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/* 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.com
*/
/* 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 ltc_ecc_projective_add_point.c
ECC Crypto, Tom St Denis
*/
#if defined(MECC) && (!defined(MECC_ACCEL) || defined(LTM_DESC))
/**
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_projective_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;
}
/* should we dbl instead? */
if ((err = mp_sub(modulus, Q->y, t1)) != CRYPT_OK) { goto done; }
if ( (mp_cmp(P->x, Q->x) == LTC_MP_EQ) &&
(Q->z != NULL && mp_cmp(P->z, Q->z) == LTC_MP_EQ) &&
(mp_cmp(P->y, Q->y) == LTC_MP_EQ || mp_cmp(P->y, t1) == LTC_MP_EQ)) {
mp_clear_multi(t1, t2, x, y, z, NULL);
return ltc_ecc_projective_dbl_point(P, R, modulus, mp);
}
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; }
/* if Z is one then these are no-operations */
if (Q->z != NULL) {
/* 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 (Q->z != NULL) {
/* 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;
done:
mp_clear_multi(t1, t2, x, y, z, NULL);
return err;
}
#endif
/* $Source: /cvs/libtom/libtomcrypt/src/pk/ecc/ltc_ecc_projective_add_point.c,v $ */
/* $Revision: 1.13 $ */
/* $Date: 2006/12/04 05:07:59 $ */
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