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65e81670 BM |
1 | /* crypto/ec/ec_mult.c */ |
2 | /* ==================================================================== | |
3 | * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. | |
4 | * | |
5 | * Redistribution and use in source and binary forms, with or without | |
6 | * modification, are permitted provided that the following conditions | |
7 | * are met: | |
8 | * | |
9 | * 1. Redistributions of source code must retain the above copyright | |
10 | * notice, this list of conditions and the following disclaimer. | |
11 | * | |
12 | * 2. Redistributions in binary form must reproduce the above copyright | |
13 | * notice, this list of conditions and the following disclaimer in | |
14 | * the documentation and/or other materials provided with the | |
15 | * distribution. | |
16 | * | |
17 | * 3. All advertising materials mentioning features or use of this | |
18 | * software must display the following acknowledgment: | |
19 | * "This product includes software developed by the OpenSSL Project | |
20 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
21 | * | |
22 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
23 | * endorse or promote products derived from this software without | |
24 | * prior written permission. For written permission, please contact | |
25 | * openssl-core@openssl.org. | |
26 | * | |
27 | * 5. Products derived from this software may not be called "OpenSSL" | |
28 | * nor may "OpenSSL" appear in their names without prior written | |
29 | * permission of the OpenSSL Project. | |
30 | * | |
31 | * 6. Redistributions of any form whatsoever must retain the following | |
32 | * acknowledgment: | |
33 | * "This product includes software developed by the OpenSSL Project | |
34 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
35 | * | |
36 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
37 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
38 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
39 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
40 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
41 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
42 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
43 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
44 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
45 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
46 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
47 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
48 | * ==================================================================== | |
49 | * | |
50 | * This product includes cryptographic software written by Eric Young | |
51 | * (eay@cryptsoft.com). This product includes software written by Tim | |
52 | * Hudson (tjh@cryptsoft.com). | |
53 | * | |
54 | */ | |
55 | ||
48fe4d62 BM |
56 | #include <openssl/err.h> |
57 | ||
65e81670 | 58 | #include "ec_lcl.h" |
48fe4d62 BM |
59 | |
60 | ||
e3a4f8b8 | 61 | /* TODO: optional precomputation of multiples of the generator */ |
48fe4d62 BM |
62 | |
63 | ||
3ba1f111 BM |
64 | #if 1 |
65 | /* | |
66 | * wNAF-based interleaving multi-exponentation method | |
67 | */ | |
68 | ||
69 | ||
70 | ||
71 | /* Determine the width-(w+1) Non-Adjacent Form of 'scalar'. | |
72 | * This is an array r[] of values that are either zero or odd with an | |
73 | * absolute value less than 2^w satisfying | |
74 | * scalar = \sum_j r[j]*2^j | |
75 | * where at most one of any w+1 consecutive digits is non-zero. | |
76 | */ | |
77 | static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx) | |
78 | { | |
79 | BIGNUM *c; | |
80 | int ok = 0; | |
81 | signed char *r = NULL; | |
82 | int sign = 1; | |
83 | int bit, next_bit, mask; | |
84 | size_t len, j; | |
85 | ||
86 | BN_CTX_start(ctx); | |
87 | c = BN_CTX_get(ctx); | |
88 | if (c == NULL) goto err; | |
89 | ||
90 | if (w <= 0 || w > 7) /* 'unsigned char' can represent integers with absolute values less than 2^7 */ | |
91 | { | |
92 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
93 | goto err; | |
94 | } | |
95 | bit = 1 << w; /* at most 128 */ | |
96 | next_bit = bit << 1; /* at most 256 */ | |
97 | mask = next_bit - 1; /* at most 255 */ | |
98 | ||
99 | if (!BN_copy(c, scalar)) goto err; | |
100 | if (c->neg) | |
101 | { | |
102 | sign = -1; | |
103 | c->neg = 0; | |
104 | } | |
105 | ||
106 | len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */ | |
107 | r = OPENSSL_malloc(len); | |
108 | if (r == NULL) goto err; | |
109 | ||
110 | j = 0; | |
111 | while (!BN_is_zero(c)) | |
112 | { | |
113 | int u = 0; | |
114 | ||
115 | if (BN_is_odd(c)) | |
116 | { | |
117 | if (c->d == NULL || c->top == 0) | |
118 | { | |
119 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
120 | goto err; | |
121 | } | |
122 | u = c->d[0] & mask; | |
123 | if (u & bit) | |
124 | { | |
125 | u -= next_bit; | |
126 | /* u < 0 */ | |
127 | if (!BN_add_word(c, -u)) goto err; | |
128 | } | |
129 | else | |
130 | { | |
131 | /* u > 0 */ | |
132 | if (!BN_sub_word(c, u)) goto err; | |
133 | } | |
134 | ||
135 | if (u <= -bit || u >= bit || !(u & 1) || c->neg) | |
136 | { | |
137 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
138 | goto err; | |
139 | } | |
140 | } | |
141 | ||
142 | r[j++] = sign * u; | |
143 | ||
144 | if (BN_is_odd(c)) | |
145 | { | |
146 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
147 | goto err; | |
148 | } | |
149 | if (!BN_rshift1(c, c)) goto err; | |
150 | } | |
151 | ||
152 | if (j > len) | |
153 | { | |
154 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); | |
155 | goto err; | |
156 | } | |
157 | len = j; | |
158 | ok = 1; | |
159 | ||
160 | err: | |
161 | BN_CTX_end(ctx); | |
162 | if (!ok) | |
163 | { | |
164 | OPENSSL_free(r); | |
165 | r = NULL; | |
166 | } | |
167 | if (ok) | |
168 | *ret_len = len; | |
169 | return r; | |
170 | } | |
171 | ||
172 | ||
173 | /* TODO: table should be optimised for the wNAF-based implementation */ | |
174 | #define EC_window_bits_for_scalar_size(b) \ | |
175 | ((b) >= 2000 ? 6 : \ | |
176 | (b) >= 800 ? 5 : \ | |
177 | (b) >= 300 ? 4 : \ | |
178 | (b) >= 70 ? 3 : \ | |
179 | (b) >= 20 ? 2 : \ | |
180 | 1) | |
181 | ||
182 | /* Compute | |
183 | * \sum scalars[i]*points[i], | |
184 | * also including | |
185 | * scalar*generator | |
186 | * in the addition if scalar != NULL | |
187 | */ | |
188 | int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, | |
189 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) | |
190 | { | |
191 | BN_CTX *new_ctx = NULL; | |
192 | EC_POINT *generator = NULL; | |
193 | EC_POINT *tmp = NULL; | |
194 | size_t totalnum; | |
195 | size_t i, j; | |
196 | int k; | |
197 | int r_is_inverted = 0; | |
198 | int r_is_at_infinity = 1; | |
199 | size_t *wsize = NULL; /* individual window sizes */ | |
200 | size_t *wNAF_len = NULL; | |
201 | size_t max_len = 0; | |
202 | signed char **wNAF = NULL; /* individual wNAFs */ | |
203 | size_t num_val; | |
204 | EC_POINT **val = NULL; /* precomputation */ | |
205 | EC_POINT **v; | |
206 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ | |
207 | int ret = 0; | |
208 | ||
209 | if (scalar != NULL) | |
210 | { | |
211 | generator = EC_GROUP_get0_generator(group); | |
212 | if (generator == NULL) | |
213 | { | |
214 | ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); | |
215 | return 0; | |
216 | } | |
217 | } | |
218 | ||
219 | for (i = 0; i < num; i++) | |
220 | { | |
221 | if (group->meth != points[i]->meth) | |
222 | { | |
223 | ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
224 | return 0; | |
225 | } | |
226 | } | |
227 | ||
228 | totalnum = num + (scalar != NULL); | |
229 | ||
230 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); | |
231 | wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); | |
232 | wNAF = OPENSSL_malloc(totalnum * sizeof wNAF[0] + 1); | |
233 | if (wNAF != NULL) | |
234 | { | |
235 | wNAF[0] = NULL; /* preliminary pivot */ | |
236 | } | |
237 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err; | |
238 | ||
239 | /* num_val := total number of points to precompute */ | |
240 | num_val = 0; | |
241 | for (i = 0; i < totalnum; i++) | |
242 | { | |
243 | size_t bits; | |
244 | ||
245 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
246 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
247 | num_val += 1u << (wsize[i] - 1); | |
248 | } | |
249 | ||
250 | /* all precomputed points go into a single array 'val', | |
251 | * 'val_sub[i]' is a pointer to the subarray for the i-th point */ | |
252 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); | |
253 | if (val == NULL) goto err; | |
254 | val[num_val] = NULL; /* pivot element */ | |
255 | ||
256 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); | |
257 | if (val_sub == NULL) goto err; | |
258 | ||
259 | /* allocate points for precomputation */ | |
260 | v = val; | |
261 | for (i = 0; i < totalnum; i++) | |
262 | { | |
263 | val_sub[i] = v; | |
264 | for (j = 0; j < (1u << (wsize[i] - 1)); j++) | |
265 | { | |
266 | *v = EC_POINT_new(group); | |
267 | if (*v == NULL) goto err; | |
268 | v++; | |
269 | } | |
270 | } | |
271 | if (!(v == val + num_val)) | |
272 | { | |
273 | ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR); | |
274 | goto err; | |
275 | } | |
276 | ||
277 | if (ctx == NULL) | |
278 | { | |
279 | ctx = new_ctx = BN_CTX_new(); | |
280 | if (ctx == NULL) | |
281 | goto err; | |
282 | } | |
283 | ||
284 | tmp = EC_POINT_new(group); | |
285 | if (tmp == NULL) goto err; | |
286 | ||
287 | /* prepare precomputed values: | |
288 | * val_sub[i][0] := points[i] | |
289 | * val_sub[i][1] := 3 * points[i] | |
290 | * val_sub[i][2] := 5 * points[i] | |
291 | * ... | |
292 | */ | |
293 | for (i = 0; i < totalnum; i++) | |
294 | { | |
295 | if (i < num) | |
296 | { | |
297 | if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; | |
298 | } | |
299 | else | |
300 | { | |
301 | if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; | |
302 | } | |
303 | ||
304 | if (wsize[i] > 1) | |
305 | { | |
306 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; | |
307 | for (j = 1; j < (1u << (wsize[i] - 1)); j++) | |
308 | { | |
309 | if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; | |
310 | } | |
311 | } | |
312 | ||
313 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
314 | wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i], ctx); | |
315 | if (wNAF[i] == NULL) goto err; | |
316 | if (wNAF_len[i] > max_len) | |
317 | max_len = wNAF_len[i]; | |
318 | } | |
319 | ||
320 | #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ | |
321 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; | |
322 | #endif | |
323 | ||
324 | r_is_at_infinity = 1; | |
325 | ||
326 | for (k = max_len - 1; k >= 0; k--) | |
327 | { | |
328 | if (!r_is_at_infinity) | |
329 | { | |
330 | if (!EC_POINT_dbl(group, r, r, ctx)) goto err; | |
331 | } | |
332 | ||
333 | for (i = 0; i < totalnum; i++) | |
334 | { | |
335 | if (wNAF_len[i] > k) | |
336 | { | |
337 | int digit = wNAF[i][k]; | |
338 | int is_neg; | |
339 | ||
340 | if (digit) | |
341 | { | |
342 | is_neg = digit < 0; | |
343 | ||
344 | if (is_neg) | |
345 | digit = -digit; | |
346 | ||
347 | if (is_neg != r_is_inverted) | |
348 | { | |
349 | if (!r_is_at_infinity) | |
350 | { | |
351 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
352 | } | |
353 | r_is_inverted = !r_is_inverted; | |
354 | } | |
355 | ||
356 | /* digit > 0 */ | |
357 | ||
358 | if (r_is_at_infinity) | |
359 | { | |
360 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; | |
361 | r_is_at_infinity = 0; | |
362 | } | |
363 | else | |
364 | { | |
365 | if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; | |
366 | } | |
367 | } | |
368 | } | |
369 | } | |
370 | } | |
371 | ||
372 | if (r_is_at_infinity) | |
373 | { | |
374 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
375 | } | |
376 | else | |
377 | { | |
378 | if (r_is_inverted) | |
379 | if (!EC_POINT_invert(group, r, ctx)) goto err; | |
380 | } | |
381 | ||
382 | ret = 1; | |
383 | ||
384 | err: | |
385 | if (new_ctx != NULL) | |
386 | BN_CTX_free(new_ctx); | |
387 | if (tmp != NULL) | |
388 | EC_POINT_free(tmp); | |
389 | if (wsize != NULL) | |
390 | OPENSSL_free(wsize); | |
391 | if (wNAF_len != NULL) | |
392 | OPENSSL_free(wNAF_len); | |
393 | if (wNAF != NULL) | |
394 | { | |
395 | signed char **w; | |
396 | ||
397 | for (w = wNAF; *w != NULL; w++) | |
398 | OPENSSL_free(*w); | |
399 | ||
400 | OPENSSL_free(wNAF); | |
401 | } | |
402 | if (val != NULL) | |
403 | { | |
404 | for (v = val; *v != NULL; v++) | |
405 | EC_POINT_clear_free(*v); | |
406 | ||
407 | OPENSSL_free(val); | |
408 | } | |
409 | if (val_sub != NULL) | |
410 | { | |
411 | OPENSSL_free(val_sub); | |
412 | } | |
413 | return ret; | |
414 | } | |
415 | ||
416 | #else | |
417 | ||
418 | /* | |
419 | * Basic interleaving multi-exponentation method | |
420 | */ | |
421 | ||
422 | ||
423 | ||
48fe4d62 | 424 | #define EC_window_bits_for_scalar_size(b) \ |
26fbabf3 BM |
425 | ((b) >= 2000 ? 6 : \ |
426 | (b) >= 800 ? 5 : \ | |
427 | (b) >= 300 ? 4 : \ | |
428 | (b) >= 70 ? 3 : \ | |
37cdcb4d BM |
429 | (b) >= 20 ? 2 : \ |
430 | 1) | |
431 | /* For window size 'w' (w >= 2), we compute the odd multiples | |
432 | * 1*P .. (2^w-1)*P. | |
433 | * This accounts for 2^(w-1) point additions (neglecting constants), | |
434 | * each of which requires 16 field multiplications (4 squarings | |
435 | * and 12 general multiplications) in the case of curves defined | |
436 | * over GF(p), which are the only curves we have so far. | |
437 | * | |
438 | * Converting these precomputed points into affine form takes | |
439 | * three field multiplications for inverting Z and one squaring | |
440 | * and three multiplications for adjusting X and Y, i.e. | |
441 | * 7 multiplications in total (1 squaring and 6 general multiplications), | |
442 | * again except for constants. | |
443 | * | |
444 | * The average number of windows for a 'b' bit scalar is roughly | |
445 | * b/(w+1). | |
446 | * Each of these windows (except possibly for the first one, but | |
447 | * we are ignoring constants anyway) requires one point addition. | |
448 | * As the precomputed table stores points in affine form, these | |
449 | * additions take only 11 field multiplications each (3 squarings | |
450 | * and 8 general multiplications). | |
451 | * | |
452 | * So the total workload, except for constants, is | |
453 | * | |
454 | * 2^(w-1)*[5 squarings + 18 multiplications] | |
455 | * + (b/(w+1))*[3 squarings + 8 multiplications] | |
456 | * | |
457 | * If we assume that 10 squarings are as costly as 9 multiplications, | |
458 | * our task is to find the 'w' that, given 'b', minimizes | |
459 | * | |
460 | * 2^(w-1)*(5*9 + 18*10) + (b/(w+1))*(3*9 + 8*10) | |
461 | * = 2^(w-1)*225 + (b/(w+1))*107. | |
462 | * | |
463 | * Thus optimal window sizes should be roughly as follows: | |
464 | * | |
465 | * w >= 6 if b >= 1414 | |
466 | * w = 5 if 1413 >= b >= 505 | |
467 | * w = 4 if 504 >= b >= 169 | |
468 | * w = 3 if 168 >= b >= 51 | |
469 | * w = 2 if 50 >= b >= 13 | |
470 | * w = 1 if 12 >= b | |
471 | * | |
472 | * If we assume instead that squarings are exactly as costly as | |
473 | * multiplications, we have to minimize | |
474 | * 2^(w-1)*23 + (b/(w+1))*11. | |
475 | * | |
476 | * This gives us the following (nearly unchanged) table of optimal | |
477 | * windows sizes: | |
478 | * | |
479 | * w >= 6 if b >= 1406 | |
480 | * w = 5 if 1405 >= b >= 502 | |
481 | * w = 4 if 501 >= b >= 168 | |
482 | * w = 3 if 167 >= b >= 51 | |
483 | * w = 2 if 50 >= b >= 13 | |
484 | * w = 1 if 12 >= b | |
485 | * | |
486 | * Note that neither table tries to take into account memory usage | |
26fbabf3 BM |
487 | * (allocation overhead, code locality etc.). Actual timings with |
488 | * NIST curves P-192, P-224, and P-256 with scalars of 192, 224, | |
489 | * and 256 bits, respectively, show that w = 3 (instead of 4) is | |
490 | * preferrable; timings with NIST curve P-384 and 384-bit scalars | |
491 | * confirm that w = 4 is optimal for this case; and timings with | |
492 | * NIST curve P-521 and 521-bit scalars show that w = 4 (instead | |
493 | * of 5) is preferrable. So we generously round up all the | |
37cdcb4d BM |
494 | * boundaries and use the following table: |
495 | * | |
26fbabf3 BM |
496 | * w >= 6 if b >= 2000 |
497 | * w = 5 if 1999 >= b >= 800 | |
498 | * w = 4 if 799 >= b >= 300 | |
499 | * w = 3 if 299 >= b >= 70 | |
500 | * w = 2 if 69 >= b >= 20 | |
37cdcb4d BM |
501 | * w = 1 if 19 >= b |
502 | */ | |
503 | ||
38374911 BM |
504 | int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
505 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) | |
48fe4d62 BM |
506 | { |
507 | BN_CTX *new_ctx = NULL; | |
508 | EC_POINT *generator = NULL; | |
509 | EC_POINT *tmp = NULL; | |
510 | size_t totalnum; | |
511 | size_t i, j; | |
512 | int k, t; | |
513 | int r_is_at_infinity = 1; | |
514 | size_t max_bits = 0; | |
515 | size_t *wsize = NULL; /* individual window sizes */ | |
516 | unsigned long *wbits = NULL; /* individual window contents */ | |
517 | int *wpos = NULL; /* position of bottom bit of current individual windows | |
518 | * (wpos[i] is valid if wbits[i] != 0) */ | |
519 | size_t num_val; | |
520 | EC_POINT **val = NULL; /* precomputation */ | |
521 | EC_POINT **v; | |
522 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ | |
523 | int ret = 0; | |
524 | ||
525 | if (scalar != NULL) | |
526 | { | |
527 | generator = EC_GROUP_get0_generator(group); | |
528 | if (generator == NULL) | |
529 | { | |
6f8f4431 | 530 | ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); |
48fe4d62 BM |
531 | return 0; |
532 | } | |
533 | } | |
534 | ||
535 | for (i = 0; i < num; i++) | |
536 | { | |
537 | if (group->meth != points[i]->meth) | |
538 | { | |
539 | ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); | |
540 | return 0; | |
541 | } | |
542 | } | |
543 | ||
544 | totalnum = num + (scalar != NULL); | |
545 | ||
546 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); | |
547 | wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]); | |
548 | wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]); | |
549 | if (wsize == NULL || wbits == NULL || wpos == NULL) goto err; | |
550 | ||
551 | /* num_val := total number of points to precompute */ | |
552 | num_val = 0; | |
553 | for (i = 0; i < totalnum; i++) | |
554 | { | |
555 | size_t bits; | |
556 | ||
557 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
558 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
413a4a04 | 559 | num_val += 1u << (wsize[i] - 1); |
48fe4d62 BM |
560 | if (bits > max_bits) |
561 | max_bits = bits; | |
562 | wbits[i] = 0; | |
563 | wpos[i] = 0; | |
564 | } | |
565 | ||
566 | /* all precomputed points go into a single array 'val', | |
567 | * 'val_sub[i]' is a pointer to the subarray for the i-th point */ | |
568 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); | |
569 | if (val == NULL) goto err; | |
570 | val[num_val] = NULL; /* pivot element */ | |
571 | ||
572 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); | |
573 | if (val_sub == NULL) goto err; | |
574 | ||
575 | /* allocate points for precomputation */ | |
576 | v = val; | |
577 | for (i = 0; i < totalnum; i++) | |
578 | { | |
579 | val_sub[i] = v; | |
413a4a04 | 580 | for (j = 0; j < (1u << (wsize[i] - 1)); j++) |
48fe4d62 BM |
581 | { |
582 | *v = EC_POINT_new(group); | |
583 | if (*v == NULL) goto err; | |
584 | v++; | |
585 | } | |
586 | } | |
587 | if (!(v == val + num_val)) | |
588 | { | |
589 | ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR); | |
590 | goto err; | |
591 | } | |
592 | ||
593 | if (ctx == NULL) | |
594 | { | |
595 | ctx = new_ctx = BN_CTX_new(); | |
596 | if (ctx == NULL) | |
597 | goto err; | |
598 | } | |
599 | ||
600 | tmp = EC_POINT_new(group); | |
601 | if (tmp == NULL) goto err; | |
602 | ||
603 | /* prepare precomputed values: | |
604 | * val_sub[i][0] := points[i] | |
605 | * val_sub[i][1] := 3 * points[i] | |
606 | * val_sub[i][2] := 5 * points[i] | |
607 | * ... | |
608 | */ | |
609 | for (i = 0; i < totalnum; i++) | |
610 | { | |
611 | if (i < num) | |
612 | { | |
613 | if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; | |
86a921af BM |
614 | if (scalars[i]->neg) |
615 | { | |
616 | if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err; | |
617 | } | |
48fe4d62 BM |
618 | } |
619 | else | |
620 | { | |
621 | if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; | |
86a921af BM |
622 | if (scalar->neg) |
623 | { | |
624 | if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err; | |
625 | } | |
48fe4d62 BM |
626 | } |
627 | ||
628 | if (wsize[i] > 1) | |
629 | { | |
630 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; | |
413a4a04 | 631 | for (j = 1; j < (1u << (wsize[i] - 1)); j++) |
48fe4d62 BM |
632 | { |
633 | if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; | |
634 | } | |
635 | } | |
636 | } | |
637 | ||
26fbabf3 | 638 | #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ |
48fe4d62 BM |
639 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; |
640 | #endif | |
641 | ||
642 | r_is_at_infinity = 1; | |
643 | ||
644 | for (k = max_bits - 1; k >= 0; k--) | |
645 | { | |
646 | if (!r_is_at_infinity) | |
647 | { | |
648 | if (!EC_POINT_dbl(group, r, r, ctx)) goto err; | |
649 | } | |
650 | ||
651 | for (i = 0; i < totalnum; i++) | |
652 | { | |
653 | if (wbits[i] == 0) | |
654 | { | |
38374911 | 655 | const BIGNUM *s; |
48fe4d62 BM |
656 | |
657 | s = i < num ? scalars[i] : scalar; | |
658 | ||
659 | if (BN_is_bit_set(s, k)) | |
660 | { | |
661 | /* look at bits k - wsize[i] + 1 .. k for this window */ | |
662 | t = k - wsize[i] + 1; | |
663 | while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */ | |
664 | t++; | |
665 | wpos[i] = t; | |
666 | wbits[i] = 1; | |
667 | for (t = k - 1; t >= wpos[i]; t--) | |
668 | { | |
669 | wbits[i] <<= 1; | |
670 | if (BN_is_bit_set(s, t)) | |
671 | wbits[i]++; | |
672 | } | |
673 | /* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */ | |
674 | } | |
675 | } | |
676 | ||
677 | if ((wbits[i] != 0) && (wpos[i] == k)) | |
678 | { | |
679 | if (r_is_at_infinity) | |
680 | { | |
681 | if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err; | |
682 | r_is_at_infinity = 0; | |
683 | } | |
684 | else | |
685 | { | |
686 | if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err; | |
687 | } | |
688 | wbits[i] = 0; | |
689 | } | |
690 | } | |
691 | } | |
692 | ||
693 | if (r_is_at_infinity) | |
694 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
695 | ||
696 | ret = 1; | |
697 | ||
698 | err: | |
699 | if (new_ctx != NULL) | |
700 | BN_CTX_free(new_ctx); | |
701 | if (tmp != NULL) | |
702 | EC_POINT_free(tmp); | |
703 | if (wsize != NULL) | |
704 | OPENSSL_free(wsize); | |
705 | if (wbits != NULL) | |
706 | OPENSSL_free(wbits); | |
707 | if (wpos != NULL) | |
708 | OPENSSL_free(wpos); | |
709 | if (val != NULL) | |
710 | { | |
711 | for (v = val; *v != NULL; v++) | |
712 | EC_POINT_clear_free(*v); | |
713 | ||
714 | OPENSSL_free(val); | |
715 | } | |
716 | if (val_sub != NULL) | |
717 | { | |
718 | OPENSSL_free(val_sub); | |
719 | } | |
720 | return ret; | |
721 | } | |
3ba1f111 | 722 | #endif |
38374911 BM |
723 | |
724 | ||
725 | int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) | |
726 | { | |
727 | const EC_POINT *points[1]; | |
728 | const BIGNUM *scalars[1]; | |
729 | ||
730 | points[0] = point; | |
731 | scalars[0] = p_scalar; | |
732 | ||
733 | return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx); | |
734 | } | |
735 | ||
736 | ||
194dd046 | 737 | int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
38374911 BM |
738 | { |
739 | const EC_POINT *generator; | |
740 | BN_CTX *new_ctx = NULL; | |
741 | BIGNUM *order; | |
742 | int ret = 0; | |
743 | ||
744 | generator = EC_GROUP_get0_generator(group); | |
745 | if (generator == NULL) | |
746 | { | |
194dd046 | 747 | ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); |
38374911 BM |
748 | return 0; |
749 | } | |
750 | ||
751 | if (ctx == NULL) | |
752 | { | |
753 | ctx = new_ctx = BN_CTX_new(); | |
754 | if (ctx == NULL) | |
755 | return 0; | |
756 | } | |
757 | ||
758 | BN_CTX_start(ctx); | |
759 | order = BN_CTX_get(ctx); | |
760 | if (order == NULL) goto err; | |
761 | ||
762 | if (!EC_GROUP_get_order(group, order, ctx)) return 0; | |
763 | if (BN_is_zero(order)) | |
764 | { | |
194dd046 | 765 | ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); |
38374911 BM |
766 | goto err; |
767 | } | |
768 | ||
769 | /* TODO */ | |
770 | ||
771 | ret = 1; | |
772 | ||
773 | err: | |
774 | BN_CTX_end(ctx); | |
775 | if (new_ctx != NULL) | |
776 | BN_CTX_free(new_ctx); | |
777 | return ret; | |
778 | } |