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