/*

 * 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):

 *   Stephen Fung <fungstep@hotmail.com>, Sun Microsystems Laboratories

 *

 * Last Modified Date from the Original Code: May 2017

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

#include "ecp.h"

#include "ecl-priv.h"

#include "mplogic.h"

#ifndef _KERNEL

#include <stdlib.h>

#endif

#define MAX_SCRATCH 6

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

 * Modified Jacobian coordinates.

 *

 * Assumes input is already field-encoded using field_enc, and returns

 * output that is still field-encoded.

 *

 */

mp_err

ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,

                                 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,

                                 mp_int *raz4, mp_int scratch[], const ECGroup *group)

{

        mp_err res = MP_OKAY;

        mp_int *t0, *t1, *M, *S;

        t0 = &scratch[0];

        t1 = &scratch[1];

        M = &scratch[2];

        S = &scratch[3];

#if MAX_SCRATCH < 4

#error "Scratch array defined too small "

#endif

        /* Check for point at infinity */

        if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {

                /* Set r = pt at infinity by setting rz = 0 */

                MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));

                goto CLEANUP;

        }

        /* M = 3 (px^2) + a*(pz^4) */

        MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));

        MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));

        MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));

        MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));

        /* rz = 2 * py * pz */

        MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));

        MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));

        /* t0 = 2y^2 , t1 = 8y^4 */

        MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));

        MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));

        MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));

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

        /* S = 4 * px * py^2 = 2 * px * t0 */

        MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));

        MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));

        /* rx = M^2 - 2S */

        MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));

        MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));

        MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));

        /* ry = M * (S - rx) - t1 */

        MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));

        MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));

        MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));

        /* ra*z^4 = 2*t1*(apz4) */

        MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));

        MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));

  CLEANUP:

        return res;

}

/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is

 * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.

 * Uses mixed Modified_Jacobian-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_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,

                                         const mp_int *paz4, const mp_int *qx,

                                         const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,

                                         mp_int *raz4, mp_int scratch[], const ECGroup *group)

{

        mp_err res = MP_OKAY;

        mp_int *A, *B, *C, *D, *C2, *C3;

        A = &scratch[0];

        B = &scratch[1];

        C = &scratch[2];

        D = &scratch[3];

        C2 = &scratch[4];

        C3 = &scratch[5];

#if MAX_SCRATCH < 6

#error "Scratch array defined too small "

#endif

        /* If either P or Q is the point at infinity, then return the other

         * point */

        if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {

                MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));

                MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));

                MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));

                MP_CHECKOK(group->meth->

                                   field_mul(raz4, &group->curvea, raz4, group->meth));

                goto CLEANUP;

        }

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

                MP_CHECKOK(mp_copy(px, rx));

                MP_CHECKOK(mp_copy(py, ry));

                MP_CHECKOK(mp_copy(pz, rz));

                MP_CHECKOK(mp_copy(paz4, raz4));

                goto CLEANUP;

        }

        /* A = qx * pz^2, B = qy * pz^3 */

        MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));

        MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));

        MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));

        MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));

        /*

         * Additional checks for point equality and point at infinity

         */

        if (mp_cmp(px, A) == 0 && mp_cmp(py, B) == 0) {

            /* POINT_DOUBLE(P) */

            MP_CHECKOK(ec_GFp_pt_dbl_jm(px, py, pz, paz4, rx, ry, rz, raz4,

                                        scratch, group));

            goto CLEANUP;

        }

        /* C = A - px, D = B - py */

        MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));

        MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));

        /* C2 = C^2, C3 = C^3 */

        MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));

        MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));

        /* rz = pz * C */

        MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));

        /* C = px * C^2 */

        MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));

        /* A = D^2 */

        MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));

        /* rx = D^2 - (C^3 + 2 * (px * C^2)) */

        MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));

        MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));

        MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));

        /* C3 = py * C^3 */

        MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));

        /* ry = D * (px * C^2 - rx) - py * C^3 */

        MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));

        MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));

        MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));

        /* raz4 = a * rz^4 */

        MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));

        MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));

        MP_CHECKOK(group->meth->

                           field_mul(raz4, &group->curvea, raz4, group->meth));

CLEANUP:

        return res;

}

/* 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. */

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)

{

        mp_err res = MP_OKAY;

        mp_int precomp[16][2], rz, tpx, tpy, tpz;

        mp_int raz4, tpaz4;

        mp_int scratch[MAX_SCRATCH];

        signed char *naf = NULL;

        int i, orderBitSize;

        int numDoubles, numAdds, extraDoubles, extraAdds;

        MP_DIGITS(&rz) = 0;

        MP_DIGITS(&raz4) = 0;

        MP_DIGITS(&tpx) = 0;

        MP_DIGITS(&tpy) = 0;

        MP_DIGITS(&tpz) = 0;

        MP_DIGITS(&tpaz4) = 0;

        for (i = 0; i < 16; i++) {

                MP_DIGITS(&precomp[i][0]) = 0;

                MP_DIGITS(&precomp[i][1]) = 0;

        }

        for (i = 0; i < MAX_SCRATCH; i++) {

                MP_DIGITS(&scratch[i]) = 0;

        }

        ARGCHK(group != NULL, MP_BADARG);

        ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);

        /* initialize precomputation table */

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

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

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

        MP_CHECKOK(mp_init(&tpaz4, FLAG(n)));

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

        MP_CHECKOK(mp_init(&raz4, FLAG(n)));

        for (i = 0; i < 16; i++) {

                MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));

                MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));

        }

        for (i = 0; i < MAX_SCRATCH; i++) {

                MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));

        }

        /* Set out[8] = P */

        MP_CHECKOK(mp_copy(px, &precomp[8][0]));

        MP_CHECKOK(mp_copy(py, &precomp[8][1]));

        /* Set (tpx, tpy) = 2P */

        MP_CHECKOK(group->

                           point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,

                                                 group));

        /* Set 3P, 5P, ..., 15P */

        for (i = 8; i < 15; i++) {

                MP_CHECKOK(group->

                                   point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,

                                                         &precomp[i + 1][0], &precomp[i + 1][1],

                                                         group));

        }

        /* Set -15P, -13P, ..., -P */

        for (i = 0; i < 8; i++) {

                MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));

                MP_CHECKOK(group->meth->

                                   field_neg(&precomp[15 - i][1], &precomp[i][1],

                                                         group->meth));

        }

        /* R = inf */

        MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));

        orderBitSize = mpl_significant_bits(&group->order);

        /* Allocate memory for NAF */

#ifdef _KERNEL

        naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));

#else

        naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));

        if (naf == NULL) {

                res = MP_MEM;

                goto CLEANUP;

        }

#endif

        /* Compute 5NAF */

        ec_compute_wNAF(naf, orderBitSize, n, 5);

        numAdds = 0;

        numDoubles = orderBitSize;

        /* wNAF method */

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

                if (ec_GFp_pt_is_inf_jac(rx, ry, &rz) == MP_YES) {

                  numDoubles--;

                }

                /* R = 2R */

                ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,

                                             &raz4, scratch, group);

                if (naf[i] != 0) {

                        ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,

                                                                 &precomp[(naf[i] + 15) / 2][0],

                                                                 &precomp[(naf[i] + 15) / 2][1], rx, ry,

                                                                 &rz, &raz4, scratch, group);

                        numAdds++;

                }

        }

        /* extra operations to make timing less dependent on secrets */

        if (timing) {

                /* low-order bit of timing argument contains no entropy */

                timing >>= 1;

                MP_CHECKOK(ec_GFp_pt_set_inf_jac(&tpx, &tpy, &tpz));

                mp_zero(&tpaz4);

                /* Set the temp value to a non-infinite point */

                ec_GFp_pt_add_jm_aff(&tpx, &tpy, &tpz, &tpaz4,

                                                                 &precomp[8][0],

                                                                 &precomp[8][1], &tpx, &tpy,

                                                                 &tpz, &tpaz4, scratch, group);

                /* two bits of extra adds */

                extraAdds = timing & 0x3;

                timing >>= 2;

                /* Window size is 5, so the maximum number of additions is ceil(orderBitSize/5) */

                /* This is the same as (orderBitSize + 4) / 5 */

                for(i = numAdds; i <= (orderBitSize + 4) / 5 + extraAdds; i++) {

                        ec_GFp_pt_add_jm_aff(&tpx, &tpy, &tpz, &tpaz4,

                                                                 &precomp[9 + (i % 3)][0],

                                                                 &precomp[9 + (i % 3)][1], &tpx, &tpy,

                                                                 &tpz, &tpaz4, scratch, group);

                }

                /* two bits of extra doubles */

                extraDoubles = timing & 0x3;

                timing >>= 2;

                for(i = numDoubles; i <= orderBitSize + extraDoubles; i++) {

                        ec_GFp_pt_dbl_jm(&tpx, &tpy, &tpz, &tpaz4, &tpx, &tpy, &tpz,

                                             &tpaz4, scratch, group);

                }

        }

        /* convert result S to affine coordinates */

        MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));

  CLEANUP:

        for (i = 0; i < MAX_SCRATCH; i++) {

                mp_clear(&scratch[i]);

        }

        for (i = 0; i < 16; i++) {

                mp_clear(&precomp[i][0]);

                mp_clear(&precomp[i][1]);

        }

        mp_clear(&tpx);

        mp_clear(&tpy);

        mp_clear(&tpz);

        mp_clear(&tpaz4);

        mp_clear(&rz);

        mp_clear(&raz4);

#ifdef _KERNEL

        kmem_free(naf, (orderBitSize + 1));

#else

        free(naf);

#endif

        return res;

}