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35b73a1f | 1 | /* |
6ec5fce2 | 2 | * Copyright 2001-2018 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 | |
36bed230 | 104 | #define EC_POINT_BN_set_flags(P, flags) do { \ |
40e48e54 BB |
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 | ||
f4675379 | 110 | /*- |
40e48e54 BB |
111 | * This functions computes (in constant time) a point multiplication over the |
112 | * EC group. | |
113 | * | |
a067a870 BB |
114 | * At a high level, it is Montgomery ladder with conditional swaps. |
115 | * | |
fe2d3975 | 116 | * It performs either a fixed point multiplication |
40e48e54 | 117 | * (scalar * generator) |
fe2d3975 | 118 | * when point is NULL, or a variable point multiplication |
40e48e54 BB |
119 | * (scalar * point) |
120 | * when point is not NULL. | |
121 | * | |
122 | * scalar should be in the range [0,n) otherwise all constant time bets are off. | |
123 | * | |
124 | * NB: This says nothing about EC_POINT_add and EC_POINT_dbl, | |
125 | * which of course are not constant time themselves. | |
126 | * | |
127 | * The product is stored in r. | |
128 | * | |
129 | * Returns 1 on success, 0 otherwise. | |
130 | */ | |
f4675379 NT |
131 | static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, |
132 | const BIGNUM *scalar, const EC_POINT *point, | |
133 | BN_CTX *ctx) | |
40e48e54 | 134 | { |
36bed230 | 135 | int i, order_bits, group_top, kbit, pbit, Z_is_one; |
40e48e54 BB |
136 | EC_POINT *s = NULL; |
137 | BIGNUM *k = NULL; | |
138 | BIGNUM *lambda = NULL; | |
139 | BN_CTX *new_ctx = NULL; | |
36bed230 | 140 | int ret = 0; |
40e48e54 | 141 | |
36bed230 | 142 | if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL) |
7d859d1c AP |
143 | return 0; |
144 | ||
145 | BN_CTX_start(ctx); | |
40e48e54 | 146 | |
40e48e54 BB |
147 | order_bits = BN_num_bits(group->order); |
148 | ||
149 | s = EC_POINT_new(group); | |
150 | if (s == NULL) | |
151 | goto err; | |
152 | ||
153 | if (point == NULL) { | |
40e48e54 BB |
154 | if (!EC_POINT_copy(s, group->generator)) |
155 | goto err; | |
156 | } else { | |
157 | if (!EC_POINT_copy(s, point)) | |
158 | goto err; | |
159 | } | |
160 | ||
36bed230 | 161 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME); |
40e48e54 | 162 | |
40e48e54 BB |
163 | lambda = BN_CTX_get(ctx); |
164 | k = BN_CTX_get(ctx); | |
165 | if (k == NULL) | |
166 | goto err; | |
167 | ||
168 | /* | |
169 | * Group orders are often on a word boundary. | |
170 | * So when we pad the scalar, some timing diff might | |
171 | * pop if it needs to be expanded due to carries. | |
172 | * So expand ahead of time. | |
173 | */ | |
174 | group_top = bn_get_top(group->order); | |
175 | if ((bn_wexpand(k, group_top + 1) == NULL) | |
176 | || (bn_wexpand(lambda, group_top + 1) == NULL)) | |
177 | goto err; | |
178 | ||
179 | if (!BN_copy(k, scalar)) | |
180 | goto err; | |
181 | ||
182 | BN_set_flags(k, BN_FLG_CONSTTIME); | |
183 | ||
184 | if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) { | |
f4675379 | 185 | /*- |
40e48e54 BB |
186 | * this is an unusual input, and we don't guarantee |
187 | * constant-timeness | |
188 | */ | |
f4675379 | 189 | if (!BN_nnmod(k, k, group->order, ctx)) |
40e48e54 BB |
190 | goto err; |
191 | } | |
192 | ||
193 | if (!BN_add(lambda, k, group->order)) | |
194 | goto err; | |
195 | BN_set_flags(lambda, BN_FLG_CONSTTIME); | |
196 | if (!BN_add(k, lambda, group->order)) | |
197 | goto err; | |
198 | /* | |
199 | * lambda := scalar + order | |
200 | * k := scalar + 2*order | |
201 | */ | |
202 | kbit = BN_is_bit_set(lambda, order_bits); | |
203 | BN_consttime_swap(kbit, k, lambda, group_top + 1); | |
204 | ||
205 | group_top = bn_get_top(group->field); | |
206 | if ((bn_wexpand(s->X, group_top) == NULL) | |
207 | || (bn_wexpand(s->Y, group_top) == NULL) | |
208 | || (bn_wexpand(s->Z, group_top) == NULL) | |
209 | || (bn_wexpand(r->X, group_top) == NULL) | |
210 | || (bn_wexpand(r->Y, group_top) == NULL) | |
211 | || (bn_wexpand(r->Z, group_top) == NULL)) | |
212 | goto err; | |
213 | ||
214 | /* top bit is a 1, in a fixed pos */ | |
215 | if (!EC_POINT_copy(r, s)) | |
216 | goto err; | |
217 | ||
36bed230 | 218 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME); |
40e48e54 BB |
219 | |
220 | if (!EC_POINT_dbl(group, s, s, ctx)) | |
221 | goto err; | |
222 | ||
223 | pbit = 0; | |
224 | ||
225 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |
226 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ | |
227 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ | |
228 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ | |
229 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |
230 | (a)->Z_is_one ^= (t); \ | |
231 | (b)->Z_is_one ^= (t); \ | |
232 | } while(0) | |
233 | ||
f4675379 | 234 | /*- |
a067a870 BB |
235 | * The ladder step, with branches, is |
236 | * | |
237 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
238 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
239 | * | |
240 | * Swapping R, S conditionally on k[i] leaves you with state | |
241 | * | |
242 | * k[i] == 0: T, U = R, S | |
243 | * k[i] == 1: T, U = S, R | |
244 | * | |
245 | * Then perform the ECC ops. | |
246 | * | |
247 | * U = add(T, U) | |
248 | * T = dbl(T) | |
249 | * | |
250 | * Which leaves you with state | |
251 | * | |
252 | * k[i] == 0: U = add(R, S), T = dbl(R) | |
253 | * k[i] == 1: U = add(S, R), T = dbl(S) | |
254 | * | |
255 | * Swapping T, U conditionally on k[i] leaves you with state | |
256 | * | |
257 | * k[i] == 0: R, S = T, U | |
258 | * k[i] == 1: R, S = U, T | |
259 | * | |
260 | * Which leaves you with state | |
261 | * | |
262 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
263 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
264 | * | |
265 | * So we get the same logic, but instead of a branch it's a | |
266 | * conditional swap, followed by ECC ops, then another conditional swap. | |
267 | * | |
268 | * Optimization: The end of iteration i and start of i-1 looks like | |
269 | * | |
270 | * ... | |
271 | * CSWAP(k[i], R, S) | |
272 | * ECC | |
273 | * CSWAP(k[i], R, S) | |
274 | * (next iteration) | |
275 | * CSWAP(k[i-1], R, S) | |
276 | * ECC | |
277 | * CSWAP(k[i-1], R, S) | |
278 | * ... | |
279 | * | |
280 | * So instead of two contiguous swaps, you can merge the condition | |
281 | * bits and do a single swap. | |
282 | * | |
f4675379 NT |
283 | * k[i] k[i-1] Outcome |
284 | * 0 0 No Swap | |
285 | * 0 1 Swap | |
286 | * 1 0 Swap | |
287 | * 1 1 No Swap | |
a067a870 BB |
288 | * |
289 | * This is XOR. pbit tracks the previous bit of k. | |
290 | */ | |
291 | ||
40e48e54 BB |
292 | for (i = order_bits - 1; i >= 0; i--) { |
293 | kbit = BN_is_bit_set(k, i) ^ pbit; | |
294 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |
295 | if (!EC_POINT_add(group, s, r, s, ctx)) | |
296 | goto err; | |
297 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
298 | goto err; | |
299 | /* | |
300 | * pbit logic merges this cswap with that of the | |
301 | * next iteration | |
302 | */ | |
303 | pbit ^= kbit; | |
304 | } | |
305 | /* one final cswap to move the right value into r */ | |
306 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |
307 | #undef EC_POINT_CSWAP | |
308 | ||
309 | ret = 1; | |
310 | ||
f4675379 | 311 | err: |
40e48e54 BB |
312 | EC_POINT_free(s); |
313 | BN_CTX_end(ctx); | |
314 | BN_CTX_free(new_ctx); | |
315 | ||
316 | return ret; | |
317 | } | |
f4675379 | 318 | |
36bed230 | 319 | #undef EC_POINT_BN_set_flags |
40e48e54 | 320 | |
0f113f3e MC |
321 | /* |
322 | * TODO: table should be optimised for the wNAF-based implementation, | |
323 | * sometimes smaller windows will give better performance (thus the | |
324 | * boundaries should be increased) | |
c05940ed | 325 | */ |
3ba1f111 | 326 | #define EC_window_bits_for_scalar_size(b) \ |
0f113f3e MC |
327 | ((size_t) \ |
328 | ((b) >= 2000 ? 6 : \ | |
329 | (b) >= 800 ? 5 : \ | |
330 | (b) >= 300 ? 4 : \ | |
331 | (b) >= 70 ? 3 : \ | |
332 | (b) >= 20 ? 2 : \ | |
333 | 1)) | |
3ba1f111 | 334 | |
c80fd6b2 MC |
335 | /*- |
336 | * Compute | |
3ba1f111 BM |
337 | * \sum scalars[i]*points[i], |
338 | * also including | |
339 | * scalar*generator | |
340 | * in the addition if scalar != NULL | |
341 | */ | |
7793f30e | 342 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
0f113f3e MC |
343 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
344 | BN_CTX *ctx) | |
345 | { | |
346 | BN_CTX *new_ctx = NULL; | |
347 | const EC_POINT *generator = NULL; | |
348 | EC_POINT *tmp = NULL; | |
349 | size_t totalnum; | |
350 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
351 | size_t pre_points_per_block = 0; | |
352 | size_t i, j; | |
353 | int k; | |
354 | int r_is_inverted = 0; | |
355 | int r_is_at_infinity = 1; | |
356 | size_t *wsize = NULL; /* individual window sizes */ | |
357 | signed char **wNAF = NULL; /* individual wNAFs */ | |
358 | size_t *wNAF_len = NULL; | |
359 | size_t max_len = 0; | |
360 | size_t num_val; | |
361 | EC_POINT **val = NULL; /* precomputation */ | |
362 | EC_POINT **v; | |
363 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
364 | * '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 | |
367 | * treated like other scalars, i.e. | |
368 | * precomputation is not available */ | |
369 | int ret = 0; | |
370 | ||
b14e6015 | 371 | if (!ec_point_is_compat(r, group)) { |
736b31e5 NT |
372 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
373 | return 0; | |
374 | } | |
375 | ||
376 | if ((scalar == NULL) && (num == 0)) { | |
377 | return EC_POINT_set_to_infinity(group, r); | |
378 | } | |
379 | ||
f4675379 NT |
380 | /*- |
381 | * Handle the common cases where the scalar is secret, enforcing a constant | |
382 | * time scalar multiplication algorithm. | |
36bed230 NT |
383 | */ |
384 | if ((scalar != NULL) && (num == 0)) { | |
f4675379 NT |
385 | /*- |
386 | * In this case we want to compute scalar * GeneratorPoint: this | |
387 | * codepath is reached most prominently by (ephemeral) key generation | |
388 | * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH | |
389 | * keygen/first half), where the scalar is always secret. This is why | |
390 | * we ignore if BN_FLG_CONSTTIME is actually set and we always call the | |
391 | * constant time version. | |
36bed230 NT |
392 | */ |
393 | return ec_mul_consttime(group, r, scalar, NULL, ctx); | |
394 | } | |
395 | if ((scalar == NULL) && (num == 1)) { | |
f4675379 NT |
396 | /*- |
397 | * In this case we want to compute scalar * GenericPoint: this codepath | |
398 | * is reached most prominently by the second half of ECDH, where the | |
399 | * secret scalar is multiplied by the peer's public point. To protect | |
400 | * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and | |
401 | * we always call the constant time version. | |
36bed230 NT |
402 | */ |
403 | return ec_mul_consttime(group, r, scalars[0], points[0], ctx); | |
404 | } | |
405 | ||
0f113f3e | 406 | for (i = 0; i < num; i++) { |
b14e6015 | 407 | if (!ec_point_is_compat(points[i], group)) { |
0f113f3e MC |
408 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
409 | return 0; | |
410 | } | |
411 | } | |
412 | ||
413 | if (ctx == NULL) { | |
414 | ctx = new_ctx = BN_CTX_new(); | |
415 | if (ctx == NULL) | |
416 | goto err; | |
417 | } | |
418 | ||
419 | if (scalar != NULL) { | |
420 | generator = EC_GROUP_get0_generator(group); | |
421 | if (generator == NULL) { | |
422 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
423 | goto err; | |
424 | } | |
425 | ||
426 | /* look if we can use precomputed multiples of generator */ | |
427 | ||
3aef36ff | 428 | pre_comp = group->pre_comp.ec; |
0f113f3e MC |
429 | if (pre_comp && pre_comp->numblocks |
430 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
431 | 0)) { | |
432 | blocksize = pre_comp->blocksize; | |
433 | ||
434 | /* | |
435 | * determine maximum number of blocks that wNAF splitting may | |
436 | * yield (NB: maximum wNAF length is bit length plus one) | |
437 | */ | |
438 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
439 | ||
440 | /* | |
441 | * we cannot use more blocks than we have precomputation for | |
442 | */ | |
443 | if (numblocks > pre_comp->numblocks) | |
444 | numblocks = pre_comp->numblocks; | |
445 | ||
446 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
447 | ||
448 | /* check that pre_comp looks sane */ | |
449 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
450 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
451 | goto err; | |
452 | } | |
453 | } else { | |
454 | /* can't use precomputation */ | |
455 | pre_comp = NULL; | |
456 | numblocks = 1; | |
457 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
458 | * 'scalars' */ | |
459 | } | |
460 | } | |
461 | ||
462 | totalnum = num + numblocks; | |
463 | ||
cbe29648 RS |
464 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
465 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); | |
466 | /* include space for pivot */ | |
467 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); | |
468 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); | |
0f113f3e MC |
469 | |
470 | /* Ensure wNAF is initialised in case we end up going to err */ | |
90945fa3 | 471 | if (wNAF != NULL) |
0f113f3e MC |
472 | wNAF[0] = NULL; /* preliminary pivot */ |
473 | ||
90945fa3 | 474 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { |
0f113f3e MC |
475 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
476 | goto err; | |
477 | } | |
478 | ||
479 | /* | |
480 | * num_val will be the total number of temporarily precomputed points | |
481 | */ | |
482 | num_val = 0; | |
483 | ||
484 | for (i = 0; i < num + num_scalar; i++) { | |
485 | size_t bits; | |
486 | ||
487 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
488 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
489 | num_val += (size_t)1 << (wsize[i] - 1); | |
490 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
491 | wNAF[i] = | |
492 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
493 | &wNAF_len[i]); | |
494 | if (wNAF[i] == NULL) | |
495 | goto err; | |
496 | if (wNAF_len[i] > max_len) | |
497 | max_len = wNAF_len[i]; | |
498 | } | |
499 | ||
500 | if (numblocks) { | |
501 | /* we go here iff scalar != NULL */ | |
502 | ||
503 | if (pre_comp == NULL) { | |
504 | if (num_scalar != 1) { | |
505 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
506 | goto err; | |
507 | } | |
508 | /* we have already generated a wNAF for 'scalar' */ | |
509 | } else { | |
510 | signed char *tmp_wNAF = NULL; | |
511 | size_t tmp_len = 0; | |
512 | ||
513 | if (num_scalar != 0) { | |
514 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
515 | goto err; | |
516 | } | |
517 | ||
518 | /* | |
519 | * use the window size for which we have precomputation | |
520 | */ | |
521 | wsize[num] = pre_comp->w; | |
522 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
523 | if (!tmp_wNAF) | |
524 | goto err; | |
525 | ||
526 | if (tmp_len <= max_len) { | |
527 | /* | |
528 | * One of the other wNAFs is at least as long as the wNAF | |
529 | * belonging to the generator, so wNAF splitting will not buy | |
530 | * us anything. | |
531 | */ | |
532 | ||
533 | numblocks = 1; | |
534 | totalnum = num + 1; /* don't use wNAF splitting */ | |
535 | wNAF[num] = tmp_wNAF; | |
536 | wNAF[num + 1] = NULL; | |
537 | wNAF_len[num] = tmp_len; | |
0f113f3e MC |
538 | /* |
539 | * pre_comp->points starts with the points that we need here: | |
540 | */ | |
541 | val_sub[num] = pre_comp->points; | |
542 | } else { | |
543 | /* | |
544 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
545 | * splitting and include the blocks | |
546 | */ | |
547 | ||
548 | signed char *pp; | |
549 | EC_POINT **tmp_points; | |
550 | ||
551 | if (tmp_len < numblocks * blocksize) { | |
552 | /* | |
553 | * possibly we can do with fewer blocks than estimated | |
554 | */ | |
555 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
556 | if (numblocks > pre_comp->numblocks) { | |
557 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 558 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
559 | goto err; |
560 | } | |
561 | totalnum = num + numblocks; | |
562 | } | |
563 | ||
564 | /* split wNAF in 'numblocks' parts */ | |
565 | pp = tmp_wNAF; | |
566 | tmp_points = pre_comp->points; | |
567 | ||
568 | for (i = num; i < totalnum; i++) { | |
569 | if (i < totalnum - 1) { | |
570 | wNAF_len[i] = blocksize; | |
571 | if (tmp_len < blocksize) { | |
572 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 573 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
574 | goto err; |
575 | } | |
576 | tmp_len -= blocksize; | |
577 | } else | |
578 | /* | |
579 | * last block gets whatever is left (this could be | |
580 | * more or less than 'blocksize'!) | |
581 | */ | |
582 | wNAF_len[i] = tmp_len; | |
583 | ||
584 | wNAF[i + 1] = NULL; | |
585 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
586 | if (wNAF[i] == NULL) { | |
587 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
588 | OPENSSL_free(tmp_wNAF); | |
589 | goto err; | |
590 | } | |
591 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
592 | if (wNAF_len[i] > max_len) | |
593 | max_len = wNAF_len[i]; | |
594 | ||
595 | if (*tmp_points == NULL) { | |
596 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
597 | OPENSSL_free(tmp_wNAF); | |
598 | goto err; | |
599 | } | |
600 | val_sub[i] = tmp_points; | |
601 | tmp_points += pre_points_per_block; | |
602 | pp += blocksize; | |
603 | } | |
604 | OPENSSL_free(tmp_wNAF); | |
605 | } | |
606 | } | |
607 | } | |
608 | ||
609 | /* | |
610 | * All points we precompute now go into a single array 'val'. | |
611 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
612 | * subarray of 'pre_comp->points' if we already have precomputation. | |
613 | */ | |
cbe29648 | 614 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
0f113f3e MC |
615 | if (val == NULL) { |
616 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
617 | goto err; | |
618 | } | |
619 | val[num_val] = NULL; /* pivot element */ | |
620 | ||
621 | /* allocate points for precomputation */ | |
622 | v = val; | |
623 | for (i = 0; i < num + num_scalar; i++) { | |
624 | val_sub[i] = v; | |
625 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
626 | *v = EC_POINT_new(group); | |
627 | if (*v == NULL) | |
628 | goto err; | |
629 | v++; | |
630 | } | |
631 | } | |
632 | if (!(v == val + num_val)) { | |
633 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
634 | goto err; | |
635 | } | |
636 | ||
75ebbd9a | 637 | if ((tmp = EC_POINT_new(group)) == NULL) |
0f113f3e MC |
638 | goto err; |
639 | ||
50e735f9 MC |
640 | /*- |
641 | * prepare precomputed values: | |
642 | * val_sub[i][0] := points[i] | |
643 | * val_sub[i][1] := 3 * points[i] | |
644 | * val_sub[i][2] := 5 * points[i] | |
645 | * ... | |
646 | */ | |
0f113f3e MC |
647 | for (i = 0; i < num + num_scalar; i++) { |
648 | if (i < num) { | |
649 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
650 | goto err; | |
651 | } else { | |
652 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
653 | goto err; | |
654 | } | |
655 | ||
656 | if (wsize[i] > 1) { | |
657 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
658 | goto err; | |
659 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
660 | if (!EC_POINT_add | |
661 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
662 | goto err; | |
663 | } | |
664 | } | |
665 | } | |
666 | ||
0f113f3e MC |
667 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
668 | goto err; | |
3ba1f111 | 669 | |
0f113f3e MC |
670 | r_is_at_infinity = 1; |
671 | ||
672 | for (k = max_len - 1; k >= 0; k--) { | |
673 | if (!r_is_at_infinity) { | |
674 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
675 | goto err; | |
676 | } | |
677 | ||
678 | for (i = 0; i < totalnum; i++) { | |
679 | if (wNAF_len[i] > (size_t)k) { | |
680 | int digit = wNAF[i][k]; | |
681 | int is_neg; | |
682 | ||
683 | if (digit) { | |
684 | is_neg = digit < 0; | |
685 | ||
686 | if (is_neg) | |
687 | digit = -digit; | |
688 | ||
689 | if (is_neg != r_is_inverted) { | |
690 | if (!r_is_at_infinity) { | |
691 | if (!EC_POINT_invert(group, r, ctx)) | |
692 | goto err; | |
693 | } | |
694 | r_is_inverted = !r_is_inverted; | |
695 | } | |
696 | ||
697 | /* digit > 0 */ | |
698 | ||
699 | if (r_is_at_infinity) { | |
700 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
701 | goto err; | |
702 | r_is_at_infinity = 0; | |
703 | } else { | |
704 | if (!EC_POINT_add | |
705 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
706 | goto err; | |
707 | } | |
708 | } | |
709 | } | |
710 | } | |
711 | } | |
712 | ||
713 | if (r_is_at_infinity) { | |
714 | if (!EC_POINT_set_to_infinity(group, r)) | |
715 | goto err; | |
716 | } else { | |
717 | if (r_is_inverted) | |
718 | if (!EC_POINT_invert(group, r, ctx)) | |
719 | goto err; | |
720 | } | |
721 | ||
722 | ret = 1; | |
3ba1f111 BM |
723 | |
724 | err: | |
23a1d5e9 | 725 | BN_CTX_free(new_ctx); |
8fdc3734 | 726 | EC_POINT_free(tmp); |
b548a1f1 RS |
727 | OPENSSL_free(wsize); |
728 | OPENSSL_free(wNAF_len); | |
0f113f3e MC |
729 | if (wNAF != NULL) { |
730 | signed char **w; | |
731 | ||
732 | for (w = wNAF; *w != NULL; w++) | |
733 | OPENSSL_free(*w); | |
734 | ||
735 | OPENSSL_free(wNAF); | |
736 | } | |
737 | if (val != NULL) { | |
738 | for (v = val; *v != NULL; v++) | |
739 | EC_POINT_clear_free(*v); | |
740 | ||
741 | OPENSSL_free(val); | |
742 | } | |
b548a1f1 | 743 | OPENSSL_free(val_sub); |
0f113f3e MC |
744 | return ret; |
745 | } | |
38374911 | 746 | |
1d97c843 TH |
747 | /*- |
748 | * ec_wNAF_precompute_mult() | |
37c660ff BM |
749 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
750 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
0f113f3e | 751 | * |
37c660ff BM |
752 | * 'pre_comp->points' is an array of multiples of the generator |
753 | * of the following form: | |
754 | * points[0] = generator; | |
755 | * points[1] = 3 * generator; | |
756 | * ... | |
757 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
758 | * points[2^(w-1)] = 2^blocksize * generator; | |
759 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
760 | * ... | |
761 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
762 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
763 | * ... | |
764 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
765 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 766 | */ |
7793f30e | 767 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
768 | { |
769 | const EC_POINT *generator; | |
770 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
771 | BN_CTX *new_ctx = NULL; | |
be2e334f | 772 | const BIGNUM *order; |
0f113f3e MC |
773 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
774 | EC_POINT **points = NULL; | |
775 | EC_PRE_COMP *pre_comp; | |
776 | int ret = 0; | |
777 | ||
778 | /* if there is an old EC_PRE_COMP object, throw it away */ | |
2c52ac9b | 779 | EC_pre_comp_free(group); |
0f113f3e MC |
780 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
781 | return 0; | |
782 | ||
783 | generator = EC_GROUP_get0_generator(group); | |
784 | if (generator == NULL) { | |
785 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); | |
786 | goto err; | |
787 | } | |
788 | ||
789 | if (ctx == NULL) { | |
790 | ctx = new_ctx = BN_CTX_new(); | |
791 | if (ctx == NULL) | |
792 | goto err; | |
793 | } | |
794 | ||
795 | BN_CTX_start(ctx); | |
0f113f3e | 796 | |
be2e334f DSH |
797 | order = EC_GROUP_get0_order(group); |
798 | if (order == NULL) | |
0f113f3e MC |
799 | goto err; |
800 | if (BN_is_zero(order)) { | |
801 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); | |
802 | goto err; | |
803 | } | |
804 | ||
805 | bits = BN_num_bits(order); | |
806 | /* | |
807 | * The following parameters mean we precompute (approximately) one point | |
808 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
809 | * bit lengths, other parameter combinations might provide better | |
810 | * efficiency. | |
811 | */ | |
812 | blocksize = 8; | |
813 | w = 4; | |
814 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
815 | /* let's not make the window too small ... */ | |
816 | w = EC_window_bits_for_scalar_size(bits); | |
817 | } | |
818 | ||
819 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
820 | * to use for wNAF | |
821 | * splitting */ | |
822 | ||
823 | pre_points_per_block = (size_t)1 << (w - 1); | |
824 | num = pre_points_per_block * numblocks; /* number of points to compute | |
825 | * and store */ | |
826 | ||
b4faea50 | 827 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
90945fa3 | 828 | if (points == NULL) { |
0f113f3e MC |
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 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
837 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
838 | goto err; | |
839 | } | |
840 | } | |
841 | ||
75ebbd9a RS |
842 | if ((tmp_point = EC_POINT_new(group)) == NULL |
843 | || (base = EC_POINT_new(group)) == NULL) { | |
0f113f3e MC |
844 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
845 | goto err; | |
846 | } | |
847 | ||
848 | if (!EC_POINT_copy(base, generator)) | |
849 | goto err; | |
850 | ||
851 | /* do the precomputation */ | |
852 | for (i = 0; i < numblocks; i++) { | |
853 | size_t j; | |
854 | ||
855 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
856 | goto err; | |
857 | ||
858 | if (!EC_POINT_copy(*var++, base)) | |
859 | goto err; | |
860 | ||
861 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
862 | /* | |
863 | * calculate odd multiples of the current base point | |
864 | */ | |
865 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
866 | goto err; | |
867 | } | |
868 | ||
869 | if (i < numblocks - 1) { | |
870 | /* | |
871 | * get the next base (multiply current one by 2^blocksize) | |
872 | */ | |
873 | size_t k; | |
874 | ||
875 | if (blocksize <= 2) { | |
876 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
877 | goto err; | |
878 | } | |
879 | ||
880 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
881 | goto err; | |
882 | for (k = 2; k < blocksize; k++) { | |
883 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
884 | goto err; | |
885 | } | |
886 | } | |
887 | } | |
888 | ||
889 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
890 | goto err; | |
891 | ||
892 | pre_comp->group = group; | |
893 | pre_comp->blocksize = blocksize; | |
894 | pre_comp->numblocks = numblocks; | |
895 | pre_comp->w = w; | |
896 | pre_comp->points = points; | |
897 | points = NULL; | |
898 | pre_comp->num = num; | |
3aef36ff | 899 | SETPRECOMP(group, ec, pre_comp); |
0f113f3e | 900 | pre_comp = NULL; |
0f113f3e | 901 | ret = 1; |
3aef36ff | 902 | |
38374911 | 903 | err: |
0f113f3e MC |
904 | if (ctx != NULL) |
905 | BN_CTX_end(ctx); | |
23a1d5e9 | 906 | BN_CTX_free(new_ctx); |
3aef36ff | 907 | EC_ec_pre_comp_free(pre_comp); |
0f113f3e MC |
908 | if (points) { |
909 | EC_POINT **p; | |
910 | ||
911 | for (p = points; *p != NULL; p++) | |
912 | EC_POINT_free(*p); | |
913 | OPENSSL_free(points); | |
914 | } | |
8fdc3734 RS |
915 | EC_POINT_free(tmp_point); |
916 | EC_POINT_free(base); | |
0f113f3e MC |
917 | return ret; |
918 | } | |
7793f30e | 919 | |
37c660ff | 920 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
0f113f3e | 921 | { |
3aef36ff | 922 | return HAVEPRECOMP(group, ec); |
0f113f3e | 923 | } |