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) 1998-2003 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 } EC_PRE_COMP;
  91
  92 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
  93 static void *ec_pre_comp_dup(void *);
  94 static void ec_pre_comp_free(void *);
  95 static void ec_pre_comp_clear_free(void *);
  96
  97 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
  98         {
  99         EC_PRE_COMP *ret = NULL;
 100
 101         if (!group)
 102                 return NULL;
 103
 104         ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
 105         if (!ret)
 106                 return ret;
 107         ret->group = group;
 108         ret->blocksize = 8; /* default */
 109         ret->numblocks = 0;
 110         ret->w = 4; /* default */
 111         ret->points = NULL;
 112         ret->num = 0;
 113         return ret;
 114         }
 115
 116 static void *ec_pre_comp_dup(void *src_)
 117         {
 118         const EC_PRE_COMP *src = src_;
 119         EC_PRE_COMP *ret = NULL;
 120
 121         ret = ec_pre_comp_new(src->group);
 122         if (!ret)
 123                 return ret;
 124         ret->blocksize = src->blocksize;
 125         ret->numblocks = src->numblocks;
 126         ret->w = src->w;
 127         ret->num = 0;
 128
 129         if (src->points)
 130                 {
 131                 EC_POINT **src_var, **dest_var;
 132
 133                 ret->points = (EC_POINT **)OPENSSL_malloc((src->num + 1) * sizeof(EC_POINT *));
 134                 if (!ret->points)
 135                         {
 136                         ec_pre_comp_free(ret);
 137                         return NULL;
 138                         }
 139
 140                 for (dest_var = ret->points, src_var = src->points; *src_var != NULL; src_var++, dest_var++)
 141                         {
 142                         *dest_var = EC_POINT_dup(*src_var, src->group);
 143                         if (*dest_var == NULL)
 144                                 {
 145                                 ec_pre_comp_free(ret);
 146                                 return NULL;
 147                                 }
 148                         ret->num++;
 149                         }
 150
 151                 ret->points[ret->num] = NULL;
 152                 if (ret->num != src->num)
 153                         {
 154                         ec_pre_comp_free(ret);
 155                         ECerr(EC_F_EC_PRE_COMP_DUP, ERR_R_INTERNAL_ERROR);
 156                         return NULL;
 157                         }
 158                 }
 159
 160         return ret;
 161         }
 162
 163 static void ec_pre_comp_free(void *pre_)
 164         {
 165         EC_PRE_COMP *pre = pre_;
 166
 167         if (!pre)
 168                 return;
 169         if (pre->points)
 170                 {
 171                 EC_POINT **var;
 172
 173                 for (var = pre->points; *var != NULL; var++)
 174                         EC_POINT_free(*var);
 175                 OPENSSL_free(pre->points);
 176                 }
 177         OPENSSL_free(pre);
 178         }
 179
 180 static void ec_pre_comp_clear_free(void *pre_)
 181         {
 182         EC_PRE_COMP *pre = pre_;
 183
 184         if (!pre)
 185                 return;
 186         if (pre->points)
 187                 {
 188                 EC_POINT **p;
 189
 190                 for (p = pre->points; *p != NULL; p++)
 191                         EC_POINT_clear_free(*p);
 192                 OPENSSL_cleanse(pre->points, sizeof pre->points);
 193                 OPENSSL_free(pre->points);
 194                 }
 195         OPENSSL_cleanse(pre, sizeof pre);
 196         OPENSSL_free(pre);
 197         }
 198
 199
 200
 201
 202 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 203  * This is an array  r[]  of values that are either zero or odd with an
 204  * absolute value less than  2^w  satisfying
 205  *     scalar = \sum_j r[j]*2^j
 206  * where at most one of any  w+1  consecutive digits is non-zero
 207  * with the exception that the most significant digit may be only
 208  * w-1 zeros away from that next non-zero digit.
 209  */
 210 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
 211         {
 212         int window_val;
 213         int ok = 0;
 214         signed char *r = NULL;
 215         int sign = 1;
 216         int bit, next_bit, mask;
 217         size_t len = 0, j;
 218
 219         if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
 220                 {
 221                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 222                 goto err;
 223                 }
 224         bit = 1 << w; /* at most 128 */
 225         next_bit = bit << 1; /* at most 256 */
 226         mask = next_bit - 1; /* at most 255 */
 227
 228         if (BN_get_sign(scalar))
 229                 {
 230                 sign = -1;
 231                 }
 232
 233         len = BN_num_bits(scalar);
 234         r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
 235                                       * (*ret_len will be set to the actual length, i.e. at most
 236                                       * BN_num_bits(scalar) + 1) */
 237         if (r == NULL) goto err;
 238
 239         if (scalar->d == NULL || scalar->top == 0)
 240                 {
 241                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
 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                 ((b) >= 2000 ? 6 : \
 333                  (b) >=  800 ? 5 : \
 334                  (b) >=  300 ? 4 : \
 335                  (b) >=   70 ? 3 : \
 336                  (b) >=   20 ? 2 : \
 337                   1)
 338
 339 /* Compute
 340  *      \sum scalars[i]*points[i],
 341  * also including
 342  *      scalar*generator
 343  * in the addition if scalar != NULL
 344  */
 345 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 346         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 347         {
 348         BN_CTX *new_ctx = NULL;
 349         EC_POINT *generator = NULL;
 350         EC_POINT *tmp = NULL;
 351         size_t totalnum;
 352         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 353         size_t pre_points_per_block = 0;
 354         size_t i, j;
 355         int k;
 356         int r_is_inverted = 0;
 357         int r_is_at_infinity = 1;
 358         size_t *wsize = NULL; /* individual window sizes */
 359         signed char **wNAF = NULL; /* individual wNAFs */
 360         size_t *wNAF_len = NULL;
 361         size_t max_len = 0;
 362         size_t num_val;
 363         EC_POINT **val = NULL; /* precomputation */
 364         EC_POINT **v;
 365         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
 366         EC_PRE_COMP *pre_comp = NULL;
 367         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
 368                              * i.e. precomputation is not available */
 369         int ret = 0;
 370
 371         if (group->meth != r->meth)
 372                 {
 373                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 374                 return 0;
 375                 }
 376
 377         if ((scalar == NULL) && (num == 0))
 378                 {
 379                 return EC_POINT_set_to_infinity(group, r);
 380                 }
 381
 382         for (i = 0; i < num; i++)
 383                 {
 384                 if (group->meth != points[i]->meth)
 385                         {
 386                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 387                         return 0;
 388                         }
 389                 }
 390
 391         if (ctx == NULL)
 392                 {
 393                 ctx = new_ctx = BN_CTX_new();
 394                 if (ctx == NULL)
 395                         goto err;
 396                 }
 397
 398         if (scalar != NULL)
 399                 {
 400                 generator = EC_GROUP_get0_generator(group);
 401                 if (generator == NULL)
 402                         {
 403                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 404                         goto err;
 405                         }
 406
 407                 /* look if we can use precomputed multiples of generator */
 408
 409                 pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 410
 411                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
 412                         {
 413                         blocksize = pre_comp->blocksize;
 414
 415                         /* determine maximum number of blocks that wNAF splitting may yield
 416                          * (NB: maximum wNAF length is bit length plus one) */
 417                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 418
 419                         /* we cannot use more blocks than we have precomputation for */
 420                         if (numblocks > pre_comp->numblocks)
 421                                 numblocks = pre_comp->numblocks;
 422
 423                         pre_points_per_block = 1u << (pre_comp->w - 1);
 424
 425                         /* check that pre_comp looks sane */
 426                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
 427                                 {
 428                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 429                                 goto err;
 430                                 }
 431                         }
 432                 else
 433                         {
 434                         /* can't use precomputation */
 435                         pre_comp = NULL;
 436                         numblocks = 1;
 437                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
 438                         }
 439                 }
 440
 441         totalnum = num + numblocks;
 442
 443         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 444         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
 445         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
 446         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 447
 448         if (!wsize || !wNAF_len || !wNAF || !val_sub)
 449                 goto err;
 450
 451         wNAF[0] = NULL; /* preliminary pivot */
 452
 453         /* num_val will be the total number of temporarily precomputed points */
 454         num_val = 0;
 455
 456         for (i = 0; i < num + num_scalar; i++)
 457                 {
 458                 size_t bits;
 459
 460                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 461                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 462                 num_val += 1u << (wsize[i] - 1);
 463                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
 464                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
 465                 if (wNAF[i] == NULL)
 466                         goto err;
 467                 if (wNAF_len[i] > max_len)
 468                         max_len = wNAF_len[i];
 469                 }
 470
 471         if (numblocks)
 472                 {
 473                 /* we go here iff scalar != NULL */
 474
 475                 if (pre_comp == NULL)
 476                         {
 477                         if (num_scalar != 1)
 478                                 {
 479                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 480                                 goto err;
 481                                 }
 482                         /* we have already generated a wNAF for 'scalar' */
 483                         }
 484                 else
 485                         {
 486                         signed char *tmp_wNAF = NULL;
 487                         size_t tmp_len = 0;
 488
 489                         if (num_scalar != 0)
 490                                 {
 491                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 492                                 goto err;
 493                                 }
 494
 495                         /* use the window size for which we have precomputation */
 496                         wsize[num] = pre_comp->w;
 497                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
 498                         if (!tmp_wNAF)
 499                                 goto err;
 500
 501                         if (tmp_len <= max_len)
 502                                 {
 503                                 /* One of the other wNAFs is at least as long
 504                                  * as the wNAF belonging to the generator,
 505                                  * so wNAF splitting will not buy us anything. */
 506
 507                                 numblocks = 1;
 508                                 totalnum = num + 1; /* don't use wNAF splitting */
 509                                 wNAF[num] = tmp_wNAF;
 510                                 wNAF[num + 1] = NULL;
 511                                 wNAF_len[num] = tmp_len;
 512                                 if (tmp_len > max_len)
 513                                         max_len = tmp_len;
 514                                 /* pre_comp->points starts with the points that we need here: */
 515                                 val_sub[num] = pre_comp->points;
 516                                 }
 517                         else
 518                                 {
 519                                 /* don't include tmp_wNAF directly into wNAF array
 520                                  * - use wNAF splitting and include the blocks */
 521
 522                                 signed char *pp;
 523                                 EC_POINT **tmp_points;
 524
 525                                 if (tmp_len < numblocks * blocksize)
 526                                         {
 527                                         /* possibly we can do with fewer blocks than estimated */
 528                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
 529                                         if (numblocks > pre_comp->numblocks)
 530                                                 {
 531                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 532                                                 goto err;
 533                                                 }
 534                                         totalnum = num + numblocks;
 535                                         }
 536
 537                                 /* split wNAF in 'numblocks' parts */
 538                                 pp = tmp_wNAF;
 539                                 tmp_points = pre_comp->points;
 540
 541                                 for (i = num; i < totalnum; i++)
 542                                         {
 543                                         if (i < totalnum - 1)
 544                                                 {
 545                                                 wNAF_len[i] = blocksize;
 546                                                 if (tmp_len < blocksize)
 547                                                         {
 548                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 549                                                         goto err;
 550                                                         }
 551                                                 tmp_len -= blocksize;
 552                                                 }
 553                                         else
 554                                                 /* last block gets whatever is left
 555                                                  * (this could be more or less than 'blocksize'!) */
 556                                                 wNAF_len[i] = tmp_len;
 557
 558                                         wNAF[i + 1] = NULL;
 559                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 560                                         if (wNAF[i] == NULL)
 561                                                 {
 562                                                 OPENSSL_free(tmp_wNAF);
 563                                                 goto err;
 564                                                 }
 565                                         memcpy(wNAF[i], pp, wNAF_len[i]);
 566                                         if (wNAF_len[i] > max_len)
 567                                                 max_len = wNAF_len[i];
 568
 569                                         if (*tmp_points == NULL)
 570                                                 {
 571                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 572                                                 OPENSSL_free(tmp_wNAF);
 573                                                 goto err;
 574                                                 }
 575                                         val_sub[i] = tmp_points;
 576                                         tmp_points += pre_points_per_block;
 577                                         pp += blocksize;
 578                                         }
 579                                 OPENSSL_free(tmp_wNAF);
 580                                 }
 581                         }
 582                 }
 583
 584         /* All points we precompute now go into a single array 'val'.
 585          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
 586          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
 587         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 588         if (val == NULL) goto err;
 589         val[num_val] = NULL; /* pivot element */
 590
 591         /* allocate points for precomputation */
 592         v = val;
 593         for (i = 0; i < num + num_scalar; i++)
 594                 {
 595                 val_sub[i] = v;
 596                 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
 597                         {
 598                         *v = EC_POINT_new(group);
 599                         if (*v == NULL) goto err;
 600                         v++;
 601                         }
 602                 }
 603         if (!(v == val + num_val))
 604                 {
 605                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 606                 goto err;
 607                 }
 608
 609         if (!(tmp = EC_POINT_new(group)))
 610                 goto err;
 611
 612         /* prepare precomputed values:
 613          *    val_sub[i][0] :=     points[i]
 614          *    val_sub[i][1] := 3 * points[i]
 615          *    val_sub[i][2] := 5 * points[i]
 616          *    ...
 617          */
 618         for (i = 0; i < num + num_scalar; i++)
 619                 {
 620                 if (i < num)
 621                         {
 622                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 623                         }
 624                 else
 625                         {
 626                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 627                         }
 628
 629                 if (wsize[i] > 1)
 630                         {
 631                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 632                         for (j = 1; j < (1u << (wsize[i] - 1)); j++)
 633                                 {
 634                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 635                                 }
 636                         }
 637                 }
 638
 639 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
 640         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 641                 goto err;
 642 #endif
 643
 644         r_is_at_infinity = 1;
 645
 646         for (k = max_len - 1; k >= 0; k--)
 647                 {
 648                 if (!r_is_at_infinity)
 649                         {
 650                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 651                         }
 652
 653                 for (i = 0; i < totalnum; i++)
 654                         {
 655                         if (wNAF_len[i] > (size_t)k)
 656                                 {
 657                                 int digit = wNAF[i][k];
 658                                 int is_neg;
 659
 660                                 if (digit)
 661                                         {
 662                                         is_neg = digit < 0;
 663
 664                                         if (is_neg)
 665                                                 digit = -digit;
 666
 667                                         if (is_neg != r_is_inverted)
 668                                                 {
 669                                                 if (!r_is_at_infinity)
 670                                                         {
 671                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 672                                                         }
 673                                                 r_is_inverted = !r_is_inverted;
 674                                                 }
 675
 676                                         /* digit > 0 */
 677
 678                                         if (r_is_at_infinity)
 679                                                 {
 680                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
 681                                                 r_is_at_infinity = 0;
 682                                                 }
 683                                         else
 684                                                 {
 685                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
 686                                                 }
 687                                         }
 688                                 }
 689                         }
 690                 }
 691
 692         if (r_is_at_infinity)
 693                 {
 694                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 695                 }
 696         else
 697                 {
 698                 if (r_is_inverted)
 699                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 700                 }
 701
 702         ret = 1;
 703
 704  err:
 705         if (new_ctx != NULL)
 706                 BN_CTX_free(new_ctx);
 707         if (tmp != NULL)
 708                 EC_POINT_free(tmp);
 709         if (wsize != NULL)
 710                 OPENSSL_free(wsize);
 711         if (wNAF_len != NULL)
 712                 OPENSSL_free(wNAF_len);
 713         if (wNAF != NULL)
 714                 {
 715                 signed char **w;
 716
 717                 for (w = wNAF; *w != NULL; w++)
 718                         OPENSSL_free(*w);
 719
 720                 OPENSSL_free(wNAF);
 721                 }
 722         if (val != NULL)
 723                 {
 724                 for (v = val; *v != NULL; v++)
 725                         EC_POINT_clear_free(*v);
 726
 727                 OPENSSL_free(val);
 728                 }
 729         if (val_sub != NULL)
 730                 {
 731                 OPENSSL_free(val_sub);
 732                 }
 733         return ret;
 734         }
 735
 736
 737 /* ec_wNAF_precompute_mult()
 738  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 739  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 740  *
 741  * 'pre_comp->points' is an array of multiples of the generator
 742  * of the following form:
 743  * points[0] =     generator;
 744  * points[1] = 3 * generator;
 745  * ...
 746  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 747  * points[2^(w-1)]   =     2^blocksize * generator;
 748  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 749  * ...
 750  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 751  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 752  * ...
 753  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 754  * points[2^(w-1)*numblocks]       = NULL
 755  */
 756 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 757         {
 758         const EC_POINT *generator;
 759         EC_POINT *tmp_point = NULL, *base = NULL, **var;
 760         BN_CTX *new_ctx = NULL;
 761         BIGNUM *order;
 762         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 763         EC_POINT **points = NULL;
 764         EC_PRE_COMP *pre_comp, *new_pre_comp = NULL;
 765         int ret = 0;
 766
 767         pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 768         if (pre_comp == NULL)
 769                 if ((pre_comp = new_pre_comp = ec_pre_comp_new(group)) == NULL)
 770                         return 0;
 771
 772         generator = EC_GROUP_get0_generator(group);
 773         if (generator == NULL)
 774                 {
 775                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 776                 goto err;
 777                 }
 778
 779         if (ctx == NULL)
 780                 {
 781                 ctx = new_ctx = BN_CTX_new();
 782                 if (ctx == NULL)
 783                         goto err;
 784                 }
 785
 786         BN_CTX_start(ctx);
 787         order = BN_CTX_get(ctx);
 788         if (order == NULL) goto err;
 789
 790         if (!EC_GROUP_get_order(group, order, ctx)) goto err;
 791         if (BN_is_zero(order))
 792                 {
 793                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 794                 goto err;
 795                 }
 796
 797         bits = BN_num_bits(order);
 798         /* The following parameters mean we precompute (approximately)
 799          * one point per bit.
 800          *
 801          * TBD: The combination  8, 4  is perfect for 160 bits; for other
 802          * bit lengths, other parameter combinations might provide better
 803          * efficiency.
 804          */
 805         blocksize = 8;
 806         w = 4;
 807         if (EC_window_bits_for_scalar_size(bits) > w)
 808                 {
 809                 /* let's not make the window too small ... */
 810                 w = EC_window_bits_for_scalar_size(bits);
 811                 }
 812
 813         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
 814
 815         pre_points_per_block = 1u << (w - 1);
 816         num = pre_points_per_block * numblocks; /* number of points to compute and store */
 817
 818         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
 819         if (!points)
 820                 {
 821                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 822                 goto err;
 823                 }
 824
 825         var = points;
 826         var[num] = NULL; /* pivot */
 827         for (i = 0; i < num; i++)
 828                 {
 829                 if ((var[i] = EC_POINT_new(group)) == NULL)
 830                         {
 831                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 832                         goto err;
 833                         }
 834                 }
 835
 836         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
 837                 {
 838                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 839                 goto err;
 840                 }
 841
 842         if (!EC_POINT_copy(base, generator))
 843                 goto err;
 844
 845         /* do the precomputation */
 846         for (i = 0; i < numblocks; i++)
 847                 {
 848                 size_t j;
 849
 850                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 851                         goto err;
 852
 853                 if (!EC_POINT_copy(*var++, base))
 854                         goto err;
 855
 856                 for (j = 1; j < pre_points_per_block; j++, var++)
 857                         {
 858                         /* calculate odd multiples of the current base point */
 859                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 860                                 goto err;
 861                         }
 862
 863                 if (i < numblocks - 1)
 864                         {
 865                         /* get the next base (multiply current one by 2^blocksize) */
 866                         size_t k;
 867
 868                         if (blocksize <= 2)
 869                                 {
 870                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 871                                 goto err;
 872                                 }
 873
 874                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 875                                 goto err;
 876                         for (k = 2; k < blocksize; k++)
 877                                 {
 878                                 if (!EC_POINT_dbl(group,base,base,ctx))
 879                                         goto err;
 880                                 }
 881                         }
 882                 }
 883
 884         if (!EC_POINTs_make_affine(group, num, points, ctx))
 885                 goto err;
 886
 887         pre_comp->group = group;
 888         pre_comp->blocksize = blocksize;
 889         pre_comp->numblocks = numblocks;
 890         pre_comp->w = w;
 891         if (pre_comp->points)
 892                 {
 893                 EC_POINT **p;
 894
 895                 for (p = pre_comp->points; *p != NULL; p++)
 896                         EC_POINT_free(*p);
 897                 OPENSSL_free(pre_comp->points);
 898                 }
 899         pre_comp->points = points;
 900         points = NULL;
 901         pre_comp->num = num;
 902
 903         if (new_pre_comp)
 904                 {
 905                 if (!EC_GROUP_set_extra_data(group, new_pre_comp, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
 906                         goto err;
 907                 new_pre_comp = NULL;
 908                 }
 909
 910         ret = 1;
 911  err:
 912         BN_CTX_end(ctx);
 913         if (new_ctx != NULL)
 914                 BN_CTX_free(new_ctx);
 915         if (new_pre_comp)
 916                 ec_pre_comp_free(new_pre_comp);
 917         if (points)
 918                 {
 919                 EC_POINT **p;
 920
 921                 for (p = points; *p != NULL; p++)
 922                         EC_POINT_free(*p);
 923                 OPENSSL_free(points);
 924                 }
 925         if (tmp_point)
 926                 EC_POINT_free(tmp_point);
 927         if (base)
 928                 EC_POINT_free(base);
 929         return ret;
 930         }
 931
 932
 933 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 934         {
 935         if (EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
 936                 return 1;
 937         else
 938                 return 0;
 939         }