y)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(R->y, 0) == LTC_MP_LT) {
if ((err = mp_add(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
}
err = CRYPT_OK;
goto done;
done:
mp_clear_multi(t1, t2, NULL);
return err;
}
/**
Add two ECC points
@param P The point to add
@param Q The point to add
@param R [out] The destination of the double
@param modulus The modulus of the field the ECC curve is in
@param mp The "b" value from montgomery_setup()
@return CRYPT_OK on success
*/
int ltc_ecc_add_point(ecc_point *P, ecc_point *Q, ecc_point *R, void *modulus, void *mp)
{
void *t1, *t2, *x, *y, *z;
int err;
LTC_ARGCHK(P != NULL);
LTC_ARGCHK(Q != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
LTC_ARGCHK(mp != NULL);
if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != CRYPT_OK) {
return err;
}
if ((err = mp_copy(P->x, x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(P->y, y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(P->z, z)) != CRYPT_OK) { goto done; }
/* T1 = Z' * Z' */
if ((err = mp_sqr(Q->z, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = X * T1 */
if ((err = mp_mul(t1, x, x)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = Z' * T1 */
if ((err = mp_mul(Q->z, t1, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* Y = Y * T1 */
if ((err = mp_mul(t1, y, y)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(y, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = Z*Z */
if ((err = mp_sqr(z, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* T2 = X' * T1 */
if ((err = mp_mul(Q->x, t1, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = Z * T1 */
if ((err = mp_mul(z, t1, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = Y' * T1 */
if ((err = mp_mul(Q->y, t1, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* Y = Y - T1 */
if ((err = mp_sub(y, t1, y)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(y, 0) == LTC_MP_LT) {
if ((err = mp_add(y, modulus, y)) != CRYPT_OK) { goto done; }
}
/* T1 = 2T1 */
if ((err = mp_add(t1, t1, t1)) != CRYPT_OK) { goto done; }
if (mp_cmp(t1, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
}
/* T1 = Y + T1 */
if ((err = mp_add(t1, y, t1)) != CRYPT_OK) { goto done; }
if (mp_cmp(t1, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
}
/* X = X - T2 */
if ((err = mp_sub(x, t2, x)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(x, 0) == LTC_MP_LT) {
if ((err = mp_add(x, modulus, x)) != CRYPT_OK) { goto done; }
}
/* T2 = 2T2 */
if ((err = mp_add(t2, t2, t2)) != CRYPT_OK) { goto done; }
if (mp_cmp(t2, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
/* T2 = X + T2 */
if ((err = mp_add(t2, x, t2)) != CRYPT_OK) { goto done; }
if (mp_cmp(t2, modulus) != LTC_MP_LT) {
if ((err = mp_sub(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
/* if Z' != 1 */
if (mp_cmp_d(Q->z, 1) != LTC_MP_EQ) {
/* Z = Z * Z' */
if ((err = mp_mul(z, Q->z, z)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(z, modulus, mp)) != CRYPT_OK) { goto done; }
}
/* Z = Z * X */
if ((err = mp_mul(z, x, z)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(z, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = T1 * X */
if ((err = mp_mul(t1, x, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = X * X */
if ((err = mp_sqr(x, x)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK) { goto done; }
/* T2 = T2 * x */
if ((err = mp_mul(t2, x, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
/* T1 = T1 * X */
if ((err = mp_mul(t1, x, t1)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = Y*Y */
if ((err = mp_sqr(y, x)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK) { goto done; }
/* X = X - T2 */
if ((err = mp_sub(x, t2, x)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(x, 0) == LTC_MP_LT) {
if ((err = mp_add(x, modulus, x)) != CRYPT_OK) { goto done; }
}
/* T2 = T2 - X */
if ((err = mp_sub(t2, x, t2)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
/* T2 = T2 - X */
if ((err = mp_sub(t2, x, t2)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
}
/* T2 = T2 * Y */
if ((err = mp_mul(t2, y, t2)) != CRYPT_OK) { goto done; }
if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
/* Y = T2 - T1 */
if ((err = mp_sub(t2, t1, y)) != CRYPT_OK) { goto done; }
if (mp_cmp_d(y, 0) == LTC_MP_LT) {
if ((err = mp_add(y, modulus, y)) != CRYPT_OK) { goto done; }
}
/* Y = Y/2 */
if (mp_isodd(y)) {
if ((err = mp_add(y, modulus, y)) != CRYPT_OK) { goto done; }
}
if ((err = mp_div_2(y, y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(x, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(z, R->z)) != CRYPT_OK) { goto done; }
err = CRYPT_OK;
goto done;
done:
mp_clear_multi(t1, t2, x, y, z, NULL);
return err;
}
/* size of sliding window, don't change this! */
#define WINSIZE 4
#ifdef LTC_ECC_TIMING_RESISTANT
/**
Perform a point multiplication (timing resistant)
@param k The scalar to multiply by
@param G The base point
@param R [out] Destination for kG
@param modulus The modulus of the field the ECC curve is in
@param map Boolean whether to map back to affine or not (1==map, 0 == leave in projective)
@return CRYPT_OK on success
*/
int ltc_ecc_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map)
{
ecc_point *tG, *M[3];
int i, j, err;
void *mu, *mp;
unsigned long buf;
int first, bitbuf, bitcpy, bitcnt, mode, digidx;
/* Call accelerator if present */
if (ltc_mp.ecc_ptmul != NULL) {
return ltc_mp.ecc_ptmul(k, G, R, modulus, map);
}
LTC_ARGCHK(k != NULL);
LTC_ARGCHK(G != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
/* init montgomery reduction */
if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) {
return err;
}
if ((err = mp_init(&mu)) != CRYPT_OK) {
return err;
}
if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
mp_montgomery_free(mp);
mp_clear(mu);
return err;
}
/* alloc ram for window temps */
for (i = 0; i < 3; i++) {
M[i] = ltc_ecc_new_point();
if (M[i] == NULL) {
for (j = 0; j < i; j++) {
ltc_ecc_del_point(M[j]);
}
mp_montgomery_free(mp);
mp_clear(mu);
return CRYPT_MEM;
}
}
/* make a copy of G incase R==G */
tG = ltc_ecc_new_point();
if (tG == NULL) { err = CRYPT_MEM; goto done; }
/* tG = G and convert to montgomery */
if ((err = mp_mulmod(G->x, mu, modulus, tG->x)) != CRYPT_OK) { goto done; }
if ((err = mp_mulmod(G->y, mu, modulus, tG->y)) != CRYPT_OK) { goto done; }
if ((err = mp_mulmod(G->z, mu, modulus, tG->z)) != CRYPT_OK) { goto done; }
mp_clear(mu);
/* calc the M tab, which holds kG for k==8..15 */
/* M[0] == G */
if ((err = mp_copy(tG->x, M[0]->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(tG->y, M[0]->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(tG->z, M[0]->z)) != CRYPT_OK) { goto done; }
/* M[1] == 2G */
if ((err = ltc_ecc_dbl_point(tG, M[1], modulus, mp)) != CRYPT_OK) { goto done; }
/* setup sliding window */
mode = 0;
bitcnt = 1;
buf = 0;
digidx = mp_get_digit_count(k) - 1;
bitcpy = bitbuf = 0;
first = 1;
/* perform ops */
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = mp_get_digit(k, digidx);
bitcnt = (int) MP_DIGIT_BIT;
--digidx;
}
/* grab the next msb from the ltiplicand */
i = (buf >> (MP_DIGIT_BIT - 1)) & 1;
buf <<= 1;
if (mode == 0 && i == 0) {
/* dummy operations */
if ((err = ltc_ecc_add_point(M[0], M[1], M[2], modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_dbl_point(M[1], M[2], modulus, mp)) != CRYPT_OK) { goto done; }
continue;
}
if (mode == 0 && i == 1) {
mode = 1;
/* dummy operations */
if ((err = ltc_ecc_add_point(M[0], M[1], M[2], modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_dbl_point(M[1], M[2], modulus, mp)) != CRYPT_OK) { goto done; }
continue;
}
if ((err = ltc_ecc_add_point(M[0], M[1], M[i^1], modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_dbl_point(M[i], M[i], modulus, mp)) != CRYPT_OK) { goto done; }
}
/* copy result out */
if ((err = mp_copy(M[0]->x, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(M[0]->y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(M[0]->z, R->z)) != CRYPT_OK) { goto done; }
/* map R back from projective space */
if (map) {
err = ltc_ecc_map(R, modulus, mp);
} else {
err = CRYPT_OK;
}
done:
mp_montgomery_free(mp);
ltc_ecc_del_point(tG);
for (i = 0; i < 3; i++) {
ltc_ecc_del_point(M[i]);
}
return err;
}
#else
/**
Perform a point multiplication
@param k The scalar to multiply by
@param G The base point
@param R [out] Destination for kG
@param modulus The modulus of the field the ECC curve is in
@param map Boolean whether to map back to affine or not (1==map, 0 == leave in projective)
@return CRYPT_OK on success
*/
int ltc_ecc_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map)
{
ecc_point *tG, *M[8];
int i, j, err;
void *mu, *mp;
unsigned long buf;
int first, bitbuf, bitcpy, bitcnt, mode, digidx;
/* Call accelerator if present */
if (ltc_mp.ecc_ptmul != NULL) {
return ltc_mp.ecc_ptmul(k, G, R, modulus, map);
}
LTC_ARGCHK(k != NULL);
LTC_ARGCHK(G != NULL);
LTC_ARGCHK(R != NULL);
LTC_ARGCHK(modulus != NULL);
/* init montgomery reduction */
if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) {
return err;
}
if ((err = mp_init(&mu)) != CRYPT_OK) {
return err;
}
if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
mp_montgomery_free(mp);
mp_clear(mu);
return err;
}
/* alloc ram for window temps */
for (i = 0; i < 8; i++) {
M[i] = ltc_ecc_new_point();
if (M[i] == NULL) {
for (j = 0; j < i; j++) {
ltc_ecc_del_point(M[j]);
}
mp_montgomery_free(mp);
mp_clear(mu);
return CRYPT_MEM;
}
}
/* make a copy of G incase R==G */
tG = ltc_ecc_new_point();
if (tG == NULL) { err = CRYPT_MEM; goto done; }
/* tG = G and convert to montgomery */
if ((err = mp_mulmod(G->x, mu, modulus, tG->x)) != CRYPT_OK) { goto done; }
if ((err = mp_mulmod(G->y, mu, modulus, tG->y)) != CRYPT_OK) { goto done; }
if ((err = mp_mulmod(G->z, mu, modulus, tG->z)) != CRYPT_OK) { goto done; }
mp_clear(mu);
/* calc the M tab, which holds kG for k==8..15 */
/* M[0] == 8G */
if ((err = ltc_ecc_dbl_point(tG, M[0], modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_dbl_point(M[0], M[0], modulus, mp)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_dbl_point(M[0], M[0], modulus, mp)) != CRYPT_OK) { goto done; }
/* now find (8+k)G for k=1..7 */
for (j = 9; j < 16; j++) {
if ((err = ltc_ecc_add_point(M[j-9], tG, M[j-8], modulus, mp)) != CRYPT_OK) { goto done; }
}
/* setup sliding window */
mode = 0;
bitcnt = 1;
buf = 0;
digidx = mp_get_digit_count(k) - 1;
bitcpy = bitbuf = 0;
first = 1;
/* perform ops */
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = mp_get_digit(k, digidx);
bitcnt = (int) MP_DIGIT_BIT;
--digidx;
}
/* grab the next msb from the ltiplicand */
i = (buf >> (MP_DIGIT_BIT - 1)) & 1;
buf <<= 1;
/* skip leading zero bits */
if (mode == 0 && i == 0) {
continue;
}
/* if the bit is zero and mode == 1 then we double */
if (mode == 1 && i == 0) {
if ((err = ltc_ecc_dbl_point(R, R, modulus, mp)) != CRYPT_OK) { goto done; }
continue;
}
/* else we add it to the window */
bitbuf |= (i << (WINSIZE - ++bitcpy));
mode = 2;
if (bitcpy == WINSIZE) {
/* if this is the first window we do a simple copy */
if (first == 1) {
/* R = kG [k = first window] */
if ((err = mp_copy(M[bitbuf-8]->x, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(M[bitbuf-8]->y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(M[bitbuf-8]->z, R->z)) != CRYPT_OK) { goto done; }
first = 0;
} else {
/* normal window */
/* ok window is filled so double as required and add */
/* double first */
for (j = 0; j < WINSIZE; j++) {
if ((err = ltc_ecc_dbl_point(R, R, modulus, mp)) != CRYPT_OK) { goto done; }
}
/* then add, bitbuf will be 8..15 [8..2^WINSIZE] guaranteed */
if ((err = ltc_ecc_add_point(R, M[bitbuf-8], R, modulus, mp)) != CRYPT_OK) { goto done; }
}
/* empty window and reset */
bitcpy = bitbuf = 0;
mode = 1;
}
}
/* if bits remain then double/add */
if (mode == 2 && bitcpy > 0) {
/* double then add */
for (j = 0; j < bitcpy; j++) {
/* only double if we have had at least one add first */
if (first == 0) {
if ((err = ltc_ecc_dbl_point(R, R, modulus, mp)) != CRYPT_OK) { goto done; }
}
bitbuf <<= 1;
if ((bitbuf & (1 << WINSIZE)) != 0) {
if (first == 1){
/* first add, so copy */
if ((err = mp_copy(tG->x, R->x)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(tG->y, R->y)) != CRYPT_OK) { goto done; }
if ((err = mp_copy(tG->z, R->z)) != CRYPT_OK) { goto done; }
first = 0;
} else {
/* then add */
if ((err = ltc_ecc_add_point(R, tG, R, modulus, mp)) != CRYPT_OK) { goto done; }
}
}
}
}
/* map R back from projective space */
if (map) {
err = ltc_ecc_map(R, modulus, mp);
} else {
err = CRYPT_OK;
}
done:
mp_montgomery_free(mp);
ltc_ecc_del_point(tG);
for (i = 0; i < 8; i++) {
ltc_ecc_del_point(M[i]);
}
return err;
}
#endif
#undef WINSIZE
/**
Perform on the ECC system
@return CRYPT_OK if successful
*/
int ecc_test(void)
{
void *modulus, *order;
ecc_point *G, *GG;
int i, err, primality;
if ((err = mp_init_multi(&modulus, &order, NULL)) != CRYPT_OK) {
return err;
}
G = ltc_ecc_new_point();
GG = ltc_ecc_new_point();
if (G == NULL || GG == NULL) {
mp_clear_multi(modulus, order, NULL);
ltc_ecc_del_point(G);
ltc_ecc_del_point(GG);
return CRYPT_MEM;
}
for (i = 0; ltc_ecc_sets[i].size; i++) {
#if 0
printf("Testing %d\n", ltc_ecc_sets[i].size);
#endif
if ((err = mp_read_radix(modulus, (char *)ltc_ecc_sets[i].prime, 64)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(order, (char *)ltc_ecc_sets[i].order, 64)) != CRYPT_OK) { goto done; }
/* is prime actually prime? */
if ((err = mp_prime_is_prime(modulus, 8, &primality)) != CRYPT_OK) { goto done; }
if (primality == 0) {
err = CRYPT_FAIL_TESTVECTOR;
goto done;
}
/* is order prime ? */
if ((err = mp_prime_is_prime(order, 8, &primality)) != CRYPT_OK) { goto done; }
if (primality == 0) {
err = CRYPT_FAIL_TESTVECTOR;
goto done;
}
if ((err = mp_read_radix(G->x, (char *)ltc_ecc_sets[i].Gx, 64)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(G->y, (char *)ltc_ecc_sets[i].Gy, 64)) != CRYPT_OK) { goto done; }
mp_set(G->z, 1);
/* then we should have G == (order + 1)G */
if ((err = mp_add_d(order, 1, order)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_mulmod(order, G, GG, modulus, 1)) != CRYPT_OK) { goto done; }
if (mp_cmp(G->x, GG->x) != LTC_MP_EQ || mp_cmp(G->y, GG->y) != LTC_MP_EQ) {
err = CRYPT_FAIL_TESTVECTOR;
goto done;
}
}
err = CRYPT_OK;
goto done;
done:
ltc_ecc_del_point(GG);
ltc_ecc_del_point(G);
mp_clear_multi(order, modulus, NULL);
return err;
}
void ecc_sizes(int *low, int *high)
{
int i;
LTC_ARGCHK(low != NULL);
LTC_ARGCHK(high != NULL);
*low = INT_MAX;
*high = 0;
for (i = 0; ltc_ecc_sets[i].size != 0; i++) {
if (ltc_ecc_sets[i].size < *low) {
*low = ltc_ecc_sets[i].size;
}
if (ltc_ecc_sets[i].size > *high) {
*high = ltc_ecc_sets[i].size;
}
}
}
/**
Make a new ECC key
@param prng An active PRNG state
@param wprng The index of the PRNG you wish to use
@param keysize The keysize for the new key (in octets from 20 to 65 bytes)
@param key [out] Destination of the newly created key
@return CRYPT_OK if successful, upon error all allocated memory will be freed
*/
int ecc_make_key(prng_state *prng, int wprng, int keysize, ecc_key *key)
{
int x, err;
ecc_point *base;
void *prime;
unsigned char *buf;
LTC_ARGCHK(key != NULL);
/* good prng? */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
/* find key size */
for (x = 0; (keysize > ltc_ecc_sets[x].size) && (ltc_ecc_sets[x].size != 0); x++);
keysize = ltc_ecc_sets[x].size;
if (keysize > ECC_MAXSIZE || ltc_ecc_sets[x].size == 0) {
return CRYPT_INVALID_KEYSIZE;
}
key->idx = x;
/* allocate ram */
base = NULL;
buf = XMALLOC(ECC_MAXSIZE);
if (buf == NULL) {
return CRYPT_MEM;
}
/* make up random string */
if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
err = CRYPT_ERROR_READPRNG;
goto LBL_ERR2;
}
/* setup the key variables */
if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, &prime, NULL)) != CRYPT_OK) {
goto done;
}
base = ltc_ecc_new_point();
if (base == NULL) {
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, prime, NULL);
err = CRYPT_MEM;
goto done;
}
/* read in the specs for this key */
if ((err = mp_read_radix(prime, (char *)ltc_ecc_sets[key->idx].prime, 64)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(base->x, (char *)ltc_ecc_sets[key->idx].Gx, 64)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(base->y, (char *)ltc_ecc_sets[key->idx].Gy, 64)) != CRYPT_OK) { goto done; }
mp_set(base->z, 1);
if ((err = mp_read_unsigned_bin(key->k, (unsigned char *)buf, keysize)) != CRYPT_OK) { goto done; }
/* make the public key */
if ((err = ltc_ecc_mulmod(key->k, base, &key->pubkey, prime, 1)) != CRYPT_OK) { goto done; }
key->type = PK_PRIVATE;
/* free up ram */
err = CRYPT_OK;
done:
ltc_ecc_del_point(base);
mp_clear(prime);
LBL_ERR2:
#ifdef LTC_CLEAN_STACK
zeromem(buf, ECC_MAXSIZE);
#endif
XFREE(buf);
return err;
}
/**
Free an ECC key from memory
@param key The key you wish to free
*/
void ecc_free(ecc_key *key)
{
LTC_ARGCHK(key != NULL);
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
}
/**
Export an ECC key as a binary packet
@param out [out] Destination for the key
@param outlen [in/out] Max size and resulting size of the exported key
@param type The type of key you want to export (PK_PRIVATE or PK_PUBLIC)
@param key The key to export
@return CRYPT_OK if successful
*/
int ecc_export(unsigned char *out, unsigned long *outlen, int type, ecc_key *key)
{
int err;
unsigned char flags[1];
unsigned long key_size;
LTC_ARGCHK(out != NULL);
LTC_ARGCHK(outlen != NULL);
LTC_ARGCHK(key != NULL);
/* type valid? */
if (key->type != PK_PRIVATE && type == PK_PRIVATE) {
return CRYPT_PK_TYPE_MISMATCH;
}
if (is_valid_idx(key->idx) == 0) {
return CRYPT_INVALID_ARG;
}
/* we store the NIST byte size */
key_size = ltc_ecc_sets[key->idx].size;
if (type == PK_PRIVATE) {
flags[0] = 1;
err = der_encode_sequence_multi(out, outlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_INTEGER, 1UL, key->k,
LTC_ASN1_EOL, 0UL, NULL);
} else {
flags[0] = 0;
err = der_encode_sequence_multi(out, outlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_EOL, 0UL, NULL);
}
return err;
}
/**
Import an ECC key from a binary packet
@param in The packet to import
@param inlen The length of the packet
@param key [out] The destination of the import
@return CRYPT_OK if successful, upon error all allocated memory will be freed
*/
int ecc_import(const unsigned char *in, unsigned long inlen, ecc_key *key)
{
unsigned long key_size;
unsigned char flags[1];
int err;
LTC_ARGCHK(in != NULL);
LTC_ARGCHK(key != NULL);
/* init key */
if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, NULL) != CRYPT_OK) {
return CRYPT_MEM;
}
/* find out what type of key it is */
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, &flags,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
if (flags[0] == 1) {
/* private key */
key->type = PK_PRIVATE;
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_INTEGER, 1UL, key->k,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
} else {
/* public key */
/* private key */
key->type = PK_PUBLIC;
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
}
/* find the idx */
for (key->idx = 0; ltc_ecc_sets[key->idx].size && (unsigned long)ltc_ecc_sets[key->idx].size != key_size; ++key->idx);
if (ltc_ecc_sets[key->idx].size == 0) {
err = CRYPT_INVALID_PACKET;
goto done;
}
/* set z */
mp_set(key->pubkey.z, 1);
/* we're good */
return CRYPT_OK;
done:
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
return err;
}
/**
Create an ECC shared secret between two keys
@param private_key The private ECC key
@param public_key The public key
@param out [out] Destination of the shared secret (Conforms to EC-DH from ANSI X9.63)
@param outlen [in/out] The max size and resulting size of the shared secret
@return CRYPT_OK if successful
*/
int ecc_shared_secret(ecc_key *private_key, ecc_key *public_key,
unsigned char *out, unsigned long *outlen)
{
unsigned long x;
ecc_point *result;
void *prime;
int err;
LTC_ARGCHK(private_key != NULL);
LTC_ARGCHK(public_key != NULL);
LTC_ARGCHK(out != NULL);
LTC_ARGCHK(outlen != NULL);
/* type valid? */
if (private_key->type != PK_PRIVATE) {
return CRYPT_PK_NOT_PRIVATE;
}
if (is_valid_idx(private_key->idx) == 0) {
return CRYPT_INVALID_ARG;
}
if (private_key->idx != public_key->idx) {
return CRYPT_PK_TYPE_MISMATCH;
}
/* make new point */
result = ltc_ecc_new_point();
if (result == NULL) {
return CRYPT_MEM;
}
if ((err = mp_init(&prime)) != CRYPT_OK) {
ltc_ecc_del_point(result);
return err;
}
if ((err = mp_read_radix(prime, (char *)ltc_ecc_sets[private_key->idx].prime, 64)) != CRYPT_OK) { goto done; }
if ((err = ltc_ecc_mulmod(private_key->k, &public_key->pubkey, result, prime, 1)) != CRYPT_OK) { goto done; }
x = (unsigned long)mp_unsigned_bin_size(prime);
if (*outlen < x) {
err = CRYPT_BUFFER_OVERFLOW;
goto done;
}
zeromem(out, x);
if ((err = mp_to_unsigned_bin(result->x, out + (x - mp_unsigned_bin_size(result->x)))) != CRYPT_OK) { goto done; }
err = CRYPT_OK;
*outlen = x;
done:
mp_clear(prime);
ltc_ecc_del_point(result);
return err;
}
/**
Get the size of an ECC key
@param key The key to get the size of
@return The size (octets) of the key or INT_MAX on error
*/
int ecc_get_size(ecc_key *key)
{
LTC_ARGCHK(key != NULL);
if (is_valid_idx(key->idx))
return ltc_ecc_sets[key->idx].size;
else
return INT_MAX; /* large value known to cause it to fail when passed to ecc_make_key() */
}
#include "ecc_sys.c"
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */