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