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>
72 * This file implements the wNAF-based interleaving multi-exponentation method
73 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
74 * for multiplication with precomputation, we use wNAF splitting
75 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
81 /* structure for precomputed multiples of the generator */
82 typedef struct ec_pre_comp_st {
83 const EC_GROUP *group; /* parent EC_GROUP object */
84 size_t blocksize; /* block size for wNAF splitting */
85 size_t numblocks; /* max. number of blocks for which we have precomputation */
86 size_t w; /* window size */
87 EC_POINT **points; /* array with pre-calculated multiples of generator:
88 * 'num' pointers to EC_POINT objects followed by a NULL */
89 size_t num; /* numblocks * 2^(w-1) */
93 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
94 static void *ec_pre_comp_dup(void *);
95 static void ec_pre_comp_free(void *);
96 static void ec_pre_comp_clear_free(void *);
98 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
100 EC_PRE_COMP *ret = NULL;
105 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
108 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
112 ret->blocksize = 8; /* default */
114 ret->w = 4; /* default */
121 static void *ec_pre_comp_dup(void *src_)
123 EC_PRE_COMP *src = src_;
125 /* no need to actually copy, these objects never change! */
127 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
132 static void ec_pre_comp_free(void *pre_)
135 EC_PRE_COMP *pre = pre_;
140 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
148 for (p = pre->points; *p != NULL; p++)
150 OPENSSL_free(pre->points);
155 static void ec_pre_comp_clear_free(void *pre_)
158 EC_PRE_COMP *pre = pre_;
163 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
171 for (p = pre->points; *p != NULL; p++)
172 EC_POINT_clear_free(*p);
173 OPENSSL_cleanse(pre->points, sizeof pre->points);
174 OPENSSL_free(pre->points);
176 OPENSSL_cleanse(pre, sizeof pre);
183 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
184 * This is an array r[] of values that are either zero or odd with an
185 * absolute value less than 2^w satisfying
186 * scalar = \sum_j r[j]*2^j
187 * where at most one of any w+1 consecutive digits is non-zero
188 * with the exception that the most significant digit may be only
189 * w-1 zeros away from that next non-zero digit.
191 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
195 signed char *r = NULL;
197 int bit, next_bit, mask;
200 if (BN_is_zero(scalar))
202 r = OPENSSL_malloc(1);
205 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
213 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
215 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
218 bit = 1 << w; /* at most 128 */
219 next_bit = bit << 1; /* at most 256 */
220 mask = next_bit - 1; /* at most 255 */
222 if (BN_is_negative(scalar))
227 len = BN_num_bits(scalar);
228 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
229 * (*ret_len will be set to the actual length, i.e. at most
230 * BN_num_bits(scalar) + 1) */
233 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
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) \
339 * \sum scalars[i]*points[i],
342 * in the addition if scalar != NULL
344 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
345 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
347 BN_CTX *new_ctx = NULL;
348 const EC_POINT *generator = NULL;
349 EC_POINT *tmp = NULL;
351 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
352 size_t pre_points_per_block = 0;
355 int r_is_inverted = 0;
356 int r_is_at_infinity = 1;
357 size_t *wsize = NULL; /* individual window sizes */
358 signed char **wNAF = NULL; /* individual wNAFs */
359 size_t *wNAF_len = NULL;
362 EC_POINT **val = NULL; /* precomputation */
364 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or '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 treated like other scalars,
367 * i.e. precomputation is not available */
370 if (group->meth != r->meth)
372 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
376 if ((scalar == NULL) && (num == 0))
378 return EC_POINT_set_to_infinity(group, r);
381 for (i = 0; i < num; i++)
383 if (group->meth != points[i]->meth)
385 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
392 ctx = new_ctx = BN_CTX_new();
399 generator = EC_GROUP_get0_generator(group);
400 if (generator == NULL)
402 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
406 /* look if we can use precomputed multiples of generator */
408 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
410 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
412 blocksize = pre_comp->blocksize;
414 /* determine maximum number of blocks that wNAF splitting may yield
415 * (NB: maximum wNAF length is bit length plus one) */
416 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
418 /* we cannot use more blocks than we have precomputation for */
419 if (numblocks > pre_comp->numblocks)
420 numblocks = pre_comp->numblocks;
422 pre_points_per_block = 1u << (pre_comp->w - 1);
424 /* check that pre_comp looks sane */
425 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
427 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
433 /* can't use precomputation */
436 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
440 totalnum = num + numblocks;
442 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
443 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
444 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
445 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
447 if (!wsize || !wNAF_len || !wNAF || !val_sub)
449 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
453 wNAF[0] = NULL; /* preliminary pivot */
455 /* num_val will be the total number of temporarily precomputed points */
458 for (i = 0; i < num + num_scalar; i++)
462 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
463 wsize[i] = EC_window_bits_for_scalar_size(bits);
464 num_val += 1u << (wsize[i] - 1);
465 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
466 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
469 if (wNAF_len[i] > max_len)
470 max_len = wNAF_len[i];
475 /* we go here iff scalar != NULL */
477 if (pre_comp == NULL)
481 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
484 /* we have already generated a wNAF for 'scalar' */
488 signed char *tmp_wNAF = NULL;
493 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
497 /* use the window size for which we have precomputation */
498 wsize[num] = pre_comp->w;
499 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
503 if (tmp_len <= max_len)
505 /* One of the other wNAFs is at least as long
506 * as the wNAF belonging to the generator,
507 * so wNAF splitting will not buy us anything. */
510 totalnum = num + 1; /* don't use wNAF splitting */
511 wNAF[num] = tmp_wNAF;
512 wNAF[num + 1] = NULL;
513 wNAF_len[num] = tmp_len;
514 if (tmp_len > max_len)
516 /* pre_comp->points starts with the points that we need here: */
517 val_sub[num] = pre_comp->points;
521 /* don't include tmp_wNAF directly into wNAF array
522 * - use wNAF splitting and include the blocks */
525 EC_POINT **tmp_points;
527 if (tmp_len < numblocks * blocksize)
529 /* possibly we can do with fewer blocks than estimated */
530 numblocks = (tmp_len + blocksize - 1) / blocksize;
531 if (numblocks > pre_comp->numblocks)
533 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
536 totalnum = num + numblocks;
539 /* split wNAF in 'numblocks' parts */
541 tmp_points = pre_comp->points;
543 for (i = num; i < totalnum; i++)
545 if (i < totalnum - 1)
547 wNAF_len[i] = blocksize;
548 if (tmp_len < blocksize)
550 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
553 tmp_len -= blocksize;
556 /* last block gets whatever is left
557 * (this could be more or less than 'blocksize'!) */
558 wNAF_len[i] = tmp_len;
561 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
564 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
565 OPENSSL_free(tmp_wNAF);
568 memcpy(wNAF[i], pp, wNAF_len[i]);
569 if (wNAF_len[i] > max_len)
570 max_len = wNAF_len[i];
572 if (*tmp_points == NULL)
574 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
575 OPENSSL_free(tmp_wNAF);
578 val_sub[i] = tmp_points;
579 tmp_points += pre_points_per_block;
582 OPENSSL_free(tmp_wNAF);
587 /* All points we precompute now go into a single array 'val'.
588 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
589 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
590 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
593 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
596 val[num_val] = NULL; /* pivot element */
598 /* allocate points for precomputation */
600 for (i = 0; i < num + num_scalar; i++)
603 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
605 *v = EC_POINT_new(group);
606 if (*v == NULL) goto err;
610 if (!(v == val + num_val))
612 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
616 if (!(tmp = EC_POINT_new(group)))
619 /* prepare precomputed values:
620 * val_sub[i][0] := points[i]
621 * val_sub[i][1] := 3 * points[i]
622 * val_sub[i][2] := 5 * points[i]
625 for (i = 0; i < num + num_scalar; i++)
629 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
633 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
638 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
639 for (j = 1; j < (1u << (wsize[i] - 1)); j++)
641 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
646 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
647 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
651 r_is_at_infinity = 1;
653 for (k = max_len - 1; k >= 0; k--)
655 if (!r_is_at_infinity)
657 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
660 for (i = 0; i < totalnum; i++)
662 if (wNAF_len[i] > (size_t)k)
664 int digit = wNAF[i][k];
674 if (is_neg != r_is_inverted)
676 if (!r_is_at_infinity)
678 if (!EC_POINT_invert(group, r, ctx)) goto err;
680 r_is_inverted = !r_is_inverted;
685 if (r_is_at_infinity)
687 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
688 r_is_at_infinity = 0;
692 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
699 if (r_is_at_infinity)
701 if (!EC_POINT_set_to_infinity(group, r)) goto err;
706 if (!EC_POINT_invert(group, r, ctx)) goto err;
713 BN_CTX_free(new_ctx);
718 if (wNAF_len != NULL)
719 OPENSSL_free(wNAF_len);
724 for (w = wNAF; *w != NULL; w++)
731 for (v = val; *v != NULL; v++)
732 EC_POINT_clear_free(*v);
738 OPENSSL_free(val_sub);
744 /* ec_wNAF_precompute_mult()
745 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
746 * for use with wNAF splitting as implemented in ec_wNAF_mul().
748 * 'pre_comp->points' is an array of multiples of the generator
749 * of the following form:
750 * points[0] = generator;
751 * points[1] = 3 * generator;
753 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
754 * points[2^(w-1)] = 2^blocksize * generator;
755 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
757 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
758 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
760 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
761 * points[2^(w-1)*numblocks] = NULL
763 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
765 const EC_POINT *generator;
766 EC_POINT *tmp_point = NULL, *base = NULL, **var;
767 BN_CTX *new_ctx = NULL;
769 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
770 EC_POINT **points = NULL;
771 EC_PRE_COMP *pre_comp;
774 /* if there is an old EC_PRE_COMP object, throw it away */
775 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
777 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
780 generator = EC_GROUP_get0_generator(group);
781 if (generator == NULL)
783 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
789 ctx = new_ctx = BN_CTX_new();
795 order = BN_CTX_get(ctx);
796 if (order == NULL) goto err;
798 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
799 if (BN_is_zero(order))
801 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
805 bits = BN_num_bits(order);
806 /* The following parameters mean we precompute (approximately)
809 * TBD: The combination 8, 4 is perfect for 160 bits; for other
810 * bit lengths, other parameter combinations might provide better
815 if (EC_window_bits_for_scalar_size(bits) > w)
817 /* let's not make the window too small ... */
818 w = EC_window_bits_for_scalar_size(bits);
821 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
823 pre_points_per_block = 1u << (w - 1);
824 num = pre_points_per_block * numblocks; /* number of points to compute and store */
826 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
829 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
834 var[num] = NULL; /* pivot */
835 for (i = 0; i < num; i++)
837 if ((var[i] = EC_POINT_new(group)) == NULL)
839 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
844 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
846 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
850 if (!EC_POINT_copy(base, generator))
853 /* do the precomputation */
854 for (i = 0; i < numblocks; i++)
858 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
861 if (!EC_POINT_copy(*var++, base))
864 for (j = 1; j < pre_points_per_block; j++, var++)
866 /* calculate odd multiples of the current base point */
867 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
871 if (i < numblocks - 1)
873 /* get the next base (multiply current one by 2^blocksize) */
878 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
882 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
884 for (k = 2; k < blocksize; k++)
886 if (!EC_POINT_dbl(group,base,base,ctx))
892 if (!EC_POINTs_make_affine(group, num, points, ctx))
895 pre_comp->group = group;
896 pre_comp->blocksize = blocksize;
897 pre_comp->numblocks = numblocks;
899 pre_comp->points = points;
903 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
904 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
913 BN_CTX_free(new_ctx);
915 ec_pre_comp_free(pre_comp);
920 for (p = points; *p != NULL; p++)
922 OPENSSL_free(points);
925 EC_POINT_free(tmp_point);
932 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
934 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)