ecp.h

/*
 * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
 * Use is subject to license terms.
 *
 * This 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 2.1 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 library; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

/* *********************************************************************
 *
 * The Original Code is the elliptic curve math library for prime field curves.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 2003
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *   Douglas Stebila <[email protected]>, Sun Microsystems Laboratories
 *
 * Last Modified Date from the Original Code: May 2017
 *********************************************************************** */

#ifndef _ECP_H
#define _ECP_H

#include "ecl-priv.h"

/* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
mp_err ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py);

/* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
mp_err ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py);

/* Computes R = P + Q where R is (rx, ry), P is (px, py) and Q is (qx,
 * qy). Uses affine coordinates. */
mp_err ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py,
                                                 const mp_int *qx, const mp_int *qy, mp_int *rx,
                                                 mp_int *ry, const ECGroup *group);

/* Computes R = P - Q.  Uses affine coordinates. */
mp_err ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py,
                                                 const mp_int *qx, const mp_int *qy, mp_int *rx,
                                                 mp_int *ry, const ECGroup *group);

/* Computes R = 2P.  Uses affine coordinates. */
mp_err ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
                                                 mp_int *ry, const ECGroup *group);

/* Validates a point on a GFp curve. */
mp_err ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group);

#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
 * a, b and p are the elliptic curve coefficients and the prime that
 * determines the field GFp.  Uses affine coordinates. */
mp_err ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px,
                                                 const mp_int *py, mp_int *rx, mp_int *ry,
                                                 const ECGroup *group);
#endif

/* Converts a point P(px, py) from affine coordinates to Jacobian
 * projective coordinates R(rx, ry, rz). */
mp_err ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
                                                 mp_int *ry, mp_int *rz, const ECGroup *group);

/* Converts a point P(px, py, pz) from Jacobian projective coordinates to
 * affine coordinates R(rx, ry). */
mp_err ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py,
                                                 const mp_int *pz, mp_int *rx, mp_int *ry,
                                                 const ECGroup *group);

/* Checks if point P(px, py, pz) is at infinity.  Uses Jacobian
 * coordinates. */
mp_err ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py,
                                                        const mp_int *pz);

/* Sets P(px, py, pz) to be the point at infinity.  Uses Jacobian
 * coordinates. */
mp_err ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz);

/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 * (qx, qy, qz).  Uses Jacobian coordinates. */
mp_err ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py,
                                                         const mp_int *pz, const mp_int *qx,
                                                         const mp_int *qy, mp_int *rx, mp_int *ry,
                                                         mp_int *rz, const ECGroup *group);

/* Computes R = 2P.  Uses Jacobian coordinates. */
mp_err ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py,
                                                 const mp_int *pz, mp_int *rx, mp_int *ry,
                                                 mp_int *rz, const ECGroup *group);

#ifdef ECL_ENABLE_GFP_PT_MUL_JAC
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
 * a, b and p are the elliptic curve coefficients and the prime that
 * determines the field GFp.  Uses Jacobian coordinates. */
mp_err ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px,
                                                 const mp_int *py, mp_int *rx, mp_int *ry,
                                                 const ECGroup *group);
#endif

/* Computes R(x, y) = k1 * G + k2 * P(x, y), where G is the generator
 * (base point) of the group of points on the elliptic curve. Allows k1 =
 * NULL or { k2, P } = NULL.  Implemented using mixed Jacobian-affine
 * coordinates. Input and output values are assumed to be NOT
 * field-encoded and are in affine form. */
mp_err
 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
                                        const mp_int *py, mp_int *rx, mp_int *ry,
                                        const ECGroup *group, int timing);

/* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
 * curve points P and R can be identical. Uses mixed Modified-Jacobian
 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
 * additions. Assumes input is already field-encoded using field_enc, and
 * returns output that is still field-encoded. Uses 5-bit window NAF
 * method (algorithm 11) for scalar-point multiplication from Brown,
 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
 * Curves Over Prime Fields. The implementation includes a countermeasure
 * that attempts to hide the size of n from timing channels. This counter-
 * measure is enabled using the timing argument. The high-rder bits of timing
 * must be uniformly random in order for this countermeasure to work. */
mp_err
 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
                                           mp_int *rx, mp_int *ry, const ECGroup *group,
                                           int timing);

#endif /* _ECP_H */