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1 | /* | |
2 | * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project. | |
3 | */ | |
4 | /* ==================================================================== | |
5 | * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved. | |
6 | * | |
7 | * Redistribution and use in source and binary forms, with or without | |
8 | * modification, are permitted provided that the following conditions | |
9 | * are met: | |
10 | * | |
11 | * 1. Redistributions of source code must retain the above copyright | |
12 | * notice, this list of conditions and the following disclaimer. | |
13 | * | |
14 | * 2. Redistributions in binary form must reproduce the above copyright | |
15 | * notice, this list of conditions and the following disclaimer in | |
16 | * the documentation and/or other materials provided with the | |
17 | * distribution. | |
18 | * | |
19 | * 3. All advertising materials mentioning features or use of this | |
20 | * software must display the following acknowledgment: | |
21 | * "This product includes software developed by the OpenSSL Project | |
22 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
23 | * | |
24 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
25 | * endorse or promote products derived from this software without | |
26 | * prior written permission. For written permission, please contact | |
27 | * openssl-core@openssl.org. | |
28 | * | |
29 | * 5. Products derived from this software may not be called "OpenSSL" | |
30 | * nor may "OpenSSL" appear in their names without prior written | |
31 | * permission of the OpenSSL Project. | |
32 | * | |
33 | * 6. Redistributions of any form whatsoever must retain the following | |
34 | * acknowledgment: | |
35 | * "This product includes software developed by the OpenSSL Project | |
36 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
37 | * | |
38 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
39 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
40 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
41 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
42 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
43 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
44 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
45 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
46 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
47 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
48 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
49 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
50 | * ==================================================================== | |
51 | * | |
52 | * This product includes cryptographic software written by Eric Young | |
53 | * (eay@cryptsoft.com). This product includes software written by Tim | |
54 | * Hudson (tjh@cryptsoft.com). | |
55 | * | |
56 | */ | |
57 | /* ==================================================================== | |
58 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
59 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
60 | * and contributed to the OpenSSL project. | |
61 | */ | |
62 | ||
63 | #include <string.h> | |
64 | #include <openssl/err.h> | |
65 | ||
66 | #include "internal/bn_int.h" | |
67 | #include "ec_lcl.h" | |
68 | ||
69 | /* | |
70 | * This file implements the wNAF-based interleaving multi-exponentation method | |
71 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); | |
72 | * for multiplication with precomputation, we use wNAF splitting | |
73 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>). | |
74 | */ | |
75 | ||
76 | /* structure for precomputed multiples of the generator */ | |
77 | struct ec_pre_comp_st { | |
78 | const EC_GROUP *group; /* parent EC_GROUP object */ | |
79 | size_t blocksize; /* block size for wNAF splitting */ | |
80 | size_t numblocks; /* max. number of blocks for which we have | |
81 | * precomputation */ | |
82 | size_t w; /* window size */ | |
83 | EC_POINT **points; /* array with pre-calculated multiples of | |
84 | * generator: 'num' pointers to EC_POINT | |
85 | * objects followed by a NULL */ | |
86 | size_t num; /* numblocks * 2^(w-1) */ | |
87 | int references; | |
88 | }; | |
89 | ||
90 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
91 | { | |
92 | EC_PRE_COMP *ret = NULL; | |
93 | ||
94 | if (!group) | |
95 | return NULL; | |
96 | ||
97 | ret = OPENSSL_zalloc(sizeof(*ret)); | |
98 | if (ret == NULL) { | |
99 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
100 | return ret; | |
101 | } | |
102 | ret->group = group; | |
103 | ret->blocksize = 8; /* default */ | |
104 | ret->w = 4; /* default */ | |
105 | ret->references = 1; | |
106 | return ret; | |
107 | } | |
108 | ||
109 | EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) | |
110 | { | |
111 | if (pre != NULL) | |
112 | CRYPTO_add(&pre->references, 1, CRYPTO_LOCK_EC_PRE_COMP); | |
113 | return pre; | |
114 | } | |
115 | ||
116 | void EC_ec_pre_comp_free(EC_PRE_COMP *pre) | |
117 | { | |
118 | if (pre == NULL | |
119 | || CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP) > 0) | |
120 | return; | |
121 | ||
122 | if (pre->points != NULL) { | |
123 | EC_POINT **pts; | |
124 | ||
125 | for (pts = pre->points; *pts != NULL; pts++) | |
126 | EC_POINT_free(*pts); | |
127 | OPENSSL_free(pre->points); | |
128 | } | |
129 | OPENSSL_free(pre); | |
130 | } | |
131 | ||
132 | /* | |
133 | * TODO: table should be optimised for the wNAF-based implementation, | |
134 | * sometimes smaller windows will give better performance (thus the | |
135 | * boundaries should be increased) | |
136 | */ | |
137 | #define EC_window_bits_for_scalar_size(b) \ | |
138 | ((size_t) \ | |
139 | ((b) >= 2000 ? 6 : \ | |
140 | (b) >= 800 ? 5 : \ | |
141 | (b) >= 300 ? 4 : \ | |
142 | (b) >= 70 ? 3 : \ | |
143 | (b) >= 20 ? 2 : \ | |
144 | 1)) | |
145 | ||
146 | /*- | |
147 | * Compute | |
148 | * \sum scalars[i]*points[i], | |
149 | * also including | |
150 | * scalar*generator | |
151 | * in the addition if scalar != NULL | |
152 | */ | |
153 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, | |
154 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], | |
155 | BN_CTX *ctx) | |
156 | { | |
157 | BN_CTX *new_ctx = NULL; | |
158 | const EC_POINT *generator = NULL; | |
159 | EC_POINT *tmp = NULL; | |
160 | size_t totalnum; | |
161 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
162 | size_t pre_points_per_block = 0; | |
163 | size_t i, j; | |
164 | int k; | |
165 | int r_is_inverted = 0; | |
166 | int r_is_at_infinity = 1; | |
167 | size_t *wsize = NULL; /* individual window sizes */ | |
168 | signed char **wNAF = NULL; /* individual wNAFs */ | |
169 | size_t *wNAF_len = NULL; | |
170 | size_t max_len = 0; | |
171 | size_t num_val; | |
172 | EC_POINT **val = NULL; /* precomputation */ | |
173 | EC_POINT **v; | |
174 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
175 | * 'pre_comp->points' */ | |
176 | const EC_PRE_COMP *pre_comp = NULL; | |
177 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be | |
178 | * treated like other scalars, i.e. | |
179 | * precomputation is not available */ | |
180 | int ret = 0; | |
181 | ||
182 | if (group->meth != r->meth) { | |
183 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
184 | return 0; | |
185 | } | |
186 | ||
187 | if ((scalar == NULL) && (num == 0)) { | |
188 | return EC_POINT_set_to_infinity(group, r); | |
189 | } | |
190 | ||
191 | for (i = 0; i < num; i++) { | |
192 | if (group->meth != points[i]->meth) { | |
193 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
194 | return 0; | |
195 | } | |
196 | } | |
197 | ||
198 | if (ctx == NULL) { | |
199 | ctx = new_ctx = BN_CTX_new(); | |
200 | if (ctx == NULL) | |
201 | goto err; | |
202 | } | |
203 | ||
204 | if (scalar != NULL) { | |
205 | generator = EC_GROUP_get0_generator(group); | |
206 | if (generator == NULL) { | |
207 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
208 | goto err; | |
209 | } | |
210 | ||
211 | /* look if we can use precomputed multiples of generator */ | |
212 | ||
213 | pre_comp = group->pre_comp.ec; | |
214 | if (pre_comp && pre_comp->numblocks | |
215 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
216 | 0)) { | |
217 | blocksize = pre_comp->blocksize; | |
218 | ||
219 | /* | |
220 | * determine maximum number of blocks that wNAF splitting may | |
221 | * yield (NB: maximum wNAF length is bit length plus one) | |
222 | */ | |
223 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
224 | ||
225 | /* | |
226 | * we cannot use more blocks than we have precomputation for | |
227 | */ | |
228 | if (numblocks > pre_comp->numblocks) | |
229 | numblocks = pre_comp->numblocks; | |
230 | ||
231 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
232 | ||
233 | /* check that pre_comp looks sane */ | |
234 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
235 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
236 | goto err; | |
237 | } | |
238 | } else { | |
239 | /* can't use precomputation */ | |
240 | pre_comp = NULL; | |
241 | numblocks = 1; | |
242 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
243 | * 'scalars' */ | |
244 | } | |
245 | } | |
246 | ||
247 | totalnum = num + numblocks; | |
248 | ||
249 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); | |
250 | wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); | |
251 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space | |
252 | * for pivot */ | |
253 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); | |
254 | ||
255 | /* Ensure wNAF is initialised in case we end up going to err */ | |
256 | if (wNAF != NULL) | |
257 | wNAF[0] = NULL; /* preliminary pivot */ | |
258 | ||
259 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { | |
260 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
261 | goto err; | |
262 | } | |
263 | ||
264 | /* | |
265 | * num_val will be the total number of temporarily precomputed points | |
266 | */ | |
267 | num_val = 0; | |
268 | ||
269 | for (i = 0; i < num + num_scalar; i++) { | |
270 | size_t bits; | |
271 | ||
272 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
273 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
274 | num_val += (size_t)1 << (wsize[i] - 1); | |
275 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
276 | wNAF[i] = | |
277 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
278 | &wNAF_len[i]); | |
279 | if (wNAF[i] == NULL) | |
280 | goto err; | |
281 | if (wNAF_len[i] > max_len) | |
282 | max_len = wNAF_len[i]; | |
283 | } | |
284 | ||
285 | if (numblocks) { | |
286 | /* we go here iff scalar != NULL */ | |
287 | ||
288 | if (pre_comp == NULL) { | |
289 | if (num_scalar != 1) { | |
290 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
291 | goto err; | |
292 | } | |
293 | /* we have already generated a wNAF for 'scalar' */ | |
294 | } else { | |
295 | signed char *tmp_wNAF = NULL; | |
296 | size_t tmp_len = 0; | |
297 | ||
298 | if (num_scalar != 0) { | |
299 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
300 | goto err; | |
301 | } | |
302 | ||
303 | /* | |
304 | * use the window size for which we have precomputation | |
305 | */ | |
306 | wsize[num] = pre_comp->w; | |
307 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
308 | if (!tmp_wNAF) | |
309 | goto err; | |
310 | ||
311 | if (tmp_len <= max_len) { | |
312 | /* | |
313 | * One of the other wNAFs is at least as long as the wNAF | |
314 | * belonging to the generator, so wNAF splitting will not buy | |
315 | * us anything. | |
316 | */ | |
317 | ||
318 | numblocks = 1; | |
319 | totalnum = num + 1; /* don't use wNAF splitting */ | |
320 | wNAF[num] = tmp_wNAF; | |
321 | wNAF[num + 1] = NULL; | |
322 | wNAF_len[num] = tmp_len; | |
323 | if (tmp_len > max_len) | |
324 | max_len = tmp_len; | |
325 | /* | |
326 | * pre_comp->points starts with the points that we need here: | |
327 | */ | |
328 | val_sub[num] = pre_comp->points; | |
329 | } else { | |
330 | /* | |
331 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
332 | * splitting and include the blocks | |
333 | */ | |
334 | ||
335 | signed char *pp; | |
336 | EC_POINT **tmp_points; | |
337 | ||
338 | if (tmp_len < numblocks * blocksize) { | |
339 | /* | |
340 | * possibly we can do with fewer blocks than estimated | |
341 | */ | |
342 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
343 | if (numblocks > pre_comp->numblocks) { | |
344 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
345 | goto err; | |
346 | } | |
347 | totalnum = num + numblocks; | |
348 | } | |
349 | ||
350 | /* split wNAF in 'numblocks' parts */ | |
351 | pp = tmp_wNAF; | |
352 | tmp_points = pre_comp->points; | |
353 | ||
354 | for (i = num; i < totalnum; i++) { | |
355 | if (i < totalnum - 1) { | |
356 | wNAF_len[i] = blocksize; | |
357 | if (tmp_len < blocksize) { | |
358 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
359 | goto err; | |
360 | } | |
361 | tmp_len -= blocksize; | |
362 | } else | |
363 | /* | |
364 | * last block gets whatever is left (this could be | |
365 | * more or less than 'blocksize'!) | |
366 | */ | |
367 | wNAF_len[i] = tmp_len; | |
368 | ||
369 | wNAF[i + 1] = NULL; | |
370 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
371 | if (wNAF[i] == NULL) { | |
372 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
373 | OPENSSL_free(tmp_wNAF); | |
374 | goto err; | |
375 | } | |
376 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
377 | if (wNAF_len[i] > max_len) | |
378 | max_len = wNAF_len[i]; | |
379 | ||
380 | if (*tmp_points == NULL) { | |
381 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
382 | OPENSSL_free(tmp_wNAF); | |
383 | goto err; | |
384 | } | |
385 | val_sub[i] = tmp_points; | |
386 | tmp_points += pre_points_per_block; | |
387 | pp += blocksize; | |
388 | } | |
389 | OPENSSL_free(tmp_wNAF); | |
390 | } | |
391 | } | |
392 | } | |
393 | ||
394 | /* | |
395 | * All points we precompute now go into a single array 'val'. | |
396 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
397 | * subarray of 'pre_comp->points' if we already have precomputation. | |
398 | */ | |
399 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); | |
400 | if (val == NULL) { | |
401 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
402 | goto err; | |
403 | } | |
404 | val[num_val] = NULL; /* pivot element */ | |
405 | ||
406 | /* allocate points for precomputation */ | |
407 | v = val; | |
408 | for (i = 0; i < num + num_scalar; i++) { | |
409 | val_sub[i] = v; | |
410 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
411 | *v = EC_POINT_new(group); | |
412 | if (*v == NULL) | |
413 | goto err; | |
414 | v++; | |
415 | } | |
416 | } | |
417 | if (!(v == val + num_val)) { | |
418 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
419 | goto err; | |
420 | } | |
421 | ||
422 | if ((tmp = EC_POINT_new(group)) == NULL) | |
423 | goto err; | |
424 | ||
425 | /*- | |
426 | * prepare precomputed values: | |
427 | * val_sub[i][0] := points[i] | |
428 | * val_sub[i][1] := 3 * points[i] | |
429 | * val_sub[i][2] := 5 * points[i] | |
430 | * ... | |
431 | */ | |
432 | for (i = 0; i < num + num_scalar; i++) { | |
433 | if (i < num) { | |
434 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
435 | goto err; | |
436 | } else { | |
437 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
438 | goto err; | |
439 | } | |
440 | ||
441 | if (wsize[i] > 1) { | |
442 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
443 | goto err; | |
444 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
445 | if (!EC_POINT_add | |
446 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
447 | goto err; | |
448 | } | |
449 | } | |
450 | } | |
451 | ||
452 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) | |
453 | goto err; | |
454 | ||
455 | r_is_at_infinity = 1; | |
456 | ||
457 | for (k = max_len - 1; k >= 0; k--) { | |
458 | if (!r_is_at_infinity) { | |
459 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
460 | goto err; | |
461 | } | |
462 | ||
463 | for (i = 0; i < totalnum; i++) { | |
464 | if (wNAF_len[i] > (size_t)k) { | |
465 | int digit = wNAF[i][k]; | |
466 | int is_neg; | |
467 | ||
468 | if (digit) { | |
469 | is_neg = digit < 0; | |
470 | ||
471 | if (is_neg) | |
472 | digit = -digit; | |
473 | ||
474 | if (is_neg != r_is_inverted) { | |
475 | if (!r_is_at_infinity) { | |
476 | if (!EC_POINT_invert(group, r, ctx)) | |
477 | goto err; | |
478 | } | |
479 | r_is_inverted = !r_is_inverted; | |
480 | } | |
481 | ||
482 | /* digit > 0 */ | |
483 | ||
484 | if (r_is_at_infinity) { | |
485 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
486 | goto err; | |
487 | r_is_at_infinity = 0; | |
488 | } else { | |
489 | if (!EC_POINT_add | |
490 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
491 | goto err; | |
492 | } | |
493 | } | |
494 | } | |
495 | } | |
496 | } | |
497 | ||
498 | if (r_is_at_infinity) { | |
499 | if (!EC_POINT_set_to_infinity(group, r)) | |
500 | goto err; | |
501 | } else { | |
502 | if (r_is_inverted) | |
503 | if (!EC_POINT_invert(group, r, ctx)) | |
504 | goto err; | |
505 | } | |
506 | ||
507 | ret = 1; | |
508 | ||
509 | err: | |
510 | BN_CTX_free(new_ctx); | |
511 | EC_POINT_free(tmp); | |
512 | OPENSSL_free(wsize); | |
513 | OPENSSL_free(wNAF_len); | |
514 | if (wNAF != NULL) { | |
515 | signed char **w; | |
516 | ||
517 | for (w = wNAF; *w != NULL; w++) | |
518 | OPENSSL_free(*w); | |
519 | ||
520 | OPENSSL_free(wNAF); | |
521 | } | |
522 | if (val != NULL) { | |
523 | for (v = val; *v != NULL; v++) | |
524 | EC_POINT_clear_free(*v); | |
525 | ||
526 | OPENSSL_free(val); | |
527 | } | |
528 | OPENSSL_free(val_sub); | |
529 | return ret; | |
530 | } | |
531 | ||
532 | /*- | |
533 | * ec_wNAF_precompute_mult() | |
534 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator | |
535 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
536 | * | |
537 | * 'pre_comp->points' is an array of multiples of the generator | |
538 | * of the following form: | |
539 | * points[0] = generator; | |
540 | * points[1] = 3 * generator; | |
541 | * ... | |
542 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
543 | * points[2^(w-1)] = 2^blocksize * generator; | |
544 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
545 | * ... | |
546 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
547 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
548 | * ... | |
549 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
550 | * points[2^(w-1)*numblocks] = NULL | |
551 | */ | |
552 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
553 | { | |
554 | const EC_POINT *generator; | |
555 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
556 | BN_CTX *new_ctx = NULL; | |
557 | BIGNUM *order; | |
558 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; | |
559 | EC_POINT **points = NULL; | |
560 | EC_PRE_COMP *pre_comp; | |
561 | int ret = 0; | |
562 | ||
563 | /* if there is an old EC_PRE_COMP object, throw it away */ | |
564 | EC_pre_comp_free(group); | |
565 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) | |
566 | return 0; | |
567 | ||
568 | generator = EC_GROUP_get0_generator(group); | |
569 | if (generator == NULL) { | |
570 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); | |
571 | goto err; | |
572 | } | |
573 | ||
574 | if (ctx == NULL) { | |
575 | ctx = new_ctx = BN_CTX_new(); | |
576 | if (ctx == NULL) | |
577 | goto err; | |
578 | } | |
579 | ||
580 | BN_CTX_start(ctx); | |
581 | order = BN_CTX_get(ctx); | |
582 | if (order == NULL) | |
583 | goto err; | |
584 | ||
585 | if (!EC_GROUP_get_order(group, order, ctx)) | |
586 | goto err; | |
587 | if (BN_is_zero(order)) { | |
588 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); | |
589 | goto err; | |
590 | } | |
591 | ||
592 | bits = BN_num_bits(order); | |
593 | /* | |
594 | * The following parameters mean we precompute (approximately) one point | |
595 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
596 | * bit lengths, other parameter combinations might provide better | |
597 | * efficiency. | |
598 | */ | |
599 | blocksize = 8; | |
600 | w = 4; | |
601 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
602 | /* let's not make the window too small ... */ | |
603 | w = EC_window_bits_for_scalar_size(bits); | |
604 | } | |
605 | ||
606 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
607 | * to use for wNAF | |
608 | * splitting */ | |
609 | ||
610 | pre_points_per_block = (size_t)1 << (w - 1); | |
611 | num = pre_points_per_block * numblocks; /* number of points to compute | |
612 | * and store */ | |
613 | ||
614 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); | |
615 | if (points == NULL) { | |
616 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
617 | goto err; | |
618 | } | |
619 | ||
620 | var = points; | |
621 | var[num] = NULL; /* pivot */ | |
622 | for (i = 0; i < num; i++) { | |
623 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
624 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
625 | goto err; | |
626 | } | |
627 | } | |
628 | ||
629 | if ((tmp_point = EC_POINT_new(group)) == NULL | |
630 | || (base = EC_POINT_new(group)) == NULL) { | |
631 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
632 | goto err; | |
633 | } | |
634 | ||
635 | if (!EC_POINT_copy(base, generator)) | |
636 | goto err; | |
637 | ||
638 | /* do the precomputation */ | |
639 | for (i = 0; i < numblocks; i++) { | |
640 | size_t j; | |
641 | ||
642 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
643 | goto err; | |
644 | ||
645 | if (!EC_POINT_copy(*var++, base)) | |
646 | goto err; | |
647 | ||
648 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
649 | /* | |
650 | * calculate odd multiples of the current base point | |
651 | */ | |
652 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
653 | goto err; | |
654 | } | |
655 | ||
656 | if (i < numblocks - 1) { | |
657 | /* | |
658 | * get the next base (multiply current one by 2^blocksize) | |
659 | */ | |
660 | size_t k; | |
661 | ||
662 | if (blocksize <= 2) { | |
663 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
664 | goto err; | |
665 | } | |
666 | ||
667 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
668 | goto err; | |
669 | for (k = 2; k < blocksize; k++) { | |
670 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
671 | goto err; | |
672 | } | |
673 | } | |
674 | } | |
675 | ||
676 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
677 | goto err; | |
678 | ||
679 | pre_comp->group = group; | |
680 | pre_comp->blocksize = blocksize; | |
681 | pre_comp->numblocks = numblocks; | |
682 | pre_comp->w = w; | |
683 | pre_comp->points = points; | |
684 | points = NULL; | |
685 | pre_comp->num = num; | |
686 | SETPRECOMP(group, ec, pre_comp); | |
687 | pre_comp = NULL; | |
688 | ret = 1; | |
689 | ||
690 | err: | |
691 | if (ctx != NULL) | |
692 | BN_CTX_end(ctx); | |
693 | BN_CTX_free(new_ctx); | |
694 | EC_ec_pre_comp_free(pre_comp); | |
695 | if (points) { | |
696 | EC_POINT **p; | |
697 | ||
698 | for (p = points; *p != NULL; p++) | |
699 | EC_POINT_free(*p); | |
700 | OPENSSL_free(points); | |
701 | } | |
702 | EC_POINT_free(tmp_point); | |
703 | EC_POINT_free(base); | |
704 | return ret; | |
705 | } | |
706 | ||
707 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) | |
708 | { | |
709 | return HAVEPRECOMP(group, ec); | |
710 | } |