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 = OPENSSL_zalloc(sizeof(*ret));
105 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
109 ret->blocksize = 8; /* default */
110 ret->w = 4; /* default */
115 static void *ec_pre_comp_dup(void *src_)
117 EC_PRE_COMP *src = src_;
119 /* no need to actually copy, these objects never change! */
121 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
126 static void ec_pre_comp_free(void *pre_)
129 EC_PRE_COMP *pre = pre_;
134 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
141 for (p = pre->points; *p != NULL; p++)
143 OPENSSL_free(pre->points);
148 static void ec_pre_comp_clear_free(void *pre_)
151 EC_PRE_COMP *pre = pre_;
156 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
163 for (p = pre->points; *p != NULL; p++) {
164 EC_POINT_clear_free(*p);
165 OPENSSL_cleanse(p, sizeof(*p));
167 OPENSSL_free(pre->points);
169 OPENSSL_clear_free(pre, sizeof(*pre));
173 * TODO: table should be optimised for the wNAF-based implementation,
174 * sometimes smaller windows will give better performance (thus the
175 * boundaries should be increased)
177 #define EC_window_bits_for_scalar_size(b) \
188 * \sum scalars[i]*points[i],
191 * in the addition if scalar != NULL
193 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
194 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
197 BN_CTX *new_ctx = NULL;
198 const EC_POINT *generator = NULL;
199 EC_POINT *tmp = NULL;
201 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
202 size_t pre_points_per_block = 0;
205 int r_is_inverted = 0;
206 int r_is_at_infinity = 1;
207 size_t *wsize = NULL; /* individual window sizes */
208 signed char **wNAF = NULL; /* individual wNAFs */
209 size_t *wNAF_len = NULL;
212 EC_POINT **val = NULL; /* precomputation */
214 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
215 * 'pre_comp->points' */
216 const EC_PRE_COMP *pre_comp = NULL;
217 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
218 * treated like other scalars, i.e.
219 * precomputation is not available */
222 if (group->meth != r->meth) {
223 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
227 if ((scalar == NULL) && (num == 0)) {
228 return EC_POINT_set_to_infinity(group, r);
231 for (i = 0; i < num; i++) {
232 if (group->meth != points[i]->meth) {
233 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
239 ctx = new_ctx = BN_CTX_new();
244 if (scalar != NULL) {
245 generator = EC_GROUP_get0_generator(group);
246 if (generator == NULL) {
247 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
251 /* look if we can use precomputed multiples of generator */
254 EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup,
255 ec_pre_comp_free, ec_pre_comp_clear_free);
257 if (pre_comp && pre_comp->numblocks
258 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
260 blocksize = pre_comp->blocksize;
263 * determine maximum number of blocks that wNAF splitting may
264 * yield (NB: maximum wNAF length is bit length plus one)
266 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
269 * we cannot use more blocks than we have precomputation for
271 if (numblocks > pre_comp->numblocks)
272 numblocks = pre_comp->numblocks;
274 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
276 /* check that pre_comp looks sane */
277 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
278 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
282 /* can't use precomputation */
285 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
290 totalnum = num + numblocks;
292 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
293 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
294 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
296 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
298 /* Ensure wNAF is initialised in case we end up going to err */
300 wNAF[0] = NULL; /* preliminary pivot */
302 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
303 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
308 * num_val will be the total number of temporarily precomputed points
312 for (i = 0; i < num + num_scalar; i++) {
315 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
316 wsize[i] = EC_window_bits_for_scalar_size(bits);
317 num_val += (size_t)1 << (wsize[i] - 1);
318 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
320 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
324 if (wNAF_len[i] > max_len)
325 max_len = wNAF_len[i];
329 /* we go here iff scalar != NULL */
331 if (pre_comp == NULL) {
332 if (num_scalar != 1) {
333 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
336 /* we have already generated a wNAF for 'scalar' */
338 signed char *tmp_wNAF = NULL;
341 if (num_scalar != 0) {
342 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
347 * use the window size for which we have precomputation
349 wsize[num] = pre_comp->w;
350 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
354 if (tmp_len <= max_len) {
356 * One of the other wNAFs is at least as long as the wNAF
357 * belonging to the generator, so wNAF splitting will not buy
362 totalnum = num + 1; /* don't use wNAF splitting */
363 wNAF[num] = tmp_wNAF;
364 wNAF[num + 1] = NULL;
365 wNAF_len[num] = tmp_len;
366 if (tmp_len > max_len)
369 * pre_comp->points starts with the points that we need here:
371 val_sub[num] = pre_comp->points;
374 * don't include tmp_wNAF directly into wNAF array - use wNAF
375 * splitting and include the blocks
379 EC_POINT **tmp_points;
381 if (tmp_len < numblocks * blocksize) {
383 * possibly we can do with fewer blocks than estimated
385 numblocks = (tmp_len + blocksize - 1) / blocksize;
386 if (numblocks > pre_comp->numblocks) {
387 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
390 totalnum = num + numblocks;
393 /* split wNAF in 'numblocks' parts */
395 tmp_points = pre_comp->points;
397 for (i = num; i < totalnum; i++) {
398 if (i < totalnum - 1) {
399 wNAF_len[i] = blocksize;
400 if (tmp_len < blocksize) {
401 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
404 tmp_len -= blocksize;
407 * last block gets whatever is left (this could be
408 * more or less than 'blocksize'!)
410 wNAF_len[i] = tmp_len;
413 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
414 if (wNAF[i] == NULL) {
415 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
416 OPENSSL_free(tmp_wNAF);
419 memcpy(wNAF[i], pp, wNAF_len[i]);
420 if (wNAF_len[i] > max_len)
421 max_len = wNAF_len[i];
423 if (*tmp_points == NULL) {
424 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
425 OPENSSL_free(tmp_wNAF);
428 val_sub[i] = tmp_points;
429 tmp_points += pre_points_per_block;
432 OPENSSL_free(tmp_wNAF);
438 * All points we precompute now go into a single array 'val'.
439 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
440 * subarray of 'pre_comp->points' if we already have precomputation.
442 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
444 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
447 val[num_val] = NULL; /* pivot element */
449 /* allocate points for precomputation */
451 for (i = 0; i < num + num_scalar; i++) {
453 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
454 *v = EC_POINT_new(group);
460 if (!(v == val + num_val)) {
461 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
465 if ((tmp = EC_POINT_new(group)) == NULL)
469 * prepare precomputed values:
470 * val_sub[i][0] := points[i]
471 * val_sub[i][1] := 3 * points[i]
472 * val_sub[i][2] := 5 * points[i]
475 for (i = 0; i < num + num_scalar; i++) {
477 if (!EC_POINT_copy(val_sub[i][0], points[i]))
480 if (!EC_POINT_copy(val_sub[i][0], generator))
485 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
487 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
489 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
495 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
498 r_is_at_infinity = 1;
500 for (k = max_len - 1; k >= 0; k--) {
501 if (!r_is_at_infinity) {
502 if (!EC_POINT_dbl(group, r, r, ctx))
506 for (i = 0; i < totalnum; i++) {
507 if (wNAF_len[i] > (size_t)k) {
508 int digit = wNAF[i][k];
517 if (is_neg != r_is_inverted) {
518 if (!r_is_at_infinity) {
519 if (!EC_POINT_invert(group, r, ctx))
522 r_is_inverted = !r_is_inverted;
527 if (r_is_at_infinity) {
528 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
530 r_is_at_infinity = 0;
533 (group, r, r, val_sub[i][digit >> 1], ctx))
541 if (r_is_at_infinity) {
542 if (!EC_POINT_set_to_infinity(group, r))
546 if (!EC_POINT_invert(group, r, ctx))
553 BN_CTX_free(new_ctx);
556 OPENSSL_free(wNAF_len);
560 for (w = wNAF; *w != NULL; w++)
566 for (v = val; *v != NULL; v++)
567 EC_POINT_clear_free(*v);
571 OPENSSL_free(val_sub);
576 * ec_wNAF_precompute_mult()
577 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
578 * for use with wNAF splitting as implemented in ec_wNAF_mul().
580 * 'pre_comp->points' is an array of multiples of the generator
581 * of the following form:
582 * points[0] = generator;
583 * points[1] = 3 * generator;
585 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
586 * points[2^(w-1)] = 2^blocksize * generator;
587 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
589 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
590 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
592 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
593 * points[2^(w-1)*numblocks] = NULL
595 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
597 const EC_POINT *generator;
598 EC_POINT *tmp_point = NULL, *base = NULL, **var;
599 BN_CTX *new_ctx = NULL;
601 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
602 EC_POINT **points = NULL;
603 EC_PRE_COMP *pre_comp;
606 /* if there is an old EC_PRE_COMP object, throw it away */
607 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup,
608 ec_pre_comp_free, ec_pre_comp_clear_free);
610 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
613 generator = EC_GROUP_get0_generator(group);
614 if (generator == NULL) {
615 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
620 ctx = new_ctx = BN_CTX_new();
626 order = BN_CTX_get(ctx);
630 if (!EC_GROUP_get_order(group, order, ctx))
632 if (BN_is_zero(order)) {
633 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
637 bits = BN_num_bits(order);
639 * The following parameters mean we precompute (approximately) one point
640 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
641 * bit lengths, other parameter combinations might provide better
646 if (EC_window_bits_for_scalar_size(bits) > w) {
647 /* let's not make the window too small ... */
648 w = EC_window_bits_for_scalar_size(bits);
651 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
655 pre_points_per_block = (size_t)1 << (w - 1);
656 num = pre_points_per_block * numblocks; /* number of points to compute
659 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
660 if (points == NULL) {
661 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
666 var[num] = NULL; /* pivot */
667 for (i = 0; i < num; i++) {
668 if ((var[i] = EC_POINT_new(group)) == NULL) {
669 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
674 if ((tmp_point = EC_POINT_new(group)) == NULL
675 || (base = EC_POINT_new(group)) == NULL) {
676 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
680 if (!EC_POINT_copy(base, generator))
683 /* do the precomputation */
684 for (i = 0; i < numblocks; i++) {
687 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
690 if (!EC_POINT_copy(*var++, base))
693 for (j = 1; j < pre_points_per_block; j++, var++) {
695 * calculate odd multiples of the current base point
697 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
701 if (i < numblocks - 1) {
703 * get the next base (multiply current one by 2^blocksize)
707 if (blocksize <= 2) {
708 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
712 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
714 for (k = 2; k < blocksize; k++) {
715 if (!EC_POINT_dbl(group, base, base, ctx))
721 if (!EC_POINTs_make_affine(group, num, points, ctx))
724 pre_comp->group = group;
725 pre_comp->blocksize = blocksize;
726 pre_comp->numblocks = numblocks;
728 pre_comp->points = points;
732 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
733 ec_pre_comp_dup, ec_pre_comp_free,
734 ec_pre_comp_clear_free))
742 BN_CTX_free(new_ctx);
743 ec_pre_comp_free(pre_comp);
747 for (p = points; *p != NULL; p++)
749 OPENSSL_free(points);
751 EC_POINT_free(tmp_point);
756 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
758 if (EC_EX_DATA_get_data
759 (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free,
760 ec_pre_comp_clear_free) != NULL)