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.
67 #include <openssl/err.h>
69 #include "internal/bn_int.h"
74 * This file implements the wNAF-based interleaving multi-exponentation method
75 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
76 * for multiplication with precomputation, we use wNAF splitting
77 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
83 /* structure for precomputed multiples of the generator */
84 typedef struct ec_pre_comp_st {
85 const EC_GROUP *group; /* parent EC_GROUP object */
86 size_t blocksize; /* block size for wNAF splitting */
87 size_t numblocks; /* max. number of blocks for which we have precomputation */
88 size_t w; /* window size */
89 EC_POINT **points; /* array with pre-calculated multiples of generator:
90 * 'num' pointers to EC_POINT objects followed by a NULL */
91 size_t num; /* numblocks * 2^(w-1) */
95 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
96 static void *ec_pre_comp_dup(void *);
97 static void ec_pre_comp_free(void *);
98 static void ec_pre_comp_clear_free(void *);
100 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
102 EC_PRE_COMP *ret = NULL;
107 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
110 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
114 ret->blocksize = 8; /* default */
116 ret->w = 4; /* default */
123 static void *ec_pre_comp_dup(void *src_)
125 EC_PRE_COMP *src = src_;
127 /* no need to actually copy, these objects never change! */
129 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
134 static void ec_pre_comp_free(void *pre_)
137 EC_PRE_COMP *pre = pre_;
142 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
150 for (p = pre->points; *p != NULL; p++)
152 OPENSSL_free(pre->points);
157 static void ec_pre_comp_clear_free(void *pre_)
160 EC_PRE_COMP *pre = pre_;
165 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
173 for (p = pre->points; *p != NULL; p++)
175 EC_POINT_clear_free(*p);
176 OPENSSL_cleanse(p, sizeof *p);
178 OPENSSL_free(pre->points);
180 OPENSSL_cleanse(pre, sizeof *pre);
190 /* TODO: table should be optimised for the wNAF-based implementation,
191 * sometimes smaller windows will give better performance
192 * (thus the boundaries should be increased)
194 #define EC_window_bits_for_scalar_size(b) \
204 * \sum scalars[i]*points[i],
207 * in the addition if scalar != NULL
209 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
210 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
212 BN_CTX *new_ctx = NULL;
213 const EC_POINT *generator = NULL;
214 EC_POINT *tmp = NULL;
216 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
217 size_t pre_points_per_block = 0;
220 int r_is_inverted = 0;
221 int r_is_at_infinity = 1;
222 size_t *wsize = NULL; /* individual window sizes */
223 signed char **wNAF = NULL; /* individual wNAFs */
224 size_t *wNAF_len = NULL;
227 EC_POINT **val = NULL; /* precomputation */
229 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
230 const EC_PRE_COMP *pre_comp = NULL;
231 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
232 * i.e. precomputation is not available */
235 if (group->meth != r->meth)
237 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
241 if ((scalar == NULL) && (num == 0))
243 return EC_POINT_set_to_infinity(group, r);
246 for (i = 0; i < num; i++)
248 if (group->meth != points[i]->meth)
250 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
257 ctx = new_ctx = BN_CTX_new();
264 generator = EC_GROUP_get0_generator(group);
265 if (generator == NULL)
267 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
271 /* look if we can use precomputed multiples of generator */
273 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
275 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
277 blocksize = pre_comp->blocksize;
279 /* determine maximum number of blocks that wNAF splitting may yield
280 * (NB: maximum wNAF length is bit length plus one) */
281 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
283 /* we cannot use more blocks than we have precomputation for */
284 if (numblocks > pre_comp->numblocks)
285 numblocks = pre_comp->numblocks;
287 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
289 /* check that pre_comp looks sane */
290 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
292 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
298 /* can't use precomputation */
301 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
305 totalnum = num + numblocks;
307 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
308 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
309 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
310 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
312 /* Ensure wNAF is initialised in case we end up going to err */
313 if (wNAF) wNAF[0] = NULL; /* preliminary pivot */
315 if (!wsize || !wNAF_len || !wNAF || !val_sub)
317 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
321 /* num_val will be the total number of temporarily precomputed points */
324 for (i = 0; i < num + num_scalar; i++)
328 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
329 wsize[i] = EC_window_bits_for_scalar_size(bits);
330 num_val += (size_t)1 << (wsize[i] - 1);
331 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
332 wNAF[i] = bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
335 if (wNAF_len[i] > max_len)
336 max_len = wNAF_len[i];
341 /* we go here iff scalar != NULL */
343 if (pre_comp == NULL)
347 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
350 /* we have already generated a wNAF for 'scalar' */
354 signed char *tmp_wNAF = NULL;
359 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
363 /* use the window size for which we have precomputation */
364 wsize[num] = pre_comp->w;
365 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
369 if (tmp_len <= max_len)
371 /* One of the other wNAFs is at least as long
372 * as the wNAF belonging to the generator,
373 * so wNAF splitting will not buy us anything. */
376 totalnum = num + 1; /* don't use wNAF splitting */
377 wNAF[num] = tmp_wNAF;
378 wNAF[num + 1] = NULL;
379 wNAF_len[num] = tmp_len;
380 if (tmp_len > max_len)
382 /* pre_comp->points starts with the points that we need here: */
383 val_sub[num] = pre_comp->points;
387 /* don't include tmp_wNAF directly into wNAF array
388 * - use wNAF splitting and include the blocks */
391 EC_POINT **tmp_points;
393 if (tmp_len < numblocks * blocksize)
395 /* possibly we can do with fewer blocks than estimated */
396 numblocks = (tmp_len + blocksize - 1) / blocksize;
397 if (numblocks > pre_comp->numblocks)
399 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
402 totalnum = num + numblocks;
405 /* split wNAF in 'numblocks' parts */
407 tmp_points = pre_comp->points;
409 for (i = num; i < totalnum; i++)
411 if (i < totalnum - 1)
413 wNAF_len[i] = blocksize;
414 if (tmp_len < blocksize)
416 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
419 tmp_len -= blocksize;
422 /* last block gets whatever is left
423 * (this could be more or less than 'blocksize'!) */
424 wNAF_len[i] = tmp_len;
427 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
430 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
431 OPENSSL_free(tmp_wNAF);
434 memcpy(wNAF[i], pp, wNAF_len[i]);
435 if (wNAF_len[i] > max_len)
436 max_len = wNAF_len[i];
438 if (*tmp_points == NULL)
440 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
441 OPENSSL_free(tmp_wNAF);
444 val_sub[i] = tmp_points;
445 tmp_points += pre_points_per_block;
448 OPENSSL_free(tmp_wNAF);
453 /* All points we precompute now go into a single array 'val'.
454 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
455 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
456 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
459 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
462 val[num_val] = NULL; /* pivot element */
464 /* allocate points for precomputation */
466 for (i = 0; i < num + num_scalar; i++)
469 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
471 *v = EC_POINT_new(group);
472 if (*v == NULL) goto err;
476 if (!(v == val + num_val))
478 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
482 if (!(tmp = EC_POINT_new(group)))
486 * prepare precomputed values:
487 * val_sub[i][0] := points[i]
488 * val_sub[i][1] := 3 * points[i]
489 * val_sub[i][2] := 5 * points[i]
492 for (i = 0; i < num + num_scalar; i++)
496 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
500 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
505 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
506 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
508 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
513 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
514 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
518 r_is_at_infinity = 1;
520 for (k = max_len - 1; k >= 0; k--)
522 if (!r_is_at_infinity)
524 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
527 for (i = 0; i < totalnum; i++)
529 if (wNAF_len[i] > (size_t)k)
531 int digit = wNAF[i][k];
541 if (is_neg != r_is_inverted)
543 if (!r_is_at_infinity)
545 if (!EC_POINT_invert(group, r, ctx)) goto err;
547 r_is_inverted = !r_is_inverted;
552 if (r_is_at_infinity)
554 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
555 r_is_at_infinity = 0;
559 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
566 if (r_is_at_infinity)
568 if (!EC_POINT_set_to_infinity(group, r)) goto err;
573 if (!EC_POINT_invert(group, r, ctx)) goto err;
580 BN_CTX_free(new_ctx);
585 if (wNAF_len != NULL)
586 OPENSSL_free(wNAF_len);
591 for (w = wNAF; *w != NULL; w++)
598 for (v = val; *v != NULL; v++)
599 EC_POINT_clear_free(*v);
605 OPENSSL_free(val_sub);
612 * ec_wNAF_precompute_mult()
613 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
614 * for use with wNAF splitting as implemented in ec_wNAF_mul().
616 * 'pre_comp->points' is an array of multiples of the generator
617 * of the following form:
618 * points[0] = generator;
619 * points[1] = 3 * generator;
621 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
622 * points[2^(w-1)] = 2^blocksize * generator;
623 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
625 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
626 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
628 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
629 * points[2^(w-1)*numblocks] = NULL
631 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
633 const EC_POINT *generator;
634 EC_POINT *tmp_point = NULL, *base = NULL, **var;
635 BN_CTX *new_ctx = NULL;
637 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
638 EC_POINT **points = NULL;
639 EC_PRE_COMP *pre_comp;
642 /* if there is an old EC_PRE_COMP object, throw it away */
643 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
645 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
648 generator = EC_GROUP_get0_generator(group);
649 if (generator == NULL)
651 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
657 ctx = new_ctx = BN_CTX_new();
663 order = BN_CTX_get(ctx);
664 if (order == NULL) goto err;
666 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
667 if (BN_is_zero(order))
669 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
673 bits = BN_num_bits(order);
674 /* The following parameters mean we precompute (approximately)
677 * TBD: The combination 8, 4 is perfect for 160 bits; for other
678 * bit lengths, other parameter combinations might provide better
683 if (EC_window_bits_for_scalar_size(bits) > w)
685 /* let's not make the window too small ... */
686 w = EC_window_bits_for_scalar_size(bits);
689 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
691 pre_points_per_block = (size_t)1 << (w - 1);
692 num = pre_points_per_block * numblocks; /* number of points to compute and store */
694 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
697 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
702 var[num] = NULL; /* pivot */
703 for (i = 0; i < num; i++)
705 if ((var[i] = EC_POINT_new(group)) == NULL)
707 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
712 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
714 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
718 if (!EC_POINT_copy(base, generator))
721 /* do the precomputation */
722 for (i = 0; i < numblocks; i++)
726 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
729 if (!EC_POINT_copy(*var++, base))
732 for (j = 1; j < pre_points_per_block; j++, var++)
734 /* calculate odd multiples of the current base point */
735 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
739 if (i < numblocks - 1)
741 /* get the next base (multiply current one by 2^blocksize) */
746 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
750 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
752 for (k = 2; k < blocksize; k++)
754 if (!EC_POINT_dbl(group,base,base,ctx))
760 if (!EC_POINTs_make_affine(group, num, points, ctx))
763 pre_comp->group = group;
764 pre_comp->blocksize = blocksize;
765 pre_comp->numblocks = numblocks;
767 pre_comp->points = points;
771 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
772 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
781 BN_CTX_free(new_ctx);
783 ec_pre_comp_free(pre_comp);
788 for (p = points; *p != NULL; p++)
790 OPENSSL_free(points);
793 EC_POINT_free(tmp_point);
800 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
802 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)