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