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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 | * |
a7f182b7 | 5 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
4f22f405 RS |
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 | |
579422c8 P |
11 | /* |
12 | * ECDSA low level APIs are deprecated for public use, but still ok for | |
13 | * internal use. | |
14 | */ | |
15 | #include "internal/deprecated.h" | |
16 | ||
28f573a2 | 17 | #include <string.h> |
48fe4d62 BM |
18 | #include <openssl/err.h> |
19 | ||
9b398ef2 | 20 | #include "internal/cryptlib.h" |
25f2138b | 21 | #include "crypto/bn.h" |
706457b7 | 22 | #include "ec_local.h" |
cd420b0b | 23 | #include "internal/refcount.h" |
48fe4d62 | 24 | |
37c660ff | 25 | /* |
0d4fb843 | 26 | * This file implements the wNAF-based interleaving multi-exponentiation method |
dea0eb2c RS |
27 | * Formerly at: |
28 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp | |
29 | * You might now find it here: | |
30 | * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 | |
31 | * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf | |
32 | * For multiplication with precomputation, we use wNAF splitting, formerly at: | |
33 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp | |
37c660ff | 34 | */ |
48fe4d62 | 35 | |
37c660ff | 36 | /* structure for precomputed multiples of the generator */ |
3aef36ff | 37 | struct ec_pre_comp_st { |
0f113f3e MC |
38 | const EC_GROUP *group; /* parent EC_GROUP object */ |
39 | size_t blocksize; /* block size for wNAF splitting */ | |
40 | size_t numblocks; /* max. number of blocks for which we have | |
41 | * precomputation */ | |
42 | size_t w; /* window size */ | |
43 | EC_POINT **points; /* array with pre-calculated multiples of | |
44 | * generator: 'num' pointers to EC_POINT | |
45 | * objects followed by a NULL */ | |
46 | size_t num; /* numblocks * 2^(w-1) */ | |
2f545ae4 | 47 | CRYPTO_REF_COUNT references; |
9b398ef2 | 48 | CRYPTO_RWLOCK *lock; |
3aef36ff | 49 | }; |
37c660ff BM |
50 | |
51 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
0f113f3e MC |
52 | { |
53 | EC_PRE_COMP *ret = NULL; | |
54 | ||
55 | if (!group) | |
56 | return NULL; | |
57 | ||
64b25758 | 58 | ret = OPENSSL_zalloc(sizeof(*ret)); |
90945fa3 | 59 | if (ret == NULL) { |
0f113f3e MC |
60 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
61 | return ret; | |
62 | } | |
9b398ef2 | 63 | |
0f113f3e MC |
64 | ret->group = group; |
65 | ret->blocksize = 8; /* default */ | |
0f113f3e | 66 | ret->w = 4; /* default */ |
0f113f3e | 67 | ret->references = 1; |
9b398ef2 AG |
68 | |
69 | ret->lock = CRYPTO_THREAD_lock_new(); | |
70 | if (ret->lock == NULL) { | |
71 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
72 | OPENSSL_free(ret); | |
73 | return NULL; | |
74 | } | |
0f113f3e MC |
75 | return ret; |
76 | } | |
37c660ff | 77 | |
3aef36ff | 78 | EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) |
0f113f3e | 79 | { |
9b398ef2 | 80 | int i; |
3aef36ff | 81 | if (pre != NULL) |
2f545ae4 | 82 | CRYPTO_UP_REF(&pre->references, &i, pre->lock); |
3aef36ff | 83 | return pre; |
0f113f3e | 84 | } |
37c660ff | 85 | |
3aef36ff | 86 | void EC_ec_pre_comp_free(EC_PRE_COMP *pre) |
0f113f3e | 87 | { |
9b398ef2 AG |
88 | int i; |
89 | ||
90 | if (pre == NULL) | |
91 | return; | |
92 | ||
2f545ae4 | 93 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
9b398ef2 AG |
94 | REF_PRINT_COUNT("EC_ec", pre); |
95 | if (i > 0) | |
0f113f3e | 96 | return; |
9b398ef2 | 97 | REF_ASSERT_ISNT(i < 0); |
ba729265 | 98 | |
3aef36ff RS |
99 | if (pre->points != NULL) { |
100 | EC_POINT **pts; | |
37c660ff | 101 | |
3aef36ff RS |
102 | for (pts = pre->points; *pts != NULL; pts++) |
103 | EC_POINT_free(*pts); | |
0f113f3e MC |
104 | OPENSSL_free(pre->points); |
105 | } | |
9b398ef2 | 106 | CRYPTO_THREAD_lock_free(pre->lock); |
0f113f3e MC |
107 | OPENSSL_free(pre); |
108 | } | |
37c660ff | 109 | |
36bed230 | 110 | #define EC_POINT_BN_set_flags(P, flags) do { \ |
40e48e54 BB |
111 | BN_set_flags((P)->X, (flags)); \ |
112 | BN_set_flags((P)->Y, (flags)); \ | |
113 | BN_set_flags((P)->Z, (flags)); \ | |
114 | } while(0) | |
115 | ||
f4675379 | 116 | /*- |
37124360 NT |
117 | * This functions computes a single point multiplication over the EC group, |
118 | * using, at a high level, a Montgomery ladder with conditional swaps, with | |
119 | * various timing attack defenses. | |
a067a870 | 120 | * |
fe2d3975 | 121 | * It performs either a fixed point multiplication |
40e48e54 | 122 | * (scalar * generator) |
fe2d3975 | 123 | * when point is NULL, or a variable point multiplication |
40e48e54 BB |
124 | * (scalar * point) |
125 | * when point is not NULL. | |
126 | * | |
37124360 NT |
127 | * `scalar` cannot be NULL and should be in the range [0,n) otherwise all |
128 | * constant time bets are off (where n is the cardinality of the EC group). | |
40e48e54 | 129 | * |
01ad66f8 NT |
130 | * This function expects `group->order` and `group->cardinality` to be well |
131 | * defined and non-zero: it fails with an error code otherwise. | |
132 | * | |
37124360 NT |
133 | * NB: This says nothing about the constant-timeness of the ladder step |
134 | * implementation (i.e., the default implementation is based on EC_POINT_add and | |
135 | * EC_POINT_dbl, which of course are not constant time themselves) or the | |
136 | * underlying multiprecision arithmetic. | |
40e48e54 | 137 | * |
37124360 | 138 | * The product is stored in `r`. |
40e48e54 | 139 | * |
01ad66f8 NT |
140 | * This is an internal function: callers are in charge of ensuring that the |
141 | * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. | |
142 | * | |
40e48e54 BB |
143 | * Returns 1 on success, 0 otherwise. |
144 | */ | |
37124360 NT |
145 | int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, |
146 | const BIGNUM *scalar, const EC_POINT *point, | |
147 | BN_CTX *ctx) | |
40e48e54 | 148 | { |
a766aab9 | 149 | int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; |
37124360 | 150 | EC_POINT *p = NULL; |
40e48e54 BB |
151 | EC_POINT *s = NULL; |
152 | BIGNUM *k = NULL; | |
153 | BIGNUM *lambda = NULL; | |
a766aab9 | 154 | BIGNUM *cardinality = NULL; |
36bed230 | 155 | int ret = 0; |
40e48e54 | 156 | |
37124360 NT |
157 | /* early exit if the input point is the point at infinity */ |
158 | if (point != NULL && EC_POINT_is_at_infinity(group, point)) | |
159 | return EC_POINT_set_to_infinity(group, r); | |
160 | ||
01ad66f8 NT |
161 | if (BN_is_zero(group->order)) { |
162 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER); | |
7d859d1c | 163 | return 0; |
01ad66f8 | 164 | } |
ac2b52c6 | 165 | if (BN_is_zero(group->cofactor)) { |
01ad66f8 NT |
166 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR); |
167 | return 0; | |
168 | } | |
7d859d1c AP |
169 | |
170 | BN_CTX_start(ctx); | |
40e48e54 | 171 | |
37124360 NT |
172 | if (((p = EC_POINT_new(group)) == NULL) |
173 | || ((s = EC_POINT_new(group)) == NULL)) { | |
174 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); | |
40e48e54 | 175 | goto err; |
37124360 | 176 | } |
40e48e54 BB |
177 | |
178 | if (point == NULL) { | |
37124360 NT |
179 | if (!EC_POINT_copy(p, group->generator)) { |
180 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); | |
40e48e54 | 181 | goto err; |
37124360 | 182 | } |
40e48e54 | 183 | } else { |
37124360 NT |
184 | if (!EC_POINT_copy(p, point)) { |
185 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); | |
40e48e54 | 186 | goto err; |
37124360 | 187 | } |
40e48e54 BB |
188 | } |
189 | ||
37124360 NT |
190 | EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME); |
191 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME); | |
36bed230 | 192 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME); |
40e48e54 | 193 | |
a766aab9 | 194 | cardinality = BN_CTX_get(ctx); |
40e48e54 BB |
195 | lambda = BN_CTX_get(ctx); |
196 | k = BN_CTX_get(ctx); | |
37124360 NT |
197 | if (k == NULL) { |
198 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); | |
199 | goto err; | |
200 | } | |
201 | ||
202 | if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) { | |
203 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 204 | goto err; |
37124360 | 205 | } |
40e48e54 BB |
206 | |
207 | /* | |
a766aab9 | 208 | * Group cardinalities are often on a word boundary. |
40e48e54 BB |
209 | * So when we pad the scalar, some timing diff might |
210 | * pop if it needs to be expanded due to carries. | |
211 | * So expand ahead of time. | |
212 | */ | |
a766aab9 BB |
213 | cardinality_bits = BN_num_bits(cardinality); |
214 | group_top = bn_get_top(cardinality); | |
99540ec7 P |
215 | if ((bn_wexpand(k, group_top + 2) == NULL) |
216 | || (bn_wexpand(lambda, group_top + 2) == NULL)) { | |
37124360 | 217 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
40e48e54 | 218 | goto err; |
37124360 | 219 | } |
40e48e54 | 220 | |
37124360 NT |
221 | if (!BN_copy(k, scalar)) { |
222 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 223 | goto err; |
37124360 | 224 | } |
40e48e54 BB |
225 | |
226 | BN_set_flags(k, BN_FLG_CONSTTIME); | |
227 | ||
a766aab9 | 228 | if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) { |
f4675379 | 229 | /*- |
40e48e54 BB |
230 | * this is an unusual input, and we don't guarantee |
231 | * constant-timeness | |
232 | */ | |
37124360 NT |
233 | if (!BN_nnmod(k, k, cardinality, ctx)) { |
234 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 235 | goto err; |
37124360 | 236 | } |
40e48e54 BB |
237 | } |
238 | ||
37124360 NT |
239 | if (!BN_add(lambda, k, cardinality)) { |
240 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 241 | goto err; |
37124360 | 242 | } |
40e48e54 | 243 | BN_set_flags(lambda, BN_FLG_CONSTTIME); |
37124360 NT |
244 | if (!BN_add(k, lambda, cardinality)) { |
245 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 246 | goto err; |
37124360 | 247 | } |
40e48e54 | 248 | /* |
a766aab9 BB |
249 | * lambda := scalar + cardinality |
250 | * k := scalar + 2*cardinality | |
40e48e54 | 251 | */ |
a766aab9 | 252 | kbit = BN_is_bit_set(lambda, cardinality_bits); |
99540ec7 | 253 | BN_consttime_swap(kbit, k, lambda, group_top + 2); |
40e48e54 BB |
254 | |
255 | group_top = bn_get_top(group->field); | |
256 | if ((bn_wexpand(s->X, group_top) == NULL) | |
257 | || (bn_wexpand(s->Y, group_top) == NULL) | |
258 | || (bn_wexpand(s->Z, group_top) == NULL) | |
259 | || (bn_wexpand(r->X, group_top) == NULL) | |
260 | || (bn_wexpand(r->Y, group_top) == NULL) | |
37124360 NT |
261 | || (bn_wexpand(r->Z, group_top) == NULL) |
262 | || (bn_wexpand(p->X, group_top) == NULL) | |
263 | || (bn_wexpand(p->Y, group_top) == NULL) | |
264 | || (bn_wexpand(p->Z, group_top) == NULL)) { | |
265 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 266 | goto err; |
37124360 | 267 | } |
40e48e54 | 268 | |
f667820c SH |
269 | /*- |
270 | * Apply coordinate blinding for EC_POINT. | |
271 | * | |
272 | * The underlying EC_METHOD can optionally implement this function: | |
273 | * ec_point_blind_coordinates() returns 0 in case of errors or 1 on | |
274 | * success or if coordinate blinding is not implemented for this | |
275 | * group. | |
276 | */ | |
37124360 NT |
277 | if (!ec_point_blind_coordinates(group, p, ctx)) { |
278 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE); | |
40e48e54 | 279 | goto err; |
37124360 | 280 | } |
40e48e54 | 281 | |
37124360 NT |
282 | /* Initialize the Montgomery ladder */ |
283 | if (!ec_point_ladder_pre(group, r, s, p, ctx)) { | |
284 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE); | |
40e48e54 | 285 | goto err; |
37124360 | 286 | } |
40e48e54 | 287 | |
37124360 NT |
288 | /* top bit is a 1, in a fixed pos */ |
289 | pbit = 1; | |
40e48e54 BB |
290 | |
291 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |
292 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ | |
293 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ | |
294 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ | |
295 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |
296 | (a)->Z_is_one ^= (t); \ | |
297 | (b)->Z_is_one ^= (t); \ | |
298 | } while(0) | |
299 | ||
f4675379 | 300 | /*- |
a067a870 BB |
301 | * The ladder step, with branches, is |
302 | * | |
303 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
304 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
305 | * | |
306 | * Swapping R, S conditionally on k[i] leaves you with state | |
307 | * | |
308 | * k[i] == 0: T, U = R, S | |
309 | * k[i] == 1: T, U = S, R | |
310 | * | |
311 | * Then perform the ECC ops. | |
312 | * | |
313 | * U = add(T, U) | |
314 | * T = dbl(T) | |
315 | * | |
316 | * Which leaves you with state | |
317 | * | |
318 | * k[i] == 0: U = add(R, S), T = dbl(R) | |
319 | * k[i] == 1: U = add(S, R), T = dbl(S) | |
320 | * | |
321 | * Swapping T, U conditionally on k[i] leaves you with state | |
322 | * | |
323 | * k[i] == 0: R, S = T, U | |
324 | * k[i] == 1: R, S = U, T | |
325 | * | |
326 | * Which leaves you with state | |
327 | * | |
328 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
329 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
330 | * | |
331 | * So we get the same logic, but instead of a branch it's a | |
332 | * conditional swap, followed by ECC ops, then another conditional swap. | |
333 | * | |
334 | * Optimization: The end of iteration i and start of i-1 looks like | |
335 | * | |
336 | * ... | |
337 | * CSWAP(k[i], R, S) | |
338 | * ECC | |
339 | * CSWAP(k[i], R, S) | |
340 | * (next iteration) | |
341 | * CSWAP(k[i-1], R, S) | |
342 | * ECC | |
343 | * CSWAP(k[i-1], R, S) | |
344 | * ... | |
345 | * | |
346 | * So instead of two contiguous swaps, you can merge the condition | |
347 | * bits and do a single swap. | |
348 | * | |
f4675379 NT |
349 | * k[i] k[i-1] Outcome |
350 | * 0 0 No Swap | |
351 | * 0 1 Swap | |
352 | * 1 0 Swap | |
353 | * 1 1 No Swap | |
a067a870 BB |
354 | * |
355 | * This is XOR. pbit tracks the previous bit of k. | |
356 | */ | |
357 | ||
a766aab9 | 358 | for (i = cardinality_bits - 1; i >= 0; i--) { |
40e48e54 BB |
359 | kbit = BN_is_bit_set(k, i) ^ pbit; |
360 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |
37124360 NT |
361 | |
362 | /* Perform a single step of the Montgomery ladder */ | |
363 | if (!ec_point_ladder_step(group, r, s, p, ctx)) { | |
364 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE); | |
40e48e54 | 365 | goto err; |
37124360 | 366 | } |
40e48e54 BB |
367 | /* |
368 | * pbit logic merges this cswap with that of the | |
369 | * next iteration | |
370 | */ | |
371 | pbit ^= kbit; | |
372 | } | |
373 | /* one final cswap to move the right value into r */ | |
374 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |
375 | #undef EC_POINT_CSWAP | |
376 | ||
37124360 NT |
377 | /* Finalize ladder (and recover full point coordinates) */ |
378 | if (!ec_point_ladder_post(group, r, s, p, ctx)) { | |
379 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE); | |
380 | goto err; | |
381 | } | |
382 | ||
40e48e54 BB |
383 | ret = 1; |
384 | ||
f4675379 | 385 | err: |
37124360 | 386 | EC_POINT_free(p); |
8a74bb5c | 387 | EC_POINT_clear_free(s); |
40e48e54 | 388 | BN_CTX_end(ctx); |
40e48e54 BB |
389 | |
390 | return ret; | |
391 | } | |
f4675379 | 392 | |
36bed230 | 393 | #undef EC_POINT_BN_set_flags |
40e48e54 | 394 | |
0f113f3e MC |
395 | /* |
396 | * TODO: table should be optimised for the wNAF-based implementation, | |
397 | * sometimes smaller windows will give better performance (thus the | |
398 | * boundaries should be increased) | |
c05940ed | 399 | */ |
3ba1f111 | 400 | #define EC_window_bits_for_scalar_size(b) \ |
0f113f3e MC |
401 | ((size_t) \ |
402 | ((b) >= 2000 ? 6 : \ | |
403 | (b) >= 800 ? 5 : \ | |
404 | (b) >= 300 ? 4 : \ | |
405 | (b) >= 70 ? 3 : \ | |
406 | (b) >= 20 ? 2 : \ | |
407 | 1)) | |
3ba1f111 | 408 | |
c80fd6b2 MC |
409 | /*- |
410 | * Compute | |
3ba1f111 BM |
411 | * \sum scalars[i]*points[i], |
412 | * also including | |
413 | * scalar*generator | |
414 | * in the addition if scalar != NULL | |
415 | */ | |
7793f30e | 416 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
0f113f3e MC |
417 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
418 | BN_CTX *ctx) | |
419 | { | |
0f113f3e MC |
420 | const EC_POINT *generator = NULL; |
421 | EC_POINT *tmp = NULL; | |
422 | size_t totalnum; | |
423 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
424 | size_t pre_points_per_block = 0; | |
425 | size_t i, j; | |
426 | int k; | |
427 | int r_is_inverted = 0; | |
428 | int r_is_at_infinity = 1; | |
429 | size_t *wsize = NULL; /* individual window sizes */ | |
430 | signed char **wNAF = NULL; /* individual wNAFs */ | |
431 | size_t *wNAF_len = NULL; | |
432 | size_t max_len = 0; | |
433 | size_t num_val; | |
434 | EC_POINT **val = NULL; /* precomputation */ | |
435 | EC_POINT **v; | |
436 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
437 | * 'pre_comp->points' */ | |
438 | const EC_PRE_COMP *pre_comp = NULL; | |
439 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be | |
440 | * treated like other scalars, i.e. | |
441 | * precomputation is not available */ | |
442 | int ret = 0; | |
443 | ||
de72274d | 444 | if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) { |
f4675379 | 445 | /*- |
37124360 NT |
446 | * Handle the common cases where the scalar is secret, enforcing a |
447 | * scalar multiplication implementation based on a Montgomery ladder, | |
448 | * with various timing attack defenses. | |
36bed230 | 449 | */ |
3051bf2a | 450 | if ((scalar != group->order) && (scalar != NULL) && (num == 0)) { |
de72274d BB |
451 | /*- |
452 | * In this case we want to compute scalar * GeneratorPoint: this | |
37124360 NT |
453 | * codepath is reached most prominently by (ephemeral) key |
454 | * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, | |
455 | * ECDH keygen/first half), where the scalar is always secret. This | |
456 | * is why we ignore if BN_FLG_CONSTTIME is actually set and we | |
457 | * always call the ladder version. | |
de72274d | 458 | */ |
37124360 | 459 | return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); |
de72274d | 460 | } |
3051bf2a | 461 | if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) { |
de72274d | 462 | /*- |
37124360 NT |
463 | * In this case we want to compute scalar * VariablePoint: this |
464 | * codepath is reached most prominently by the second half of ECDH, | |
465 | * where the secret scalar is multiplied by the peer's public point. | |
466 | * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is | |
467 | * actually set and we always call the ladder version. | |
de72274d | 468 | */ |
37124360 | 469 | return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); |
de72274d | 470 | } |
36bed230 NT |
471 | } |
472 | ||
0f113f3e MC |
473 | if (scalar != NULL) { |
474 | generator = EC_GROUP_get0_generator(group); | |
475 | if (generator == NULL) { | |
476 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
477 | goto err; | |
478 | } | |
479 | ||
480 | /* look if we can use precomputed multiples of generator */ | |
481 | ||
3aef36ff | 482 | pre_comp = group->pre_comp.ec; |
0f113f3e MC |
483 | if (pre_comp && pre_comp->numblocks |
484 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
485 | 0)) { | |
486 | blocksize = pre_comp->blocksize; | |
487 | ||
488 | /* | |
489 | * determine maximum number of blocks that wNAF splitting may | |
490 | * yield (NB: maximum wNAF length is bit length plus one) | |
491 | */ | |
492 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
493 | ||
494 | /* | |
495 | * we cannot use more blocks than we have precomputation for | |
496 | */ | |
497 | if (numblocks > pre_comp->numblocks) | |
498 | numblocks = pre_comp->numblocks; | |
499 | ||
500 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
501 | ||
502 | /* check that pre_comp looks sane */ | |
503 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
504 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
505 | goto err; | |
506 | } | |
507 | } else { | |
508 | /* can't use precomputation */ | |
509 | pre_comp = NULL; | |
510 | numblocks = 1; | |
511 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
512 | * 'scalars' */ | |
513 | } | |
514 | } | |
515 | ||
516 | totalnum = num + numblocks; | |
517 | ||
cbe29648 RS |
518 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
519 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); | |
520 | /* include space for pivot */ | |
521 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); | |
522 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); | |
0f113f3e MC |
523 | |
524 | /* Ensure wNAF is initialised in case we end up going to err */ | |
90945fa3 | 525 | if (wNAF != NULL) |
0f113f3e MC |
526 | wNAF[0] = NULL; /* preliminary pivot */ |
527 | ||
90945fa3 | 528 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { |
0f113f3e MC |
529 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
530 | goto err; | |
531 | } | |
532 | ||
533 | /* | |
534 | * num_val will be the total number of temporarily precomputed points | |
535 | */ | |
536 | num_val = 0; | |
537 | ||
538 | for (i = 0; i < num + num_scalar; i++) { | |
539 | size_t bits; | |
540 | ||
541 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
542 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
543 | num_val += (size_t)1 << (wsize[i] - 1); | |
544 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
545 | wNAF[i] = | |
546 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
547 | &wNAF_len[i]); | |
548 | if (wNAF[i] == NULL) | |
549 | goto err; | |
550 | if (wNAF_len[i] > max_len) | |
551 | max_len = wNAF_len[i]; | |
552 | } | |
553 | ||
554 | if (numblocks) { | |
555 | /* we go here iff scalar != NULL */ | |
556 | ||
557 | if (pre_comp == NULL) { | |
558 | if (num_scalar != 1) { | |
559 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
560 | goto err; | |
561 | } | |
562 | /* we have already generated a wNAF for 'scalar' */ | |
563 | } else { | |
564 | signed char *tmp_wNAF = NULL; | |
565 | size_t tmp_len = 0; | |
566 | ||
567 | if (num_scalar != 0) { | |
568 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
569 | goto err; | |
570 | } | |
571 | ||
572 | /* | |
573 | * use the window size for which we have precomputation | |
574 | */ | |
575 | wsize[num] = pre_comp->w; | |
576 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
577 | if (!tmp_wNAF) | |
578 | goto err; | |
579 | ||
580 | if (tmp_len <= max_len) { | |
581 | /* | |
582 | * One of the other wNAFs is at least as long as the wNAF | |
583 | * belonging to the generator, so wNAF splitting will not buy | |
584 | * us anything. | |
585 | */ | |
586 | ||
587 | numblocks = 1; | |
588 | totalnum = num + 1; /* don't use wNAF splitting */ | |
589 | wNAF[num] = tmp_wNAF; | |
590 | wNAF[num + 1] = NULL; | |
591 | wNAF_len[num] = tmp_len; | |
0f113f3e MC |
592 | /* |
593 | * pre_comp->points starts with the points that we need here: | |
594 | */ | |
595 | val_sub[num] = pre_comp->points; | |
596 | } else { | |
597 | /* | |
598 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
599 | * splitting and include the blocks | |
600 | */ | |
601 | ||
602 | signed char *pp; | |
603 | EC_POINT **tmp_points; | |
604 | ||
605 | if (tmp_len < numblocks * blocksize) { | |
606 | /* | |
607 | * possibly we can do with fewer blocks than estimated | |
608 | */ | |
609 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
610 | if (numblocks > pre_comp->numblocks) { | |
611 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 612 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
613 | goto err; |
614 | } | |
615 | totalnum = num + numblocks; | |
616 | } | |
617 | ||
618 | /* split wNAF in 'numblocks' parts */ | |
619 | pp = tmp_wNAF; | |
620 | tmp_points = pre_comp->points; | |
621 | ||
622 | for (i = num; i < totalnum; i++) { | |
623 | if (i < totalnum - 1) { | |
624 | wNAF_len[i] = blocksize; | |
625 | if (tmp_len < blocksize) { | |
626 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 627 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
628 | goto err; |
629 | } | |
630 | tmp_len -= blocksize; | |
631 | } else | |
632 | /* | |
633 | * last block gets whatever is left (this could be | |
634 | * more or less than 'blocksize'!) | |
635 | */ | |
636 | wNAF_len[i] = tmp_len; | |
637 | ||
638 | wNAF[i + 1] = NULL; | |
639 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
640 | if (wNAF[i] == NULL) { | |
641 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
642 | OPENSSL_free(tmp_wNAF); | |
643 | goto err; | |
644 | } | |
645 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
646 | if (wNAF_len[i] > max_len) | |
647 | max_len = wNAF_len[i]; | |
648 | ||
649 | if (*tmp_points == NULL) { | |
650 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
651 | OPENSSL_free(tmp_wNAF); | |
652 | goto err; | |
653 | } | |
654 | val_sub[i] = tmp_points; | |
655 | tmp_points += pre_points_per_block; | |
656 | pp += blocksize; | |
657 | } | |
658 | OPENSSL_free(tmp_wNAF); | |
659 | } | |
660 | } | |
661 | } | |
662 | ||
663 | /* | |
664 | * All points we precompute now go into a single array 'val'. | |
665 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
666 | * subarray of 'pre_comp->points' if we already have precomputation. | |
667 | */ | |
cbe29648 | 668 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
0f113f3e MC |
669 | if (val == NULL) { |
670 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
671 | goto err; | |
672 | } | |
673 | val[num_val] = NULL; /* pivot element */ | |
674 | ||
675 | /* allocate points for precomputation */ | |
676 | v = val; | |
677 | for (i = 0; i < num + num_scalar; i++) { | |
678 | val_sub[i] = v; | |
679 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
680 | *v = EC_POINT_new(group); | |
681 | if (*v == NULL) | |
682 | goto err; | |
683 | v++; | |
684 | } | |
685 | } | |
686 | if (!(v == val + num_val)) { | |
687 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
688 | goto err; | |
689 | } | |
690 | ||
75ebbd9a | 691 | if ((tmp = EC_POINT_new(group)) == NULL) |
0f113f3e MC |
692 | goto err; |
693 | ||
50e735f9 MC |
694 | /*- |
695 | * prepare precomputed values: | |
696 | * val_sub[i][0] := points[i] | |
697 | * val_sub[i][1] := 3 * points[i] | |
698 | * val_sub[i][2] := 5 * points[i] | |
699 | * ... | |
700 | */ | |
0f113f3e MC |
701 | for (i = 0; i < num + num_scalar; i++) { |
702 | if (i < num) { | |
703 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
704 | goto err; | |
705 | } else { | |
706 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
707 | goto err; | |
708 | } | |
709 | ||
710 | if (wsize[i] > 1) { | |
711 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
712 | goto err; | |
713 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
714 | if (!EC_POINT_add | |
715 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
716 | goto err; | |
717 | } | |
718 | } | |
719 | } | |
720 | ||
0f113f3e MC |
721 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
722 | goto err; | |
3ba1f111 | 723 | |
0f113f3e MC |
724 | r_is_at_infinity = 1; |
725 | ||
726 | for (k = max_len - 1; k >= 0; k--) { | |
727 | if (!r_is_at_infinity) { | |
728 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
729 | goto err; | |
730 | } | |
731 | ||
732 | for (i = 0; i < totalnum; i++) { | |
733 | if (wNAF_len[i] > (size_t)k) { | |
734 | int digit = wNAF[i][k]; | |
735 | int is_neg; | |
736 | ||
737 | if (digit) { | |
738 | is_neg = digit < 0; | |
739 | ||
740 | if (is_neg) | |
741 | digit = -digit; | |
742 | ||
743 | if (is_neg != r_is_inverted) { | |
744 | if (!r_is_at_infinity) { | |
745 | if (!EC_POINT_invert(group, r, ctx)) | |
746 | goto err; | |
747 | } | |
748 | r_is_inverted = !r_is_inverted; | |
749 | } | |
750 | ||
751 | /* digit > 0 */ | |
752 | ||
753 | if (r_is_at_infinity) { | |
754 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
755 | goto err; | |
756 | r_is_at_infinity = 0; | |
757 | } else { | |
758 | if (!EC_POINT_add | |
759 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
760 | goto err; | |
761 | } | |
762 | } | |
763 | } | |
764 | } | |
765 | } | |
766 | ||
767 | if (r_is_at_infinity) { | |
768 | if (!EC_POINT_set_to_infinity(group, r)) | |
769 | goto err; | |
770 | } else { | |
771 | if (r_is_inverted) | |
772 | if (!EC_POINT_invert(group, r, ctx)) | |
773 | goto err; | |
774 | } | |
775 | ||
776 | ret = 1; | |
3ba1f111 BM |
777 | |
778 | err: | |
8fdc3734 | 779 | EC_POINT_free(tmp); |
b548a1f1 RS |
780 | OPENSSL_free(wsize); |
781 | OPENSSL_free(wNAF_len); | |
0f113f3e MC |
782 | if (wNAF != NULL) { |
783 | signed char **w; | |
784 | ||
785 | for (w = wNAF; *w != NULL; w++) | |
786 | OPENSSL_free(*w); | |
787 | ||
788 | OPENSSL_free(wNAF); | |
789 | } | |
790 | if (val != NULL) { | |
791 | for (v = val; *v != NULL; v++) | |
792 | EC_POINT_clear_free(*v); | |
793 | ||
794 | OPENSSL_free(val); | |
795 | } | |
b548a1f1 | 796 | OPENSSL_free(val_sub); |
0f113f3e MC |
797 | return ret; |
798 | } | |
38374911 | 799 | |
1d97c843 TH |
800 | /*- |
801 | * ec_wNAF_precompute_mult() | |
37c660ff BM |
802 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
803 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
0f113f3e | 804 | * |
37c660ff BM |
805 | * 'pre_comp->points' is an array of multiples of the generator |
806 | * of the following form: | |
807 | * points[0] = generator; | |
808 | * points[1] = 3 * generator; | |
809 | * ... | |
810 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
811 | * points[2^(w-1)] = 2^blocksize * generator; | |
812 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
813 | * ... | |
814 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
815 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
816 | * ... | |
817 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
818 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 819 | */ |
7793f30e | 820 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
821 | { |
822 | const EC_POINT *generator; | |
823 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
be2e334f | 824 | const BIGNUM *order; |
0f113f3e MC |
825 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
826 | EC_POINT **points = NULL; | |
827 | EC_PRE_COMP *pre_comp; | |
828 | int ret = 0; | |
a9612d6c MC |
829 | #ifndef FIPS_MODE |
830 | BN_CTX *new_ctx = NULL; | |
831 | #endif | |
0f113f3e MC |
832 | |
833 | /* if there is an old EC_PRE_COMP object, throw it away */ | |
2c52ac9b | 834 | EC_pre_comp_free(group); |
0f113f3e MC |
835 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
836 | return 0; | |
837 | ||
838 | generator = EC_GROUP_get0_generator(group); | |
839 | if (generator == NULL) { | |
840 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); | |
841 | goto err; | |
842 | } | |
843 | ||
a9612d6c MC |
844 | #ifndef FIPS_MODE |
845 | if (ctx == NULL) | |
0f113f3e | 846 | ctx = new_ctx = BN_CTX_new(); |
a9612d6c MC |
847 | #endif |
848 | if (ctx == NULL) | |
849 | goto err; | |
0f113f3e MC |
850 | |
851 | BN_CTX_start(ctx); | |
0f113f3e | 852 | |
be2e334f DSH |
853 | order = EC_GROUP_get0_order(group); |
854 | if (order == NULL) | |
0f113f3e MC |
855 | goto err; |
856 | if (BN_is_zero(order)) { | |
857 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); | |
858 | goto err; | |
859 | } | |
860 | ||
861 | bits = BN_num_bits(order); | |
862 | /* | |
863 | * The following parameters mean we precompute (approximately) one point | |
864 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
865 | * bit lengths, other parameter combinations might provide better | |
866 | * efficiency. | |
867 | */ | |
868 | blocksize = 8; | |
869 | w = 4; | |
870 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
871 | /* let's not make the window too small ... */ | |
872 | w = EC_window_bits_for_scalar_size(bits); | |
873 | } | |
874 | ||
875 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
876 | * to use for wNAF | |
877 | * splitting */ | |
878 | ||
879 | pre_points_per_block = (size_t)1 << (w - 1); | |
880 | num = pre_points_per_block * numblocks; /* number of points to compute | |
881 | * and store */ | |
882 | ||
b4faea50 | 883 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
90945fa3 | 884 | if (points == NULL) { |
0f113f3e MC |
885 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
886 | goto err; | |
887 | } | |
888 | ||
889 | var = points; | |
890 | var[num] = NULL; /* pivot */ | |
891 | for (i = 0; i < num; i++) { | |
892 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
893 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
894 | goto err; | |
895 | } | |
896 | } | |
897 | ||
75ebbd9a RS |
898 | if ((tmp_point = EC_POINT_new(group)) == NULL |
899 | || (base = EC_POINT_new(group)) == NULL) { | |
0f113f3e MC |
900 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
901 | goto err; | |
902 | } | |
903 | ||
904 | if (!EC_POINT_copy(base, generator)) | |
905 | goto err; | |
906 | ||
907 | /* do the precomputation */ | |
908 | for (i = 0; i < numblocks; i++) { | |
909 | size_t j; | |
910 | ||
911 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
912 | goto err; | |
913 | ||
914 | if (!EC_POINT_copy(*var++, base)) | |
915 | goto err; | |
916 | ||
917 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
918 | /* | |
919 | * calculate odd multiples of the current base point | |
920 | */ | |
921 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
922 | goto err; | |
923 | } | |
924 | ||
925 | if (i < numblocks - 1) { | |
926 | /* | |
927 | * get the next base (multiply current one by 2^blocksize) | |
928 | */ | |
929 | size_t k; | |
930 | ||
931 | if (blocksize <= 2) { | |
932 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
933 | goto err; | |
934 | } | |
935 | ||
936 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
937 | goto err; | |
938 | for (k = 2; k < blocksize; k++) { | |
939 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
940 | goto err; | |
941 | } | |
942 | } | |
943 | } | |
944 | ||
945 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
946 | goto err; | |
947 | ||
948 | pre_comp->group = group; | |
949 | pre_comp->blocksize = blocksize; | |
950 | pre_comp->numblocks = numblocks; | |
951 | pre_comp->w = w; | |
952 | pre_comp->points = points; | |
953 | points = NULL; | |
954 | pre_comp->num = num; | |
3aef36ff | 955 | SETPRECOMP(group, ec, pre_comp); |
0f113f3e | 956 | pre_comp = NULL; |
0f113f3e | 957 | ret = 1; |
3aef36ff | 958 | |
38374911 | 959 | err: |
ce1415ed | 960 | BN_CTX_end(ctx); |
a9612d6c | 961 | #ifndef FIPS_MODE |
23a1d5e9 | 962 | BN_CTX_free(new_ctx); |
a9612d6c | 963 | #endif |
3aef36ff | 964 | EC_ec_pre_comp_free(pre_comp); |
0f113f3e MC |
965 | if (points) { |
966 | EC_POINT **p; | |
967 | ||
968 | for (p = points; *p != NULL; p++) | |
969 | EC_POINT_free(*p); | |
970 | OPENSSL_free(points); | |
971 | } | |
8fdc3734 RS |
972 | EC_POINT_free(tmp_point); |
973 | EC_POINT_free(base); | |
0f113f3e MC |
974 | return ret; |
975 | } | |
7793f30e | 976 | |
37c660ff | 977 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
0f113f3e | 978 | { |
3aef36ff | 979 | return HAVEPRECOMP(group, ec); |
0f113f3e | 980 | } |