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35b73a1f | 1 | /* |
677963e5 | 2 | * Copyright 2001-2017 The OpenSSL Project Authors. All Rights Reserved. |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
65e81670 | 4 | * |
4f22f405 RS |
5 | * Licensed under the OpenSSL license (the "License"). You may not use |
6 | * this file except in compliance with the License. You can obtain a copy | |
7 | * in the file LICENSE in the source distribution or at | |
8 | * https://www.openssl.org/source/license.html | |
65e81670 | 9 | */ |
4f22f405 | 10 | |
28f573a2 | 11 | #include <string.h> |
48fe4d62 BM |
12 | #include <openssl/err.h> |
13 | ||
9b398ef2 | 14 | #include "internal/cryptlib.h" |
5784a521 | 15 | #include "internal/bn_int.h" |
65e81670 | 16 | #include "ec_lcl.h" |
cd420b0b | 17 | #include "internal/refcount.h" |
48fe4d62 | 18 | |
37c660ff | 19 | /* |
0d4fb843 | 20 | * This file implements the wNAF-based interleaving multi-exponentiation method |
dea0eb2c RS |
21 | * Formerly at: |
22 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp | |
23 | * You might now find it here: | |
24 | * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 | |
25 | * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf | |
26 | * For multiplication with precomputation, we use wNAF splitting, formerly at: | |
27 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp | |
37c660ff | 28 | */ |
48fe4d62 | 29 | |
37c660ff | 30 | /* structure for precomputed multiples of the generator */ |
3aef36ff | 31 | struct ec_pre_comp_st { |
0f113f3e MC |
32 | const EC_GROUP *group; /* parent EC_GROUP object */ |
33 | size_t blocksize; /* block size for wNAF splitting */ | |
34 | size_t numblocks; /* max. number of blocks for which we have | |
35 | * precomputation */ | |
36 | size_t w; /* window size */ | |
37 | EC_POINT **points; /* array with pre-calculated multiples of | |
38 | * generator: 'num' pointers to EC_POINT | |
39 | * objects followed by a NULL */ | |
40 | size_t num; /* numblocks * 2^(w-1) */ | |
2f545ae4 | 41 | CRYPTO_REF_COUNT references; |
9b398ef2 | 42 | CRYPTO_RWLOCK *lock; |
3aef36ff | 43 | }; |
37c660ff BM |
44 | |
45 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
0f113f3e MC |
46 | { |
47 | EC_PRE_COMP *ret = NULL; | |
48 | ||
49 | if (!group) | |
50 | return NULL; | |
51 | ||
64b25758 | 52 | ret = OPENSSL_zalloc(sizeof(*ret)); |
90945fa3 | 53 | if (ret == NULL) { |
0f113f3e MC |
54 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
55 | return ret; | |
56 | } | |
9b398ef2 | 57 | |
0f113f3e MC |
58 | ret->group = group; |
59 | ret->blocksize = 8; /* default */ | |
0f113f3e | 60 | ret->w = 4; /* default */ |
0f113f3e | 61 | ret->references = 1; |
9b398ef2 AG |
62 | |
63 | ret->lock = CRYPTO_THREAD_lock_new(); | |
64 | if (ret->lock == NULL) { | |
65 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
66 | OPENSSL_free(ret); | |
67 | return NULL; | |
68 | } | |
0f113f3e MC |
69 | return ret; |
70 | } | |
37c660ff | 71 | |
3aef36ff | 72 | EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) |
0f113f3e | 73 | { |
9b398ef2 | 74 | int i; |
3aef36ff | 75 | if (pre != NULL) |
2f545ae4 | 76 | CRYPTO_UP_REF(&pre->references, &i, pre->lock); |
3aef36ff | 77 | return pre; |
0f113f3e | 78 | } |
37c660ff | 79 | |
3aef36ff | 80 | void EC_ec_pre_comp_free(EC_PRE_COMP *pre) |
0f113f3e | 81 | { |
9b398ef2 AG |
82 | int i; |
83 | ||
84 | if (pre == NULL) | |
85 | return; | |
86 | ||
2f545ae4 | 87 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
9b398ef2 AG |
88 | REF_PRINT_COUNT("EC_ec", pre); |
89 | if (i > 0) | |
0f113f3e | 90 | return; |
9b398ef2 | 91 | REF_ASSERT_ISNT(i < 0); |
ba729265 | 92 | |
3aef36ff RS |
93 | if (pre->points != NULL) { |
94 | EC_POINT **pts; | |
37c660ff | 95 | |
3aef36ff RS |
96 | for (pts = pre->points; *pts != NULL; pts++) |
97 | EC_POINT_free(*pts); | |
0f113f3e MC |
98 | OPENSSL_free(pre->points); |
99 | } | |
9b398ef2 | 100 | CRYPTO_THREAD_lock_free(pre->lock); |
0f113f3e MC |
101 | OPENSSL_free(pre); |
102 | } | |
37c660ff | 103 | |
40e48e54 BB |
104 | #define EC_POINT_set_flags(P, flags) do { \ |
105 | BN_set_flags((P)->X, (flags)); \ | |
106 | BN_set_flags((P)->Y, (flags)); \ | |
107 | BN_set_flags((P)->Z, (flags)); \ | |
108 | } while(0) | |
109 | ||
110 | /* | |
111 | * This functions computes (in constant time) a point multiplication over the | |
112 | * EC group. | |
113 | * | |
114 | * It performs either a fixed scalar point multiplication | |
115 | * (scalar * generator) | |
116 | * when point is NULL, or a generic scalar point multiplication | |
117 | * (scalar * point) | |
118 | * when point is not NULL. | |
119 | * | |
120 | * scalar should be in the range [0,n) otherwise all constant time bets are off. | |
121 | * | |
122 | * NB: This says nothing about EC_POINT_add and EC_POINT_dbl, | |
123 | * which of course are not constant time themselves. | |
124 | * | |
125 | * The product is stored in r. | |
126 | * | |
127 | * Returns 1 on success, 0 otherwise. | |
128 | */ | |
129 | static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, | |
130 | const EC_POINT *point, BN_CTX *ctx) | |
131 | { | |
132 | int i, order_bits, group_top, kbit, pbit, Z_is_one, ret; | |
133 | ret = 0; | |
134 | EC_POINT *s = NULL; | |
135 | BIGNUM *k = NULL; | |
136 | BIGNUM *lambda = NULL; | |
137 | BN_CTX *new_ctx = NULL; | |
138 | ||
139 | if (ctx == NULL) | |
140 | if ((ctx = new_ctx = BN_CTX_secure_new()) == NULL) | |
141 | return 0; | |
142 | ||
143 | if ((group->order == NULL) || (group->field == NULL)) | |
144 | goto err; | |
145 | ||
146 | order_bits = BN_num_bits(group->order); | |
147 | ||
148 | s = EC_POINT_new(group); | |
149 | if (s == NULL) | |
150 | goto err; | |
151 | ||
152 | if (point == NULL) { | |
153 | if (group->generator == NULL) | |
154 | goto err; | |
155 | if (!EC_POINT_copy(s, group->generator)) | |
156 | goto err; | |
157 | } else { | |
158 | if (!EC_POINT_copy(s, point)) | |
159 | goto err; | |
160 | } | |
161 | ||
162 | EC_POINT_set_flags(s, BN_FLG_CONSTTIME); | |
163 | ||
164 | BN_CTX_start(ctx); | |
165 | lambda = BN_CTX_get(ctx); | |
166 | k = BN_CTX_get(ctx); | |
167 | if (k == NULL) | |
168 | goto err; | |
169 | ||
170 | /* | |
171 | * Group orders are often on a word boundary. | |
172 | * So when we pad the scalar, some timing diff might | |
173 | * pop if it needs to be expanded due to carries. | |
174 | * So expand ahead of time. | |
175 | */ | |
176 | group_top = bn_get_top(group->order); | |
177 | if ((bn_wexpand(k, group_top + 1) == NULL) | |
178 | || (bn_wexpand(lambda, group_top + 1) == NULL)) | |
179 | goto err; | |
180 | ||
181 | if (!BN_copy(k, scalar)) | |
182 | goto err; | |
183 | ||
184 | BN_set_flags(k, BN_FLG_CONSTTIME); | |
185 | ||
186 | if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) { | |
187 | /* | |
188 | * this is an unusual input, and we don't guarantee | |
189 | * constant-timeness | |
190 | */ | |
191 | if(!BN_nnmod(k, k, group->order, ctx)) | |
192 | goto err; | |
193 | } | |
194 | ||
195 | if (!BN_add(lambda, k, group->order)) | |
196 | goto err; | |
197 | BN_set_flags(lambda, BN_FLG_CONSTTIME); | |
198 | if (!BN_add(k, lambda, group->order)) | |
199 | goto err; | |
200 | /* | |
201 | * lambda := scalar + order | |
202 | * k := scalar + 2*order | |
203 | */ | |
204 | kbit = BN_is_bit_set(lambda, order_bits); | |
205 | BN_consttime_swap(kbit, k, lambda, group_top + 1); | |
206 | ||
207 | group_top = bn_get_top(group->field); | |
208 | if ((bn_wexpand(s->X, group_top) == NULL) | |
209 | || (bn_wexpand(s->Y, group_top) == NULL) | |
210 | || (bn_wexpand(s->Z, group_top) == NULL) | |
211 | || (bn_wexpand(r->X, group_top) == NULL) | |
212 | || (bn_wexpand(r->Y, group_top) == NULL) | |
213 | || (bn_wexpand(r->Z, group_top) == NULL)) | |
214 | goto err; | |
215 | ||
216 | /* top bit is a 1, in a fixed pos */ | |
217 | if (!EC_POINT_copy(r, s)) | |
218 | goto err; | |
219 | ||
220 | EC_POINT_set_flags(r, BN_FLG_CONSTTIME); | |
221 | ||
222 | if (!EC_POINT_dbl(group, s, s, ctx)) | |
223 | goto err; | |
224 | ||
225 | pbit = 0; | |
226 | ||
227 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |
228 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ | |
229 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ | |
230 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ | |
231 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |
232 | (a)->Z_is_one ^= (t); \ | |
233 | (b)->Z_is_one ^= (t); \ | |
234 | } while(0) | |
235 | ||
236 | for (i = order_bits - 1; i >= 0; i--) { | |
237 | kbit = BN_is_bit_set(k, i) ^ pbit; | |
238 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |
239 | if (!EC_POINT_add(group, s, r, s, ctx)) | |
240 | goto err; | |
241 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
242 | goto err; | |
243 | /* | |
244 | * pbit logic merges this cswap with that of the | |
245 | * next iteration | |
246 | */ | |
247 | pbit ^= kbit; | |
248 | } | |
249 | /* one final cswap to move the right value into r */ | |
250 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |
251 | #undef EC_POINT_CSWAP | |
252 | ||
253 | ret = 1; | |
254 | ||
255 | err: | |
256 | EC_POINT_free(s); | |
257 | BN_CTX_end(ctx); | |
258 | BN_CTX_free(new_ctx); | |
259 | ||
260 | return ret; | |
261 | } | |
262 | #undef EC_POINT_set_flags | |
263 | ||
0f113f3e MC |
264 | /* |
265 | * TODO: table should be optimised for the wNAF-based implementation, | |
266 | * sometimes smaller windows will give better performance (thus the | |
267 | * boundaries should be increased) | |
c05940ed | 268 | */ |
3ba1f111 | 269 | #define EC_window_bits_for_scalar_size(b) \ |
0f113f3e MC |
270 | ((size_t) \ |
271 | ((b) >= 2000 ? 6 : \ | |
272 | (b) >= 800 ? 5 : \ | |
273 | (b) >= 300 ? 4 : \ | |
274 | (b) >= 70 ? 3 : \ | |
275 | (b) >= 20 ? 2 : \ | |
276 | 1)) | |
3ba1f111 | 277 | |
c80fd6b2 MC |
278 | /*- |
279 | * Compute | |
3ba1f111 BM |
280 | * \sum scalars[i]*points[i], |
281 | * also including | |
282 | * scalar*generator | |
283 | * in the addition if scalar != NULL | |
284 | */ | |
7793f30e | 285 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
0f113f3e MC |
286 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
287 | BN_CTX *ctx) | |
288 | { | |
40e48e54 BB |
289 | if ((scalar != NULL) && (num == 0)) { |
290 | /* In this case we want to compute scalar * GeneratorPoint: | |
291 | * this codepath is reached most prominently by (ephemeral) key | |
292 | * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, | |
293 | * ECDH keygen/first half), where the scalar is always secret. | |
294 | * This is why we ignore if BN_FLG_CONSTTIME is actually set and we | |
295 | * always call the constant time version. | |
296 | */ | |
297 | return ec_mul_consttime(group, r, scalar, NULL, ctx); | |
298 | } | |
299 | ||
300 | if ((scalar == NULL) && (num == 1)) { | |
301 | /* In this case we want to compute scalar * GenericPoint: | |
302 | * this codepath is reached most prominently by the second half of | |
303 | * ECDH, where the secret scalar is multiplied by the peer's public | |
304 | * point. | |
305 | * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is | |
306 | * actually set and we always call the constant time version. | |
307 | */ | |
308 | return ec_mul_consttime(group, r, scalars[0], points[0], ctx); | |
309 | } | |
310 | ||
0f113f3e MC |
311 | BN_CTX *new_ctx = NULL; |
312 | const EC_POINT *generator = NULL; | |
313 | EC_POINT *tmp = NULL; | |
314 | size_t totalnum; | |
315 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
316 | size_t pre_points_per_block = 0; | |
317 | size_t i, j; | |
318 | int k; | |
319 | int r_is_inverted = 0; | |
320 | int r_is_at_infinity = 1; | |
321 | size_t *wsize = NULL; /* individual window sizes */ | |
322 | signed char **wNAF = NULL; /* individual wNAFs */ | |
323 | size_t *wNAF_len = NULL; | |
324 | size_t max_len = 0; | |
325 | size_t num_val; | |
326 | EC_POINT **val = NULL; /* precomputation */ | |
327 | EC_POINT **v; | |
328 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
329 | * 'pre_comp->points' */ | |
330 | const EC_PRE_COMP *pre_comp = NULL; | |
331 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be | |
332 | * treated like other scalars, i.e. | |
333 | * precomputation is not available */ | |
334 | int ret = 0; | |
335 | ||
336 | if (group->meth != r->meth) { | |
337 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
338 | return 0; | |
339 | } | |
340 | ||
341 | if ((scalar == NULL) && (num == 0)) { | |
342 | return EC_POINT_set_to_infinity(group, r); | |
343 | } | |
344 | ||
345 | for (i = 0; i < num; i++) { | |
346 | if (group->meth != points[i]->meth) { | |
347 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
348 | return 0; | |
349 | } | |
350 | } | |
351 | ||
352 | if (ctx == NULL) { | |
353 | ctx = new_ctx = BN_CTX_new(); | |
354 | if (ctx == NULL) | |
355 | goto err; | |
356 | } | |
357 | ||
358 | if (scalar != NULL) { | |
359 | generator = EC_GROUP_get0_generator(group); | |
360 | if (generator == NULL) { | |
361 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
362 | goto err; | |
363 | } | |
364 | ||
365 | /* look if we can use precomputed multiples of generator */ | |
366 | ||
3aef36ff | 367 | pre_comp = group->pre_comp.ec; |
0f113f3e MC |
368 | if (pre_comp && pre_comp->numblocks |
369 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
370 | 0)) { | |
371 | blocksize = pre_comp->blocksize; | |
372 | ||
373 | /* | |
374 | * determine maximum number of blocks that wNAF splitting may | |
375 | * yield (NB: maximum wNAF length is bit length plus one) | |
376 | */ | |
377 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
378 | ||
379 | /* | |
380 | * we cannot use more blocks than we have precomputation for | |
381 | */ | |
382 | if (numblocks > pre_comp->numblocks) | |
383 | numblocks = pre_comp->numblocks; | |
384 | ||
385 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
386 | ||
387 | /* check that pre_comp looks sane */ | |
388 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
389 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
390 | goto err; | |
391 | } | |
392 | } else { | |
393 | /* can't use precomputation */ | |
394 | pre_comp = NULL; | |
395 | numblocks = 1; | |
396 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
397 | * 'scalars' */ | |
398 | } | |
399 | } | |
400 | ||
401 | totalnum = num + numblocks; | |
402 | ||
cbe29648 RS |
403 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
404 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); | |
405 | /* include space for pivot */ | |
406 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); | |
407 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); | |
0f113f3e MC |
408 | |
409 | /* Ensure wNAF is initialised in case we end up going to err */ | |
90945fa3 | 410 | if (wNAF != NULL) |
0f113f3e MC |
411 | wNAF[0] = NULL; /* preliminary pivot */ |
412 | ||
90945fa3 | 413 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { |
0f113f3e MC |
414 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
415 | goto err; | |
416 | } | |
417 | ||
418 | /* | |
419 | * num_val will be the total number of temporarily precomputed points | |
420 | */ | |
421 | num_val = 0; | |
422 | ||
423 | for (i = 0; i < num + num_scalar; i++) { | |
424 | size_t bits; | |
425 | ||
426 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
427 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
428 | num_val += (size_t)1 << (wsize[i] - 1); | |
429 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
430 | wNAF[i] = | |
431 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
432 | &wNAF_len[i]); | |
433 | if (wNAF[i] == NULL) | |
434 | goto err; | |
435 | if (wNAF_len[i] > max_len) | |
436 | max_len = wNAF_len[i]; | |
437 | } | |
438 | ||
439 | if (numblocks) { | |
440 | /* we go here iff scalar != NULL */ | |
441 | ||
442 | if (pre_comp == NULL) { | |
443 | if (num_scalar != 1) { | |
444 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
445 | goto err; | |
446 | } | |
447 | /* we have already generated a wNAF for 'scalar' */ | |
448 | } else { | |
449 | signed char *tmp_wNAF = NULL; | |
450 | size_t tmp_len = 0; | |
451 | ||
452 | if (num_scalar != 0) { | |
453 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
454 | goto err; | |
455 | } | |
456 | ||
457 | /* | |
458 | * use the window size for which we have precomputation | |
459 | */ | |
460 | wsize[num] = pre_comp->w; | |
461 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
462 | if (!tmp_wNAF) | |
463 | goto err; | |
464 | ||
465 | if (tmp_len <= max_len) { | |
466 | /* | |
467 | * One of the other wNAFs is at least as long as the wNAF | |
468 | * belonging to the generator, so wNAF splitting will not buy | |
469 | * us anything. | |
470 | */ | |
471 | ||
472 | numblocks = 1; | |
473 | totalnum = num + 1; /* don't use wNAF splitting */ | |
474 | wNAF[num] = tmp_wNAF; | |
475 | wNAF[num + 1] = NULL; | |
476 | wNAF_len[num] = tmp_len; | |
0f113f3e MC |
477 | /* |
478 | * pre_comp->points starts with the points that we need here: | |
479 | */ | |
480 | val_sub[num] = pre_comp->points; | |
481 | } else { | |
482 | /* | |
483 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
484 | * splitting and include the blocks | |
485 | */ | |
486 | ||
487 | signed char *pp; | |
488 | EC_POINT **tmp_points; | |
489 | ||
490 | if (tmp_len < numblocks * blocksize) { | |
491 | /* | |
492 | * possibly we can do with fewer blocks than estimated | |
493 | */ | |
494 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
495 | if (numblocks > pre_comp->numblocks) { | |
496 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 497 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
498 | goto err; |
499 | } | |
500 | totalnum = num + numblocks; | |
501 | } | |
502 | ||
503 | /* split wNAF in 'numblocks' parts */ | |
504 | pp = tmp_wNAF; | |
505 | tmp_points = pre_comp->points; | |
506 | ||
507 | for (i = num; i < totalnum; i++) { | |
508 | if (i < totalnum - 1) { | |
509 | wNAF_len[i] = blocksize; | |
510 | if (tmp_len < blocksize) { | |
511 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 512 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
513 | goto err; |
514 | } | |
515 | tmp_len -= blocksize; | |
516 | } else | |
517 | /* | |
518 | * last block gets whatever is left (this could be | |
519 | * more or less than 'blocksize'!) | |
520 | */ | |
521 | wNAF_len[i] = tmp_len; | |
522 | ||
523 | wNAF[i + 1] = NULL; | |
524 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
525 | if (wNAF[i] == NULL) { | |
526 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
527 | OPENSSL_free(tmp_wNAF); | |
528 | goto err; | |
529 | } | |
530 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
531 | if (wNAF_len[i] > max_len) | |
532 | max_len = wNAF_len[i]; | |
533 | ||
534 | if (*tmp_points == NULL) { | |
535 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
536 | OPENSSL_free(tmp_wNAF); | |
537 | goto err; | |
538 | } | |
539 | val_sub[i] = tmp_points; | |
540 | tmp_points += pre_points_per_block; | |
541 | pp += blocksize; | |
542 | } | |
543 | OPENSSL_free(tmp_wNAF); | |
544 | } | |
545 | } | |
546 | } | |
547 | ||
548 | /* | |
549 | * All points we precompute now go into a single array 'val'. | |
550 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
551 | * subarray of 'pre_comp->points' if we already have precomputation. | |
552 | */ | |
cbe29648 | 553 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
0f113f3e MC |
554 | if (val == NULL) { |
555 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
556 | goto err; | |
557 | } | |
558 | val[num_val] = NULL; /* pivot element */ | |
559 | ||
560 | /* allocate points for precomputation */ | |
561 | v = val; | |
562 | for (i = 0; i < num + num_scalar; i++) { | |
563 | val_sub[i] = v; | |
564 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
565 | *v = EC_POINT_new(group); | |
566 | if (*v == NULL) | |
567 | goto err; | |
568 | v++; | |
569 | } | |
570 | } | |
571 | if (!(v == val + num_val)) { | |
572 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
573 | goto err; | |
574 | } | |
575 | ||
75ebbd9a | 576 | if ((tmp = EC_POINT_new(group)) == NULL) |
0f113f3e MC |
577 | goto err; |
578 | ||
50e735f9 MC |
579 | /*- |
580 | * prepare precomputed values: | |
581 | * val_sub[i][0] := points[i] | |
582 | * val_sub[i][1] := 3 * points[i] | |
583 | * val_sub[i][2] := 5 * points[i] | |
584 | * ... | |
585 | */ | |
0f113f3e MC |
586 | for (i = 0; i < num + num_scalar; i++) { |
587 | if (i < num) { | |
588 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
589 | goto err; | |
590 | } else { | |
591 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
592 | goto err; | |
593 | } | |
594 | ||
595 | if (wsize[i] > 1) { | |
596 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
597 | goto err; | |
598 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
599 | if (!EC_POINT_add | |
600 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
601 | goto err; | |
602 | } | |
603 | } | |
604 | } | |
605 | ||
0f113f3e MC |
606 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
607 | goto err; | |
3ba1f111 | 608 | |
0f113f3e MC |
609 | r_is_at_infinity = 1; |
610 | ||
611 | for (k = max_len - 1; k >= 0; k--) { | |
612 | if (!r_is_at_infinity) { | |
613 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
614 | goto err; | |
615 | } | |
616 | ||
617 | for (i = 0; i < totalnum; i++) { | |
618 | if (wNAF_len[i] > (size_t)k) { | |
619 | int digit = wNAF[i][k]; | |
620 | int is_neg; | |
621 | ||
622 | if (digit) { | |
623 | is_neg = digit < 0; | |
624 | ||
625 | if (is_neg) | |
626 | digit = -digit; | |
627 | ||
628 | if (is_neg != r_is_inverted) { | |
629 | if (!r_is_at_infinity) { | |
630 | if (!EC_POINT_invert(group, r, ctx)) | |
631 | goto err; | |
632 | } | |
633 | r_is_inverted = !r_is_inverted; | |
634 | } | |
635 | ||
636 | /* digit > 0 */ | |
637 | ||
638 | if (r_is_at_infinity) { | |
639 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
640 | goto err; | |
641 | r_is_at_infinity = 0; | |
642 | } else { | |
643 | if (!EC_POINT_add | |
644 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
645 | goto err; | |
646 | } | |
647 | } | |
648 | } | |
649 | } | |
650 | } | |
651 | ||
652 | if (r_is_at_infinity) { | |
653 | if (!EC_POINT_set_to_infinity(group, r)) | |
654 | goto err; | |
655 | } else { | |
656 | if (r_is_inverted) | |
657 | if (!EC_POINT_invert(group, r, ctx)) | |
658 | goto err; | |
659 | } | |
660 | ||
661 | ret = 1; | |
3ba1f111 BM |
662 | |
663 | err: | |
23a1d5e9 | 664 | BN_CTX_free(new_ctx); |
8fdc3734 | 665 | EC_POINT_free(tmp); |
b548a1f1 RS |
666 | OPENSSL_free(wsize); |
667 | OPENSSL_free(wNAF_len); | |
0f113f3e MC |
668 | if (wNAF != NULL) { |
669 | signed char **w; | |
670 | ||
671 | for (w = wNAF; *w != NULL; w++) | |
672 | OPENSSL_free(*w); | |
673 | ||
674 | OPENSSL_free(wNAF); | |
675 | } | |
676 | if (val != NULL) { | |
677 | for (v = val; *v != NULL; v++) | |
678 | EC_POINT_clear_free(*v); | |
679 | ||
680 | OPENSSL_free(val); | |
681 | } | |
b548a1f1 | 682 | OPENSSL_free(val_sub); |
0f113f3e MC |
683 | return ret; |
684 | } | |
38374911 | 685 | |
1d97c843 TH |
686 | /*- |
687 | * ec_wNAF_precompute_mult() | |
37c660ff BM |
688 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
689 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
0f113f3e | 690 | * |
37c660ff BM |
691 | * 'pre_comp->points' is an array of multiples of the generator |
692 | * of the following form: | |
693 | * points[0] = generator; | |
694 | * points[1] = 3 * generator; | |
695 | * ... | |
696 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
697 | * points[2^(w-1)] = 2^blocksize * generator; | |
698 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
699 | * ... | |
700 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
701 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
702 | * ... | |
703 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
704 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 705 | */ |
7793f30e | 706 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
707 | { |
708 | const EC_POINT *generator; | |
709 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
710 | BN_CTX *new_ctx = NULL; | |
be2e334f | 711 | const BIGNUM *order; |
0f113f3e MC |
712 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
713 | EC_POINT **points = NULL; | |
714 | EC_PRE_COMP *pre_comp; | |
715 | int ret = 0; | |
716 | ||
717 | /* if there is an old EC_PRE_COMP object, throw it away */ | |
2c52ac9b | 718 | EC_pre_comp_free(group); |
0f113f3e MC |
719 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
720 | return 0; | |
721 | ||
722 | generator = EC_GROUP_get0_generator(group); | |
723 | if (generator == NULL) { | |
724 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); | |
725 | goto err; | |
726 | } | |
727 | ||
728 | if (ctx == NULL) { | |
729 | ctx = new_ctx = BN_CTX_new(); | |
730 | if (ctx == NULL) | |
731 | goto err; | |
732 | } | |
733 | ||
734 | BN_CTX_start(ctx); | |
0f113f3e | 735 | |
be2e334f DSH |
736 | order = EC_GROUP_get0_order(group); |
737 | if (order == NULL) | |
0f113f3e MC |
738 | goto err; |
739 | if (BN_is_zero(order)) { | |
740 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); | |
741 | goto err; | |
742 | } | |
743 | ||
744 | bits = BN_num_bits(order); | |
745 | /* | |
746 | * The following parameters mean we precompute (approximately) one point | |
747 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
748 | * bit lengths, other parameter combinations might provide better | |
749 | * efficiency. | |
750 | */ | |
751 | blocksize = 8; | |
752 | w = 4; | |
753 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
754 | /* let's not make the window too small ... */ | |
755 | w = EC_window_bits_for_scalar_size(bits); | |
756 | } | |
757 | ||
758 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
759 | * to use for wNAF | |
760 | * splitting */ | |
761 | ||
762 | pre_points_per_block = (size_t)1 << (w - 1); | |
763 | num = pre_points_per_block * numblocks; /* number of points to compute | |
764 | * and store */ | |
765 | ||
b4faea50 | 766 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
90945fa3 | 767 | if (points == NULL) { |
0f113f3e MC |
768 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
769 | goto err; | |
770 | } | |
771 | ||
772 | var = points; | |
773 | var[num] = NULL; /* pivot */ | |
774 | for (i = 0; i < num; i++) { | |
775 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
776 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
777 | goto err; | |
778 | } | |
779 | } | |
780 | ||
75ebbd9a RS |
781 | if ((tmp_point = EC_POINT_new(group)) == NULL |
782 | || (base = EC_POINT_new(group)) == NULL) { | |
0f113f3e MC |
783 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
784 | goto err; | |
785 | } | |
786 | ||
787 | if (!EC_POINT_copy(base, generator)) | |
788 | goto err; | |
789 | ||
790 | /* do the precomputation */ | |
791 | for (i = 0; i < numblocks; i++) { | |
792 | size_t j; | |
793 | ||
794 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
795 | goto err; | |
796 | ||
797 | if (!EC_POINT_copy(*var++, base)) | |
798 | goto err; | |
799 | ||
800 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
801 | /* | |
802 | * calculate odd multiples of the current base point | |
803 | */ | |
804 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
805 | goto err; | |
806 | } | |
807 | ||
808 | if (i < numblocks - 1) { | |
809 | /* | |
810 | * get the next base (multiply current one by 2^blocksize) | |
811 | */ | |
812 | size_t k; | |
813 | ||
814 | if (blocksize <= 2) { | |
815 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
816 | goto err; | |
817 | } | |
818 | ||
819 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
820 | goto err; | |
821 | for (k = 2; k < blocksize; k++) { | |
822 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
823 | goto err; | |
824 | } | |
825 | } | |
826 | } | |
827 | ||
828 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
829 | goto err; | |
830 | ||
831 | pre_comp->group = group; | |
832 | pre_comp->blocksize = blocksize; | |
833 | pre_comp->numblocks = numblocks; | |
834 | pre_comp->w = w; | |
835 | pre_comp->points = points; | |
836 | points = NULL; | |
837 | pre_comp->num = num; | |
3aef36ff | 838 | SETPRECOMP(group, ec, pre_comp); |
0f113f3e | 839 | pre_comp = NULL; |
0f113f3e | 840 | ret = 1; |
3aef36ff | 841 | |
38374911 | 842 | err: |
0f113f3e MC |
843 | if (ctx != NULL) |
844 | BN_CTX_end(ctx); | |
23a1d5e9 | 845 | BN_CTX_free(new_ctx); |
3aef36ff | 846 | EC_ec_pre_comp_free(pre_comp); |
0f113f3e MC |
847 | if (points) { |
848 | EC_POINT **p; | |
849 | ||
850 | for (p = points; *p != NULL; p++) | |
851 | EC_POINT_free(*p); | |
852 | OPENSSL_free(points); | |
853 | } | |
8fdc3734 RS |
854 | EC_POINT_free(tmp_point); |
855 | EC_POINT_free(base); | |
0f113f3e MC |
856 | return ret; |
857 | } | |
7793f30e | 858 | |
37c660ff | 859 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
0f113f3e | 860 | { |
3aef36ff | 861 | return HAVEPRECOMP(group, ec); |
0f113f3e | 862 | } |