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)
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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 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 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
93 EC_PRE_COMP *ret = NULL;
98 ret = OPENSSL_zalloc(sizeof(*ret));
100 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
104 ret->blocksize = 8; /* default */
105 ret->w = 4; /* default */
110 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
113 CRYPTO_add(&pre->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
117 void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
120 || CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP) > 0)
123 if (pre->points != NULL) {
126 for (pts = pre->points; *pts != NULL; pts++)
128 OPENSSL_free(pre->points);
134 * TODO: table should be optimised for the wNAF-based implementation,
135 * sometimes smaller windows will give better performance (thus the
136 * boundaries should be increased)
138 #define EC_window_bits_for_scalar_size(b) \
149 * \sum scalars[i]*points[i],
152 * in the addition if scalar != NULL
154 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
155 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
158 BN_CTX *new_ctx = NULL;
159 const EC_POINT *generator = NULL;
160 EC_POINT *tmp = NULL;
162 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
163 size_t pre_points_per_block = 0;
166 int r_is_inverted = 0;
167 int r_is_at_infinity = 1;
168 size_t *wsize = NULL; /* individual window sizes */
169 signed char **wNAF = NULL; /* individual wNAFs */
170 size_t *wNAF_len = NULL;
173 EC_POINT **val = NULL; /* precomputation */
175 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
176 * 'pre_comp->points' */
177 const EC_PRE_COMP *pre_comp = NULL;
178 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
179 * treated like other scalars, i.e.
180 * precomputation is not available */
183 if (group->meth != r->meth) {
184 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
188 if ((scalar == NULL) && (num == 0)) {
189 return EC_POINT_set_to_infinity(group, r);
192 for (i = 0; i < num; i++) {
193 if (group->meth != points[i]->meth) {
194 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
200 ctx = new_ctx = BN_CTX_new();
205 if (scalar != NULL) {
206 generator = EC_GROUP_get0_generator(group);
207 if (generator == NULL) {
208 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
212 /* look if we can use precomputed multiples of generator */
214 pre_comp = group->pre_comp.ec;
215 if (pre_comp && pre_comp->numblocks
216 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
218 blocksize = pre_comp->blocksize;
221 * determine maximum number of blocks that wNAF splitting may
222 * yield (NB: maximum wNAF length is bit length plus one)
224 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
227 * we cannot use more blocks than we have precomputation for
229 if (numblocks > pre_comp->numblocks)
230 numblocks = pre_comp->numblocks;
232 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
234 /* check that pre_comp looks sane */
235 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
236 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
240 /* can't use precomputation */
243 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
248 totalnum = num + numblocks;
250 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
251 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
252 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
254 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
256 /* Ensure wNAF is initialised in case we end up going to err */
258 wNAF[0] = NULL; /* preliminary pivot */
260 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
261 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
266 * num_val will be the total number of temporarily precomputed points
270 for (i = 0; i < num + num_scalar; i++) {
273 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
274 wsize[i] = EC_window_bits_for_scalar_size(bits);
275 num_val += (size_t)1 << (wsize[i] - 1);
276 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
278 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
282 if (wNAF_len[i] > max_len)
283 max_len = wNAF_len[i];
287 /* we go here iff scalar != NULL */
289 if (pre_comp == NULL) {
290 if (num_scalar != 1) {
291 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
294 /* we have already generated a wNAF for 'scalar' */
296 signed char *tmp_wNAF = NULL;
299 if (num_scalar != 0) {
300 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
305 * use the window size for which we have precomputation
307 wsize[num] = pre_comp->w;
308 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
312 if (tmp_len <= max_len) {
314 * One of the other wNAFs is at least as long as the wNAF
315 * belonging to the generator, so wNAF splitting will not buy
320 totalnum = num + 1; /* don't use wNAF splitting */
321 wNAF[num] = tmp_wNAF;
322 wNAF[num + 1] = NULL;
323 wNAF_len[num] = tmp_len;
324 if (tmp_len > max_len)
327 * pre_comp->points starts with the points that we need here:
329 val_sub[num] = pre_comp->points;
332 * don't include tmp_wNAF directly into wNAF array - use wNAF
333 * splitting and include the blocks
337 EC_POINT **tmp_points;
339 if (tmp_len < numblocks * blocksize) {
341 * possibly we can do with fewer blocks than estimated
343 numblocks = (tmp_len + blocksize - 1) / blocksize;
344 if (numblocks > pre_comp->numblocks) {
345 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
348 totalnum = num + numblocks;
351 /* split wNAF in 'numblocks' parts */
353 tmp_points = pre_comp->points;
355 for (i = num; i < totalnum; i++) {
356 if (i < totalnum - 1) {
357 wNAF_len[i] = blocksize;
358 if (tmp_len < blocksize) {
359 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
362 tmp_len -= blocksize;
365 * last block gets whatever is left (this could be
366 * more or less than 'blocksize'!)
368 wNAF_len[i] = tmp_len;
371 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
372 if (wNAF[i] == NULL) {
373 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
374 OPENSSL_free(tmp_wNAF);
377 memcpy(wNAF[i], pp, wNAF_len[i]);
378 if (wNAF_len[i] > max_len)
379 max_len = wNAF_len[i];
381 if (*tmp_points == NULL) {
382 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
383 OPENSSL_free(tmp_wNAF);
386 val_sub[i] = tmp_points;
387 tmp_points += pre_points_per_block;
390 OPENSSL_free(tmp_wNAF);
396 * All points we precompute now go into a single array 'val'.
397 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
398 * subarray of 'pre_comp->points' if we already have precomputation.
400 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
402 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
405 val[num_val] = NULL; /* pivot element */
407 /* allocate points for precomputation */
409 for (i = 0; i < num + num_scalar; i++) {
411 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
412 *v = EC_POINT_new(group);
418 if (!(v == val + num_val)) {
419 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
423 if ((tmp = EC_POINT_new(group)) == NULL)
427 * prepare precomputed values:
428 * val_sub[i][0] := points[i]
429 * val_sub[i][1] := 3 * points[i]
430 * val_sub[i][2] := 5 * points[i]
433 for (i = 0; i < num + num_scalar; i++) {
435 if (!EC_POINT_copy(val_sub[i][0], points[i]))
438 if (!EC_POINT_copy(val_sub[i][0], generator))
443 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
445 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
447 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
453 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
456 r_is_at_infinity = 1;
458 for (k = max_len - 1; k >= 0; k--) {
459 if (!r_is_at_infinity) {
460 if (!EC_POINT_dbl(group, r, r, ctx))
464 for (i = 0; i < totalnum; i++) {
465 if (wNAF_len[i] > (size_t)k) {
466 int digit = wNAF[i][k];
475 if (is_neg != r_is_inverted) {
476 if (!r_is_at_infinity) {
477 if (!EC_POINT_invert(group, r, ctx))
480 r_is_inverted = !r_is_inverted;
485 if (r_is_at_infinity) {
486 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
488 r_is_at_infinity = 0;
491 (group, r, r, val_sub[i][digit >> 1], ctx))
499 if (r_is_at_infinity) {
500 if (!EC_POINT_set_to_infinity(group, r))
504 if (!EC_POINT_invert(group, r, ctx))
511 BN_CTX_free(new_ctx);
514 OPENSSL_free(wNAF_len);
518 for (w = wNAF; *w != NULL; w++)
524 for (v = val; *v != NULL; v++)
525 EC_POINT_clear_free(*v);
529 OPENSSL_free(val_sub);
534 * ec_wNAF_precompute_mult()
535 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
536 * for use with wNAF splitting as implemented in ec_wNAF_mul().
538 * 'pre_comp->points' is an array of multiples of the generator
539 * of the following form:
540 * points[0] = generator;
541 * points[1] = 3 * generator;
543 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
544 * points[2^(w-1)] = 2^blocksize * generator;
545 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
547 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
548 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
550 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
551 * points[2^(w-1)*numblocks] = NULL
553 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
555 const EC_POINT *generator;
556 EC_POINT *tmp_point = NULL, *base = NULL, **var;
557 BN_CTX *new_ctx = NULL;
559 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
560 EC_POINT **points = NULL;
561 EC_PRE_COMP *pre_comp;
564 /* if there is an old EC_PRE_COMP object, throw it away */
565 EC_pre_comp_free(group);
566 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
569 generator = EC_GROUP_get0_generator(group);
570 if (generator == NULL) {
571 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
576 ctx = new_ctx = BN_CTX_new();
582 order = BN_CTX_get(ctx);
586 if (!EC_GROUP_get_order(group, order, ctx))
588 if (BN_is_zero(order)) {
589 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
593 bits = BN_num_bits(order);
595 * The following parameters mean we precompute (approximately) one point
596 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
597 * bit lengths, other parameter combinations might provide better
602 if (EC_window_bits_for_scalar_size(bits) > w) {
603 /* let's not make the window too small ... */
604 w = EC_window_bits_for_scalar_size(bits);
607 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
611 pre_points_per_block = (size_t)1 << (w - 1);
612 num = pre_points_per_block * numblocks; /* number of points to compute
615 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
616 if (points == NULL) {
617 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
622 var[num] = NULL; /* pivot */
623 for (i = 0; i < num; i++) {
624 if ((var[i] = EC_POINT_new(group)) == NULL) {
625 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
630 if ((tmp_point = EC_POINT_new(group)) == NULL
631 || (base = EC_POINT_new(group)) == NULL) {
632 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
636 if (!EC_POINT_copy(base, generator))
639 /* do the precomputation */
640 for (i = 0; i < numblocks; i++) {
643 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
646 if (!EC_POINT_copy(*var++, base))
649 for (j = 1; j < pre_points_per_block; j++, var++) {
651 * calculate odd multiples of the current base point
653 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
657 if (i < numblocks - 1) {
659 * get the next base (multiply current one by 2^blocksize)
663 if (blocksize <= 2) {
664 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
668 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
670 for (k = 2; k < blocksize; k++) {
671 if (!EC_POINT_dbl(group, base, base, ctx))
677 if (!EC_POINTs_make_affine(group, num, points, ctx))
680 pre_comp->group = group;
681 pre_comp->blocksize = blocksize;
682 pre_comp->numblocks = numblocks;
684 pre_comp->points = points;
687 SETPRECOMP(group, ec, pre_comp);
694 BN_CTX_free(new_ctx);
695 EC_ec_pre_comp_free(pre_comp);
699 for (p = points; *p != NULL; p++)
701 OPENSSL_free(points);
703 EC_POINT_free(tmp_point);
708 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
710 return HAVEPRECOMP(group, ec);