/*

 * 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 binary polynomial 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):

 *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,

 *   Stephen Fung <fungstep@hotmail.com>, and

 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.

 *

 *  Last Modified Date from the Original Code: May 2017

 *********************************************************************** */

#include "ec2.h"

#include "mplogic.h"

#include "mp_gf2m.h"

#ifndef _KERNEL

#include <stdlib.h>

#endif

/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery

 * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.

 * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)

 * without precomputation". modified to not require precomputation of

 * c=b^{2^{m-1}}. */

static mp_err

gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag)

{

        mp_err res = MP_OKAY;

        mp_int t1;

        MP_DIGITS(&t1) = 0;

        MP_CHECKOK(mp_init(&t1, kmflag));

        MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));

        MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));

        MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));

        MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));

        MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));

        MP_CHECKOK(group->meth->

                           field_mul(&group->curveb, &t1, &t1, group->meth));

        MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));

  CLEANUP:

        mp_clear(&t1);

        return res;

}

/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in

 * Montgomery projective coordinates. Uses algorithm Madd in appendix of

 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over

 * GF(2^m) without precomputation". */

static mp_err

gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,

                  const ECGroup *group, int kmflag)

{

        mp_err res = MP_OKAY;

        mp_int t1, t2;

        MP_DIGITS(&t1) = 0;

        MP_DIGITS(&t2) = 0;

        MP_CHECKOK(mp_init(&t1, kmflag));

        MP_CHECKOK(mp_init(&t2, kmflag));

        MP_CHECKOK(mp_copy(x, &t1));

        MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));

        MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));

        MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));

        MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));

        MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));

        MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));

        MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));

  CLEANUP:

        mp_clear(&t1);

        mp_clear(&t2);

        return res;

}

/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)

 * using Montgomery point multiplication algorithm Mxy() in appendix of

 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over

 * GF(2^m) without precomputation". Returns: 0 on error 1 if return value

 * should be the point at infinity 2 otherwise */

static int

gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,

                 mp_int *x2, mp_int *z2, const ECGroup *group)

{

        mp_err res = MP_OKAY;

        int ret = 0;

        mp_int t3, t4, t5;

        MP_DIGITS(&t3) = 0;

        MP_DIGITS(&t4) = 0;

        MP_DIGITS(&t5) = 0;

        MP_CHECKOK(mp_init(&t3, FLAG(x2)));

        MP_CHECKOK(mp_init(&t4, FLAG(x2)));

        MP_CHECKOK(mp_init(&t5, FLAG(x2)));

        if (mp_cmp_z(z1) == 0) {

                mp_zero(x2);

                mp_zero(z2);

                ret = 1;

                goto CLEANUP;

        }

        if (mp_cmp_z(z2) == 0) {

                MP_CHECKOK(mp_copy(x, x2));

                MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));

                ret = 2;

                goto CLEANUP;

        }

        MP_CHECKOK(mp_set_int(&t5, 1));

        if (group->meth->field_enc) {

                MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));

        }

        MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));

        MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));

        MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));

        MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));

        MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));

        MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));

        MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));

        MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));

        MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));

        MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));

        MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));

        MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));

        MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));

        MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));

        MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));

        MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));

        MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));

        MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));

        ret = 2;

  CLEANUP:

        mp_clear(&t3);

        mp_clear(&t4);

        mp_clear(&t5);

        if (res == MP_OKAY) {

                return ret;

        } else {

                return 0;

        }

}

/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast

 * multiplication on elliptic curves over GF(2^m) without

 * precomputation". Elliptic curve points P and R can be identical. Uses

 * Montgomery projective coordinates. The timing parameter is ignored

 * because this algorithm resists timing attacks by default. */

mp_err

ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,

                                        mp_int *rx, mp_int *ry, const ECGroup *group,

                                        int timing)

{

        mp_err res = MP_OKAY;

        mp_int x1, x2, z1, z2;

        int i, j;

        mp_digit top_bit, mask;

        MP_DIGITS(&x1) = 0;

        MP_DIGITS(&x2) = 0;

        MP_DIGITS(&z1) = 0;

        MP_DIGITS(&z2) = 0;

        MP_CHECKOK(mp_init(&x1, FLAG(n)));

        MP_CHECKOK(mp_init(&x2, FLAG(n)));

        MP_CHECKOK(mp_init(&z1, FLAG(n)));

        MP_CHECKOK(mp_init(&z2, FLAG(n)));

        /* if result should be point at infinity */

        if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {

                MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));

                goto CLEANUP;

        }

        MP_CHECKOK(mp_copy(px, &x1));   /* x1 = px */

        MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */

        MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));      /* z2 =

                                                                                                                                 * x1^2 =

                                                                                                                                 * px^2 */

        MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));

        MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));      /* x2

                                                                                                                                                                 * =

                                                                                                                                                                 * px^4

                                                                                                                                                                 * +

                                                                                                                                                                 * b

                                                                                                                                                                 */

        /* find top-most bit and go one past it */

        i = MP_USED(n) - 1;

        j = MP_DIGIT_BIT - 1;

        top_bit = 1;

        top_bit <<= MP_DIGIT_BIT - 1;

        mask = top_bit;

        while (!(MP_DIGITS(n)[i] & mask)) {

                mask >>= 1;

                j--;

        }

        mask >>= 1;

        j--;

        /* if top most bit was at word break, go to next word */

        if (!mask) {

                i--;

                j = MP_DIGIT_BIT - 1;

                mask = top_bit;

        }

        for (; i >= 0; i--) {

                for (; j >= 0; j--) {

                        if (MP_DIGITS(n)[i] & mask) {

                                MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n)));

                                MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));

                        } else {

                                MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));

                                MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));

                        }

                        mask >>= 1;

                }

                j = MP_DIGIT_BIT - 1;

                mask = top_bit;

        }

        /* convert out of "projective" coordinates */

        i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);

        if (i == 0) {

                res = MP_BADARG;

                goto CLEANUP;

        } else if (i == 1) {

                MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));

        } else {

                MP_CHECKOK(mp_copy(&x2, rx));

                MP_CHECKOK(mp_copy(&z2, ry));

        }

  CLEANUP:

        mp_clear(&x1);

        mp_clear(&x2);

        mp_clear(&z1);

        mp_clear(&z2);

        return res;

}