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65e81670 | 1 | /* crypto/ec/ec_mult.c */ |
35b73a1f | 2 | /* |
37c660ff | 3 | * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project. |
35b73a1f | 4 | */ |
65e81670 | 5 | /* ==================================================================== |
19f6c524 | 6 | * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved. |
65e81670 BM |
7 | * |
8 | * Redistribution and use in source and binary forms, with or without | |
9 | * modification, are permitted provided that the following conditions | |
10 | * are met: | |
11 | * | |
12 | * 1. Redistributions of source code must retain the above copyright | |
13 | * notice, this list of conditions and the following disclaimer. | |
14 | * | |
15 | * 2. Redistributions in binary form must reproduce the above copyright | |
16 | * notice, this list of conditions and the following disclaimer in | |
17 | * the documentation and/or other materials provided with the | |
18 | * distribution. | |
19 | * | |
20 | * 3. All advertising materials mentioning features or use of this | |
21 | * software must display the following acknowledgment: | |
22 | * "This product includes software developed by the OpenSSL Project | |
23 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
24 | * | |
25 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
26 | * endorse or promote products derived from this software without | |
27 | * prior written permission. For written permission, please contact | |
28 | * openssl-core@openssl.org. | |
29 | * | |
30 | * 5. Products derived from this software may not be called "OpenSSL" | |
31 | * nor may "OpenSSL" appear in their names without prior written | |
32 | * permission of the OpenSSL Project. | |
33 | * | |
34 | * 6. Redistributions of any form whatsoever must retain the following | |
35 | * acknowledgment: | |
36 | * "This product includes software developed by the OpenSSL Project | |
37 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
38 | * | |
39 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
40 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
41 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
42 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
43 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
44 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
45 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
46 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
47 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
48 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
49 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
50 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
51 | * ==================================================================== | |
52 | * | |
53 | * This product includes cryptographic software written by Eric Young | |
54 | * (eay@cryptsoft.com). This product includes software written by Tim | |
55 | * Hudson (tjh@cryptsoft.com). | |
56 | * | |
57 | */ | |
7793f30e BM |
58 | /* ==================================================================== |
59 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
60 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
61 | * and contributed to the OpenSSL project. | |
62 | */ | |
65e81670 | 63 | |
28f573a2 RL |
64 | #include <string.h> |
65 | ||
48fe4d62 BM |
66 | #include <openssl/err.h> |
67 | ||
65e81670 | 68 | #include "ec_lcl.h" |
48fe4d62 BM |
69 | |
70 | ||
37c660ff BM |
71 | /* |
72 | * This file implements the wNAF-based interleaving multi-exponentation method | |
73 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); | |
74 | * for multiplication with precomputation, we use wNAF splitting | |
75 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>). | |
76 | */ | |
48fe4d62 BM |
77 | |
78 | ||
f916052e | 79 | |
37c660ff BM |
80 | |
81 | /* structure for precomputed multiples of the generator */ | |
82 | typedef struct ec_pre_comp_st { | |
83 | const EC_GROUP *group; /* parent EC_GROUP object */ | |
84 | size_t blocksize; /* block size for wNAF splitting */ | |
85 | size_t numblocks; /* max. number of blocks for which we have precomputation */ | |
86 | size_t w; /* window size */ | |
87 | EC_POINT **points; /* array with pre-calculated multiples of generator: | |
88 | * 'num' pointers to EC_POINT objects followed by a NULL */ | |
89 | size_t num; /* numblocks * 2^(w-1) */ | |
ba729265 | 90 | int references; |
37c660ff BM |
91 | } EC_PRE_COMP; |
92 | ||
93 | /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ | |
94 | static void *ec_pre_comp_dup(void *); | |
95 | static void ec_pre_comp_free(void *); | |
96 | static void ec_pre_comp_clear_free(void *); | |
97 | ||
98 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
99 | { | |
100 | EC_PRE_COMP *ret = NULL; | |
101 | ||
102 | if (!group) | |
103 | return NULL; | |
104 | ||
105 | ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); | |
106 | if (!ret) | |
19f6c524 BM |
107 | { |
108 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
37c660ff | 109 | return ret; |
19f6c524 | 110 | } |
37c660ff BM |
111 | ret->group = group; |
112 | ret->blocksize = 8; /* default */ | |
113 | ret->numblocks = 0; | |
114 | ret->w = 4; /* default */ | |
115 | ret->points = NULL; | |
116 | ret->num = 0; | |
ba729265 | 117 | ret->references = 1; |
37c660ff BM |
118 | return ret; |
119 | } | |
120 | ||
121 | static void *ec_pre_comp_dup(void *src_) | |
122 | { | |
ba729265 | 123 | EC_PRE_COMP *src = src_; |
37c660ff | 124 | |
ba729265 | 125 | /* no need to actually copy, these objects never change! */ |
37c660ff | 126 | |
ba729265 | 127 | CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); |
37c660ff | 128 | |
ba729265 | 129 | return src_; |
37c660ff BM |
130 | } |
131 | ||
132 | static void ec_pre_comp_free(void *pre_) | |
133 | { | |
ba729265 | 134 | int i; |
37c660ff BM |
135 | EC_PRE_COMP *pre = pre_; |
136 | ||
137 | if (!pre) | |
138 | return; | |
ba729265 BM |
139 | |
140 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); | |
141 | if (i > 0) | |
142 | return; | |
143 | ||
37c660ff BM |
144 | if (pre->points) |
145 | { | |
ba729265 | 146 | EC_POINT **p; |
37c660ff | 147 | |
ba729265 BM |
148 | for (p = pre->points; *p != NULL; p++) |
149 | EC_POINT_free(*p); | |
37c660ff BM |
150 | OPENSSL_free(pre->points); |
151 | } | |
152 | OPENSSL_free(pre); | |
153 | } | |
154 | ||
155 | static void ec_pre_comp_clear_free(void *pre_) | |
156 | { | |
ba729265 | 157 | int i; |
37c660ff BM |
158 | EC_PRE_COMP *pre = pre_; |
159 | ||
160 | if (!pre) | |
161 | return; | |
ba729265 BM |
162 | |
163 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); | |
164 | if (i > 0) | |
165 | return; | |
166 | ||
37c660ff BM |
167 | if (pre->points) |
168 | { | |
169 | EC_POINT **p; | |
170 | ||
171 | for (p = pre->points; *p != NULL; p++) | |
172 | EC_POINT_clear_free(*p); | |
173 | OPENSSL_cleanse(pre->points, sizeof pre->points); | |
174 | OPENSSL_free(pre->points); | |
175 | } | |
176 | OPENSSL_cleanse(pre, sizeof pre); | |
177 | OPENSSL_free(pre); | |
178 | } | |
179 | ||
180 | ||
3ba1f111 BM |
181 | |
182 | ||
2c8d0dcc | 183 | /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. |
3ba1f111 BM |
184 | * This is an array r[] of values that are either zero or odd with an |
185 | * absolute value less than 2^w satisfying | |
186 | * scalar = \sum_j r[j]*2^j | |
2c8d0dcc BM |
187 | * where at most one of any w+1 consecutive digits is non-zero |
188 | * with the exception that the most significant digit may be only | |
189 | * w-1 zeros away from that next non-zero digit. | |
3ba1f111 | 190 | */ |
2c8d0dcc | 191 | static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) |
3ba1f111 | 192 | { |
2c8d0dcc | 193 | int window_val; |
3ba1f111 BM |
194 | int ok = 0; |
195 | signed char *r = NULL; | |
196 | int sign = 1; | |
197 | int bit, next_bit, mask; | |
e71adb85 | 198 | size_t len = 0, j; |
3ba1f111 | 199 | |
19f6c524 BM |
200 | if (BN_is_zero(scalar)) |
201 | { | |
202 | r = OPENSSL_malloc(1); | |
203 | if (!r) | |
204 | { | |
205 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); | |
206 | goto err; | |
207 | } | |
208 | r[0] = 0; | |
209 | *ret_len = 1; | |
210 | return r; | |
211 | } | |
212 | ||
c78515f5 | 213 | if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ |
3ba1f111 BM |
214 | { |
215 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
216 | goto err; | |
217 | } | |
218 | bit = 1 << w; /* at most 128 */ | |
219 | next_bit = bit << 1; /* at most 256 */ | |
220 | mask = next_bit - 1; /* at most 255 */ | |
221 | ||
ff22e913 | 222 | if (BN_is_negative(scalar)) |
3ba1f111 BM |
223 | { |
224 | sign = -1; | |
3ba1f111 BM |
225 | } |
226 | ||
57a6ac7c BL |
227 | if (scalar->d == NULL || scalar->top == 0) |
228 | { | |
229 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
230 | goto err; | |
231 | } | |
232 | ||
2c8d0dcc | 233 | len = BN_num_bits(scalar); |
37c660ff BM |
234 | r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation |
235 | * (*ret_len will be set to the actual length, i.e. at most | |
236 | * BN_num_bits(scalar) + 1) */ | |
19f6c524 BM |
237 | if (r == NULL) |
238 | { | |
239 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); | |
240 | goto err; | |
241 | } | |
2c8d0dcc | 242 | window_val = scalar->d[0] & mask; |
3ba1f111 | 243 | j = 0; |
2c8d0dcc | 244 | while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ |
3ba1f111 | 245 | { |
2c8d0dcc | 246 | int digit = 0; |
3ba1f111 | 247 | |
2c8d0dcc BM |
248 | /* 0 <= window_val <= 2^(w+1) */ |
249 | ||
250 | if (window_val & 1) | |
3ba1f111 | 251 | { |
2c8d0dcc BM |
252 | /* 0 < window_val < 2^(w+1) */ |
253 | ||
254 | if (window_val & bit) | |
3ba1f111 | 255 | { |
2c8d0dcc BM |
256 | digit = window_val - next_bit; /* -2^w < digit < 0 */ |
257 | ||
258 | #if 1 /* modified wNAF */ | |
259 | if (j + w + 1 >= len) | |
260 | { | |
261 | /* special case for generating modified wNAFs: | |
262 | * no new bits will be added into window_val, | |
263 | * so using a positive digit here will decrease | |
264 | * the total length of the representation */ | |
265 | ||
266 | digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ | |
267 | } | |
268 | #endif | |
3ba1f111 | 269 | } |
2c8d0dcc | 270 | else |
3ba1f111 | 271 | { |
2c8d0dcc | 272 | digit = window_val; /* 0 < digit < 2^w */ |
3ba1f111 | 273 | } |
2c8d0dcc BM |
274 | |
275 | if (digit <= -bit || digit >= bit || !(digit & 1)) | |
3ba1f111 | 276 | { |
2c8d0dcc BM |
277 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
278 | goto err; | |
3ba1f111 BM |
279 | } |
280 | ||
2c8d0dcc BM |
281 | window_val -= digit; |
282 | ||
283 | /* now window_val is 0 or 2^(w+1) in standard wNAF generation; | |
284 | * for modified window NAFs, it may also be 2^w | |
285 | */ | |
286 | if (window_val != 0 && window_val != next_bit && window_val != bit) | |
3ba1f111 BM |
287 | { |
288 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
289 | goto err; | |
290 | } | |
291 | } | |
292 | ||
2c8d0dcc BM |
293 | r[j++] = sign * digit; |
294 | ||
295 | window_val >>= 1; | |
296 | window_val += bit * BN_is_bit_set(scalar, j + w); | |
297 | ||
298 | if (window_val > next_bit) | |
3ba1f111 BM |
299 | { |
300 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
301 | goto err; | |
302 | } | |
3ba1f111 BM |
303 | } |
304 | ||
2c8d0dcc | 305 | if (j > len + 1) |
3ba1f111 BM |
306 | { |
307 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
308 | goto err; | |
309 | } | |
310 | len = j; | |
311 | ok = 1; | |
312 | ||
313 | err: | |
3ba1f111 BM |
314 | if (!ok) |
315 | { | |
316 | OPENSSL_free(r); | |
317 | r = NULL; | |
318 | } | |
319 | if (ok) | |
320 | *ret_len = len; | |
321 | return r; | |
322 | } | |
323 | ||
324 | ||
c05940ed BM |
325 | /* TODO: table should be optimised for the wNAF-based implementation, |
326 | * sometimes smaller windows will give better performance | |
327 | * (thus the boundaries should be increased) | |
328 | */ | |
3ba1f111 | 329 | #define EC_window_bits_for_scalar_size(b) \ |
513c01a5 RL |
330 | ((size_t) \ |
331 | ((b) >= 2000 ? 6 : \ | |
332 | (b) >= 800 ? 5 : \ | |
333 | (b) >= 300 ? 4 : \ | |
334 | (b) >= 70 ? 3 : \ | |
335 | (b) >= 20 ? 2 : \ | |
336 | 1)) | |
3ba1f111 BM |
337 | |
338 | /* Compute | |
339 | * \sum scalars[i]*points[i], | |
340 | * also including | |
341 | * scalar*generator | |
342 | * in the addition if scalar != NULL | |
343 | */ | |
7793f30e | 344 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
3ba1f111 BM |
345 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) |
346 | { | |
347 | BN_CTX *new_ctx = NULL; | |
9dd84053 | 348 | const EC_POINT *generator = NULL; |
3ba1f111 BM |
349 | EC_POINT *tmp = NULL; |
350 | size_t totalnum; | |
37c660ff BM |
351 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ |
352 | size_t pre_points_per_block = 0; | |
3ba1f111 BM |
353 | size_t i, j; |
354 | int k; | |
355 | int r_is_inverted = 0; | |
356 | int r_is_at_infinity = 1; | |
357 | size_t *wsize = NULL; /* individual window sizes */ | |
c78515f5 | 358 | signed char **wNAF = NULL; /* individual wNAFs */ |
3ba1f111 BM |
359 | size_t *wNAF_len = NULL; |
360 | size_t max_len = 0; | |
3ba1f111 BM |
361 | size_t num_val; |
362 | EC_POINT **val = NULL; /* precomputation */ | |
363 | EC_POINT **v; | |
37c660ff | 364 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */ |
ba729265 | 365 | const EC_PRE_COMP *pre_comp = NULL; |
37c660ff BM |
366 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars, |
367 | * i.e. precomputation is not available */ | |
3ba1f111 BM |
368 | int ret = 0; |
369 | ||
37c660ff | 370 | if (group->meth != r->meth) |
3ba1f111 | 371 | { |
37c660ff BM |
372 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
373 | return 0; | |
3ba1f111 | 374 | } |
37c660ff BM |
375 | |
376 | if ((scalar == NULL) && (num == 0)) | |
377 | { | |
378 | return EC_POINT_set_to_infinity(group, r); | |
379 | } | |
380 | ||
3ba1f111 BM |
381 | for (i = 0; i < num; i++) |
382 | { | |
383 | if (group->meth != points[i]->meth) | |
384 | { | |
7793f30e | 385 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
3ba1f111 BM |
386 | return 0; |
387 | } | |
388 | } | |
389 | ||
37c660ff BM |
390 | if (ctx == NULL) |
391 | { | |
392 | ctx = new_ctx = BN_CTX_new(); | |
393 | if (ctx == NULL) | |
394 | goto err; | |
395 | } | |
3ba1f111 | 396 | |
37c660ff | 397 | if (scalar != NULL) |
3ba1f111 | 398 | { |
37c660ff BM |
399 | generator = EC_GROUP_get0_generator(group); |
400 | if (generator == NULL) | |
401 | { | |
402 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
403 | goto err; | |
404 | } | |
405 | ||
406 | /* look if we can use precomputed multiples of generator */ | |
407 | ||
9dd84053 | 408 | pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); |
37c660ff BM |
409 | |
410 | if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) | |
411 | { | |
412 | blocksize = pre_comp->blocksize; | |
413 | ||
414 | /* determine maximum number of blocks that wNAF splitting may yield | |
415 | * (NB: maximum wNAF length is bit length plus one) */ | |
416 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
417 | ||
418 | /* we cannot use more blocks than we have precomputation for */ | |
419 | if (numblocks > pre_comp->numblocks) | |
420 | numblocks = pre_comp->numblocks; | |
421 | ||
422 | pre_points_per_block = 1u << (pre_comp->w - 1); | |
423 | ||
424 | /* check that pre_comp looks sane */ | |
425 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) | |
426 | { | |
427 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
428 | goto err; | |
429 | } | |
430 | } | |
431 | else | |
432 | { | |
433 | /* can't use precomputation */ | |
434 | pre_comp = NULL; | |
435 | numblocks = 1; | |
436 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */ | |
437 | } | |
3ba1f111 | 438 | } |
37c660ff BM |
439 | |
440 | totalnum = num + numblocks; | |
441 | ||
442 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); | |
443 | wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); | |
444 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */ | |
445 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); | |
446 | ||
447 | if (!wsize || !wNAF_len || !wNAF || !val_sub) | |
19f6c524 BM |
448 | { |
449 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
37c660ff | 450 | goto err; |
19f6c524 | 451 | } |
3ba1f111 | 452 | |
37c660ff BM |
453 | wNAF[0] = NULL; /* preliminary pivot */ |
454 | ||
455 | /* num_val will be the total number of temporarily precomputed points */ | |
3ba1f111 | 456 | num_val = 0; |
37c660ff BM |
457 | |
458 | for (i = 0; i < num + num_scalar; i++) | |
3ba1f111 BM |
459 | { |
460 | size_t bits; | |
461 | ||
462 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
463 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
464 | num_val += 1u << (wsize[i] - 1); | |
37c660ff BM |
465 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ |
466 | wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); | |
467 | if (wNAF[i] == NULL) | |
468 | goto err; | |
469 | if (wNAF_len[i] > max_len) | |
470 | max_len = wNAF_len[i]; | |
3ba1f111 BM |
471 | } |
472 | ||
37c660ff BM |
473 | if (numblocks) |
474 | { | |
475 | /* we go here iff scalar != NULL */ | |
476 | ||
477 | if (pre_comp == NULL) | |
478 | { | |
479 | if (num_scalar != 1) | |
480 | { | |
481 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
482 | goto err; | |
483 | } | |
484 | /* we have already generated a wNAF for 'scalar' */ | |
485 | } | |
486 | else | |
487 | { | |
488 | signed char *tmp_wNAF = NULL; | |
489 | size_t tmp_len = 0; | |
490 | ||
491 | if (num_scalar != 0) | |
492 | { | |
493 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
494 | goto err; | |
495 | } | |
496 | ||
497 | /* use the window size for which we have precomputation */ | |
498 | wsize[num] = pre_comp->w; | |
499 | tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); | |
500 | if (!tmp_wNAF) | |
501 | goto err; | |
502 | ||
503 | if (tmp_len <= max_len) | |
504 | { | |
505 | /* One of the other wNAFs is at least as long | |
506 | * as the wNAF belonging to the generator, | |
507 | * so wNAF splitting will not buy us anything. */ | |
508 | ||
509 | numblocks = 1; | |
510 | totalnum = num + 1; /* don't use wNAF splitting */ | |
511 | wNAF[num] = tmp_wNAF; | |
512 | wNAF[num + 1] = NULL; | |
513 | wNAF_len[num] = tmp_len; | |
514 | if (tmp_len > max_len) | |
515 | max_len = tmp_len; | |
516 | /* pre_comp->points starts with the points that we need here: */ | |
517 | val_sub[num] = pre_comp->points; | |
518 | } | |
519 | else | |
520 | { | |
521 | /* don't include tmp_wNAF directly into wNAF array | |
522 | * - use wNAF splitting and include the blocks */ | |
523 | ||
524 | signed char *pp; | |
525 | EC_POINT **tmp_points; | |
526 | ||
527 | if (tmp_len < numblocks * blocksize) | |
528 | { | |
529 | /* possibly we can do with fewer blocks than estimated */ | |
530 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
531 | if (numblocks > pre_comp->numblocks) | |
532 | { | |
533 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
534 | goto err; | |
535 | } | |
536 | totalnum = num + numblocks; | |
537 | } | |
538 | ||
539 | /* split wNAF in 'numblocks' parts */ | |
540 | pp = tmp_wNAF; | |
541 | tmp_points = pre_comp->points; | |
542 | ||
543 | for (i = num; i < totalnum; i++) | |
544 | { | |
545 | if (i < totalnum - 1) | |
546 | { | |
547 | wNAF_len[i] = blocksize; | |
548 | if (tmp_len < blocksize) | |
549 | { | |
550 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
551 | goto err; | |
552 | } | |
553 | tmp_len -= blocksize; | |
554 | } | |
555 | else | |
556 | /* last block gets whatever is left | |
557 | * (this could be more or less than 'blocksize'!) */ | |
558 | wNAF_len[i] = tmp_len; | |
559 | ||
560 | wNAF[i + 1] = NULL; | |
561 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
562 | if (wNAF[i] == NULL) | |
563 | { | |
19f6c524 | 564 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
37c660ff BM |
565 | OPENSSL_free(tmp_wNAF); |
566 | goto err; | |
567 | } | |
568 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
569 | if (wNAF_len[i] > max_len) | |
570 | max_len = wNAF_len[i]; | |
571 | ||
572 | if (*tmp_points == NULL) | |
573 | { | |
574 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
575 | OPENSSL_free(tmp_wNAF); | |
576 | goto err; | |
577 | } | |
578 | val_sub[i] = tmp_points; | |
579 | tmp_points += pre_points_per_block; | |
580 | pp += blocksize; | |
581 | } | |
582 | OPENSSL_free(tmp_wNAF); | |
583 | } | |
584 | } | |
585 | } | |
586 | ||
587 | /* All points we precompute now go into a single array 'val'. | |
588 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, | |
589 | * or to a subarray of 'pre_comp->points' if we already have precomputation. */ | |
3ba1f111 | 590 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); |
19f6c524 BM |
591 | if (val == NULL) |
592 | { | |
593 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
594 | goto err; | |
595 | } | |
3ba1f111 BM |
596 | val[num_val] = NULL; /* pivot element */ |
597 | ||
3ba1f111 BM |
598 | /* allocate points for precomputation */ |
599 | v = val; | |
37c660ff | 600 | for (i = 0; i < num + num_scalar; i++) |
3ba1f111 BM |
601 | { |
602 | val_sub[i] = v; | |
603 | for (j = 0; j < (1u << (wsize[i] - 1)); j++) | |
604 | { | |
605 | *v = EC_POINT_new(group); | |
606 | if (*v == NULL) goto err; | |
607 | v++; | |
608 | } | |
609 | } | |
610 | if (!(v == val + num_val)) | |
611 | { | |
7793f30e | 612 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
3ba1f111 BM |
613 | goto err; |
614 | } | |
615 | ||
37c660ff BM |
616 | if (!(tmp = EC_POINT_new(group))) |
617 | goto err; | |
3ba1f111 BM |
618 | |
619 | /* prepare precomputed values: | |
620 | * val_sub[i][0] := points[i] | |
621 | * val_sub[i][1] := 3 * points[i] | |
622 | * val_sub[i][2] := 5 * points[i] | |
623 | * ... | |
624 | */ | |
37c660ff | 625 | for (i = 0; i < num + num_scalar; i++) |
3ba1f111 BM |
626 | { |
627 | if (i < num) | |
628 | { | |
629 | if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; | |
630 | } | |
631 | else | |
632 | { | |
633 | if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; | |
634 | } | |
635 | ||
636 | if (wsize[i] > 1) | |
637 | { | |
638 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; | |
639 | for (j = 1; j < (1u << (wsize[i] - 1)); j++) | |
640 | { | |
641 | if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; | |
642 | } | |
643 | } | |
3ba1f111 BM |
644 | } |
645 | ||
646 | #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ | |
37c660ff BM |
647 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
648 | goto err; | |
3ba1f111 BM |
649 | #endif |
650 | ||
651 | r_is_at_infinity = 1; | |
652 | ||
653 | for (k = max_len - 1; k >= 0; k--) | |
654 | { | |
655 | if (!r_is_at_infinity) | |
656 | { | |
657 | if (!EC_POINT_dbl(group, r, r, ctx)) goto err; | |
658 | } | |
659 | ||
660 | for (i = 0; i < totalnum; i++) | |
661 | { | |
b77fcddb | 662 | if (wNAF_len[i] > (size_t)k) |
3ba1f111 BM |
663 | { |
664 | int digit = wNAF[i][k]; | |
665 | int is_neg; | |
666 | ||
667 | if (digit) | |
668 | { | |
669 | is_neg = digit < 0; | |
670 | ||
671 | if (is_neg) | |
672 | digit = -digit; | |
673 | ||
674 | if (is_neg != r_is_inverted) | |
675 | { | |
676 | if (!r_is_at_infinity) | |
677 | { | |
678 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
679 | } | |
680 | r_is_inverted = !r_is_inverted; | |
681 | } | |
682 | ||
683 | /* digit > 0 */ | |
684 | ||
685 | if (r_is_at_infinity) | |
686 | { | |
687 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; | |
688 | r_is_at_infinity = 0; | |
689 | } | |
690 | else | |
691 | { | |
692 | if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; | |
693 | } | |
694 | } | |
695 | } | |
696 | } | |
697 | } | |
698 | ||
699 | if (r_is_at_infinity) | |
700 | { | |
701 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
702 | } | |
703 | else | |
704 | { | |
705 | if (r_is_inverted) | |
706 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
707 | } | |
708 | ||
709 | ret = 1; | |
710 | ||
711 | err: | |
712 | if (new_ctx != NULL) | |
713 | BN_CTX_free(new_ctx); | |
714 | if (tmp != NULL) | |
715 | EC_POINT_free(tmp); | |
716 | if (wsize != NULL) | |
717 | OPENSSL_free(wsize); | |
718 | if (wNAF_len != NULL) | |
719 | OPENSSL_free(wNAF_len); | |
720 | if (wNAF != NULL) | |
721 | { | |
722 | signed char **w; | |
723 | ||
724 | for (w = wNAF; *w != NULL; w++) | |
725 | OPENSSL_free(*w); | |
726 | ||
727 | OPENSSL_free(wNAF); | |
728 | } | |
729 | if (val != NULL) | |
730 | { | |
731 | for (v = val; *v != NULL; v++) | |
732 | EC_POINT_clear_free(*v); | |
733 | ||
734 | OPENSSL_free(val); | |
735 | } | |
736 | if (val_sub != NULL) | |
737 | { | |
738 | OPENSSL_free(val_sub); | |
739 | } | |
740 | return ret; | |
741 | } | |
742 | ||
38374911 | 743 | |
37c660ff BM |
744 | /* ec_wNAF_precompute_mult() |
745 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator | |
746 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
747 | * | |
748 | * 'pre_comp->points' is an array of multiples of the generator | |
749 | * of the following form: | |
750 | * points[0] = generator; | |
751 | * points[1] = 3 * generator; | |
752 | * ... | |
753 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
754 | * points[2^(w-1)] = 2^blocksize * generator; | |
755 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
756 | * ... | |
757 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
758 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
759 | * ... | |
760 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
761 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 762 | */ |
7793f30e | 763 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
38374911 BM |
764 | { |
765 | const EC_POINT *generator; | |
37c660ff | 766 | EC_POINT *tmp_point = NULL, *base = NULL, **var; |
38374911 BM |
767 | BN_CTX *new_ctx = NULL; |
768 | BIGNUM *order; | |
37c660ff BM |
769 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
770 | EC_POINT **points = NULL; | |
ba729265 | 771 | EC_PRE_COMP *pre_comp; |
38374911 BM |
772 | int ret = 0; |
773 | ||
ba729265 | 774 | /* if there is an old EC_PRE_COMP object, throw it away */ |
9dd84053 | 775 | EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); |
ba729265 BM |
776 | |
777 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) | |
778 | return 0; | |
37c660ff | 779 | |
38374911 BM |
780 | generator = EC_GROUP_get0_generator(group); |
781 | if (generator == NULL) | |
782 | { | |
7793f30e | 783 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); |
37c660ff | 784 | goto err; |
38374911 BM |
785 | } |
786 | ||
787 | if (ctx == NULL) | |
788 | { | |
789 | ctx = new_ctx = BN_CTX_new(); | |
790 | if (ctx == NULL) | |
37c660ff | 791 | goto err; |
38374911 BM |
792 | } |
793 | ||
794 | BN_CTX_start(ctx); | |
795 | order = BN_CTX_get(ctx); | |
796 | if (order == NULL) goto err; | |
797 | ||
37c660ff | 798 | if (!EC_GROUP_get_order(group, order, ctx)) goto err; |
38374911 BM |
799 | if (BN_is_zero(order)) |
800 | { | |
7793f30e | 801 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); |
38374911 BM |
802 | goto err; |
803 | } | |
804 | ||
37c660ff | 805 | bits = BN_num_bits(order); |
82871eaa BM |
806 | /* The following parameters mean we precompute (approximately) |
807 | * one point per bit. | |
808 | * | |
809 | * TBD: The combination 8, 4 is perfect for 160 bits; for other | |
810 | * bit lengths, other parameter combinations might provide better | |
811 | * efficiency. | |
812 | */ | |
37c660ff BM |
813 | blocksize = 8; |
814 | w = 4; | |
815 | if (EC_window_bits_for_scalar_size(bits) > w) | |
816 | { | |
817 | /* let's not make the window too small ... */ | |
818 | w = EC_window_bits_for_scalar_size(bits); | |
819 | } | |
820 | ||
821 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ | |
822 | ||
823 | pre_points_per_block = 1u << (w - 1); | |
824 | num = pre_points_per_block * numblocks; /* number of points to compute and store */ | |
825 | ||
826 | points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1)); | |
827 | if (!points) | |
828 | { | |
829 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
830 | goto err; | |
831 | } | |
832 | ||
833 | var = points; | |
834 | var[num] = NULL; /* pivot */ | |
835 | for (i = 0; i < num; i++) | |
836 | { | |
837 | if ((var[i] = EC_POINT_new(group)) == NULL) | |
838 | { | |
839 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
840 | goto err; | |
841 | } | |
842 | } | |
38374911 | 843 | |
37c660ff BM |
844 | if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) |
845 | { | |
846 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
847 | goto err; | |
848 | } | |
849 | ||
850 | if (!EC_POINT_copy(base, generator)) | |
851 | goto err; | |
852 | ||
853 | /* do the precomputation */ | |
854 | for (i = 0; i < numblocks; i++) | |
855 | { | |
856 | size_t j; | |
857 | ||
858 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
859 | goto err; | |
860 | ||
861 | if (!EC_POINT_copy(*var++, base)) | |
862 | goto err; | |
863 | ||
864 | for (j = 1; j < pre_points_per_block; j++, var++) | |
865 | { | |
866 | /* calculate odd multiples of the current base point */ | |
867 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
868 | goto err; | |
869 | } | |
870 | ||
871 | if (i < numblocks - 1) | |
872 | { | |
873 | /* get the next base (multiply current one by 2^blocksize) */ | |
874 | size_t k; | |
875 | ||
876 | if (blocksize <= 2) | |
877 | { | |
878 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
879 | goto err; | |
880 | } | |
881 | ||
882 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
883 | goto err; | |
884 | for (k = 2; k < blocksize; k++) | |
885 | { | |
886 | if (!EC_POINT_dbl(group,base,base,ctx)) | |
887 | goto err; | |
888 | } | |
889 | } | |
890 | } | |
891 | ||
892 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
893 | goto err; | |
38374911 | 894 | |
37c660ff BM |
895 | pre_comp->group = group; |
896 | pre_comp->blocksize = blocksize; | |
897 | pre_comp->numblocks = numblocks; | |
898 | pre_comp->w = w; | |
37c660ff BM |
899 | pre_comp->points = points; |
900 | points = NULL; | |
901 | pre_comp->num = num; | |
902 | ||
9dd84053 | 903 | if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, |
ba729265 BM |
904 | ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free)) |
905 | goto err; | |
906 | pre_comp = NULL; | |
37c660ff BM |
907 | |
908 | ret = 1; | |
38374911 | 909 | err: |
eeb821f7 NL |
910 | if (ctx != NULL) |
911 | BN_CTX_end(ctx); | |
38374911 BM |
912 | if (new_ctx != NULL) |
913 | BN_CTX_free(new_ctx); | |
ba729265 BM |
914 | if (pre_comp) |
915 | ec_pre_comp_free(pre_comp); | |
37c660ff BM |
916 | if (points) |
917 | { | |
918 | EC_POINT **p; | |
919 | ||
920 | for (p = points; *p != NULL; p++) | |
921 | EC_POINT_free(*p); | |
922 | OPENSSL_free(points); | |
923 | } | |
924 | if (tmp_point) | |
925 | EC_POINT_free(tmp_point); | |
926 | if (base) | |
927 | EC_POINT_free(base); | |
38374911 BM |
928 | return ret; |
929 | } | |
7793f30e BM |
930 | |
931 | ||
37c660ff | 932 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
7793f30e | 933 | { |
9dd84053 | 934 | if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) |
7793f30e | 935 | return 1; |
37c660ff BM |
936 | else |
937 | return 0; | |
7793f30e | 938 | } |