crypto/ec/ec_mult.c

   1 /*
   2  * Copyright 2001-2023 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
   4  *
   5  * Licensed under the Apache License 2.0 (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 /*
  12  * ECDSA low level APIs are deprecated for public use, but still ok for
  13  * internal use.
  14  */
  15 #include "internal/deprecated.h"
  16
  17 #include <string.h>
  18 #include <openssl/err.h>
  19
  20 #include "internal/cryptlib.h"
  21 #include "crypto/bn.h"
  22 #include "ec_local.h"
  23 #include "internal/refcount.h"
  24
  25 /*
  26  * This file implements the wNAF-based interleaving multi-exponentiation method
  27  * Formerly at:
  28  *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
  29  * You might now find it here:
  30  *   http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
  31  *   http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
  32  * For multiplication with precomputation, we use wNAF splitting, formerly at:
  33  *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
  34  */
  35
  36 /* structure for precomputed multiples of the generator */
  37 struct ec_pre_comp_st {
  38     const EC_GROUP *group;      /* parent EC_GROUP object */
  39     size_t blocksize;           /* block size for wNAF splitting */
  40     size_t numblocks;           /* max. number of blocks for which we have
  41                                  * precomputation */
  42     size_t w;                   /* window size */
  43     EC_POINT **points;          /* array with pre-calculated multiples of
  44                                  * generator: 'num' pointers to EC_POINT
  45                                  * objects followed by a NULL */
  46     size_t num;                 /* numblocks * 2^(w-1) */
  47     CRYPTO_REF_COUNT references;
  48 };
  49
  50 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
  51 {
  52     EC_PRE_COMP *ret = NULL;
  53
  54     if (!group)
  55         return NULL;
  56
  57     ret = OPENSSL_zalloc(sizeof(*ret));
  58     if (ret == NULL)
  59         return ret;
  60
  61     ret->group = group;
  62     ret->blocksize = 8;         /* default */
  63     ret->w = 4;                 /* default */
  64
  65     if (!CRYPTO_NEW_REF(&ret->references, 1)) {
  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);
  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);
  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_FREE_REF(&pre->references);
 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 a single point multiplication over the EC group,
 112  * using, at a high level, a Montgomery ladder with conditional swaps, with
 113  * various timing attack defenses.
 114  *
 115  * It performs either a fixed point multiplication
 116  *          (scalar * generator)
 117  * when point is NULL, or a variable point multiplication
 118  *          (scalar * point)
 119  * when point is not NULL.
 120  *
 121  * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
 122  * constant time bets are off (where n is the cardinality of the EC group).
 123  *
 124  * This function expects `group->order` and `group->cardinality` to be well
 125  * defined and non-zero: it fails with an error code otherwise.
 126  *
 127  * NB: This says nothing about the constant-timeness of the ladder step
 128  * implementation (i.e., the default implementation is based on EC_POINT_add and
 129  * EC_POINT_dbl, which of course are not constant time themselves) or the
 130  * underlying multiprecision arithmetic.
 131  *
 132  * The product is stored in `r`.
 133  *
 134  * This is an internal function: callers are in charge of ensuring that the
 135  * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
 136  *
 137  * Returns 1 on success, 0 otherwise.
 138  */
 139 int ossl_ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
 140                               const BIGNUM *scalar, const EC_POINT *point,
 141                               BN_CTX *ctx)
 142 {
 143     int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
 144     EC_POINT *p = NULL;
 145     EC_POINT *s = NULL;
 146     BIGNUM *k = NULL;
 147     BIGNUM *lambda = NULL;
 148     BIGNUM *cardinality = NULL;
 149     int ret = 0;
 150
 151     /* early exit if the input point is the point at infinity */
 152     if (point != NULL && EC_POINT_is_at_infinity(group, point))
 153         return EC_POINT_set_to_infinity(group, r);
 154
 155     if (BN_is_zero(group->order)) {
 156         ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
 157         return 0;
 158     }
 159     if (BN_is_zero(group->cofactor)) {
 160         ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_COFACTOR);
 161         return 0;
 162     }
 163
 164     BN_CTX_start(ctx);
 165
 166     if (((p = EC_POINT_new(group)) == NULL)
 167         || ((s = EC_POINT_new(group)) == NULL)) {
 168         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 169         goto err;
 170     }
 171
 172     if (point == NULL) {
 173         if (!EC_POINT_copy(p, group->generator)) {
 174             ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 175             goto err;
 176         }
 177     } else {
 178         if (!EC_POINT_copy(p, point)) {
 179             ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 180             goto err;
 181         }
 182     }
 183
 184     EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);
 185     EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
 186     EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
 187
 188     cardinality = BN_CTX_get(ctx);
 189     lambda = BN_CTX_get(ctx);
 190     k = BN_CTX_get(ctx);
 191     if (k == NULL) {
 192         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 193         goto err;
 194     }
 195
 196     if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {
 197         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 198         goto err;
 199     }
 200
 201     /*
 202      * Group cardinalities are often on a word boundary.
 203      * So when we pad the scalar, some timing diff might
 204      * pop if it needs to be expanded due to carries.
 205      * So expand ahead of time.
 206      */
 207     cardinality_bits = BN_num_bits(cardinality);
 208     group_top = bn_get_top(cardinality);
 209     if ((bn_wexpand(k, group_top + 2) == NULL)
 210         || (bn_wexpand(lambda, group_top + 2) == NULL)) {
 211         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 212         goto err;
 213     }
 214
 215     if (!BN_copy(k, scalar)) {
 216         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 217         goto err;
 218     }
 219
 220     BN_set_flags(k, BN_FLG_CONSTTIME);
 221
 222     if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
 223         /*-
 224          * this is an unusual input, and we don't guarantee
 225          * constant-timeness
 226          */
 227         if (!BN_nnmod(k, k, cardinality, ctx)) {
 228             ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 229             goto err;
 230         }
 231     }
 232
 233     if (!BN_add(lambda, k, cardinality)) {
 234         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 235         goto err;
 236     }
 237     BN_set_flags(lambda, BN_FLG_CONSTTIME);
 238     if (!BN_add(k, lambda, cardinality)) {
 239         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 240         goto err;
 241     }
 242     /*
 243      * lambda := scalar + cardinality
 244      * k := scalar + 2*cardinality
 245      */
 246     kbit = BN_is_bit_set(lambda, cardinality_bits);
 247     BN_consttime_swap(kbit, k, lambda, group_top + 2);
 248
 249     group_top = bn_get_top(group->field);
 250     if ((bn_wexpand(s->X, group_top) == NULL)
 251         || (bn_wexpand(s->Y, group_top) == NULL)
 252         || (bn_wexpand(s->Z, group_top) == NULL)
 253         || (bn_wexpand(r->X, group_top) == NULL)
 254         || (bn_wexpand(r->Y, group_top) == NULL)
 255         || (bn_wexpand(r->Z, group_top) == NULL)
 256         || (bn_wexpand(p->X, group_top) == NULL)
 257         || (bn_wexpand(p->Y, group_top) == NULL)
 258         || (bn_wexpand(p->Z, group_top) == NULL)) {
 259         ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
 260         goto err;
 261     }
 262
 263     /* ensure input point is in affine coords for ladder step efficiency */
 264     if (!p->Z_is_one && (group->meth->make_affine == NULL
 265                          || !group->meth->make_affine(group, p, ctx))) {
 266             ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 267             goto err;
 268     }
 269
 270     /* Initialize the Montgomery ladder */
 271     if (!ec_point_ladder_pre(group, r, s, p, ctx)) {
 272         ERR_raise(ERR_LIB_EC, EC_R_LADDER_PRE_FAILURE);
 273         goto err;
 274     }
 275
 276     /* top bit is a 1, in a fixed pos */
 277     pbit = 1;
 278
 279 #define EC_POINT_CSWAP(c, a, b, w, t) do {         \
 280         BN_consttime_swap(c, (a)->X, (b)->X, w);   \
 281         BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
 282         BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
 283         t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
 284         (a)->Z_is_one ^= (t);                      \
 285         (b)->Z_is_one ^= (t);                      \
 286 } while(0)
 287
 288     /*-
 289      * The ladder step, with branches, is
 290      *
 291      * k[i] == 0: S = add(R, S), R = dbl(R)
 292      * k[i] == 1: R = add(S, R), S = dbl(S)
 293      *
 294      * Swapping R, S conditionally on k[i] leaves you with state
 295      *
 296      * k[i] == 0: T, U = R, S
 297      * k[i] == 1: T, U = S, R
 298      *
 299      * Then perform the ECC ops.
 300      *
 301      * U = add(T, U)
 302      * T = dbl(T)
 303      *
 304      * Which leaves you with state
 305      *
 306      * k[i] == 0: U = add(R, S), T = dbl(R)
 307      * k[i] == 1: U = add(S, R), T = dbl(S)
 308      *
 309      * Swapping T, U conditionally on k[i] leaves you with state
 310      *
 311      * k[i] == 0: R, S = T, U
 312      * k[i] == 1: R, S = U, T
 313      *
 314      * Which leaves you with state
 315      *
 316      * k[i] == 0: S = add(R, S), R = dbl(R)
 317      * k[i] == 1: R = add(S, R), S = dbl(S)
 318      *
 319      * So we get the same logic, but instead of a branch it's a
 320      * conditional swap, followed by ECC ops, then another conditional swap.
 321      *
 322      * Optimization: The end of iteration i and start of i-1 looks like
 323      *
 324      * ...
 325      * CSWAP(k[i], R, S)
 326      * ECC
 327      * CSWAP(k[i], R, S)
 328      * (next iteration)
 329      * CSWAP(k[i-1], R, S)
 330      * ECC
 331      * CSWAP(k[i-1], R, S)
 332      * ...
 333      *
 334      * So instead of two contiguous swaps, you can merge the condition
 335      * bits and do a single swap.
 336      *
 337      * k[i]   k[i-1]    Outcome
 338      * 0      0         No Swap
 339      * 0      1         Swap
 340      * 1      0         Swap
 341      * 1      1         No Swap
 342      *
 343      * This is XOR. pbit tracks the previous bit of k.
 344      */
 345
 346     for (i = cardinality_bits - 1; i >= 0; i--) {
 347         kbit = BN_is_bit_set(k, i) ^ pbit;
 348         EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
 349
 350         /* Perform a single step of the Montgomery ladder */
 351         if (!ec_point_ladder_step(group, r, s, p, ctx)) {
 352             ERR_raise(ERR_LIB_EC, EC_R_LADDER_STEP_FAILURE);
 353             goto err;
 354         }
 355         /*
 356          * pbit logic merges this cswap with that of the
 357          * next iteration
 358          */
 359         pbit ^= kbit;
 360     }
 361     /* one final cswap to move the right value into r */
 362     EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
 363 #undef EC_POINT_CSWAP
 364
 365     /* Finalize ladder (and recover full point coordinates) */
 366     if (!ec_point_ladder_post(group, r, s, p, ctx)) {
 367         ERR_raise(ERR_LIB_EC, EC_R_LADDER_POST_FAILURE);
 368         goto err;
 369     }
 370
 371     ret = 1;
 372
 373  err:
 374     EC_POINT_free(p);
 375     EC_POINT_clear_free(s);
 376     BN_CTX_end(ctx);
 377
 378     return ret;
 379 }
 380
 381 #undef EC_POINT_BN_set_flags
 382
 383 /*
 384  * Table could be optimised for the wNAF-based implementation,
 385  * sometimes smaller windows will give better performance (thus the
 386  * boundaries should be increased)
 387  */
 388 #define EC_window_bits_for_scalar_size(b) \
 389                 ((size_t) \
 390                  ((b) >= 2000 ? 6 : \
 391                   (b) >=  800 ? 5 : \
 392                   (b) >=  300 ? 4 : \
 393                   (b) >=   70 ? 3 : \
 394                   (b) >=   20 ? 2 : \
 395                   1))
 396
 397 /*-
 398  * Compute
 399  *      \sum scalars[i]*points[i],
 400  * also including
 401  *      scalar*generator
 402  * in the addition if scalar != NULL
 403  */
 404 int ossl_ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 405                      size_t num, const EC_POINT *points[],
 406                      const BIGNUM *scalars[], BN_CTX *ctx)
 407 {
 408     const EC_POINT *generator = NULL;
 409     EC_POINT *tmp = NULL;
 410     size_t totalnum;
 411     size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
 412     size_t pre_points_per_block = 0;
 413     size_t i, j;
 414     int k;
 415     int r_is_inverted = 0;
 416     int r_is_at_infinity = 1;
 417     size_t *wsize = NULL;       /* individual window sizes */
 418     signed char **wNAF = NULL;  /* individual wNAFs */
 419     size_t *wNAF_len = NULL;
 420     size_t max_len = 0;
 421     size_t num_val;
 422     EC_POINT **val = NULL;      /* precomputation */
 423     EC_POINT **v;
 424     EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
 425                                  * 'pre_comp->points' */
 426     const EC_PRE_COMP *pre_comp = NULL;
 427     int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be
 428                                  * treated like other scalars, i.e.
 429                                  * precomputation is not available */
 430     int ret = 0;
 431
 432     if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) {
 433         /*-
 434          * Handle the common cases where the scalar is secret, enforcing a
 435          * scalar multiplication implementation based on a Montgomery ladder,
 436          * with various timing attack defenses.
 437          */
 438         if ((scalar != group->order) && (scalar != NULL) && (num == 0)) {
 439             /*-
 440              * In this case we want to compute scalar * GeneratorPoint: this
 441              * codepath is reached most prominently by (ephemeral) key
 442              * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
 443              * ECDH keygen/first half), where the scalar is always secret. This
 444              * is why we ignore if BN_FLG_CONSTTIME is actually set and we
 445              * always call the ladder version.
 446              */
 447             return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
 448         }
 449         if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) {
 450             /*-
 451              * In this case we want to compute scalar * VariablePoint: this
 452              * codepath is reached most prominently by the second half of ECDH,
 453              * where the secret scalar is multiplied by the peer's public point.
 454              * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
 455              * actually set and we always call the ladder version.
 456              */
 457             return ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0],
 458                                              ctx);
 459         }
 460     }
 461
 462     if (scalar != NULL) {
 463         generator = EC_GROUP_get0_generator(group);
 464         if (generator == NULL) {
 465             ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
 466             goto err;
 467         }
 468
 469         /* look if we can use precomputed multiples of generator */
 470
 471         pre_comp = group->pre_comp.ec;
 472         if (pre_comp && pre_comp->numblocks
 473             && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
 474                 0)) {
 475             blocksize = pre_comp->blocksize;
 476
 477             /*
 478              * determine maximum number of blocks that wNAF splitting may
 479              * yield (NB: maximum wNAF length is bit length plus one)
 480              */
 481             numblocks = (BN_num_bits(scalar) / blocksize) + 1;
 482
 483             /*
 484              * we cannot use more blocks than we have precomputation for
 485              */
 486             if (numblocks > pre_comp->numblocks)
 487                 numblocks = pre_comp->numblocks;
 488
 489             pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
 490
 491             /* check that pre_comp looks sane */
 492             if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
 493                 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 494                 goto err;
 495             }
 496         } else {
 497             /* can't use precomputation */
 498             pre_comp = NULL;
 499             numblocks = 1;
 500             num_scalar = 1;     /* treat 'scalar' like 'num'-th element of
 501                                  * 'scalars' */
 502         }
 503     }
 504
 505     totalnum = num + numblocks;
 506
 507     wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
 508     wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
 509     /* include space for pivot */
 510     wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
 511     val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
 512
 513     /* Ensure wNAF is initialised in case we end up going to err */
 514     if (wNAF != NULL)
 515         wNAF[0] = NULL;         /* preliminary pivot */
 516
 517     if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL)
 518         goto err;
 519
 520     /*
 521      * num_val will be the total number of temporarily precomputed points
 522      */
 523     num_val = 0;
 524
 525     for (i = 0; i < num + num_scalar; i++) {
 526         size_t bits;
 527
 528         bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
 529         wsize[i] = EC_window_bits_for_scalar_size(bits);
 530         num_val += (size_t)1 << (wsize[i] - 1);
 531         wNAF[i + 1] = NULL;     /* make sure we always have a pivot */
 532         wNAF[i] =
 533             bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
 534                             &wNAF_len[i]);
 535         if (wNAF[i] == NULL)
 536             goto err;
 537         if (wNAF_len[i] > max_len)
 538             max_len = wNAF_len[i];
 539     }
 540
 541     if (numblocks) {
 542         /* we go here iff scalar != NULL */
 543
 544         if (pre_comp == NULL) {
 545             if (num_scalar != 1) {
 546                 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 547                 goto err;
 548             }
 549             /* we have already generated a wNAF for 'scalar' */
 550         } else {
 551             signed char *tmp_wNAF = NULL;
 552             size_t tmp_len = 0;
 553
 554             if (num_scalar != 0) {
 555                 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 556                 goto err;
 557             }
 558
 559             /*
 560              * use the window size for which we have precomputation
 561              */
 562             wsize[num] = pre_comp->w;
 563             tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
 564             if (!tmp_wNAF)
 565                 goto err;
 566
 567             if (tmp_len <= max_len) {
 568                 /*
 569                  * One of the other wNAFs is at least as long as the wNAF
 570                  * belonging to the generator, so wNAF splitting will not buy
 571                  * us anything.
 572                  */
 573
 574                 numblocks = 1;
 575                 totalnum = num + 1; /* don't use wNAF splitting */
 576                 wNAF[num] = tmp_wNAF;
 577                 wNAF[num + 1] = NULL;
 578                 wNAF_len[num] = tmp_len;
 579                 /*
 580                  * pre_comp->points starts with the points that we need here:
 581                  */
 582                 val_sub[num] = pre_comp->points;
 583             } else {
 584                 /*
 585                  * don't include tmp_wNAF directly into wNAF array - use wNAF
 586                  * splitting and include the blocks
 587                  */
 588
 589                 signed char *pp;
 590                 EC_POINT **tmp_points;
 591
 592                 if (tmp_len < numblocks * blocksize) {
 593                     /*
 594                      * possibly we can do with fewer blocks than estimated
 595                      */
 596                     numblocks = (tmp_len + blocksize - 1) / blocksize;
 597                     if (numblocks > pre_comp->numblocks) {
 598                         ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 599                         OPENSSL_free(tmp_wNAF);
 600                         goto err;
 601                     }
 602                     totalnum = num + numblocks;
 603                 }
 604
 605                 /* split wNAF in 'numblocks' parts */
 606                 pp = tmp_wNAF;
 607                 tmp_points = pre_comp->points;
 608
 609                 for (i = num; i < totalnum; i++) {
 610                     if (i < totalnum - 1) {
 611                         wNAF_len[i] = blocksize;
 612                         if (tmp_len < blocksize) {
 613                             ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 614                             OPENSSL_free(tmp_wNAF);
 615                             goto err;
 616                         }
 617                         tmp_len -= blocksize;
 618                     } else
 619                         /*
 620                          * last block gets whatever is left (this could be
 621                          * more or less than 'blocksize'!)
 622                          */
 623                         wNAF_len[i] = tmp_len;
 624
 625                     wNAF[i + 1] = NULL;
 626                     wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
 627                     if (wNAF[i] == NULL) {
 628                         OPENSSL_free(tmp_wNAF);
 629                         goto err;
 630                     }
 631                     memcpy(wNAF[i], pp, wNAF_len[i]);
 632                     if (wNAF_len[i] > max_len)
 633                         max_len = wNAF_len[i];
 634
 635                     if (*tmp_points == NULL) {
 636                         ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 637                         OPENSSL_free(tmp_wNAF);
 638                         goto err;
 639                     }
 640                     val_sub[i] = tmp_points;
 641                     tmp_points += pre_points_per_block;
 642                     pp += blocksize;
 643                 }
 644                 OPENSSL_free(tmp_wNAF);
 645             }
 646         }
 647     }
 648
 649     /*
 650      * All points we precompute now go into a single array 'val'.
 651      * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
 652      * subarray of 'pre_comp->points' if we already have precomputation.
 653      */
 654     val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
 655     if (val == NULL)
 656         goto err;
 657     val[num_val] = NULL;        /* pivot element */
 658
 659     /* allocate points for precomputation */
 660     v = val;
 661     for (i = 0; i < num + num_scalar; i++) {
 662         val_sub[i] = v;
 663         for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 664             *v = EC_POINT_new(group);
 665             if (*v == NULL)
 666                 goto err;
 667             v++;
 668         }
 669     }
 670     if (!(v == val + num_val)) {
 671         ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 672         goto err;
 673     }
 674
 675     if ((tmp = EC_POINT_new(group)) == NULL)
 676         goto err;
 677
 678     /*-
 679      * prepare precomputed values:
 680      *    val_sub[i][0] :=     points[i]
 681      *    val_sub[i][1] := 3 * points[i]
 682      *    val_sub[i][2] := 5 * points[i]
 683      *    ...
 684      */
 685     for (i = 0; i < num + num_scalar; i++) {
 686         if (i < num) {
 687             if (!EC_POINT_copy(val_sub[i][0], points[i]))
 688                 goto err;
 689         } else {
 690             if (!EC_POINT_copy(val_sub[i][0], generator))
 691                 goto err;
 692         }
 693
 694         if (wsize[i] > 1) {
 695             if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
 696                 goto err;
 697             for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
 698                 if (!EC_POINT_add
 699                     (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
 700                     goto err;
 701             }
 702         }
 703     }
 704
 705     if (group->meth->points_make_affine == NULL
 706         || !group->meth->points_make_affine(group, num_val, val, ctx))
 707         goto err;
 708
 709     r_is_at_infinity = 1;
 710
 711     for (k = max_len - 1; k >= 0; k--) {
 712         if (!r_is_at_infinity) {
 713             if (!EC_POINT_dbl(group, r, r, ctx))
 714                 goto err;
 715         }
 716
 717         for (i = 0; i < totalnum; i++) {
 718             if (wNAF_len[i] > (size_t)k) {
 719                 int digit = wNAF[i][k];
 720                 int is_neg;
 721
 722                 if (digit) {
 723                     is_neg = digit < 0;
 724
 725                     if (is_neg)
 726                         digit = -digit;
 727
 728                     if (is_neg != r_is_inverted) {
 729                         if (!r_is_at_infinity) {
 730                             if (!EC_POINT_invert(group, r, ctx))
 731                                 goto err;
 732                         }
 733                         r_is_inverted = !r_is_inverted;
 734                     }
 735
 736                     /* digit > 0 */
 737
 738                     if (r_is_at_infinity) {
 739                         if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
 740                             goto err;
 741
 742                         /*-
 743                          * Apply coordinate blinding for EC_POINT.
 744                          *
 745                          * The underlying EC_METHOD can optionally implement this function:
 746                          * ossl_ec_point_blind_coordinates() returns 0 in case of errors or 1 on
 747                          * success or if coordinate blinding is not implemented for this
 748                          * group.
 749                          */
 750                         if (!ossl_ec_point_blind_coordinates(group, r, ctx)) {
 751                             ERR_raise(ERR_LIB_EC, EC_R_POINT_COORDINATES_BLIND_FAILURE);
 752                             goto err;
 753                         }
 754
 755                         r_is_at_infinity = 0;
 756                     } else {
 757                         if (!EC_POINT_add
 758                             (group, r, r, val_sub[i][digit >> 1], ctx))
 759                             goto err;
 760                     }
 761                 }
 762             }
 763         }
 764     }
 765
 766     if (r_is_at_infinity) {
 767         if (!EC_POINT_set_to_infinity(group, r))
 768             goto err;
 769     } else {
 770         if (r_is_inverted)
 771             if (!EC_POINT_invert(group, r, ctx))
 772                 goto err;
 773     }
 774
 775     ret = 1;
 776
 777  err:
 778     EC_POINT_free(tmp);
 779     OPENSSL_free(wsize);
 780     OPENSSL_free(wNAF_len);
 781     if (wNAF != NULL) {
 782         signed char **w;
 783
 784         for (w = wNAF; *w != NULL; w++)
 785             OPENSSL_free(*w);
 786
 787         OPENSSL_free(wNAF);
 788     }
 789     if (val != NULL) {
 790         for (v = val; *v != NULL; v++)
 791             EC_POINT_clear_free(*v);
 792
 793         OPENSSL_free(val);
 794     }
 795     OPENSSL_free(val_sub);
 796     return ret;
 797 }
 798
 799 /*-
 800  * ossl_ec_wNAF_precompute_mult()
 801  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 802  * for use with wNAF splitting as implemented in ossl_ec_wNAF_mul().
 803  *
 804  * 'pre_comp->points' is an array of multiples of the generator
 805  * of the following form:
 806  * points[0] =     generator;
 807  * points[1] = 3 * generator;
 808  * ...
 809  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 810  * points[2^(w-1)]   =     2^blocksize * generator;
 811  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 812  * ...
 813  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 814  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 815  * ...
 816  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 817  * points[2^(w-1)*numblocks]       = NULL
 818  */
 819 int ossl_ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
 820 {
 821     const EC_POINT *generator;
 822     EC_POINT *tmp_point = NULL, *base = NULL, **var;
 823     const BIGNUM *order;
 824     size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
 825     EC_POINT **points = NULL;
 826     EC_PRE_COMP *pre_comp;
 827     int ret = 0;
 828     int used_ctx = 0;
 829 #ifndef FIPS_MODULE
 830     BN_CTX *new_ctx = NULL;
 831 #endif
 832
 833     /* if there is an old EC_PRE_COMP object, throw it away */
 834     EC_pre_comp_free(group);
 835     if ((pre_comp = ec_pre_comp_new(group)) == NULL)
 836         return 0;
 837
 838     generator = EC_GROUP_get0_generator(group);
 839     if (generator == NULL) {
 840         ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
 841         goto err;
 842     }
 843
 844 #ifndef FIPS_MODULE
 845     if (ctx == NULL)
 846         ctx = new_ctx = BN_CTX_new();
 847 #endif
 848     if (ctx == NULL)
 849         goto err;
 850
 851     BN_CTX_start(ctx);
 852     used_ctx = 1;
 853
 854     order = EC_GROUP_get0_order(group);
 855     if (order == NULL)
 856         goto err;
 857     if (BN_is_zero(order)) {
 858         ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
 859         goto err;
 860     }
 861
 862     bits = BN_num_bits(order);
 863     /*
 864      * The following parameters mean we precompute (approximately) one point
 865      * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
 866      * bit lengths, other parameter combinations might provide better
 867      * efficiency.
 868      */
 869     blocksize = 8;
 870     w = 4;
 871     if (EC_window_bits_for_scalar_size(bits) > w) {
 872         /* let's not make the window too small ... */
 873         w = EC_window_bits_for_scalar_size(bits);
 874     }
 875
 876     numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
 877                                                      * to use for wNAF
 878                                                      * splitting */
 879
 880     pre_points_per_block = (size_t)1 << (w - 1);
 881     num = pre_points_per_block * numblocks; /* number of points to compute
 882                                              * and store */
 883
 884     points = OPENSSL_malloc(sizeof(*points) * (num + 1));
 885     if (points == NULL)
 886         goto err;
 887
 888     var = points;
 889     var[num] = NULL;            /* pivot */
 890     for (i = 0; i < num; i++) {
 891         if ((var[i] = EC_POINT_new(group)) == NULL) {
 892             ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 893             goto err;
 894         }
 895     }
 896
 897     if ((tmp_point = EC_POINT_new(group)) == NULL
 898         || (base = EC_POINT_new(group)) == NULL) {
 899         ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
 900         goto err;
 901     }
 902
 903     if (!EC_POINT_copy(base, generator))
 904         goto err;
 905
 906     /* do the precomputation */
 907     for (i = 0; i < numblocks; i++) {
 908         size_t j;
 909
 910         if (!EC_POINT_dbl(group, tmp_point, base, ctx))
 911             goto err;
 912
 913         if (!EC_POINT_copy(*var++, base))
 914             goto err;
 915
 916         for (j = 1; j < pre_points_per_block; j++, var++) {
 917             /*
 918              * calculate odd multiples of the current base point
 919              */
 920             if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
 921                 goto err;
 922         }
 923
 924         if (i < numblocks - 1) {
 925             /*
 926              * get the next base (multiply current one by 2^blocksize)
 927              */
 928             size_t k;
 929
 930             if (blocksize <= 2) {
 931                 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
 932                 goto err;
 933             }
 934
 935             if (!EC_POINT_dbl(group, base, tmp_point, ctx))
 936                 goto err;
 937             for (k = 2; k < blocksize; k++) {
 938                 if (!EC_POINT_dbl(group, base, base, ctx))
 939                     goto err;
 940             }
 941         }
 942     }
 943
 944     if (group->meth->points_make_affine == NULL
 945         || !group->meth->points_make_affine(group, num, points, ctx))
 946         goto err;
 947
 948     pre_comp->group = group;
 949     pre_comp->blocksize = blocksize;
 950     pre_comp->numblocks = numblocks;
 951     pre_comp->w = w;
 952     pre_comp->points = points;
 953     points = NULL;
 954     pre_comp->num = num;
 955     SETPRECOMP(group, ec, pre_comp);
 956     pre_comp = NULL;
 957     ret = 1;
 958
 959  err:
 960     if (used_ctx)
 961         BN_CTX_end(ctx);
 962 #ifndef FIPS_MODULE
 963     BN_CTX_free(new_ctx);
 964 #endif
 965     EC_ec_pre_comp_free(pre_comp);
 966     if (points) {
 967         EC_POINT **p;
 968
 969         for (p = points; *p != NULL; p++)
 970             EC_POINT_free(*p);
 971         OPENSSL_free(points);
 972     }
 973     EC_POINT_free(tmp_point);
 974     EC_POINT_free(base);
 975     return ret;
 976 }
 977
 978 int ossl_ec_wNAF_have_precompute_mult(const EC_GROUP *group)
 979 {
 980     return HAVEPRECOMP(group, ec);
 981 }