1 /* crypto/ec/ec_mult.c */
3 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2003 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 #include <openssl/err.h>
70 * This file implements the wNAF-based interleaving multi-exponentation method
71 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
72 * for multiplication with precomputation, we use wNAF splitting
73 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
79 /* structure for precomputed multiples of the generator */
80 typedef struct ec_pre_comp_st {
81 const EC_GROUP *group; /* parent EC_GROUP object */
82 size_t blocksize; /* block size for wNAF splitting */
83 size_t numblocks; /* max. number of blocks for which we have precomputation */
84 size_t w; /* window size */
85 EC_POINT **points; /* array with pre-calculated multiples of generator:
86 * 'num' pointers to EC_POINT objects followed by a NULL */
87 size_t num; /* numblocks * 2^(w-1) */
90 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
91 static void *ec_pre_comp_dup(void *);
92 static void ec_pre_comp_free(void *);
93 static void ec_pre_comp_clear_free(void *);
95 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
97 EC_PRE_COMP *ret = NULL;
102 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
106 ret->blocksize = 8; /* default */
108 ret->w = 4; /* default */
114 static void *ec_pre_comp_dup(void *src_)
116 const EC_PRE_COMP *src = src_;
117 EC_PRE_COMP *ret = NULL;
119 ret = ec_pre_comp_new(src->group);
122 ret->blocksize = src->blocksize;
123 ret->numblocks = src->numblocks;
129 EC_POINT **src_var, **dest_var;
131 ret->points = (EC_POINT **)OPENSSL_malloc((src->num + 1) * sizeof(EC_POINT *));
134 ec_pre_comp_free(ret);
138 for (dest_var = ret->points, src_var = src->points; *src_var != NULL; src_var++, dest_var++)
140 *dest_var = EC_POINT_dup(*src_var, src->group);
141 if (*dest_var == NULL)
143 ec_pre_comp_free(ret);
149 ret->points[ret->num] = NULL;
150 if (ret->num != src->num)
152 ec_pre_comp_free(ret);
153 ECerr(EC_F_EC_PRE_COMP_DUP, ERR_R_INTERNAL_ERROR);
161 static void ec_pre_comp_free(void *pre_)
163 EC_PRE_COMP *pre = pre_;
171 for (var = pre->points; *var != NULL; var++)
173 OPENSSL_free(pre->points);
178 static void ec_pre_comp_clear_free(void *pre_)
180 EC_PRE_COMP *pre = pre_;
188 for (p = pre->points; *p != NULL; p++)
189 EC_POINT_clear_free(*p);
190 OPENSSL_cleanse(pre->points, sizeof pre->points);
191 OPENSSL_free(pre->points);
193 OPENSSL_cleanse(pre, sizeof pre);
200 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
201 * This is an array r[] of values that are either zero or odd with an
202 * absolute value less than 2^w satisfying
203 * scalar = \sum_j r[j]*2^j
204 * where at most one of any w+1 consecutive digits is non-zero
205 * with the exception that the most significant digit may be only
206 * w-1 zeros away from that next non-zero digit.
208 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
212 signed char *r = NULL;
214 int bit, next_bit, mask;
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_get_sign(scalar))
231 len = BN_num_bits(scalar);
232 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
233 * (*ret_len will be set to the actual length, i.e. at most
234 * BN_num_bits(scalar) + 1) */
235 if (r == NULL) goto err;
237 if (scalar->d == NULL || scalar->top == 0)
239 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
242 window_val = scalar->d[0] & mask;
244 while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
248 /* 0 <= window_val <= 2^(w+1) */
252 /* 0 < window_val < 2^(w+1) */
254 if (window_val & bit)
256 digit = window_val - next_bit; /* -2^w < digit < 0 */
258 #if 1 /* modified wNAF */
259 if (j + w + 1 >= len)
261 /* special case for generating modified wNAFs:
262 * no new bits will be added into window_val,
263 * so using a positive digit here will decrease
264 * the total length of the representation */
266 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
272 digit = window_val; /* 0 < digit < 2^w */
275 if (digit <= -bit || digit >= bit || !(digit & 1))
277 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
283 /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
284 * for modified window NAFs, it may also be 2^w
286 if (window_val != 0 && window_val != next_bit && window_val != bit)
288 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
293 r[j++] = sign * digit;
296 window_val += bit * BN_is_bit_set(scalar, j + w);
298 if (window_val > next_bit)
300 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
307 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
325 /* TODO: table should be optimised for the wNAF-based implementation,
326 * sometimes smaller windows will give better performance
327 * (thus the boundaries should be increased)
329 #define EC_window_bits_for_scalar_size(b) \
338 * \sum scalars[i]*points[i],
341 * in the addition if scalar != NULL
343 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
344 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
346 BN_CTX *new_ctx = NULL;
347 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 'pre_comp->points' */
364 EC_PRE_COMP *pre_comp = NULL;
365 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
366 * i.e. precomputation is not available */
369 if (group->meth != r->meth)
371 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
375 if ((scalar == NULL) && (num == 0))
377 return EC_POINT_set_to_infinity(group, r);
380 for (i = 0; i < num; i++)
382 if (group->meth != points[i]->meth)
384 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
391 ctx = new_ctx = BN_CTX_new();
398 generator = EC_GROUP_get0_generator(group);
399 if (generator == NULL)
401 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
405 /* look if we can use precomputed multiples of generator */
407 pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
409 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
411 blocksize = pre_comp->blocksize;
413 /* determine maximum number of blocks that wNAF splitting may yield
414 * (NB: maximum wNAF length is bit length plus one) */
415 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
417 /* we cannot use more blocks than we have precomputation for */
418 if (numblocks > pre_comp->numblocks)
419 numblocks = pre_comp->numblocks;
421 pre_points_per_block = 1u << (pre_comp->w - 1);
423 /* check that pre_comp looks sane */
424 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
426 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
432 /* can't use precomputation */
435 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
439 totalnum = num + numblocks;
441 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
442 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
443 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
444 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
446 if (!wsize || !wNAF_len || !wNAF || !val_sub)
449 wNAF[0] = NULL; /* preliminary pivot */
451 /* num_val will be the total number of temporarily precomputed points */
454 for (i = 0; i < num + num_scalar; i++)
458 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
459 wsize[i] = EC_window_bits_for_scalar_size(bits);
460 num_val += 1u << (wsize[i] - 1);
461 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
462 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
465 if (wNAF_len[i] > max_len)
466 max_len = wNAF_len[i];
471 /* we go here iff scalar != NULL */
473 if (pre_comp == NULL)
477 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
480 /* we have already generated a wNAF for 'scalar' */
484 signed char *tmp_wNAF = NULL;
489 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
493 /* use the window size for which we have precomputation */
494 wsize[num] = pre_comp->w;
495 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
499 if (tmp_len <= max_len)
501 /* One of the other wNAFs is at least as long
502 * as the wNAF belonging to the generator,
503 * so wNAF splitting will not buy us anything. */
506 totalnum = num + 1; /* don't use wNAF splitting */
507 wNAF[num] = tmp_wNAF;
508 wNAF[num + 1] = NULL;
509 wNAF_len[num] = tmp_len;
510 if (tmp_len > max_len)
512 /* pre_comp->points starts with the points that we need here: */
513 val_sub[num] = pre_comp->points;
517 /* don't include tmp_wNAF directly into wNAF array
518 * - use wNAF splitting and include the blocks */
521 EC_POINT **tmp_points;
523 if (tmp_len < numblocks * blocksize)
525 /* possibly we can do with fewer blocks than estimated */
526 numblocks = (tmp_len + blocksize - 1) / blocksize;
527 if (numblocks > pre_comp->numblocks)
529 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
532 totalnum = num + numblocks;
535 /* split wNAF in 'numblocks' parts */
537 tmp_points = pre_comp->points;
539 for (i = num; i < totalnum; i++)
541 if (i < totalnum - 1)
543 wNAF_len[i] = blocksize;
544 if (tmp_len < blocksize)
546 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
549 tmp_len -= blocksize;
552 /* last block gets whatever is left
553 * (this could be more or less than 'blocksize'!) */
554 wNAF_len[i] = tmp_len;
557 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
560 OPENSSL_free(tmp_wNAF);
563 memcpy(wNAF[i], pp, wNAF_len[i]);
564 if (wNAF_len[i] > max_len)
565 max_len = wNAF_len[i];
567 if (*tmp_points == NULL)
569 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
570 OPENSSL_free(tmp_wNAF);
573 val_sub[i] = tmp_points;
574 tmp_points += pre_points_per_block;
577 OPENSSL_free(tmp_wNAF);
582 /* All points we precompute now go into a single array 'val'.
583 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
584 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
585 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
586 if (val == NULL) goto err;
587 val[num_val] = NULL; /* pivot element */
589 /* allocate points for precomputation */
591 for (i = 0; i < num + num_scalar; i++)
594 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
596 *v = EC_POINT_new(group);
597 if (*v == NULL) goto err;
601 if (!(v == val + num_val))
603 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
607 if (!(tmp = EC_POINT_new(group)))
610 /* prepare precomputed values:
611 * val_sub[i][0] := points[i]
612 * val_sub[i][1] := 3 * points[i]
613 * val_sub[i][2] := 5 * points[i]
616 for (i = 0; i < num + num_scalar; i++)
620 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
624 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
629 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
630 for (j = 1; j < (1u << (wsize[i] - 1)); j++)
632 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
637 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
638 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
642 r_is_at_infinity = 1;
644 for (k = max_len - 1; k >= 0; k--)
646 if (!r_is_at_infinity)
648 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
651 for (i = 0; i < totalnum; i++)
653 if (wNAF_len[i] > (size_t)k)
655 int digit = wNAF[i][k];
665 if (is_neg != r_is_inverted)
667 if (!r_is_at_infinity)
669 if (!EC_POINT_invert(group, r, ctx)) goto err;
671 r_is_inverted = !r_is_inverted;
676 if (r_is_at_infinity)
678 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
679 r_is_at_infinity = 0;
683 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
690 if (r_is_at_infinity)
692 if (!EC_POINT_set_to_infinity(group, r)) goto err;
697 if (!EC_POINT_invert(group, r, ctx)) goto err;
704 BN_CTX_free(new_ctx);
709 if (wNAF_len != NULL)
710 OPENSSL_free(wNAF_len);
715 for (w = wNAF; *w != NULL; w++)
722 for (v = val; *v != NULL; v++)
723 EC_POINT_clear_free(*v);
729 OPENSSL_free(val_sub);
735 /* ec_wNAF_precompute_mult()
736 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
737 * for use with wNAF splitting as implemented in ec_wNAF_mul().
739 * 'pre_comp->points' is an array of multiples of the generator
740 * of the following form:
741 * points[0] = generator;
742 * points[1] = 3 * generator;
744 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
745 * points[2^(w-1)] = 2^blocksize * generator;
746 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
748 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
749 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
751 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
752 * points[2^(w-1)*numblocks] = NULL
754 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
756 const EC_POINT *generator;
757 EC_POINT *tmp_point = NULL, *base = NULL, **var;
758 BN_CTX *new_ctx = NULL;
760 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
761 EC_POINT **points = NULL;
762 EC_PRE_COMP *pre_comp, *new_pre_comp = NULL;
765 pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
766 if (pre_comp == NULL)
767 if ((pre_comp = new_pre_comp = ec_pre_comp_new(group)) == NULL)
770 generator = EC_GROUP_get0_generator(group);
771 if (generator == NULL)
773 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
779 ctx = new_ctx = BN_CTX_new();
785 order = BN_CTX_get(ctx);
786 if (order == NULL) goto err;
788 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
789 if (BN_is_zero(order))
791 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
795 bits = BN_num_bits(order);
796 /* The following parameters mean we precompute (approximately)
799 * TBD: The combination 8, 4 is perfect for 160 bits; for other
800 * bit lengths, other parameter combinations might provide better
805 if (EC_window_bits_for_scalar_size(bits) > w)
807 /* let's not make the window too small ... */
808 w = EC_window_bits_for_scalar_size(bits);
811 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
813 pre_points_per_block = 1u << (w - 1);
814 num = pre_points_per_block * numblocks; /* number of points to compute and store */
816 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
819 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
824 var[num] = NULL; /* pivot */
825 for (i = 0; i < num; i++)
827 if ((var[i] = EC_POINT_new(group)) == NULL)
829 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
834 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
836 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
840 if (!EC_POINT_copy(base, generator))
843 /* do the precomputation */
844 for (i = 0; i < numblocks; i++)
848 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
851 if (!EC_POINT_copy(*var++, base))
854 for (j = 1; j < pre_points_per_block; j++, var++)
856 /* calculate odd multiples of the current base point */
857 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
861 if (i < numblocks - 1)
863 /* get the next base (multiply current one by 2^blocksize) */
868 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
872 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
874 for (k = 2; k < blocksize; k++)
876 if (!EC_POINT_dbl(group,base,base,ctx))
882 if (!EC_POINTs_make_affine(group, num, points, ctx))
885 pre_comp->group = group;
886 pre_comp->blocksize = blocksize;
887 pre_comp->numblocks = numblocks;
889 if (pre_comp->points)
893 for (p = pre_comp->points; *p != NULL; p++)
895 OPENSSL_free(pre_comp->points);
897 pre_comp->points = points;
903 if (!EC_GROUP_set_extra_data(group, new_pre_comp, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
912 BN_CTX_free(new_ctx);
914 ec_pre_comp_free(new_pre_comp);
919 for (p = points; *p != NULL; p++)
921 OPENSSL_free(points);
924 EC_POINT_free(tmp_point);
931 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
933 if (EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)