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