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     /*-
 215      * Apply coordinate blinding for EC_POINT.
 216      *
 217      * The underlying EC_METHOD can optionally implement this function:
 218      * ec_point_blind_coordinates() returns 0 in case of errors or 1 on
 219      * success or if coordinate blinding is not implemented for this
 220      * group.
 221      */
 222     if (!ec_point_blind_coordinates(group, s, ctx))
 223         goto err;
 224
 225     /* top bit is a 1, in a fixed pos */
 226     if (!EC_POINT_copy(r, s))
 227         goto err;
 228
 229     EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
 230
 231     if (!EC_POINT_dbl(group, s, s, ctx))
 232         goto err;
 233
 234     pbit = 0;
 235
 236 #define EC_POINT_CSWAP(c, a, b, w, t) do {         \
 237         BN_consttime_swap(c, (a)->X, (b)->X, w);   \
 238         BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
 239         BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
 240         t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
 241         (a)->Z_is_one ^= (t);                      \
 242         (b)->Z_is_one ^= (t);                      \
 243 } while(0)
 244
 245     /*-
 246      * The ladder step, with branches, is
 247      *
 248      * k[i] == 0: S = add(R, S), R = dbl(R)
 249      * k[i] == 1: R = add(S, R), S = dbl(S)
 250      *
 251      * Swapping R, S conditionally on k[i] leaves you with state
 252      *
 253      * k[i] == 0: T, U = R, S
 254      * k[i] == 1: T, U = S, R
 255      *
 256      * Then perform the ECC ops.
 257      *
 258      * U = add(T, U)
 259      * T = dbl(T)
 260      *
 261      * Which leaves you with state
 262      *
 263      * k[i] == 0: U = add(R, S), T = dbl(R)
 264      * k[i] == 1: U = add(S, R), T = dbl(S)
 265      *
 266      * Swapping T, U conditionally on k[i] leaves you with state
 267      *
 268      * k[i] == 0: R, S = T, U
 269      * k[i] == 1: R, S = U, T
 270      *
 271      * Which leaves you with state
 272      *
 273      * k[i] == 0: S = add(R, S), R = dbl(R)
 274      * k[i] == 1: R = add(S, R), S = dbl(S)
 275      *
 276      * So we get the same logic, but instead of a branch it's a
 277      * conditional swap, followed by ECC ops, then another conditional swap.
 278      *
 279      * Optimization: The end of iteration i and start of i-1 looks like
 280      *
 281      * ...
 282      * CSWAP(k[i], R, S)
 283      * ECC
 284      * CSWAP(k[i], R, S)
 285      * (next iteration)
 286      * CSWAP(k[i-1], R, S)
 287      * ECC
 288      * CSWAP(k[i-1], R, S)
 289      * ...
 290      *
 291      * So instead of two contiguous swaps, you can merge the condition
 292      * bits and do a single swap.
 293      *
 294      * k[i]   k[i-1]    Outcome
 295      * 0      0         No Swap
 296      * 0      1         Swap
 297      * 1      0         Swap
 298      * 1      1         No Swap
 299      *
 300      * This is XOR. pbit tracks the previous bit of k.
 301      */
 302
 303     for (i = order_bits - 1; i >= 0; i--) {
 304         kbit = BN_is_bit_set(k, i) ^ pbit;
 305         EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
 306         if (!EC_POINT_add(group, s, r, s, ctx))
 307             goto err;
 308         if (!EC_POINT_dbl(group, r, r, ctx))
 309             goto err;
 310         /*
 311          * pbit logic merges this cswap with that of the
 312          * next iteration
 313          */
 314         pbit ^= kbit;
 315     }
 316     /* one final cswap to move the right value into r */
 317     EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
 318 #undef EC_POINT_CSWAP
 319
 320     ret = 1;
 321
 322  err:
 323     EC_POINT_free(s);
 324     BN_CTX_end(ctx);
 325     BN_CTX_free(new_ctx);
 326
 327     return ret;
 328 }
 329
 330 #undef EC_POINT_BN_set_flags
 331
 332 /*
 333  * TODO: table should be optimised for the wNAF-based implementation,
 334  * sometimes smaller windows will give better performance (thus the
 335  * boundaries should be increased)
 336  */
 337 #define EC_window_bits_for_scalar_size(b) \
 338                 ((size_t) \
 339                  ((b) >= 2000 ? 6 : \
 340                   (b) >=  800 ? 5 : \
 341                   (b) >=  300 ? 4 : \
 342                   (b) >=   70 ? 3 : \
 343                   (b) >=   20 ? 2 : \
 344                   1))
 345
 346 /*-
 347  * Compute
 348  *      \sum scalars[i]*points[i],
 349  * also including
 350  *      scalar*generator
 351  * in the addition if scalar != NULL
 352  */
 353 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 354                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 355                 BN_CTX *ctx)
 356 {
 357     BN_CTX *new_ctx = NULL;
 358     const EC_POINT *generator = NULL;
 359     EC_POINT *tmp = NULL;
 360     size_t totalnum;
 361     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 362     size_t pre_points_per_block = 0;
 363     size_t i, j;
 364     int k;
 365     int r_is_inverted = 0;
 366     int r_is_at_infinity = 1;
 367     size_t *wsize = NULL;       /* individual window sizes */
 368     signed char **wNAF = NULL;  /* individual wNAFs */
 369     size_t *wNAF_len = NULL;
 370     size_t max_len = 0;
 371     size_t num_val;
 372     EC_POINT **val = NULL;      /* precomputation */
 373     EC_POINT **v;
 374     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 375                                  * 'pre_comp->points' */
 376     const EC_PRE_COMP *pre_comp = NULL;
 377     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 378                                  * treated like other scalars, i.e.
 379                                  * precomputation is not available */
 380     int ret = 0;
 381
 382     if (!ec_point_is_compat(r, group)) {
 383         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 384         return 0;
 385     }
 386
 387     if ((scalar == NULL) && (num == 0)) {
 388         return EC_POINT_set_to_infinity(group, r);
 389     }
 390
 391     /*-
 392      * Handle the common cases where the scalar is secret, enforcing a constant
 393      * time scalar multiplication algorithm.
 394      */
 395     if ((scalar != NULL) && (num == 0)) {
 396         /*-
 397          * In this case we want to compute scalar * GeneratorPoint: this
 398          * codepath is reached most prominently by (ephemeral) key generation
 399          * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
 400          * keygen/first half), where the scalar is always secret. This is why
 401          * we ignore if BN_FLG_CONSTTIME is actually set and we always call the
 402          * constant time version.
 403          */
 404         return ec_mul_consttime(group, r, scalar, NULL, ctx);
 405     }
 406     if ((scalar == NULL) && (num == 1)) {
 407         /*-
 408          * In this case we want to compute scalar * GenericPoint: this codepath
 409          * is reached most prominently by the second half of ECDH, where the
 410          * secret scalar is multiplied by the peer's public point. To protect
 411          * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
 412          * we always call the constant time version.
 413          */
 414         return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
 415     }
 416
 417     for (i = 0; i < num; i++) {
 418         if (!ec_point_is_compat(points[i], group)) {
 419             ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
 420             return 0;
 421         }
 422     }
 423
 424     if (ctx == NULL) {
 425         ctx = new_ctx = BN_CTX_new();
 426         if (ctx == NULL)
 427             goto err;
 428     }
 429
 430     if (scalar != NULL) {
 431         generator = EC_GROUP_get0_generator(group);
 432         if (generator == NULL) {
 433             ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
 434             goto err;
 435         }
 436
 437         /* look if we can use precomputed multiples of generator */
 438
 439         pre_comp = group->pre_comp.ec;
 440         if (pre_comp && pre_comp->numblocks
 441             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 442                 0)) {
 443             blocksize = pre_comp->blocksize;
 444
 445             /*
 446              * determine maximum number of blocks that wNAF splitting may
 447              * yield (NB: maximum wNAF length is bit length plus one)
 448              */
 449             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 450
 451             /*
 452              * we cannot use more blocks than we have precomputation for
 453              */
 454             if (numblocks > pre_comp->numblocks)
 455                 numblocks = pre_comp->numblocks;
 456
 457             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 458
 459             /* check that pre_comp looks sane */
 460             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 461                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 462                 goto err;
 463             }
 464         } else {
 465             /* can't use precomputation */
 466             pre_comp = NULL;
 467             numblocks = 1;
 468             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 469                                  * 'scalars' */
 470         }
 471     }
 472
 473     totalnum = num + numblocks;
 474
 475     wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
 476     wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
 477     /* include space for pivot */
 478     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
 479     val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
 480
 481     /* Ensure wNAF is initialised in case we end up going to err */
 482     if (wNAF != NULL)
 483         wNAF[0] = NULL;         /* preliminary pivot */
 484
 485     if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
 486         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 487         goto err;
 488     }
 489
 490     /*
 491      * num_val will be the total number of temporarily precomputed points
 492      */
 493     num_val = 0;
 494
 495     for (i = 0; i < num + num_scalar; i++) {
 496         size_t bits;
 497
 498         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 499         wsize[i] = EC_window_bits_for_scalar_size(bits);
 500         num_val += (size_t)1 << (wsize[i] - 1);
 501         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 502         wNAF[i] =
 503             bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 504                             &wNAF_len[i]);
 505         if (wNAF[i] == NULL)
 506             goto err;
 507         if (wNAF_len[i] > max_len)
 508             max_len = wNAF_len[i];
 509     }
 510
 511     if (numblocks) {
 512         /* we go here iff scalar != NULL */
 513
 514         if (pre_comp == NULL) {
 515             if (num_scalar != 1) {
 516                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 517                 goto err;
 518             }
 519             /* we have already generated a wNAF for 'scalar' */
 520         } else {
 521             signed char *tmp_wNAF = NULL;
 522             size_t tmp_len = 0;
 523
 524             if (num_scalar != 0) {
 525                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 526                 goto err;
 527             }
 528
 529             /*
 530              * use the window size for which we have precomputation
 531              */
 532             wsize[num] = pre_comp->w;
 533             tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 534             if (!tmp_wNAF)
 535                 goto err;
 536
 537             if (tmp_len <= max_len) {
 538                 /*
 539                  * One of the other wNAFs is at least as long as the wNAF
 540                  * belonging to the generator, so wNAF splitting will not buy
 541                  * us anything.
 542                  */
 543
 544                 numblocks = 1;
 545                 totalnum = num + 1; /* don't use wNAF splitting */
 546                 wNAF[num] = tmp_wNAF;
 547                 wNAF[num + 1] = NULL;
 548                 wNAF_len[num] = tmp_len;
 549                 /*
 550                  * pre_comp->points starts with the points that we need here:
 551                  */
 552                 val_sub[num] = pre_comp->points;
 553             } else {
 554                 /*
 555                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 556                  * splitting and include the blocks
 557                  */
 558
 559                 signed char *pp;
 560                 EC_POINT **tmp_points;
 561
 562                 if (tmp_len < numblocks * blocksize) {
 563                     /*
 564                      * possibly we can do with fewer blocks than estimated
 565                      */
 566                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 567                     if (numblocks > pre_comp->numblocks) {
 568                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 569                         OPENSSL_free(tmp_wNAF);
 570                         goto err;
 571                     }
 572                     totalnum = num + numblocks;
 573                 }
 574
 575                 /* split wNAF in 'numblocks' parts */
 576                 pp = tmp_wNAF;
 577                 tmp_points = pre_comp->points;
 578
 579                 for (i = num; i < totalnum; i++) {
 580                     if (i < totalnum - 1) {
 581                         wNAF_len[i] = blocksize;
 582                         if (tmp_len < blocksize) {
 583                             ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 584                             OPENSSL_free(tmp_wNAF);
 585                             goto err;
 586                         }
 587                         tmp_len -= blocksize;
 588                     } else
 589                         /*
 590                          * last block gets whatever is left (this could be
 591                          * more or less than 'blocksize'!)
 592                          */
 593                         wNAF_len[i] = tmp_len;
 594
 595                     wNAF[i + 1] = NULL;
 596                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 597                     if (wNAF[i] == NULL) {
 598                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 599                         OPENSSL_free(tmp_wNAF);
 600                         goto err;
 601                     }
 602                     memcpy(wNAF[i], pp, wNAF_len[i]);
 603                     if (wNAF_len[i] > max_len)
 604                         max_len = wNAF_len[i];
 605
 606                     if (*tmp_points == NULL) {
 607                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 608                         OPENSSL_free(tmp_wNAF);
 609                         goto err;
 610                     }
 611                     val_sub[i] = tmp_points;
 612                     tmp_points += pre_points_per_block;
 613                     pp += blocksize;
 614                 }
 615                 OPENSSL_free(tmp_wNAF);
 616             }
 617         }
 618     }
 619
 620     /*
 621      * All points we precompute now go into a single array 'val'.
 622      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 623      * subarray of 'pre_comp->points' if we already have precomputation.
 624      */
 625     val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
 626     if (val == NULL) {
 627         ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
 628         goto err;
 629     }
 630     val[num_val] = NULL;        /* pivot element */
 631
 632     /* allocate points for precomputation */
 633     v = val;
 634     for (i = 0; i < num + num_scalar; i++) {
 635         val_sub[i] = v;
 636         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 637             *v = EC_POINT_new(group);
 638             if (*v == NULL)
 639                 goto err;
 640             v++;
 641         }
 642     }
 643     if (!(v == val + num_val)) {
 644         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
 645         goto err;
 646     }
 647
 648     if ((tmp = EC_POINT_new(group)) == NULL)
 649         goto err;
 650
 651     /*-
 652      * prepare precomputed values:
 653      *    val_sub[i][0] :=     points[i]
 654      *    val_sub[i][1] := 3 * points[i]
 655      *    val_sub[i][2] := 5 * points[i]
 656      *    ...
 657      */
 658     for (i = 0; i < num + num_scalar; i++) {
 659         if (i < num) {
 660             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 661                 goto err;
 662         } else {
 663             if (!EC_POINT_copy(val_sub[i][0], generator))
 664                 goto err;
 665         }
 666
 667         if (wsize[i] > 1) {
 668             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 669                 goto err;
 670             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 671                 if (!EC_POINT_add
 672                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 673                     goto err;
 674             }
 675         }
 676     }
 677
 678     if (!EC_POINTs_make_affine(group, num_val, val, ctx))
 679         goto err;
 680
 681     r_is_at_infinity = 1;
 682
 683     for (k = max_len - 1; k >= 0; k--) {
 684         if (!r_is_at_infinity) {
 685             if (!EC_POINT_dbl(group, r, r, ctx))
 686                 goto err;
 687         }
 688
 689         for (i = 0; i < totalnum; i++) {
 690             if (wNAF_len[i] > (size_t)k) {
 691                 int digit = wNAF[i][k];
 692                 int is_neg;
 693
 694                 if (digit) {
 695                     is_neg = digit < 0;
 696
 697                     if (is_neg)
 698                         digit = -digit;
 699
 700                     if (is_neg != r_is_inverted) {
 701                         if (!r_is_at_infinity) {
 702                             if (!EC_POINT_invert(group, r, ctx))
 703                                 goto err;
 704                         }
 705                         r_is_inverted = !r_is_inverted;
 706                     }
 707
 708                     /* digit > 0 */
 709
 710                     if (r_is_at_infinity) {
 711                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 712                             goto err;
 713                         r_is_at_infinity = 0;
 714                     } else {
 715                         if (!EC_POINT_add
 716                             (group, r, r, val_sub[i][digit >> 1], ctx))
 717                             goto err;
 718                     }
 719                 }
 720             }
 721         }
 722     }
 723
 724     if (r_is_at_infinity) {
 725         if (!EC_POINT_set_to_infinity(group, r))
 726             goto err;
 727     } else {
 728         if (r_is_inverted)
 729             if (!EC_POINT_invert(group, r, ctx))
 730                 goto err;
 731     }
 732
 733     ret = 1;
 734
 735  err:
 736     BN_CTX_free(new_ctx);
 737     EC_POINT_free(tmp);
 738     OPENSSL_free(wsize);
 739     OPENSSL_free(wNAF_len);
 740     if (wNAF != NULL) {
 741         signed char **w;
 742
 743         for (w = wNAF; *w != NULL; w++)
 744             OPENSSL_free(*w);
 745
 746         OPENSSL_free(wNAF);
 747     }
 748     if (val != NULL) {
 749         for (v = val; *v != NULL; v++)
 750             EC_POINT_clear_free(*v);
 751
 752         OPENSSL_free(val);
 753     }
 754     OPENSSL_free(val_sub);
 755     return ret;
 756 }
 757
 758 /*-
 759  * ec_wNAF_precompute_mult()
 760  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 761  * for use with wNAF splitting as implemented in ec_wNAF_mul().
 762  *
 763  * 'pre_comp->points' is an array of multiples of the generator
 764  * of the following form:
 765  * points[0] =     generator;
 766  * points[1] = 3 * generator;
 767  * ...
 768  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 769  * points[2^(w-1)]   =     2^blocksize * generator;
 770  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 771  * ...
 772  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 773  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 774  * ...
 775  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 776  * points[2^(w-1)*numblocks]       = NULL
 777  */
 778 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 779 {
 780     const EC_POINT *generator;
 781     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 782     BN_CTX *new_ctx = NULL;
 783     const BIGNUM *order;
 784     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 785     EC_POINT **points = NULL;
 786     EC_PRE_COMP *pre_comp;
 787     int ret = 0;
 788
 789     /* if there is an old EC_PRE_COMP object, throw it away */
 790     EC_pre_comp_free(group);
 791     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 792         return 0;
 793
 794     generator = EC_GROUP_get0_generator(group);
 795     if (generator == NULL) {
 796         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
 797         goto err;
 798     }
 799
 800     if (ctx == NULL) {
 801         ctx = new_ctx = BN_CTX_new();
 802         if (ctx == NULL)
 803             goto err;
 804     }
 805
 806     BN_CTX_start(ctx);
 807
 808     order = EC_GROUP_get0_order(group);
 809     if (order == NULL)
 810         goto err;
 811     if (BN_is_zero(order)) {
 812         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
 813         goto err;
 814     }
 815
 816     bits = BN_num_bits(order);
 817     /*
 818      * The following parameters mean we precompute (approximately) one point
 819      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 820      * bit lengths, other parameter combinations might provide better
 821      * efficiency.
 822      */
 823     blocksize = 8;
 824     w = 4;
 825     if (EC_window_bits_for_scalar_size(bits) > w) {
 826         /* let's not make the window too small ... */
 827         w = EC_window_bits_for_scalar_size(bits);
 828     }
 829
 830     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 831                                                      * to use for wNAF
 832                                                      * splitting */
 833
 834     pre_points_per_block = (size_t)1 << (w - 1);
 835     num = pre_points_per_block * numblocks; /* number of points to compute
 836                                              * and store */
 837
 838     points = OPENSSL_malloc(sizeof(*points) * (num + 1));
 839     if (points == NULL) {
 840         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 841         goto err;
 842     }
 843
 844     var = points;
 845     var[num] = NULL;            /* pivot */
 846     for (i = 0; i < num; i++) {
 847         if ((var[i] = EC_POINT_new(group)) == NULL) {
 848             ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 849             goto err;
 850         }
 851     }
 852
 853     if ((tmp_point = EC_POINT_new(group)) == NULL
 854         || (base = EC_POINT_new(group)) == NULL) {
 855         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
 856         goto err;
 857     }
 858
 859     if (!EC_POINT_copy(base, generator))
 860         goto err;
 861
 862     /* do the precomputation */
 863     for (i = 0; i < numblocks; i++) {
 864         size_t j;
 865
 866         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 867             goto err;
 868
 869         if (!EC_POINT_copy(*var++, base))
 870             goto err;
 871
 872         for (j = 1; j < pre_points_per_block; j++, var++) {
 873             /*
 874              * calculate odd multiples of the current base point
 875              */
 876             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 877                 goto err;
 878         }
 879
 880         if (i < numblocks - 1) {
 881             /*
 882              * get the next base (multiply current one by 2^blocksize)
 883              */
 884             size_t k;
 885
 886             if (blocksize <= 2) {
 887                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
 888                 goto err;
 889             }
 890
 891             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 892                 goto err;
 893             for (k = 2; k < blocksize; k++) {
 894                 if (!EC_POINT_dbl(group, base, base, ctx))
 895                     goto err;
 896             }
 897         }
 898     }
 899
 900     if (!EC_POINTs_make_affine(group, num, points, ctx))
 901         goto err;
 902
 903     pre_comp->group = group;
 904     pre_comp->blocksize = blocksize;
 905     pre_comp->numblocks = numblocks;
 906     pre_comp->w = w;
 907     pre_comp->points = points;
 908     points = NULL;
 909     pre_comp->num = num;
 910     SETPRECOMP(group, ec, pre_comp);
 911     pre_comp = NULL;
 912     ret = 1;
 913
 914  err:
 915     if (ctx != NULL)
 916         BN_CTX_end(ctx);
 917     BN_CTX_free(new_ctx);
 918     EC_ec_pre_comp_free(pre_comp);
 919     if (points) {
 920         EC_POINT **p;
 921
 922         for (p = points; *p != NULL; p++)
 923             EC_POINT_free(*p);
 924         OPENSSL_free(points);
 925     }
 926     EC_POINT_free(tmp_point);
 927     EC_POINT_free(base);
 928     return ret;
 929 }
 930
 931 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 932 {
 933     return HAVEPRECOMP(group, ec);
 934 }