1 | /* |
2 | * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved. |
3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
4 | * |
5 | * Licensed under the Apache License 2.0 (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 |
9 | */ |
10 | |
11 | #include <string.h> |
12 | #include <openssl/err.h> |
13 | |
14 | #include "internal/cryptlib.h" |
15 | #include "crypto/bn.h" |
16 | #include "ec_local.h" |
17 | #include "internal/refcount.h" |
18 | |
19 | /* |
20 | * This file implements the wNAF-based interleaving multi-exponentiation method |
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 |
28 | */ |
29 | |
30 | /* structure for precomputed multiples of the generator */ |
31 | struct ec_pre_comp_st { |
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) */ |
41 | CRYPTO_REF_COUNT references; |
42 | CRYPTO_RWLOCK *lock; |
43 | }; |
44 | |
45 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) |
46 | { |
47 | EC_PRE_COMP *ret = NULL; |
48 | |
49 | if (!group) |
50 | return NULL; |
51 | |
52 | ret = OPENSSL_zalloc(sizeof(*ret)); |
53 | if (ret == NULL) { |
54 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
55 | return ret; |
56 | } |
57 | |
58 | ret->group = group; |
59 | ret->blocksize = 8; /* default */ |
60 | ret->w = 4; /* default */ |
61 | ret->references = 1; |
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 | } |
69 | return ret; |
70 | } |
71 | |
72 | EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) |
73 | { |
74 | int i; |
75 | if (pre != NULL) |
76 | CRYPTO_UP_REF(&pre->references, &i, pre->lock); |
77 | return pre; |
78 | } |
79 | |
80 | void EC_ec_pre_comp_free(EC_PRE_COMP *pre) |
81 | { |
82 | int i; |
83 | |
84 | if (pre == NULL) |
85 | return; |
86 | |
87 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
88 | REF_PRINT_COUNT("EC_ec" , pre); |
89 | if (i > 0) |
90 | return; |
91 | REF_ASSERT_ISNT(i < 0); |
92 | |
93 | if (pre->points != NULL) { |
94 | EC_POINT **pts; |
95 | |
96 | for (pts = pre->points; *pts != NULL; pts++) |
97 | EC_POINT_free(*pts); |
98 | OPENSSL_free(pre->points); |
99 | } |
100 | CRYPTO_THREAD_lock_free(pre->lock); |
101 | OPENSSL_free(pre); |
102 | } |
103 | |
104 | #define EC_POINT_BN_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 a single point multiplication over the EC group, |
112 | * using, at a high level, a Montgomery ladder with conditional swaps, with |
113 | * various timing attack defenses. |
114 | * |
115 | * It performs either a fixed point multiplication |
116 | * (scalar * generator) |
117 | * when point is NULL, or a variable point multiplication |
118 | * (scalar * point) |
119 | * when point is not NULL. |
120 | * |
121 | * `scalar` cannot be NULL and should be in the range [0,n) otherwise all |
122 | * constant time bets are off (where n is the cardinality of the EC group). |
123 | * |
124 | * This function expects `group->order` and `group->cardinality` to be well |
125 | * defined and non-zero: it fails with an error code otherwise. |
126 | * |
127 | * NB: This says nothing about the constant-timeness of the ladder step |
128 | * implementation (i.e., the default implementation is based on EC_POINT_add and |
129 | * EC_POINT_dbl, which of course are not constant time themselves) or the |
130 | * underlying multiprecision arithmetic. |
131 | * |
132 | * The product is stored in `r`. |
133 | * |
134 | * This is an internal function: callers are in charge of ensuring that the |
135 | * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. |
136 | * |
137 | * Returns 1 on success, 0 otherwise. |
138 | */ |
139 | int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, |
140 | const BIGNUM *scalar, const EC_POINT *point, |
141 | BN_CTX *ctx) |
142 | { |
143 | int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; |
144 | EC_POINT *p = NULL; |
145 | EC_POINT *s = NULL; |
146 | BIGNUM *k = NULL; |
147 | BIGNUM *lambda = NULL; |
148 | BIGNUM *cardinality = NULL; |
149 | int ret = 0; |
150 | |
151 | /* early exit if the input point is the point at infinity */ |
152 | if (point != NULL && EC_POINT_is_at_infinity(group, point)) |
153 | return EC_POINT_set_to_infinity(group, r); |
154 | |
155 | if (BN_is_zero(group->order)) { |
156 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER); |
157 | return 0; |
158 | } |
159 | if (BN_is_zero(group->cofactor)) { |
160 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR); |
161 | return 0; |
162 | } |
163 | |
164 | BN_CTX_start(ctx); |
165 | |
166 | if (((p = EC_POINT_new(group)) == NULL) |
167 | || ((s = EC_POINT_new(group)) == NULL)) { |
168 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); |
169 | goto err; |
170 | } |
171 | |
172 | if (point == NULL) { |
173 | if (!EC_POINT_copy(p, group->generator)) { |
174 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); |
175 | goto err; |
176 | } |
177 | } else { |
178 | if (!EC_POINT_copy(p, point)) { |
179 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); |
180 | goto err; |
181 | } |
182 | } |
183 | |
184 | EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME); |
185 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME); |
186 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME); |
187 | |
188 | cardinality = BN_CTX_get(ctx); |
189 | lambda = BN_CTX_get(ctx); |
190 | k = BN_CTX_get(ctx); |
191 | if (k == NULL) { |
192 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); |
193 | goto err; |
194 | } |
195 | |
196 | if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) { |
197 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
198 | goto err; |
199 | } |
200 | |
201 | /* |
202 | * Group cardinalities are often on a word boundary. |
203 | * So when we pad the scalar, some timing diff might |
204 | * pop if it needs to be expanded due to carries. |
205 | * So expand ahead of time. |
206 | */ |
207 | cardinality_bits = BN_num_bits(cardinality); |
208 | group_top = bn_get_top(cardinality); |
209 | if ((bn_wexpand(k, group_top + 2) == NULL) |
210 | || (bn_wexpand(lambda, group_top + 2) == NULL)) { |
211 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
212 | goto err; |
213 | } |
214 | |
215 | if (!BN_copy(k, scalar)) { |
216 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
217 | goto err; |
218 | } |
219 | |
220 | BN_set_flags(k, BN_FLG_CONSTTIME); |
221 | |
222 | if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) { |
223 | /*- |
224 | * this is an unusual input, and we don't guarantee |
225 | * constant-timeness |
226 | */ |
227 | if (!BN_nnmod(k, k, cardinality, ctx)) { |
228 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
229 | goto err; |
230 | } |
231 | } |
232 | |
233 | if (!BN_add(lambda, k, cardinality)) { |
234 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
235 | goto err; |
236 | } |
237 | BN_set_flags(lambda, BN_FLG_CONSTTIME); |
238 | if (!BN_add(k, lambda, cardinality)) { |
239 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
240 | goto err; |
241 | } |
242 | /* |
243 | * lambda := scalar + cardinality |
244 | * k := scalar + 2*cardinality |
245 | */ |
246 | kbit = BN_is_bit_set(lambda, cardinality_bits); |
247 | BN_consttime_swap(kbit, k, lambda, group_top + 2); |
248 | |
249 | group_top = bn_get_top(group->field); |
250 | if ((bn_wexpand(s->X, group_top) == NULL) |
251 | || (bn_wexpand(s->Y, group_top) == NULL) |
252 | || (bn_wexpand(s->Z, group_top) == NULL) |
253 | || (bn_wexpand(r->X, group_top) == NULL) |
254 | || (bn_wexpand(r->Y, group_top) == NULL) |
255 | || (bn_wexpand(r->Z, group_top) == NULL) |
256 | || (bn_wexpand(p->X, group_top) == NULL) |
257 | || (bn_wexpand(p->Y, group_top) == NULL) |
258 | || (bn_wexpand(p->Z, group_top) == NULL)) { |
259 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
260 | goto err; |
261 | } |
262 | |
263 | /*- |
264 | * Apply coordinate blinding for EC_POINT. |
265 | * |
266 | * The underlying EC_METHOD can optionally implement this function: |
267 | * ec_point_blind_coordinates() returns 0 in case of errors or 1 on |
268 | * success or if coordinate blinding is not implemented for this |
269 | * group. |
270 | */ |
271 | if (!ec_point_blind_coordinates(group, p, ctx)) { |
272 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE); |
273 | goto err; |
274 | } |
275 | |
276 | /* Initialize the Montgomery ladder */ |
277 | if (!ec_point_ladder_pre(group, r, s, p, ctx)) { |
278 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE); |
279 | goto err; |
280 | } |
281 | |
282 | /* top bit is a 1, in a fixed pos */ |
283 | pbit = 1; |
284 | |
285 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ |
286 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ |
287 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ |
288 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ |
289 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ |
290 | (a)->Z_is_one ^= (t); \ |
291 | (b)->Z_is_one ^= (t); \ |
292 | } while(0) |
293 | |
294 | /*- |
295 | * The ladder step, with branches, is |
296 | * |
297 | * k[i] == 0: S = add(R, S), R = dbl(R) |
298 | * k[i] == 1: R = add(S, R), S = dbl(S) |
299 | * |
300 | * Swapping R, S conditionally on k[i] leaves you with state |
301 | * |
302 | * k[i] == 0: T, U = R, S |
303 | * k[i] == 1: T, U = S, R |
304 | * |
305 | * Then perform the ECC ops. |
306 | * |
307 | * U = add(T, U) |
308 | * T = dbl(T) |
309 | * |
310 | * Which leaves you with state |
311 | * |
312 | * k[i] == 0: U = add(R, S), T = dbl(R) |
313 | * k[i] == 1: U = add(S, R), T = dbl(S) |
314 | * |
315 | * Swapping T, U conditionally on k[i] leaves you with state |
316 | * |
317 | * k[i] == 0: R, S = T, U |
318 | * k[i] == 1: R, S = U, T |
319 | * |
320 | * Which leaves you with state |
321 | * |
322 | * k[i] == 0: S = add(R, S), R = dbl(R) |
323 | * k[i] == 1: R = add(S, R), S = dbl(S) |
324 | * |
325 | * So we get the same logic, but instead of a branch it's a |
326 | * conditional swap, followed by ECC ops, then another conditional swap. |
327 | * |
328 | * Optimization: The end of iteration i and start of i-1 looks like |
329 | * |
330 | * ... |
331 | * CSWAP(k[i], R, S) |
332 | * ECC |
333 | * CSWAP(k[i], R, S) |
334 | * (next iteration) |
335 | * CSWAP(k[i-1], R, S) |
336 | * ECC |
337 | * CSWAP(k[i-1], R, S) |
338 | * ... |
339 | * |
340 | * So instead of two contiguous swaps, you can merge the condition |
341 | * bits and do a single swap. |
342 | * |
343 | * k[i] k[i-1] Outcome |
344 | * 0 0 No Swap |
345 | * 0 1 Swap |
346 | * 1 0 Swap |
347 | * 1 1 No Swap |
348 | * |
349 | * This is XOR. pbit tracks the previous bit of k. |
350 | */ |
351 | |
352 | for (i = cardinality_bits - 1; i >= 0; i--) { |
353 | kbit = BN_is_bit_set(k, i) ^ pbit; |
354 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); |
355 | |
356 | /* Perform a single step of the Montgomery ladder */ |
357 | if (!ec_point_ladder_step(group, r, s, p, ctx)) { |
358 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE); |
359 | goto err; |
360 | } |
361 | /* |
362 | * pbit logic merges this cswap with that of the |
363 | * next iteration |
364 | */ |
365 | pbit ^= kbit; |
366 | } |
367 | /* one final cswap to move the right value into r */ |
368 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); |
369 | #undef EC_POINT_CSWAP |
370 | |
371 | /* Finalize ladder (and recover full point coordinates) */ |
372 | if (!ec_point_ladder_post(group, r, s, p, ctx)) { |
373 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE); |
374 | goto err; |
375 | } |
376 | |
377 | ret = 1; |
378 | |
379 | err: |
380 | EC_POINT_free(p); |
381 | EC_POINT_clear_free(s); |
382 | BN_CTX_end(ctx); |
383 | |
384 | return ret; |
385 | } |
386 | |
387 | #undef EC_POINT_BN_set_flags |
388 | |
389 | /* |
390 | * TODO: table should be optimised for the wNAF-based implementation, |
391 | * sometimes smaller windows will give better performance (thus the |
392 | * boundaries should be increased) |
393 | */ |
394 | #define EC_window_bits_for_scalar_size(b) \ |
395 | ((size_t) \ |
396 | ((b) >= 2000 ? 6 : \ |
397 | (b) >= 800 ? 5 : \ |
398 | (b) >= 300 ? 4 : \ |
399 | (b) >= 70 ? 3 : \ |
400 | (b) >= 20 ? 2 : \ |
401 | 1)) |
402 | |
403 | /*- |
404 | * Compute |
405 | * \sum scalars[i]*points[i], |
406 | * also including |
407 | * scalar*generator |
408 | * in the addition if scalar != NULL |
409 | */ |
410 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
411 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
412 | BN_CTX *ctx) |
413 | { |
414 | const EC_POINT *generator = NULL; |
415 | EC_POINT *tmp = NULL; |
416 | size_t totalnum; |
417 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ |
418 | size_t pre_points_per_block = 0; |
419 | size_t i, j; |
420 | int k; |
421 | int r_is_inverted = 0; |
422 | int r_is_at_infinity = 1; |
423 | size_t *wsize = NULL; /* individual window sizes */ |
424 | signed char **wNAF = NULL; /* individual wNAFs */ |
425 | size_t *wNAF_len = NULL; |
426 | size_t max_len = 0; |
427 | size_t num_val; |
428 | EC_POINT **val = NULL; /* precomputation */ |
429 | EC_POINT **v; |
430 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or |
431 | * 'pre_comp->points' */ |
432 | const EC_PRE_COMP *pre_comp = NULL; |
433 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be |
434 | * treated like other scalars, i.e. |
435 | * precomputation is not available */ |
436 | int ret = 0; |
437 | |
438 | if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) { |
439 | /*- |
440 | * Handle the common cases where the scalar is secret, enforcing a |
441 | * scalar multiplication implementation based on a Montgomery ladder, |
442 | * with various timing attack defenses. |
443 | */ |
444 | if ((scalar != group->order) && (scalar != NULL) && (num == 0)) { |
445 | /*- |
446 | * In this case we want to compute scalar * GeneratorPoint: this |
447 | * codepath is reached most prominently by (ephemeral) key |
448 | * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, |
449 | * ECDH keygen/first half), where the scalar is always secret. This |
450 | * is why we ignore if BN_FLG_CONSTTIME is actually set and we |
451 | * always call the ladder version. |
452 | */ |
453 | return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); |
454 | } |
455 | if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) { |
456 | /*- |
457 | * In this case we want to compute scalar * VariablePoint: this |
458 | * codepath is reached most prominently by the second half of ECDH, |
459 | * where the secret scalar is multiplied by the peer's public point. |
460 | * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is |
461 | * actually set and we always call the ladder version. |
462 | */ |
463 | return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); |
464 | } |
465 | } |
466 | |
467 | if (scalar != NULL) { |
468 | generator = EC_GROUP_get0_generator(group); |
469 | if (generator == NULL) { |
470 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); |
471 | goto err; |
472 | } |
473 | |
474 | /* look if we can use precomputed multiples of generator */ |
475 | |
476 | pre_comp = group->pre_comp.ec; |
477 | if (pre_comp && pre_comp->numblocks |
478 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == |
479 | 0)) { |
480 | blocksize = pre_comp->blocksize; |
481 | |
482 | /* |
483 | * determine maximum number of blocks that wNAF splitting may |
484 | * yield (NB: maximum wNAF length is bit length plus one) |
485 | */ |
486 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; |
487 | |
488 | /* |
489 | * we cannot use more blocks than we have precomputation for |
490 | */ |
491 | if (numblocks > pre_comp->numblocks) |
492 | numblocks = pre_comp->numblocks; |
493 | |
494 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); |
495 | |
496 | /* check that pre_comp looks sane */ |
497 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { |
498 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
499 | goto err; |
500 | } |
501 | } else { |
502 | /* can't use precomputation */ |
503 | pre_comp = NULL; |
504 | numblocks = 1; |
505 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of |
506 | * 'scalars' */ |
507 | } |
508 | } |
509 | |
510 | totalnum = num + numblocks; |
511 | |
512 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
513 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); |
514 | /* include space for pivot */ |
515 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); |
516 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); |
517 | |
518 | /* Ensure wNAF is initialised in case we end up going to err */ |
519 | if (wNAF != NULL) |
520 | wNAF[0] = NULL; /* preliminary pivot */ |
521 | |
522 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { |
523 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
524 | goto err; |
525 | } |
526 | |
527 | /* |
528 | * num_val will be the total number of temporarily precomputed points |
529 | */ |
530 | num_val = 0; |
531 | |
532 | for (i = 0; i < num + num_scalar; i++) { |
533 | size_t bits; |
534 | |
535 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); |
536 | wsize[i] = EC_window_bits_for_scalar_size(bits); |
537 | num_val += (size_t)1 << (wsize[i] - 1); |
538 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ |
539 | wNAF[i] = |
540 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], |
541 | &wNAF_len[i]); |
542 | if (wNAF[i] == NULL) |
543 | goto err; |
544 | if (wNAF_len[i] > max_len) |
545 | max_len = wNAF_len[i]; |
546 | } |
547 | |
548 | if (numblocks) { |
549 | /* we go here iff scalar != NULL */ |
550 | |
551 | if (pre_comp == NULL) { |
552 | if (num_scalar != 1) { |
553 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
554 | goto err; |
555 | } |
556 | /* we have already generated a wNAF for 'scalar' */ |
557 | } else { |
558 | signed char *tmp_wNAF = NULL; |
559 | size_t tmp_len = 0; |
560 | |
561 | if (num_scalar != 0) { |
562 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
563 | goto err; |
564 | } |
565 | |
566 | /* |
567 | * use the window size for which we have precomputation |
568 | */ |
569 | wsize[num] = pre_comp->w; |
570 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); |
571 | if (!tmp_wNAF) |
572 | goto err; |
573 | |
574 | if (tmp_len <= max_len) { |
575 | /* |
576 | * One of the other wNAFs is at least as long as the wNAF |
577 | * belonging to the generator, so wNAF splitting will not buy |
578 | * us anything. |
579 | */ |
580 | |
581 | numblocks = 1; |
582 | totalnum = num + 1; /* don't use wNAF splitting */ |
583 | wNAF[num] = tmp_wNAF; |
584 | wNAF[num + 1] = NULL; |
585 | wNAF_len[num] = tmp_len; |
586 | /* |
587 | * pre_comp->points starts with the points that we need here: |
588 | */ |
589 | val_sub[num] = pre_comp->points; |
590 | } else { |
591 | /* |
592 | * don't include tmp_wNAF directly into wNAF array - use wNAF |
593 | * splitting and include the blocks |
594 | */ |
595 | |
596 | signed char *pp; |
597 | EC_POINT **tmp_points; |
598 | |
599 | if (tmp_len < numblocks * blocksize) { |
600 | /* |
601 | * possibly we can do with fewer blocks than estimated |
602 | */ |
603 | numblocks = (tmp_len + blocksize - 1) / blocksize; |
604 | if (numblocks > pre_comp->numblocks) { |
605 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
606 | OPENSSL_free(tmp_wNAF); |
607 | goto err; |
608 | } |
609 | totalnum = num + numblocks; |
610 | } |
611 | |
612 | /* split wNAF in 'numblocks' parts */ |
613 | pp = tmp_wNAF; |
614 | tmp_points = pre_comp->points; |
615 | |
616 | for (i = num; i < totalnum; i++) { |
617 | if (i < totalnum - 1) { |
618 | wNAF_len[i] = blocksize; |
619 | if (tmp_len < blocksize) { |
620 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
621 | OPENSSL_free(tmp_wNAF); |
622 | goto err; |
623 | } |
624 | tmp_len -= blocksize; |
625 | } else |
626 | /* |
627 | * last block gets whatever is left (this could be |
628 | * more or less than 'blocksize'!) |
629 | */ |
630 | wNAF_len[i] = tmp_len; |
631 | |
632 | wNAF[i + 1] = NULL; |
633 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); |
634 | if (wNAF[i] == NULL) { |
635 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
636 | OPENSSL_free(tmp_wNAF); |
637 | goto err; |
638 | } |
639 | memcpy(wNAF[i], pp, wNAF_len[i]); |
640 | if (wNAF_len[i] > max_len) |
641 | max_len = wNAF_len[i]; |
642 | |
643 | if (*tmp_points == NULL) { |
644 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
645 | OPENSSL_free(tmp_wNAF); |
646 | goto err; |
647 | } |
648 | val_sub[i] = tmp_points; |
649 | tmp_points += pre_points_per_block; |
650 | pp += blocksize; |
651 | } |
652 | OPENSSL_free(tmp_wNAF); |
653 | } |
654 | } |
655 | } |
656 | |
657 | /* |
658 | * All points we precompute now go into a single array 'val'. |
659 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a |
660 | * subarray of 'pre_comp->points' if we already have precomputation. |
661 | */ |
662 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
663 | if (val == NULL) { |
664 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
665 | goto err; |
666 | } |
667 | val[num_val] = NULL; /* pivot element */ |
668 | |
669 | /* allocate points for precomputation */ |
670 | v = val; |
671 | for (i = 0; i < num + num_scalar; i++) { |
672 | val_sub[i] = v; |
673 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { |
674 | *v = EC_POINT_new(group); |
675 | if (*v == NULL) |
676 | goto err; |
677 | v++; |
678 | } |
679 | } |
680 | if (!(v == val + num_val)) { |
681 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
682 | goto err; |
683 | } |
684 | |
685 | if ((tmp = EC_POINT_new(group)) == NULL) |
686 | goto err; |
687 | |
688 | /*- |
689 | * prepare precomputed values: |
690 | * val_sub[i][0] := points[i] |
691 | * val_sub[i][1] := 3 * points[i] |
692 | * val_sub[i][2] := 5 * points[i] |
693 | * ... |
694 | */ |
695 | for (i = 0; i < num + num_scalar; i++) { |
696 | if (i < num) { |
697 | if (!EC_POINT_copy(val_sub[i][0], points[i])) |
698 | goto err; |
699 | } else { |
700 | if (!EC_POINT_copy(val_sub[i][0], generator)) |
701 | goto err; |
702 | } |
703 | |
704 | if (wsize[i] > 1) { |
705 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) |
706 | goto err; |
707 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { |
708 | if (!EC_POINT_add |
709 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) |
710 | goto err; |
711 | } |
712 | } |
713 | } |
714 | |
715 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
716 | goto err; |
717 | |
718 | r_is_at_infinity = 1; |
719 | |
720 | for (k = max_len - 1; k >= 0; k--) { |
721 | if (!r_is_at_infinity) { |
722 | if (!EC_POINT_dbl(group, r, r, ctx)) |
723 | goto err; |
724 | } |
725 | |
726 | for (i = 0; i < totalnum; i++) { |
727 | if (wNAF_len[i] > (size_t)k) { |
728 | int digit = wNAF[i][k]; |
729 | int is_neg; |
730 | |
731 | if (digit) { |
732 | is_neg = digit < 0; |
733 | |
734 | if (is_neg) |
735 | digit = -digit; |
736 | |
737 | if (is_neg != r_is_inverted) { |
738 | if (!r_is_at_infinity) { |
739 | if (!EC_POINT_invert(group, r, ctx)) |
740 | goto err; |
741 | } |
742 | r_is_inverted = !r_is_inverted; |
743 | } |
744 | |
745 | /* digit > 0 */ |
746 | |
747 | if (r_is_at_infinity) { |
748 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) |
749 | goto err; |
750 | r_is_at_infinity = 0; |
751 | } else { |
752 | if (!EC_POINT_add |
753 | (group, r, r, val_sub[i][digit >> 1], ctx)) |
754 | goto err; |
755 | } |
756 | } |
757 | } |
758 | } |
759 | } |
760 | |
761 | if (r_is_at_infinity) { |
762 | if (!EC_POINT_set_to_infinity(group, r)) |
763 | goto err; |
764 | } else { |
765 | if (r_is_inverted) |
766 | if (!EC_POINT_invert(group, r, ctx)) |
767 | goto err; |
768 | } |
769 | |
770 | ret = 1; |
771 | |
772 | err: |
773 | EC_POINT_free(tmp); |
774 | OPENSSL_free(wsize); |
775 | OPENSSL_free(wNAF_len); |
776 | if (wNAF != NULL) { |
777 | signed char **w; |
778 | |
779 | for (w = wNAF; *w != NULL; w++) |
780 | OPENSSL_free(*w); |
781 | |
782 | OPENSSL_free(wNAF); |
783 | } |
784 | if (val != NULL) { |
785 | for (v = val; *v != NULL; v++) |
786 | EC_POINT_clear_free(*v); |
787 | |
788 | OPENSSL_free(val); |
789 | } |
790 | OPENSSL_free(val_sub); |
791 | return ret; |
792 | } |
793 | |
794 | /*- |
795 | * ec_wNAF_precompute_mult() |
796 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
797 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). |
798 | * |
799 | * 'pre_comp->points' is an array of multiples of the generator |
800 | * of the following form: |
801 | * points[0] = generator; |
802 | * points[1] = 3 * generator; |
803 | * ... |
804 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; |
805 | * points[2^(w-1)] = 2^blocksize * generator; |
806 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; |
807 | * ... |
808 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator |
809 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator |
810 | * ... |
811 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator |
812 | * points[2^(w-1)*numblocks] = NULL |
813 | */ |
814 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
815 | { |
816 | const EC_POINT *generator; |
817 | EC_POINT *tmp_point = NULL, *base = NULL, **var; |
818 | const BIGNUM *order; |
819 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
820 | EC_POINT **points = NULL; |
821 | EC_PRE_COMP *pre_comp; |
822 | int ret = 0; |
823 | #ifndef FIPS_MODE |
824 | BN_CTX *new_ctx = NULL; |
825 | #endif |
826 | |
827 | /* if there is an old EC_PRE_COMP object, throw it away */ |
828 | EC_pre_comp_free(group); |
829 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
830 | return 0; |
831 | |
832 | generator = EC_GROUP_get0_generator(group); |
833 | if (generator == NULL) { |
834 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); |
835 | goto err; |
836 | } |
837 | |
838 | #ifndef FIPS_MODE |
839 | if (ctx == NULL) |
840 | ctx = new_ctx = BN_CTX_new(); |
841 | #endif |
842 | if (ctx == NULL) |
843 | goto err; |
844 | |
845 | BN_CTX_start(ctx); |
846 | |
847 | order = EC_GROUP_get0_order(group); |
848 | if (order == NULL) |
849 | goto err; |
850 | if (BN_is_zero(order)) { |
851 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); |
852 | goto err; |
853 | } |
854 | |
855 | bits = BN_num_bits(order); |
856 | /* |
857 | * The following parameters mean we precompute (approximately) one point |
858 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other |
859 | * bit lengths, other parameter combinations might provide better |
860 | * efficiency. |
861 | */ |
862 | blocksize = 8; |
863 | w = 4; |
864 | if (EC_window_bits_for_scalar_size(bits) > w) { |
865 | /* let's not make the window too small ... */ |
866 | w = EC_window_bits_for_scalar_size(bits); |
867 | } |
868 | |
869 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks |
870 | * to use for wNAF |
871 | * splitting */ |
872 | |
873 | pre_points_per_block = (size_t)1 << (w - 1); |
874 | num = pre_points_per_block * numblocks; /* number of points to compute |
875 | * and store */ |
876 | |
877 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
878 | if (points == NULL) { |
879 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
880 | goto err; |
881 | } |
882 | |
883 | var = points; |
884 | var[num] = NULL; /* pivot */ |
885 | for (i = 0; i < num; i++) { |
886 | if ((var[i] = EC_POINT_new(group)) == NULL) { |
887 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
888 | goto err; |
889 | } |
890 | } |
891 | |
892 | if ((tmp_point = EC_POINT_new(group)) == NULL |
893 | || (base = EC_POINT_new(group)) == NULL) { |
894 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
895 | goto err; |
896 | } |
897 | |
898 | if (!EC_POINT_copy(base, generator)) |
899 | goto err; |
900 | |
901 | /* do the precomputation */ |
902 | for (i = 0; i < numblocks; i++) { |
903 | size_t j; |
904 | |
905 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) |
906 | goto err; |
907 | |
908 | if (!EC_POINT_copy(*var++, base)) |
909 | goto err; |
910 | |
911 | for (j = 1; j < pre_points_per_block; j++, var++) { |
912 | /* |
913 | * calculate odd multiples of the current base point |
914 | */ |
915 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) |
916 | goto err; |
917 | } |
918 | |
919 | if (i < numblocks - 1) { |
920 | /* |
921 | * get the next base (multiply current one by 2^blocksize) |
922 | */ |
923 | size_t k; |
924 | |
925 | if (blocksize <= 2) { |
926 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); |
927 | goto err; |
928 | } |
929 | |
930 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) |
931 | goto err; |
932 | for (k = 2; k < blocksize; k++) { |
933 | if (!EC_POINT_dbl(group, base, base, ctx)) |
934 | goto err; |
935 | } |
936 | } |
937 | } |
938 | |
939 | if (!EC_POINTs_make_affine(group, num, points, ctx)) |
940 | goto err; |
941 | |
942 | pre_comp->group = group; |
943 | pre_comp->blocksize = blocksize; |
944 | pre_comp->numblocks = numblocks; |
945 | pre_comp->w = w; |
946 | pre_comp->points = points; |
947 | points = NULL; |
948 | pre_comp->num = num; |
949 | SETPRECOMP(group, ec, pre_comp); |
950 | pre_comp = NULL; |
951 | ret = 1; |
952 | |
953 | err: |
954 | BN_CTX_end(ctx); |
955 | #ifndef FIPS_MODE |
956 | BN_CTX_free(new_ctx); |
957 | #endif |
958 | EC_ec_pre_comp_free(pre_comp); |
959 | if (points) { |
960 | EC_POINT **p; |
961 | |
962 | for (p = points; *p != NULL; p++) |
963 | EC_POINT_free(*p); |
964 | OPENSSL_free(points); |
965 | } |
966 | EC_POINT_free(tmp_point); |
967 | EC_POINT_free(base); |
968 | return ret; |
969 | } |
970 | |
971 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
972 | { |
973 | return HAVEPRECOMP(group, ec); |
974 | } |
975 | |