crypto/ecc/ecl_mult.c

f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/*
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * ***** BEGIN LICENSE BLOCK *****
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Version: MPL 1.1/GPL 2.0/LGPL 2.1
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The contents of this file are subject to the Mozilla Public License Version
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * 1.1 (the "License"); you may not use this file except in compliance with
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the License. You may obtain a copy of the License at
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * http://www.mozilla.org/MPL/
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Software distributed under the License is distributed on an "AS IS" basis,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * for the specific language governing rights and limitations under the
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * License.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The Original Code is the elliptic curve math library.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * The Initial Developer of the Original Code is
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Sun Microsystems, Inc.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Portions created by the Initial Developer are Copyright (C) 2003
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the Initial Developer. All Rights Reserved.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Contributor(s):
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Alternatively, the contents of this file may be used under the terms of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * either the GNU General Public License Version 2 or later (the "GPL"), or
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * in which case the provisions of the GPL or the LGPL are applicable instead
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * of those above. If you wish to allow use of your version of this file only
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * under the terms of either the GPL or the LGPL, and not to allow others to
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * use your version of this file under the terms of the MPL, indicate your
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * decision by deleting the provisions above and replace them with the notice
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * and other provisions required by the GPL or the LGPL. If you do not delete
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the provisions above, a recipient may use your version of this file under
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * the terms of any one of the MPL, the GPL or the LGPL.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * ***** END LICENSE BLOCK ***** */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/*
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Use is subject to license terms.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers *
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Sun elects to use this software under the MPL license.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#pragma ident   "%Z%%M% %I% %E% SMI"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "mpi.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "mplogic.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "ecl.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include "ecl-priv.h"
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#ifndef _KERNEL
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#include <stdlib.h>
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers#endif
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * y).  If x, y = NULL, then P is assumed to be the generator (base point)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * of the group of points on the elliptic curve. Input and output values
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * are assumed to be NOT field-encoded. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            const mp_int *py, mp_int *rx, mp_int *ry)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int kt;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&kt) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* want scalar to be less than or equal to group order */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (mp_cmp(k, &group->order) > 0) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_init(&kt, FLAG(k)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_mod(k, &group->order, &kt));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_SIGN(&kt) = MP_ZPOS;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_USED(&kt) = MP_USED(k);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_ALLOC(&kt) = MP_ALLOC(k);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_DIGITS(&kt) = MP_DIGITS(k);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if ((px == NULL) || (py == NULL)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (group->base_point_mul) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                       point_mul(&kt, &group->genx, &group->geny, rx, ry,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                                 group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (group->meth->field_enc) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (group->meth->field_dec) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        mp_clear(&kt);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * k2 * P(x, y), where G is the generator (base point) of the group of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Input and output values are assumed to be NOT field-encoded. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                 const mp_int *py, mp_int *rx, mp_int *ry,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                 const ECGroup *group)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int sx, sy;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK(group != NULL, MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK(!((k1 == NULL)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers             && ((k2 == NULL) || (px == NULL)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                 || (py == NULL))), MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* if some arguments are not defined used ECPoint_mul */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (k1 == NULL) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return ECPoint_mul(group, k2, px, py, rx, ry);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&sx) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&sy) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(mp_init(&sx, FLAG(k1)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(mp_init(&sy, FLAG(k1)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (group->meth->field_enc) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (group->meth->field_dec) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_clear(&sx);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_clear(&sy);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * k2 * P(x, y), where G is the generator (base point) of the group of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Input and output values are assumed to be NOT field-encoded. Uses
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * algorithm 15 (simultaneous multiple point multiplication) from Brown,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Hankerson, Lopez, Menezes. Software Implementation of the NIST
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Elliptic Curves over Prime Fields. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                    const mp_int *py, mp_int *rx, mp_int *ry,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                    const ECGroup *group)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int precomp[4][4][2];
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    const mp_int *a, *b;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    int i, j;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    int ai, bi, d;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK(group != NULL, MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK(!((k1 == NULL)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers             && ((k2 == NULL) || (px == NULL)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                 || (py == NULL))), MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* if some arguments are not defined used ECPoint_mul */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (k1 == NULL) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return ECPoint_mul(group, k2, px, py, rx, ry);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* initialize precomputation table */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 0; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        for (j = 0; j < 4; j++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_DIGITS(&precomp[i][j][0]) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_DIGITS(&precomp[i][j][1]) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 0; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        for (j = 0; j < 4; j++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers             MP_CHECKOK( mp_init_size(&precomp[i][j][0],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                     ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers             MP_CHECKOK( mp_init_size(&precomp[i][j][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                     ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* fill precomputation table */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        a = k2;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        b = k1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (group->meth->field_enc) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                       field_enc(px, &precomp[1][0][0], group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                       field_enc(py, &precomp[1][0][1], group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        a = k1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        b = k2;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (group->meth->field_enc) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                       field_enc(px, &precomp[0][1][0], group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(group->meth->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                       field_enc(py, &precomp[0][1][1], group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* precompute [*][0][*] */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_zero(&precomp[0][0][0]);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_zero(&precomp[0][0][1]);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers               point_dbl(&precomp[1][0][0], &precomp[1][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[2][0][0], &precomp[2][0][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers               point_add(&precomp[1][0][0], &precomp[1][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[2][0][0], &precomp[2][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[3][0][0], &precomp[3][0][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* precompute [*][1][*] */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 1; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                   point_add(&precomp[0][1][0], &precomp[0][1][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][0][0], &precomp[i][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][1][0], &precomp[i][1][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* precompute [*][2][*] */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers               point_dbl(&precomp[0][1][0], &precomp[0][1][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[0][2][0], &precomp[0][2][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 1; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                   point_add(&precomp[0][2][0], &precomp[0][2][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][0][0], &precomp[i][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][2][0], &precomp[i][2][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* precompute [*][3][*] */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers               point_add(&precomp[0][1][0], &precomp[0][1][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[0][2][0], &precomp[0][2][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                         &precomp[0][3][0], &precomp[0][3][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 1; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                   point_add(&precomp[0][3][0], &precomp[0][3][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][0][0], &precomp[i][0][1],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[i][3][0], &precomp[i][3][1], group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    d = (mpl_significant_bits(a) + 1) / 2;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* R = inf */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_zero(rx);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_zero(ry);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = d - 1; i >= 0; i--) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        ai = MP_GET_BIT(a, 2 * i + 1);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        ai <<= 1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        ai |= MP_GET_BIT(a, 2 * i);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        bi = MP_GET_BIT(b, 2 * i + 1);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        bi <<= 1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        bi |= MP_GET_BIT(b, 2 * i);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        /* R = 2^2 * R */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        /* R = R + (ai * A + bi * B) */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                   point_add(rx, ry, &precomp[ai][bi][0],
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers                             &precomp[ai][bi][1], rx, ry, group));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (group->meth->field_dec) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    for (i = 0; i < 4; i++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        for (j = 0; j < 4; j++) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            mp_clear(&precomp[i][j][0]);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            mp_clear(&precomp[i][j][1]);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * k2 * P(x, y), where G is the generator (base point) of the group of
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers * Input and output values are assumed to be NOT field-encoded. */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersmp_err
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowersECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers             const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers{
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_err res = MP_OKAY;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_int k1t, k2t;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    const mp_int *k1p, *k2p;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&k1t) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    MP_DIGITS(&k2t) = 0;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    ARGCHK(group != NULL, MP_BADARG);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* want scalar to be less than or equal to group order */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (k1 != NULL) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (mp_cmp(k1, &group->order) >= 0) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            k1p = &k1t;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            k1p = k1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        k1p = k1;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (k2 != NULL) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        if (mp_cmp(k2, &group->order) >= 0) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            k2p = &k2t;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers            k2p = k2;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        k2p = k2;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    /* if points_mul is defined, then use it */
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    if (group->points_mul) {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    } else {
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers        res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    }
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers  CLEANUP:
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_clear(&k1t);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    mp_clear(&k2t);
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers    return res;
f9fbec18f5b458b560ecf45d3db8e8bd56bf6942mcpowers}