crypto/openssl/crypto/ec/ec_mult.c

   1 /* crypto/ec/ec_mult.c */
   2 /*
   3  * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2007 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58 /* ====================================================================
  59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60  * Portions of this software developed by SUN MICROSYSTEMS, INC.,
  61  * and contributed to the OpenSSL project.
  62  */
  63
  64 #include <string.h>
  65
  66 #include <openssl/err.h>
  67
  68 #include "ec_lcl.h"
  69
  70 /*
  71  * This file implements the wNAF-based interleaving multi-exponentation method
  72  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
  73  * for multiplication with precomputation, we use wNAF splitting
  74  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
  75  */
  76
  77 /* structure for precomputed multiples of the generator */
  78 typedef struct ec_pre_comp_st {
  79     const EC_GROUP *group;      /* parent EC_GROUP object */
  80     size_t blocksize;           /* block size for wNAF splitting */
  81     size_t numblocks;           /* max. number of blocks for which we have
  82                                  * precomputation */
  83     size_t w;                   /* window size */
  84     EC_POINT **points;          /* array with pre-calculated multiples of
  85                                  * generator: 'num' pointers to EC_POINT
  86                                  * objects followed by a NULL */
  87     size_t num;                 /* numblocks * 2^(w-1) */
  88     int references;
  89 } EC_PRE_COMP;
  90
  91 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
  92 static void *ec_pre_comp_dup(void *);
  93 static void ec_pre_comp_free(void *);
  94 static void ec_pre_comp_clear_free(void *);
  95
  96 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
  97 {
  98     EC_PRE_COMP *ret = NULL;
  99
 100     if (!group)
 101         return NULL;
 102
 103     ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
 104     if (!ret) {
 105         ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
 106         return ret;
 107     }
 108     ret->group = group;
 109     ret->blocksize = 8;         /* default */
 110     ret->numblocks = 0;
 111     ret->w = 4;                 /* default */
 112     ret->points = NULL;
 113     ret->num = 0;
 114     ret->references = 1;
 115     return ret;
 116 }
 117
 118 static void *ec_pre_comp_dup(void *src_)
 119 {
 120     EC_PRE_COMP *src = src_;
 121
 122     /* no need to actually copy, these objects never change! */
 123
 124     CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
 125
 126     return src_;
 127 }
 128
 129 static void ec_pre_comp_free(void *pre_)
 130 {
 131     int i;
 132     EC_PRE_COMP *pre = pre_;
 133
 134     if (!pre)
 135         return;
 136
 137     i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 138     if (i > 0)
 139         return;
 140
 141     if (pre->points) {
 142         EC_POINT **p;
 143
 144         for (p = pre->points; *p != NULL; p++)
 145             EC_POINT_free(*p);
 146         OPENSSL_free(pre->points);
 147     }
 148     OPENSSL_free(pre);
 149 }
 150
 151 static void ec_pre_comp_clear_free(void *pre_)
 152 {
 153     int i;
 154     EC_PRE_COMP *pre = pre_;
 155
 156     if (!pre)
 157         return;
 158
 159     i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 160     if (i > 0)
 161         return;
 162
 163     if (pre->points) {
 164         EC_POINT **p;
 165
 166         for (p = pre->points; *p != NULL; p++) {
 167             EC_POINT_clear_free(*p);
 168             OPENSSL_cleanse(p, sizeof *p);
 169         }
 170         OPENSSL_free(pre->points);
 171     }
 172     OPENSSL_cleanse(pre, sizeof *pre);
 173     OPENSSL_free(pre);
 174 }
 175
 176 /*-
 177  * Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 178  * This is an array  r[]  of values that are either zero or odd with an
 179  * absolute value less than  2^w  satisfying
 180  *     scalar = \sum_j r[j]*2^j
 181  * where at most one of any  w+1  consecutive digits is non-zero
 182  * with the exception that the most significant digit may be only
 183  * w-1 zeros away from that next non-zero digit.
 184  */
 185 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
 186 {
 187     int window_val;
 188     int ok = 0;
 189     signed char *r = NULL;
 190     int sign = 1;
 191     int bit, next_bit, mask;
 192     size_t len = 0, j;
 193
 194     if (BN_is_zero(scalar)) {
 195         r = OPENSSL_malloc(1);
 196         if (!r) {
 197             ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 198             goto err;
 199         }
 200         r[0] = 0;
 201         *ret_len = 1;
 202         return r;
 203     }
 204
 205     if (w <= 0 || w > 7) {      /* 'signed char' can represent integers with
 206                                  * absolute values less than 2^7 */
 207         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 208         goto err;
 209     }
 210     bit = 1 << w;               /* at most 128 */
 211     next_bit = bit << 1;        /* at most 256 */
 212     mask = next_bit - 1;        /* at most 255 */
 213
 214     if (BN_is_negative(scalar)) {
 215         sign = -1;
 216     }
 217
 218     if (scalar->d == NULL || scalar->top == 0) {
 219         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 220         goto err;
 221     }
 222
 223     len = BN_num_bits(scalar);
 224     r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer
 225                                   * than binary representation (*ret_len will
 226                                   * be set to the actual length, i.e. at most
 227                                   * BN_num_bits(scalar) + 1) */
 228     if (r == NULL) {
 229         ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 230         goto err;
 231     }
 232     window_val = scalar->d[0] & mask;
 233     j = 0;
 234     while ((window_val != 0) || (j + w + 1 < len)) { /* if j+w+1 >= len,
 235                                                       * window_val will not
 236                                                       * increase */
 237         int digit = 0;
 238
 239         /* 0 <= window_val <= 2^(w+1) */
 240
 241         if (window_val & 1) {
 242             /* 0 < window_val < 2^(w+1) */
 243
 244             if (window_val & bit) {
 245                 digit = window_val - next_bit; /* -2^w < digit < 0 */
 246
 247 #if 1                           /* modified wNAF */
 248                 if (j + w + 1 >= len) {
 249                     /*
 250                      * special case for generating modified wNAFs: no new
 251                      * bits will be added into window_val, so using a
 252                      * positive digit here will decrease the total length of
 253                      * the representation
 254                      */
 255
 256                     digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
 257                 }
 258 #endif
 259             } else {
 260                 digit = window_val; /* 0 < digit < 2^w */
 261             }
 262
 263             if (digit <= -bit || digit >= bit || !(digit & 1)) {
 264                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 265                 goto err;
 266             }
 267
 268             window_val -= digit;
 269
 270             /*
 271              * now window_val is 0 or 2^(w+1) in standard wNAF generation;
 272              * for modified window NAFs, it may also be 2^w
 273              */
 274             if (window_val != 0 && window_val != next_bit
 275                 && window_val != bit) {
 276                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 277                 goto err;
 278             }
 279         }
 280
 281         r[j++] = sign * digit;
 282
 283         window_val >>= 1;
 284         window_val += bit * BN_is_bit_set(scalar, j + w);
 285
 286         if (window_val > next_bit) {
 287             ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 288             goto err;
 289         }
 290     }
 291
 292     if (j > len + 1) {
 293         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 294         goto err;
 295     }
 296     len = j;
 297     ok = 1;
 298
 299  err:
 300     if (!ok) {
 301         OPENSSL_free(r);
 302         r = NULL;
 303     }
 304     if (ok)
 305         *ret_len = len;
 306     return r;
 307 }
 308
 309 /*
 310  * TODO: table should be optimised for the wNAF-based implementation,
 311  * sometimes smaller windows will give better performance (thus the
 312  * boundaries should be increased)
 313  */
 314 #define EC_window_bits_for_scalar_size(b) \
 315                 ((size_t) \
 316                  ((b) >= 2000 ? 6 : \
 317                   (b) >=  800 ? 5 : \
 318                   (b) >=  300 ? 4 : \
 319                   (b) >=   70 ? 3 : \
 320                   (b) >=   20 ? 2 : \
 321                   1))
 322
 323 /*-
 324  * Compute
 325  *      \sum scalars[i]*points[i],
 326  * also including
 327  *      scalar*generator
 328  * in the addition if scalar != NULL
 329  */
 330 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 331                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 332                 BN_CTX *ctx)
 333 {
 334     BN_CTX *new_ctx = NULL;
 335     const EC_POINT *generator = NULL;
 336     EC_POINT *tmp = NULL;
 337     size_t totalnum;
 338     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 339     size_t pre_points_per_block = 0;
 340     size_t i, j;
 341     int k;
 342     int r_is_inverted = 0;
 343     int r_is_at_infinity = 1;
 344     size_t *wsize = NULL;       /* individual window sizes */
 345     signed char **wNAF = NULL;  /* individual wNAFs */
 346     size_t *wNAF_len = NULL;
 347     size_t max_len = 0;
 348     size_t num_val;
 349     EC_POINT **val = NULL;      /* precomputation */
 350     EC_POINT **v;
 351     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 352                                  * 'pre_comp->points' */
 353     const EC_PRE_COMP *pre_comp = NULL;
 354     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 355                                  * treated like other scalars, i.e.
 356                                  * precomputation is not available */
 357     int ret = 0;
 358
 359     if (group->meth != r->meth) {
 360         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 361         return 0;
 362     }
 363
 364     if ((scalar == NULL) && (num == 0)) {
 365         return EC_POINT_set_to_infinity(group, r);
 366     }
 367
 368     for (i = 0; i < num; i++) {
 369         if (group->meth != points[i]->meth) {
 370             ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 371             return 0;
 372         }
 373     }
 374
 375     if (ctx == NULL) {
 376         ctx = new_ctx = BN_CTX_new();
 377         if (ctx == NULL)
 378             goto err;
 379     }
 380
 381     if (scalar != NULL) {
 382         generator = EC_GROUP_get0_generator(group);
 383         if (generator == NULL) {
 384             ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 385             goto err;
 386         }
 387
 388         /* look if we can use precomputed multiples of generator */
 389
 390         pre_comp =
 391             EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup,
 392                                 ec_pre_comp_free, ec_pre_comp_clear_free);
 393
 394         if (pre_comp && pre_comp->numblocks
 395             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 396                 0)) {
 397             blocksize = pre_comp->blocksize;
 398
 399             /*
 400              * determine maximum number of blocks that wNAF splitting may
 401              * yield (NB: maximum wNAF length is bit length plus one)
 402              */
 403             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 404
 405             /*
 406              * we cannot use more blocks than we have precomputation for
 407              */
 408             if (numblocks > pre_comp->numblocks)
 409                 numblocks = pre_comp->numblocks;
 410
 411             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 412
 413             /* check that pre_comp looks sane */
 414             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 415                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 416                 goto err;
 417             }
 418         } else {
 419             /* can't use precomputation */
 420             pre_comp = NULL;
 421             numblocks = 1;
 422             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 423                                  * 'scalars' */
 424         }
 425     }
 426
 427     totalnum = num + numblocks;
 428
 429     wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 430     wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
 431     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
 432                                                              * for pivot */
 433     val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 434
 435     /* Ensure wNAF is initialised in case we end up going to err */
 436     if (wNAF)
 437         wNAF[0] = NULL;         /* preliminary pivot */
 438
 439     if (!wsize || !wNAF_len || !wNAF || !val_sub) {
 440         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 441         goto err;
 442     }
 443
 444     /*
 445      * num_val will be the total number of temporarily precomputed points
 446      */
 447     num_val = 0;
 448
 449     for (i = 0; i < num + num_scalar; i++) {
 450         size_t bits;
 451
 452         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 453         wsize[i] = EC_window_bits_for_scalar_size(bits);
 454         num_val += (size_t)1 << (wsize[i] - 1);
 455         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 456         wNAF[i] =
 457             compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 458                          &wNAF_len[i]);
 459         if (wNAF[i] == NULL)
 460             goto err;
 461         if (wNAF_len[i] > max_len)
 462             max_len = wNAF_len[i];
 463     }
 464
 465     if (numblocks) {
 466         /* we go here iff scalar != NULL */
 467
 468         if (pre_comp == NULL) {
 469             if (num_scalar != 1) {
 470                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 471                 goto err;
 472             }
 473             /* we have already generated a wNAF for 'scalar' */
 474         } else {
 475             signed char *tmp_wNAF = NULL;
 476             size_t tmp_len = 0;
 477
 478             if (num_scalar != 0) {
 479                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 480                 goto err;
 481             }
 482
 483             /*
 484              * use the window size for which we have precomputation
 485              */
 486             wsize[num] = pre_comp->w;
 487             tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
 488             if (!tmp_wNAF)
 489                 goto err;
 490
 491             if (tmp_len <= max_len) {
 492                 /*
 493                  * One of the other wNAFs is at least as long as the wNAF
 494                  * belonging to the generator, so wNAF splitting will not buy
 495                  * us anything.
 496                  */
 497
 498                 numblocks = 1;
 499                 totalnum = num + 1; /* don't use wNAF splitting */
 500                 wNAF[num] = tmp_wNAF;
 501                 wNAF[num + 1] = NULL;
 502                 wNAF_len[num] = tmp_len;
 503                 if (tmp_len > max_len)
 504                     max_len = tmp_len;
 505                 /*
 506                  * pre_comp->points starts with the points that we need here:
 507                  */
 508                 val_sub[num] = pre_comp->points;
 509             } else {
 510                 /*
 511                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 512                  * splitting and include the blocks
 513                  */
 514
 515                 signed char *pp;
 516                 EC_POINT **tmp_points;
 517
 518                 if (tmp_len < numblocks * blocksize) {
 519                     /*
 520                      * possibly we can do with fewer blocks than estimated
 521                      */
 522                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 523                     if (numblocks > pre_comp->numblocks) {
 524                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 525                         goto err;
 526                     }
 527                     totalnum = num + numblocks;
 528                 }
 529
 530                 /* split wNAF in 'numblocks' parts */
 531                 pp = tmp_wNAF;
 532                 tmp_points = pre_comp->points;
 533
 534                 for (i = num; i < totalnum; i++) {
 535                     if (i < totalnum - 1) {
 536                         wNAF_len[i] = blocksize;
 537                         if (tmp_len < blocksize) {
 538                             ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 539                             goto err;
 540                         }
 541                         tmp_len -= blocksize;
 542                     } else
 543                         /*
 544                          * last block gets whatever is left (this could be
 545                          * more or less than 'blocksize'!)
 546                          */
 547                         wNAF_len[i] = tmp_len;
 548
 549                     wNAF[i + 1] = NULL;
 550                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 551                     if (wNAF[i] == NULL) {
 552                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 553                         OPENSSL_free(tmp_wNAF);
 554                         goto err;
 555                     }
 556                     memcpy(wNAF[i], pp, wNAF_len[i]);
 557                     if (wNAF_len[i] > max_len)
 558                         max_len = wNAF_len[i];
 559
 560                     if (*tmp_points == NULL) {
 561                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 562                         OPENSSL_free(tmp_wNAF);
 563                         goto err;
 564                     }
 565                     val_sub[i] = tmp_points;
 566                     tmp_points += pre_points_per_block;
 567                     pp += blocksize;
 568                 }
 569                 OPENSSL_free(tmp_wNAF);
 570             }
 571         }
 572     }
 573
 574     /*
 575      * All points we precompute now go into a single array 'val'.
 576      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 577      * subarray of 'pre_comp->points' if we already have precomputation.
 578      */
 579     val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 580     if (val == NULL) {
 581         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 582         goto err;
 583     }
 584     val[num_val] = NULL;        /* pivot element */
 585
 586     /* allocate points for precomputation */
 587     v = val;
 588     for (i = 0; i < num + num_scalar; i++) {
 589         val_sub[i] = v;
 590         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 591             *v = EC_POINT_new(group);
 592             if (*v == NULL)
 593                 goto err;
 594             v++;
 595         }
 596     }
 597     if (!(v == val + num_val)) {
 598         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 599         goto err;
 600     }
 601
 602     if (!(tmp = EC_POINT_new(group)))
 603         goto err;
 604
 605     /*-
 606      * prepare precomputed values:
 607      *    val_sub[i][0] :=     points[i]
 608      *    val_sub[i][1] := 3 * points[i]
 609      *    val_sub[i][2] := 5 * points[i]
 610      *    ...
 611      */
 612     for (i = 0; i < num + num_scalar; i++) {
 613         if (i < num) {
 614             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 615                 goto err;
 616         } else {
 617             if (!EC_POINT_copy(val_sub[i][0], generator))
 618                 goto err;
 619         }
 620
 621         if (wsize[i] > 1) {
 622             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 623                 goto err;
 624             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 625                 if (!EC_POINT_add
 626                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 627                     goto err;
 628             }
 629         }
 630     }
 631
 632 #if 1                           /* optional; EC_window_bits_for_scalar_size
 633                                  * assumes we do this step */
 634     if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 635         goto err;
 636 #endif
 637
 638     r_is_at_infinity = 1;
 639
 640     for (k = max_len - 1; k >= 0; k--) {
 641         if (!r_is_at_infinity) {
 642             if (!EC_POINT_dbl(group, r, r, ctx))
 643                 goto err;
 644         }
 645
 646         for (i = 0; i < totalnum; i++) {
 647             if (wNAF_len[i] > (size_t)k) {
 648                 int digit = wNAF[i][k];
 649                 int is_neg;
 650
 651                 if (digit) {
 652                     is_neg = digit < 0;
 653
 654                     if (is_neg)
 655                         digit = -digit;
 656
 657                     if (is_neg != r_is_inverted) {
 658                         if (!r_is_at_infinity) {
 659                             if (!EC_POINT_invert(group, r, ctx))
 660                                 goto err;
 661                         }
 662                         r_is_inverted = !r_is_inverted;
 663                     }
 664
 665                     /* digit > 0 */
 666
 667                     if (r_is_at_infinity) {
 668                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 669                             goto err;
 670                         r_is_at_infinity = 0;
 671                     } else {
 672                         if (!EC_POINT_add
 673                             (group, r, r, val_sub[i][digit >> 1], ctx))
 674                             goto err;
 675                     }
 676                 }
 677             }
 678         }
 679     }
 680
 681     if (r_is_at_infinity) {
 682         if (!EC_POINT_set_to_infinity(group, r))
 683             goto err;
 684     } else {
 685         if (r_is_inverted)
 686             if (!EC_POINT_invert(group, r, ctx))
 687                 goto err;
 688     }
 689
 690     ret = 1;
 691
 692  err:
 693     if (new_ctx != NULL)
 694         BN_CTX_free(new_ctx);
 695     if (tmp != NULL)
 696         EC_POINT_free(tmp);
 697     if (wsize != NULL)
 698         OPENSSL_free(wsize);
 699     if (wNAF_len != NULL)
 700         OPENSSL_free(wNAF_len);
 701     if (wNAF != NULL) {
 702         signed char **w;
 703
 704         for (w = wNAF; *w != NULL; w++)
 705             OPENSSL_free(*w);
 706
 707         OPENSSL_free(wNAF);
 708     }
 709     if (val != NULL) {
 710         for (v = val; *v != NULL; v++)
 711             EC_POINT_clear_free(*v);
 712
 713         OPENSSL_free(val);
 714     }
 715     if (val_sub != NULL) {
 716         OPENSSL_free(val_sub);
 717     }
 718     return ret;
 719 }
 720
 721 /*-
 722  * ec_wNAF_precompute_mult()
 723  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 724  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 725  *
 726  * 'pre_comp->points' is an array of multiples of the generator
 727  * of the following form:
 728  * points[0] =     generator;
 729  * points[1] = 3 * generator;
 730  * ...
 731  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 732  * points[2^(w-1)]   =     2^blocksize * generator;
 733  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 734  * ...
 735  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 736  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 737  * ...
 738  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 739  * points[2^(w-1)*numblocks]       = NULL
 740  */
 741 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 742 {
 743     const EC_POINT *generator;
 744     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 745     BN_CTX *new_ctx = NULL;
 746     BIGNUM *order;
 747     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 748     EC_POINT **points = NULL;
 749     EC_PRE_COMP *pre_comp;
 750     int ret = 0;
 751
 752     /* if there is an old EC_PRE_COMP object, throw it away */
 753     EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup,
 754                          ec_pre_comp_free, ec_pre_comp_clear_free);
 755
 756     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 757         return 0;
 758
 759     generator = EC_GROUP_get0_generator(group);
 760     if (generator == NULL) {
 761         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 762         goto err;
 763     }
 764
 765     if (ctx == NULL) {
 766         ctx = new_ctx = BN_CTX_new();
 767         if (ctx == NULL)
 768             goto err;
 769     }
 770
 771     BN_CTX_start(ctx);
 772     order = BN_CTX_get(ctx);
 773     if (order == NULL)
 774         goto err;
 775
 776     if (!EC_GROUP_get_order(group, order, ctx))
 777         goto err;
 778     if (BN_is_zero(order)) {
 779         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 780         goto err;
 781     }
 782
 783     bits = BN_num_bits(order);
 784     /*
 785      * The following parameters mean we precompute (approximately) one point
 786      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 787      * bit lengths, other parameter combinations might provide better
 788      * efficiency.
 789      */
 790     blocksize = 8;
 791     w = 4;
 792     if (EC_window_bits_for_scalar_size(bits) > w) {
 793         /* let's not make the window too small ... */
 794         w = EC_window_bits_for_scalar_size(bits);
 795     }
 796
 797     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 798                                                      * to use for wNAF
 799                                                      * splitting */
 800
 801     pre_points_per_block = (size_t)1 << (w - 1);
 802     num = pre_points_per_block * numblocks; /* number of points to compute
 803                                              * and store */
 804
 805     points = OPENSSL_malloc(sizeof(EC_POINT *) * (num + 1));
 806     if (!points) {
 807         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 808         goto err;
 809     }
 810
 811     var = points;
 812     var[num] = NULL;            /* pivot */
 813     for (i = 0; i < num; i++) {
 814         if ((var[i] = EC_POINT_new(group)) == NULL) {
 815             ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 816             goto err;
 817         }
 818     }
 819
 820     if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) {
 821         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 822         goto err;
 823     }
 824
 825     if (!EC_POINT_copy(base, generator))
 826         goto err;
 827
 828     /* do the precomputation */
 829     for (i = 0; i < numblocks; i++) {
 830         size_t j;
 831
 832         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 833             goto err;
 834
 835         if (!EC_POINT_copy(*var++, base))
 836             goto err;
 837
 838         for (j = 1; j < pre_points_per_block; j++, var++) {
 839             /*
 840              * calculate odd multiples of the current base point
 841              */
 842             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 843                 goto err;
 844         }
 845
 846         if (i < numblocks - 1) {
 847             /*
 848              * get the next base (multiply current one by 2^blocksize)
 849              */
 850             size_t k;
 851
 852             if (blocksize <= 2) {
 853                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 854                 goto err;
 855             }
 856
 857             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 858                 goto err;
 859             for (k = 2; k < blocksize; k++) {
 860                 if (!EC_POINT_dbl(group, base, base, ctx))
 861                     goto err;
 862             }
 863         }
 864     }
 865
 866     if (!EC_POINTs_make_affine(group, num, points, ctx))
 867         goto err;
 868
 869     pre_comp->group = group;
 870     pre_comp->blocksize = blocksize;
 871     pre_comp->numblocks = numblocks;
 872     pre_comp->w = w;
 873     pre_comp->points = points;
 874     points = NULL;
 875     pre_comp->num = num;
 876
 877     if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
 878                              ec_pre_comp_dup, ec_pre_comp_free,
 879                              ec_pre_comp_clear_free))
 880         goto err;
 881     pre_comp = NULL;
 882
 883     ret = 1;
 884  err:
 885     if (ctx != NULL)
 886         BN_CTX_end(ctx);
 887     if (new_ctx != NULL)
 888         BN_CTX_free(new_ctx);
 889     if (pre_comp)
 890         ec_pre_comp_free(pre_comp);
 891     if (points) {
 892         EC_POINT **p;
 893
 894         for (p = points; *p != NULL; p++)
 895             EC_POINT_free(*p);
 896         OPENSSL_free(points);
 897     }
 898     if (tmp_point)
 899         EC_POINT_free(tmp_point);
 900     if (base)
 901         EC_POINT_free(base);
 902     return ret;
 903 }
 904
 905 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 906 {
 907     if (EC_EX_DATA_get_data
 908         (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free,
 909          ec_pre_comp_clear_free) != NULL)
 910         return 1;
 911     else
 912         return 0;
 913 }