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
  65
  66 #include <string.h>
  67
  68 #include <openssl/err.h>
  69
  70 #include "ec_lcl.h"
  71
  72
  73 /*
  74  * This file implements the wNAF-based interleaving multi-exponentation method
  75  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
  76  * for multiplication with precomputation, we use wNAF splitting
  77  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
  78  */
  79
  80
  81
  82
  83 /* structure for precomputed multiples of the generator */
  84 typedef struct ec_pre_comp_st {
  85         const EC_GROUP *group; /* parent EC_GROUP object */
  86         size_t blocksize;      /* block size for wNAF splitting */
  87         size_t numblocks;      /* max. number of blocks for which we have precomputation */
  88         size_t w;              /* window size */
  89         EC_POINT **points;     /* array with pre-calculated multiples of generator:
  90                                 * 'num' pointers to EC_POINT objects followed by a NULL */
  91         size_t num;            /* numblocks * 2^(w-1) */
  92         int references;
  93 } EC_PRE_COMP;
  94
  95 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
  96 static void *ec_pre_comp_dup(void *);
  97 static void ec_pre_comp_free(void *);
  98 static void ec_pre_comp_clear_free(void *);
  99
 100 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
 101         {
 102         EC_PRE_COMP *ret = NULL;
 103
 104         if (!group)
 105                 return NULL;
 106
 107         ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
 108         if (!ret)
 109                 {
 110                 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
 111                 return ret;
 112                 }
 113         ret->group = group;
 114         ret->blocksize = 8; /* default */
 115         ret->numblocks = 0;
 116         ret->w = 4; /* default */
 117         ret->points = NULL;
 118         ret->num = 0;
 119         ret->references = 1;
 120         return ret;
 121         }
 122
 123 static void *ec_pre_comp_dup(void *src_)
 124         {
 125         EC_PRE_COMP *src = src_;
 126
 127         /* no need to actually copy, these objects never change! */
 128
 129         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
 130
 131         return src_;
 132         }
 133
 134 static void ec_pre_comp_free(void *pre_)
 135         {
 136         int i;
 137         EC_PRE_COMP *pre = pre_;
 138
 139         if (!pre)
 140                 return;
 141
 142         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 143         if (i > 0)
 144                 return;
 145
 146         if (pre->points)
 147                 {
 148                 EC_POINT **p;
 149
 150                 for (p = pre->points; *p != NULL; p++)
 151                         EC_POINT_free(*p);
 152                 OPENSSL_free(pre->points);
 153                 }
 154         OPENSSL_free(pre);
 155         }
 156
 157 static void ec_pre_comp_clear_free(void *pre_)
 158         {
 159         int i;
 160         EC_PRE_COMP *pre = pre_;
 161
 162         if (!pre)
 163                 return;
 164
 165         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 166         if (i > 0)
 167                 return;
 168
 169         if (pre->points)
 170                 {
 171                 EC_POINT **p;
 172
 173                 for (p = pre->points; *p != NULL; p++)
 174                         {
 175                         EC_POINT_clear_free(*p);
 176                         OPENSSL_cleanse(p, sizeof *p);
 177                         }
 178                 OPENSSL_free(pre->points);
 179                 }
 180         OPENSSL_cleanse(pre, sizeof *pre);
 181         OPENSSL_free(pre);
 182         }
 183
 184
 185
 186
 187 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 188  * This is an array  r[]  of values that are either zero or odd with an
 189  * absolute value less than  2^w  satisfying
 190  *     scalar = \sum_j r[j]*2^j
 191  * where at most one of any  w+1  consecutive digits is non-zero
 192  * with the exception that the most significant digit may be only
 193  * w-1 zeros away from that next non-zero digit.
 194  */
 195 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
 196         {
 197         int window_val;
 198         int ok = 0;
 199         signed char *r = NULL;
 200         int sign = 1;
 201         int bit, next_bit, mask;
 202         size_t len = 0, j;
 203
 204         if (BN_is_zero(scalar))
 205                 {
 206                 r = OPENSSL_malloc(1);
 207                 if (!r)
 208                         {
 209                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 210                         goto err;
 211                         }
 212                 r[0] = 0;
 213                 *ret_len = 1;
 214                 return r;
 215                 }
 216
 217         if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
 218                 {
 219                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 220                 goto err;
 221                 }
 222         bit = 1 << w; /* at most 128 */
 223         next_bit = bit << 1; /* at most 256 */
 224         mask = next_bit - 1; /* at most 255 */
 225
 226         if (BN_is_negative(scalar))
 227                 {
 228                 sign = -1;
 229                 }
 230
 231         if (scalar->d == NULL || scalar->top == 0)
 232                 {
 233                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 234                 goto err;
 235                 }
 236
 237         len = BN_num_bits(scalar);
 238         r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
 239                                       * (*ret_len will be set to the actual length, i.e. at most
 240                                       * BN_num_bits(scalar) + 1) */
 241         if (r == NULL)
 242                 {
 243                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
 244                 goto err;
 245                 }
 246         window_val = scalar->d[0] & mask;
 247         j = 0;
 248         while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
 249                 {
 250                 int digit = 0;
 251
 252                 /* 0 <= window_val <= 2^(w+1) */
 253
 254                 if (window_val & 1)
 255                         {
 256                         /* 0 < window_val < 2^(w+1) */
 257
 258                         if (window_val & bit)
 259                                 {
 260                                 digit = window_val - next_bit; /* -2^w < digit < 0 */
 261
 262 #if 1 /* modified wNAF */
 263                                 if (j + w + 1 >= len)
 264                                         {
 265                                         /* special case for generating modified wNAFs:
 266                                          * no new bits will be added into window_val,
 267                                          * so using a positive digit here will decrease
 268                                          * the total length of the representation */
 269
 270                                         digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
 271                                         }
 272 #endif
 273                                 }
 274                         else
 275                                 {
 276                                 digit = window_val; /* 0 < digit < 2^w */
 277                                 }
 278
 279                         if (digit <= -bit || digit >= bit || !(digit & 1))
 280                                 {
 281                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 282                                 goto err;
 283                                 }
 284
 285                         window_val -= digit;
 286
 287                         /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
 288                          * for modified window NAFs, it may also be 2^w
 289                          */
 290                         if (window_val != 0 && window_val != next_bit && window_val != bit)
 291                                 {
 292                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 293                                 goto err;
 294                                 }
 295                         }
 296
 297                 r[j++] = sign * digit;
 298
 299                 window_val >>= 1;
 300                 window_val += bit * BN_is_bit_set(scalar, j + w);
 301
 302                 if (window_val > next_bit)
 303                         {
 304                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 305                         goto err;
 306                         }
 307                 }
 308
 309         if (j > len + 1)
 310                 {
 311                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 312                 goto err;
 313                 }
 314         len = j;
 315         ok = 1;
 316
 317  err:
 318         if (!ok)
 319                 {
 320                 OPENSSL_free(r);
 321                 r = NULL;
 322                 }
 323         if (ok)
 324                 *ret_len = len;
 325         return r;
 326         }
 327
 328
 329 /* TODO: table should be optimised for the wNAF-based implementation,
 330  *       sometimes smaller windows will give better performance
 331  *       (thus the boundaries should be increased)
 332  */
 333 #define EC_window_bits_for_scalar_size(b) \
 334                 ((size_t) \
 335                  ((b) >= 2000 ? 6 : \
 336                   (b) >=  800 ? 5 : \
 337                   (b) >=  300 ? 4 : \
 338                   (b) >=   70 ? 3 : \
 339                   (b) >=   20 ? 2 : \
 340                   1))
 341
 342 /* Compute
 343  *      \sum scalars[i]*points[i],
 344  * also including
 345  *      scalar*generator
 346  * in the addition if scalar != NULL
 347  */
 348 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 349         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 350         {
 351         BN_CTX *new_ctx = NULL;
 352         const EC_POINT *generator = NULL;
 353         EC_POINT *tmp = NULL;
 354         size_t totalnum;
 355         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 356         size_t pre_points_per_block = 0;
 357         size_t i, j;
 358         int k;
 359         int r_is_inverted = 0;
 360         int r_is_at_infinity = 1;
 361         size_t *wsize = NULL; /* individual window sizes */
 362         signed char **wNAF = NULL; /* individual wNAFs */
 363         size_t *wNAF_len = NULL;
 364         size_t max_len = 0;
 365         size_t num_val;
 366         EC_POINT **val = NULL; /* precomputation */
 367         EC_POINT **v;
 368         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
 369         const EC_PRE_COMP *pre_comp = NULL;
 370         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
 371                              * i.e. precomputation is not available */
 372         int ret = 0;
 373
 374         if (group->meth != r->meth)
 375                 {
 376                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 377                 return 0;
 378                 }
 379
 380         if ((scalar == NULL) && (num == 0))
 381                 {
 382                 return EC_POINT_set_to_infinity(group, r);
 383                 }
 384
 385         for (i = 0; i < num; i++)
 386                 {
 387                 if (group->meth != points[i]->meth)
 388                         {
 389                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 390                         return 0;
 391                         }
 392                 }
 393
 394         if (ctx == NULL)
 395                 {
 396                 ctx = new_ctx = BN_CTX_new();
 397                 if (ctx == NULL)
 398                         goto err;
 399                 }
 400
 401         if (scalar != NULL)
 402                 {
 403                 generator = EC_GROUP_get0_generator(group);
 404                 if (generator == NULL)
 405                         {
 406                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 407                         goto err;
 408                         }
 409
 410                 /* look if we can use precomputed multiples of generator */
 411
 412                 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 413
 414                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
 415                         {
 416                         blocksize = pre_comp->blocksize;
 417
 418                         /* determine maximum number of blocks that wNAF splitting may yield
 419                          * (NB: maximum wNAF length is bit length plus one) */
 420                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 421
 422                         /* we cannot use more blocks than we have precomputation for */
 423                         if (numblocks > pre_comp->numblocks)
 424                                 numblocks = pre_comp->numblocks;
 425
 426                         pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 427
 428                         /* check that pre_comp looks sane */
 429                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
 430                                 {
 431                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 432                                 goto err;
 433                                 }
 434                         }
 435                 else
 436                         {
 437                         /* can't use precomputation */
 438                         pre_comp = NULL;
 439                         numblocks = 1;
 440                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
 441                         }
 442                 }
 443
 444         totalnum = num + numblocks;
 445
 446         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 447         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
 448         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
 449         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 450
 451         /* Ensure wNAF is initialised in case we end up going to err */
 452         if (wNAF) wNAF[0] = NULL;       /* preliminary pivot */
 453
 454         if (!wsize || !wNAF_len || !wNAF || !val_sub)
 455                 {
 456                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 457                 goto err;
 458                 }
 459
 460         /* num_val will be the total number of temporarily precomputed points */
 461         num_val = 0;
 462
 463         for (i = 0; i < num + num_scalar; i++)
 464                 {
 465                 size_t bits;
 466
 467                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 468                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 469                 num_val += (size_t)1 << (wsize[i] - 1);
 470                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
 471                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
 472                 if (wNAF[i] == NULL)
 473                         goto err;
 474                 if (wNAF_len[i] > max_len)
 475                         max_len = wNAF_len[i];
 476                 }
 477
 478         if (numblocks)
 479                 {
 480                 /* we go here iff scalar != NULL */
 481
 482                 if (pre_comp == NULL)
 483                         {
 484                         if (num_scalar != 1)
 485                                 {
 486                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 487                                 goto err;
 488                                 }
 489                         /* we have already generated a wNAF for 'scalar' */
 490                         }
 491                 else
 492                         {
 493                         signed char *tmp_wNAF = NULL;
 494                         size_t tmp_len = 0;
 495
 496                         if (num_scalar != 0)
 497                                 {
 498                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 499                                 goto err;
 500                                 }
 501
 502                         /* use the window size for which we have precomputation */
 503                         wsize[num] = pre_comp->w;
 504                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
 505                         if (!tmp_wNAF)
 506                                 goto err;
 507
 508                         if (tmp_len <= max_len)
 509                                 {
 510                                 /* One of the other wNAFs is at least as long
 511                                  * as the wNAF belonging to the generator,
 512                                  * so wNAF splitting will not buy us anything. */
 513
 514                                 numblocks = 1;
 515                                 totalnum = num + 1; /* don't use wNAF splitting */
 516                                 wNAF[num] = tmp_wNAF;
 517                                 wNAF[num + 1] = NULL;
 518                                 wNAF_len[num] = tmp_len;
 519                                 if (tmp_len > max_len)
 520                                         max_len = tmp_len;
 521                                 /* pre_comp->points starts with the points that we need here: */
 522                                 val_sub[num] = pre_comp->points;
 523                                 }
 524                         else
 525                                 {
 526                                 /* don't include tmp_wNAF directly into wNAF array
 527                                  * - use wNAF splitting and include the blocks */
 528
 529                                 signed char *pp;
 530                                 EC_POINT **tmp_points;
 531
 532                                 if (tmp_len < numblocks * blocksize)
 533                                         {
 534                                         /* possibly we can do with fewer blocks than estimated */
 535                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
 536                                         if (numblocks > pre_comp->numblocks)
 537                                                 {
 538                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 539                                                 goto err;
 540                                                 }
 541                                         totalnum = num + numblocks;
 542                                         }
 543
 544                                 /* split wNAF in 'numblocks' parts */
 545                                 pp = tmp_wNAF;
 546                                 tmp_points = pre_comp->points;
 547
 548                                 for (i = num; i < totalnum; i++)
 549                                         {
 550                                         if (i < totalnum - 1)
 551                                                 {
 552                                                 wNAF_len[i] = blocksize;
 553                                                 if (tmp_len < blocksize)
 554                                                         {
 555                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 556                                                         goto err;
 557                                                         }
 558                                                 tmp_len -= blocksize;
 559                                                 }
 560                                         else
 561                                                 /* last block gets whatever is left
 562                                                  * (this could be more or less than 'blocksize'!) */
 563                                                 wNAF_len[i] = tmp_len;
 564
 565                                         wNAF[i + 1] = NULL;
 566                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 567                                         if (wNAF[i] == NULL)
 568                                                 {
 569                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 570                                                 OPENSSL_free(tmp_wNAF);
 571                                                 goto err;
 572                                                 }
 573                                         memcpy(wNAF[i], pp, wNAF_len[i]);
 574                                         if (wNAF_len[i] > max_len)
 575                                                 max_len = wNAF_len[i];
 576
 577                                         if (*tmp_points == NULL)
 578                                                 {
 579                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 580                                                 OPENSSL_free(tmp_wNAF);
 581                                                 goto err;
 582                                                 }
 583                                         val_sub[i] = tmp_points;
 584                                         tmp_points += pre_points_per_block;
 585                                         pp += blocksize;
 586                                         }
 587                                 OPENSSL_free(tmp_wNAF);
 588                                 }
 589                         }
 590                 }
 591
 592         /* All points we precompute now go into a single array 'val'.
 593          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
 594          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
 595         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 596         if (val == NULL)
 597                 {
 598                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 599                 goto err;
 600                 }
 601         val[num_val] = NULL; /* pivot element */
 602
 603         /* allocate points for precomputation */
 604         v = val;
 605         for (i = 0; i < num + num_scalar; i++)
 606                 {
 607                 val_sub[i] = v;
 608                 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
 609                         {
 610                         *v = EC_POINT_new(group);
 611                         if (*v == NULL) goto err;
 612                         v++;
 613                         }
 614                 }
 615         if (!(v == val + num_val))
 616                 {
 617                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 618                 goto err;
 619                 }
 620
 621         if (!(tmp = EC_POINT_new(group)))
 622                 goto err;
 623
 624         /* prepare precomputed values:
 625          *    val_sub[i][0] :=     points[i]
 626          *    val_sub[i][1] := 3 * points[i]
 627          *    val_sub[i][2] := 5 * points[i]
 628          *    ...
 629          */
 630         for (i = 0; i < num + num_scalar; i++)
 631                 {
 632                 if (i < num)
 633                         {
 634                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 635                         }
 636                 else
 637                         {
 638                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 639                         }
 640
 641                 if (wsize[i] > 1)
 642                         {
 643                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 644                         for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
 645                                 {
 646                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 647                                 }
 648                         }
 649                 }
 650
 651 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
 652         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 653                 goto err;
 654 #endif
 655
 656         r_is_at_infinity = 1;
 657
 658         for (k = max_len - 1; k >= 0; k--)
 659                 {
 660                 if (!r_is_at_infinity)
 661                         {
 662                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 663                         }
 664
 665                 for (i = 0; i < totalnum; i++)
 666                         {
 667                         if (wNAF_len[i] > (size_t)k)
 668                                 {
 669                                 int digit = wNAF[i][k];
 670                                 int is_neg;
 671
 672                                 if (digit)
 673                                         {
 674                                         is_neg = digit < 0;
 675
 676                                         if (is_neg)
 677                                                 digit = -digit;
 678
 679                                         if (is_neg != r_is_inverted)
 680                                                 {
 681                                                 if (!r_is_at_infinity)
 682                                                         {
 683                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 684                                                         }
 685                                                 r_is_inverted = !r_is_inverted;
 686                                                 }
 687
 688                                         /* digit > 0 */
 689
 690                                         if (r_is_at_infinity)
 691                                                 {
 692                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
 693                                                 r_is_at_infinity = 0;
 694                                                 }
 695                                         else
 696                                                 {
 697                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
 698                                                 }
 699                                         }
 700                                 }
 701                         }
 702                 }
 703
 704         if (r_is_at_infinity)
 705                 {
 706                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 707                 }
 708         else
 709                 {
 710                 if (r_is_inverted)
 711                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 712                 }
 713
 714         ret = 1;
 715
 716  err:
 717         if (new_ctx != NULL)
 718                 BN_CTX_free(new_ctx);
 719         if (tmp != NULL)
 720                 EC_POINT_free(tmp);
 721         if (wsize != NULL)
 722                 OPENSSL_free(wsize);
 723         if (wNAF_len != NULL)
 724                 OPENSSL_free(wNAF_len);
 725         if (wNAF != NULL)
 726                 {
 727                 signed char **w;
 728
 729                 for (w = wNAF; *w != NULL; w++)
 730                         OPENSSL_free(*w);
 731
 732                 OPENSSL_free(wNAF);
 733                 }
 734         if (val != NULL)
 735                 {
 736                 for (v = val; *v != NULL; v++)
 737                         EC_POINT_clear_free(*v);
 738
 739                 OPENSSL_free(val);
 740                 }
 741         if (val_sub != NULL)
 742                 {
 743                 OPENSSL_free(val_sub);
 744                 }
 745         return ret;
 746         }
 747
 748
 749 /* ec_wNAF_precompute_mult()
 750  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 751  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 752  *
 753  * 'pre_comp->points' is an array of multiples of the generator
 754  * of the following form:
 755  * points[0] =     generator;
 756  * points[1] = 3 * generator;
 757  * ...
 758  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 759  * points[2^(w-1)]   =     2^blocksize * generator;
 760  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 761  * ...
 762  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 763  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 764  * ...
 765  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 766  * points[2^(w-1)*numblocks]       = NULL
 767  */
 768 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 769         {
 770         const EC_POINT *generator;
 771         EC_POINT *tmp_point = NULL, *base = NULL, **var;
 772         BN_CTX *new_ctx = NULL;
 773         BIGNUM *order;
 774         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 775         EC_POINT **points = NULL;
 776         EC_PRE_COMP *pre_comp;
 777         int ret = 0;
 778
 779         /* if there is an old EC_PRE_COMP object, throw it away */
 780         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 781
 782         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 783                 return 0;
 784
 785         generator = EC_GROUP_get0_generator(group);
 786         if (generator == NULL)
 787                 {
 788                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 789                 goto err;
 790                 }
 791
 792         if (ctx == NULL)
 793                 {
 794                 ctx = new_ctx = BN_CTX_new();
 795                 if (ctx == NULL)
 796                         goto err;
 797                 }
 798
 799         BN_CTX_start(ctx);
 800         order = BN_CTX_get(ctx);
 801         if (order == NULL) goto err;
 802
 803         if (!EC_GROUP_get_order(group, order, ctx)) goto err;
 804         if (BN_is_zero(order))
 805                 {
 806                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 807                 goto err;
 808                 }
 809
 810         bits = BN_num_bits(order);
 811         /* The following parameters mean we precompute (approximately)
 812          * one point per bit.
 813          *
 814          * TBD: The combination  8, 4  is perfect for 160 bits; for other
 815          * bit lengths, other parameter combinations might provide better
 816          * efficiency.
 817          */
 818         blocksize = 8;
 819         w = 4;
 820         if (EC_window_bits_for_scalar_size(bits) > w)
 821                 {
 822                 /* let's not make the window too small ... */
 823                 w = EC_window_bits_for_scalar_size(bits);
 824                 }
 825
 826         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
 827
 828         pre_points_per_block = (size_t)1 << (w - 1);
 829         num = pre_points_per_block * numblocks; /* number of points to compute and store */
 830
 831         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
 832         if (!points)
 833                 {
 834                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 835                 goto err;
 836                 }
 837
 838         var = points;
 839         var[num] = NULL; /* pivot */
 840         for (i = 0; i < num; i++)
 841                 {
 842                 if ((var[i] = EC_POINT_new(group)) == NULL)
 843                         {
 844                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 845                         goto err;
 846                         }
 847                 }
 848
 849         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
 850                 {
 851                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 852                 goto err;
 853                 }
 854
 855         if (!EC_POINT_copy(base, generator))
 856                 goto err;
 857
 858         /* do the precomputation */
 859         for (i = 0; i < numblocks; i++)
 860                 {
 861                 size_t j;
 862
 863                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 864                         goto err;
 865
 866                 if (!EC_POINT_copy(*var++, base))
 867                         goto err;
 868
 869                 for (j = 1; j < pre_points_per_block; j++, var++)
 870                         {
 871                         /* calculate odd multiples of the current base point */
 872                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 873                                 goto err;
 874                         }
 875
 876                 if (i < numblocks - 1)
 877                         {
 878                         /* get the next base (multiply current one by 2^blocksize) */
 879                         size_t k;
 880
 881                         if (blocksize <= 2)
 882                                 {
 883                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 884                                 goto err;
 885                                 }
 886
 887                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 888                                 goto err;
 889                         for (k = 2; k < blocksize; k++)
 890                                 {
 891                                 if (!EC_POINT_dbl(group,base,base,ctx))
 892                                         goto err;
 893                                 }
 894                         }
 895                 }
 896
 897         if (!EC_POINTs_make_affine(group, num, points, ctx))
 898                 goto err;
 899
 900         pre_comp->group = group;
 901         pre_comp->blocksize = blocksize;
 902         pre_comp->numblocks = numblocks;
 903         pre_comp->w = w;
 904         pre_comp->points = points;
 905         points = NULL;
 906         pre_comp->num = num;
 907
 908         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
 909                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
 910                 goto err;
 911         pre_comp = NULL;
 912
 913         ret = 1;
 914  err:
 915         if (ctx != NULL)
 916                 BN_CTX_end(ctx);
 917         if (new_ctx != NULL)
 918                 BN_CTX_free(new_ctx);
 919         if (pre_comp)
 920                 ec_pre_comp_free(pre_comp);
 921         if (points)
 922                 {
 923                 EC_POINT **p;
 924
 925                 for (p = points; *p != NULL; p++)
 926                         EC_POINT_free(*p);
 927                 OPENSSL_free(points);
 928                 }
 929         if (tmp_point)
 930                 EC_POINT_free(tmp_point);
 931         if (base)
 932                 EC_POINT_free(base);
 933         return ret;
 934         }
 935
 936
 937 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 938         {
 939         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
 940                 return 1;
 941         else
 942                 return 0;
 943         }