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_BN_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  * At a high level, it is Montgomery ladder with conditional swaps.
 115  *
 116  * It performs either a fixed scalar point multiplication
 117  *          (scalar * generator)
 118  * when point is NULL, or a generic scalar point multiplication
 119  *          (scalar * point)
 120  * when point is not NULL.
 121  *
 122  * scalar should be in the range [0,n) otherwise all constant time bets are off.
 123  *
 124  * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
 125  * which of course are not constant time themselves.
 126  *
 127  * The product is stored in r.
 128  *
 129  * Returns 1 on success, 0 otherwise.
 130  */
 131 static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
 132                             const BIGNUM *scalar, const EC_POINT *point,
 133                             BN_CTX *ctx)
 134 {
 135     int i, order_bits, group_top, kbit, pbit, Z_is_one;
 136     EC_POINT *s = NULL;
 137     BIGNUM *k = NULL;
 138     BIGNUM *lambda = NULL;
 139     BN_CTX *new_ctx = NULL;
 140     int ret = 0;
 141
 142     if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
 143         goto err;
 144
 145     if ((group->order == NULL) || (group->field == NULL))
 146         goto err;
 147
 148     order_bits = BN_num_bits(group->order);
 149
 150     s = EC_POINT_new(group);
 151     if (s == NULL)
 152         goto err;
 153
 154     if (point == NULL) {
 155         if (group->generator == NULL)
 156             goto err;
 157         if (!EC_POINT_copy(s, group->generator))
 158             goto err;
 159     } else {
 160         if (!EC_POINT_copy(s, point))
 161             goto err;
 162     }
 163
 164     EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
 165
 166     BN_CTX_start(ctx);
 167     lambda = BN_CTX_get(ctx);
 168     k = BN_CTX_get(ctx);
 169     if (k == NULL)
 170         goto err;
 171
 172     /*
 173      * Group orders are often on a word boundary.
 174      * So when we pad the scalar, some timing diff might
 175      * pop if it needs to be expanded due to carries.
 176      * So expand ahead of time.
 177      */
 178     group_top = bn_get_top(group->order);
 179     if ((bn_wexpand(k, group_top + 1) == NULL)
 180         || (bn_wexpand(lambda, group_top + 1) == NULL))
 181         goto err;
 182
 183     if (!BN_copy(k, scalar))
 184         goto err;
 185
 186     BN_set_flags(k, BN_FLG_CONSTTIME);
 187
 188     if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
 189         /*-
 190          * this is an unusual input, and we don't guarantee
 191          * constant-timeness
 192          */
 193         if (!BN_nnmod(k, k, group->order, ctx))
 194             goto err;
 195     }
 196
 197     if (!BN_add(lambda, k, group->order))
 198         goto err;
 199     BN_set_flags(lambda, BN_FLG_CONSTTIME);
 200     if (!BN_add(k, lambda, group->order))
 201         goto err;
 202     /*
 203      * lambda := scalar + order
 204      * k := scalar + 2*order
 205      */
 206     kbit = BN_is_bit_set(lambda, order_bits);
 207     BN_consttime_swap(kbit, k, lambda, group_top + 1);
 208
 209     group_top = bn_get_top(group->field);
 210     if ((bn_wexpand(s->X, group_top) == NULL)
 211         || (bn_wexpand(s->Y, group_top) == NULL)
 212         || (bn_wexpand(s->Z, group_top) == NULL)
 213         || (bn_wexpand(r->X, group_top) == NULL)
 214         || (bn_wexpand(r->Y, group_top) == NULL)
 215         || (bn_wexpand(r->Z, group_top) == NULL))
 216         goto err;
 217
 218     /* top bit is a 1, in a fixed pos */
 219     if (!EC_POINT_copy(r, s))
 220         goto err;
 221
 222     EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
 223
 224     if (!EC_POINT_dbl(group, s, s, ctx))
 225         goto err;
 226
 227     pbit = 0;
 228
 229 #define EC_POINT_CSWAP(c, a, b, w, t) do {         \
 230         BN_consttime_swap(c, (a)->X, (b)->X, w);   \
 231         BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
 232         BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
 233         t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
 234         (a)->Z_is_one ^= (t);                      \
 235         (b)->Z_is_one ^= (t);                      \
 236 } while(0)
 237
 238     /*-
 239      * The ladder step, with branches, is
 240      *
 241      * k[i] == 0: S = add(R, S), R = dbl(R)
 242      * k[i] == 1: R = add(S, R), S = dbl(S)
 243      *
 244      * Swapping R, S conditionally on k[i] leaves you with state
 245      *
 246      * k[i] == 0: T, U = R, S
 247      * k[i] == 1: T, U = S, R
 248      *
 249      * Then perform the ECC ops.
 250      *
 251      * U = add(T, U)
 252      * T = dbl(T)
 253      *
 254      * Which leaves you with state
 255      *
 256      * k[i] == 0: U = add(R, S), T = dbl(R)
 257      * k[i] == 1: U = add(S, R), T = dbl(S)
 258      *
 259      * Swapping T, U conditionally on k[i] leaves you with state
 260      *
 261      * k[i] == 0: R, S = T, U
 262      * k[i] == 1: R, S = U, T
 263      *
 264      * Which leaves you with state
 265      *
 266      * k[i] == 0: S = add(R, S), R = dbl(R)
 267      * k[i] == 1: R = add(S, R), S = dbl(S)
 268      *
 269      * So we get the same logic, but instead of a branch it's a
 270      * conditional swap, followed by ECC ops, then another conditional swap.
 271      *
 272      * Optimization: The end of iteration i and start of i-1 looks like
 273      *
 274      * ...
 275      * CSWAP(k[i], R, S)
 276      * ECC
 277      * CSWAP(k[i], R, S)
 278      * (next iteration)
 279      * CSWAP(k[i-1], R, S)
 280      * ECC
 281      * CSWAP(k[i-1], R, S)
 282      * ...
 283      *
 284      * So instead of two contiguous swaps, you can merge the condition
 285      * bits and do a single swap.
 286      *
 287      * k[i]   k[i-1]    Outcome
 288      * 0      0         No Swap
 289      * 0      1         Swap
 290      * 1      0         Swap
 291      * 1      1         No Swap
 292      *
 293      * This is XOR. pbit tracks the previous bit of k.
 294      */
 295
 296     for (i = order_bits - 1; i >= 0; i--) {
 297         kbit = BN_is_bit_set(k, i) ^ pbit;
 298         EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
 299         if (!EC_POINT_add(group, s, r, s, ctx))
 300             goto err;
 301         if (!EC_POINT_dbl(group, r, r, ctx))
 302             goto err;
 303         /*
 304          * pbit logic merges this cswap with that of the
 305          * next iteration
 306          */
 307         pbit ^= kbit;
 308     }
 309     /* one final cswap to move the right value into r */
 310     EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
 311 #undef EC_POINT_CSWAP
 312
 313     ret = 1;
 314
 315  err:
 316     EC_POINT_free(s);
 317     BN_CTX_end(ctx);
 318     BN_CTX_free(new_ctx);
 319
 320     return ret;
 321 }
 322
 323 #undef EC_POINT_BN_set_flags
 324
 325 /*
 326  * TODO: table should be optimised for the wNAF-based implementation,
 327  * sometimes smaller windows will give better performance (thus the
 328  * boundaries should be increased)
 329  */
 330 #define EC_window_bits_for_scalar_size(b) \
 331                 ((size_t) \
 332                  ((b) >= 2000 ? 6 : \
 333                   (b) >=  800 ? 5 : \
 334                   (b) >=  300 ? 4 : \
 335                   (b) >=   70 ? 3 : \
 336                   (b) >=   20 ? 2 : \
 337                   1))
 338
 339 /*-
 340  * Compute
 341  *      \sum scalars[i]*points[i],
 342  * also including
 343  *      scalar*generator
 344  * in the addition if scalar != NULL
 345  */
 346 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 347                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 348                 BN_CTX *ctx)
 349 {
 350     BN_CTX *new_ctx = NULL;
 351     const EC_POINT *generator = NULL;
 352     EC_POINT *tmp = NULL;
 353     size_t totalnum;
 354     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 355     size_t pre_points_per_block = 0;
 356     size_t i, j;
 357     int k;
 358     int r_is_inverted = 0;
 359     int r_is_at_infinity = 1;
 360     size_t *wsize = NULL;       /* individual window sizes */
 361     signed char **wNAF = NULL;  /* individual wNAFs */
 362     size_t *wNAF_len = NULL;
 363     size_t max_len = 0;
 364     size_t num_val;
 365     EC_POINT **val = NULL;      /* precomputation */
 366     EC_POINT **v;
 367     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 368                                  * 'pre_comp->points' */
 369     const EC_PRE_COMP *pre_comp = NULL;
 370     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 371                                  * treated like other scalars, i.e.
 372                                  * precomputation is not available */
 373     int ret = 0;
 374
 375     /*-
 376      * Handle the common cases where the scalar is secret, enforcing a constant
 377      * time scalar multiplication algorithm.
 378      */
 379     if ((scalar != NULL) && (num == 0)) {
 380         /*-
 381          * In this case we want to compute scalar * GeneratorPoint: this
 382          * codepath is reached most prominently by (ephemeral) key generation
 383          * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
 384          * keygen/first half), where the scalar is always secret. This is why
 385          * we ignore if BN_FLG_CONSTTIME is actually set and we always call the
 386          * constant time version.
 387          */
 388         return ec_mul_consttime(group, r, scalar, NULL, ctx);
 389     }
 390     if ((scalar == NULL) && (num == 1)) {
 391         /*-
 392          * In this case we want to compute scalar * GenericPoint: this codepath
 393          * is reached most prominently by the second half of ECDH, where the
 394          * secret scalar is multiplied by the peer's public point. To protect
 395          * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
 396          * we always call the constant time version.
 397          */
 398         return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
 399     }
 400
 401     if (group->meth != r->meth) {
 402         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 403         return 0;
 404     }
 405
 406     if ((scalar == NULL) && (num == 0)) {
 407         return EC_POINT_set_to_infinity(group, r);
 408     }
 409
 410     for (i = 0; i < num; i++) {
 411         if (group->meth != points[i]->meth) {
 412             ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 413             return 0;
 414         }
 415     }
 416
 417     if (ctx == NULL) {
 418         ctx = new_ctx = BN_CTX_new();
 419         if (ctx == NULL)
 420             goto err;
 421     }
 422
 423     if (scalar != NULL) {
 424         generator = EC_GROUP_get0_generator(group);
 425         if (generator == NULL) {
 426             ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 427             goto err;
 428         }
 429
 430         /* look if we can use precomputed multiples of generator */
 431
 432         pre_comp = group->pre_comp.ec;
 433         if (pre_comp && pre_comp->numblocks
 434             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 435                 0)) {
 436             blocksize = pre_comp->blocksize;
 437
 438             /*
 439              * determine maximum number of blocks that wNAF splitting may
 440              * yield (NB: maximum wNAF length is bit length plus one)
 441              */
 442             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 443
 444             /*
 445              * we cannot use more blocks than we have precomputation for
 446              */
 447             if (numblocks > pre_comp->numblocks)
 448                 numblocks = pre_comp->numblocks;
 449
 450             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 451
 452             /* check that pre_comp looks sane */
 453             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 454                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 455                 goto err;
 456             }
 457         } else {
 458             /* can't use precomputation */
 459             pre_comp = NULL;
 460             numblocks = 1;
 461             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 462                                  * 'scalars' */
 463         }
 464     }
 465
 466     totalnum = num + numblocks;
 467
 468     wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
 469     wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
 470     /* include space for pivot */
 471     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
 472     val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
 473
 474     /* Ensure wNAF is initialised in case we end up going to err */
 475     if (wNAF != NULL)
 476         wNAF[0] = NULL;         /* preliminary pivot */
 477
 478     if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
 479         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 480         goto err;
 481     }
 482
 483     /*
 484      * num_val will be the total number of temporarily precomputed points
 485      */
 486     num_val = 0;
 487
 488     for (i = 0; i < num + num_scalar; i++) {
 489         size_t bits;
 490
 491         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 492         wsize[i] = EC_window_bits_for_scalar_size(bits);
 493         num_val += (size_t)1 << (wsize[i] - 1);
 494         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 495         wNAF[i] =
 496             bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 497                             &wNAF_len[i]);
 498         if (wNAF[i] == NULL)
 499             goto err;
 500         if (wNAF_len[i] > max_len)
 501             max_len = wNAF_len[i];
 502     }
 503
 504     if (numblocks) {
 505         /* we go here iff scalar != NULL */
 506
 507         if (pre_comp == NULL) {
 508             if (num_scalar != 1) {
 509                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 510                 goto err;
 511             }
 512             /* we have already generated a wNAF for 'scalar' */
 513         } else {
 514             signed char *tmp_wNAF = NULL;
 515             size_t tmp_len = 0;
 516
 517             if (num_scalar != 0) {
 518                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 519                 goto err;
 520             }
 521
 522             /*
 523              * use the window size for which we have precomputation
 524              */
 525             wsize[num] = pre_comp->w;
 526             tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 527             if (!tmp_wNAF)
 528                 goto err;
 529
 530             if (tmp_len <= max_len) {
 531                 /*
 532                  * One of the other wNAFs is at least as long as the wNAF
 533                  * belonging to the generator, so wNAF splitting will not buy
 534                  * us anything.
 535                  */
 536
 537                 numblocks = 1;
 538                 totalnum = num + 1; /* don't use wNAF splitting */
 539                 wNAF[num] = tmp_wNAF;
 540                 wNAF[num + 1] = NULL;
 541                 wNAF_len[num] = tmp_len;
 542                 /*
 543                  * pre_comp->points starts with the points that we need here:
 544                  */
 545                 val_sub[num] = pre_comp->points;
 546             } else {
 547                 /*
 548                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 549                  * splitting and include the blocks
 550                  */
 551
 552                 signed char *pp;
 553                 EC_POINT **tmp_points;
 554
 555                 if (tmp_len < numblocks * blocksize) {
 556                     /*
 557                      * possibly we can do with fewer blocks than estimated
 558                      */
 559                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 560                     if (numblocks > pre_comp->numblocks) {
 561                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 562                         OPENSSL_free(tmp_wNAF);
 563                         goto err;
 564                     }
 565                     totalnum = num + numblocks;
 566                 }
 567
 568                 /* split wNAF in 'numblocks' parts */
 569                 pp = tmp_wNAF;
 570                 tmp_points = pre_comp->points;
 571
 572                 for (i = num; i < totalnum; i++) {
 573                     if (i < totalnum - 1) {
 574                         wNAF_len[i] = blocksize;
 575                         if (tmp_len < blocksize) {
 576                             ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 577                             OPENSSL_free(tmp_wNAF);
 578                             goto err;
 579                         }
 580                         tmp_len -= blocksize;
 581                     } else
 582                         /*
 583                          * last block gets whatever is left (this could be
 584                          * more or less than 'blocksize'!)
 585                          */
 586                         wNAF_len[i] = tmp_len;
 587
 588                     wNAF[i + 1] = NULL;
 589                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 590                     if (wNAF[i] == NULL) {
 591                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 592                         OPENSSL_free(tmp_wNAF);
 593                         goto err;
 594                     }
 595                     memcpy(wNAF[i], pp, wNAF_len[i]);
 596                     if (wNAF_len[i] > max_len)
 597                         max_len = wNAF_len[i];
 598
 599                     if (*tmp_points == NULL) {
 600                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 601                         OPENSSL_free(tmp_wNAF);
 602                         goto err;
 603                     }
 604                     val_sub[i] = tmp_points;
 605                     tmp_points += pre_points_per_block;
 606                     pp += blocksize;
 607                 }
 608                 OPENSSL_free(tmp_wNAF);
 609             }
 610         }
 611     }
 612
 613     /*
 614      * All points we precompute now go into a single array 'val'.
 615      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 616      * subarray of 'pre_comp->points' if we already have precomputation.
 617      */
 618     val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
 619     if (val == NULL) {
 620         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 621         goto err;
 622     }
 623     val[num_val] = NULL;        /* pivot element */
 624
 625     /* allocate points for precomputation */
 626     v = val;
 627     for (i = 0; i < num + num_scalar; i++) {
 628         val_sub[i] = v;
 629         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 630             *v = EC_POINT_new(group);
 631             if (*v == NULL)
 632                 goto err;
 633             v++;
 634         }
 635     }
 636     if (!(v == val + num_val)) {
 637         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 638         goto err;
 639     }
 640
 641     if ((tmp = EC_POINT_new(group)) == NULL)
 642         goto err;
 643
 644     /*-
 645      * prepare precomputed values:
 646      *    val_sub[i][0] :=     points[i]
 647      *    val_sub[i][1] := 3 * points[i]
 648      *    val_sub[i][2] := 5 * points[i]
 649      *    ...
 650      */
 651     for (i = 0; i < num + num_scalar; i++) {
 652         if (i < num) {
 653             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 654                 goto err;
 655         } else {
 656             if (!EC_POINT_copy(val_sub[i][0], generator))
 657                 goto err;
 658         }
 659
 660         if (wsize[i] > 1) {
 661             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 662                 goto err;
 663             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 664                 if (!EC_POINT_add
 665                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 666                     goto err;
 667             }
 668         }
 669     }
 670
 671     if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 672         goto err;
 673
 674     r_is_at_infinity = 1;
 675
 676     for (k = max_len - 1; k >= 0; k--) {
 677         if (!r_is_at_infinity) {
 678             if (!EC_POINT_dbl(group, r, r, ctx))
 679                 goto err;
 680         }
 681
 682         for (i = 0; i < totalnum; i++) {
 683             if (wNAF_len[i] > (size_t)k) {
 684                 int digit = wNAF[i][k];
 685                 int is_neg;
 686
 687                 if (digit) {
 688                     is_neg = digit < 0;
 689
 690                     if (is_neg)
 691                         digit = -digit;
 692
 693                     if (is_neg != r_is_inverted) {
 694                         if (!r_is_at_infinity) {
 695                             if (!EC_POINT_invert(group, r, ctx))
 696                                 goto err;
 697                         }
 698                         r_is_inverted = !r_is_inverted;
 699                     }
 700
 701                     /* digit > 0 */
 702
 703                     if (r_is_at_infinity) {
 704                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 705                             goto err;
 706                         r_is_at_infinity = 0;
 707                     } else {
 708                         if (!EC_POINT_add
 709                             (group, r, r, val_sub[i][digit >> 1], ctx))
 710                             goto err;
 711                     }
 712                 }
 713             }
 714         }
 715     }
 716
 717     if (r_is_at_infinity) {
 718         if (!EC_POINT_set_to_infinity(group, r))
 719             goto err;
 720     } else {
 721         if (r_is_inverted)
 722             if (!EC_POINT_invert(group, r, ctx))
 723                 goto err;
 724     }
 725
 726     ret = 1;
 727
 728  err:
 729     BN_CTX_free(new_ctx);
 730     EC_POINT_free(tmp);
 731     OPENSSL_free(wsize);
 732     OPENSSL_free(wNAF_len);
 733     if (wNAF != NULL) {
 734         signed char **w;
 735
 736         for (w = wNAF; *w != NULL; w++)
 737             OPENSSL_free(*w);
 738
 739         OPENSSL_free(wNAF);
 740     }
 741     if (val != NULL) {
 742         for (v = val; *v != NULL; v++)
 743             EC_POINT_clear_free(*v);
 744
 745         OPENSSL_free(val);
 746     }
 747     OPENSSL_free(val_sub);
 748     return ret;
 749 }
 750
 751 /*-
 752  * ec_wNAF_precompute_mult()
 753  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 754  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 755  *
 756  * 'pre_comp->points' is an array of multiples of the generator
 757  * of the following form:
 758  * points[0] =     generator;
 759  * points[1] = 3 * generator;
 760  * ...
 761  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 762  * points[2^(w-1)]   =     2^blocksize * generator;
 763  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 764  * ...
 765  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 766  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 767  * ...
 768  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 769  * points[2^(w-1)*numblocks]       = NULL
 770  */
 771 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 772 {
 773     const EC_POINT *generator;
 774     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 775     BN_CTX *new_ctx = NULL;
 776     const BIGNUM *order;
 777     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 778     EC_POINT **points = NULL;
 779     EC_PRE_COMP *pre_comp;
 780     int ret = 0;
 781
 782     /* if there is an old EC_PRE_COMP object, throw it away */
 783     EC_pre_comp_free(group);
 784     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 785         return 0;
 786
 787     generator = EC_GROUP_get0_generator(group);
 788     if (generator == NULL) {
 789         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 790         goto err;
 791     }
 792
 793     if (ctx == NULL) {
 794         ctx = new_ctx = BN_CTX_new();
 795         if (ctx == NULL)
 796             goto err;
 797     }
 798
 799     BN_CTX_start(ctx);
 800
 801     order = EC_GROUP_get0_order(group);
 802     if (order == NULL)
 803         goto err;
 804     if (BN_is_zero(order)) {
 805         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 806         goto err;
 807     }
 808
 809     bits = BN_num_bits(order);
 810     /*
 811      * The following parameters mean we precompute (approximately) one point
 812      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 813      * bit lengths, other parameter combinations might provide better
 814      * efficiency.
 815      */
 816     blocksize = 8;
 817     w = 4;
 818     if (EC_window_bits_for_scalar_size(bits) > w) {
 819         /* let's not make the window too small ... */
 820         w = EC_window_bits_for_scalar_size(bits);
 821     }
 822
 823     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 824                                                      * to use for wNAF
 825                                                      * splitting */
 826
 827     pre_points_per_block = (size_t)1 << (w - 1);
 828     num = pre_points_per_block * numblocks; /* number of points to compute
 829                                              * and store */
 830
 831     points = OPENSSL_malloc(sizeof(*points) * (num + 1));
 832     if (points == NULL) {
 833         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 834         goto err;
 835     }
 836
 837     var = points;
 838     var[num] = NULL;            /* pivot */
 839     for (i = 0; i < num; i++) {
 840         if ((var[i] = EC_POINT_new(group)) == NULL) {
 841             ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 842             goto err;
 843         }
 844     }
 845
 846     if ((tmp_point = EC_POINT_new(group)) == NULL
 847         || (base = EC_POINT_new(group)) == NULL) {
 848         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 849         goto err;
 850     }
 851
 852     if (!EC_POINT_copy(base, generator))
 853         goto err;
 854
 855     /* do the precomputation */
 856     for (i = 0; i < numblocks; i++) {
 857         size_t j;
 858
 859         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 860             goto err;
 861
 862         if (!EC_POINT_copy(*var++, base))
 863             goto err;
 864
 865         for (j = 1; j < pre_points_per_block; j++, var++) {
 866             /*
 867              * calculate odd multiples of the current base point
 868              */
 869             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 870                 goto err;
 871         }
 872
 873         if (i < numblocks - 1) {
 874             /*
 875              * get the next base (multiply current one by 2^blocksize)
 876              */
 877             size_t k;
 878
 879             if (blocksize <= 2) {
 880                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 881                 goto err;
 882             }
 883
 884             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 885                 goto err;
 886             for (k = 2; k < blocksize; k++) {
 887                 if (!EC_POINT_dbl(group, base, base, ctx))
 888                     goto err;
 889             }
 890         }
 891     }
 892
 893     if (!EC_POINTs_make_affine(group, num, points, ctx))
 894         goto err;
 895
 896     pre_comp->group = group;
 897     pre_comp->blocksize = blocksize;
 898     pre_comp->numblocks = numblocks;
 899     pre_comp->w = w;
 900     pre_comp->points = points;
 901     points = NULL;
 902     pre_comp->num = num;
 903     SETPRECOMP(group, ec, pre_comp);
 904     pre_comp = NULL;
 905     ret = 1;
 906
 907  err:
 908     if (ctx != NULL)
 909         BN_CTX_end(ctx);
 910     BN_CTX_free(new_ctx);
 911     EC_ec_pre_comp_free(pre_comp);
 912     if (points) {
 913         EC_POINT **p;
 914
 915         for (p = points; *p != NULL; p++)
 916             EC_POINT_free(*p);
 917         OPENSSL_free(points);
 918     }
 919     EC_POINT_free(tmp_point);
 920     EC_POINT_free(base);
 921     return ret;
 922 }
 923
 924 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 925 {
 926     return HAVEPRECOMP(group, ec);
 927 }