Fix bug in DSA, EC methods.
[openssl.git] / crypto / ec / ec_mult.c
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) 1998-2003 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
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                 return ret;
108         ret->group = group;
109         ret->blocksize = 8; /* default */
110         ret->numblocks = 0;
111         ret->w = 4; /* default */
112         ret->points = NULL;
113         ret->num = 0;
114         ret->references = 1;
115         return ret;
116         }
117
118 static void *ec_pre_comp_dup(void *src_)
119         {
120         EC_PRE_COMP *src = src_;
121
122         /* no need to actually copy, these objects never change! */
123
124         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
125
126         return src_;
127         }
128
129 static void ec_pre_comp_free(void *pre_)
130         {
131         int i;
132         EC_PRE_COMP *pre = pre_;
133
134         if (!pre)
135                 return;
136
137         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
138         if (i > 0)
139                 return;
140
141         if (pre->points)
142                 {
143                 EC_POINT **p;
144
145                 for (p = pre->points; *p != NULL; p++)
146                         EC_POINT_free(*p);
147                 OPENSSL_free(pre->points);
148                 }
149         OPENSSL_free(pre);
150         }
151
152 static void ec_pre_comp_clear_free(void *pre_)
153         {
154         int i;
155         EC_PRE_COMP *pre = pre_;
156
157         if (!pre)
158                 return;
159
160         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
161         if (i > 0)
162                 return;
163
164         if (pre->points)
165                 {
166                 EC_POINT **p;
167
168                 for (p = pre->points; *p != NULL; p++)
169                         EC_POINT_clear_free(*p);
170                 OPENSSL_cleanse(pre->points, sizeof pre->points);
171                 OPENSSL_free(pre->points);
172                 }
173         OPENSSL_cleanse(pre, sizeof pre);
174         OPENSSL_free(pre);
175         }
176
177
178
179
180 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
181  * This is an array  r[]  of values that are either zero or odd with an
182  * absolute value less than  2^w  satisfying
183  *     scalar = \sum_j r[j]*2^j
184  * where at most one of any  w+1  consecutive digits is non-zero
185  * with the exception that the most significant digit may be only
186  * w-1 zeros away from that next non-zero digit.
187  */
188 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
189         {
190         int window_val;
191         int ok = 0;
192         signed char *r = NULL;
193         int sign = 1;
194         int bit, next_bit, mask;
195         size_t len = 0, j;
196         
197         if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
198                 {
199                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
200                 goto err;
201                 }
202         bit = 1 << w; /* at most 128 */
203         next_bit = bit << 1; /* at most 256 */
204         mask = next_bit - 1; /* at most 255 */
205
206         if (BN_is_negative(scalar))
207                 {
208                 sign = -1;
209                 }
210
211         len = BN_num_bits(scalar);
212         r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
213                                       * (*ret_len will be set to the actual length, i.e. at most
214                                       * BN_num_bits(scalar) + 1) */
215         if (r == NULL) goto err;
216
217         if (scalar->d == NULL || scalar->top == 0)
218                 {
219                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
220                 goto err;
221                 }
222         window_val = scalar->d[0] & mask;
223         j = 0;
224         while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
225                 {
226                 int digit = 0;
227
228                 /* 0 <= window_val <= 2^(w+1) */
229
230                 if (window_val & 1)
231                         {
232                         /* 0 < window_val < 2^(w+1) */
233
234                         if (window_val & bit)
235                                 {
236                                 digit = window_val - next_bit; /* -2^w < digit < 0 */
237
238 #if 1 /* modified wNAF */
239                                 if (j + w + 1 >= len)
240                                         {
241                                         /* special case for generating modified wNAFs:
242                                          * no new bits will be added into window_val,
243                                          * so using a positive digit here will decrease
244                                          * the total length of the representation */
245                                         
246                                         digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
247                                         }
248 #endif
249                                 }
250                         else
251                                 {
252                                 digit = window_val; /* 0 < digit < 2^w */
253                                 }
254                         
255                         if (digit <= -bit || digit >= bit || !(digit & 1))
256                                 {
257                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
258                                 goto err;
259                                 }
260
261                         window_val -= digit;
262
263                         /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
264                          * for modified window NAFs, it may also be 2^w
265                          */
266                         if (window_val != 0 && window_val != next_bit && window_val != bit)
267                                 {
268                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
269                                 goto err;
270                                 }
271                         }
272
273                 r[j++] = sign * digit;
274
275                 window_val >>= 1;
276                 window_val += bit * BN_is_bit_set(scalar, j + w);
277
278                 if (window_val > next_bit)
279                         {
280                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
281                         goto err;
282                         }
283                 }
284
285         if (j > len + 1)
286                 {
287                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
288                 goto err;
289                 }
290         len = j;
291         ok = 1;
292
293  err:
294         if (!ok)
295                 {
296                 OPENSSL_free(r);
297                 r = NULL;
298                 }
299         if (ok)
300                 *ret_len = len;
301         return r;
302         }
303
304
305 /* TODO: table should be optimised for the wNAF-based implementation,
306  *       sometimes smaller windows will give better performance
307  *       (thus the boundaries should be increased)
308  */
309 #define EC_window_bits_for_scalar_size(b) \
310                 ((size_t) \
311                  ((b) >= 2000 ? 6 : \
312                   (b) >=  800 ? 5 : \
313                   (b) >=  300 ? 4 : \
314                   (b) >=   70 ? 3 : \
315                   (b) >=   20 ? 2 : \
316                   1))
317
318 /* Compute
319  *      \sum scalars[i]*points[i],
320  * also including
321  *      scalar*generator
322  * in the addition if scalar != NULL
323  */
324 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
325         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
326         {
327         BN_CTX *new_ctx = NULL;
328         const EC_POINT *generator = NULL;
329         EC_POINT *tmp = NULL;
330         size_t totalnum;
331         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
332         size_t pre_points_per_block = 0;
333         size_t i, j;
334         int k;
335         int r_is_inverted = 0;
336         int r_is_at_infinity = 1;
337         size_t *wsize = NULL; /* individual window sizes */
338         signed char **wNAF = NULL; /* individual wNAFs */
339         size_t *wNAF_len = NULL;
340         size_t max_len = 0;
341         size_t num_val;
342         EC_POINT **val = NULL; /* precomputation */
343         EC_POINT **v;
344         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
345         const EC_PRE_COMP *pre_comp = NULL;
346         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
347                              * i.e. precomputation is not available */
348         int ret = 0;
349         
350         if (group->meth != r->meth)
351                 {
352                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
353                 return 0;
354                 }
355
356         if ((scalar == NULL) && (num == 0))
357                 {
358                 return EC_POINT_set_to_infinity(group, r);
359                 }
360
361         for (i = 0; i < num; i++)
362                 {
363                 if (group->meth != points[i]->meth)
364                         {
365                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
366                         return 0;
367                         }
368                 }
369
370         if (ctx == NULL)
371                 {
372                 ctx = new_ctx = BN_CTX_new();
373                 if (ctx == NULL)
374                         goto err;
375                 }
376
377         if (scalar != NULL)
378                 {
379                 generator = EC_GROUP_get0_generator(group);
380                 if (generator == NULL)
381                         {
382                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
383                         goto err;
384                         }
385                 
386                 /* look if we can use precomputed multiples of generator */
387
388                 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
389
390                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
391                         {
392                         blocksize = pre_comp->blocksize;
393
394                         /* determine maximum number of blocks that wNAF splitting may yield
395                          * (NB: maximum wNAF length is bit length plus one) */
396                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
397
398                         /* we cannot use more blocks than we have precomputation for */
399                         if (numblocks > pre_comp->numblocks)
400                                 numblocks = pre_comp->numblocks;
401
402                         pre_points_per_block = 1u << (pre_comp->w - 1);
403
404                         /* check that pre_comp looks sane */
405                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
406                                 {
407                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
408                                 goto err;
409                                 }
410                         }
411                 else
412                         {
413                         /* can't use precomputation */
414                         pre_comp = NULL;
415                         numblocks = 1;
416                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
417                         }
418                 }
419         
420         totalnum = num + numblocks;
421
422         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
423         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
424         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
425         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
426                  
427         if (!wsize || !wNAF_len || !wNAF || !val_sub)
428                 goto err;
429
430         wNAF[0] = NULL; /* preliminary pivot */
431
432         /* num_val will be the total number of temporarily precomputed points */
433         num_val = 0;
434
435         for (i = 0; i < num + num_scalar; i++)
436                 {
437                 size_t bits;
438
439                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
440                 wsize[i] = EC_window_bits_for_scalar_size(bits);
441                 num_val += 1u << (wsize[i] - 1);
442                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
443                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
444                 if (wNAF[i] == NULL)
445                         goto err;
446                 if (wNAF_len[i] > max_len)
447                         max_len = wNAF_len[i];
448                 }
449
450         if (numblocks)
451                 {
452                 /* we go here iff scalar != NULL */
453                 
454                 if (pre_comp == NULL)
455                         {
456                         if (num_scalar != 1)
457                                 {
458                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
459                                 goto err;
460                                 }
461                         /* we have already generated a wNAF for 'scalar' */
462                         }
463                 else
464                         {
465                         signed char *tmp_wNAF = NULL;
466                         size_t tmp_len = 0;
467                         
468                         if (num_scalar != 0)
469                                 {
470                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
471                                 goto err;
472                                 }
473
474                         /* use the window size for which we have precomputation */
475                         wsize[num] = pre_comp->w;
476                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
477                         if (!tmp_wNAF)
478                                 goto err;
479
480                         if (tmp_len <= max_len)
481                                 {
482                                 /* One of the other wNAFs is at least as long
483                                  * as the wNAF belonging to the generator,
484                                  * so wNAF splitting will not buy us anything. */
485
486                                 numblocks = 1;
487                                 totalnum = num + 1; /* don't use wNAF splitting */
488                                 wNAF[num] = tmp_wNAF;
489                                 wNAF[num + 1] = NULL;
490                                 wNAF_len[num] = tmp_len;
491                                 if (tmp_len > max_len)
492                                         max_len = tmp_len;
493                                 /* pre_comp->points starts with the points that we need here: */
494                                 val_sub[num] = pre_comp->points;
495                                 }
496                         else
497                                 {
498                                 /* don't include tmp_wNAF directly into wNAF array
499                                  * - use wNAF splitting and include the blocks */
500
501                                 signed char *pp;
502                                 EC_POINT **tmp_points;
503                                 
504                                 if (tmp_len < numblocks * blocksize)
505                                         {
506                                         /* possibly we can do with fewer blocks than estimated */
507                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
508                                         if (numblocks > pre_comp->numblocks)
509                                                 {
510                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
511                                                 goto err;
512                                                 }
513                                         totalnum = num + numblocks;
514                                         }
515                                 
516                                 /* split wNAF in 'numblocks' parts */
517                                 pp = tmp_wNAF;
518                                 tmp_points = pre_comp->points;
519
520                                 for (i = num; i < totalnum; i++)
521                                         {
522                                         if (i < totalnum - 1)
523                                                 {
524                                                 wNAF_len[i] = blocksize;
525                                                 if (tmp_len < blocksize)
526                                                         {
527                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
528                                                         goto err;
529                                                         }
530                                                 tmp_len -= blocksize;
531                                                 }
532                                         else
533                                                 /* last block gets whatever is left
534                                                  * (this could be more or less than 'blocksize'!) */
535                                                 wNAF_len[i] = tmp_len;
536                                         
537                                         wNAF[i + 1] = NULL;
538                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
539                                         if (wNAF[i] == NULL)
540                                                 {
541                                                 OPENSSL_free(tmp_wNAF);
542                                                 goto err;
543                                                 }
544                                         memcpy(wNAF[i], pp, wNAF_len[i]);
545                                         if (wNAF_len[i] > max_len)
546                                                 max_len = wNAF_len[i];
547
548                                         if (*tmp_points == NULL)
549                                                 {
550                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
551                                                 OPENSSL_free(tmp_wNAF);
552                                                 goto err;
553                                                 }
554                                         val_sub[i] = tmp_points;
555                                         tmp_points += pre_points_per_block;
556                                         pp += blocksize;
557                                         }
558                                 OPENSSL_free(tmp_wNAF);
559                                 }
560                         }
561                 }
562
563         /* All points we precompute now go into a single array 'val'.
564          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
565          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
566         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
567         if (val == NULL) goto err;
568         val[num_val] = NULL; /* pivot element */
569
570         /* allocate points for precomputation */
571         v = val;
572         for (i = 0; i < num + num_scalar; i++)
573                 {
574                 val_sub[i] = v;
575                 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
576                         {
577                         *v = EC_POINT_new(group);
578                         if (*v == NULL) goto err;
579                         v++;
580                         }
581                 }
582         if (!(v == val + num_val))
583                 {
584                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
585                 goto err;
586                 }
587
588         if (!(tmp = EC_POINT_new(group)))
589                 goto err;
590
591         /* prepare precomputed values:
592          *    val_sub[i][0] :=     points[i]
593          *    val_sub[i][1] := 3 * points[i]
594          *    val_sub[i][2] := 5 * points[i]
595          *    ...
596          */
597         for (i = 0; i < num + num_scalar; i++)
598                 {
599                 if (i < num)
600                         {
601                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
602                         }
603                 else
604                         {
605                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
606                         }
607
608                 if (wsize[i] > 1)
609                         {
610                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
611                         for (j = 1; j < (1u << (wsize[i] - 1)); j++)
612                                 {
613                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
614                                 }
615                         }
616                 }
617
618 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
619         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
620                 goto err;
621 #endif
622
623         r_is_at_infinity = 1;
624
625         for (k = max_len - 1; k >= 0; k--)
626                 {
627                 if (!r_is_at_infinity)
628                         {
629                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
630                         }
631                 
632                 for (i = 0; i < totalnum; i++)
633                         {
634                         if (wNAF_len[i] > (size_t)k)
635                                 {
636                                 int digit = wNAF[i][k];
637                                 int is_neg;
638
639                                 if (digit) 
640                                         {
641                                         is_neg = digit < 0;
642
643                                         if (is_neg)
644                                                 digit = -digit;
645
646                                         if (is_neg != r_is_inverted)
647                                                 {
648                                                 if (!r_is_at_infinity)
649                                                         {
650                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
651                                                         }
652                                                 r_is_inverted = !r_is_inverted;
653                                                 }
654
655                                         /* digit > 0 */
656
657                                         if (r_is_at_infinity)
658                                                 {
659                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
660                                                 r_is_at_infinity = 0;
661                                                 }
662                                         else
663                                                 {
664                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
665                                                 }
666                                         }
667                                 }
668                         }
669                 }
670
671         if (r_is_at_infinity)
672                 {
673                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
674                 }
675         else
676                 {
677                 if (r_is_inverted)
678                         if (!EC_POINT_invert(group, r, ctx)) goto err;
679                 }
680         
681         ret = 1;
682
683  err:
684         if (new_ctx != NULL)
685                 BN_CTX_free(new_ctx);
686         if (tmp != NULL)
687                 EC_POINT_free(tmp);
688         if (wsize != NULL)
689                 OPENSSL_free(wsize);
690         if (wNAF_len != NULL)
691                 OPENSSL_free(wNAF_len);
692         if (wNAF != NULL)
693                 {
694                 signed char **w;
695                 
696                 for (w = wNAF; *w != NULL; w++)
697                         OPENSSL_free(*w);
698                 
699                 OPENSSL_free(wNAF);
700                 }
701         if (val != NULL)
702                 {
703                 for (v = val; *v != NULL; v++)
704                         EC_POINT_clear_free(*v);
705
706                 OPENSSL_free(val);
707                 }
708         if (val_sub != NULL)
709                 {
710                 OPENSSL_free(val_sub);
711                 }
712         return ret;
713         }
714
715
716 /* ec_wNAF_precompute_mult()
717  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
718  * for use with wNAF splitting as implemented in ec_wNAF_mul().
719  * 
720  * 'pre_comp->points' is an array of multiples of the generator
721  * of the following form:
722  * points[0] =     generator;
723  * points[1] = 3 * generator;
724  * ...
725  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
726  * points[2^(w-1)]   =     2^blocksize * generator;
727  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
728  * ...
729  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
730  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
731  * ...
732  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
733  * points[2^(w-1)*numblocks]       = NULL
734  */
735 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
736         {
737         const EC_POINT *generator;
738         EC_POINT *tmp_point = NULL, *base = NULL, **var;
739         BN_CTX *new_ctx = NULL;
740         BIGNUM *order;
741         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
742         EC_POINT **points = NULL;
743         EC_PRE_COMP *pre_comp;
744         int ret = 0;
745
746         /* if there is an old EC_PRE_COMP object, throw it away */
747         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
748
749         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
750                 return 0;
751
752         generator = EC_GROUP_get0_generator(group);
753         if (generator == NULL)
754                 {
755                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
756                 goto err;
757                 }
758
759         if (ctx == NULL)
760                 {
761                 ctx = new_ctx = BN_CTX_new();
762                 if (ctx == NULL)
763                         goto err;
764                 }
765         
766         BN_CTX_start(ctx);
767         order = BN_CTX_get(ctx);
768         if (order == NULL) goto err;
769         
770         if (!EC_GROUP_get_order(group, order, ctx)) goto err;           
771         if (BN_is_zero(order))
772                 {
773                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
774                 goto err;
775                 }
776
777         bits = BN_num_bits(order);
778         /* The following parameters mean we precompute (approximately)
779          * one point per bit.
780          *
781          * TBD: The combination  8, 4  is perfect for 160 bits; for other
782          * bit lengths, other parameter combinations might provide better
783          * efficiency.
784          */
785         blocksize = 8;
786         w = 4;
787         if (EC_window_bits_for_scalar_size(bits) > w)
788                 {
789                 /* let's not make the window too small ... */
790                 w = EC_window_bits_for_scalar_size(bits);
791                 }
792
793         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
794         
795         pre_points_per_block = 1u << (w - 1);
796         num = pre_points_per_block * numblocks; /* number of points to compute and store */
797
798         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
799         if (!points)
800                 {
801                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
802                 goto err;
803                 }
804
805         var = points;
806         var[num] = NULL; /* pivot */
807         for (i = 0; i < num; i++)
808                 {
809                 if ((var[i] = EC_POINT_new(group)) == NULL)
810                         {
811                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
812                         goto err;
813                         }
814                 }
815
816         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
817                 {
818                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
819                 goto err;
820                 }       
821         
822         if (!EC_POINT_copy(base, generator))
823                 goto err;
824         
825         /* do the precomputation */
826         for (i = 0; i < numblocks; i++)
827                 {
828                 size_t j;
829
830                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
831                         goto err;
832
833                 if (!EC_POINT_copy(*var++, base))
834                         goto err;
835
836                 for (j = 1; j < pre_points_per_block; j++, var++)
837                         {
838                         /* calculate odd multiples of the current base point */
839                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
840                                 goto err;
841                         }
842
843                 if (i < numblocks - 1)
844                         {
845                         /* get the next base (multiply current one by 2^blocksize) */
846                         size_t k;
847
848                         if (blocksize <= 2)
849                                 {
850                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
851                                 goto err;
852                                 }                               
853
854                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
855                                 goto err;
856                         for (k = 2; k < blocksize; k++)
857                                 {
858                                 if (!EC_POINT_dbl(group,base,base,ctx))
859                                         goto err;
860                                 }
861                         }
862                 }
863
864         if (!EC_POINTs_make_affine(group, num, points, ctx))
865                 goto err;
866         
867         pre_comp->group = group;
868         pre_comp->blocksize = blocksize;
869         pre_comp->numblocks = numblocks;
870         pre_comp->w = w;
871         pre_comp->points = points;
872         points = NULL;
873         pre_comp->num = num;
874
875         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
876                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
877                 goto err;
878         pre_comp = NULL;
879
880         ret = 1;
881  err:
882         if (ctx != NULL)
883                 BN_CTX_end(ctx);
884         if (new_ctx != NULL)
885                 BN_CTX_free(new_ctx);
886         if (pre_comp)
887                 ec_pre_comp_free(pre_comp);
888         if (points)
889                 {
890                 EC_POINT **p;
891
892                 for (p = points; *p != NULL; p++)
893                         EC_POINT_free(*p);
894                 OPENSSL_free(points);
895                 }
896         if (tmp_point)
897                 EC_POINT_free(tmp_point);
898         if (base)
899                 EC_POINT_free(base);
900         return ret;
901         }
902
903
904 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
905         {
906         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
907                 return 1;
908         else
909                 return 0;
910         }