mirror of
https://github.com/rn10950/RetroZilla.git
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357 lines
11 KiB
C
357 lines
11 KiB
C
/*
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* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is the elliptic curve math library.
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*
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* The Initial Developer of the Original Code is
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* Sun Microsystems, Inc.
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* Portions created by the Initial Developer are Copyright (C) 2003
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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* Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
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*
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* Alternatively, the contents of this file may be used under the terms of
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* either the GNU General Public License Version 2 or later (the "GPL"), or
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* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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* in which case the provisions of the GPL or the LGPL are applicable instead
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* of those above. If you wish to allow use of your version of this file only
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* under the terms of either the GPL or the LGPL, and not to allow others to
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* use your version of this file under the terms of the MPL, indicate your
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* decision by deleting the provisions above and replace them with the notice
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* and other provisions required by the GPL or the LGPL. If you do not delete
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* the provisions above, a recipient may use your version of this file under
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* the terms of any one of the MPL, the GPL or the LGPL.
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*
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* ***** END LICENSE BLOCK ***** */
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#include "mpi.h"
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#include "mplogic.h"
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#include "ecl.h"
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#include "ecl-priv.h"
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#include <stdlib.h>
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
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* y). If x, y = NULL, then P is assumed to be the generator (base point)
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* of the group of points on the elliptic curve. Input and output values
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* are assumed to be NOT field-encoded. */
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mp_err
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ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
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const mp_int *py, mp_int *rx, mp_int *ry)
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{
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mp_err res = MP_OKAY;
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mp_int kt;
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ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
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MP_DIGITS(&kt) = 0;
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/* want scalar to be less than or equal to group order */
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if (mp_cmp(k, &group->order) > 0) {
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MP_CHECKOK(mp_init(&kt));
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MP_CHECKOK(mp_mod(k, &group->order, &kt));
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} else {
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MP_SIGN(&kt) = MP_ZPOS;
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MP_USED(&kt) = MP_USED(k);
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MP_ALLOC(&kt) = MP_ALLOC(k);
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MP_DIGITS(&kt) = MP_DIGITS(k);
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}
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if ((px == NULL) || (py == NULL)) {
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if (group->base_point_mul) {
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MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
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} else {
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MP_CHECKOK(group->
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point_mul(&kt, &group->genx, &group->geny, rx, ry,
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group));
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}
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} else {
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
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MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
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MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
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} else {
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MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
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}
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}
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if (group->meth->field_dec) {
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MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
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MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
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}
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CLEANUP:
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if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
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mp_clear(&kt);
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}
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return res;
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}
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
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* k2 * P(x, y), where G is the generator (base point) of the group of
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* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
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* Input and output values are assumed to be NOT field-encoded. */
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mp_err
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ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
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const mp_int *py, mp_int *rx, mp_int *ry,
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const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int sx, sy;
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ARGCHK(group != NULL, MP_BADARG);
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ARGCHK(!((k1 == NULL)
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&& ((k2 == NULL) || (px == NULL)
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|| (py == NULL))), MP_BADARG);
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/* if some arguments are not defined used ECPoint_mul */
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if (k1 == NULL) {
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return ECPoint_mul(group, k2, px, py, rx, ry);
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} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
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return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
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}
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MP_DIGITS(&sx) = 0;
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MP_DIGITS(&sy) = 0;
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MP_CHECKOK(mp_init(&sx));
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MP_CHECKOK(mp_init(&sy));
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MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
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MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
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MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
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MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
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MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
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}
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MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
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if (group->meth->field_dec) {
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MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
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MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
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}
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CLEANUP:
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mp_clear(&sx);
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mp_clear(&sy);
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return res;
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}
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
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* k2 * P(x, y), where G is the generator (base point) of the group of
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* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
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* Input and output values are assumed to be NOT field-encoded. Uses
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* algorithm 15 (simultaneous multiple point multiplication) from Brown,
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* Hankerson, Lopez, Menezes. Software Implementation of the NIST
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* Elliptic Curves over Prime Fields. */
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mp_err
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ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
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const mp_int *py, mp_int *rx, mp_int *ry,
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const ECGroup *group)
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{
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mp_err res = MP_OKAY;
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mp_int precomp[4][4][2];
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const mp_int *a, *b;
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int i, j;
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int ai, bi, d;
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ARGCHK(group != NULL, MP_BADARG);
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ARGCHK(!((k1 == NULL)
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&& ((k2 == NULL) || (px == NULL)
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|| (py == NULL))), MP_BADARG);
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/* if some arguments are not defined used ECPoint_mul */
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if (k1 == NULL) {
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return ECPoint_mul(group, k2, px, py, rx, ry);
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} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
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return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
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}
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/* initialize precomputation table */
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for (i = 0; i < 4; i++) {
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for (j = 0; j < 4; j++) {
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MP_DIGITS(&precomp[i][j][0]) = 0;
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MP_DIGITS(&precomp[i][j][1]) = 0;
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}
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}
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for (i = 0; i < 4; i++) {
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for (j = 0; j < 4; j++) {
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MP_CHECKOK( mp_init_size(&precomp[i][j][0],
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ECL_MAX_FIELD_SIZE_DIGITS) );
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MP_CHECKOK( mp_init_size(&precomp[i][j][1],
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ECL_MAX_FIELD_SIZE_DIGITS) );
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}
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}
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/* fill precomputation table */
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/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
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if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
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a = k2;
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b = k1;
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->
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field_enc(px, &precomp[1][0][0], group->meth));
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MP_CHECKOK(group->meth->
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field_enc(py, &precomp[1][0][1], group->meth));
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} else {
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MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
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MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
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}
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MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
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MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
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} else {
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a = k1;
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b = k2;
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MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
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MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
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if (group->meth->field_enc) {
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MP_CHECKOK(group->meth->
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field_enc(px, &precomp[0][1][0], group->meth));
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MP_CHECKOK(group->meth->
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field_enc(py, &precomp[0][1][1], group->meth));
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} else {
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MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
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MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
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}
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}
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/* precompute [*][0][*] */
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mp_zero(&precomp[0][0][0]);
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mp_zero(&precomp[0][0][1]);
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MP_CHECKOK(group->
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point_dbl(&precomp[1][0][0], &precomp[1][0][1],
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&precomp[2][0][0], &precomp[2][0][1], group));
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MP_CHECKOK(group->
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point_add(&precomp[1][0][0], &precomp[1][0][1],
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&precomp[2][0][0], &precomp[2][0][1],
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&precomp[3][0][0], &precomp[3][0][1], group));
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/* precompute [*][1][*] */
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for (i = 1; i < 4; i++) {
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MP_CHECKOK(group->
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point_add(&precomp[0][1][0], &precomp[0][1][1],
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&precomp[i][0][0], &precomp[i][0][1],
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&precomp[i][1][0], &precomp[i][1][1], group));
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}
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/* precompute [*][2][*] */
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MP_CHECKOK(group->
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point_dbl(&precomp[0][1][0], &precomp[0][1][1],
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&precomp[0][2][0], &precomp[0][2][1], group));
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for (i = 1; i < 4; i++) {
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MP_CHECKOK(group->
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point_add(&precomp[0][2][0], &precomp[0][2][1],
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&precomp[i][0][0], &precomp[i][0][1],
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&precomp[i][2][0], &precomp[i][2][1], group));
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}
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/* precompute [*][3][*] */
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MP_CHECKOK(group->
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point_add(&precomp[0][1][0], &precomp[0][1][1],
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&precomp[0][2][0], &precomp[0][2][1],
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&precomp[0][3][0], &precomp[0][3][1], group));
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for (i = 1; i < 4; i++) {
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MP_CHECKOK(group->
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point_add(&precomp[0][3][0], &precomp[0][3][1],
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&precomp[i][0][0], &precomp[i][0][1],
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&precomp[i][3][0], &precomp[i][3][1], group));
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}
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d = (mpl_significant_bits(a) + 1) / 2;
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/* R = inf */
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mp_zero(rx);
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mp_zero(ry);
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for (i = d - 1; i >= 0; i--) {
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ai = MP_GET_BIT(a, 2 * i + 1);
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ai <<= 1;
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ai |= MP_GET_BIT(a, 2 * i);
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bi = MP_GET_BIT(b, 2 * i + 1);
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bi <<= 1;
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bi |= MP_GET_BIT(b, 2 * i);
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/* R = 2^2 * R */
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MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
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MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
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/* R = R + (ai * A + bi * B) */
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MP_CHECKOK(group->
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point_add(rx, ry, &precomp[ai][bi][0],
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&precomp[ai][bi][1], rx, ry, group));
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}
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if (group->meth->field_dec) {
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MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
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MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
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}
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CLEANUP:
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for (i = 0; i < 4; i++) {
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for (j = 0; j < 4; j++) {
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mp_clear(&precomp[i][j][0]);
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mp_clear(&precomp[i][j][1]);
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}
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}
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return res;
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}
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/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
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* k2 * P(x, y), where G is the generator (base point) of the group of
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* points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
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* Input and output values are assumed to be NOT field-encoded. */
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mp_err
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ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
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const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
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{
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mp_err res = MP_OKAY;
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mp_int k1t, k2t;
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const mp_int *k1p, *k2p;
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MP_DIGITS(&k1t) = 0;
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MP_DIGITS(&k2t) = 0;
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ARGCHK(group != NULL, MP_BADARG);
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/* want scalar to be less than or equal to group order */
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if (k1 != NULL) {
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if (mp_cmp(k1, &group->order) >= 0) {
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MP_CHECKOK(mp_init(&k1t));
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MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
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k1p = &k1t;
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} else {
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k1p = k1;
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}
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} else {
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k1p = k1;
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}
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if (k2 != NULL) {
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if (mp_cmp(k2, &group->order) >= 0) {
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MP_CHECKOK(mp_init(&k2t));
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MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
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k2p = &k2t;
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} else {
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k2p = k2;
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}
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} else {
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k2p = k2;
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}
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/* if points_mul is defined, then use it */
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if (group->points_mul) {
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res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
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} else {
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res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
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}
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CLEANUP:
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mp_clear(&k1t);
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mp_clear(&k2t);
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return res;
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}
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