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

 *

 * Sun elects to have this file available under and governed by the

 * Mozilla Public License Version 1.1 ("MPL") (see

 * http://www.mozilla.org/MPL/ for full license text). For the avoidance

 * of doubt and subject to the following, Sun also elects to allow

 * licensees to use this file under the MPL, the GNU General Public

 * License version 2 only or the Lesser General Public License version

 * 2.1 only. Any references to the "GNU General Public License version 2

 * or later" or "GPL" in the following shall be construed to mean the

 * GNU General Public License version 2 only. Any references to the "GNU

 * Lesser General Public License version 2.1 or later" or "LGPL" in the

 * following shall be construed to mean the GNU Lesser General Public

 * License version 2.1 only. However, the following notice accompanied

 * the original version of this file:

 *

 * Version: MPL 1.1/GPL 2.0/LGPL 2.1

 *

 * The contents of this file are subject to the Mozilla Public License Version

 * 1.1 (the "License"); you may not use this file except in compliance with

 * the License. You may obtain a copy of the License at

 * http://www.mozilla.org/MPL/

 *

 * Software distributed under the License is distributed on an "AS IS" basis,

 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License

 * for the specific language governing rights and limitations under the

 * License.

 *

 * 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):

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

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

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

 *   Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,

 *   Nils Larsch <nla@trustcenter.de>, and

 *   Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project

 *

 * Alternatively, the contents of this file may be used under the terms of

 * either the GNU General Public License Version 2 or later (the "GPL"), or

 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),

 * in which case the provisions of the GPL or the LGPL are applicable instead

 * of those above. If you wish to allow use of your version of this file only

 * under the terms of either the GPL or the LGPL, and not to allow others to

 * use your version of this file under the terms of the MPL, indicate your

 * decision by deleting the provisions above and replace them with the notice

 * and other provisions required by the GPL or the LGPL. If you do not delete

 * the provisions above, a recipient may use your version of this file under

 * the terms of any one of the MPL, the GPL or the LGPL.

 *

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

/*

 * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.

 * Use is subject to license terms.

 */

#pragma ident   "%Z%%M% %I%     %E% SMI"

#include "ecp.h"

#include "mplogic.h"

#ifndef _KERNEL

#include <stdlib.h>

#endif

/* 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)

{

        if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {

                return MP_YES;

        } else {

                return MP_NO;

        }

}

/* 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)

{

        mp_zero(px);

        mp_zero(py);

        return MP_OKAY;

}

/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,

 * Q, and R can all be identical. Uses affine coordinates. Assumes input

 * is already field-encoded using field_enc, and returns output that is

 * still field-encoded. */

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)

{

        mp_err res = MP_OKAY;

        mp_int lambda, temp, tempx, tempy;

        MP_DIGITS(&lambda) = 0;

        MP_DIGITS(&temp) = 0;

        MP_DIGITS(&tempx) = 0;

        MP_DIGITS(&tempy) = 0;

        MP_CHECKOK(mp_init(&lambda, FLAG(px)));

        MP_CHECKOK(mp_init(&temp, FLAG(px)));

        MP_CHECKOK(mp_init(&tempx, FLAG(px)));

        MP_CHECKOK(mp_init(&tempy, FLAG(px)));

        /* if P = inf, then R = Q */

        if (ec_GFp_pt_is_inf_aff(px, py) == 0) {

                MP_CHECKOK(mp_copy(qx, rx));

                MP_CHECKOK(mp_copy(qy, ry));

                res = MP_OKAY;

                goto CLEANUP;

        }

        /* if Q = inf, then R = P */

        if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {

                MP_CHECKOK(mp_copy(px, rx));

                MP_CHECKOK(mp_copy(py, ry));

                res = MP_OKAY;

                goto CLEANUP;

        }

        /* if px != qx, then lambda = (py-qy) / (px-qx) */

        if (mp_cmp(px, qx) != 0) {

                MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));

                MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));

                MP_CHECKOK(group->meth->

                                   field_div(&tempy, &tempx, &lambda, group->meth));

        } else {

                /* if py != qy or qy = 0, then R = inf */

                if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {

                        mp_zero(rx);

                        mp_zero(ry);

                        res = MP_OKAY;

                        goto CLEANUP;

                }

                /* lambda = (3qx^2+a) / (2qy) */

                MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));

                MP_CHECKOK(mp_set_int(&temp, 3));

                if (group->meth->field_enc) {

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

                }

                MP_CHECKOK(group->meth->

                                   field_mul(&tempx, &temp, &tempx, group->meth));

                MP_CHECKOK(group->meth->

                                   field_add(&tempx, &group->curvea, &tempx, group->meth));

                MP_CHECKOK(mp_set_int(&temp, 2));

                if (group->meth->field_enc) {

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

                }

                MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));

                MP_CHECKOK(group->meth->

                                   field_div(&tempx, &tempy, &lambda, group->meth));

        }

        /* rx = lambda^2 - px - qx */

        MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));

        MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));

        MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));

        /* ry = (x1-x2) * lambda - y1 */

        MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));

        MP_CHECKOK(group->meth->

                           field_mul(&tempy, &lambda, &tempy, group->meth));

        MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));

        MP_CHECKOK(mp_copy(&tempx, rx));

        MP_CHECKOK(mp_copy(&tempy, ry));

  CLEANUP:

        mp_clear(&lambda);

        mp_clear(&temp);

        mp_clear(&tempx);

        mp_clear(&tempy);

        return res;

}

/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be

 * identical. Uses affine coordinates. Assumes input is already

 * field-encoded using field_enc, and returns output that is still

 * field-encoded. */

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)

{

        mp_err res = MP_OKAY;

        mp_int nqy;

        MP_DIGITS(&nqy) = 0;

        MP_CHECKOK(mp_init(&nqy, FLAG(px)));

        /* nqy = -qy */

        MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));

        res = group->point_add(px, py, qx, &nqy, rx, ry, group);

  CLEANUP:

        mp_clear(&nqy);

        return res;

}

/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses

 * affine coordinates. Assumes input is already field-encoded using

 * field_enc, and returns output that is still field-encoded. */

mp_err

ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,

                                  mp_int *ry, const ECGroup *group)

{

        return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);

}

/* by default, this routine is unused and thus doesn't need to be compiled */

#ifdef ECL_ENABLE_GFP_PT_MUL_AFF

/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and

 * R can be identical. Uses affine coordinates. Assumes input is already

 * field-encoded using field_enc, and returns output that is still

 * field-encoded. */

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)

{

        mp_err res = MP_OKAY;

        mp_int k, k3, qx, qy, sx, sy;

        int b1, b3, i, l;

        MP_DIGITS(&k) = 0;

        MP_DIGITS(&k3) = 0;

        MP_DIGITS(&qx) = 0;

        MP_DIGITS(&qy) = 0;

        MP_DIGITS(&sx) = 0;

        MP_DIGITS(&sy) = 0;

        MP_CHECKOK(mp_init(&k));

        MP_CHECKOK(mp_init(&k3));

        MP_CHECKOK(mp_init(&qx));

        MP_CHECKOK(mp_init(&qy));

        MP_CHECKOK(mp_init(&sx));

        MP_CHECKOK(mp_init(&sy));

        /* if n = 0 then r = inf */

        if (mp_cmp_z(n) == 0) {

                mp_zero(rx);

                mp_zero(ry);

                res = MP_OKAY;

                goto CLEANUP;

        }

        /* Q = P, k = n */

        MP_CHECKOK(mp_copy(px, &qx));

        MP_CHECKOK(mp_copy(py, &qy));

        MP_CHECKOK(mp_copy(n, &k));

        /* if n < 0 then Q = -Q, k = -k */

        if (mp_cmp_z(n) < 0) {

                MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));

                MP_CHECKOK(mp_neg(&k, &k));

        }

#ifdef ECL_DEBUG                                /* basic double and add method */

        l = mpl_significant_bits(&k) - 1;

        MP_CHECKOK(mp_copy(&qx, &sx));

        MP_CHECKOK(mp_copy(&qy, &sy));

        for (i = l - 1; i >= 0; i--) {

                /* S = 2S */

                MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));

                /* if k_i = 1, then S = S + Q */

                if (mpl_get_bit(&k, i) != 0) {

                        MP_CHECKOK(group->

                                           point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));

                }

        }

#else                                                   /* double and add/subtract method from

                                                                 * standard */

        /* k3 = 3 * k */

        MP_CHECKOK(mp_set_int(&k3, 3));

        MP_CHECKOK(mp_mul(&k, &k3, &k3));

        /* S = Q */

        MP_CHECKOK(mp_copy(&qx, &sx));

        MP_CHECKOK(mp_copy(&qy, &sy));

        /* l = index of high order bit in binary representation of 3*k */

        l = mpl_significant_bits(&k3) - 1;

        /* for i = l-1 downto 1 */

        for (i = l - 1; i >= 1; i--) {

                /* S = 2S */

                MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));

                b3 = MP_GET_BIT(&k3, i);

                b1 = MP_GET_BIT(&k, i);

                /* if k3_i = 1 and k_i = 0, then S = S + Q */

                if ((b3 == 1) && (b1 == 0)) {

                        MP_CHECKOK(group->

                                           point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));

                        /* if k3_i = 0 and k_i = 1, then S = S - Q */

                } else if ((b3 == 0) && (b1 == 1)) {

                        MP_CHECKOK(group->

                                           point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));

                }

        }

#endif

        /* output S */

        MP_CHECKOK(mp_copy(&sx, rx));

        MP_CHECKOK(mp_copy(&sy, ry));

  CLEANUP:

        mp_clear(&k);

        mp_clear(&k3);

        mp_clear(&qx);

        mp_clear(&qy);

        mp_clear(&sx);

        mp_clear(&sy);

        return res;

}

#endif

/* Validates a point on a GFp curve. */

mp_err

ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)

{

        mp_err res = MP_NO;

        mp_int accl, accr, tmp, pxt, pyt;

        MP_DIGITS(&accl) = 0;

        MP_DIGITS(&accr) = 0;

        MP_DIGITS(&tmp) = 0;

        MP_DIGITS(&pxt) = 0;

        MP_DIGITS(&pyt) = 0;

        MP_CHECKOK(mp_init(&accl, FLAG(px)));

        MP_CHECKOK(mp_init(&accr, FLAG(px)));

        MP_CHECKOK(mp_init(&tmp, FLAG(px)));

        MP_CHECKOK(mp_init(&pxt, FLAG(px)));

        MP_CHECKOK(mp_init(&pyt, FLAG(px)));

    /* 1: Verify that publicValue is not the point at infinity */

        if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {

                res = MP_NO;

                goto CLEANUP;

        }

    /* 2: Verify that the coordinates of publicValue are elements

     *    of the field.

     */

        if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||

                (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {

                res = MP_NO;

                goto CLEANUP;

        }

    /* 3: Verify that publicValue is on the curve. */

        if (group->meth->field_enc) {

                group->meth->field_enc(px, &pxt, group->meth);

                group->meth->field_enc(py, &pyt, group->meth);

        } else {

                mp_copy(px, &pxt);

                mp_copy(py, &pyt);

        }

        /* left-hand side: y^2  */

        MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );

        /* right-hand side: x^3 + a*x + b */

        MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );

        MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );

        MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );

        MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );

        MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );

        /* check LHS - RHS == 0 */

        MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );

        if (mp_cmp_z(&accr) != 0) {

                res = MP_NO;

                goto CLEANUP;

        }

    /* 4: Verify that the order of the curve times the publicValue

     *    is the point at infinity.

     */

        MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );

        if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {

                res = MP_NO;

                goto CLEANUP;

        }

        res = MP_YES;

CLEANUP:

        mp_clear(&accl);

        mp_clear(&accr);

        mp_clear(&tmp);

        mp_clear(&pxt);

        mp_clear(&pyt);

        return res;

}