crypto/ec/ec_mult.c

   1 /*
   2  * Copyright 2001-2018 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     order_bits = BN_num_bits(group->order);
 146
 147     s = EC_POINT_new(group);
 148     if (s == NULL)
 149         goto err;
 150
 151     if (point == NULL) {
 152         if (!EC_POINT_copy(s, group->generator))
 153             goto err;
 154     } else {
 155         if (!EC_POINT_copy(s, point))
 156             goto err;
 157     }
 158
 159     EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
 160
 161     BN_CTX_start(ctx);
 162     lambda = BN_CTX_get(ctx);
 163     k = BN_CTX_get(ctx);
 164     if (k == NULL)
 165         goto err;
 166
 167     /*
 168      * Group orders are often on a word boundary.
 169      * So when we pad the scalar, some timing diff might
 170      * pop if it needs to be expanded due to carries.
 171      * So expand ahead of time.
 172      */
 173     group_top = bn_get_top(group->order);
 174     if ((bn_wexpand(k, group_top + 1) == NULL)
 175         || (bn_wexpand(lambda, group_top + 1) == NULL))
 176         goto err;
 177
 178     if (!BN_copy(k, scalar))
 179         goto err;
 180
 181     BN_set_flags(k, BN_FLG_CONSTTIME);
 182
 183     if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
 184         /*-
 185          * this is an unusual input, and we don't guarantee
 186          * constant-timeness
 187          */
 188         if (!BN_nnmod(k, k, group->order, ctx))
 189             goto err;
 190     }
 191
 192     if (!BN_add(lambda, k, group->order))
 193         goto err;
 194     BN_set_flags(lambda, BN_FLG_CONSTTIME);
 195     if (!BN_add(k, lambda, group->order))
 196         goto err;
 197     /*
 198      * lambda := scalar + order
 199      * k := scalar + 2*order
 200      */
 201     kbit = BN_is_bit_set(lambda, order_bits);
 202     BN_consttime_swap(kbit, k, lambda, group_top + 1);
 203
 204     group_top = bn_get_top(group->field);
 205     if ((bn_wexpand(s->X, group_top) == NULL)
 206         || (bn_wexpand(s->Y, group_top) == NULL)
 207         || (bn_wexpand(s->Z, group_top) == NULL)
 208         || (bn_wexpand(r->X, group_top) == NULL)
 209         || (bn_wexpand(r->Y, group_top) == NULL)
 210         || (bn_wexpand(r->Z, group_top) == NULL))
 211         goto err;
 212
 213     /* top bit is a 1, in a fixed pos */
 214     if (!EC_POINT_copy(r, s))
 215         goto err;
 216
 217     EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
 218
 219     if (!EC_POINT_dbl(group, s, s, ctx))
 220         goto err;
 221
 222     pbit = 0;
 223
 224 #define EC_POINT_CSWAP(c, a, b, w, t) do {         \
 225         BN_consttime_swap(c, (a)->X, (b)->X, w);   \
 226         BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
 227         BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
 228         t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
 229         (a)->Z_is_one ^= (t);                      \
 230         (b)->Z_is_one ^= (t);                      \
 231 } while(0)
 232
 233     /*-
 234      * The ladder step, with branches, is
 235      *
 236      * k[i] == 0: S = add(R, S), R = dbl(R)
 237      * k[i] == 1: R = add(S, R), S = dbl(S)
 238      *
 239      * Swapping R, S conditionally on k[i] leaves you with state
 240      *
 241      * k[i] == 0: T, U = R, S
 242      * k[i] == 1: T, U = S, R
 243      *
 244      * Then perform the ECC ops.
 245      *
 246      * U = add(T, U)
 247      * T = dbl(T)
 248      *
 249      * Which leaves you with state
 250      *
 251      * k[i] == 0: U = add(R, S), T = dbl(R)
 252      * k[i] == 1: U = add(S, R), T = dbl(S)
 253      *
 254      * Swapping T, U conditionally on k[i] leaves you with state
 255      *
 256      * k[i] == 0: R, S = T, U
 257      * k[i] == 1: R, S = U, T
 258      *
 259      * Which leaves you with state
 260      *
 261      * k[i] == 0: S = add(R, S), R = dbl(R)
 262      * k[i] == 1: R = add(S, R), S = dbl(S)
 263      *
 264      * So we get the same logic, but instead of a branch it's a
 265      * conditional swap, followed by ECC ops, then another conditional swap.
 266      *
 267      * Optimization: The end of iteration i and start of i-1 looks like
 268      *
 269      * ...
 270      * CSWAP(k[i], R, S)
 271      * ECC
 272      * CSWAP(k[i], R, S)
 273      * (next iteration)
 274      * CSWAP(k[i-1], R, S)
 275      * ECC
 276      * CSWAP(k[i-1], R, S)
 277      * ...
 278      *
 279      * So instead of two contiguous swaps, you can merge the condition
 280      * bits and do a single swap.
 281      *
 282      * k[i]   k[i-1]    Outcome
 283      * 0      0         No Swap
 284      * 0      1         Swap
 285      * 1      0         Swap
 286      * 1      1         No Swap
 287      *
 288      * This is XOR. pbit tracks the previous bit of k.
 289      */
 290
 291     for (i = order_bits - 1; i >= 0; i--) {
 292         kbit = BN_is_bit_set(k, i) ^ pbit;
 293         EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
 294         if (!EC_POINT_add(group, s, r, s, ctx))
 295             goto err;
 296         if (!EC_POINT_dbl(group, r, r, ctx))
 297             goto err;
 298         /*
 299          * pbit logic merges this cswap with that of the
 300          * next iteration
 301          */
 302         pbit ^= kbit;
 303     }
 304     /* one final cswap to move the right value into r */
 305     EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
 306 #undef EC_POINT_CSWAP
 307
 308     ret = 1;
 309
 310  err:
 311     EC_POINT_free(s);
 312     BN_CTX_end(ctx);
 313     BN_CTX_free(new_ctx);
 314
 315     return ret;
 316 }
 317
 318 #undef EC_POINT_BN_set_flags
 319
 320 /*
 321  * TODO: table should be optimised for the wNAF-based implementation,
 322  * sometimes smaller windows will give better performance (thus the
 323  * boundaries should be increased)
 324  */
 325 #define EC_window_bits_for_scalar_size(b) \
 326                 ((size_t) \
 327                  ((b) >= 2000 ? 6 : \
 328                   (b) >=  800 ? 5 : \
 329                   (b) >=  300 ? 4 : \
 330                   (b) >=   70 ? 3 : \
 331                   (b) >=   20 ? 2 : \
 332                   1))
 333
 334 /*-
 335  * Compute
 336  *      \sum scalars[i]*points[i],
 337  * also including
 338  *      scalar*generator
 339  * in the addition if scalar != NULL
 340  */
 341 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 342                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 343                 BN_CTX *ctx)
 344 {
 345     BN_CTX *new_ctx = NULL;
 346     const EC_POINT *generator = NULL;
 347     EC_POINT *tmp = NULL;
 348     size_t totalnum;
 349     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 350     size_t pre_points_per_block = 0;
 351     size_t i, j;
 352     int k;
 353     int r_is_inverted = 0;
 354     int r_is_at_infinity = 1;
 355     size_t *wsize = NULL;       /* individual window sizes */
 356     signed char **wNAF = NULL;  /* individual wNAFs */
 357     size_t *wNAF_len = NULL;
 358     size_t max_len = 0;
 359     size_t num_val;
 360     EC_POINT **val = NULL;      /* precomputation */
 361     EC_POINT **v;
 362     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 363                                  * 'pre_comp->points' */
 364     const EC_PRE_COMP *pre_comp = NULL;
 365     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 366                                  * treated like other scalars, i.e.
 367                                  * precomputation is not available */
 368     int ret = 0;
 369
 370     if (group->meth != r->meth) {
 371         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 372         return 0;
 373     }
 374
 375     if ((scalar == NULL) && (num == 0)) {
 376         return EC_POINT_set_to_infinity(group, r);
 377     }
 378
 379     /*-
 380      * Handle the common cases where the scalar is secret, enforcing a constant
 381      * time scalar multiplication algorithm.
 382      */
 383     if ((scalar != NULL) && (num == 0)) {
 384         /*-
 385          * In this case we want to compute scalar * GeneratorPoint: this
 386          * codepath is reached most prominently by (ephemeral) key generation
 387          * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
 388          * keygen/first half), where the scalar is always secret. This is why
 389          * we ignore if BN_FLG_CONSTTIME is actually set and we always call the
 390          * constant time version.
 391          */
 392         return ec_mul_consttime(group, r, scalar, NULL, ctx);
 393     }
 394     if ((scalar == NULL) && (num == 1)) {
 395         /*-
 396          * In this case we want to compute scalar * GenericPoint: this codepath
 397          * is reached most prominently by the second half of ECDH, where the
 398          * secret scalar is multiplied by the peer's public point. To protect
 399          * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
 400          * we always call the constant time version.
 401          */
 402         return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
 403     }
 404
 405     for (i = 0; i < num; i++) {
 406         if (group->meth != points[i]->meth) {
 407             ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 408             return 0;
 409         }
 410     }
 411
 412     if (ctx == NULL) {
 413         ctx = new_ctx = BN_CTX_new();
 414         if (ctx == NULL)
 415             goto err;
 416     }
 417
 418     if (scalar != NULL) {
 419         generator = EC_GROUP_get0_generator(group);
 420         if (generator == NULL) {
 421             ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 422             goto err;
 423         }
 424
 425         /* look if we can use precomputed multiples of generator */
 426
 427         pre_comp = group->pre_comp.ec;
 428         if (pre_comp && pre_comp->numblocks
 429             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 430                 0)) {
 431             blocksize = pre_comp->blocksize;
 432
 433             /*
 434              * determine maximum number of blocks that wNAF splitting may
 435              * yield (NB: maximum wNAF length is bit length plus one)
 436              */
 437             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 438
 439             /*
 440              * we cannot use more blocks than we have precomputation for
 441              */
 442             if (numblocks > pre_comp->numblocks)
 443                 numblocks = pre_comp->numblocks;
 444
 445             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 446
 447             /* check that pre_comp looks sane */
 448             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 449                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 450                 goto err;
 451             }
 452         } else {
 453             /* can't use precomputation */
 454             pre_comp = NULL;
 455             numblocks = 1;
 456             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 457                                  * 'scalars' */
 458         }
 459     }
 460
 461     totalnum = num + numblocks;
 462
 463     wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
 464     wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
 465     /* include space for pivot */
 466     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
 467     val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
 468
 469     /* Ensure wNAF is initialised in case we end up going to err */
 470     if (wNAF != NULL)
 471         wNAF[0] = NULL;         /* preliminary pivot */
 472
 473     if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
 474         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 475         goto err;
 476     }
 477
 478     /*
 479      * num_val will be the total number of temporarily precomputed points
 480      */
 481     num_val = 0;
 482
 483     for (i = 0; i < num + num_scalar; i++) {
 484         size_t bits;
 485
 486         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 487         wsize[i] = EC_window_bits_for_scalar_size(bits);
 488         num_val += (size_t)1 << (wsize[i] - 1);
 489         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 490         wNAF[i] =
 491             bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 492                             &wNAF_len[i]);
 493         if (wNAF[i] == NULL)
 494             goto err;
 495         if (wNAF_len[i] > max_len)
 496             max_len = wNAF_len[i];
 497     }
 498
 499     if (numblocks) {
 500         /* we go here iff scalar != NULL */
 501
 502         if (pre_comp == NULL) {
 503             if (num_scalar != 1) {
 504                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 505                 goto err;
 506             }
 507             /* we have already generated a wNAF for 'scalar' */
 508         } else {
 509             signed char *tmp_wNAF = NULL;
 510             size_t tmp_len = 0;
 511
 512             if (num_scalar != 0) {
 513                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 514                 goto err;
 515             }
 516
 517             /*
 518              * use the window size for which we have precomputation
 519              */
 520             wsize[num] = pre_comp->w;
 521             tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 522             if (!tmp_wNAF)
 523                 goto err;
 524
 525             if (tmp_len <= max_len) {
 526                 /*
 527                  * One of the other wNAFs is at least as long as the wNAF
 528                  * belonging to the generator, so wNAF splitting will not buy
 529                  * us anything.
 530                  */
 531
 532                 numblocks = 1;
 533                 totalnum = num + 1; /* don't use wNAF splitting */
 534                 wNAF[num] = tmp_wNAF;
 535                 wNAF[num + 1] = NULL;
 536                 wNAF_len[num] = tmp_len;
 537                 /*
 538                  * pre_comp->points starts with the points that we need here:
 539                  */
 540                 val_sub[num] = pre_comp->points;
 541             } else {
 542                 /*
 543                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 544                  * splitting and include the blocks
 545                  */
 546
 547                 signed char *pp;
 548                 EC_POINT **tmp_points;
 549
 550                 if (tmp_len < numblocks * blocksize) {
 551                     /*
 552                      * possibly we can do with fewer blocks than estimated
 553                      */
 554                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 555                     if (numblocks > pre_comp->numblocks) {
 556                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 557                         OPENSSL_free(tmp_wNAF);
 558                         goto err;
 559                     }
 560                     totalnum = num + numblocks;
 561                 }
 562
 563                 /* split wNAF in 'numblocks' parts */
 564                 pp = tmp_wNAF;
 565                 tmp_points = pre_comp->points;
 566
 567                 for (i = num; i < totalnum; i++) {
 568                     if (i < totalnum - 1) {
 569                         wNAF_len[i] = blocksize;
 570                         if (tmp_len < blocksize) {
 571                             ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 572                             OPENSSL_free(tmp_wNAF);
 573                             goto err;
 574                         }
 575                         tmp_len -= blocksize;
 576                     } else
 577                         /*
 578                          * last block gets whatever is left (this could be
 579                          * more or less than 'blocksize'!)
 580                          */
 581                         wNAF_len[i] = tmp_len;
 582
 583                     wNAF[i + 1] = NULL;
 584                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 585                     if (wNAF[i] == NULL) {
 586                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 587                         OPENSSL_free(tmp_wNAF);
 588                         goto err;
 589                     }
 590                     memcpy(wNAF[i], pp, wNAF_len[i]);
 591                     if (wNAF_len[i] > max_len)
 592                         max_len = wNAF_len[i];
 593
 594                     if (*tmp_points == NULL) {
 595                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 596                         OPENSSL_free(tmp_wNAF);
 597                         goto err;
 598                     }
 599                     val_sub[i] = tmp_points;
 600                     tmp_points += pre_points_per_block;
 601                     pp += blocksize;
 602                 }
 603                 OPENSSL_free(tmp_wNAF);
 604             }
 605         }
 606     }
 607
 608     /*
 609      * All points we precompute now go into a single array 'val'.
 610      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 611      * subarray of 'pre_comp->points' if we already have precomputation.
 612      */
 613     val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
 614     if (val == NULL) {
 615         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 616         goto err;
 617     }
 618     val[num_val] = NULL;        /* pivot element */
 619
 620     /* allocate points for precomputation */
 621     v = val;
 622     for (i = 0; i < num + num_scalar; i++) {
 623         val_sub[i] = v;
 624         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 625             *v = EC_POINT_new(group);
 626             if (*v == NULL)
 627                 goto err;
 628             v++;
 629         }
 630     }
 631     if (!(v == val + num_val)) {
 632         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 633         goto err;
 634     }
 635
 636     if ((tmp = EC_POINT_new(group)) == NULL)
 637         goto err;
 638
 639     /*-
 640      * prepare precomputed values:
 641      *    val_sub[i][0] :=     points[i]
 642      *    val_sub[i][1] := 3 * points[i]
 643      *    val_sub[i][2] := 5 * points[i]
 644      *    ...
 645      */
 646     for (i = 0; i < num + num_scalar; i++) {
 647         if (i < num) {
 648             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 649                 goto err;
 650         } else {
 651             if (!EC_POINT_copy(val_sub[i][0], generator))
 652                 goto err;
 653         }
 654
 655         if (wsize[i] > 1) {
 656             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 657                 goto err;
 658             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 659                 if (!EC_POINT_add
 660                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 661                     goto err;
 662             }
 663         }
 664     }
 665
 666     if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 667         goto err;
 668
 669     r_is_at_infinity = 1;
 670
 671     for (k = max_len - 1; k >= 0; k--) {
 672         if (!r_is_at_infinity) {
 673             if (!EC_POINT_dbl(group, r, r, ctx))
 674                 goto err;
 675         }
 676
 677         for (i = 0; i < totalnum; i++) {
 678             if (wNAF_len[i] > (size_t)k) {
 679                 int digit = wNAF[i][k];
 680                 int is_neg;
 681
 682                 if (digit) {
 683                     is_neg = digit < 0;
 684
 685                     if (is_neg)
 686                         digit = -digit;
 687
 688                     if (is_neg != r_is_inverted) {
 689                         if (!r_is_at_infinity) {
 690                             if (!EC_POINT_invert(group, r, ctx))
 691                                 goto err;
 692                         }
 693                         r_is_inverted = !r_is_inverted;
 694                     }
 695
 696                     /* digit > 0 */
 697
 698                     if (r_is_at_infinity) {
 699                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 700                             goto err;
 701                         r_is_at_infinity = 0;
 702                     } else {
 703                         if (!EC_POINT_add
 704                             (group, r, r, val_sub[i][digit >> 1], ctx))
 705                             goto err;
 706                     }
 707                 }
 708             }
 709         }
 710     }
 711
 712     if (r_is_at_infinity) {
 713         if (!EC_POINT_set_to_infinity(group, r))
 714             goto err;
 715     } else {
 716         if (r_is_inverted)
 717             if (!EC_POINT_invert(group, r, ctx))
 718                 goto err;
 719     }
 720
 721     ret = 1;
 722
 723  err:
 724     BN_CTX_free(new_ctx);
 725     EC_POINT_free(tmp);
 726     OPENSSL_free(wsize);
 727     OPENSSL_free(wNAF_len);
 728     if (wNAF != NULL) {
 729         signed char **w;
 730
 731         for (w = wNAF; *w != NULL; w++)
 732             OPENSSL_free(*w);
 733
 734         OPENSSL_free(wNAF);
 735     }
 736     if (val != NULL) {
 737         for (v = val; *v != NULL; v++)
 738             EC_POINT_clear_free(*v);
 739
 740         OPENSSL_free(val);
 741     }
 742     OPENSSL_free(val_sub);
 743     return ret;
 744 }
 745
 746 /*-
 747  * ec_wNAF_precompute_mult()
 748  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 749  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 750  *
 751  * 'pre_comp->points' is an array of multiples of the generator
 752  * of the following form:
 753  * points[0] =     generator;
 754  * points[1] = 3 * generator;
 755  * ...
 756  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 757  * points[2^(w-1)]   =     2^blocksize * generator;
 758  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 759  * ...
 760  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 761  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 762  * ...
 763  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 764  * points[2^(w-1)*numblocks]       = NULL
 765  */
 766 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 767 {
 768     const EC_POINT *generator;
 769     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 770     BN_CTX *new_ctx = NULL;
 771     const BIGNUM *order;
 772     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 773     EC_POINT **points = NULL;
 774     EC_PRE_COMP *pre_comp;
 775     int ret = 0;
 776
 777     /* if there is an old EC_PRE_COMP object, throw it away */
 778     EC_pre_comp_free(group);
 779     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 780         return 0;
 781
 782     generator = EC_GROUP_get0_generator(group);
 783     if (generator == NULL) {
 784         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 785         goto err;
 786     }
 787
 788     if (ctx == NULL) {
 789         ctx = new_ctx = BN_CTX_new();
 790         if (ctx == NULL)
 791             goto err;
 792     }
 793
 794     BN_CTX_start(ctx);
 795
 796     order = EC_GROUP_get0_order(group);
 797     if (order == NULL)
 798         goto err;
 799     if (BN_is_zero(order)) {
 800         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 801         goto err;
 802     }
 803
 804     bits = BN_num_bits(order);
 805     /*
 806      * The following parameters mean we precompute (approximately) one point
 807      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 808      * bit lengths, other parameter combinations might provide better
 809      * efficiency.
 810      */
 811     blocksize = 8;
 812     w = 4;
 813     if (EC_window_bits_for_scalar_size(bits) > w) {
 814         /* let's not make the window too small ... */
 815         w = EC_window_bits_for_scalar_size(bits);
 816     }
 817
 818     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 819                                                      * to use for wNAF
 820                                                      * splitting */
 821
 822     pre_points_per_block = (size_t)1 << (w - 1);
 823     num = pre_points_per_block * numblocks; /* number of points to compute
 824                                              * and store */
 825
 826     points = OPENSSL_malloc(sizeof(*points) * (num + 1));
 827     if (points == NULL) {
 828         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 829         goto err;
 830     }
 831
 832     var = points;
 833     var[num] = NULL;            /* pivot */
 834     for (i = 0; i < num; i++) {
 835         if ((var[i] = EC_POINT_new(group)) == NULL) {
 836             ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 837             goto err;
 838         }
 839     }
 840
 841     if ((tmp_point = EC_POINT_new(group)) == NULL
 842         || (base = EC_POINT_new(group)) == NULL) {
 843         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 844         goto err;
 845     }
 846
 847     if (!EC_POINT_copy(base, generator))
 848         goto err;
 849
 850     /* do the precomputation */
 851     for (i = 0; i < numblocks; i++) {
 852         size_t j;
 853
 854         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 855             goto err;
 856
 857         if (!EC_POINT_copy(*var++, base))
 858             goto err;
 859
 860         for (j = 1; j < pre_points_per_block; j++, var++) {
 861             /*
 862              * calculate odd multiples of the current base point
 863              */
 864             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 865                 goto err;
 866         }
 867
 868         if (i < numblocks - 1) {
 869             /*
 870              * get the next base (multiply current one by 2^blocksize)
 871              */
 872             size_t k;
 873
 874             if (blocksize <= 2) {
 875                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 876                 goto err;
 877             }
 878
 879             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 880                 goto err;
 881             for (k = 2; k < blocksize; k++) {
 882                 if (!EC_POINT_dbl(group, base, base, ctx))
 883                     goto err;
 884             }
 885         }
 886     }
 887
 888     if (!EC_POINTs_make_affine(group, num, points, ctx))
 889         goto err;
 890
 891     pre_comp->group = group;
 892     pre_comp->blocksize = blocksize;
 893     pre_comp->numblocks = numblocks;
 894     pre_comp->w = w;
 895     pre_comp->points = points;
 896     points = NULL;
 897     pre_comp->num = num;
 898     SETPRECOMP(group, ec, pre_comp);
 899     pre_comp = NULL;
 900     ret = 1;
 901
 902  err:
 903     if (ctx != NULL)
 904         BN_CTX_end(ctx);
 905     BN_CTX_free(new_ctx);
 906     EC_ec_pre_comp_free(pre_comp);
 907     if (points) {
 908         EC_POINT **p;
 909
 910         for (p = points; *p != NULL; p++)
 911             EC_POINT_free(*p);
 912         OPENSSL_free(points);
 913     }
 914     EC_POINT_free(tmp_point);
 915     EC_POINT_free(base);
 916     return ret;
 917 }
 918
 919 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 920 {
 921     return HAVEPRECOMP(group, ec);
 922 }