usr/src/common/crypto/ecc/ecp_jac.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  *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
  24  *   Stephen Fung <fungstep@hotmail.com>, and
  25  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
  26  *   Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
  27  *   Nils Larsch <nla@trustcenter.de>, and
  28  *   Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
  29  *
  30  * Alternatively, the contents of this file may be used under the terms of
  31  * either the GNU General Public License Version 2 or later (the "GPL"), or
  32  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
  33  * in which case the provisions of the GPL or the LGPL are applicable instead
  34  * of those above. If you wish to allow use of your version of this file only
  35  * under the terms of either the GPL or the LGPL, and not to allow others to
  36  * use your version of this file under the terms of the MPL, indicate your
  37  * decision by deleting the provisions above and replace them with the notice
  38  * and other provisions required by the GPL or the LGPL. If you do not delete
  39  * the provisions above, a recipient may use your version of this file under
  40  * the terms of any one of the MPL, the GPL or the LGPL.
  41  *
  42  * ***** END LICENSE BLOCK ***** */
  43 /*
  44  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
  45  * Use is subject to license terms.
  46  *
  47  * Sun elects to use this software under the MPL license.
  48  */
  49
  50 #pragma ident   "%Z%%M% %I%     %E% SMI"
  51
  52 #include "ecp.h"
  53 #include "mplogic.h"
  54 #ifndef _KERNEL
  55 #include <stdlib.h>
  56 #endif
  57 #ifdef ECL_DEBUG
  58 #include <assert.h>
  59 #endif
  60
  61 /* Converts a point P(px, py) from affine coordinates to Jacobian
  62  * projective coordinates R(rx, ry, rz). Assumes input is already
  63  * field-encoded using field_enc, and returns output that is still
  64  * field-encoded. */
  65 mp_err
  66 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
  67                                   mp_int *ry, mp_int *rz, const ECGroup *group)
  68 {
  69         mp_err res = MP_OKAY;
  70
  71         if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
  72                 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
  73         } else {
  74                 MP_CHECKOK(mp_copy(px, rx));
  75                 MP_CHECKOK(mp_copy(py, ry));
  76                 MP_CHECKOK(mp_set_int(rz, 1));
  77                 if (group->meth->field_enc) {
  78                         MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
  79                 }
  80         }
  81   CLEANUP:
  82         return res;
  83 }
  84
  85 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to
  86  * affine coordinates R(rx, ry).  P and R can share x and y coordinates.
  87  * Assumes input is already field-encoded using field_enc, and returns
  88  * output that is still field-encoded. */
  89 mp_err
  90 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
  91                                   mp_int *rx, mp_int *ry, const ECGroup *group)
  92 {
  93         mp_err res = MP_OKAY;
  94         mp_int z1, z2, z3;
  95
  96         MP_DIGITS(&z1) = 0;
  97         MP_DIGITS(&z2) = 0;
  98         MP_DIGITS(&z3) = 0;
  99         MP_CHECKOK(mp_init(&z1, FLAG(px)));
 100         MP_CHECKOK(mp_init(&z2, FLAG(px)));
 101         MP_CHECKOK(mp_init(&z3, FLAG(px)));
 102
 103         /* if point at infinity, then set point at infinity and exit */
 104         if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
 105                 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
 106                 goto CLEANUP;
 107         }
 108
 109         /* transform (px, py, pz) into (px / pz^2, py / pz^3) */
 110         if (mp_cmp_d(pz, 1) == 0) {
 111                 MP_CHECKOK(mp_copy(px, rx));
 112                 MP_CHECKOK(mp_copy(py, ry));
 113         } else {
 114                 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
 115                 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
 116                 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
 117                 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
 118                 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
 119         }
 120
 121   CLEANUP:
 122         mp_clear(&z1);
 123         mp_clear(&z2);
 124         mp_clear(&z3);
 125         return res;
 126 }
 127
 128 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
 129  * coordinates. */
 130 mp_err
 131 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz)
 132 {
 133         return mp_cmp_z(pz);
 134 }
 135
 136 /* Sets P(px, py, pz) to be the point at infinity.  Uses Jacobian
 137  * coordinates. */
 138 mp_err
 139 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz)
 140 {
 141         mp_zero(pz);
 142         return MP_OKAY;
 143 }
 144
 145 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
 146  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
 147  * Uses mixed Jacobian-affine coordinates. Assumes input is already
 148  * field-encoded using field_enc, and returns output that is still
 149  * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
 150  * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
 151  * Fields. */
 152 mp_err
 153 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
 154                                           const mp_int *qx, const mp_int *qy, mp_int *rx,
 155                                           mp_int *ry, mp_int *rz, const ECGroup *group)
 156 {
 157         mp_err res = MP_OKAY;
 158         mp_int A, B, C, D, C2, C3;
 159
 160         MP_DIGITS(&A) = 0;
 161         MP_DIGITS(&B) = 0;
 162         MP_DIGITS(&C) = 0;
 163         MP_DIGITS(&D) = 0;
 164         MP_DIGITS(&C2) = 0;
 165         MP_DIGITS(&C3) = 0;
 166         MP_CHECKOK(mp_init(&A, FLAG(px)));
 167         MP_CHECKOK(mp_init(&B, FLAG(px)));
 168         MP_CHECKOK(mp_init(&C, FLAG(px)));
 169         MP_CHECKOK(mp_init(&D, FLAG(px)));
 170         MP_CHECKOK(mp_init(&C2, FLAG(px)));
 171         MP_CHECKOK(mp_init(&C3, FLAG(px)));
 172
 173         /* If either P or Q is the point at infinity, then return the other
 174          * point */
 175         if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
 176                 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
 177                 goto CLEANUP;
 178         }
 179         if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
 180                 MP_CHECKOK(mp_copy(px, rx));
 181                 MP_CHECKOK(mp_copy(py, ry));
 182                 MP_CHECKOK(mp_copy(pz, rz));
 183                 goto CLEANUP;
 184         }
 185
 186         /* A = qx * pz^2, B = qy * pz^3 */
 187         MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
 188         MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
 189         MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
 190         MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
 191
 192         /* C = A - px, D = B - py */
 193         MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
 194         MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
 195
 196         /* C2 = C^2, C3 = C^3 */
 197         MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
 198         MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
 199
 200         /* rz = pz * C */
 201         MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
 202
 203         /* C = px * C^2 */
 204         MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
 205         /* A = D^2 */
 206         MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
 207
 208         /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
 209         MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
 210         MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
 211         MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
 212
 213         /* C3 = py * C^3 */
 214         MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
 215
 216         /* ry = D * (px * C^2 - rx) - py * C^3 */
 217         MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
 218         MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
 219         MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
 220
 221   CLEANUP:
 222         mp_clear(&A);
 223         mp_clear(&B);
 224         mp_clear(&C);
 225         mp_clear(&D);
 226         mp_clear(&C2);
 227         mp_clear(&C3);
 228         return res;
 229 }
 230
 231 /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
 232  * Jacobian coordinates.
 233  *
 234  * Assumes input is already field-encoded using field_enc, and returns
 235  * output that is still field-encoded.
 236  *
 237  * This routine implements Point Doubling in the Jacobian Projective
 238  * space as described in the paper "Efficient elliptic curve exponentiation
 239  * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
 240  */
 241 mp_err
 242 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
 243                                   mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
 244 {
 245         mp_err res = MP_OKAY;
 246         mp_int t0, t1, M, S;
 247
 248         MP_DIGITS(&t0) = 0;
 249         MP_DIGITS(&t1) = 0;
 250         MP_DIGITS(&M) = 0;
 251         MP_DIGITS(&S) = 0;
 252         MP_CHECKOK(mp_init(&t0, FLAG(px)));
 253         MP_CHECKOK(mp_init(&t1, FLAG(px)));
 254         MP_CHECKOK(mp_init(&M, FLAG(px)));
 255         MP_CHECKOK(mp_init(&S, FLAG(px)));
 256
 257         if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
 258                 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
 259                 goto CLEANUP;
 260         }
 261
 262         if (mp_cmp_d(pz, 1) == 0) {
 263                 /* M = 3 * px^2 + a */
 264                 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
 265                 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
 266                 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
 267                 MP_CHECKOK(group->meth->
 268                                    field_add(&t0, &group->curvea, &M, group->meth));
 269         } else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) {
 270                 /* M = 3 * (px + pz^2) * (px - pz^2) */
 271                 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
 272                 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
 273                 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
 274                 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
 275                 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
 276                 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
 277         } else {
 278                 /* M = 3 * (px^2) + a * (pz^4) */
 279                 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
 280                 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
 281                 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
 282                 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
 283                 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
 284                 MP_CHECKOK(group->meth->
 285                                    field_mul(&M, &group->curvea, &M, group->meth));
 286                 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
 287         }
 288
 289         /* rz = 2 * py * pz */
 290         /* t0 = 4 * py^2 */
 291         if (mp_cmp_d(pz, 1) == 0) {
 292                 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
 293                 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
 294         } else {
 295                 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
 296                 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
 297                 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
 298         }
 299
 300         /* S = 4 * px * py^2 = px * (2 * py)^2 */
 301         MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
 302
 303         /* rx = M^2 - 2 * S */
 304         MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
 305         MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
 306         MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
 307
 308         /* ry = M * (S - rx) - 8 * py^4 */
 309         MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
 310         if (mp_isodd(&t1)) {
 311                 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
 312         }
 313         MP_CHECKOK(mp_div_2(&t1, &t1));
 314         MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
 315         MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
 316         MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
 317
 318   CLEANUP:
 319         mp_clear(&t0);
 320         mp_clear(&t1);
 321         mp_clear(&M);
 322         mp_clear(&S);
 323         return res;
 324 }
 325
 326 /* by default, this routine is unused and thus doesn't need to be compiled */
 327 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC
 328 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
 329  * a, b and p are the elliptic curve coefficients and the prime that
 330  * determines the field GFp.  Elliptic curve points P and R can be
 331  * identical.  Uses mixed Jacobian-affine coordinates. Assumes input is
 332  * already field-encoded using field_enc, and returns output that is still
 333  * field-encoded. Uses 4-bit window method. */
 334 mp_err
 335 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py,
 336                                   mp_int *rx, mp_int *ry, const ECGroup *group)
 337 {
 338         mp_err res = MP_OKAY;
 339         mp_int precomp[16][2], rz;
 340         int i, ni, d;
 341
 342         MP_DIGITS(&rz) = 0;
 343         for (i = 0; i < 16; i++) {
 344                 MP_DIGITS(&precomp[i][0]) = 0;
 345                 MP_DIGITS(&precomp[i][1]) = 0;
 346         }
 347
 348         ARGCHK(group != NULL, MP_BADARG);
 349         ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
 350
 351         /* initialize precomputation table */
 352         for (i = 0; i < 16; i++) {
 353                 MP_CHECKOK(mp_init(&precomp[i][0]));
 354                 MP_CHECKOK(mp_init(&precomp[i][1]));
 355         }
 356
 357         /* fill precomputation table */
 358         mp_zero(&precomp[0][0]);
 359         mp_zero(&precomp[0][1]);
 360         MP_CHECKOK(mp_copy(px, &precomp[1][0]));
 361         MP_CHECKOK(mp_copy(py, &precomp[1][1]));
 362         for (i = 2; i < 16; i++) {
 363                 MP_CHECKOK(group->
 364                                    point_add(&precomp[1][0], &precomp[1][1],
 365                                                          &precomp[i - 1][0], &precomp[i - 1][1],
 366                                                          &precomp[i][0], &precomp[i][1], group));
 367         }
 368
 369         d = (mpl_significant_bits(n) + 3) / 4;
 370
 371         /* R = inf */
 372         MP_CHECKOK(mp_init(&rz));
 373         MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
 374
 375         for (i = d - 1; i >= 0; i--) {
 376                 /* compute window ni */
 377                 ni = MP_GET_BIT(n, 4 * i + 3);
 378                 ni <<= 1;
 379                 ni |= MP_GET_BIT(n, 4 * i + 2);
 380                 ni <<= 1;
 381                 ni |= MP_GET_BIT(n, 4 * i + 1);
 382                 ni <<= 1;
 383                 ni |= MP_GET_BIT(n, 4 * i);
 384                 /* R = 2^4 * R */
 385                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 386                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 387                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 388                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 389                 /* R = R + (ni * P) */
 390                 MP_CHECKOK(ec_GFp_pt_add_jac_aff
 391                                    (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
 392                                         &rz, group));
 393         }
 394
 395         /* convert result S to affine coordinates */
 396         MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
 397
 398   CLEANUP:
 399         mp_clear(&rz);
 400         for (i = 0; i < 16; i++) {
 401                 mp_clear(&precomp[i][0]);
 402                 mp_clear(&precomp[i][1]);
 403         }
 404         return res;
 405 }
 406 #endif
 407
 408 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 409  * k2 * P(x, y), where G is the generator (base point) of the group of
 410  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 411  * Uses mixed Jacobian-affine coordinates. Input and output values are
 412  * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous
 413  * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes.
 414  * Software Implementation of the NIST Elliptic Curves over Prime Fields. */
 415 mp_err
 416 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
 417                                    const mp_int *py, mp_int *rx, mp_int *ry,
 418                                    const ECGroup *group)
 419 {
 420         mp_err res = MP_OKAY;
 421         mp_int precomp[4][4][2];
 422         mp_int rz;
 423         const mp_int *a, *b;
 424         int i, j;
 425         int ai, bi, d;
 426
 427         for (i = 0; i < 4; i++) {
 428                 for (j = 0; j < 4; j++) {
 429                         MP_DIGITS(&precomp[i][j][0]) = 0;
 430                         MP_DIGITS(&precomp[i][j][1]) = 0;
 431                 }
 432         }
 433         MP_DIGITS(&rz) = 0;
 434
 435         ARGCHK(group != NULL, MP_BADARG);
 436         ARGCHK(!((k1 == NULL)
 437                          && ((k2 == NULL) || (px == NULL)
 438                                  || (py == NULL))), MP_BADARG);
 439
 440         /* if some arguments are not defined used ECPoint_mul */
 441         if (k1 == NULL) {
 442                 return ECPoint_mul(group, k2, px, py, rx, ry);
 443         } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
 444                 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
 445         }
 446
 447         /* initialize precomputation table */
 448         for (i = 0; i < 4; i++) {
 449                 for (j = 0; j < 4; j++) {
 450                         MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1)));
 451                         MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1)));
 452                 }
 453         }
 454
 455         /* fill precomputation table */
 456         /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
 457         if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
 458                 a = k2;
 459                 b = k1;
 460                 if (group->meth->field_enc) {
 461                         MP_CHECKOK(group->meth->
 462                                            field_enc(px, &precomp[1][0][0], group->meth));
 463                         MP_CHECKOK(group->meth->
 464                                            field_enc(py, &precomp[1][0][1], group->meth));
 465                 } else {
 466                         MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
 467                         MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
 468                 }
 469                 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
 470                 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
 471         } else {
 472                 a = k1;
 473                 b = k2;
 474                 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
 475                 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
 476                 if (group->meth->field_enc) {
 477                         MP_CHECKOK(group->meth->
 478                                            field_enc(px, &precomp[0][1][0], group->meth));
 479                         MP_CHECKOK(group->meth->
 480                                            field_enc(py, &precomp[0][1][1], group->meth));
 481                 } else {
 482                         MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
 483                         MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
 484                 }
 485         }
 486         /* precompute [*][0][*] */
 487         mp_zero(&precomp[0][0][0]);
 488         mp_zero(&precomp[0][0][1]);
 489         MP_CHECKOK(group->
 490                            point_dbl(&precomp[1][0][0], &precomp[1][0][1],
 491                                                  &precomp[2][0][0], &precomp[2][0][1], group));
 492         MP_CHECKOK(group->
 493                            point_add(&precomp[1][0][0], &precomp[1][0][1],
 494                                                  &precomp[2][0][0], &precomp[2][0][1],
 495                                                  &precomp[3][0][0], &precomp[3][0][1], group));
 496         /* precompute [*][1][*] */
 497         for (i = 1; i < 4; i++) {
 498                 MP_CHECKOK(group->
 499                                    point_add(&precomp[0][1][0], &precomp[0][1][1],
 500                                                          &precomp[i][0][0], &precomp[i][0][1],
 501                                                          &precomp[i][1][0], &precomp[i][1][1], group));
 502         }
 503         /* precompute [*][2][*] */
 504         MP_CHECKOK(group->
 505                            point_dbl(&precomp[0][1][0], &precomp[0][1][1],
 506                                                  &precomp[0][2][0], &precomp[0][2][1], group));
 507         for (i = 1; i < 4; i++) {
 508                 MP_CHECKOK(group->
 509                                    point_add(&precomp[0][2][0], &precomp[0][2][1],
 510                                                          &precomp[i][0][0], &precomp[i][0][1],
 511                                                          &precomp[i][2][0], &precomp[i][2][1], group));
 512         }
 513         /* precompute [*][3][*] */
 514         MP_CHECKOK(group->
 515                            point_add(&precomp[0][1][0], &precomp[0][1][1],
 516                                                  &precomp[0][2][0], &precomp[0][2][1],
 517                                                  &precomp[0][3][0], &precomp[0][3][1], group));
 518         for (i = 1; i < 4; i++) {
 519                 MP_CHECKOK(group->
 520                                    point_add(&precomp[0][3][0], &precomp[0][3][1],
 521                                                          &precomp[i][0][0], &precomp[i][0][1],
 522                                                          &precomp[i][3][0], &precomp[i][3][1], group));
 523         }
 524
 525         d = (mpl_significant_bits(a) + 1) / 2;
 526
 527         /* R = inf */
 528         MP_CHECKOK(mp_init(&rz, FLAG(k1)));
 529         MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
 530
 531         for (i = d - 1; i >= 0; i--) {
 532                 ai = MP_GET_BIT(a, 2 * i + 1);
 533                 ai <<= 1;
 534                 ai |= MP_GET_BIT(a, 2 * i);
 535                 bi = MP_GET_BIT(b, 2 * i + 1);
 536                 bi <<= 1;
 537                 bi |= MP_GET_BIT(b, 2 * i);
 538                 /* R = 2^2 * R */
 539                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 540                 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
 541                 /* R = R + (ai * A + bi * B) */
 542                 MP_CHECKOK(ec_GFp_pt_add_jac_aff
 543                                    (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1],
 544                                         rx, ry, &rz, group));
 545         }
 546
 547         MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
 548
 549         if (group->meth->field_dec) {
 550                 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
 551                 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
 552         }
 553
 554   CLEANUP:
 555         mp_clear(&rz);
 556         for (i = 0; i < 4; i++) {
 557                 for (j = 0; j < 4; j++) {
 558                         mp_clear(&precomp[i][j][0]);
 559                         mp_clear(&precomp[i][j][1]);
 560                 }
 561         }
 562         return res;
 563 }