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 #define OPENSSL_FIPSAPI
  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         if (!wsize || !wNAF_len || !wNAF || !val_sub)
 452                 {
 453                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 454                 goto err;
 455                 }
 456
 457         wNAF[0] = NULL; /* preliminary pivot */
 458
 459         /* num_val will be the total number of temporarily precomputed points */
 460         num_val = 0;
 461
 462         for (i = 0; i < num + num_scalar; i++)
 463                 {
 464                 size_t bits;
 465
 466                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 467                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 468                 num_val += (size_t)1 << (wsize[i] - 1);
 469                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
 470                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
 471                 if (wNAF[i] == NULL)
 472                         goto err;
 473                 if (wNAF_len[i] > max_len)
 474                         max_len = wNAF_len[i];
 475                 }
 476
 477         if (numblocks)
 478                 {
 479                 /* we go here iff scalar != NULL */
 480
 481                 if (pre_comp == NULL)
 482                         {
 483                         if (num_scalar != 1)
 484                                 {
 485                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 486                                 goto err;
 487                                 }
 488                         /* we have already generated a wNAF for 'scalar' */
 489                         }
 490                 else
 491                         {
 492                         signed char *tmp_wNAF = NULL;
 493                         size_t tmp_len = 0;
 494
 495                         if (num_scalar != 0)
 496                                 {
 497                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 498                                 goto err;
 499                                 }
 500
 501                         /* use the window size for which we have precomputation */
 502                         wsize[num] = pre_comp->w;
 503                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
 504                         if (!tmp_wNAF)
 505                                 goto err;
 506
 507                         if (tmp_len <= max_len)
 508                                 {
 509                                 /* One of the other wNAFs is at least as long
 510                                  * as the wNAF belonging to the generator,
 511                                  * so wNAF splitting will not buy us anything. */
 512
 513                                 numblocks = 1;
 514                                 totalnum = num + 1; /* don't use wNAF splitting */
 515                                 wNAF[num] = tmp_wNAF;
 516                                 wNAF[num + 1] = NULL;
 517                                 wNAF_len[num] = tmp_len;
 518                                 if (tmp_len > max_len)
 519                                         max_len = tmp_len;
 520                                 /* pre_comp->points starts with the points that we need here: */
 521                                 val_sub[num] = pre_comp->points;
 522                                 }
 523                         else
 524                                 {
 525                                 /* don't include tmp_wNAF directly into wNAF array
 526                                  * - use wNAF splitting and include the blocks */
 527
 528                                 signed char *pp;
 529                                 EC_POINT **tmp_points;
 530
 531                                 if (tmp_len < numblocks * blocksize)
 532                                         {
 533                                         /* possibly we can do with fewer blocks than estimated */
 534                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
 535                                         if (numblocks > pre_comp->numblocks)
 536                                                 {
 537                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 538                                                 goto err;
 539                                                 }
 540                                         totalnum = num + numblocks;
 541                                         }
 542
 543                                 /* split wNAF in 'numblocks' parts */
 544                                 pp = tmp_wNAF;
 545                                 tmp_points = pre_comp->points;
 546
 547                                 for (i = num; i < totalnum; i++)
 548                                         {
 549                                         if (i < totalnum - 1)
 550                                                 {
 551                                                 wNAF_len[i] = blocksize;
 552                                                 if (tmp_len < blocksize)
 553                                                         {
 554                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 555                                                         goto err;
 556                                                         }
 557                                                 tmp_len -= blocksize;
 558                                                 }
 559                                         else
 560                                                 /* last block gets whatever is left
 561                                                  * (this could be more or less than 'blocksize'!) */
 562                                                 wNAF_len[i] = tmp_len;
 563
 564                                         wNAF[i + 1] = NULL;
 565                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 566                                         if (wNAF[i] == NULL)
 567                                                 {
 568                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 569                                                 OPENSSL_free(tmp_wNAF);
 570                                                 goto err;
 571                                                 }
 572                                         memcpy(wNAF[i], pp, wNAF_len[i]);
 573                                         if (wNAF_len[i] > max_len)
 574                                                 max_len = wNAF_len[i];
 575
 576                                         if (*tmp_points == NULL)
 577                                                 {
 578                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 579                                                 OPENSSL_free(tmp_wNAF);
 580                                                 goto err;
 581                                                 }
 582                                         val_sub[i] = tmp_points;
 583                                         tmp_points += pre_points_per_block;
 584                                         pp += blocksize;
 585                                         }
 586                                 OPENSSL_free(tmp_wNAF);
 587                                 }
 588                         }
 589                 }
 590
 591         /* All points we precompute now go into a single array 'val'.
 592          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
 593          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
 594         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 595         if (val == NULL)
 596                 {
 597                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 598                 goto err;
 599                 }
 600         val[num_val] = NULL; /* pivot element */
 601
 602         /* allocate points for precomputation */
 603         v = val;
 604         for (i = 0; i < num + num_scalar; i++)
 605                 {
 606                 val_sub[i] = v;
 607                 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
 608                         {
 609                         *v = EC_POINT_new(group);
 610                         if (*v == NULL) goto err;
 611                         v++;
 612                         }
 613                 }
 614         if (!(v == val + num_val))
 615                 {
 616                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 617                 goto err;
 618                 }
 619
 620         if (!(tmp = EC_POINT_new(group)))
 621                 goto err;
 622
 623         /* prepare precomputed values:
 624          *    val_sub[i][0] :=     points[i]
 625          *    val_sub[i][1] := 3 * points[i]
 626          *    val_sub[i][2] := 5 * points[i]
 627          *    ...
 628          */
 629         for (i = 0; i < num + num_scalar; i++)
 630                 {
 631                 if (i < num)
 632                         {
 633                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 634                         }
 635                 else
 636                         {
 637                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 638                         }
 639
 640                 if (wsize[i] > 1)
 641                         {
 642                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 643                         for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
 644                                 {
 645                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 646                                 }
 647                         }
 648                 }
 649
 650 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
 651         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 652                 goto err;
 653 #endif
 654
 655         r_is_at_infinity = 1;
 656
 657         for (k = max_len - 1; k >= 0; k--)
 658                 {
 659                 if (!r_is_at_infinity)
 660                         {
 661                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 662                         }
 663
 664                 for (i = 0; i < totalnum; i++)
 665                         {
 666                         if (wNAF_len[i] > (size_t)k)
 667                                 {
 668                                 int digit = wNAF[i][k];
 669                                 int is_neg;
 670
 671                                 if (digit)
 672                                         {
 673                                         is_neg = digit < 0;
 674
 675                                         if (is_neg)
 676                                                 digit = -digit;
 677
 678                                         if (is_neg != r_is_inverted)
 679                                                 {
 680                                                 if (!r_is_at_infinity)
 681                                                         {
 682                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 683                                                         }
 684                                                 r_is_inverted = !r_is_inverted;
 685                                                 }
 686
 687                                         /* digit > 0 */
 688
 689                                         if (r_is_at_infinity)
 690                                                 {
 691                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
 692                                                 r_is_at_infinity = 0;
 693                                                 }
 694                                         else
 695                                                 {
 696                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
 697                                                 }
 698                                         }
 699                                 }
 700                         }
 701                 }
 702
 703         if (r_is_at_infinity)
 704                 {
 705                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 706                 }
 707         else
 708                 {
 709                 if (r_is_inverted)
 710                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 711                 }
 712
 713         ret = 1;
 714
 715  err:
 716         if (new_ctx != NULL)
 717                 BN_CTX_free(new_ctx);
 718         if (tmp != NULL)
 719                 EC_POINT_free(tmp);
 720         if (wsize != NULL)
 721                 OPENSSL_free(wsize);
 722         if (wNAF_len != NULL)
 723                 OPENSSL_free(wNAF_len);
 724         if (wNAF != NULL)
 725                 {
 726                 signed char **w;
 727
 728                 for (w = wNAF; *w != NULL; w++)
 729                         OPENSSL_free(*w);
 730
 731                 OPENSSL_free(wNAF);
 732                 }
 733         if (val != NULL)
 734                 {
 735                 for (v = val; *v != NULL; v++)
 736                         EC_POINT_clear_free(*v);
 737
 738                 OPENSSL_free(val);
 739                 }
 740         if (val_sub != NULL)
 741                 {
 742                 OPENSSL_free(val_sub);
 743                 }
 744         return ret;
 745         }
 746
 747
 748 /* ec_wNAF_precompute_mult()
 749  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 750  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 751  *
 752  * 'pre_comp->points' is an array of multiples of the generator
 753  * of the following form:
 754  * points[0] =     generator;
 755  * points[1] = 3 * generator;
 756  * ...
 757  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 758  * points[2^(w-1)]   =     2^blocksize * generator;
 759  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 760  * ...
 761  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 762  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 763  * ...
 764  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 765  * points[2^(w-1)*numblocks]       = NULL
 766  */
 767 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 768         {
 769         const EC_POINT *generator;
 770         EC_POINT *tmp_point = NULL, *base = NULL, **var;
 771         BN_CTX *new_ctx = NULL;
 772         BIGNUM *order;
 773         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 774         EC_POINT **points = NULL;
 775         EC_PRE_COMP *pre_comp;
 776         int ret = 0;
 777
 778         /* if there is an old EC_PRE_COMP object, throw it away */
 779         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 780
 781         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 782                 return 0;
 783
 784         generator = EC_GROUP_get0_generator(group);
 785         if (generator == NULL)
 786                 {
 787                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 788                 goto err;
 789                 }
 790
 791         if (ctx == NULL)
 792                 {
 793                 ctx = new_ctx = BN_CTX_new();
 794                 if (ctx == NULL)
 795                         goto err;
 796                 }
 797
 798         BN_CTX_start(ctx);
 799         order = BN_CTX_get(ctx);
 800         if (order == NULL) goto err;
 801
 802         if (!EC_GROUP_get_order(group, order, ctx)) goto err;
 803         if (BN_is_zero(order))
 804                 {
 805                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 806                 goto err;
 807                 }
 808
 809         bits = BN_num_bits(order);
 810         /* The following parameters mean we precompute (approximately)
 811          * one point per bit.
 812          *
 813          * TBD: The combination  8, 4  is perfect for 160 bits; for other
 814          * bit lengths, other parameter combinations might provide better
 815          * efficiency.
 816          */
 817         blocksize = 8;
 818         w = 4;
 819         if (EC_window_bits_for_scalar_size(bits) > w)
 820                 {
 821                 /* let's not make the window too small ... */
 822                 w = EC_window_bits_for_scalar_size(bits);
 823                 }
 824
 825         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
 826
 827         pre_points_per_block = (size_t)1 << (w - 1);
 828         num = pre_points_per_block * numblocks; /* number of points to compute and store */
 829
 830         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
 831         if (!points)
 832                 {
 833                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 834                 goto err;
 835                 }
 836
 837         var = points;
 838         var[num] = NULL; /* pivot */
 839         for (i = 0; i < num; i++)
 840                 {
 841                 if ((var[i] = EC_POINT_new(group)) == NULL)
 842                         {
 843                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 844                         goto err;
 845                         }
 846                 }
 847
 848         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
 849                 {
 850                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 851                 goto err;
 852                 }
 853
 854         if (!EC_POINT_copy(base, generator))
 855                 goto err;
 856
 857         /* do the precomputation */
 858         for (i = 0; i < numblocks; i++)
 859                 {
 860                 size_t j;
 861
 862                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 863                         goto err;
 864
 865                 if (!EC_POINT_copy(*var++, base))
 866                         goto err;
 867
 868                 for (j = 1; j < pre_points_per_block; j++, var++)
 869                         {
 870                         /* calculate odd multiples of the current base point */
 871                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 872                                 goto err;
 873                         }
 874
 875                 if (i < numblocks - 1)
 876                         {
 877                         /* get the next base (multiply current one by 2^blocksize) */
 878                         size_t k;
 879
 880                         if (blocksize <= 2)
 881                                 {
 882                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 883                                 goto err;
 884                                 }
 885
 886                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 887                                 goto err;
 888                         for (k = 2; k < blocksize; k++)
 889                                 {
 890                                 if (!EC_POINT_dbl(group,base,base,ctx))
 891                                         goto err;
 892                                 }
 893                         }
 894                 }
 895
 896         if (!EC_POINTs_make_affine(group, num, points, ctx))
 897                 goto err;
 898
 899         pre_comp->group = group;
 900         pre_comp->blocksize = blocksize;
 901         pre_comp->numblocks = numblocks;
 902         pre_comp->w = w;
 903         pre_comp->points = points;
 904         points = NULL;
 905         pre_comp->num = num;
 906
 907         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
 908                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
 909                 goto err;
 910         pre_comp = NULL;
 911
 912         ret = 1;
 913  err:
 914         if (ctx != NULL)
 915                 BN_CTX_end(ctx);
 916         if (new_ctx != NULL)
 917                 BN_CTX_free(new_ctx);
 918         if (pre_comp)
 919                 ec_pre_comp_free(pre_comp);
 920         if (points)
 921                 {
 922                 EC_POINT **p;
 923
 924                 for (p = points; *p != NULL; p++)
 925                         EC_POINT_free(*p);
 926                 OPENSSL_free(points);
 927                 }
 928         if (tmp_point)
 929                 EC_POINT_free(tmp_point);
 930         if (base)
 931                 EC_POINT_free(base);
 932         return ret;
 933         }
 934
 935
 936 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 937         {
 938         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
 939                 return 1;
 940         else
 941                 return 0;
 942         }