usr/src/common/crypto/ecc/ecp_jm.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 for prime field curves.
  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  *   Stephen Fung <fungstep@hotmail.com>, 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 "ecp.h"
  48 #include "ecl-priv.h"
  49 #include "mplogic.h"
  50 #ifndef _KERNEL
  51 #include <stdlib.h>
  52 #endif
  53
  54 #define MAX_SCRATCH 6
  55
  56 /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
  57  * Modified Jacobian coordinates.
  58  *
  59  * Assumes input is already field-encoded using field_enc, and returns
  60  * output that is still field-encoded.
  61  *
  62  */
  63 mp_err
  64 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
  65                                  const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
  66                                  mp_int *raz4, mp_int scratch[], const ECGroup *group)
  67 {
  68         mp_err res = MP_OKAY;
  69         mp_int *t0, *t1, *M, *S;
  70
  71         t0 = &scratch[0];
  72         t1 = &scratch[1];
  73         M = &scratch[2];
  74         S = &scratch[3];
  75
  76 #if MAX_SCRATCH < 4
  77 #error "Scratch array defined too small "
  78 #endif
  79
  80         /* Check for point at infinity */
  81         if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
  82                 /* Set r = pt at infinity by setting rz = 0 */
  83
  84                 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
  85                 goto CLEANUP;
  86         }
  87
  88         /* M = 3 (px^2) + a*(pz^4) */
  89         MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
  90         MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
  91         MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
  92         MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
  93
  94         /* rz = 2 * py * pz */
  95         MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
  96         MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
  97
  98         /* t0 = 2y^2 , t1 = 8y^4 */
  99         MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
 100         MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
 101         MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
 102         MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
 103
 104         /* S = 4 * px * py^2 = 2 * px * t0 */
 105         MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
 106         MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
 107
 108
 109         /* rx = M^2 - 2S */
 110         MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
 111         MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
 112         MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
 113
 114         /* ry = M * (S - rx) - t1 */
 115         MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
 116         MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
 117         MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
 118
 119         /* ra*z^4 = 2*t1*(apz4) */
 120         MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
 121         MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
 122
 123
 124   CLEANUP:
 125         return res;
 126 }
 127
 128 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 129  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
 130  * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
 131  * already field-encoded using field_enc, and returns output that is still
 132  * field-encoded. */
 133 mp_err
 134 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
 135                                          const mp_int *paz4, const mp_int *qx,
 136                                          const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
 137                                          mp_int *raz4, mp_int scratch[], const ECGroup *group)
 138 {
 139         mp_err res = MP_OKAY;
 140         mp_int *A, *B, *C, *D, *C2, *C3;
 141
 142         A = &scratch[0];
 143         B = &scratch[1];
 144         C = &scratch[2];
 145         D = &scratch[3];
 146         C2 = &scratch[4];
 147         C3 = &scratch[5];
 148
 149 #if MAX_SCRATCH < 6
 150 #error "Scratch array defined too small "
 151 #endif
 152
 153         /* If either P or Q is the point at infinity, then return the other
 154          * point */
 155         if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
 156                 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
 157                 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
 158                 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
 159                 MP_CHECKOK(group->meth->
 160                                    field_mul(raz4, &group->curvea, raz4, group->meth));
 161                 goto CLEANUP;
 162         }
 163         if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
 164                 MP_CHECKOK(mp_copy(px, rx));
 165                 MP_CHECKOK(mp_copy(py, ry));
 166                 MP_CHECKOK(mp_copy(pz, rz));
 167                 MP_CHECKOK(mp_copy(paz4, raz4));
 168                 goto CLEANUP;
 169         }
 170
 171         /* A = qx * pz^2, B = qy * pz^3 */
 172         MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
 173         MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
 174         MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
 175         MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
 176
 177         /* C = A - px, D = B - py */
 178         MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
 179         MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
 180
 181         /* C2 = C^2, C3 = C^3 */
 182         MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
 183         MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
 184
 185         /* rz = pz * C */
 186         MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
 187
 188         /* C = px * C^2 */
 189         MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
 190         /* A = D^2 */
 191         MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
 192
 193         /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
 194         MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
 195         MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
 196         MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
 197
 198         /* C3 = py * C^3 */
 199         MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
 200
 201         /* ry = D * (px * C^2 - rx) - py * C^3 */
 202         MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
 203         MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
 204         MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
 205
 206         /* raz4 = a * rz^4 */
 207         MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
 208         MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
 209         MP_CHECKOK(group->meth->
 210                            field_mul(raz4, &group->curvea, raz4, group->meth));
 211 CLEANUP:
 212         return res;
 213 }
 214
 215 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
 216  * curve points P and R can be identical. Uses mixed Modified-Jacobian
 217  * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
 218  * additions. Assumes input is already field-encoded using field_enc, and
 219  * returns output that is still field-encoded. Uses 5-bit window NAF
 220  * method (algorithm 11) for scalar-point multiplication from Brown,
 221  * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
 222  * Curves Over Prime Fields. */
 223 mp_err
 224 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
 225                                           mp_int *rx, mp_int *ry, const ECGroup *group)
 226 {
 227         mp_err res = MP_OKAY;
 228         mp_int precomp[16][2], rz, tpx, tpy;
 229         mp_int raz4;
 230         mp_int scratch[MAX_SCRATCH];
 231         signed char *naf = NULL;
 232         int i, orderBitSize;
 233
 234         MP_DIGITS(&rz) = 0;
 235         MP_DIGITS(&raz4) = 0;
 236         MP_DIGITS(&tpx) = 0;
 237         MP_DIGITS(&tpy) = 0;
 238         for (i = 0; i < 16; i++) {
 239                 MP_DIGITS(&precomp[i][0]) = 0;
 240                 MP_DIGITS(&precomp[i][1]) = 0;
 241         }
 242         for (i = 0; i < MAX_SCRATCH; i++) {
 243                 MP_DIGITS(&scratch[i]) = 0;
 244         }
 245
 246         ARGCHK(group != NULL, MP_BADARG);
 247         ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
 248
 249         /* initialize precomputation table */
 250         MP_CHECKOK(mp_init(&tpx, FLAG(n)));
 251         MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
 252         MP_CHECKOK(mp_init(&rz, FLAG(n)));
 253         MP_CHECKOK(mp_init(&raz4, FLAG(n)));
 254
 255         for (i = 0; i < 16; i++) {
 256                 MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
 257                 MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
 258         }
 259         for (i = 0; i < MAX_SCRATCH; i++) {
 260                 MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
 261         }
 262
 263         /* Set out[8] = P */
 264         MP_CHECKOK(mp_copy(px, &precomp[8][0]));
 265         MP_CHECKOK(mp_copy(py, &precomp[8][1]));
 266
 267         /* Set (tpx, tpy) = 2P */
 268         MP_CHECKOK(group->
 269                            point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
 270                                                  group));
 271
 272         /* Set 3P, 5P, ..., 15P */
 273         for (i = 8; i < 15; i++) {
 274                 MP_CHECKOK(group->
 275                                    point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
 276                                                          &precomp[i + 1][0], &precomp[i + 1][1],
 277                                                          group));
 278         }
 279
 280         /* Set -15P, -13P, ..., -P */
 281         for (i = 0; i < 8; i++) {
 282                 MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
 283                 MP_CHECKOK(group->meth->
 284                                    field_neg(&precomp[15 - i][1], &precomp[i][1],
 285                                                          group->meth));
 286         }
 287
 288         /* R = inf */
 289         MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
 290
 291         orderBitSize = mpl_significant_bits(&group->order);
 292
 293         /* Allocate memory for NAF */
 294 #ifdef _KERNEL
 295         naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
 296 #else
 297         naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
 298         if (naf == NULL) {
 299                 res = MP_MEM;
 300                 goto CLEANUP;
 301         }
 302 #endif
 303
 304         /* Compute 5NAF */
 305         ec_compute_wNAF(naf, orderBitSize, n, 5);
 306
 307         /* wNAF method */
 308         for (i = orderBitSize; i >= 0; i--) {
 309                 /* R = 2R */
 310                 ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
 311                                              &raz4, scratch, group);
 312                 if (naf[i] != 0) {
 313                         ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
 314                                                                  &precomp[(naf[i] + 15) / 2][0],
 315                                                                  &precomp[(naf[i] + 15) / 2][1], rx, ry,
 316                                                                  &rz, &raz4, scratch, group);
 317                 }
 318         }
 319
 320         /* convert result S to affine coordinates */
 321         MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
 322
 323   CLEANUP:
 324         for (i = 0; i < MAX_SCRATCH; i++) {
 325                 mp_clear(&scratch[i]);
 326         }
 327         for (i = 0; i < 16; i++) {
 328                 mp_clear(&precomp[i][0]);
 329                 mp_clear(&precomp[i][1]);
 330         }
 331         mp_clear(&tpx);
 332         mp_clear(&tpy);
 333         mp_clear(&rz);
 334         mp_clear(&raz4);
 335 #ifdef _KERNEL
 336         kmem_free(naf, (orderBitSize + 1));
 337 #else
 338         free(naf);
 339 #endif
 340         return res;
 341 }