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.
65 #include <openssl/err.h>
67 #include "internal/bn_int.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 * TODO: table should be optimised for the wNAF-based implementation,
178 * sometimes smaller windows will give better performance (thus the
179 * boundaries should be increased)
181 #define EC_window_bits_for_scalar_size(b) \
192 * \sum scalars[i]*points[i],
195 * in the addition if scalar != NULL
197 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
198 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
201 BN_CTX *new_ctx = NULL;
202 const EC_POINT *generator = NULL;
203 EC_POINT *tmp = NULL;
205 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
206 size_t pre_points_per_block = 0;
209 int r_is_inverted = 0;
210 int r_is_at_infinity = 1;
211 size_t *wsize = NULL; /* individual window sizes */
212 signed char **wNAF = NULL; /* individual wNAFs */
213 size_t *wNAF_len = NULL;
216 EC_POINT **val = NULL; /* precomputation */
218 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
219 * 'pre_comp->points' */
220 const EC_PRE_COMP *pre_comp = NULL;
221 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
222 * treated like other scalars, i.e.
223 * precomputation is not available */
226 if (group->meth != r->meth) {
227 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
231 if ((scalar == NULL) && (num == 0)) {
232 return EC_POINT_set_to_infinity(group, r);
235 for (i = 0; i < num; i++) {
236 if (group->meth != points[i]->meth) {
237 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
243 ctx = new_ctx = BN_CTX_new();
248 if (scalar != NULL) {
249 generator = EC_GROUP_get0_generator(group);
250 if (generator == NULL) {
251 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
255 /* look if we can use precomputed multiples of generator */
258 EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup,
259 ec_pre_comp_free, ec_pre_comp_clear_free);
261 if (pre_comp && pre_comp->numblocks
262 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
264 blocksize = pre_comp->blocksize;
267 * determine maximum number of blocks that wNAF splitting may
268 * yield (NB: maximum wNAF length is bit length plus one)
270 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
273 * we cannot use more blocks than we have precomputation for
275 if (numblocks > pre_comp->numblocks)
276 numblocks = pre_comp->numblocks;
278 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
280 /* check that pre_comp looks sane */
281 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
282 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
286 /* can't use precomputation */
289 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
294 totalnum = num + numblocks;
296 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
297 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
298 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
300 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
302 /* Ensure wNAF is initialised in case we end up going to err */
304 wNAF[0] = NULL; /* preliminary pivot */
306 if (!wsize || !wNAF_len || !wNAF || !val_sub) {
307 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
312 * num_val will be the total number of temporarily precomputed points
316 for (i = 0; i < num + num_scalar; i++) {
319 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
320 wsize[i] = EC_window_bits_for_scalar_size(bits);
321 num_val += (size_t)1 << (wsize[i] - 1);
322 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
324 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
328 if (wNAF_len[i] > max_len)
329 max_len = wNAF_len[i];
333 /* we go here iff scalar != NULL */
335 if (pre_comp == NULL) {
336 if (num_scalar != 1) {
337 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
340 /* we have already generated a wNAF for 'scalar' */
342 signed char *tmp_wNAF = NULL;
345 if (num_scalar != 0) {
346 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
351 * use the window size for which we have precomputation
353 wsize[num] = pre_comp->w;
354 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
358 if (tmp_len <= max_len) {
360 * One of the other wNAFs is at least as long as the wNAF
361 * belonging to the generator, so wNAF splitting will not buy
366 totalnum = num + 1; /* don't use wNAF splitting */
367 wNAF[num] = tmp_wNAF;
368 wNAF[num + 1] = NULL;
369 wNAF_len[num] = tmp_len;
370 if (tmp_len > max_len)
373 * pre_comp->points starts with the points that we need here:
375 val_sub[num] = pre_comp->points;
378 * don't include tmp_wNAF directly into wNAF array - use wNAF
379 * splitting and include the blocks
383 EC_POINT **tmp_points;
385 if (tmp_len < numblocks * blocksize) {
387 * possibly we can do with fewer blocks than estimated
389 numblocks = (tmp_len + blocksize - 1) / blocksize;
390 if (numblocks > pre_comp->numblocks) {
391 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
394 totalnum = num + numblocks;
397 /* split wNAF in 'numblocks' parts */
399 tmp_points = pre_comp->points;
401 for (i = num; i < totalnum; i++) {
402 if (i < totalnum - 1) {
403 wNAF_len[i] = blocksize;
404 if (tmp_len < blocksize) {
405 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
408 tmp_len -= blocksize;
411 * last block gets whatever is left (this could be
412 * more or less than 'blocksize'!)
414 wNAF_len[i] = tmp_len;
417 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
418 if (wNAF[i] == NULL) {
419 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
420 OPENSSL_free(tmp_wNAF);
423 memcpy(wNAF[i], pp, wNAF_len[i]);
424 if (wNAF_len[i] > max_len)
425 max_len = wNAF_len[i];
427 if (*tmp_points == NULL) {
428 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
429 OPENSSL_free(tmp_wNAF);
432 val_sub[i] = tmp_points;
433 tmp_points += pre_points_per_block;
436 OPENSSL_free(tmp_wNAF);
442 * All points we precompute now go into a single array 'val'.
443 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
444 * subarray of 'pre_comp->points' if we already have precomputation.
446 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
448 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
451 val[num_val] = NULL; /* pivot element */
453 /* allocate points for precomputation */
455 for (i = 0; i < num + num_scalar; i++) {
457 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
458 *v = EC_POINT_new(group);
464 if (!(v == val + num_val)) {
465 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
469 if (!(tmp = EC_POINT_new(group)))
473 * prepare precomputed values:
474 * val_sub[i][0] := points[i]
475 * val_sub[i][1] := 3 * points[i]
476 * val_sub[i][2] := 5 * points[i]
479 for (i = 0; i < num + num_scalar; i++) {
481 if (!EC_POINT_copy(val_sub[i][0], points[i]))
484 if (!EC_POINT_copy(val_sub[i][0], generator))
489 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
491 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
493 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
499 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
502 r_is_at_infinity = 1;
504 for (k = max_len - 1; k >= 0; k--) {
505 if (!r_is_at_infinity) {
506 if (!EC_POINT_dbl(group, r, r, ctx))
510 for (i = 0; i < totalnum; i++) {
511 if (wNAF_len[i] > (size_t)k) {
512 int digit = wNAF[i][k];
521 if (is_neg != r_is_inverted) {
522 if (!r_is_at_infinity) {
523 if (!EC_POINT_invert(group, r, ctx))
526 r_is_inverted = !r_is_inverted;
531 if (r_is_at_infinity) {
532 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
534 r_is_at_infinity = 0;
537 (group, r, r, val_sub[i][digit >> 1], ctx))
545 if (r_is_at_infinity) {
546 if (!EC_POINT_set_to_infinity(group, r))
550 if (!EC_POINT_invert(group, r, ctx))
558 BN_CTX_free(new_ctx);
562 if (wNAF_len != NULL)
563 OPENSSL_free(wNAF_len);
567 for (w = wNAF; *w != NULL; w++)
573 for (v = val; *v != NULL; v++)
574 EC_POINT_clear_free(*v);
578 if (val_sub != NULL) {
579 OPENSSL_free(val_sub);
585 * ec_wNAF_precompute_mult()
586 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
587 * for use with wNAF splitting as implemented in ec_wNAF_mul().
589 * 'pre_comp->points' is an array of multiples of the generator
590 * of the following form:
591 * points[0] = generator;
592 * points[1] = 3 * generator;
594 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
595 * points[2^(w-1)] = 2^blocksize * generator;
596 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
598 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
599 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
601 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
602 * points[2^(w-1)*numblocks] = NULL
604 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
606 const EC_POINT *generator;
607 EC_POINT *tmp_point = NULL, *base = NULL, **var;
608 BN_CTX *new_ctx = NULL;
610 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
611 EC_POINT **points = NULL;
612 EC_PRE_COMP *pre_comp;
615 /* if there is an old EC_PRE_COMP object, throw it away */
616 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup,
617 ec_pre_comp_free, ec_pre_comp_clear_free);
619 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
622 generator = EC_GROUP_get0_generator(group);
623 if (generator == NULL) {
624 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
629 ctx = new_ctx = BN_CTX_new();
635 order = BN_CTX_get(ctx);
639 if (!EC_GROUP_get_order(group, order, ctx))
641 if (BN_is_zero(order)) {
642 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
646 bits = BN_num_bits(order);
648 * The following parameters mean we precompute (approximately) one point
649 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
650 * bit lengths, other parameter combinations might provide better
655 if (EC_window_bits_for_scalar_size(bits) > w) {
656 /* let's not make the window too small ... */
657 w = EC_window_bits_for_scalar_size(bits);
660 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
664 pre_points_per_block = (size_t)1 << (w - 1);
665 num = pre_points_per_block * numblocks; /* number of points to compute
668 points = OPENSSL_malloc(sizeof(EC_POINT *) * (num + 1));
670 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
675 var[num] = NULL; /* pivot */
676 for (i = 0; i < num; i++) {
677 if ((var[i] = EC_POINT_new(group)) == NULL) {
678 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
683 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) {
684 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
688 if (!EC_POINT_copy(base, generator))
691 /* do the precomputation */
692 for (i = 0; i < numblocks; i++) {
695 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
698 if (!EC_POINT_copy(*var++, base))
701 for (j = 1; j < pre_points_per_block; j++, var++) {
703 * calculate odd multiples of the current base point
705 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
709 if (i < numblocks - 1) {
711 * get the next base (multiply current one by 2^blocksize)
715 if (blocksize <= 2) {
716 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
720 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
722 for (k = 2; k < blocksize; k++) {
723 if (!EC_POINT_dbl(group, base, base, ctx))
729 if (!EC_POINTs_make_affine(group, num, points, ctx))
732 pre_comp->group = group;
733 pre_comp->blocksize = blocksize;
734 pre_comp->numblocks = numblocks;
736 pre_comp->points = points;
740 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
741 ec_pre_comp_dup, ec_pre_comp_free,
742 ec_pre_comp_clear_free))
751 BN_CTX_free(new_ctx);
753 ec_pre_comp_free(pre_comp);
757 for (p = points; *p != NULL; p++)
759 OPENSSL_free(points);
761 EC_POINT_free(tmp_point);
766 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
768 if (EC_EX_DATA_get_data
769 (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free,
770 ec_pre_comp_clear_free) != NULL)