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/*
* Copyright (C) 2011 Free Software Foundation, Inc.
*
* This file is part of GNUTLS.
*
* The GNUTLS library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public License
* as published by the Free Software Foundation; either version 3 of
* the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>
*
*/
/* Based on public domain code of LibTomCrypt by Tom St Denis.
* Adapted to gmp and nettle by Nikos Mavrogiannopoulos.
*/
#include "ecc.h"
/*
@file ecc_projective_add_point.c
ECC Crypto, Tom St Denis
*/
/*
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 a Curve's a value
@param modulus The modulus of the field the ECC curve is in
@return 0 on success
*/
int
ecc_projective_add_point (ecc_point * P, ecc_point * Q, ecc_point * R,
mpz_t a, mpz_t modulus)
{
mpz_t t1, t2, x, y, z;
int err;
if (P == NULL || Q == NULL || R == NULL || modulus == NULL)
return -1;
if ((err = mp_init_multi (&t1, &t2, &x, &y, &z, NULL)) != 0)
{
return err;
}
/* Check if P == Q and do doubling in that case
* If Q == -P then P+Q=point at infinity
*/
if ((mpz_cmp (P->x, Q->x) == 0) &&
(mpz_cmp (P->z, Q->z) == 0))
{
/* x and z coordinates match. Check if P->y = Q->y, or P->y = -Q->y
*/
if (mpz_cmp (P->y, Q->y) == 0)
{
mp_clear_multi (&t1, &t2, &x, &y, &z, NULL);
return ecc_projective_dbl_point (P, R, a, modulus);
}
mpz_sub (t1, modulus, Q->y);
if (mpz_cmp (P->y, t1) == 0)
{
mp_clear_multi (&t1, &t2, &x, &y, &z, NULL);
mpz_set_ui(R->x, 1);
mpz_set_ui(R->y, 1);
mpz_set_ui(R->z, 0);
return 0;
}
}
mpz_set (x, P->x);
mpz_set (y, P->y);
mpz_set (z, P->z);
/* if Z is one then these are no-operations */
if (mpz_cmp_ui (Q->z, 1) != 0)
{
/* T1 = Z' * Z' */
mpz_mul (t1, Q->z, Q->z);
mpz_mod (t1, t1, modulus);
/* X = X * T1 */
mpz_mul (x, x, t1);
mpz_mod (x, x, modulus);
/* T1 = Z' * T1 */
mpz_mul (t1, t1, Q->z);
mpz_mod (t1, t1, modulus);
/* Y = Y * T1 */
mpz_mul (y, y, t1);
mpz_mod (y, y, modulus);
}
/* T1 = Z*Z */
mpz_mul (t1, z, z);
mpz_mod (t1, t1, modulus);
/* T2 = X' * T1 */
mpz_mul (t2, t1, Q->x);
mpz_mod (t2, t2, modulus);
/* T1 = Z * T1 */
mpz_mul (t1, t1, z);
mpz_mod (t1, t1, modulus);
/* T1 = Y' * T1 */
mpz_mul (t1, t1, Q->y);
mpz_mod (t1, t1, modulus);
/* Y = Y - T1 */
mpz_sub (y, y, t1);
if (mpz_cmp_ui (y, 0) < 0)
{
mpz_add (y, y, modulus);
}
/* T1 = 2T1 */
mpz_add (t1, t1, t1);
if (mpz_cmp (t1, modulus) >= 0)
{
mpz_sub (t1, t1, modulus);
}
/* T1 = Y + T1 */
mpz_add (t1, t1, y);
if (mpz_cmp (t1, modulus) >= 0)
{
mpz_sub (t1, t1, modulus);
}
/* X = X - T2 */
mpz_sub (x, x, t2);
if (mpz_cmp_ui (x, 0) < 0)
{
mpz_add (x, x, modulus);
}
/* T2 = 2T2 */
mpz_add (t2, t2, t2);
if (mpz_cmp (t2, modulus) >= 0)
{
mpz_sub (t2, t2, modulus);
}
/* T2 = X + T2 */
mpz_add (t2, t2, x);
if (mpz_cmp (t2, modulus) >= 0)
{
mpz_sub (t2, t2, modulus);
}
/* if Z' != 1 */
if (mpz_cmp_ui (Q->z, 1) != 0)
{
/* Z = Z * Z' */
mpz_mul (z, z, Q->z);
mpz_mod (z, z, modulus);
}
/* Z = Z * X */
mpz_mul (z, z, x);
mpz_mod (z, z, modulus);
/* T1 = T1 * X */
mpz_mul (t1, t1, x);
mpz_mod (t1, t1, modulus);
/* X = X * X */
mpz_mul (x, x, x);
mpz_mod (x, x, modulus);
/* T2 = T2 * x */
mpz_mul (t2, t2, x);
mpz_mod (t2, t2, modulus);
/* T1 = T1 * X */
mpz_mul (t1, t1, x);
mpz_mod (t1, t1, modulus);
/* X = Y*Y */
mpz_mul (x, y, y);
mpz_mod (x, x, modulus);
/* X = X - T2 */
mpz_sub (x, x, t2);
if (mpz_cmp_ui (x, 0) < 0)
{
mpz_add (x, x, modulus);
}
/* T2 = T2 - X */
mpz_sub (t2, t2, x);
if (mpz_cmp_ui (t2, 0) < 0)
{
mpz_add (t2, t2, modulus);
}
/* T2 = T2 - X */
mpz_sub (t2, t2, x);
if (mpz_cmp_ui (t2, 0) < 0)
{
mpz_add (t2, t2, modulus);
}
/* T2 = T2 * Y */
mpz_mul (t2, t2, y);
mpz_mod (t2, t2, modulus);
/* Y = T2 - T1 */
mpz_sub (y, t2, t1);
if (mpz_cmp_ui (y, 0) < 0)
{
mpz_add (y, y, modulus);
}
/* Y = Y/2 */
if (mpz_odd_p (y))
{
mpz_add (y, y, modulus);
}
mpz_divexact_ui (y, y, 2);
mpz_set (R->x, x);
mpz_set (R->y, y);
mpz_set (R->z, z);
err = 0;
mp_clear_multi (&t1, &t2, &x, &y, &z, NULL);
return err;
}
/* $Source: /cvs/libtom/libtomcrypt/src/pk/ecc/ecc_projective_add_point.c,v $ */
/* $Revision: 1.16 $ */
/* $Date: 2007/05/12 14:32:35 $ */
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