ec_mult.c: fix C4334 win64 compiler warning.
[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 #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                 {
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
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
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
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  */
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  */
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  */
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
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         }