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1 /* crypto/ec/ec_mult.c */
2 /*
3  * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
4  */
5 /* ====================================================================
6  * Copyright (c) 1998-2007 The OpenSSL Project.  All rights reserved.
7  *
8  * Redistribution and use in source and binary forms, with or without
9  * modification, are permitted provided that the following conditions
10  * are met:
11  *
12  * 1. Redistributions of source code must retain the above copyright
13  *    notice, this list of conditions and the following disclaimer.
14  *
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
18  *    distribution.
19  *
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/)"
24  *
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.
29  *
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.
33  *
34  * 6. Redistributions of any form whatsoever must retain the following
35  *    acknowledgment:
36  *    "This product includes software developed by the OpenSSL Project
37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38  *
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  * ====================================================================
52  *
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).
56  *
57  */
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.
62  */
63 
64 #include <string.h>
65 
66 #include <openssl/err.h>
67 
68 #include "ec_lcl.h"
69 
70 
71 /*
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>).
76  */
77 
78 
79 
80 
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) */
90 	int references;
91 } EC_PRE_COMP;
92 
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 *);
97 
ec_pre_comp_new(const EC_GROUP * group)98 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
99 	{
100 	EC_PRE_COMP *ret = NULL;
101 
102 	if (!group)
103 		return NULL;
104 
105 	ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
106 	if (!ret)
107 		{
108 		ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
109 		return ret;
110 		}
111 	ret->group = group;
112 	ret->blocksize = 8; /* default */
113 	ret->numblocks = 0;
114 	ret->w = 4; /* default */
115 	ret->points = NULL;
116 	ret->num = 0;
117 	ret->references = 1;
118 	return ret;
119 	}
120 
ec_pre_comp_dup(void * src_)121 static void *ec_pre_comp_dup(void *src_)
122 	{
123 	EC_PRE_COMP *src = src_;
124 
125 	/* no need to actually copy, these objects never change! */
126 
127 	CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
128 
129 	return src_;
130 	}
131 
ec_pre_comp_free(void * pre_)132 static void ec_pre_comp_free(void *pre_)
133 	{
134 	int i;
135 	EC_PRE_COMP *pre = pre_;
136 
137 	if (!pre)
138 		return;
139 
140 	i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
141 	if (i > 0)
142 		return;
143 
144 	if (pre->points)
145 		{
146 		EC_POINT **p;
147 
148 		for (p = pre->points; *p != NULL; p++)
149 			EC_POINT_free(*p);
150 		OPENSSL_free(pre->points);
151 		}
152 	OPENSSL_free(pre);
153 	}
154 
ec_pre_comp_clear_free(void * pre_)155 static void ec_pre_comp_clear_free(void *pre_)
156 	{
157 	int i;
158 	EC_PRE_COMP *pre = pre_;
159 
160 	if (!pre)
161 		return;
162 
163 	i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
164 	if (i > 0)
165 		return;
166 
167 	if (pre->points)
168 		{
169 		EC_POINT **p;
170 
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);
175 		}
176 	OPENSSL_cleanse(pre, sizeof pre);
177 	OPENSSL_free(pre);
178 	}
179 
180 
181 
182 
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.
190  */
compute_wNAF(const BIGNUM * scalar,int w,size_t * ret_len)191 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
192 	{
193 	int window_val;
194 	int ok = 0;
195 	signed char *r = NULL;
196 	int sign = 1;
197 	int bit, next_bit, mask;
198 	size_t len = 0, j;
199 
200 	if (BN_is_zero(scalar))
201 		{
202 		r = OPENSSL_malloc(1);
203 		if (!r)
204 			{
205 			ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
206 			goto err;
207 			}
208 		r[0] = 0;
209 		*ret_len = 1;
210 		return r;
211 		}
212 
213 	if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
214 		{
215 		ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
216 		goto err;
217 		}
218 	bit = 1 << w; /* at most 128 */
219 	next_bit = bit << 1; /* at most 256 */
220 	mask = next_bit - 1; /* at most 255 */
221 
222 	if (BN_is_negative(scalar))
223 		{
224 		sign = -1;
225 		}
226 
227 	if (scalar->d == NULL || scalar->top == 0)
228 		{
229 		ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
230 		goto err;
231 		}
232 
233 	len = BN_num_bits(scalar);
234 	r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
235 	                              * (*ret_len will be set to the actual length, i.e. at most
236 	                              * BN_num_bits(scalar) + 1) */
237 	if (r == NULL)
238 		{
239 		ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
240 		goto err;
241 		}
242 	window_val = scalar->d[0] & mask;
243 	j = 0;
244 	while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
245 		{
246 		int digit = 0;
247 
248 		/* 0 <= window_val <= 2^(w+1) */
249 
250 		if (window_val & 1)
251 			{
252 			/* 0 < window_val < 2^(w+1) */
253 
254 			if (window_val & bit)
255 				{
256 				digit = window_val - next_bit; /* -2^w < digit < 0 */
257 
258 #if 1 /* modified wNAF */
259 				if (j + w + 1 >= len)
260 					{
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 */
265 
266 					digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
267 					}
268 #endif
269 				}
270 			else
271 				{
272 				digit = window_val; /* 0 < digit < 2^w */
273 				}
274 
275 			if (digit <= -bit || digit >= bit || !(digit & 1))
276 				{
277 				ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
278 				goto err;
279 				}
280 
281 			window_val -= digit;
282 
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
285 			 */
286 			if (window_val != 0 && window_val != next_bit && window_val != bit)
287 				{
288 				ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
289 				goto err;
290 				}
291 			}
292 
293 		r[j++] = sign * digit;
294 
295 		window_val >>= 1;
296 		window_val += bit * BN_is_bit_set(scalar, j + w);
297 
298 		if (window_val > next_bit)
299 			{
300 			ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
301 			goto err;
302 			}
303 		}
304 
305 	if (j > len + 1)
306 		{
307 		ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
308 		goto err;
309 		}
310 	len = j;
311 	ok = 1;
312 
313  err:
314 	if (!ok)
315 		{
316 		OPENSSL_free(r);
317 		r = NULL;
318 		}
319 	if (ok)
320 		*ret_len = len;
321 	return r;
322 	}
323 
324 
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)
328  */
329 #define EC_window_bits_for_scalar_size(b) \
330 		((size_t) \
331 		 ((b) >= 2000 ? 6 : \
332 		  (b) >=  800 ? 5 : \
333 		  (b) >=  300 ? 4 : \
334 		  (b) >=   70 ? 3 : \
335 		  (b) >=   20 ? 2 : \
336 		  1))
337 
338 /* Compute
339  *      \sum scalars[i]*points[i],
340  * also including
341  *      scalar*generator
342  * in the addition if scalar != NULL
343  */
ec_wNAF_mul(const EC_GROUP * group,EC_POINT * r,const BIGNUM * scalar,size_t num,const EC_POINT * points[],const BIGNUM * scalars[],BN_CTX * ctx)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)
346 	{
347 	BN_CTX *new_ctx = NULL;
348 	const EC_POINT *generator = NULL;
349 	EC_POINT *tmp = NULL;
350 	size_t totalnum;
351 	size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
352 	size_t pre_points_per_block = 0;
353 	size_t i, j;
354 	int k;
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;
360 	size_t max_len = 0;
361 	size_t num_val;
362 	EC_POINT **val = NULL; /* precomputation */
363 	EC_POINT **v;
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 */
368 	int ret = 0;
369 
370 	if (group->meth != r->meth)
371 		{
372 		ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
373 		return 0;
374 		}
375 
376 	if ((scalar == NULL) && (num == 0))
377 		{
378 		return EC_POINT_set_to_infinity(group, r);
379 		}
380 
381 	for (i = 0; i < num; i++)
382 		{
383 		if (group->meth != points[i]->meth)
384 			{
385 			ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
386 			return 0;
387 			}
388 		}
389 
390 	if (ctx == NULL)
391 		{
392 		ctx = new_ctx = BN_CTX_new();
393 		if (ctx == NULL)
394 			goto err;
395 		}
396 
397 	if (scalar != NULL)
398 		{
399 		generator = EC_GROUP_get0_generator(group);
400 		if (generator == NULL)
401 			{
402 			ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
403 			goto err;
404 			}
405 
406 		/* look if we can use precomputed multiples of generator */
407 
408 		pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
409 
410 		if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
411 			{
412 			blocksize = pre_comp->blocksize;
413 
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;
417 
418 			/* we cannot use more blocks than we have precomputation for */
419 			if (numblocks > pre_comp->numblocks)
420 				numblocks = pre_comp->numblocks;
421 
422 			pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
423 
424 			/* check that pre_comp looks sane */
425 			if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
426 				{
427 				ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
428 				goto err;
429 				}
430 			}
431 		else
432 			{
433 			/* can't use precomputation */
434 			pre_comp = NULL;
435 			numblocks = 1;
436 			num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
437 			}
438 		}
439 
440 	totalnum = num + numblocks;
441 
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]);
446 
447 	if (!wsize || !wNAF_len || !wNAF || !val_sub)
448 		{
449 		ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
450 		goto err;
451 		}
452 
453 	wNAF[0] = NULL;	/* preliminary pivot */
454 
455 	/* num_val will be the total number of temporarily precomputed points */
456 	num_val = 0;
457 
458 	for (i = 0; i < num + num_scalar; i++)
459 		{
460 		size_t bits;
461 
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 += (size_t)1 << (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]);
467 		if (wNAF[i] == NULL)
468 			goto err;
469 		if (wNAF_len[i] > max_len)
470 			max_len = wNAF_len[i];
471 		}
472 
473 	if (numblocks)
474 		{
475 		/* we go here iff scalar != NULL */
476 
477 		if (pre_comp == NULL)
478 			{
479 			if (num_scalar != 1)
480 				{
481 				ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
482 				goto err;
483 				}
484 			/* we have already generated a wNAF for 'scalar' */
485 			}
486 		else
487 			{
488 			signed char *tmp_wNAF = NULL;
489 			size_t tmp_len = 0;
490 
491 			if (num_scalar != 0)
492 				{
493 				ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
494 				goto err;
495 				}
496 
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);
500 			if (!tmp_wNAF)
501 				goto err;
502 
503 			if (tmp_len <= max_len)
504 				{
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. */
508 
509 				numblocks = 1;
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)
515 					max_len = tmp_len;
516 				/* pre_comp->points starts with the points that we need here: */
517 				val_sub[num] = pre_comp->points;
518 				}
519 			else
520 				{
521 				/* don't include tmp_wNAF directly into wNAF array
522 				 * - use wNAF splitting and include the blocks */
523 
524 				signed char *pp;
525 				EC_POINT **tmp_points;
526 
527 				if (tmp_len < numblocks * blocksize)
528 					{
529 					/* possibly we can do with fewer blocks than estimated */
530 					numblocks = (tmp_len + blocksize - 1) / blocksize;
531 					if (numblocks > pre_comp->numblocks)
532 						{
533 						ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
534 						goto err;
535 						}
536 					totalnum = num + numblocks;
537 					}
538 
539 				/* split wNAF in 'numblocks' parts */
540 				pp = tmp_wNAF;
541 				tmp_points = pre_comp->points;
542 
543 				for (i = num; i < totalnum; i++)
544 					{
545 					if (i < totalnum - 1)
546 						{
547 						wNAF_len[i] = blocksize;
548 						if (tmp_len < blocksize)
549 							{
550 							ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
551 							goto err;
552 							}
553 						tmp_len -= blocksize;
554 						}
555 					else
556 						/* last block gets whatever is left
557 						 * (this could be more or less than 'blocksize'!) */
558 						wNAF_len[i] = tmp_len;
559 
560 					wNAF[i + 1] = NULL;
561 					wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
562 					if (wNAF[i] == NULL)
563 						{
564 						ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
565 						OPENSSL_free(tmp_wNAF);
566 						goto err;
567 						}
568 					memcpy(wNAF[i], pp, wNAF_len[i]);
569 					if (wNAF_len[i] > max_len)
570 						max_len = wNAF_len[i];
571 
572 					if (*tmp_points == NULL)
573 						{
574 						ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
575 						OPENSSL_free(tmp_wNAF);
576 						goto err;
577 						}
578 					val_sub[i] = tmp_points;
579 					tmp_points += pre_points_per_block;
580 					pp += blocksize;
581 					}
582 				OPENSSL_free(tmp_wNAF);
583 				}
584 			}
585 		}
586 
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]);
591 	if (val == NULL)
592 		{
593 		ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
594 		goto err;
595 		}
596 	val[num_val] = NULL; /* pivot element */
597 
598 	/* allocate points for precomputation */
599 	v = val;
600 	for (i = 0; i < num + num_scalar; i++)
601 		{
602 		val_sub[i] = v;
603 		for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
604 			{
605 			*v = EC_POINT_new(group);
606 			if (*v == NULL) goto err;
607 			v++;
608 			}
609 		}
610 	if (!(v == val + num_val))
611 		{
612 		ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
613 		goto err;
614 		}
615 
616 	if (!(tmp = EC_POINT_new(group)))
617 		goto err;
618 
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]
623 	 *    ...
624 	 */
625 	for (i = 0; i < num + num_scalar; i++)
626 		{
627 		if (i < num)
628 			{
629 			if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
630 			}
631 		else
632 			{
633 			if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
634 			}
635 
636 		if (wsize[i] > 1)
637 			{
638 			if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
639 			for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
640 				{
641 				if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
642 				}
643 			}
644 		}
645 
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))
648 		goto err;
649 #endif
650 
651 	r_is_at_infinity = 1;
652 
653 	for (k = max_len - 1; k >= 0; k--)
654 		{
655 		if (!r_is_at_infinity)
656 			{
657 			if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
658 			}
659 
660 		for (i = 0; i < totalnum; i++)
661 			{
662 			if (wNAF_len[i] > (size_t)k)
663 				{
664 				int digit = wNAF[i][k];
665 				int is_neg;
666 
667 				if (digit)
668 					{
669 					is_neg = digit < 0;
670 
671 					if (is_neg)
672 						digit = -digit;
673 
674 					if (is_neg != r_is_inverted)
675 						{
676 						if (!r_is_at_infinity)
677 							{
678 							if (!EC_POINT_invert(group, r, ctx)) goto err;
679 							}
680 						r_is_inverted = !r_is_inverted;
681 						}
682 
683 					/* digit > 0 */
684 
685 					if (r_is_at_infinity)
686 						{
687 						if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
688 						r_is_at_infinity = 0;
689 						}
690 					else
691 						{
692 						if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
693 						}
694 					}
695 				}
696 			}
697 		}
698 
699 	if (r_is_at_infinity)
700 		{
701 		if (!EC_POINT_set_to_infinity(group, r)) goto err;
702 		}
703 	else
704 		{
705 		if (r_is_inverted)
706 			if (!EC_POINT_invert(group, r, ctx)) goto err;
707 		}
708 
709 	ret = 1;
710 
711  err:
712 	if (new_ctx != NULL)
713 		BN_CTX_free(new_ctx);
714 	if (tmp != NULL)
715 		EC_POINT_free(tmp);
716 	if (wsize != NULL)
717 		OPENSSL_free(wsize);
718 	if (wNAF_len != NULL)
719 		OPENSSL_free(wNAF_len);
720 	if (wNAF != NULL)
721 		{
722 		signed char **w;
723 
724 		for (w = wNAF; *w != NULL; w++)
725 			OPENSSL_free(*w);
726 
727 		OPENSSL_free(wNAF);
728 		}
729 	if (val != NULL)
730 		{
731 		for (v = val; *v != NULL; v++)
732 			EC_POINT_clear_free(*v);
733 
734 		OPENSSL_free(val);
735 		}
736 	if (val_sub != NULL)
737 		{
738 		OPENSSL_free(val_sub);
739 		}
740 	return ret;
741 	}
742 
743 
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().
747  *
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;
752  * ...
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;
756  * ...
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
759  * ...
760  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
761  * points[2^(w-1)*numblocks]       = NULL
762  */
ec_wNAF_precompute_mult(EC_GROUP * group,BN_CTX * ctx)763 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
764 	{
765 	const EC_POINT *generator;
766 	EC_POINT *tmp_point = NULL, *base = NULL, **var;
767 	BN_CTX *new_ctx = NULL;
768 	BIGNUM *order;
769 	size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
770 	EC_POINT **points = NULL;
771 	EC_PRE_COMP *pre_comp;
772 	int ret = 0;
773 
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);
776 
777 	if ((pre_comp = ec_pre_comp_new(group)) == NULL)
778 		return 0;
779 
780 	generator = EC_GROUP_get0_generator(group);
781 	if (generator == NULL)
782 		{
783 		ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
784 		goto err;
785 		}
786 
787 	if (ctx == NULL)
788 		{
789 		ctx = new_ctx = BN_CTX_new();
790 		if (ctx == NULL)
791 			goto err;
792 		}
793 
794 	BN_CTX_start(ctx);
795 	order = BN_CTX_get(ctx);
796 	if (order == NULL) goto err;
797 
798 	if (!EC_GROUP_get_order(group, order, ctx)) goto err;
799 	if (BN_is_zero(order))
800 		{
801 		ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
802 		goto err;
803 		}
804 
805 	bits = BN_num_bits(order);
806 	/* The following parameters mean we precompute (approximately)
807 	 * one point per bit.
808 	 *
809 	 * TBD: The combination  8, 4  is perfect for 160 bits; for other
810 	 * bit lengths, other parameter combinations might provide better
811 	 * efficiency.
812 	 */
813 	blocksize = 8;
814 	w = 4;
815 	if (EC_window_bits_for_scalar_size(bits) > w)
816 		{
817 		/* let's not make the window too small ... */
818 		w = EC_window_bits_for_scalar_size(bits);
819 		}
820 
821 	numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
822 
823 	pre_points_per_block = (size_t)1 << (w - 1);
824 	num = pre_points_per_block * numblocks; /* number of points to compute and store */
825 
826 	points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
827 	if (!points)
828 		{
829 		ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
830 		goto err;
831 		}
832 
833 	var = points;
834 	var[num] = NULL; /* pivot */
835 	for (i = 0; i < num; i++)
836 		{
837 		if ((var[i] = EC_POINT_new(group)) == NULL)
838 			{
839 			ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
840 			goto err;
841 			}
842 		}
843 
844 	if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
845 		{
846 		ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
847 		goto err;
848 		}
849 
850 	if (!EC_POINT_copy(base, generator))
851 		goto err;
852 
853 	/* do the precomputation */
854 	for (i = 0; i < numblocks; i++)
855 		{
856 		size_t j;
857 
858 		if (!EC_POINT_dbl(group, tmp_point, base, ctx))
859 			goto err;
860 
861 		if (!EC_POINT_copy(*var++, base))
862 			goto err;
863 
864 		for (j = 1; j < pre_points_per_block; j++, var++)
865 			{
866 			/* calculate odd multiples of the current base point */
867 			if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
868 				goto err;
869 			}
870 
871 		if (i < numblocks - 1)
872 			{
873 			/* get the next base (multiply current one by 2^blocksize) */
874 			size_t k;
875 
876 			if (blocksize <= 2)
877 				{
878 				ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
879 				goto err;
880 				}
881 
882 			if (!EC_POINT_dbl(group, base, tmp_point, ctx))
883 				goto err;
884 			for (k = 2; k < blocksize; k++)
885 				{
886 				if (!EC_POINT_dbl(group,base,base,ctx))
887 					goto err;
888 				}
889 			}
890  		}
891 
892 	if (!EC_POINTs_make_affine(group, num, points, ctx))
893 		goto err;
894 
895 	pre_comp->group = group;
896 	pre_comp->blocksize = blocksize;
897 	pre_comp->numblocks = numblocks;
898 	pre_comp->w = w;
899 	pre_comp->points = points;
900 	points = NULL;
901 	pre_comp->num = num;
902 
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))
905 		goto err;
906 	pre_comp = NULL;
907 
908 	ret = 1;
909  err:
910 	if (ctx != NULL)
911 		BN_CTX_end(ctx);
912 	if (new_ctx != NULL)
913 		BN_CTX_free(new_ctx);
914 	if (pre_comp)
915 		ec_pre_comp_free(pre_comp);
916 	if (points)
917 		{
918 		EC_POINT **p;
919 
920 		for (p = points; *p != NULL; p++)
921 			EC_POINT_free(*p);
922 		OPENSSL_free(points);
923 		}
924 	if (tmp_point)
925 		EC_POINT_free(tmp_point);
926 	if (base)
927 		EC_POINT_free(base);
928 	return ret;
929 	}
930 
931 
ec_wNAF_have_precompute_mult(const EC_GROUP * group)932 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
933 	{
934 	if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
935 		return 1;
936 	else
937 		return 0;
938 	}
939