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.
64 #define OPENSSL_FIPSAPI
68 #include <openssl/err.h>
74 * This file implements the wNAF-based interleaving multi-exponentation method
75 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
76 * for multiplication with precomputation, we use wNAF splitting
77 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
83 /* structure for precomputed multiples of the generator */
84 typedef struct ec_pre_comp_st {
85 const EC_GROUP *group; /* parent EC_GROUP object */
86 size_t blocksize; /* block size for wNAF splitting */
87 size_t numblocks; /* max. number of blocks for which we have precomputation */
88 size_t w; /* window size */
89 EC_POINT **points; /* array with pre-calculated multiples of generator:
90 * 'num' pointers to EC_POINT objects followed by a NULL */
91 size_t num; /* numblocks * 2^(w-1) */
95 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
96 static void *ec_pre_comp_dup(void *);
97 static void ec_pre_comp_free(void *);
98 static void ec_pre_comp_clear_free(void *);
100 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
102 EC_PRE_COMP *ret = NULL;
107 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
110 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
114 ret->blocksize = 8; /* default */
116 ret->w = 4; /* default */
123 static void *ec_pre_comp_dup(void *src_)
125 EC_PRE_COMP *src = src_;
127 /* no need to actually copy, these objects never change! */
129 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
134 static void ec_pre_comp_free(void *pre_)
137 EC_PRE_COMP *pre = pre_;
142 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
150 for (p = pre->points; *p != NULL; p++)
152 OPENSSL_free(pre->points);
157 static void ec_pre_comp_clear_free(void *pre_)
160 EC_PRE_COMP *pre = pre_;
165 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
173 for (p = pre->points; *p != NULL; p++)
175 EC_POINT_clear_free(*p);
176 OPENSSL_cleanse(p, sizeof *p);
178 OPENSSL_free(pre->points);
180 OPENSSL_cleanse(pre, sizeof *pre);
187 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
188 * This is an array r[] of values that are either zero or odd with an
189 * absolute value less than 2^w satisfying
190 * scalar = \sum_j r[j]*2^j
191 * where at most one of any w+1 consecutive digits is non-zero
192 * with the exception that the most significant digit may be only
193 * w-1 zeros away from that next non-zero digit.
195 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
199 signed char *r = NULL;
201 int bit, next_bit, mask;
204 if (BN_is_zero(scalar))
206 r = OPENSSL_malloc(1);
209 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
217 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
219 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
222 bit = 1 << w; /* at most 128 */
223 next_bit = bit << 1; /* at most 256 */
224 mask = next_bit - 1; /* at most 255 */
226 if (BN_is_negative(scalar))
231 if (scalar->d == NULL || scalar->top == 0)
233 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
237 len = BN_num_bits(scalar);
238 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
239 * (*ret_len will be set to the actual length, i.e. at most
240 * BN_num_bits(scalar) + 1) */
243 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
246 window_val = scalar->d[0] & mask;
248 while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
252 /* 0 <= window_val <= 2^(w+1) */
256 /* 0 < window_val < 2^(w+1) */
258 if (window_val & bit)
260 digit = window_val - next_bit; /* -2^w < digit < 0 */
262 #if 1 /* modified wNAF */
263 if (j + w + 1 >= len)
265 /* special case for generating modified wNAFs:
266 * no new bits will be added into window_val,
267 * so using a positive digit here will decrease
268 * the total length of the representation */
270 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
276 digit = window_val; /* 0 < digit < 2^w */
279 if (digit <= -bit || digit >= bit || !(digit & 1))
281 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
287 /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
288 * for modified window NAFs, it may also be 2^w
290 if (window_val != 0 && window_val != next_bit && window_val != bit)
292 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
297 r[j++] = sign * digit;
300 window_val += bit * BN_is_bit_set(scalar, j + w);
302 if (window_val > next_bit)
304 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
311 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
329 /* TODO: table should be optimised for the wNAF-based implementation,
330 * sometimes smaller windows will give better performance
331 * (thus the boundaries should be increased)
333 #define EC_window_bits_for_scalar_size(b) \
343 * \sum scalars[i]*points[i],
346 * in the addition if scalar != NULL
348 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
349 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
351 BN_CTX *new_ctx = NULL;
352 const EC_POINT *generator = NULL;
353 EC_POINT *tmp = NULL;
355 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
356 size_t pre_points_per_block = 0;
359 int r_is_inverted = 0;
360 int r_is_at_infinity = 1;
361 size_t *wsize = NULL; /* individual window sizes */
362 signed char **wNAF = NULL; /* individual wNAFs */
363 size_t *wNAF_len = NULL;
366 EC_POINT **val = NULL; /* precomputation */
368 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
369 const EC_PRE_COMP *pre_comp = NULL;
370 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
371 * i.e. precomputation is not available */
374 if (group->meth != r->meth)
376 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
380 if ((scalar == NULL) && (num == 0))
382 return EC_POINT_set_to_infinity(group, r);
385 for (i = 0; i < num; i++)
387 if (group->meth != points[i]->meth)
389 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
396 ctx = new_ctx = BN_CTX_new();
403 generator = EC_GROUP_get0_generator(group);
404 if (generator == NULL)
406 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
410 /* look if we can use precomputed multiples of generator */
412 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
414 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
416 blocksize = pre_comp->blocksize;
418 /* determine maximum number of blocks that wNAF splitting may yield
419 * (NB: maximum wNAF length is bit length plus one) */
420 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
422 /* we cannot use more blocks than we have precomputation for */
423 if (numblocks > pre_comp->numblocks)
424 numblocks = pre_comp->numblocks;
426 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
428 /* check that pre_comp looks sane */
429 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
431 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
437 /* can't use precomputation */
440 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
444 totalnum = num + numblocks;
446 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
447 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
448 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
449 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
451 if (!wsize || !wNAF_len || !wNAF || !val_sub)
453 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
457 wNAF[0] = NULL; /* preliminary pivot */
459 /* num_val will be the total number of temporarily precomputed points */
462 for (i = 0; i < num + num_scalar; i++)
466 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
467 wsize[i] = EC_window_bits_for_scalar_size(bits);
468 num_val += (size_t)1 << (wsize[i] - 1);
469 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
470 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
473 if (wNAF_len[i] > max_len)
474 max_len = wNAF_len[i];
479 /* we go here iff scalar != NULL */
481 if (pre_comp == NULL)
485 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
488 /* we have already generated a wNAF for 'scalar' */
492 signed char *tmp_wNAF = NULL;
497 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
501 /* use the window size for which we have precomputation */
502 wsize[num] = pre_comp->w;
503 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
507 if (tmp_len <= max_len)
509 /* One of the other wNAFs is at least as long
510 * as the wNAF belonging to the generator,
511 * so wNAF splitting will not buy us anything. */
514 totalnum = num + 1; /* don't use wNAF splitting */
515 wNAF[num] = tmp_wNAF;
516 wNAF[num + 1] = NULL;
517 wNAF_len[num] = tmp_len;
518 if (tmp_len > max_len)
520 /* pre_comp->points starts with the points that we need here: */
521 val_sub[num] = pre_comp->points;
525 /* don't include tmp_wNAF directly into wNAF array
526 * - use wNAF splitting and include the blocks */
529 EC_POINT **tmp_points;
531 if (tmp_len < numblocks * blocksize)
533 /* possibly we can do with fewer blocks than estimated */
534 numblocks = (tmp_len + blocksize - 1) / blocksize;
535 if (numblocks > pre_comp->numblocks)
537 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
540 totalnum = num + numblocks;
543 /* split wNAF in 'numblocks' parts */
545 tmp_points = pre_comp->points;
547 for (i = num; i < totalnum; i++)
549 if (i < totalnum - 1)
551 wNAF_len[i] = blocksize;
552 if (tmp_len < blocksize)
554 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
557 tmp_len -= blocksize;
560 /* last block gets whatever is left
561 * (this could be more or less than 'blocksize'!) */
562 wNAF_len[i] = tmp_len;
565 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
568 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
569 OPENSSL_free(tmp_wNAF);
572 memcpy(wNAF[i], pp, wNAF_len[i]);
573 if (wNAF_len[i] > max_len)
574 max_len = wNAF_len[i];
576 if (*tmp_points == NULL)
578 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
579 OPENSSL_free(tmp_wNAF);
582 val_sub[i] = tmp_points;
583 tmp_points += pre_points_per_block;
586 OPENSSL_free(tmp_wNAF);
591 /* All points we precompute now go into a single array 'val'.
592 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
593 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
594 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
597 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
600 val[num_val] = NULL; /* pivot element */
602 /* allocate points for precomputation */
604 for (i = 0; i < num + num_scalar; i++)
607 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
609 *v = EC_POINT_new(group);
610 if (*v == NULL) goto err;
614 if (!(v == val + num_val))
616 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
620 if (!(tmp = EC_POINT_new(group)))
623 /* prepare precomputed values:
624 * val_sub[i][0] := points[i]
625 * val_sub[i][1] := 3 * points[i]
626 * val_sub[i][2] := 5 * points[i]
629 for (i = 0; i < num + num_scalar; i++)
633 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
637 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
642 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
643 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
645 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
650 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
651 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
655 r_is_at_infinity = 1;
657 for (k = max_len - 1; k >= 0; k--)
659 if (!r_is_at_infinity)
661 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
664 for (i = 0; i < totalnum; i++)
666 if (wNAF_len[i] > (size_t)k)
668 int digit = wNAF[i][k];
678 if (is_neg != r_is_inverted)
680 if (!r_is_at_infinity)
682 if (!EC_POINT_invert(group, r, ctx)) goto err;
684 r_is_inverted = !r_is_inverted;
689 if (r_is_at_infinity)
691 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
692 r_is_at_infinity = 0;
696 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
703 if (r_is_at_infinity)
705 if (!EC_POINT_set_to_infinity(group, r)) goto err;
710 if (!EC_POINT_invert(group, r, ctx)) goto err;
717 BN_CTX_free(new_ctx);
722 if (wNAF_len != NULL)
723 OPENSSL_free(wNAF_len);
728 for (w = wNAF; *w != NULL; w++)
735 for (v = val; *v != NULL; v++)
736 EC_POINT_clear_free(*v);
742 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_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
781 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
784 generator = EC_GROUP_get0_generator(group);
785 if (generator == NULL)
787 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
793 ctx = new_ctx = BN_CTX_new();
799 order = BN_CTX_get(ctx);
800 if (order == NULL) goto err;
802 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
803 if (BN_is_zero(order))
805 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
809 bits = BN_num_bits(order);
810 /* The following parameters mean we precompute (approximately)
813 * TBD: The combination 8, 4 is perfect for 160 bits; for other
814 * bit lengths, other parameter combinations might provide better
819 if (EC_window_bits_for_scalar_size(bits) > w)
821 /* let's not make the window too small ... */
822 w = EC_window_bits_for_scalar_size(bits);
825 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
827 pre_points_per_block = (size_t)1 << (w - 1);
828 num = pre_points_per_block * numblocks; /* number of points to compute and store */
830 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
833 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
838 var[num] = NULL; /* pivot */
839 for (i = 0; i < num; i++)
841 if ((var[i] = EC_POINT_new(group)) == NULL)
843 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
848 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
850 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
854 if (!EC_POINT_copy(base, generator))
857 /* do the precomputation */
858 for (i = 0; i < numblocks; i++)
862 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
865 if (!EC_POINT_copy(*var++, base))
868 for (j = 1; j < pre_points_per_block; j++, var++)
870 /* calculate odd multiples of the current base point */
871 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
875 if (i < numblocks - 1)
877 /* get the next base (multiply current one by 2^blocksize) */
882 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
886 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
888 for (k = 2; k < blocksize; k++)
890 if (!EC_POINT_dbl(group,base,base,ctx))
896 if (!EC_POINTs_make_affine(group, num, points, ctx))
899 pre_comp->group = group;
900 pre_comp->blocksize = blocksize;
901 pre_comp->numblocks = numblocks;
903 pre_comp->points = points;
907 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
908 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
917 BN_CTX_free(new_ctx);
919 ec_pre_comp_free(pre_comp);
924 for (p = points; *p != NULL; p++)
926 OPENSSL_free(points);
929 EC_POINT_free(tmp_point);
936 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
938 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)