Merge remote-tracking branch 'trevp/pemfix' into trev-pem-fix
[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) 1998-2007 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 #define OPENSSL_FIPSAPI
65
66 #include <string.h>
67
68 #include <openssl/err.h>
69
70 #include "ec_lcl.h"
71
72
73 /*
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>).
78  */
79
80
81
82
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) */
92         int references;
93 } EC_PRE_COMP;
94  
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 *);
99
100 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
101         {
102         EC_PRE_COMP *ret = NULL;
103
104         if (!group)
105                 return NULL;
106
107         ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
108         if (!ret)
109                 {
110                 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
111                 return ret;
112                 }
113         ret->group = group;
114         ret->blocksize = 8; /* default */
115         ret->numblocks = 0;
116         ret->w = 4; /* default */
117         ret->points = NULL;
118         ret->num = 0;
119         ret->references = 1;
120         return ret;
121         }
122
123 static void *ec_pre_comp_dup(void *src_)
124         {
125         EC_PRE_COMP *src = src_;
126
127         /* no need to actually copy, these objects never change! */
128
129         CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
130
131         return src_;
132         }
133
134 static void ec_pre_comp_free(void *pre_)
135         {
136         int i;
137         EC_PRE_COMP *pre = pre_;
138
139         if (!pre)
140                 return;
141
142         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
143         if (i > 0)
144                 return;
145
146         if (pre->points)
147                 {
148                 EC_POINT **p;
149
150                 for (p = pre->points; *p != NULL; p++)
151                         EC_POINT_free(*p);
152                 OPENSSL_free(pre->points);
153                 }
154         OPENSSL_free(pre);
155         }
156
157 static void ec_pre_comp_clear_free(void *pre_)
158         {
159         int i;
160         EC_PRE_COMP *pre = pre_;
161
162         if (!pre)
163                 return;
164
165         i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
166         if (i > 0)
167                 return;
168
169         if (pre->points)
170                 {
171                 EC_POINT **p;
172
173                 for (p = pre->points; *p != NULL; p++)
174                         {
175                         EC_POINT_clear_free(*p);
176                         OPENSSL_cleanse(p, sizeof *p);
177                         }
178                 OPENSSL_free(pre->points);
179                 }
180         OPENSSL_cleanse(pre, sizeof *pre);
181         OPENSSL_free(pre);
182         }
183
184
185
186
187 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
188  * This is an array  r[]  of values that are either zero or odd with an
189  * absolute value less than  2^w  satisfying
190  *     scalar = \sum_j r[j]*2^j
191  * where at most one of any  w+1  consecutive digits is non-zero
192  * with the exception that the most significant digit may be only
193  * w-1 zeros away from that next non-zero digit.
194  */
195 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
196         {
197         int window_val;
198         int ok = 0;
199         signed char *r = NULL;
200         int sign = 1;
201         int bit, next_bit, mask;
202         size_t len = 0, j;
203         
204         if (BN_is_zero(scalar))
205                 {
206                 r = OPENSSL_malloc(1);
207                 if (!r)
208                         {
209                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
210                         goto err;
211                         }
212                 r[0] = 0;
213                 *ret_len = 1;
214                 return r;
215                 }
216                 
217         if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
218                 {
219                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
220                 goto err;
221                 }
222         bit = 1 << w; /* at most 128 */
223         next_bit = bit << 1; /* at most 256 */
224         mask = next_bit - 1; /* at most 255 */
225
226         if (BN_is_negative(scalar))
227                 {
228                 sign = -1;
229                 }
230
231         if (scalar->d == NULL || scalar->top == 0)
232                 {
233                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
234                 goto err;
235                 }
236
237         len = BN_num_bits(scalar);
238         r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
239                                       * (*ret_len will be set to the actual length, i.e. at most
240                                       * BN_num_bits(scalar) + 1) */
241         if (r == NULL)
242                 {
243                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
244                 goto err;
245                 }
246         window_val = scalar->d[0] & mask;
247         j = 0;
248         while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
249                 {
250                 int digit = 0;
251
252                 /* 0 <= window_val <= 2^(w+1) */
253
254                 if (window_val & 1)
255                         {
256                         /* 0 < window_val < 2^(w+1) */
257
258                         if (window_val & bit)
259                                 {
260                                 digit = window_val - next_bit; /* -2^w < digit < 0 */
261
262 #if 1 /* modified wNAF */
263                                 if (j + w + 1 >= len)
264                                         {
265                                         /* special case for generating modified wNAFs:
266                                          * no new bits will be added into window_val,
267                                          * so using a positive digit here will decrease
268                                          * the total length of the representation */
269                                         
270                                         digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
271                                         }
272 #endif
273                                 }
274                         else
275                                 {
276                                 digit = window_val; /* 0 < digit < 2^w */
277                                 }
278                         
279                         if (digit <= -bit || digit >= bit || !(digit & 1))
280                                 {
281                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
282                                 goto err;
283                                 }
284
285                         window_val -= digit;
286
287                         /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
288                          * for modified window NAFs, it may also be 2^w
289                          */
290                         if (window_val != 0 && window_val != next_bit && window_val != bit)
291                                 {
292                                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
293                                 goto err;
294                                 }
295                         }
296
297                 r[j++] = sign * digit;
298
299                 window_val >>= 1;
300                 window_val += bit * BN_is_bit_set(scalar, j + w);
301
302                 if (window_val > next_bit)
303                         {
304                         ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
305                         goto err;
306                         }
307                 }
308
309         if (j > len + 1)
310                 {
311                 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
312                 goto err;
313                 }
314         len = j;
315         ok = 1;
316
317  err:
318         if (!ok)
319                 {
320                 OPENSSL_free(r);
321                 r = NULL;
322                 }
323         if (ok)
324                 *ret_len = len;
325         return r;
326         }
327
328
329 /* TODO: table should be optimised for the wNAF-based implementation,
330  *       sometimes smaller windows will give better performance
331  *       (thus the boundaries should be increased)
332  */
333 #define EC_window_bits_for_scalar_size(b) \
334                 ((size_t) \
335                  ((b) >= 2000 ? 6 : \
336                   (b) >=  800 ? 5 : \
337                   (b) >=  300 ? 4 : \
338                   (b) >=   70 ? 3 : \
339                   (b) >=   20 ? 2 : \
340                   1))
341
342 /* Compute
343  *      \sum scalars[i]*points[i],
344  * also including
345  *      scalar*generator
346  * in the addition if scalar != NULL
347  */
348 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
349         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
350         {
351         BN_CTX *new_ctx = NULL;
352         const EC_POINT *generator = NULL;
353         EC_POINT *tmp = NULL;
354         size_t totalnum;
355         size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
356         size_t pre_points_per_block = 0;
357         size_t i, j;
358         int k;
359         int r_is_inverted = 0;
360         int r_is_at_infinity = 1;
361         size_t *wsize = NULL; /* individual window sizes */
362         signed char **wNAF = NULL; /* individual wNAFs */
363         size_t *wNAF_len = NULL;
364         size_t max_len = 0;
365         size_t num_val;
366         EC_POINT **val = NULL; /* precomputation */
367         EC_POINT **v;
368         EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
369         const EC_PRE_COMP *pre_comp = NULL;
370         int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
371                              * i.e. precomputation is not available */
372         int ret = 0;
373         
374         if (group->meth != r->meth)
375                 {
376                 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
377                 return 0;
378                 }
379
380         if ((scalar == NULL) && (num == 0))
381                 {
382                 return EC_POINT_set_to_infinity(group, r);
383                 }
384
385         for (i = 0; i < num; i++)
386                 {
387                 if (group->meth != points[i]->meth)
388                         {
389                         ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
390                         return 0;
391                         }
392                 }
393
394         if (ctx == NULL)
395                 {
396                 ctx = new_ctx = BN_CTX_new();
397                 if (ctx == NULL)
398                         goto err;
399                 }
400
401         if (scalar != NULL)
402                 {
403                 generator = EC_GROUP_get0_generator(group);
404                 if (generator == NULL)
405                         {
406                         ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
407                         goto err;
408                         }
409                 
410                 /* look if we can use precomputed multiples of generator */
411
412                 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
413
414                 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
415                         {
416                         blocksize = pre_comp->blocksize;
417
418                         /* determine maximum number of blocks that wNAF splitting may yield
419                          * (NB: maximum wNAF length is bit length plus one) */
420                         numblocks = (BN_num_bits(scalar) / blocksize) + 1;
421
422                         /* we cannot use more blocks than we have precomputation for */
423                         if (numblocks > pre_comp->numblocks)
424                                 numblocks = pre_comp->numblocks;
425
426                         pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
427
428                         /* check that pre_comp looks sane */
429                         if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
430                                 {
431                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
432                                 goto err;
433                                 }
434                         }
435                 else
436                         {
437                         /* can't use precomputation */
438                         pre_comp = NULL;
439                         numblocks = 1;
440                         num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
441                         }
442                 }
443         
444         totalnum = num + numblocks;
445
446         wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
447         wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
448         wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
449         val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
450                  
451         if (!wsize || !wNAF_len || !wNAF || !val_sub)
452                 {
453                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
454                 goto err;
455                 }
456
457         wNAF[0] = NULL; /* preliminary pivot */
458
459         /* num_val will be the total number of temporarily precomputed points */
460         num_val = 0;
461
462         for (i = 0; i < num + num_scalar; i++)
463                 {
464                 size_t bits;
465
466                 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
467                 wsize[i] = EC_window_bits_for_scalar_size(bits);
468                 num_val += (size_t)1 << (wsize[i] - 1);
469                 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
470                 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
471                 if (wNAF[i] == NULL)
472                         goto err;
473                 if (wNAF_len[i] > max_len)
474                         max_len = wNAF_len[i];
475                 }
476
477         if (numblocks)
478                 {
479                 /* we go here iff scalar != NULL */
480                 
481                 if (pre_comp == NULL)
482                         {
483                         if (num_scalar != 1)
484                                 {
485                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
486                                 goto err;
487                                 }
488                         /* we have already generated a wNAF for 'scalar' */
489                         }
490                 else
491                         {
492                         signed char *tmp_wNAF = NULL;
493                         size_t tmp_len = 0;
494                         
495                         if (num_scalar != 0)
496                                 {
497                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
498                                 goto err;
499                                 }
500
501                         /* use the window size for which we have precomputation */
502                         wsize[num] = pre_comp->w;
503                         tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
504                         if (!tmp_wNAF)
505                                 goto err;
506
507                         if (tmp_len <= max_len)
508                                 {
509                                 /* One of the other wNAFs is at least as long
510                                  * as the wNAF belonging to the generator,
511                                  * so wNAF splitting will not buy us anything. */
512
513                                 numblocks = 1;
514                                 totalnum = num + 1; /* don't use wNAF splitting */
515                                 wNAF[num] = tmp_wNAF;
516                                 wNAF[num + 1] = NULL;
517                                 wNAF_len[num] = tmp_len;
518                                 if (tmp_len > max_len)
519                                         max_len = tmp_len;
520                                 /* pre_comp->points starts with the points that we need here: */
521                                 val_sub[num] = pre_comp->points;
522                                 }
523                         else
524                                 {
525                                 /* don't include tmp_wNAF directly into wNAF array
526                                  * - use wNAF splitting and include the blocks */
527
528                                 signed char *pp;
529                                 EC_POINT **tmp_points;
530                                 
531                                 if (tmp_len < numblocks * blocksize)
532                                         {
533                                         /* possibly we can do with fewer blocks than estimated */
534                                         numblocks = (tmp_len + blocksize - 1) / blocksize;
535                                         if (numblocks > pre_comp->numblocks)
536                                                 {
537                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
538                                                 goto err;
539                                                 }
540                                         totalnum = num + numblocks;
541                                         }
542                                 
543                                 /* split wNAF in 'numblocks' parts */
544                                 pp = tmp_wNAF;
545                                 tmp_points = pre_comp->points;
546
547                                 for (i = num; i < totalnum; i++)
548                                         {
549                                         if (i < totalnum - 1)
550                                                 {
551                                                 wNAF_len[i] = blocksize;
552                                                 if (tmp_len < blocksize)
553                                                         {
554                                                         ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
555                                                         goto err;
556                                                         }
557                                                 tmp_len -= blocksize;
558                                                 }
559                                         else
560                                                 /* last block gets whatever is left
561                                                  * (this could be more or less than 'blocksize'!) */
562                                                 wNAF_len[i] = tmp_len;
563                                         
564                                         wNAF[i + 1] = NULL;
565                                         wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
566                                         if (wNAF[i] == NULL)
567                                                 {
568                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
569                                                 OPENSSL_free(tmp_wNAF);
570                                                 goto err;
571                                                 }
572                                         memcpy(wNAF[i], pp, wNAF_len[i]);
573                                         if (wNAF_len[i] > max_len)
574                                                 max_len = wNAF_len[i];
575
576                                         if (*tmp_points == NULL)
577                                                 {
578                                                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
579                                                 OPENSSL_free(tmp_wNAF);
580                                                 goto err;
581                                                 }
582                                         val_sub[i] = tmp_points;
583                                         tmp_points += pre_points_per_block;
584                                         pp += blocksize;
585                                         }
586                                 OPENSSL_free(tmp_wNAF);
587                                 }
588                         }
589                 }
590
591         /* All points we precompute now go into a single array 'val'.
592          * 'val_sub[i]' is a pointer to the subarray for the i-th point,
593          * or to a subarray of 'pre_comp->points' if we already have precomputation. */
594         val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
595         if (val == NULL)
596                 {
597                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
598                 goto err;
599                 }
600         val[num_val] = NULL; /* pivot element */
601
602         /* allocate points for precomputation */
603         v = val;
604         for (i = 0; i < num + num_scalar; i++)
605                 {
606                 val_sub[i] = v;
607                 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
608                         {
609                         *v = EC_POINT_new(group);
610                         if (*v == NULL) goto err;
611                         v++;
612                         }
613                 }
614         if (!(v == val + num_val))
615                 {
616                 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
617                 goto err;
618                 }
619
620         if (!(tmp = EC_POINT_new(group)))
621                 goto err;
622
623         /* prepare precomputed values:
624          *    val_sub[i][0] :=     points[i]
625          *    val_sub[i][1] := 3 * points[i]
626          *    val_sub[i][2] := 5 * points[i]
627          *    ...
628          */
629         for (i = 0; i < num + num_scalar; i++)
630                 {
631                 if (i < num)
632                         {
633                         if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
634                         }
635                 else
636                         {
637                         if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
638                         }
639
640                 if (wsize[i] > 1)
641                         {
642                         if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
643                         for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
644                                 {
645                                 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
646                                 }
647                         }
648                 }
649
650 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
651         if (!EC_POINTs_make_affine(group, num_val, val, ctx))
652                 goto err;
653 #endif
654
655         r_is_at_infinity = 1;
656
657         for (k = max_len - 1; k >= 0; k--)
658                 {
659                 if (!r_is_at_infinity)
660                         {
661                         if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
662                         }
663                 
664                 for (i = 0; i < totalnum; i++)
665                         {
666                         if (wNAF_len[i] > (size_t)k)
667                                 {
668                                 int digit = wNAF[i][k];
669                                 int is_neg;
670
671                                 if (digit) 
672                                         {
673                                         is_neg = digit < 0;
674
675                                         if (is_neg)
676                                                 digit = -digit;
677
678                                         if (is_neg != r_is_inverted)
679                                                 {
680                                                 if (!r_is_at_infinity)
681                                                         {
682                                                         if (!EC_POINT_invert(group, r, ctx)) goto err;
683                                                         }
684                                                 r_is_inverted = !r_is_inverted;
685                                                 }
686
687                                         /* digit > 0 */
688
689                                         if (r_is_at_infinity)
690                                                 {
691                                                 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
692                                                 r_is_at_infinity = 0;
693                                                 }
694                                         else
695                                                 {
696                                                 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
697                                                 }
698                                         }
699                                 }
700                         }
701                 }
702
703         if (r_is_at_infinity)
704                 {
705                 if (!EC_POINT_set_to_infinity(group, r)) goto err;
706                 }
707         else
708                 {
709                 if (r_is_inverted)
710                         if (!EC_POINT_invert(group, r, ctx)) goto err;
711                 }
712         
713         ret = 1;
714
715  err:
716         if (new_ctx != NULL)
717                 BN_CTX_free(new_ctx);
718         if (tmp != NULL)
719                 EC_POINT_free(tmp);
720         if (wsize != NULL)
721                 OPENSSL_free(wsize);
722         if (wNAF_len != NULL)
723                 OPENSSL_free(wNAF_len);
724         if (wNAF != NULL)
725                 {
726                 signed char **w;
727                 
728                 for (w = wNAF; *w != NULL; w++)
729                         OPENSSL_free(*w);
730                 
731                 OPENSSL_free(wNAF);
732                 }
733         if (val != NULL)
734                 {
735                 for (v = val; *v != NULL; v++)
736                         EC_POINT_clear_free(*v);
737
738                 OPENSSL_free(val);
739                 }
740         if (val_sub != NULL)
741                 {
742                 OPENSSL_free(val_sub);
743                 }
744         return ret;
745         }
746
747
748 /* ec_wNAF_precompute_mult()
749  * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
750  * for use with wNAF splitting as implemented in ec_wNAF_mul().
751  * 
752  * 'pre_comp->points' is an array of multiples of the generator
753  * of the following form:
754  * points[0] =     generator;
755  * points[1] = 3 * generator;
756  * ...
757  * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
758  * points[2^(w-1)]   =     2^blocksize * generator;
759  * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
760  * ...
761  * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
762  * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
763  * ...
764  * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
765  * points[2^(w-1)*numblocks]       = NULL
766  */
767 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
768         {
769         const EC_POINT *generator;
770         EC_POINT *tmp_point = NULL, *base = NULL, **var;
771         BN_CTX *new_ctx = NULL;
772         BIGNUM *order;
773         size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
774         EC_POINT **points = NULL;
775         EC_PRE_COMP *pre_comp;
776         int ret = 0;
777
778         /* if there is an old EC_PRE_COMP object, throw it away */
779         EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
780
781         if ((pre_comp = ec_pre_comp_new(group)) == NULL)
782                 return 0;
783
784         generator = EC_GROUP_get0_generator(group);
785         if (generator == NULL)
786                 {
787                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
788                 goto err;
789                 }
790
791         if (ctx == NULL)
792                 {
793                 ctx = new_ctx = BN_CTX_new();
794                 if (ctx == NULL)
795                         goto err;
796                 }
797         
798         BN_CTX_start(ctx);
799         order = BN_CTX_get(ctx);
800         if (order == NULL) goto err;
801         
802         if (!EC_GROUP_get_order(group, order, ctx)) goto err;           
803         if (BN_is_zero(order))
804                 {
805                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
806                 goto err;
807                 }
808
809         bits = BN_num_bits(order);
810         /* The following parameters mean we precompute (approximately)
811          * one point per bit.
812          *
813          * TBD: The combination  8, 4  is perfect for 160 bits; for other
814          * bit lengths, other parameter combinations might provide better
815          * efficiency.
816          */
817         blocksize = 8;
818         w = 4;
819         if (EC_window_bits_for_scalar_size(bits) > w)
820                 {
821                 /* let's not make the window too small ... */
822                 w = EC_window_bits_for_scalar_size(bits);
823                 }
824
825         numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
826         
827         pre_points_per_block = (size_t)1 << (w - 1);
828         num = pre_points_per_block * numblocks; /* number of points to compute and store */
829
830         points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
831         if (!points)
832                 {
833                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
834                 goto err;
835                 }
836
837         var = points;
838         var[num] = NULL; /* pivot */
839         for (i = 0; i < num; i++)
840                 {
841                 if ((var[i] = EC_POINT_new(group)) == NULL)
842                         {
843                         ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
844                         goto err;
845                         }
846                 }
847
848         if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
849                 {
850                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
851                 goto err;
852                 }       
853         
854         if (!EC_POINT_copy(base, generator))
855                 goto err;
856         
857         /* do the precomputation */
858         for (i = 0; i < numblocks; i++)
859                 {
860                 size_t j;
861
862                 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
863                         goto err;
864
865                 if (!EC_POINT_copy(*var++, base))
866                         goto err;
867
868                 for (j = 1; j < pre_points_per_block; j++, var++)
869                         {
870                         /* calculate odd multiples of the current base point */
871                         if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
872                                 goto err;
873                         }
874
875                 if (i < numblocks - 1)
876                         {
877                         /* get the next base (multiply current one by 2^blocksize) */
878                         size_t k;
879
880                         if (blocksize <= 2)
881                                 {
882                                 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
883                                 goto err;
884                                 }                               
885
886                         if (!EC_POINT_dbl(group, base, tmp_point, ctx))
887                                 goto err;
888                         for (k = 2; k < blocksize; k++)
889                                 {
890                                 if (!EC_POINT_dbl(group,base,base,ctx))
891                                         goto err;
892                                 }
893                         }
894                 }
895
896         if (!EC_POINTs_make_affine(group, num, points, ctx))
897                 goto err;
898         
899         pre_comp->group = group;
900         pre_comp->blocksize = blocksize;
901         pre_comp->numblocks = numblocks;
902         pre_comp->w = w;
903         pre_comp->points = points;
904         points = NULL;
905         pre_comp->num = num;
906
907         if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
908                 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
909                 goto err;
910         pre_comp = NULL;
911
912         ret = 1;
913  err:
914         if (ctx != NULL)
915                 BN_CTX_end(ctx);
916         if (new_ctx != NULL)
917                 BN_CTX_free(new_ctx);
918         if (pre_comp)
919                 ec_pre_comp_free(pre_comp);
920         if (points)
921                 {
922                 EC_POINT **p;
923
924                 for (p = points; *p != NULL; p++)
925                         EC_POINT_free(*p);
926                 OPENSSL_free(points);
927                 }
928         if (tmp_point)
929                 EC_POINT_free(tmp_point);
930         if (base)
931                 EC_POINT_free(base);
932         return ret;
933         }
934
935
936 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
937         {
938         if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
939                 return 1;
940         else
941                 return 0;
942         }