crypto/ec/ec_mult.c

   1 /* crypto/ec/ec_mult.c */
   2 /*
   3  * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2007 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58 /* ====================================================================
  59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60  * Portions of this software developed by SUN MICROSYSTEMS, INC.,
  61  * and contributed to the OpenSSL project.
  62  */
  63
  64
  65
  66 #include <string.h>
  67 #include <openssl/err.h>
  68
  69 #include "internal/bn_int.h"
  70 #include "ec_lcl.h"
  71
  72
  73 /*
  74  * This file implements the wNAF-based interleaving multi-exponentation method
  75  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
  76  * for multiplication with precomputation, we use wNAF splitting
  77  * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
  78  */
  79
  80
  81
  82
  83 /* structure for precomputed multiples of the generator */
  84 typedef struct ec_pre_comp_st {
  85         const EC_GROUP *group; /* parent EC_GROUP object */
  86         size_t blocksize;      /* block size for wNAF splitting */
  87         size_t numblocks;      /* max. number of blocks for which we have precomputation */
  88         size_t w;              /* window size */
  89         EC_POINT **points;     /* array with pre-calculated multiples of generator:
  90                                 * 'num' pointers to EC_POINT objects followed by a NULL */
  91         size_t num;            /* numblocks * 2^(w-1) */
  92         int references;
  93 } EC_PRE_COMP;
  94
  95 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
  96 static void *ec_pre_comp_dup(void *);
  97 static void ec_pre_comp_free(void *);
  98 static void ec_pre_comp_clear_free(void *);
  99
 100 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
 101         {
 102         EC_PRE_COMP *ret = NULL;
 103
 104         if (!group)
 105                 return NULL;
 106
 107         ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
 108         if (!ret)
 109                 {
 110                 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
 111                 return ret;
 112                 }
 113         ret->group = group;
 114         ret->blocksize = 8; /* default */
 115         ret->numblocks = 0;
 116         ret->w = 4; /* default */
 117         ret->points = NULL;
 118         ret->num = 0;
 119         ret->references = 1;
 120         return ret;
 121         }
 122
 123 static void *ec_pre_comp_dup(void *src_)
 124         {
 125         EC_PRE_COMP *src = src_;
 126
 127         /* no need to actually copy, these objects never change! */
 128
 129         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
 130
 131         return src_;
 132         }
 133
 134 static void ec_pre_comp_free(void *pre_)
 135         {
 136         int i;
 137         EC_PRE_COMP *pre = pre_;
 138
 139         if (!pre)
 140                 return;
 141
 142         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 143         if (i > 0)
 144                 return;
 145
 146         if (pre->points)
 147                 {
 148                 EC_POINT **p;
 149
 150                 for (p = pre->points; *p != NULL; p++)
 151                         EC_POINT_free(*p);
 152                 OPENSSL_free(pre->points);
 153                 }
 154         OPENSSL_free(pre);
 155         }
 156
 157 static void ec_pre_comp_clear_free(void *pre_)
 158         {
 159         int i;
 160         EC_PRE_COMP *pre = pre_;
 161
 162         if (!pre)
 163                 return;
 164
 165         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
 166         if (i > 0)
 167                 return;
 168
 169         if (pre->points)
 170                 {
 171                 EC_POINT **p;
 172
 173                 for (p = pre->points; *p != NULL; p++)
 174                         {
 175                         EC_POINT_clear_free(*p);
 176                         OPENSSL_cleanse(p, sizeof *p);
 177                         }
 178                 OPENSSL_free(pre->points);
 179                 }
 180         OPENSSL_cleanse(pre, sizeof *pre);
 181         OPENSSL_free(pre);
 182         }
 183
 184
 185 /* TODO: table should be optimised for the wNAF-based implementation,
 186  *       sometimes smaller windows will give better performance
 187  *       (thus the boundaries should be increased)
 188  */
 189 #define EC_window_bits_for_scalar_size(b) \
 190                 ((size_t) \
 191                  ((b) >= 2000 ? 6 : \
 192                   (b) >=  800 ? 5 : \
 193                   (b) >=  300 ? 4 : \
 194                   (b) >=   70 ? 3 : \
 195                   (b) >=   20 ? 2 : \
 196                   1))
 197
 198 /*-
 199  * Compute
 200  *      \sum scalars[i]*points[i],
 201  * also including
 202  *      scalar*generator
 203  * in the addition if scalar != NULL
 204  */
 205 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 206         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 207         {
 208         BN_CTX *new_ctx = NULL;
 209         const EC_POINT *generator = NULL;
 210         EC_POINT *tmp = NULL;
 211         size_t totalnum;
 212         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 213         size_t pre_points_per_block = 0;
 214         size_t i, j;
 215         int k;
 216         int r_is_inverted = 0;
 217         int r_is_at_infinity = 1;
 218         size_t *wsize = NULL; /* individual window sizes */
 219         signed char **wNAF = NULL; /* individual wNAFs */
 220         size_t *wNAF_len = NULL;
 221         size_t max_len = 0;
 222         size_t num_val;
 223         EC_POINT **val = NULL; /* precomputation */
 224         EC_POINT **v;
 225         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
 226         const EC_PRE_COMP *pre_comp = NULL;
 227         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
 228                              * i.e. precomputation is not available */
 229         int ret = 0;
 230
 231         if (group->meth != r->meth)
 232                 {
 233                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 234                 return 0;
 235                 }
 236
 237         if ((scalar == NULL) && (num == 0))
 238                 {
 239                 return EC_POINT_set_to_infinity(group, r);
 240                 }
 241
 242         for (i = 0; i < num; i++)
 243                 {
 244                 if (group->meth != points[i]->meth)
 245                         {
 246                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 247                         return 0;
 248                         }
 249                 }
 250
 251         if (ctx == NULL)
 252                 {
 253                 ctx = new_ctx = BN_CTX_new();
 254                 if (ctx == NULL)
 255                         goto err;
 256                 }
 257
 258         if (scalar != NULL)
 259                 {
 260                 generator = EC_GROUP_get0_generator(group);
 261                 if (generator == NULL)
 262                         {
 263                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 264                         goto err;
 265                         }
 266
 267                 /* look if we can use precomputed multiples of generator */
 268
 269                 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 270
 271                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
 272                         {
 273                         blocksize = pre_comp->blocksize;
 274
 275                         /* determine maximum number of blocks that wNAF splitting may yield
 276                          * (NB: maximum wNAF length is bit length plus one) */
 277                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 278
 279                         /* we cannot use more blocks than we have precomputation for */
 280                         if (numblocks > pre_comp->numblocks)
 281                                 numblocks = pre_comp->numblocks;
 282
 283                         pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 284
 285                         /* check that pre_comp looks sane */
 286                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
 287                                 {
 288                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 289                                 goto err;
 290                                 }
 291                         }
 292                 else
 293                         {
 294                         /* can't use precomputation */
 295                         pre_comp = NULL;
 296                         numblocks = 1;
 297                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
 298                         }
 299                 }
 300
 301         totalnum = num + numblocks;
 302
 303         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
 304         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
 305         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
 306         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
 307
 308         /* Ensure wNAF is initialised in case we end up going to err */
 309         if (wNAF) wNAF[0] = NULL;       /* preliminary pivot */
 310
 311         if (!wsize || !wNAF_len || !wNAF || !val_sub)
 312                 {
 313                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 314                 goto err;
 315                 }
 316
 317         /* num_val will be the total number of temporarily precomputed points */
 318         num_val = 0;
 319
 320         for (i = 0; i < num + num_scalar; i++)
 321                 {
 322                 size_t bits;
 323
 324                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 325                 wsize[i] = EC_window_bits_for_scalar_size(bits);
 326                 num_val += (size_t)1 << (wsize[i] - 1);
 327                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
 328                 wNAF[i] = bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
 329                 if (wNAF[i] == NULL)
 330                         goto err;
 331                 if (wNAF_len[i] > max_len)
 332                         max_len = wNAF_len[i];
 333                 }
 334
 335         if (numblocks)
 336                 {
 337                 /* we go here iff scalar != NULL */
 338
 339                 if (pre_comp == NULL)
 340                         {
 341                         if (num_scalar != 1)
 342                                 {
 343                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 344                                 goto err;
 345                                 }
 346                         /* we have already generated a wNAF for 'scalar' */
 347                         }
 348                 else
 349                         {
 350                         signed char *tmp_wNAF = NULL;
 351                         size_t tmp_len = 0;
 352
 353                         if (num_scalar != 0)
 354                                 {
 355                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 356                                 goto err;
 357                                 }
 358
 359                         /* use the window size for which we have precomputation */
 360                         wsize[num] = pre_comp->w;
 361                         tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 362                         if (!tmp_wNAF)
 363                                 goto err;
 364
 365                         if (tmp_len <= max_len)
 366                                 {
 367                                 /* One of the other wNAFs is at least as long
 368                                  * as the wNAF belonging to the generator,
 369                                  * so wNAF splitting will not buy us anything. */
 370
 371                                 numblocks = 1;
 372                                 totalnum = num + 1; /* don't use wNAF splitting */
 373                                 wNAF[num] = tmp_wNAF;
 374                                 wNAF[num + 1] = NULL;
 375                                 wNAF_len[num] = tmp_len;
 376                                 if (tmp_len > max_len)
 377                                         max_len = tmp_len;
 378                                 /* pre_comp->points starts with the points that we need here: */
 379                                 val_sub[num] = pre_comp->points;
 380                                 }
 381                         else
 382                                 {
 383                                 /* don't include tmp_wNAF directly into wNAF array
 384                                  * - use wNAF splitting and include the blocks */
 385
 386                                 signed char *pp;
 387                                 EC_POINT **tmp_points;
 388
 389                                 if (tmp_len < numblocks * blocksize)
 390                                         {
 391                                         /* possibly we can do with fewer blocks than estimated */
 392                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
 393                                         if (numblocks > pre_comp->numblocks)
 394                                                 {
 395                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 396                                                 goto err;
 397                                                 }
 398                                         totalnum = num + numblocks;
 399                                         }
 400
 401                                 /* split wNAF in 'numblocks' parts */
 402                                 pp = tmp_wNAF;
 403                                 tmp_points = pre_comp->points;
 404
 405                                 for (i = num; i < totalnum; i++)
 406                                         {
 407                                         if (i < totalnum - 1)
 408                                                 {
 409                                                 wNAF_len[i] = blocksize;
 410                                                 if (tmp_len < blocksize)
 411                                                         {
 412                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 413                                                         goto err;
 414                                                         }
 415                                                 tmp_len -= blocksize;
 416                                                 }
 417                                         else
 418                                                 /* last block gets whatever is left
 419                                                  * (this could be more or less than 'blocksize'!) */
 420                                                 wNAF_len[i] = tmp_len;
 421
 422                                         wNAF[i + 1] = NULL;
 423                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 424                                         if (wNAF[i] == NULL)
 425                                                 {
 426                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 427                                                 OPENSSL_free(tmp_wNAF);
 428                                                 goto err;
 429                                                 }
 430                                         memcpy(wNAF[i], pp, wNAF_len[i]);
 431                                         if (wNAF_len[i] > max_len)
 432                                                 max_len = wNAF_len[i];
 433
 434                                         if (*tmp_points == NULL)
 435                                                 {
 436                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 437                                                 OPENSSL_free(tmp_wNAF);
 438                                                 goto err;
 439                                                 }
 440                                         val_sub[i] = tmp_points;
 441                                         tmp_points += pre_points_per_block;
 442                                         pp += blocksize;
 443                                         }
 444                                 OPENSSL_free(tmp_wNAF);
 445                                 }
 446                         }
 447                 }
 448
 449         /* All points we precompute now go into a single array 'val'.
 450          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
 451          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
 452         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
 453         if (val == NULL)
 454                 {
 455                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 456                 goto err;
 457                 }
 458         val[num_val] = NULL; /* pivot element */
 459
 460         /* allocate points for precomputation */
 461         v = val;
 462         for (i = 0; i < num + num_scalar; i++)
 463                 {
 464                 val_sub[i] = v;
 465                 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
 466                         {
 467                         *v = EC_POINT_new(group);
 468                         if (*v == NULL) goto err;
 469                         v++;
 470                         }
 471                 }
 472         if (!(v == val + num_val))
 473                 {
 474                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 475                 goto err;
 476                 }
 477
 478         if (!(tmp = EC_POINT_new(group)))
 479                 goto err;
 480
 481         /*-
 482          * prepare precomputed values:
 483          *    val_sub[i][0] :=     points[i]
 484          *    val_sub[i][1] := 3 * points[i]
 485          *    val_sub[i][2] := 5 * points[i]
 486          *    ...
 487          */
 488         for (i = 0; i < num + num_scalar; i++)
 489                 {
 490                 if (i < num)
 491                         {
 492                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
 493                         }
 494                 else
 495                         {
 496                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
 497                         }
 498
 499                 if (wsize[i] > 1)
 500                         {
 501                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
 502                         for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
 503                                 {
 504                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
 505                                 }
 506                         }
 507                 }
 508
 509 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
 510         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 511                 goto err;
 512 #endif
 513
 514         r_is_at_infinity = 1;
 515
 516         for (k = max_len - 1; k >= 0; k--)
 517                 {
 518                 if (!r_is_at_infinity)
 519                         {
 520                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
 521                         }
 522
 523                 for (i = 0; i < totalnum; i++)
 524                         {
 525                         if (wNAF_len[i] > (size_t)k)
 526                                 {
 527                                 int digit = wNAF[i][k];
 528                                 int is_neg;
 529
 530                                 if (digit)
 531                                         {
 532                                         is_neg = digit < 0;
 533
 534                                         if (is_neg)
 535                                                 digit = -digit;
 536
 537                                         if (is_neg != r_is_inverted)
 538                                                 {
 539                                                 if (!r_is_at_infinity)
 540                                                         {
 541                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 542                                                         }
 543                                                 r_is_inverted = !r_is_inverted;
 544                                                 }
 545
 546                                         /* digit > 0 */
 547
 548                                         if (r_is_at_infinity)
 549                                                 {
 550                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
 551                                                 r_is_at_infinity = 0;
 552                                                 }
 553                                         else
 554                                                 {
 555                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
 556                                                 }
 557                                         }
 558                                 }
 559                         }
 560                 }
 561
 562         if (r_is_at_infinity)
 563                 {
 564                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
 565                 }
 566         else
 567                 {
 568                 if (r_is_inverted)
 569                         if (!EC_POINT_invert(group, r, ctx)) goto err;
 570                 }
 571
 572         ret = 1;
 573
 574  err:
 575         if (new_ctx != NULL)
 576                 BN_CTX_free(new_ctx);
 577         if (tmp != NULL)
 578                 EC_POINT_free(tmp);
 579         if (wsize != NULL)
 580                 OPENSSL_free(wsize);
 581         if (wNAF_len != NULL)
 582                 OPENSSL_free(wNAF_len);
 583         if (wNAF != NULL)
 584                 {
 585                 signed char **w;
 586
 587                 for (w = wNAF; *w != NULL; w++)
 588                         OPENSSL_free(*w);
 589
 590                 OPENSSL_free(wNAF);
 591                 }
 592         if (val != NULL)
 593                 {
 594                 for (v = val; *v != NULL; v++)
 595                         EC_POINT_clear_free(*v);
 596
 597                 OPENSSL_free(val);
 598                 }
 599         if (val_sub != NULL)
 600                 {
 601                 OPENSSL_free(val_sub);
 602                 }
 603         return ret;
 604         }
 605
 606
 607 /*-
 608  * ec_wNAF_precompute_mult()
 609  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 610  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 611  *
 612  * 'pre_comp->points' is an array of multiples of the generator
 613  * of the following form:
 614  * points[0] =     generator;
 615  * points[1] = 3 * generator;
 616  * ...
 617  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 618  * points[2^(w-1)]   =     2^blocksize * generator;
 619  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 620  * ...
 621  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 622  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 623  * ...
 624  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 625  * points[2^(w-1)*numblocks]       = NULL
 626  */
 627 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 628         {
 629         const EC_POINT *generator;
 630         EC_POINT *tmp_point = NULL, *base = NULL, **var;
 631         BN_CTX *new_ctx = NULL;
 632         BIGNUM *order;
 633         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 634         EC_POINT **points = NULL;
 635         EC_PRE_COMP *pre_comp;
 636         int ret = 0;
 637
 638         /* if there is an old EC_PRE_COMP object, throw it away */
 639         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
 640
 641         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 642                 return 0;
 643
 644         generator = EC_GROUP_get0_generator(group);
 645         if (generator == NULL)
 646                 {
 647                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 648                 goto err;
 649                 }
 650
 651         if (ctx == NULL)
 652                 {
 653                 ctx = new_ctx = BN_CTX_new();
 654                 if (ctx == NULL)
 655                         goto err;
 656                 }
 657
 658         BN_CTX_start(ctx);
 659         order = BN_CTX_get(ctx);
 660         if (order == NULL) goto err;
 661
 662         if (!EC_GROUP_get_order(group, order, ctx)) goto err;
 663         if (BN_is_zero(order))
 664                 {
 665                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 666                 goto err;
 667                 }
 668
 669         bits = BN_num_bits(order);
 670         /* The following parameters mean we precompute (approximately)
 671          * one point per bit.
 672          *
 673          * TBD: The combination  8, 4  is perfect for 160 bits; for other
 674          * bit lengths, other parameter combinations might provide better
 675          * efficiency.
 676          */
 677         blocksize = 8;
 678         w = 4;
 679         if (EC_window_bits_for_scalar_size(bits) > w)
 680                 {
 681                 /* let's not make the window too small ... */
 682                 w = EC_window_bits_for_scalar_size(bits);
 683                 }
 684
 685         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
 686
 687         pre_points_per_block = (size_t)1 << (w - 1);
 688         num = pre_points_per_block * numblocks; /* number of points to compute and store */
 689
 690         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
 691         if (!points)
 692                 {
 693                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 694                 goto err;
 695                 }
 696
 697         var = points;
 698         var[num] = NULL; /* pivot */
 699         for (i = 0; i < num; i++)
 700                 {
 701                 if ((var[i] = EC_POINT_new(group)) == NULL)
 702                         {
 703                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 704                         goto err;
 705                         }
 706                 }
 707
 708         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
 709                 {
 710                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 711                 goto err;
 712                 }
 713
 714         if (!EC_POINT_copy(base, generator))
 715                 goto err;
 716
 717         /* do the precomputation */
 718         for (i = 0; i < numblocks; i++)
 719                 {
 720                 size_t j;
 721
 722                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 723                         goto err;
 724
 725                 if (!EC_POINT_copy(*var++, base))
 726                         goto err;
 727
 728                 for (j = 1; j < pre_points_per_block; j++, var++)
 729                         {
 730                         /* calculate odd multiples of the current base point */
 731                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 732                                 goto err;
 733                         }
 734
 735                 if (i < numblocks - 1)
 736                         {
 737                         /* get the next base (multiply current one by 2^blocksize) */
 738                         size_t k;
 739
 740                         if (blocksize <= 2)
 741                                 {
 742                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 743                                 goto err;
 744                                 }
 745
 746                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 747                                 goto err;
 748                         for (k = 2; k < blocksize; k++)
 749                                 {
 750                                 if (!EC_POINT_dbl(group,base,base,ctx))
 751                                         goto err;
 752                                 }
 753                         }
 754                 }
 755
 756         if (!EC_POINTs_make_affine(group, num, points, ctx))
 757                 goto err;
 758
 759         pre_comp->group = group;
 760         pre_comp->blocksize = blocksize;
 761         pre_comp->numblocks = numblocks;
 762         pre_comp->w = w;
 763         pre_comp->points = points;
 764         points = NULL;
 765         pre_comp->num = num;
 766
 767         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
 768                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
 769                 goto err;
 770         pre_comp = NULL;
 771
 772         ret = 1;
 773  err:
 774         if (ctx != NULL)
 775                 BN_CTX_end(ctx);
 776         if (new_ctx != NULL)
 777                 BN_CTX_free(new_ctx);
 778         if (pre_comp)
 779                 ec_pre_comp_free(pre_comp);
 780         if (points)
 781                 {
 782                 EC_POINT **p;
 783
 784                 for (p = points; *p != NULL; p++)
 785                         EC_POINT_free(*p);
 786                 OPENSSL_free(points);
 787                 }
 788         if (tmp_point)
 789                 EC_POINT_free(tmp_point);
 790         if (base)
 791                 EC_POINT_free(base);
 792         return ret;
 793         }
 794
 795
 796 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 797         {
 798         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
 799                 return 1;
 800         else
 801                 return 0;
 802         }