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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 | /* ==================================================================== |
37c660ff | 6 | * Copyright (c) 1998-2003 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) */ | |
90 | } EC_PRE_COMP; | |
91 | ||
92 | /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ | |
93 | static void *ec_pre_comp_dup(void *); | |
94 | static void ec_pre_comp_free(void *); | |
95 | static void ec_pre_comp_clear_free(void *); | |
96 | ||
97 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
98 | { | |
99 | EC_PRE_COMP *ret = NULL; | |
100 | ||
101 | if (!group) | |
102 | return NULL; | |
103 | ||
104 | ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); | |
105 | if (!ret) | |
106 | return ret; | |
107 | ret->group = group; | |
108 | ret->blocksize = 8; /* default */ | |
109 | ret->numblocks = 0; | |
110 | ret->w = 4; /* default */ | |
111 | ret->points = NULL; | |
112 | ret->num = 0; | |
113 | return ret; | |
114 | } | |
115 | ||
116 | static void *ec_pre_comp_dup(void *src_) | |
117 | { | |
118 | const EC_PRE_COMP *src = src_; | |
119 | EC_PRE_COMP *ret = NULL; | |
120 | ||
121 | ret = ec_pre_comp_new(src->group); | |
122 | if (!ret) | |
123 | return ret; | |
124 | ret->blocksize = src->blocksize; | |
125 | ret->numblocks = src->numblocks; | |
126 | ret->w = src->w; | |
127 | ret->num = 0; | |
128 | ||
129 | if (src->points) | |
130 | { | |
131 | EC_POINT **src_var, **dest_var; | |
132 | ||
133 | ret->points = (EC_POINT **)OPENSSL_malloc((src->num + 1) * sizeof(EC_POINT *)); | |
134 | if (!ret->points) | |
135 | { | |
136 | ec_pre_comp_free(ret); | |
137 | return NULL; | |
138 | } | |
139 | ||
140 | for (dest_var = ret->points, src_var = src->points; *src_var != NULL; src_var++, dest_var++) | |
141 | { | |
142 | *dest_var = EC_POINT_dup(*src_var, src->group); | |
143 | if (*dest_var == NULL) | |
144 | { | |
145 | ec_pre_comp_free(ret); | |
146 | return NULL; | |
147 | } | |
148 | ret->num++; | |
149 | } | |
150 | ||
151 | ret->points[ret->num] = NULL; | |
152 | if (ret->num != src->num) | |
153 | { | |
154 | ec_pre_comp_free(ret); | |
155 | ECerr(EC_F_EC_PRE_COMP_DUP, ERR_R_INTERNAL_ERROR); | |
156 | return NULL; | |
157 | } | |
158 | } | |
159 | ||
160 | return ret; | |
161 | } | |
162 | ||
163 | static void ec_pre_comp_free(void *pre_) | |
164 | { | |
165 | EC_PRE_COMP *pre = pre_; | |
166 | ||
167 | if (!pre) | |
168 | return; | |
169 | if (pre->points) | |
170 | { | |
171 | EC_POINT **var; | |
172 | ||
173 | for (var = pre->points; *var != NULL; var++) | |
174 | EC_POINT_free(*var); | |
175 | OPENSSL_free(pre->points); | |
176 | } | |
177 | OPENSSL_free(pre); | |
178 | } | |
179 | ||
180 | static void ec_pre_comp_clear_free(void *pre_) | |
181 | { | |
182 | EC_PRE_COMP *pre = pre_; | |
183 | ||
184 | if (!pre) | |
185 | return; | |
186 | if (pre->points) | |
187 | { | |
188 | EC_POINT **p; | |
189 | ||
190 | for (p = pre->points; *p != NULL; p++) | |
191 | EC_POINT_clear_free(*p); | |
192 | OPENSSL_cleanse(pre->points, sizeof pre->points); | |
193 | OPENSSL_free(pre->points); | |
194 | } | |
195 | OPENSSL_cleanse(pre, sizeof pre); | |
196 | OPENSSL_free(pre); | |
197 | } | |
198 | ||
199 | ||
3ba1f111 BM |
200 | |
201 | ||
2c8d0dcc | 202 | /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. |
3ba1f111 BM |
203 | * This is an array r[] of values that are either zero or odd with an |
204 | * absolute value less than 2^w satisfying | |
205 | * scalar = \sum_j r[j]*2^j | |
2c8d0dcc BM |
206 | * where at most one of any w+1 consecutive digits is non-zero |
207 | * with the exception that the most significant digit may be only | |
208 | * w-1 zeros away from that next non-zero digit. | |
3ba1f111 | 209 | */ |
2c8d0dcc | 210 | static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) |
3ba1f111 | 211 | { |
2c8d0dcc | 212 | int window_val; |
3ba1f111 BM |
213 | int ok = 0; |
214 | signed char *r = NULL; | |
215 | int sign = 1; | |
216 | int bit, next_bit, mask; | |
e71adb85 | 217 | size_t len = 0, j; |
3ba1f111 | 218 | |
c78515f5 | 219 | if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ |
3ba1f111 BM |
220 | { |
221 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
222 | goto err; | |
223 | } | |
224 | bit = 1 << w; /* at most 128 */ | |
225 | next_bit = bit << 1; /* at most 256 */ | |
226 | mask = next_bit - 1; /* at most 255 */ | |
227 | ||
b53e44e5 | 228 | if (BN_get_sign(scalar)) |
3ba1f111 BM |
229 | { |
230 | sign = -1; | |
3ba1f111 BM |
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) */ | |
3ba1f111 BM |
237 | if (r == NULL) goto err; |
238 | ||
2c8d0dcc BM |
239 | if (scalar->d == NULL || scalar->top == 0) |
240 | { | |
241 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
242 | goto err; | |
243 | } | |
244 | window_val = scalar->d[0] & mask; | |
3ba1f111 | 245 | j = 0; |
2c8d0dcc | 246 | while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ |
3ba1f111 | 247 | { |
2c8d0dcc | 248 | int digit = 0; |
3ba1f111 | 249 | |
2c8d0dcc BM |
250 | /* 0 <= window_val <= 2^(w+1) */ |
251 | ||
252 | if (window_val & 1) | |
3ba1f111 | 253 | { |
2c8d0dcc BM |
254 | /* 0 < window_val < 2^(w+1) */ |
255 | ||
256 | if (window_val & bit) | |
3ba1f111 | 257 | { |
2c8d0dcc BM |
258 | digit = window_val - next_bit; /* -2^w < digit < 0 */ |
259 | ||
260 | #if 1 /* modified wNAF */ | |
261 | if (j + w + 1 >= len) | |
262 | { | |
263 | /* special case for generating modified wNAFs: | |
264 | * no new bits will be added into window_val, | |
265 | * so using a positive digit here will decrease | |
266 | * the total length of the representation */ | |
267 | ||
268 | digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ | |
269 | } | |
270 | #endif | |
3ba1f111 | 271 | } |
2c8d0dcc | 272 | else |
3ba1f111 | 273 | { |
2c8d0dcc | 274 | digit = window_val; /* 0 < digit < 2^w */ |
3ba1f111 | 275 | } |
2c8d0dcc BM |
276 | |
277 | if (digit <= -bit || digit >= bit || !(digit & 1)) | |
3ba1f111 | 278 | { |
2c8d0dcc BM |
279 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
280 | goto err; | |
3ba1f111 BM |
281 | } |
282 | ||
2c8d0dcc BM |
283 | window_val -= digit; |
284 | ||
285 | /* now window_val is 0 or 2^(w+1) in standard wNAF generation; | |
286 | * for modified window NAFs, it may also be 2^w | |
287 | */ | |
288 | if (window_val != 0 && window_val != next_bit && window_val != bit) | |
3ba1f111 BM |
289 | { |
290 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
291 | goto err; | |
292 | } | |
293 | } | |
294 | ||
2c8d0dcc BM |
295 | r[j++] = sign * digit; |
296 | ||
297 | window_val >>= 1; | |
298 | window_val += bit * BN_is_bit_set(scalar, j + w); | |
299 | ||
300 | if (window_val > next_bit) | |
3ba1f111 BM |
301 | { |
302 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
303 | goto err; | |
304 | } | |
3ba1f111 BM |
305 | } |
306 | ||
2c8d0dcc | 307 | if (j > len + 1) |
3ba1f111 BM |
308 | { |
309 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
310 | goto err; | |
311 | } | |
312 | len = j; | |
313 | ok = 1; | |
314 | ||
315 | err: | |
3ba1f111 BM |
316 | if (!ok) |
317 | { | |
318 | OPENSSL_free(r); | |
319 | r = NULL; | |
320 | } | |
321 | if (ok) | |
322 | *ret_len = len; | |
323 | return r; | |
324 | } | |
325 | ||
326 | ||
c05940ed BM |
327 | /* TODO: table should be optimised for the wNAF-based implementation, |
328 | * sometimes smaller windows will give better performance | |
329 | * (thus the boundaries should be increased) | |
330 | */ | |
3ba1f111 BM |
331 | #define EC_window_bits_for_scalar_size(b) \ |
332 | ((b) >= 2000 ? 6 : \ | |
333 | (b) >= 800 ? 5 : \ | |
334 | (b) >= 300 ? 4 : \ | |
335 | (b) >= 70 ? 3 : \ | |
336 | (b) >= 20 ? 2 : \ | |
337 | 1) | |
338 | ||
339 | /* Compute | |
340 | * \sum scalars[i]*points[i], | |
341 | * also including | |
342 | * scalar*generator | |
343 | * in the addition if scalar != NULL | |
344 | */ | |
7793f30e | 345 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
3ba1f111 BM |
346 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) |
347 | { | |
348 | BN_CTX *new_ctx = NULL; | |
349 | EC_POINT *generator = NULL; | |
350 | EC_POINT *tmp = NULL; | |
351 | size_t totalnum; | |
37c660ff BM |
352 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ |
353 | size_t pre_points_per_block = 0; | |
3ba1f111 BM |
354 | size_t i, j; |
355 | int k; | |
356 | int r_is_inverted = 0; | |
357 | int r_is_at_infinity = 1; | |
358 | size_t *wsize = NULL; /* individual window sizes */ | |
c78515f5 | 359 | signed char **wNAF = NULL; /* individual wNAFs */ |
3ba1f111 BM |
360 | size_t *wNAF_len = NULL; |
361 | size_t max_len = 0; | |
3ba1f111 BM |
362 | size_t num_val; |
363 | EC_POINT **val = NULL; /* precomputation */ | |
364 | EC_POINT **v; | |
37c660ff BM |
365 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */ |
366 | EC_PRE_COMP *pre_comp = NULL; | |
367 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars, | |
368 | * i.e. precomputation is not available */ | |
3ba1f111 BM |
369 | int ret = 0; |
370 | ||
37c660ff | 371 | if (group->meth != r->meth) |
3ba1f111 | 372 | { |
37c660ff BM |
373 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
374 | return 0; | |
3ba1f111 | 375 | } |
37c660ff BM |
376 | |
377 | if ((scalar == NULL) && (num == 0)) | |
378 | { | |
379 | return EC_POINT_set_to_infinity(group, r); | |
380 | } | |
381 | ||
3ba1f111 BM |
382 | for (i = 0; i < num; i++) |
383 | { | |
384 | if (group->meth != points[i]->meth) | |
385 | { | |
7793f30e | 386 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
3ba1f111 BM |
387 | return 0; |
388 | } | |
389 | } | |
390 | ||
37c660ff BM |
391 | if (ctx == NULL) |
392 | { | |
393 | ctx = new_ctx = BN_CTX_new(); | |
394 | if (ctx == NULL) | |
395 | goto err; | |
396 | } | |
3ba1f111 | 397 | |
37c660ff | 398 | if (scalar != NULL) |
3ba1f111 | 399 | { |
37c660ff BM |
400 | generator = EC_GROUP_get0_generator(group); |
401 | if (generator == NULL) | |
402 | { | |
403 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
404 | goto err; | |
405 | } | |
406 | ||
407 | /* look if we can use precomputed multiples of generator */ | |
408 | ||
409 | pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); | |
410 | ||
411 | if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) | |
412 | { | |
413 | blocksize = pre_comp->blocksize; | |
414 | ||
415 | /* determine maximum number of blocks that wNAF splitting may yield | |
416 | * (NB: maximum wNAF length is bit length plus one) */ | |
417 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
418 | ||
419 | /* we cannot use more blocks than we have precomputation for */ | |
420 | if (numblocks > pre_comp->numblocks) | |
421 | numblocks = pre_comp->numblocks; | |
422 | ||
423 | pre_points_per_block = 1u << (pre_comp->w - 1); | |
424 | ||
425 | /* check that pre_comp looks sane */ | |
426 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) | |
427 | { | |
428 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
429 | goto err; | |
430 | } | |
431 | } | |
432 | else | |
433 | { | |
434 | /* can't use precomputation */ | |
435 | pre_comp = NULL; | |
436 | numblocks = 1; | |
437 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */ | |
438 | } | |
3ba1f111 | 439 | } |
37c660ff BM |
440 | |
441 | totalnum = num + numblocks; | |
442 | ||
443 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); | |
444 | wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); | |
445 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */ | |
446 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); | |
447 | ||
448 | if (!wsize || !wNAF_len || !wNAF || !val_sub) | |
449 | goto err; | |
3ba1f111 | 450 | |
37c660ff BM |
451 | wNAF[0] = NULL; /* preliminary pivot */ |
452 | ||
453 | /* num_val will be the total number of temporarily precomputed points */ | |
3ba1f111 | 454 | num_val = 0; |
37c660ff BM |
455 | |
456 | for (i = 0; i < num + num_scalar; i++) | |
3ba1f111 BM |
457 | { |
458 | size_t bits; | |
459 | ||
460 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
461 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
462 | num_val += 1u << (wsize[i] - 1); | |
37c660ff BM |
463 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ |
464 | wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); | |
465 | if (wNAF[i] == NULL) | |
466 | goto err; | |
467 | if (wNAF_len[i] > max_len) | |
468 | max_len = wNAF_len[i]; | |
3ba1f111 BM |
469 | } |
470 | ||
37c660ff BM |
471 | if (numblocks) |
472 | { | |
473 | /* we go here iff scalar != NULL */ | |
474 | ||
475 | if (pre_comp == NULL) | |
476 | { | |
477 | if (num_scalar != 1) | |
478 | { | |
479 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
480 | goto err; | |
481 | } | |
482 | /* we have already generated a wNAF for 'scalar' */ | |
483 | } | |
484 | else | |
485 | { | |
486 | signed char *tmp_wNAF = NULL; | |
487 | size_t tmp_len = 0; | |
488 | ||
489 | if (num_scalar != 0) | |
490 | { | |
491 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
492 | goto err; | |
493 | } | |
494 | ||
495 | /* use the window size for which we have precomputation */ | |
496 | wsize[num] = pre_comp->w; | |
497 | tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); | |
498 | if (!tmp_wNAF) | |
499 | goto err; | |
500 | ||
501 | if (tmp_len <= max_len) | |
502 | { | |
503 | /* One of the other wNAFs is at least as long | |
504 | * as the wNAF belonging to the generator, | |
505 | * so wNAF splitting will not buy us anything. */ | |
506 | ||
507 | numblocks = 1; | |
508 | totalnum = num + 1; /* don't use wNAF splitting */ | |
509 | wNAF[num] = tmp_wNAF; | |
510 | wNAF[num + 1] = NULL; | |
511 | wNAF_len[num] = tmp_len; | |
512 | if (tmp_len > max_len) | |
513 | max_len = tmp_len; | |
514 | /* pre_comp->points starts with the points that we need here: */ | |
515 | val_sub[num] = pre_comp->points; | |
516 | } | |
517 | else | |
518 | { | |
519 | /* don't include tmp_wNAF directly into wNAF array | |
520 | * - use wNAF splitting and include the blocks */ | |
521 | ||
522 | signed char *pp; | |
523 | EC_POINT **tmp_points; | |
524 | ||
525 | if (tmp_len < numblocks * blocksize) | |
526 | { | |
527 | /* possibly we can do with fewer blocks than estimated */ | |
528 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
529 | if (numblocks > pre_comp->numblocks) | |
530 | { | |
531 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
532 | goto err; | |
533 | } | |
534 | totalnum = num + numblocks; | |
535 | } | |
536 | ||
537 | /* split wNAF in 'numblocks' parts */ | |
538 | pp = tmp_wNAF; | |
539 | tmp_points = pre_comp->points; | |
540 | ||
541 | for (i = num; i < totalnum; i++) | |
542 | { | |
543 | if (i < totalnum - 1) | |
544 | { | |
545 | wNAF_len[i] = blocksize; | |
546 | if (tmp_len < blocksize) | |
547 | { | |
548 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
549 | goto err; | |
550 | } | |
551 | tmp_len -= blocksize; | |
552 | } | |
553 | else | |
554 | /* last block gets whatever is left | |
555 | * (this could be more or less than 'blocksize'!) */ | |
556 | wNAF_len[i] = tmp_len; | |
557 | ||
558 | wNAF[i + 1] = NULL; | |
559 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
560 | if (wNAF[i] == NULL) | |
561 | { | |
562 | OPENSSL_free(tmp_wNAF); | |
563 | goto err; | |
564 | } | |
565 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
566 | if (wNAF_len[i] > max_len) | |
567 | max_len = wNAF_len[i]; | |
568 | ||
569 | if (*tmp_points == NULL) | |
570 | { | |
571 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
572 | OPENSSL_free(tmp_wNAF); | |
573 | goto err; | |
574 | } | |
575 | val_sub[i] = tmp_points; | |
576 | tmp_points += pre_points_per_block; | |
577 | pp += blocksize; | |
578 | } | |
579 | OPENSSL_free(tmp_wNAF); | |
580 | } | |
581 | } | |
582 | } | |
583 | ||
584 | /* All points we precompute now go into a single array 'val'. | |
585 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, | |
586 | * or to a subarray of 'pre_comp->points' if we already have precomputation. */ | |
3ba1f111 BM |
587 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); |
588 | if (val == NULL) goto err; | |
589 | val[num_val] = NULL; /* pivot element */ | |
590 | ||
3ba1f111 BM |
591 | /* allocate points for precomputation */ |
592 | v = val; | |
37c660ff | 593 | for (i = 0; i < num + num_scalar; i++) |
3ba1f111 BM |
594 | { |
595 | val_sub[i] = v; | |
596 | for (j = 0; j < (1u << (wsize[i] - 1)); j++) | |
597 | { | |
598 | *v = EC_POINT_new(group); | |
599 | if (*v == NULL) goto err; | |
600 | v++; | |
601 | } | |
602 | } | |
603 | if (!(v == val + num_val)) | |
604 | { | |
7793f30e | 605 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
3ba1f111 BM |
606 | goto err; |
607 | } | |
608 | ||
37c660ff BM |
609 | if (!(tmp = EC_POINT_new(group))) |
610 | goto err; | |
3ba1f111 BM |
611 | |
612 | /* prepare precomputed values: | |
613 | * val_sub[i][0] := points[i] | |
614 | * val_sub[i][1] := 3 * points[i] | |
615 | * val_sub[i][2] := 5 * points[i] | |
616 | * ... | |
617 | */ | |
37c660ff | 618 | for (i = 0; i < num + num_scalar; i++) |
3ba1f111 BM |
619 | { |
620 | if (i < num) | |
621 | { | |
622 | if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; | |
623 | } | |
624 | else | |
625 | { | |
626 | if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; | |
627 | } | |
628 | ||
629 | if (wsize[i] > 1) | |
630 | { | |
631 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; | |
632 | for (j = 1; j < (1u << (wsize[i] - 1)); j++) | |
633 | { | |
634 | if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; | |
635 | } | |
636 | } | |
3ba1f111 BM |
637 | } |
638 | ||
639 | #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ | |
37c660ff BM |
640 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
641 | goto err; | |
3ba1f111 BM |
642 | #endif |
643 | ||
644 | r_is_at_infinity = 1; | |
645 | ||
646 | for (k = max_len - 1; k >= 0; k--) | |
647 | { | |
648 | if (!r_is_at_infinity) | |
649 | { | |
650 | if (!EC_POINT_dbl(group, r, r, ctx)) goto err; | |
651 | } | |
652 | ||
653 | for (i = 0; i < totalnum; i++) | |
654 | { | |
b77fcddb | 655 | if (wNAF_len[i] > (size_t)k) |
3ba1f111 BM |
656 | { |
657 | int digit = wNAF[i][k]; | |
658 | int is_neg; | |
659 | ||
660 | if (digit) | |
661 | { | |
662 | is_neg = digit < 0; | |
663 | ||
664 | if (is_neg) | |
665 | digit = -digit; | |
666 | ||
667 | if (is_neg != r_is_inverted) | |
668 | { | |
669 | if (!r_is_at_infinity) | |
670 | { | |
671 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
672 | } | |
673 | r_is_inverted = !r_is_inverted; | |
674 | } | |
675 | ||
676 | /* digit > 0 */ | |
677 | ||
678 | if (r_is_at_infinity) | |
679 | { | |
680 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; | |
681 | r_is_at_infinity = 0; | |
682 | } | |
683 | else | |
684 | { | |
685 | if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; | |
686 | } | |
687 | } | |
688 | } | |
689 | } | |
690 | } | |
691 | ||
692 | if (r_is_at_infinity) | |
693 | { | |
694 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
695 | } | |
696 | else | |
697 | { | |
698 | if (r_is_inverted) | |
699 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
700 | } | |
701 | ||
702 | ret = 1; | |
703 | ||
704 | err: | |
705 | if (new_ctx != NULL) | |
706 | BN_CTX_free(new_ctx); | |
707 | if (tmp != NULL) | |
708 | EC_POINT_free(tmp); | |
709 | if (wsize != NULL) | |
710 | OPENSSL_free(wsize); | |
711 | if (wNAF_len != NULL) | |
712 | OPENSSL_free(wNAF_len); | |
713 | if (wNAF != NULL) | |
714 | { | |
715 | signed char **w; | |
716 | ||
717 | for (w = wNAF; *w != NULL; w++) | |
718 | OPENSSL_free(*w); | |
719 | ||
720 | OPENSSL_free(wNAF); | |
721 | } | |
722 | if (val != NULL) | |
723 | { | |
724 | for (v = val; *v != NULL; v++) | |
725 | EC_POINT_clear_free(*v); | |
726 | ||
727 | OPENSSL_free(val); | |
728 | } | |
729 | if (val_sub != NULL) | |
730 | { | |
731 | OPENSSL_free(val_sub); | |
732 | } | |
733 | return ret; | |
734 | } | |
735 | ||
38374911 | 736 | |
37c660ff BM |
737 | /* ec_wNAF_precompute_mult() |
738 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator | |
739 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
740 | * | |
741 | * 'pre_comp->points' is an array of multiples of the generator | |
742 | * of the following form: | |
743 | * points[0] = generator; | |
744 | * points[1] = 3 * generator; | |
745 | * ... | |
746 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
747 | * points[2^(w-1)] = 2^blocksize * generator; | |
748 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
749 | * ... | |
750 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
751 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
752 | * ... | |
753 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
754 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 755 | */ |
7793f30e | 756 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
38374911 BM |
757 | { |
758 | const EC_POINT *generator; | |
37c660ff | 759 | EC_POINT *tmp_point = NULL, *base = NULL, **var; |
38374911 BM |
760 | BN_CTX *new_ctx = NULL; |
761 | BIGNUM *order; | |
37c660ff BM |
762 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
763 | EC_POINT **points = NULL; | |
764 | EC_PRE_COMP *pre_comp, *new_pre_comp = NULL; | |
38374911 BM |
765 | int ret = 0; |
766 | ||
37c660ff BM |
767 | pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); |
768 | if (pre_comp == NULL) | |
769 | if ((pre_comp = new_pre_comp = ec_pre_comp_new(group)) == NULL) | |
770 | return 0; | |
771 | ||
38374911 BM |
772 | generator = EC_GROUP_get0_generator(group); |
773 | if (generator == NULL) | |
774 | { | |
7793f30e | 775 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); |
37c660ff | 776 | goto err; |
38374911 BM |
777 | } |
778 | ||
779 | if (ctx == NULL) | |
780 | { | |
781 | ctx = new_ctx = BN_CTX_new(); | |
782 | if (ctx == NULL) | |
37c660ff | 783 | goto err; |
38374911 BM |
784 | } |
785 | ||
786 | BN_CTX_start(ctx); | |
787 | order = BN_CTX_get(ctx); | |
788 | if (order == NULL) goto err; | |
789 | ||
37c660ff | 790 | if (!EC_GROUP_get_order(group, order, ctx)) goto err; |
38374911 BM |
791 | if (BN_is_zero(order)) |
792 | { | |
7793f30e | 793 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); |
38374911 BM |
794 | goto err; |
795 | } | |
796 | ||
37c660ff | 797 | bits = BN_num_bits(order); |
82871eaa BM |
798 | /* The following parameters mean we precompute (approximately) |
799 | * one point per bit. | |
800 | * | |
801 | * TBD: The combination 8, 4 is perfect for 160 bits; for other | |
802 | * bit lengths, other parameter combinations might provide better | |
803 | * efficiency. | |
804 | */ | |
37c660ff BM |
805 | blocksize = 8; |
806 | w = 4; | |
807 | if (EC_window_bits_for_scalar_size(bits) > w) | |
808 | { | |
809 | /* let's not make the window too small ... */ | |
810 | w = EC_window_bits_for_scalar_size(bits); | |
811 | } | |
812 | ||
813 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ | |
814 | ||
815 | pre_points_per_block = 1u << (w - 1); | |
816 | num = pre_points_per_block * numblocks; /* number of points to compute and store */ | |
817 | ||
818 | points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1)); | |
819 | if (!points) | |
820 | { | |
821 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
822 | goto err; | |
823 | } | |
824 | ||
825 | var = points; | |
826 | var[num] = NULL; /* pivot */ | |
827 | for (i = 0; i < num; i++) | |
828 | { | |
829 | if ((var[i] = EC_POINT_new(group)) == NULL) | |
830 | { | |
831 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
832 | goto err; | |
833 | } | |
834 | } | |
38374911 | 835 | |
37c660ff BM |
836 | if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) |
837 | { | |
838 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
839 | goto err; | |
840 | } | |
841 | ||
842 | if (!EC_POINT_copy(base, generator)) | |
843 | goto err; | |
844 | ||
845 | /* do the precomputation */ | |
846 | for (i = 0; i < numblocks; i++) | |
847 | { | |
848 | size_t j; | |
849 | ||
850 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
851 | goto err; | |
852 | ||
853 | if (!EC_POINT_copy(*var++, base)) | |
854 | goto err; | |
855 | ||
856 | for (j = 1; j < pre_points_per_block; j++, var++) | |
857 | { | |
858 | /* calculate odd multiples of the current base point */ | |
859 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
860 | goto err; | |
861 | } | |
862 | ||
863 | if (i < numblocks - 1) | |
864 | { | |
865 | /* get the next base (multiply current one by 2^blocksize) */ | |
866 | size_t k; | |
867 | ||
868 | if (blocksize <= 2) | |
869 | { | |
870 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
871 | goto err; | |
872 | } | |
873 | ||
874 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
875 | goto err; | |
876 | for (k = 2; k < blocksize; k++) | |
877 | { | |
878 | if (!EC_POINT_dbl(group,base,base,ctx)) | |
879 | goto err; | |
880 | } | |
881 | } | |
882 | } | |
883 | ||
884 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
885 | goto err; | |
38374911 | 886 | |
37c660ff BM |
887 | pre_comp->group = group; |
888 | pre_comp->blocksize = blocksize; | |
889 | pre_comp->numblocks = numblocks; | |
890 | pre_comp->w = w; | |
891 | if (pre_comp->points) | |
892 | { | |
893 | EC_POINT **p; | |
894 | ||
895 | for (p = pre_comp->points; *p != NULL; p++) | |
896 | EC_POINT_free(*p); | |
897 | OPENSSL_free(pre_comp->points); | |
898 | } | |
899 | pre_comp->points = points; | |
900 | points = NULL; | |
901 | pre_comp->num = num; | |
902 | ||
903 | if (new_pre_comp) | |
904 | { | |
905 | if (!EC_GROUP_set_extra_data(group, new_pre_comp, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free)) | |
906 | goto err; | |
907 | new_pre_comp = NULL; | |
908 | } | |
909 | ||
910 | ret = 1; | |
38374911 BM |
911 | err: |
912 | BN_CTX_end(ctx); | |
913 | if (new_ctx != NULL) | |
914 | BN_CTX_free(new_ctx); | |
37c660ff BM |
915 | if (new_pre_comp) |
916 | ec_pre_comp_free(new_pre_comp); | |
917 | if (points) | |
918 | { | |
919 | EC_POINT **p; | |
920 | ||
921 | for (p = points; *p != NULL; p++) | |
922 | EC_POINT_free(*p); | |
923 | OPENSSL_free(points); | |
924 | } | |
925 | if (tmp_point) | |
926 | EC_POINT_free(tmp_point); | |
927 | if (base) | |
928 | EC_POINT_free(base); | |
38374911 BM |
929 | return ret; |
930 | } | |
7793f30e BM |
931 | |
932 | ||
37c660ff | 933 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
7793f30e | 934 | { |
37c660ff | 935 | if (EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) |
7793f30e | 936 | return 1; |
37c660ff BM |
937 | else |
938 | return 0; | |
7793f30e | 939 | } |