crypto/ec/ec_mult.c

   1 /*
   2  * Copyright 2001-2017 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
   4  *
   5  * Licensed under the OpenSSL license (the "License").  You may not use
   6  * this file except in compliance with the License.  You can obtain a copy
   7  * in the file LICENSE in the source distribution or at
   8  * https://www.openssl.org/source/license.html
   9  */
  10
  11 #include <string.h>
  12 #include <openssl/err.h>
  13
  14 #include "internal/cryptlib.h"
  15 #include "internal/bn_int.h"
  16 #include "ec_lcl.h"
  17 #include "internal/refcount.h"
  18
  19 /*
  20  * This file implements the wNAF-based interleaving multi-exponentiation method
  21  * Formerly at:
  22  *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
  23  * You might now find it here:
  24  *   http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
  25  *   http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
  26  * For multiplication with precomputation, we use wNAF splitting, formerly at:
  27  *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
  28  */
  29
  30 /* structure for precomputed multiples of the generator */
  31 struct ec_pre_comp_st {
  32     const EC_GROUP *group;      /* parent EC_GROUP object */
  33     size_t blocksize;           /* block size for wNAF splitting */
  34     size_t numblocks;           /* max. number of blocks for which we have
  35                                  * precomputation */
  36     size_t w;                   /* window size */
  37     EC_POINT **points;          /* array with pre-calculated multiples of
  38                                  * generator: 'num' pointers to EC_POINT
  39                                  * objects followed by a NULL */
  40     size_t num;                 /* numblocks * 2^(w-1) */
  41     CRYPTO_REF_COUNT references;
  42     CRYPTO_RWLOCK *lock;
  43 };
  44
  45 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
  46 {
  47     EC_PRE_COMP *ret = NULL;
  48
  49     if (!group)
  50         return NULL;
  51
  52     ret = OPENSSL_zalloc(sizeof(*ret));
  53     if (ret == NULL) {
  54         ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
  55         return ret;
  56     }
  57
  58     ret->group = group;
  59     ret->blocksize = 8;         /* default */
  60     ret->w = 4;                 /* default */
  61     ret->references = 1;
  62
  63     ret->lock = CRYPTO_THREAD_lock_new();
  64     if (ret->lock == NULL) {
  65         ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
  66         OPENSSL_free(ret);
  67         return NULL;
  68     }
  69     return ret;
  70 }
  71
  72 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
  73 {
  74     int i;
  75     if (pre != NULL)
  76         CRYPTO_UP_REF(&pre->references, &i, pre->lock);
  77     return pre;
  78 }
  79
  80 void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
  81 {
  82     int i;
  83
  84     if (pre == NULL)
  85         return;
  86
  87     CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
  88     REF_PRINT_COUNT("EC_ec", pre);
  89     if (i > 0)
  90         return;
  91     REF_ASSERT_ISNT(i < 0);
  92
  93     if (pre->points != NULL) {
  94         EC_POINT **pts;
  95
  96         for (pts = pre->points; *pts != NULL; pts++)
  97             EC_POINT_free(*pts);
  98         OPENSSL_free(pre->points);
  99     }
 100     CRYPTO_THREAD_lock_free(pre->lock);
 101     OPENSSL_free(pre);
 102 }
 103
 104 #define EC_POINT_set_flags(P, flags) do { \
 105     BN_set_flags((P)->X, (flags)); \
 106     BN_set_flags((P)->Y, (flags)); \
 107     BN_set_flags((P)->Z, (flags)); \
 108 } while(0)
 109
 110 /*
 111  * This functions computes (in constant time) a point multiplication over the
 112  * EC group.
 113  *
 114  * It performs either a fixed scalar point multiplication
 115  *          (scalar * generator)
 116  * when point is NULL, or a generic scalar point multiplication
 117  *          (scalar * point)
 118  * when point is not NULL.
 119  *
 120  * scalar should be in the range [0,n) otherwise all constant time bets are off.
 121  *
 122  * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
 123  * which of course are not constant time themselves.
 124  *
 125  * The product is stored in r.
 126  *
 127  * Returns 1 on success, 0 otherwise.
 128  */
 129 static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 130                             const EC_POINT *point, BN_CTX *ctx)
 131 {
 132     int i, order_bits, group_top, kbit, pbit, Z_is_one, ret;
 133     ret = 0;
 134     EC_POINT *s = NULL;
 135     BIGNUM *k = NULL;
 136     BIGNUM *lambda = NULL;
 137     BN_CTX *new_ctx = NULL;
 138
 139     if (ctx == NULL)
 140         if ((ctx = new_ctx = BN_CTX_secure_new()) == NULL)
 141             return 0;
 142
 143     if ((group->order == NULL) || (group->field == NULL))
 144         goto err;
 145
 146     order_bits = BN_num_bits(group->order);
 147
 148     s = EC_POINT_new(group);
 149     if (s == NULL)
 150         goto err;
 151
 152     if (point == NULL) {
 153         if (group->generator == NULL)
 154             goto err;
 155         if (!EC_POINT_copy(s, group->generator))
 156             goto err;
 157     } else {
 158         if (!EC_POINT_copy(s, point))
 159             goto err;
 160     }
 161
 162     EC_POINT_set_flags(s, BN_FLG_CONSTTIME);
 163
 164     BN_CTX_start(ctx);
 165     lambda = BN_CTX_get(ctx);
 166     k = BN_CTX_get(ctx);
 167     if (k == NULL)
 168         goto err;
 169
 170     /*
 171      * Group orders are often on a word boundary.
 172      * So when we pad the scalar, some timing diff might
 173      * pop if it needs to be expanded due to carries.
 174      * So expand ahead of time.
 175      */
 176     group_top = bn_get_top(group->order);
 177     if ((bn_wexpand(k, group_top + 1) == NULL)
 178         || (bn_wexpand(lambda, group_top + 1) == NULL))
 179         goto err;
 180
 181     if (!BN_copy(k, scalar))
 182         goto err;
 183
 184     BN_set_flags(k, BN_FLG_CONSTTIME);
 185
 186     if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
 187         /*
 188          * this is an unusual input, and we don't guarantee
 189          * constant-timeness
 190          */
 191         if(!BN_nnmod(k, k, group->order, ctx))
 192             goto err;
 193     }
 194
 195     if (!BN_add(lambda, k, group->order))
 196         goto err;
 197     BN_set_flags(lambda, BN_FLG_CONSTTIME);
 198     if (!BN_add(k, lambda, group->order))
 199         goto err;
 200     /*
 201      * lambda := scalar + order
 202      * k := scalar + 2*order
 203      */
 204     kbit = BN_is_bit_set(lambda, order_bits);
 205     BN_consttime_swap(kbit, k, lambda, group_top + 1);
 206
 207     group_top = bn_get_top(group->field);
 208     if ((bn_wexpand(s->X, group_top) == NULL)
 209         || (bn_wexpand(s->Y, group_top) == NULL)
 210         || (bn_wexpand(s->Z, group_top) == NULL)
 211         || (bn_wexpand(r->X, group_top) == NULL)
 212         || (bn_wexpand(r->Y, group_top) == NULL)
 213         || (bn_wexpand(r->Z, group_top) == NULL))
 214         goto err;
 215
 216     /* top bit is a 1, in a fixed pos */
 217     if (!EC_POINT_copy(r, s))
 218         goto err;
 219
 220     EC_POINT_set_flags(r, BN_FLG_CONSTTIME);
 221
 222     if (!EC_POINT_dbl(group, s, s, ctx))
 223         goto err;
 224
 225     pbit = 0;
 226
 227 #define EC_POINT_CSWAP(c, a, b, w, t) do {         \
 228         BN_consttime_swap(c, (a)->X, (b)->X, w);   \
 229         BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
 230         BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
 231         t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
 232         (a)->Z_is_one ^= (t);                      \
 233         (b)->Z_is_one ^= (t);                      \
 234 } while(0)
 235
 236     for (i = order_bits - 1; i >= 0; i--) {
 237         kbit = BN_is_bit_set(k, i) ^ pbit;
 238         EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
 239         if (!EC_POINT_add(group, s, r, s, ctx))
 240             goto err;
 241         if (!EC_POINT_dbl(group, r, r, ctx))
 242             goto err;
 243         /*
 244          * pbit logic merges this cswap with that of the
 245          * next iteration
 246          */
 247         pbit ^= kbit;
 248     }
 249     /* one final cswap to move the right value into r */
 250     EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
 251 #undef EC_POINT_CSWAP
 252
 253     ret = 1;
 254
 255 err:
 256     EC_POINT_free(s);
 257     BN_CTX_end(ctx);
 258     BN_CTX_free(new_ctx);
 259
 260     return ret;
 261 }
 262 #undef EC_POINT_set_flags
 263
 264 /*
 265  * TODO: table should be optimised for the wNAF-based implementation,
 266  * sometimes smaller windows will give better performance (thus the
 267  * boundaries should be increased)
 268  */
 269 #define EC_window_bits_for_scalar_size(b) \
 270                 ((size_t) \
 271                  ((b) >= 2000 ? 6 : \
 272                   (b) >=  800 ? 5 : \
 273                   (b) >=  300 ? 4 : \
 274                   (b) >=   70 ? 3 : \
 275                   (b) >=   20 ? 2 : \
 276                   1))
 277
 278 /*-
 279  * Compute
 280  *      \sum scalars[i]*points[i],
 281  * also including
 282  *      scalar*generator
 283  * in the addition if scalar != NULL
 284  */
 285 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 286                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 287                 BN_CTX *ctx)
 288 {
 289     if ((scalar != NULL) && (num == 0)) {
 290         /* In this case we want to compute scalar * GeneratorPoint:
 291          * this codepath is reached most prominently by (ephemeral) key
 292          * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
 293          * ECDH keygen/first half), where the scalar is always secret.
 294          * This is why we ignore if BN_FLG_CONSTTIME is actually set and we
 295          * always call the constant time version.
 296          */
 297         return ec_mul_consttime(group, r, scalar, NULL, ctx);
 298     }
 299
 300     if ((scalar == NULL) && (num == 1)) {
 301         /* In this case we want to compute scalar * GenericPoint:
 302          * this codepath is reached most prominently by the second half of
 303          * ECDH, where the secret scalar is multiplied by the peer's public
 304          * point.
 305          * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
 306          * actually set and we always call the constant time version.
 307          */
 308         return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
 309     }
 310
 311     BN_CTX *new_ctx = NULL;
 312     const EC_POINT *generator = NULL;
 313     EC_POINT *tmp = NULL;
 314     size_t totalnum;
 315     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 316     size_t pre_points_per_block = 0;
 317     size_t i, j;
 318     int k;
 319     int r_is_inverted = 0;
 320     int r_is_at_infinity = 1;
 321     size_t *wsize = NULL;       /* individual window sizes */
 322     signed char **wNAF = NULL;  /* individual wNAFs */
 323     size_t *wNAF_len = NULL;
 324     size_t max_len = 0;
 325     size_t num_val;
 326     EC_POINT **val = NULL;      /* precomputation */
 327     EC_POINT **v;
 328     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 329                                  * 'pre_comp->points' */
 330     const EC_PRE_COMP *pre_comp = NULL;
 331     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 332                                  * treated like other scalars, i.e.
 333                                  * precomputation is not available */
 334     int ret = 0;
 335
 336     if (group->meth != r->meth) {
 337         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 338         return 0;
 339     }
 340
 341     if ((scalar == NULL) && (num == 0)) {
 342         return EC_POINT_set_to_infinity(group, r);
 343     }
 344
 345     for (i = 0; i < num; i++) {
 346         if (group->meth != points[i]->meth) {
 347             ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 348             return 0;
 349         }
 350     }
 351
 352     if (ctx == NULL) {
 353         ctx = new_ctx = BN_CTX_new();
 354         if (ctx == NULL)
 355             goto err;
 356     }
 357
 358     if (scalar != NULL) {
 359         generator = EC_GROUP_get0_generator(group);
 360         if (generator == NULL) {
 361             ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 362             goto err;
 363         }
 364
 365         /* look if we can use precomputed multiples of generator */
 366
 367         pre_comp = group->pre_comp.ec;
 368         if (pre_comp && pre_comp->numblocks
 369             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 370                 0)) {
 371             blocksize = pre_comp->blocksize;
 372
 373             /*
 374              * determine maximum number of blocks that wNAF splitting may
 375              * yield (NB: maximum wNAF length is bit length plus one)
 376              */
 377             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 378
 379             /*
 380              * we cannot use more blocks than we have precomputation for
 381              */
 382             if (numblocks > pre_comp->numblocks)
 383                 numblocks = pre_comp->numblocks;
 384
 385             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 386
 387             /* check that pre_comp looks sane */
 388             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 389                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 390                 goto err;
 391             }
 392         } else {
 393             /* can't use precomputation */
 394             pre_comp = NULL;
 395             numblocks = 1;
 396             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 397                                  * 'scalars' */
 398         }
 399     }
 400
 401     totalnum = num + numblocks;
 402
 403     wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
 404     wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
 405     /* include space for pivot */
 406     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
 407     val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
 408
 409     /* Ensure wNAF is initialised in case we end up going to err */
 410     if (wNAF != NULL)
 411         wNAF[0] = NULL;         /* preliminary pivot */
 412
 413     if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
 414         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 415         goto err;
 416     }
 417
 418     /*
 419      * num_val will be the total number of temporarily precomputed points
 420      */
 421     num_val = 0;
 422
 423     for (i = 0; i < num + num_scalar; i++) {
 424         size_t bits;
 425
 426         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 427         wsize[i] = EC_window_bits_for_scalar_size(bits);
 428         num_val += (size_t)1 << (wsize[i] - 1);
 429         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 430         wNAF[i] =
 431             bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 432                             &wNAF_len[i]);
 433         if (wNAF[i] == NULL)
 434             goto err;
 435         if (wNAF_len[i] > max_len)
 436             max_len = wNAF_len[i];
 437     }
 438
 439     if (numblocks) {
 440         /* we go here iff scalar != NULL */
 441
 442         if (pre_comp == NULL) {
 443             if (num_scalar != 1) {
 444                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 445                 goto err;
 446             }
 447             /* we have already generated a wNAF for 'scalar' */
 448         } else {
 449             signed char *tmp_wNAF = NULL;
 450             size_t tmp_len = 0;
 451
 452             if (num_scalar != 0) {
 453                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 454                 goto err;
 455             }
 456
 457             /*
 458              * use the window size for which we have precomputation
 459              */
 460             wsize[num] = pre_comp->w;
 461             tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 462             if (!tmp_wNAF)
 463                 goto err;
 464
 465             if (tmp_len <= max_len) {
 466                 /*
 467                  * One of the other wNAFs is at least as long as the wNAF
 468                  * belonging to the generator, so wNAF splitting will not buy
 469                  * us anything.
 470                  */
 471
 472                 numblocks = 1;
 473                 totalnum = num + 1; /* don't use wNAF splitting */
 474                 wNAF[num] = tmp_wNAF;
 475                 wNAF[num + 1] = NULL;
 476                 wNAF_len[num] = tmp_len;
 477                 /*
 478                  * pre_comp->points starts with the points that we need here:
 479                  */
 480                 val_sub[num] = pre_comp->points;
 481             } else {
 482                 /*
 483                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 484                  * splitting and include the blocks
 485                  */
 486
 487                 signed char *pp;
 488                 EC_POINT **tmp_points;
 489
 490                 if (tmp_len < numblocks * blocksize) {
 491                     /*
 492                      * possibly we can do with fewer blocks than estimated
 493                      */
 494                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 495                     if (numblocks > pre_comp->numblocks) {
 496                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 497                         OPENSSL_free(tmp_wNAF);
 498                         goto err;
 499                     }
 500                     totalnum = num + numblocks;
 501                 }
 502
 503                 /* split wNAF in 'numblocks' parts */
 504                 pp = tmp_wNAF;
 505                 tmp_points = pre_comp->points;
 506
 507                 for (i = num; i < totalnum; i++) {
 508                     if (i < totalnum - 1) {
 509                         wNAF_len[i] = blocksize;
 510                         if (tmp_len < blocksize) {
 511                             ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 512                             OPENSSL_free(tmp_wNAF);
 513                             goto err;
 514                         }
 515                         tmp_len -= blocksize;
 516                     } else
 517                         /*
 518                          * last block gets whatever is left (this could be
 519                          * more or less than 'blocksize'!)
 520                          */
 521                         wNAF_len[i] = tmp_len;
 522
 523                     wNAF[i + 1] = NULL;
 524                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 525                     if (wNAF[i] == NULL) {
 526                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 527                         OPENSSL_free(tmp_wNAF);
 528                         goto err;
 529                     }
 530                     memcpy(wNAF[i], pp, wNAF_len[i]);
 531                     if (wNAF_len[i] > max_len)
 532                         max_len = wNAF_len[i];
 533
 534                     if (*tmp_points == NULL) {
 535                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 536                         OPENSSL_free(tmp_wNAF);
 537                         goto err;
 538                     }
 539                     val_sub[i] = tmp_points;
 540                     tmp_points += pre_points_per_block;
 541                     pp += blocksize;
 542                 }
 543                 OPENSSL_free(tmp_wNAF);
 544             }
 545         }
 546     }
 547
 548     /*
 549      * All points we precompute now go into a single array 'val'.
 550      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 551      * subarray of 'pre_comp->points' if we already have precomputation.
 552      */
 553     val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
 554     if (val == NULL) {
 555         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 556         goto err;
 557     }
 558     val[num_val] = NULL;        /* pivot element */
 559
 560     /* allocate points for precomputation */
 561     v = val;
 562     for (i = 0; i < num + num_scalar; i++) {
 563         val_sub[i] = v;
 564         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 565             *v = EC_POINT_new(group);
 566             if (*v == NULL)
 567                 goto err;
 568             v++;
 569         }
 570     }
 571     if (!(v == val + num_val)) {
 572         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 573         goto err;
 574     }
 575
 576     if ((tmp = EC_POINT_new(group)) == NULL)
 577         goto err;
 578
 579     /*-
 580      * prepare precomputed values:
 581      *    val_sub[i][0] :=     points[i]
 582      *    val_sub[i][1] := 3 * points[i]
 583      *    val_sub[i][2] := 5 * points[i]
 584      *    ...
 585      */
 586     for (i = 0; i < num + num_scalar; i++) {
 587         if (i < num) {
 588             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 589                 goto err;
 590         } else {
 591             if (!EC_POINT_copy(val_sub[i][0], generator))
 592                 goto err;
 593         }
 594
 595         if (wsize[i] > 1) {
 596             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 597                 goto err;
 598             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 599                 if (!EC_POINT_add
 600                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 601                     goto err;
 602             }
 603         }
 604     }
 605
 606     if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 607         goto err;
 608
 609     r_is_at_infinity = 1;
 610
 611     for (k = max_len - 1; k >= 0; k--) {
 612         if (!r_is_at_infinity) {
 613             if (!EC_POINT_dbl(group, r, r, ctx))
 614                 goto err;
 615         }
 616
 617         for (i = 0; i < totalnum; i++) {
 618             if (wNAF_len[i] > (size_t)k) {
 619                 int digit = wNAF[i][k];
 620                 int is_neg;
 621
 622                 if (digit) {
 623                     is_neg = digit < 0;
 624
 625                     if (is_neg)
 626                         digit = -digit;
 627
 628                     if (is_neg != r_is_inverted) {
 629                         if (!r_is_at_infinity) {
 630                             if (!EC_POINT_invert(group, r, ctx))
 631                                 goto err;
 632                         }
 633                         r_is_inverted = !r_is_inverted;
 634                     }
 635
 636                     /* digit > 0 */
 637
 638                     if (r_is_at_infinity) {
 639                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 640                             goto err;
 641                         r_is_at_infinity = 0;
 642                     } else {
 643                         if (!EC_POINT_add
 644                             (group, r, r, val_sub[i][digit >> 1], ctx))
 645                             goto err;
 646                     }
 647                 }
 648             }
 649         }
 650     }
 651
 652     if (r_is_at_infinity) {
 653         if (!EC_POINT_set_to_infinity(group, r))
 654             goto err;
 655     } else {
 656         if (r_is_inverted)
 657             if (!EC_POINT_invert(group, r, ctx))
 658                 goto err;
 659     }
 660
 661     ret = 1;
 662
 663  err:
 664     BN_CTX_free(new_ctx);
 665     EC_POINT_free(tmp);
 666     OPENSSL_free(wsize);
 667     OPENSSL_free(wNAF_len);
 668     if (wNAF != NULL) {
 669         signed char **w;
 670
 671         for (w = wNAF; *w != NULL; w++)
 672             OPENSSL_free(*w);
 673
 674         OPENSSL_free(wNAF);
 675     }
 676     if (val != NULL) {
 677         for (v = val; *v != NULL; v++)
 678             EC_POINT_clear_free(*v);
 679
 680         OPENSSL_free(val);
 681     }
 682     OPENSSL_free(val_sub);
 683     return ret;
 684 }
 685
 686 /*-
 687  * ec_wNAF_precompute_mult()
 688  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 689  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 690  *
 691  * 'pre_comp->points' is an array of multiples of the generator
 692  * of the following form:
 693  * points[0] =     generator;
 694  * points[1] = 3 * generator;
 695  * ...
 696  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 697  * points[2^(w-1)]   =     2^blocksize * generator;
 698  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 699  * ...
 700  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 701  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 702  * ...
 703  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 704  * points[2^(w-1)*numblocks]       = NULL
 705  */
 706 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 707 {
 708     const EC_POINT *generator;
 709     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 710     BN_CTX *new_ctx = NULL;
 711     const BIGNUM *order;
 712     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 713     EC_POINT **points = NULL;
 714     EC_PRE_COMP *pre_comp;
 715     int ret = 0;
 716
 717     /* if there is an old EC_PRE_COMP object, throw it away */
 718     EC_pre_comp_free(group);
 719     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 720         return 0;
 721
 722     generator = EC_GROUP_get0_generator(group);
 723     if (generator == NULL) {
 724         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 725         goto err;
 726     }
 727
 728     if (ctx == NULL) {
 729         ctx = new_ctx = BN_CTX_new();
 730         if (ctx == NULL)
 731             goto err;
 732     }
 733
 734     BN_CTX_start(ctx);
 735
 736     order = EC_GROUP_get0_order(group);
 737     if (order == NULL)
 738         goto err;
 739     if (BN_is_zero(order)) {
 740         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 741         goto err;
 742     }
 743
 744     bits = BN_num_bits(order);
 745     /*
 746      * The following parameters mean we precompute (approximately) one point
 747      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 748      * bit lengths, other parameter combinations might provide better
 749      * efficiency.
 750      */
 751     blocksize = 8;
 752     w = 4;
 753     if (EC_window_bits_for_scalar_size(bits) > w) {
 754         /* let's not make the window too small ... */
 755         w = EC_window_bits_for_scalar_size(bits);
 756     }
 757
 758     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 759                                                      * to use for wNAF
 760                                                      * splitting */
 761
 762     pre_points_per_block = (size_t)1 << (w - 1);
 763     num = pre_points_per_block * numblocks; /* number of points to compute
 764                                              * and store */
 765
 766     points = OPENSSL_malloc(sizeof(*points) * (num + 1));
 767     if (points == NULL) {
 768         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 769         goto err;
 770     }
 771
 772     var = points;
 773     var[num] = NULL;            /* pivot */
 774     for (i = 0; i < num; i++) {
 775         if ((var[i] = EC_POINT_new(group)) == NULL) {
 776             ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 777             goto err;
 778         }
 779     }
 780
 781     if ((tmp_point = EC_POINT_new(group)) == NULL
 782         || (base = EC_POINT_new(group)) == NULL) {
 783         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 784         goto err;
 785     }
 786
 787     if (!EC_POINT_copy(base, generator))
 788         goto err;
 789
 790     /* do the precomputation */
 791     for (i = 0; i < numblocks; i++) {
 792         size_t j;
 793
 794         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 795             goto err;
 796
 797         if (!EC_POINT_copy(*var++, base))
 798             goto err;
 799
 800         for (j = 1; j < pre_points_per_block; j++, var++) {
 801             /*
 802              * calculate odd multiples of the current base point
 803              */
 804             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 805                 goto err;
 806         }
 807
 808         if (i < numblocks - 1) {
 809             /*
 810              * get the next base (multiply current one by 2^blocksize)
 811              */
 812             size_t k;
 813
 814             if (blocksize <= 2) {
 815                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 816                 goto err;
 817             }
 818
 819             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 820                 goto err;
 821             for (k = 2; k < blocksize; k++) {
 822                 if (!EC_POINT_dbl(group, base, base, ctx))
 823                     goto err;
 824             }
 825         }
 826     }
 827
 828     if (!EC_POINTs_make_affine(group, num, points, ctx))
 829         goto err;
 830
 831     pre_comp->group = group;
 832     pre_comp->blocksize = blocksize;
 833     pre_comp->numblocks = numblocks;
 834     pre_comp->w = w;
 835     pre_comp->points = points;
 836     points = NULL;
 837     pre_comp->num = num;
 838     SETPRECOMP(group, ec, pre_comp);
 839     pre_comp = NULL;
 840     ret = 1;
 841
 842  err:
 843     if (ctx != NULL)
 844         BN_CTX_end(ctx);
 845     BN_CTX_free(new_ctx);
 846     EC_ec_pre_comp_free(pre_comp);
 847     if (points) {
 848         EC_POINT **p;
 849
 850         for (p = points; *p != NULL; p++)
 851             EC_POINT_free(*p);
 852         OPENSSL_free(points);
 853     }
 854     EC_POINT_free(tmp_point);
 855     EC_POINT_free(base);
 856     return ret;
 857 }
 858
 859 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 860 {
 861     return HAVEPRECOMP(group, ec);
 862 }