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