1 /* crypto/ec/ec_mult.c */
3 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
61 * and contributed to the OpenSSL project.
66 #include <openssl/err.h>
71 * This file implements the wNAF-based interleaving multi-exponentation method
72 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
73 * for multiplication with precomputation, we use wNAF splitting
74 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
77 /* structure for precomputed multiples of the generator */
78 typedef struct ec_pre_comp_st {
79 const EC_GROUP *group; /* parent EC_GROUP object */
80 size_t blocksize; /* block size for wNAF splitting */
81 size_t numblocks; /* max. number of blocks for which we have
83 size_t w; /* window size */
84 EC_POINT **points; /* array with pre-calculated multiples of
85 * generator: 'num' pointers to EC_POINT
86 * objects followed by a NULL */
87 size_t num; /* numblocks * 2^(w-1) */
91 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
92 static void *ec_pre_comp_dup(void *);
93 static void ec_pre_comp_free(void *);
94 static void ec_pre_comp_clear_free(void *);
96 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
98 EC_PRE_COMP *ret = NULL;
103 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
105 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
109 ret->blocksize = 8; /* default */
111 ret->w = 4; /* default */
118 static void *ec_pre_comp_dup(void *src_)
120 EC_PRE_COMP *src = src_;
122 /* no need to actually copy, these objects never change! */
124 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
129 static void ec_pre_comp_free(void *pre_)
132 EC_PRE_COMP *pre = pre_;
137 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
144 for (p = pre->points; *p != NULL; p++)
146 OPENSSL_free(pre->points);
151 static void ec_pre_comp_clear_free(void *pre_)
154 EC_PRE_COMP *pre = pre_;
159 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
166 for (p = pre->points; *p != NULL; p++) {
167 EC_POINT_clear_free(*p);
168 OPENSSL_cleanse(p, sizeof *p);
170 OPENSSL_free(pre->points);
172 OPENSSL_cleanse(pre, sizeof *pre);
177 * Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
178 * This is an array r[] of values that are either zero or odd with an
179 * absolute value less than 2^w satisfying
180 * scalar = \sum_j r[j]*2^j
181 * where at most one of any w+1 consecutive digits is non-zero
182 * with the exception that the most significant digit may be only
183 * w-1 zeros away from that next non-zero digit.
185 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
189 signed char *r = NULL;
191 int bit, next_bit, mask;
194 if (BN_is_zero(scalar)) {
195 r = OPENSSL_malloc(1);
197 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
205 if (w <= 0 || w > 7) { /* 'signed char' can represent integers with
206 * absolute values less than 2^7 */
207 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
210 bit = 1 << w; /* at most 128 */
211 next_bit = bit << 1; /* at most 256 */
212 mask = next_bit - 1; /* at most 255 */
214 if (BN_is_negative(scalar)) {
218 if (scalar->d == NULL || scalar->top == 0) {
219 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
223 len = BN_num_bits(scalar);
224 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer
225 * than binary representation (*ret_len will
226 * be set to the actual length, i.e. at most
227 * BN_num_bits(scalar) + 1) */
229 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
232 window_val = scalar->d[0] & mask;
234 while ((window_val != 0) || (j + w + 1 < len)) { /* if j+w+1 >= len,
235 * window_val will not
239 /* 0 <= window_val <= 2^(w+1) */
241 if (window_val & 1) {
242 /* 0 < window_val < 2^(w+1) */
244 if (window_val & bit) {
245 digit = window_val - next_bit; /* -2^w < digit < 0 */
247 #if 1 /* modified wNAF */
248 if (j + w + 1 >= len) {
250 * special case for generating modified wNAFs: no new
251 * bits will be added into window_val, so using a
252 * positive digit here will decrease the total length of
256 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
260 digit = window_val; /* 0 < digit < 2^w */
263 if (digit <= -bit || digit >= bit || !(digit & 1)) {
264 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
271 * now window_val is 0 or 2^(w+1) in standard wNAF generation;
272 * for modified window NAFs, it may also be 2^w
274 if (window_val != 0 && window_val != next_bit
275 && window_val != bit) {
276 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
281 r[j++] = sign * digit;
284 window_val += bit * BN_is_bit_set(scalar, j + w);
286 if (window_val > next_bit) {
287 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
293 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
310 * TODO: table should be optimised for the wNAF-based implementation,
311 * sometimes smaller windows will give better performance (thus the
312 * boundaries should be increased)
314 #define EC_window_bits_for_scalar_size(b) \
325 * \sum scalars[i]*points[i],
328 * in the addition if scalar != NULL
330 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
331 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
334 BN_CTX *new_ctx = NULL;
335 const EC_POINT *generator = NULL;
336 EC_POINT *tmp = NULL;
338 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
339 size_t pre_points_per_block = 0;
342 int r_is_inverted = 0;
343 int r_is_at_infinity = 1;
344 size_t *wsize = NULL; /* individual window sizes */
345 signed char **wNAF = NULL; /* individual wNAFs */
346 size_t *wNAF_len = NULL;
349 EC_POINT **val = NULL; /* precomputation */
351 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
352 * 'pre_comp->points' */
353 const EC_PRE_COMP *pre_comp = NULL;
354 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
355 * treated like other scalars, i.e.
356 * precomputation is not available */
359 if (group->meth != r->meth) {
360 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
364 if ((scalar == NULL) && (num == 0)) {
365 return EC_POINT_set_to_infinity(group, r);
368 for (i = 0; i < num; i++) {
369 if (group->meth != points[i]->meth) {
370 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
376 ctx = new_ctx = BN_CTX_new();
381 if (scalar != NULL) {
382 generator = EC_GROUP_get0_generator(group);
383 if (generator == NULL) {
384 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
388 /* look if we can use precomputed multiples of generator */
391 EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup,
392 ec_pre_comp_free, ec_pre_comp_clear_free);
394 if (pre_comp && pre_comp->numblocks
395 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
397 blocksize = pre_comp->blocksize;
400 * determine maximum number of blocks that wNAF splitting may
401 * yield (NB: maximum wNAF length is bit length plus one)
403 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
406 * we cannot use more blocks than we have precomputation for
408 if (numblocks > pre_comp->numblocks)
409 numblocks = pre_comp->numblocks;
411 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
413 /* check that pre_comp looks sane */
414 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
415 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
419 /* can't use precomputation */
422 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
427 totalnum = num + numblocks;
429 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
430 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
431 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
433 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
435 /* Ensure wNAF is initialised in case we end up going to err */
437 wNAF[0] = NULL; /* preliminary pivot */
439 if (!wsize || !wNAF_len || !wNAF || !val_sub) {
440 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
445 * num_val will be the total number of temporarily precomputed points
449 for (i = 0; i < num + num_scalar; i++) {
452 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
453 wsize[i] = EC_window_bits_for_scalar_size(bits);
454 num_val += (size_t)1 << (wsize[i] - 1);
455 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
457 compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
461 if (wNAF_len[i] > max_len)
462 max_len = wNAF_len[i];
466 /* we go here iff scalar != NULL */
468 if (pre_comp == NULL) {
469 if (num_scalar != 1) {
470 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
473 /* we have already generated a wNAF for 'scalar' */
475 signed char *tmp_wNAF = NULL;
478 if (num_scalar != 0) {
479 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
484 * use the window size for which we have precomputation
486 wsize[num] = pre_comp->w;
487 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
491 if (tmp_len <= max_len) {
493 * One of the other wNAFs is at least as long as the wNAF
494 * belonging to the generator, so wNAF splitting will not buy
499 totalnum = num + 1; /* don't use wNAF splitting */
500 wNAF[num] = tmp_wNAF;
501 wNAF[num + 1] = NULL;
502 wNAF_len[num] = tmp_len;
503 if (tmp_len > max_len)
506 * pre_comp->points starts with the points that we need here:
508 val_sub[num] = pre_comp->points;
511 * don't include tmp_wNAF directly into wNAF array - use wNAF
512 * splitting and include the blocks
516 EC_POINT **tmp_points;
518 if (tmp_len < numblocks * blocksize) {
520 * possibly we can do with fewer blocks than estimated
522 numblocks = (tmp_len + blocksize - 1) / blocksize;
523 if (numblocks > pre_comp->numblocks) {
524 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
527 totalnum = num + numblocks;
530 /* split wNAF in 'numblocks' parts */
532 tmp_points = pre_comp->points;
534 for (i = num; i < totalnum; i++) {
535 if (i < totalnum - 1) {
536 wNAF_len[i] = blocksize;
537 if (tmp_len < blocksize) {
538 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
541 tmp_len -= blocksize;
544 * last block gets whatever is left (this could be
545 * more or less than 'blocksize'!)
547 wNAF_len[i] = tmp_len;
550 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
551 if (wNAF[i] == NULL) {
552 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
553 OPENSSL_free(tmp_wNAF);
556 memcpy(wNAF[i], pp, wNAF_len[i]);
557 if (wNAF_len[i] > max_len)
558 max_len = wNAF_len[i];
560 if (*tmp_points == NULL) {
561 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
562 OPENSSL_free(tmp_wNAF);
565 val_sub[i] = tmp_points;
566 tmp_points += pre_points_per_block;
569 OPENSSL_free(tmp_wNAF);
575 * All points we precompute now go into a single array 'val'.
576 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
577 * subarray of 'pre_comp->points' if we already have precomputation.
579 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
581 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
584 val[num_val] = NULL; /* pivot element */
586 /* allocate points for precomputation */
588 for (i = 0; i < num + num_scalar; i++) {
590 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
591 *v = EC_POINT_new(group);
597 if (!(v == val + num_val)) {
598 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
602 if (!(tmp = EC_POINT_new(group)))
606 * prepare precomputed values:
607 * val_sub[i][0] := points[i]
608 * val_sub[i][1] := 3 * points[i]
609 * val_sub[i][2] := 5 * points[i]
612 for (i = 0; i < num + num_scalar; i++) {
614 if (!EC_POINT_copy(val_sub[i][0], points[i]))
617 if (!EC_POINT_copy(val_sub[i][0], generator))
622 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
624 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
626 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
632 #if 1 /* optional; EC_window_bits_for_scalar_size
633 * assumes we do this step */
634 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
638 r_is_at_infinity = 1;
640 for (k = max_len - 1; k >= 0; k--) {
641 if (!r_is_at_infinity) {
642 if (!EC_POINT_dbl(group, r, r, ctx))
646 for (i = 0; i < totalnum; i++) {
647 if (wNAF_len[i] > (size_t)k) {
648 int digit = wNAF[i][k];
657 if (is_neg != r_is_inverted) {
658 if (!r_is_at_infinity) {
659 if (!EC_POINT_invert(group, r, ctx))
662 r_is_inverted = !r_is_inverted;
667 if (r_is_at_infinity) {
668 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
670 r_is_at_infinity = 0;
673 (group, r, r, val_sub[i][digit >> 1], ctx))
681 if (r_is_at_infinity) {
682 if (!EC_POINT_set_to_infinity(group, r))
686 if (!EC_POINT_invert(group, r, ctx))
694 BN_CTX_free(new_ctx);
699 if (wNAF_len != NULL)
700 OPENSSL_free(wNAF_len);
704 for (w = wNAF; *w != NULL; w++)
710 for (v = val; *v != NULL; v++)
711 EC_POINT_clear_free(*v);
715 if (val_sub != NULL) {
716 OPENSSL_free(val_sub);
722 * ec_wNAF_precompute_mult()
723 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
724 * for use with wNAF splitting as implemented in ec_wNAF_mul().
726 * 'pre_comp->points' is an array of multiples of the generator
727 * of the following form:
728 * points[0] = generator;
729 * points[1] = 3 * generator;
731 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
732 * points[2^(w-1)] = 2^blocksize * generator;
733 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
735 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
736 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
738 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
739 * points[2^(w-1)*numblocks] = NULL
741 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
743 const EC_POINT *generator;
744 EC_POINT *tmp_point = NULL, *base = NULL, **var;
745 BN_CTX *new_ctx = NULL;
747 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
748 EC_POINT **points = NULL;
749 EC_PRE_COMP *pre_comp;
752 /* if there is an old EC_PRE_COMP object, throw it away */
753 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup,
754 ec_pre_comp_free, ec_pre_comp_clear_free);
756 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
759 generator = EC_GROUP_get0_generator(group);
760 if (generator == NULL) {
761 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
766 ctx = new_ctx = BN_CTX_new();
772 order = BN_CTX_get(ctx);
776 if (!EC_GROUP_get_order(group, order, ctx))
778 if (BN_is_zero(order)) {
779 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
783 bits = BN_num_bits(order);
785 * The following parameters mean we precompute (approximately) one point
786 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
787 * bit lengths, other parameter combinations might provide better
792 if (EC_window_bits_for_scalar_size(bits) > w) {
793 /* let's not make the window too small ... */
794 w = EC_window_bits_for_scalar_size(bits);
797 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
801 pre_points_per_block = (size_t)1 << (w - 1);
802 num = pre_points_per_block * numblocks; /* number of points to compute
805 points = OPENSSL_malloc(sizeof(EC_POINT *) * (num + 1));
807 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
812 var[num] = NULL; /* pivot */
813 for (i = 0; i < num; i++) {
814 if ((var[i] = EC_POINT_new(group)) == NULL) {
815 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
820 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) {
821 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
825 if (!EC_POINT_copy(base, generator))
828 /* do the precomputation */
829 for (i = 0; i < numblocks; i++) {
832 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
835 if (!EC_POINT_copy(*var++, base))
838 for (j = 1; j < pre_points_per_block; j++, var++) {
840 * calculate odd multiples of the current base point
842 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
846 if (i < numblocks - 1) {
848 * get the next base (multiply current one by 2^blocksize)
852 if (blocksize <= 2) {
853 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
857 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
859 for (k = 2; k < blocksize; k++) {
860 if (!EC_POINT_dbl(group, base, base, ctx))
866 if (!EC_POINTs_make_affine(group, num, points, ctx))
869 pre_comp->group = group;
870 pre_comp->blocksize = blocksize;
871 pre_comp->numblocks = numblocks;
873 pre_comp->points = points;
877 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
878 ec_pre_comp_dup, ec_pre_comp_free,
879 ec_pre_comp_clear_free))
888 BN_CTX_free(new_ctx);
890 ec_pre_comp_free(pre_comp);
894 for (p = points; *p != NULL; p++)
896 OPENSSL_free(points);
899 EC_POINT_free(tmp_point);
905 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
907 if (EC_EX_DATA_get_data
908 (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free,
909 ec_pre_comp_clear_free) != NULL)