2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
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
12 #include <openssl/err.h>
14 #include "internal/cryptlib.h"
15 #include "internal/bn_int.h"
17 #include "internal/refcount.h"
20 * This file implements the wNAF-based interleaving multi-exponentiation method
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
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
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;
45 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
47 EC_PRE_COMP *ret = NULL;
52 ret = OPENSSL_zalloc(sizeof(*ret));
54 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
59 ret->blocksize = 8; /* default */
60 ret->w = 4; /* default */
63 ret->lock = CRYPTO_THREAD_lock_new();
64 if (ret->lock == NULL) {
65 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
72 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
76 CRYPTO_UP_REF(&pre->references, &i, pre->lock);
80 void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
87 CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
88 REF_PRINT_COUNT("EC_ec", pre);
91 REF_ASSERT_ISNT(i < 0);
93 if (pre->points != NULL) {
96 for (pts = pre->points; *pts != NULL; pts++)
98 OPENSSL_free(pre->points);
100 CRYPTO_THREAD_lock_free(pre->lock);
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)); \
111 * This functions computes (in constant time) a point multiplication over the
114 * At a high level, it is Montgomery ladder with conditional swaps.
116 * It performs either a fixed scalar point multiplication
117 * (scalar * generator)
118 * when point is NULL, or a generic scalar point multiplication
120 * when point is not NULL.
122 * scalar should be in the range [0,n) otherwise all constant time bets are off.
124 * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
125 * which of course are not constant time themselves.
127 * The product is stored in r.
129 * Returns 1 on success, 0 otherwise.
131 static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
132 const BIGNUM *scalar, const EC_POINT *point,
135 int i, order_bits, group_top, kbit, pbit, Z_is_one;
138 BIGNUM *lambda = NULL;
139 BN_CTX *new_ctx = NULL;
142 if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
147 order_bits = BN_num_bits(group->order);
149 s = EC_POINT_new(group);
154 if (!EC_POINT_copy(s, group->generator))
157 if (!EC_POINT_copy(s, point))
161 EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
163 lambda = BN_CTX_get(ctx);
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.
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))
179 if (!BN_copy(k, scalar))
182 BN_set_flags(k, BN_FLG_CONSTTIME);
184 if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
186 * this is an unusual input, and we don't guarantee
189 if (!BN_nnmod(k, k, group->order, ctx))
193 if (!BN_add(lambda, k, group->order))
195 BN_set_flags(lambda, BN_FLG_CONSTTIME);
196 if (!BN_add(k, lambda, group->order))
199 * lambda := scalar + order
200 * k := scalar + 2*order
202 kbit = BN_is_bit_set(lambda, order_bits);
203 BN_consttime_swap(kbit, k, lambda, group_top + 1);
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))
214 /* top bit is a 1, in a fixed pos */
215 if (!EC_POINT_copy(r, s))
218 EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
220 if (!EC_POINT_dbl(group, s, s, ctx))
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); \
235 * The ladder step, with branches, is
237 * k[i] == 0: S = add(R, S), R = dbl(R)
238 * k[i] == 1: R = add(S, R), S = dbl(S)
240 * Swapping R, S conditionally on k[i] leaves you with state
242 * k[i] == 0: T, U = R, S
243 * k[i] == 1: T, U = S, R
245 * Then perform the ECC ops.
250 * Which leaves you with state
252 * k[i] == 0: U = add(R, S), T = dbl(R)
253 * k[i] == 1: U = add(S, R), T = dbl(S)
255 * Swapping T, U conditionally on k[i] leaves you with state
257 * k[i] == 0: R, S = T, U
258 * k[i] == 1: R, S = U, T
260 * Which leaves you with state
262 * k[i] == 0: S = add(R, S), R = dbl(R)
263 * k[i] == 1: R = add(S, R), S = dbl(S)
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.
268 * Optimization: The end of iteration i and start of i-1 looks like
275 * CSWAP(k[i-1], R, S)
277 * CSWAP(k[i-1], R, S)
280 * So instead of two contiguous swaps, you can merge the condition
281 * bits and do a single swap.
283 * k[i] k[i-1] Outcome
289 * This is XOR. pbit tracks the previous bit of k.
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))
297 if (!EC_POINT_dbl(group, r, r, ctx))
300 * pbit logic merges this cswap with that of the
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
314 BN_CTX_free(new_ctx);
319 #undef EC_POINT_BN_set_flags
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)
326 #define EC_window_bits_for_scalar_size(b) \
337 * \sum scalars[i]*points[i],
340 * in the addition if scalar != NULL
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[],
346 BN_CTX *new_ctx = NULL;
347 const EC_POINT *generator = NULL;
348 EC_POINT *tmp = NULL;
350 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
351 size_t pre_points_per_block = 0;
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;
361 EC_POINT **val = NULL; /* precomputation */
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 */
371 if (group->meth != r->meth) {
372 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
376 if ((scalar == NULL) && (num == 0)) {
377 return EC_POINT_set_to_infinity(group, r);
381 * Handle the common cases where the scalar is secret, enforcing a constant
382 * time scalar multiplication algorithm.
384 if ((scalar != NULL) && (num == 0)) {
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.
393 return ec_mul_consttime(group, r, scalar, NULL, ctx);
395 if ((scalar == NULL) && (num == 1)) {
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.
403 return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
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);
414 ctx = new_ctx = BN_CTX_new();
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);
426 /* look if we can use precomputed multiples of generator */
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) ==
432 blocksize = pre_comp->blocksize;
435 * determine maximum number of blocks that wNAF splitting may
436 * yield (NB: maximum wNAF length is bit length plus one)
438 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
441 * we cannot use more blocks than we have precomputation for
443 if (numblocks > pre_comp->numblocks)
444 numblocks = pre_comp->numblocks;
446 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
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);
454 /* can't use precomputation */
457 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
462 totalnum = num + numblocks;
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]));
470 /* Ensure wNAF is initialised in case we end up going to err */
472 wNAF[0] = NULL; /* preliminary pivot */
474 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
475 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
480 * num_val will be the total number of temporarily precomputed points
484 for (i = 0; i < num + num_scalar; i++) {
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 */
492 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
496 if (wNAF_len[i] > max_len)
497 max_len = wNAF_len[i];
501 /* we go here iff scalar != NULL */
503 if (pre_comp == NULL) {
504 if (num_scalar != 1) {
505 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
508 /* we have already generated a wNAF for 'scalar' */
510 signed char *tmp_wNAF = NULL;
513 if (num_scalar != 0) {
514 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
519 * use the window size for which we have precomputation
521 wsize[num] = pre_comp->w;
522 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
526 if (tmp_len <= max_len) {
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
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;
539 * pre_comp->points starts with the points that we need here:
541 val_sub[num] = pre_comp->points;
544 * don't include tmp_wNAF directly into wNAF array - use wNAF
545 * splitting and include the blocks
549 EC_POINT **tmp_points;
551 if (tmp_len < numblocks * blocksize) {
553 * possibly we can do with fewer blocks than estimated
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);
561 totalnum = num + numblocks;
564 /* split wNAF in 'numblocks' parts */
566 tmp_points = pre_comp->points;
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);
576 tmp_len -= blocksize;
579 * last block gets whatever is left (this could be
580 * more or less than 'blocksize'!)
582 wNAF_len[i] = tmp_len;
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);
591 memcpy(wNAF[i], pp, wNAF_len[i]);
592 if (wNAF_len[i] > max_len)
593 max_len = wNAF_len[i];
595 if (*tmp_points == NULL) {
596 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
597 OPENSSL_free(tmp_wNAF);
600 val_sub[i] = tmp_points;
601 tmp_points += pre_points_per_block;
604 OPENSSL_free(tmp_wNAF);
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.
614 val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
616 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
619 val[num_val] = NULL; /* pivot element */
621 /* allocate points for precomputation */
623 for (i = 0; i < num + num_scalar; i++) {
625 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
626 *v = EC_POINT_new(group);
632 if (!(v == val + num_val)) {
633 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
637 if ((tmp = EC_POINT_new(group)) == NULL)
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]
647 for (i = 0; i < num + num_scalar; i++) {
649 if (!EC_POINT_copy(val_sub[i][0], points[i]))
652 if (!EC_POINT_copy(val_sub[i][0], generator))
657 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
659 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
661 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
667 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
670 r_is_at_infinity = 1;
672 for (k = max_len - 1; k >= 0; k--) {
673 if (!r_is_at_infinity) {
674 if (!EC_POINT_dbl(group, r, r, ctx))
678 for (i = 0; i < totalnum; i++) {
679 if (wNAF_len[i] > (size_t)k) {
680 int digit = wNAF[i][k];
689 if (is_neg != r_is_inverted) {
690 if (!r_is_at_infinity) {
691 if (!EC_POINT_invert(group, r, ctx))
694 r_is_inverted = !r_is_inverted;
699 if (r_is_at_infinity) {
700 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
702 r_is_at_infinity = 0;
705 (group, r, r, val_sub[i][digit >> 1], ctx))
713 if (r_is_at_infinity) {
714 if (!EC_POINT_set_to_infinity(group, r))
718 if (!EC_POINT_invert(group, r, ctx))
725 BN_CTX_free(new_ctx);
728 OPENSSL_free(wNAF_len);
732 for (w = wNAF; *w != NULL; w++)
738 for (v = val; *v != NULL; v++)
739 EC_POINT_clear_free(*v);
743 OPENSSL_free(val_sub);
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().
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;
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;
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
764 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
765 * points[2^(w-1)*numblocks] = NULL
767 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
769 const EC_POINT *generator;
770 EC_POINT *tmp_point = NULL, *base = NULL, **var;
771 BN_CTX *new_ctx = NULL;
773 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
774 EC_POINT **points = NULL;
775 EC_PRE_COMP *pre_comp;
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)
783 generator = EC_GROUP_get0_generator(group);
784 if (generator == NULL) {
785 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
790 ctx = new_ctx = BN_CTX_new();
797 order = EC_GROUP_get0_order(group);
800 if (BN_is_zero(order)) {
801 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
805 bits = BN_num_bits(order);
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
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);
819 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
823 pre_points_per_block = (size_t)1 << (w - 1);
824 num = pre_points_per_block * numblocks; /* number of points to compute
827 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
828 if (points == NULL) {
829 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
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);
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);
848 if (!EC_POINT_copy(base, generator))
851 /* do the precomputation */
852 for (i = 0; i < numblocks; i++) {
855 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
858 if (!EC_POINT_copy(*var++, base))
861 for (j = 1; j < pre_points_per_block; j++, var++) {
863 * calculate odd multiples of the current base point
865 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
869 if (i < numblocks - 1) {
871 * get the next base (multiply current one by 2^blocksize)
875 if (blocksize <= 2) {
876 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
880 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
882 for (k = 2; k < blocksize; k++) {
883 if (!EC_POINT_dbl(group, base, base, ctx))
889 if (!EC_POINTs_make_affine(group, num, points, ctx))
892 pre_comp->group = group;
893 pre_comp->blocksize = blocksize;
894 pre_comp->numblocks = numblocks;
896 pre_comp->points = points;
899 SETPRECOMP(group, ec, pre_comp);
906 BN_CTX_free(new_ctx);
907 EC_ec_pre_comp_free(pre_comp);
911 for (p = points; *p != NULL; p++)
913 OPENSSL_free(points);
915 EC_POINT_free(tmp_point);
920 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
922 return HAVEPRECOMP(group, ec);