usr/src/common/crypto/ecc/ecl_mult.c

   1 /*
   2  * ***** BEGIN LICENSE BLOCK *****
   3  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   4  *
   5  * The contents of this file are subject to the Mozilla Public License Version
   6  * 1.1 (the "License"); you may not use this file except in compliance with
   7  * the License. You may obtain a copy of the License at
   8  * http://www.mozilla.org/MPL/
   9  *
  10  * Software distributed under the License is distributed on an "AS IS" basis,
  11  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  12  * for the specific language governing rights and limitations under the
  13  * License.
  14  *
  15  * The Original Code is the elliptic curve math library.
  16  *
  17  * The Initial Developer of the Original Code is
  18  * Sun Microsystems, Inc.
  19  * Portions created by the Initial Developer are Copyright (C) 2003
  20  * the Initial Developer. All Rights Reserved.
  21  *
  22  * Contributor(s):
  23  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
  24  *
  25  * Alternatively, the contents of this file may be used under the terms of
  26  * either the GNU General Public License Version 2 or later (the "GPL"), or
  27  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  28  * in which case the provisions of the GPL or the LGPL are applicable instead
  29  * of those above. If you wish to allow use of your version of this file only
  30  * under the terms of either the GPL or the LGPL, and not to allow others to
  31  * use your version of this file under the terms of the MPL, indicate your
  32  * decision by deleting the provisions above and replace them with the notice
  33  * and other provisions required by the GPL or the LGPL. If you do not delete
  34  * the provisions above, a recipient may use your version of this file under
  35  * the terms of any one of the MPL, the GPL or the LGPL.
  36  *
  37  * ***** END LICENSE BLOCK ***** */
  38 /*
  39  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
  40  * Use is subject to license terms.
  41  *
  42  * Sun elects to use this software under the MPL license.
  43  */
  44
  45 #pragma ident   "%Z%%M% %I%     %E% SMI"
  46
  47 #include "mpi.h"
  48 #include "mplogic.h"
  49 #include "ecl.h"
  50 #include "ecl-priv.h"
  51 #ifndef _KERNEL
  52 #include <stdlib.h>
  53 #endif
  54
  55 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
  56  * y).  If x, y = NULL, then P is assumed to be the generator (base point)
  57  * of the group of points on the elliptic curve. Input and output values
  58  * are assumed to be NOT field-encoded. */
  59 mp_err
  60 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
  61                         const mp_int *py, mp_int *rx, mp_int *ry)
  62 {
  63         mp_err res = MP_OKAY;
  64         mp_int kt;
  65
  66         ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
  67         MP_DIGITS(&kt) = 0;
  68
  69         /* want scalar to be less than or equal to group order */
  70         if (mp_cmp(k, &group->order) > 0) {
  71                 MP_CHECKOK(mp_init(&kt, FLAG(k)));
  72                 MP_CHECKOK(mp_mod(k, &group->order, &kt));
  73         } else {
  74                 MP_SIGN(&kt) = MP_ZPOS;
  75                 MP_USED(&kt) = MP_USED(k);
  76                 MP_ALLOC(&kt) = MP_ALLOC(k);
  77                 MP_DIGITS(&kt) = MP_DIGITS(k);
  78         }
  79
  80         if ((px == NULL) || (py == NULL)) {
  81                 if (group->base_point_mul) {
  82                         MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
  83                 } else {
  84                         MP_CHECKOK(group->
  85                                            point_mul(&kt, &group->genx, &group->geny, rx, ry,
  86                                                                  group));
  87                 }
  88         } else {
  89                 if (group->meth->field_enc) {
  90                         MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
  91                         MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
  92                         MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
  93                 } else {
  94                         MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
  95                 }
  96         }
  97         if (group->meth->field_dec) {
  98                 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
  99                 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
 100         }
 101
 102   CLEANUP:
 103         if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
 104                 mp_clear(&kt);
 105         }
 106         return res;
 107 }
 108
 109 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 110  * k2 * P(x, y), where G is the generator (base point) of the group of
 111  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 112  * Input and output values are assumed to be NOT field-encoded. */
 113 mp_err
 114 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
 115                                  const mp_int *py, mp_int *rx, mp_int *ry,
 116                                  const ECGroup *group)
 117 {
 118         mp_err res = MP_OKAY;
 119         mp_int sx, sy;
 120
 121         ARGCHK(group != NULL, MP_BADARG);
 122         ARGCHK(!((k1 == NULL)
 123                          && ((k2 == NULL) || (px == NULL)
 124                                  || (py == NULL))), MP_BADARG);
 125
 126         /* if some arguments are not defined used ECPoint_mul */
 127         if (k1 == NULL) {
 128                 return ECPoint_mul(group, k2, px, py, rx, ry);
 129         } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
 130                 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
 131         }
 132
 133         MP_DIGITS(&sx) = 0;
 134         MP_DIGITS(&sy) = 0;
 135         MP_CHECKOK(mp_init(&sx, FLAG(k1)));
 136         MP_CHECKOK(mp_init(&sy, FLAG(k1)));
 137
 138         MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
 139         MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
 140
 141         if (group->meth->field_enc) {
 142                 MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
 143                 MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
 144                 MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
 145                 MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
 146         }
 147
 148         MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
 149
 150         if (group->meth->field_dec) {
 151                 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
 152                 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
 153         }
 154
 155   CLEANUP:
 156         mp_clear(&sx);
 157         mp_clear(&sy);
 158         return res;
 159 }
 160
 161 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 162  * k2 * P(x, y), where G is the generator (base point) of the group of
 163  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 164  * Input and output values are assumed to be NOT field-encoded. Uses
 165  * algorithm 15 (simultaneous multiple point multiplication) from Brown,
 166  * Hankerson, Lopez, Menezes. Software Implementation of the NIST
 167  * Elliptic Curves over Prime Fields. */
 168 mp_err
 169 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
 170                                         const mp_int *py, mp_int *rx, mp_int *ry,
 171                                         const ECGroup *group)
 172 {
 173         mp_err res = MP_OKAY;
 174         mp_int precomp[4][4][2];
 175         const mp_int *a, *b;
 176         int i, j;
 177         int ai, bi, d;
 178
 179         ARGCHK(group != NULL, MP_BADARG);
 180         ARGCHK(!((k1 == NULL)
 181                          && ((k2 == NULL) || (px == NULL)
 182                                  || (py == NULL))), MP_BADARG);
 183
 184         /* if some arguments are not defined used ECPoint_mul */
 185         if (k1 == NULL) {
 186                 return ECPoint_mul(group, k2, px, py, rx, ry);
 187         } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
 188                 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
 189         }
 190
 191         /* initialize precomputation table */
 192         for (i = 0; i < 4; i++) {
 193                 for (j = 0; j < 4; j++) {
 194                         MP_DIGITS(&precomp[i][j][0]) = 0;
 195                         MP_DIGITS(&precomp[i][j][1]) = 0;
 196                 }
 197         }
 198         for (i = 0; i < 4; i++) {
 199                 for (j = 0; j < 4; j++) {
 200                          MP_CHECKOK( mp_init_size(&precomp[i][j][0],
 201                                          ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
 202                          MP_CHECKOK( mp_init_size(&precomp[i][j][1],
 203                                          ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
 204                 }
 205         }
 206
 207         /* fill precomputation table */
 208         /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
 209         if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
 210                 a = k2;
 211                 b = k1;
 212                 if (group->meth->field_enc) {
 213                         MP_CHECKOK(group->meth->
 214                                            field_enc(px, &precomp[1][0][0], group->meth));
 215                         MP_CHECKOK(group->meth->
 216                                            field_enc(py, &precomp[1][0][1], group->meth));
 217                 } else {
 218                         MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
 219                         MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
 220                 }
 221                 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
 222                 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
 223         } else {
 224                 a = k1;
 225                 b = k2;
 226                 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
 227                 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
 228                 if (group->meth->field_enc) {
 229                         MP_CHECKOK(group->meth->
 230                                            field_enc(px, &precomp[0][1][0], group->meth));
 231                         MP_CHECKOK(group->meth->
 232                                            field_enc(py, &precomp[0][1][1], group->meth));
 233                 } else {
 234                         MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
 235                         MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
 236                 }
 237         }
 238         /* precompute [*][0][*] */
 239         mp_zero(&precomp[0][0][0]);
 240         mp_zero(&precomp[0][0][1]);
 241         MP_CHECKOK(group->
 242                            point_dbl(&precomp[1][0][0], &precomp[1][0][1],
 243                                                  &precomp[2][0][0], &precomp[2][0][1], group));
 244         MP_CHECKOK(group->
 245                            point_add(&precomp[1][0][0], &precomp[1][0][1],
 246                                                  &precomp[2][0][0], &precomp[2][0][1],
 247                                                  &precomp[3][0][0], &precomp[3][0][1], group));
 248         /* precompute [*][1][*] */
 249         for (i = 1; i < 4; i++) {
 250                 MP_CHECKOK(group->
 251                                    point_add(&precomp[0][1][0], &precomp[0][1][1],
 252                                                          &precomp[i][0][0], &precomp[i][0][1],
 253                                                          &precomp[i][1][0], &precomp[i][1][1], group));
 254         }
 255         /* precompute [*][2][*] */
 256         MP_CHECKOK(group->
 257                            point_dbl(&precomp[0][1][0], &precomp[0][1][1],
 258                                                  &precomp[0][2][0], &precomp[0][2][1], group));
 259         for (i = 1; i < 4; i++) {
 260                 MP_CHECKOK(group->
 261                                    point_add(&precomp[0][2][0], &precomp[0][2][1],
 262                                                          &precomp[i][0][0], &precomp[i][0][1],
 263                                                          &precomp[i][2][0], &precomp[i][2][1], group));
 264         }
 265         /* precompute [*][3][*] */
 266         MP_CHECKOK(group->
 267                            point_add(&precomp[0][1][0], &precomp[0][1][1],
 268                                                  &precomp[0][2][0], &precomp[0][2][1],
 269                                                  &precomp[0][3][0], &precomp[0][3][1], group));
 270         for (i = 1; i < 4; i++) {
 271                 MP_CHECKOK(group->
 272                                    point_add(&precomp[0][3][0], &precomp[0][3][1],
 273                                                          &precomp[i][0][0], &precomp[i][0][1],
 274                                                          &precomp[i][3][0], &precomp[i][3][1], group));
 275         }
 276
 277         d = (mpl_significant_bits(a) + 1) / 2;
 278
 279         /* R = inf */
 280         mp_zero(rx);
 281         mp_zero(ry);
 282
 283         for (i = d - 1; i >= 0; i--) {
 284                 ai = MP_GET_BIT(a, 2 * i + 1);
 285                 ai <<= 1;
 286                 ai |= MP_GET_BIT(a, 2 * i);
 287                 bi = MP_GET_BIT(b, 2 * i + 1);
 288                 bi <<= 1;
 289                 bi |= MP_GET_BIT(b, 2 * i);
 290                 /* R = 2^2 * R */
 291                 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
 292                 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
 293                 /* R = R + (ai * A + bi * B) */
 294                 MP_CHECKOK(group->
 295                                    point_add(rx, ry, &precomp[ai][bi][0],
 296                                                          &precomp[ai][bi][1], rx, ry, group));
 297         }
 298
 299         if (group->meth->field_dec) {
 300                 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
 301                 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
 302         }
 303
 304   CLEANUP:
 305         for (i = 0; i < 4; i++) {
 306                 for (j = 0; j < 4; j++) {
 307                         mp_clear(&precomp[i][j][0]);
 308                         mp_clear(&precomp[i][j][1]);
 309                 }
 310         }
 311         return res;
 312 }
 313
 314 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 315  * k2 * P(x, y), where G is the generator (base point) of the group of
 316  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 317  * Input and output values are assumed to be NOT field-encoded. */
 318 mp_err
 319 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
 320                          const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
 321 {
 322         mp_err res = MP_OKAY;
 323         mp_int k1t, k2t;
 324         const mp_int *k1p, *k2p;
 325
 326         MP_DIGITS(&k1t) = 0;
 327         MP_DIGITS(&k2t) = 0;
 328
 329         ARGCHK(group != NULL, MP_BADARG);
 330
 331         /* want scalar to be less than or equal to group order */
 332         if (k1 != NULL) {
 333                 if (mp_cmp(k1, &group->order) >= 0) {
 334                         MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
 335                         MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
 336                         k1p = &k1t;
 337                 } else {
 338                         k1p = k1;
 339                 }
 340         } else {
 341                 k1p = k1;
 342         }
 343         if (k2 != NULL) {
 344                 if (mp_cmp(k2, &group->order) >= 0) {
 345                         MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
 346                         MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
 347                         k2p = &k2t;
 348                 } else {
 349                         k2p = k2;
 350                 }
 351         } else {
 352                 k2p = k2;
 353         }
 354
 355         /* if points_mul is defined, then use it */
 356         if (group->points_mul) {
 357                 res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
 358         } else {
 359                 res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
 360         }
 361
 362   CLEANUP:
 363         mp_clear(&k1t);
 364         mp_clear(&k2t);
 365         return res;
 366 }