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 /*
  72  * This file implements the wNAF-based interleaving multi-exponentation method
  73  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
  74  * for multiplication with precomputation, we use wNAF splitting
  75  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
  76  */
  77
  78
  79
  80
  81 /* structure for precomputed multiples of the generator */
  82 typedef struct ec_pre_comp_st {
  83         const EC_GROUP *group; /* parent EC_GROUP object */
  84         size_t blocksize;      /* block size for wNAF splitting */
  85         size_t numblocks;      /* max. number of blocks for which we have precomputation */
  86         size_t w;              /* window size */
  87         EC_POINT **points;     /* array with pre-calculated multiples of generator:
  88                                 * 'num' pointers to EC_POINT objects followed by a NULL */
  89         size_t num;            /* numblocks * 2^(w-1) */
  90         int references;
  91 } EC_PRE_COMP;
  92
  93 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
  94 static void *ec_pre_comp_dup(void *);
  95 static void ec_pre_comp_free(void *);
  96 static void ec_pre_comp_clear_free(void *);
  97
  98 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
  99         {
 100         EC_PRE_COMP *ret = NULL;
 101
 102         if (!group)
 103                 return NULL;
 104
 105         ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
 106         if (!ret)
 107                 {
 108                 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
 109                 return ret;
 110                 }
 111         ret->group = group;
 112         ret->blocksize = 8; /* default */
 113         ret->numblocks = 0;
 114         ret->w = 4; /* default */
 115         ret->points = NULL;
 116         ret->num = 0;
 117         ret->references = 1;
 118         return ret;
 119         }
 120
 121 static void *ec_pre_comp_dup(void *src_)
 122         {
 123         EC_PRE_COMP *src = src_;
 124
 125         /* no need to actually copy, these objects never change! */
 126
 127         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
 128
 129         return src_;
 130         }
 131
 132 static void ec_pre_comp_free(void *pre_)
 133         {
 134         int i;
 135         EC_PRE_COMP *pre = pre_;
 136
 137         if (!pre)
 138                 return;
 139
 140         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 141         if (i > 0)
 142                 return;
 143
 144         if (pre->points)
 145                 {
 146                 EC_POINT **p;
 147
 148                 for (p = pre->points; *p != NULL; p++)
 149                         EC_POINT_free(*p);
 150                 OPENSSL_free(pre->points);
 151                 }
 152         OPENSSL_free(pre);
 153         }
 154
 155 static void ec_pre_comp_clear_free(void *pre_)
 156         {
 157         int i;
 158         EC_PRE_COMP *pre = pre_;
 159
 160         if (!pre)
 161                 return;
 162
 163         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 164         if (i > 0)
 165                 return;
 166
 167         if (pre->points)
 168                 {
 169                 EC_POINT **p;
 170
 171                 for (p = pre->points; *p != NULL; p++)
 172                         EC_POINT_clear_free(*p);
 173                 OPENSSL_cleanse(pre->points, sizeof pre->points);
 174                 OPENSSL_free(pre->points);
 175                 }
 176         OPENSSL_cleanse(pre, sizeof pre);
 177         OPENSSL_free(pre);
 178         }
 179
 180
 181
 182
 183 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 184  * This is an array  r[]  of values that are either zero or odd with an
 185  * absolute value less than  2^w  satisfying
 186  *     scalar = \sum_j r[j]*2^j
 187  * where at most one of any  w+1  consecutive digits is non-zero
 188  * with the exception that the most significant digit may be only
 189  * w-1 zeros away from that next non-zero digit.
 190  */
 191 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
 192         {
 193         int window_val;
 194         int ok = 0;
 195         signed char *r = NULL;
 196         int sign = 1;
 197         int bit, next_bit, mask;
 198         size_t len = 0, j;
 199
 200         if (BN_is_zero(scalar))
 201                 {
 202                 r = OPENSSL_malloc(1);
 203                 if (!r)
 204                         {
 205                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 206                         goto err;
 207                         }
 208                 r[0] = 0;
 209                 *ret_len = 1;
 210                 return r;
 211                 }
 212
 213         if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
 214                 {
 215                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 216                 goto err;
 217                 }
 218         bit = 1 << w; /* at most 128 */
 219         next_bit = bit << 1; /* at most 256 */
 220         mask = next_bit - 1; /* at most 255 */
 221
 222         if (BN_is_negative(scalar))
 223                 {
 224                 sign = -1;
 225                 }
 226
 227         if (scalar->d == NULL || scalar->top == 0)
 228                 {
 229                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 230                 goto err;
 231                 }
 232
 233         len = BN_num_bits(scalar);
 234         r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
 235                                       * (*ret_len will be set to the actual length, i.e. at most
 236                                       * BN_num_bits(scalar) + 1) */
 237         if (r == NULL)
 238                 {
 239                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 240                 goto err;
 241                 }
 242         window_val = scalar->d[0] & mask;
 243         j = 0;
 244         while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
 245                 {
 246                 int digit = 0;
 247
 248                 /* 0 <= window_val <= 2^(w+1) */
 249
 250                 if (window_val & 1)
 251                         {
 252                         /* 0 < window_val < 2^(w+1) */
 253
 254                         if (window_val & bit)
 255                                 {
 256                                 digit = window_val - next_bit; /* -2^w < digit < 0 */
 257
 258 #if 1 /* modified wNAF */
 259                                 if (j + w + 1 >= len)
 260                                         {
 261                                         /* special case for generating modified wNAFs:
 262                                          * no new bits will be added into window_val,
 263                                          * so using a positive digit here will decrease
 264                                          * the total length of the representation */
 265
 266                                         digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
 267                                         }
 268 #endif
 269                                 }
 270                         else
 271                                 {
 272                                 digit = window_val; /* 0 < digit < 2^w */
 273                                 }
 274
 275                         if (digit <= -bit || digit >= bit || !(digit & 1))
 276                                 {
 277                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 278                                 goto err;
 279                                 }
 280
 281                         window_val -= digit;
 282
 283                         /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
 284                          * for modified window NAFs, it may also be 2^w
 285                          */
 286                         if (window_val != 0 && window_val != next_bit && window_val != bit)
 287                                 {
 288                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 289                                 goto err;
 290                                 }
 291                         }
 292
 293                 r[j++] = sign * digit;
 294
 295                 window_val >>= 1;
 296                 window_val += bit * BN_is_bit_set(scalar, j + w);
 297
 298                 if (window_val > next_bit)
 299                         {
 300                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 301                         goto err;
 302                         }
 303                 }
 304
 305         if (j > len + 1)
 306                 {
 307                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 308                 goto err;
 309                 }
 310         len = j;
 311         ok = 1;
 312
 313  err:
 314         if (!ok)
 315                 {
 316                 OPENSSL_free(r);
 317                 r = NULL;
 318                 }
 319         if (ok)
 320                 *ret_len = len;
 321         return r;
 322         }
 323
 324
 325 /* TODO: table should be optimised for the wNAF-based implementation,
 326  *       sometimes smaller windows will give better performance
 327  *       (thus the boundaries should be increased)
 328  */
 329 #define EC_window_bits_for_scalar_size(b) \
 330                 ((size_t) \
 331                  ((b) >= 2000 ? 6 : \
 332                   (b) >=  800 ? 5 : \
 333                   (b) >=  300 ? 4 : \
 334                   (b) >=   70 ? 3 : \
 335                   (b) >=   20 ? 2 : \
 336                   1))
 337
 338 /* Compute
 339  *      \sum scalars[i]*points[i],
 340  * also including
 341  *      scalar*generator
 342  * in the addition if scalar != NULL
 343  */
 344 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 345         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 346         {
 347         BN_CTX *new_ctx = NULL;
 348         const EC_POINT *generator = NULL;
 349         EC_POINT *tmp = NULL;
 350         size_t totalnum;
 351         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 352         size_t pre_points_per_block = 0;
 353         size_t i, j;
 354         int k;
 355         int r_is_inverted = 0;
 356         int r_is_at_infinity = 1;
 357         size_t *wsize = NULL; /* individual window sizes */
 358         signed char **wNAF = NULL; /* individual wNAFs */
 359         size_t *wNAF_len = NULL;
 360         size_t max_len = 0;
 361         size_t num_val;
 362         EC_POINT **val = NULL; /* precomputation */
 363         EC_POINT **v;
 364         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
 365         const EC_PRE_COMP *pre_comp = NULL;
 366         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
 367                              * i.e. precomputation is not available */
 368         int ret = 0;
 369
 370         if (group->meth != r->meth)
 371                 {
 372                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 373                 return 0;
 374                 }
 375
 376         if ((scalar == NULL) && (num == 0))
 377                 {
 378                 return EC_POINT_set_to_infinity(group, r);
 379                 }
 380
 381         for (i = 0; i < num; i++)
 382                 {
 383                 if (group->meth != points[i]->meth)
 384                         {
 385                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 386                         return 0;
 387                         }
 388                 }
 389
 390         if (ctx == NULL)
 391                 {
 392                 ctx = new_ctx = BN_CTX_new();
 393                 if (ctx == NULL)
 394                         goto err;
 395                 }
 396
 397         if (scalar != NULL)
 398                 {
 399                 generator = EC_GROUP_get0_generator(group);
 400                 if (generator == NULL)
 401                         {
 402                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 403                         goto err;
 404                         }
 405
 406                 /* look if we can use precomputed multiples of generator */
 407
 408                 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 409
 410                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
 411                         {
 412                         blocksize = pre_comp->blocksize;
 413
 414                         /* determine maximum number of blocks that wNAF splitting may yield
 415                          * (NB: maximum wNAF length is bit length plus one) */
 416                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 417
 418                         /* we cannot use more blocks than we have precomputation for */
 419                         if (numblocks > pre_comp->numblocks)
 420                                 numblocks = pre_comp->numblocks;
 421
 422                         pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 423
 424                         /* check that pre_comp looks sane */
 425                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
 426                                 {
 427                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 428                                 goto err;
 429                                 }
 430                         }
 431                 else
 432                         {
 433                         /* can't use precomputation */
 434                         pre_comp = NULL;
 435                         numblocks = 1;
 436                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
 437                         }
 438                 }
 439
 440         totalnum = num + numblocks;
 441
 442         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 443         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
 444         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
 445         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 446
 447         if (!wsize || !wNAF_len || !wNAF || !val_sub)
 448                 {
 449                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 450                 goto err;
 451                 }
 452
 453         wNAF[0] = NULL; /* preliminary pivot */
 454
 455         /* num_val will be the total number of temporarily precomputed points */
 456         num_val = 0;
 457
 458         for (i = 0; i < num + num_scalar; i++)
 459                 {
 460                 size_t bits;
 461
 462                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 463                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 464                 num_val += (size_t)1 << (wsize[i] - 1);
 465                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
 466                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
 467                 if (wNAF[i] == NULL)
 468                         goto err;
 469                 if (wNAF_len[i] > max_len)
 470                         max_len = wNAF_len[i];
 471                 }
 472
 473         if (numblocks)
 474                 {
 475                 /* we go here iff scalar != NULL */
 476
 477                 if (pre_comp == NULL)
 478                         {
 479                         if (num_scalar != 1)
 480                                 {
 481                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 482                                 goto err;
 483                                 }
 484                         /* we have already generated a wNAF for 'scalar' */
 485                         }
 486                 else
 487                         {
 488                         signed char *tmp_wNAF = NULL;
 489                         size_t tmp_len = 0;
 490
 491                         if (num_scalar != 0)
 492                                 {
 493                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 494                                 goto err;
 495                                 }
 496
 497                         /* use the window size for which we have precomputation */
 498                         wsize[num] = pre_comp->w;
 499                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
 500                         if (!tmp_wNAF)
 501                                 goto err;
 502
 503                         if (tmp_len <= max_len)
 504                                 {
 505                                 /* One of the other wNAFs is at least as long
 506                                  * as the wNAF belonging to the generator,
 507                                  * so wNAF splitting will not buy us anything. */
 508
 509                                 numblocks = 1;
 510                                 totalnum = num + 1; /* don't use wNAF splitting */
 511                                 wNAF[num] = tmp_wNAF;
 512                                 wNAF[num + 1] = NULL;
 513                                 wNAF_len[num] = tmp_len;
 514                                 if (tmp_len > max_len)
 515                                         max_len = tmp_len;
 516                                 /* pre_comp->points starts with the points that we need here: */
 517                                 val_sub[num] = pre_comp->points;
 518                                 }
 519                         else
 520                                 {
 521                                 /* don't include tmp_wNAF directly into wNAF array
 522                                  * - use wNAF splitting and include the blocks */
 523
 524                                 signed char *pp;
 525                                 EC_POINT **tmp_points;
 526
 527                                 if (tmp_len < numblocks * blocksize)
 528                                         {
 529                                         /* possibly we can do with fewer blocks than estimated */
 530                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
 531                                         if (numblocks > pre_comp->numblocks)
 532                                                 {
 533                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 534                                                 goto err;
 535                                                 }
 536                                         totalnum = num + numblocks;
 537                                         }
 538
 539                                 /* split wNAF in 'numblocks' parts */
 540                                 pp = tmp_wNAF;
 541                                 tmp_points = pre_comp->points;
 542
 543                                 for (i = num; i < totalnum; i++)
 544                                         {
 545                                         if (i < totalnum - 1)
 546                                                 {
 547                                                 wNAF_len[i] = blocksize;
 548                                                 if (tmp_len < blocksize)
 549                                                         {
 550                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 551                                                         goto err;
 552                                                         }
 553                                                 tmp_len -= blocksize;
 554                                                 }
 555                                         else
 556                                                 /* last block gets whatever is left
 557                                                  * (this could be more or less than 'blocksize'!) */
 558                                                 wNAF_len[i] = tmp_len;
 559
 560                                         wNAF[i + 1] = NULL;
 561                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 562                                         if (wNAF[i] == NULL)
 563                                                 {
 564                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 565                                                 OPENSSL_free(tmp_wNAF);
 566                                                 goto err;
 567                                                 }
 568                                         memcpy(wNAF[i], pp, wNAF_len[i]);
 569                                         if (wNAF_len[i] > max_len)
 570                                                 max_len = wNAF_len[i];
 571
 572                                         if (*tmp_points == NULL)
 573                                                 {
 574                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 575                                                 OPENSSL_free(tmp_wNAF);
 576                                                 goto err;
 577                                                 }
 578                                         val_sub[i] = tmp_points;
 579                                         tmp_points += pre_points_per_block;
 580                                         pp += blocksize;
 581                                         }
 582                                 OPENSSL_free(tmp_wNAF);
 583                                 }
 584                         }
 585                 }
 586
 587         /* All points we precompute now go into a single array 'val'.
 588          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
 589          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
 590         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 591         if (val == NULL)
 592                 {
 593                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 594                 goto err;
 595                 }
 596         val[num_val] = NULL; /* pivot element */
 597
 598         /* allocate points for precomputation */
 599         v = val;
 600         for (i = 0; i < num + num_scalar; i++)
 601                 {
 602                 val_sub[i] = v;
 603                 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
 604                         {
 605                         *v = EC_POINT_new(group);
 606                         if (*v == NULL) goto err;
 607                         v++;
 608                         }
 609                 }
 610         if (!(v == val + num_val))
 611                 {
 612                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 613                 goto err;
 614                 }
 615
 616         if (!(tmp = EC_POINT_new(group)))
 617                 goto err;
 618
 619         /* prepare precomputed values:
 620          *    val_sub[i][0] :=     points[i]
 621          *    val_sub[i][1] := 3 * points[i]
 622          *    val_sub[i][2] := 5 * points[i]
 623          *    ...
 624          */
 625         for (i = 0; i < num + num_scalar; i++)
 626                 {
 627                 if (i < num)
 628                         {
 629                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 630                         }
 631                 else
 632                         {
 633                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 634                         }
 635
 636                 if (wsize[i] > 1)
 637                         {
 638                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 639                         for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
 640                                 {
 641                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 642                                 }
 643                         }
 644                 }
 645
 646 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
 647         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 648                 goto err;
 649 #endif
 650
 651         r_is_at_infinity = 1;
 652
 653         for (k = max_len - 1; k >= 0; k--)
 654                 {
 655                 if (!r_is_at_infinity)
 656                         {
 657                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 658                         }
 659
 660                 for (i = 0; i < totalnum; i++)
 661                         {
 662                         if (wNAF_len[i] > (size_t)k)
 663                                 {
 664                                 int digit = wNAF[i][k];
 665                                 int is_neg;
 666
 667                                 if (digit)
 668                                         {
 669                                         is_neg = digit < 0;
 670
 671                                         if (is_neg)
 672                                                 digit = -digit;
 673
 674                                         if (is_neg != r_is_inverted)
 675                                                 {
 676                                                 if (!r_is_at_infinity)
 677                                                         {
 678                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 679                                                         }
 680                                                 r_is_inverted = !r_is_inverted;
 681                                                 }
 682
 683                                         /* digit > 0 */
 684
 685                                         if (r_is_at_infinity)
 686                                                 {
 687                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
 688                                                 r_is_at_infinity = 0;
 689                                                 }
 690                                         else
 691                                                 {
 692                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
 693                                                 }
 694                                         }
 695                                 }
 696                         }
 697                 }
 698
 699         if (r_is_at_infinity)
 700                 {
 701                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 702                 }
 703         else
 704                 {
 705                 if (r_is_inverted)
 706                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 707                 }
 708
 709         ret = 1;
 710
 711  err:
 712         if (new_ctx != NULL)
 713                 BN_CTX_free(new_ctx);
 714         if (tmp != NULL)
 715                 EC_POINT_free(tmp);
 716         if (wsize != NULL)
 717                 OPENSSL_free(wsize);
 718         if (wNAF_len != NULL)
 719                 OPENSSL_free(wNAF_len);
 720         if (wNAF != NULL)
 721                 {
 722                 signed char **w;
 723
 724                 for (w = wNAF; *w != NULL; w++)
 725                         OPENSSL_free(*w);
 726
 727                 OPENSSL_free(wNAF);
 728                 }
 729         if (val != NULL)
 730                 {
 731                 for (v = val; *v != NULL; v++)
 732                         EC_POINT_clear_free(*v);
 733
 734                 OPENSSL_free(val);
 735                 }
 736         if (val_sub != NULL)
 737                 {
 738                 OPENSSL_free(val_sub);
 739                 }
 740         return ret;
 741         }
 742
 743
 744 /* ec_wNAF_precompute_mult()
 745  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 746  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 747  *
 748  * 'pre_comp->points' is an array of multiples of the generator
 749  * of the following form:
 750  * points[0] =     generator;
 751  * points[1] = 3 * generator;
 752  * ...
 753  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 754  * points[2^(w-1)]   =     2^blocksize * generator;
 755  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 756  * ...
 757  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 758  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 759  * ...
 760  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 761  * points[2^(w-1)*numblocks]       = NULL
 762  */
 763 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 764         {
 765         const EC_POINT *generator;
 766         EC_POINT *tmp_point = NULL, *base = NULL, **var;
 767         BN_CTX *new_ctx = NULL;
 768         BIGNUM *order;
 769         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 770         EC_POINT **points = NULL;
 771         EC_PRE_COMP *pre_comp;
 772         int ret = 0;
 773
 774         /* if there is an old EC_PRE_COMP object, throw it away */
 775         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 776
 777         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 778                 return 0;
 779
 780         generator = EC_GROUP_get0_generator(group);
 781         if (generator == NULL)
 782                 {
 783                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 784                 goto err;
 785                 }
 786
 787         if (ctx == NULL)
 788                 {
 789                 ctx = new_ctx = BN_CTX_new();
 790                 if (ctx == NULL)
 791                         goto err;
 792                 }
 793
 794         BN_CTX_start(ctx);
 795         order = BN_CTX_get(ctx);
 796         if (order == NULL) goto err;
 797
 798         if (!EC_GROUP_get_order(group, order, ctx)) goto err;
 799         if (BN_is_zero(order))
 800                 {
 801                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 802                 goto err;
 803                 }
 804
 805         bits = BN_num_bits(order);
 806         /* The following parameters mean we precompute (approximately)
 807          * one point per bit.
 808          *
 809          * TBD: The combination  8, 4  is perfect for 160 bits; for other
 810          * bit lengths, other parameter combinations might provide better
 811          * efficiency.
 812          */
 813         blocksize = 8;
 814         w = 4;
 815         if (EC_window_bits_for_scalar_size(bits) > w)
 816                 {
 817                 /* let's not make the window too small ... */
 818                 w = EC_window_bits_for_scalar_size(bits);
 819                 }
 820
 821         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
 822
 823         pre_points_per_block = (size_t)1 << (w - 1);
 824         num = pre_points_per_block * numblocks; /* number of points to compute and store */
 825
 826         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
 827         if (!points)
 828                 {
 829                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 830                 goto err;
 831                 }
 832
 833         var = points;
 834         var[num] = NULL; /* pivot */
 835         for (i = 0; i < num; i++)
 836                 {
 837                 if ((var[i] = EC_POINT_new(group)) == NULL)
 838                         {
 839                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 840                         goto err;
 841                         }
 842                 }
 843
 844         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
 845                 {
 846                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 847                 goto err;
 848                 }
 849
 850         if (!EC_POINT_copy(base, generator))
 851                 goto err;
 852
 853         /* do the precomputation */
 854         for (i = 0; i < numblocks; i++)
 855                 {
 856                 size_t j;
 857
 858                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 859                         goto err;
 860
 861                 if (!EC_POINT_copy(*var++, base))
 862                         goto err;
 863
 864                 for (j = 1; j < pre_points_per_block; j++, var++)
 865                         {
 866                         /* calculate odd multiples of the current base point */
 867                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 868                                 goto err;
 869                         }
 870
 871                 if (i < numblocks - 1)
 872                         {
 873                         /* get the next base (multiply current one by 2^blocksize) */
 874                         size_t k;
 875
 876                         if (blocksize <= 2)
 877                                 {
 878                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 879                                 goto err;
 880                                 }
 881
 882                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 883                                 goto err;
 884                         for (k = 2; k < blocksize; k++)
 885                                 {
 886                                 if (!EC_POINT_dbl(group,base,base,ctx))
 887                                         goto err;
 888                                 }
 889                         }
 890                 }
 891
 892         if (!EC_POINTs_make_affine(group, num, points, ctx))
 893                 goto err;
 894
 895         pre_comp->group = group;
 896         pre_comp->blocksize = blocksize;
 897         pre_comp->numblocks = numblocks;
 898         pre_comp->w = w;
 899         pre_comp->points = points;
 900         points = NULL;
 901         pre_comp->num = num;
 902
 903         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
 904                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
 905                 goto err;
 906         pre_comp = NULL;
 907
 908         ret = 1;
 909  err:
 910         if (ctx != NULL)
 911                 BN_CTX_end(ctx);
 912         if (new_ctx != NULL)
 913                 BN_CTX_free(new_ctx);
 914         if (pre_comp)
 915                 ec_pre_comp_free(pre_comp);
 916         if (points)
 917                 {
 918                 EC_POINT **p;
 919
 920                 for (p = points; *p != NULL; p++)
 921                         EC_POINT_free(*p);
 922                 OPENSSL_free(points);
 923                 }
 924         if (tmp_point)
 925                 EC_POINT_free(tmp_point);
 926         if (base)
 927                 EC_POINT_free(base);
 928         return ret;
 929         }
 930
 931
 932 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 933         {
 934         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
 935                 return 1;
 936         else
 937                 return 0;
 938         }