]>
Commit | Line | Data |
---|---|---|
35b73a1f | 1 | /* |
35fd9953 | 2 | * Copyright 2001-2019 The OpenSSL Project Authors. All Rights Reserved. |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
65e81670 | 4 | * |
4f22f405 RS |
5 | * Licensed under the OpenSSL license (the "License"). You may not use |
6 | * this file except in compliance with the License. You can obtain a copy | |
7 | * in the file LICENSE in the source distribution or at | |
8 | * https://www.openssl.org/source/license.html | |
65e81670 | 9 | */ |
4f22f405 | 10 | |
28f573a2 | 11 | #include <string.h> |
48fe4d62 BM |
12 | #include <openssl/err.h> |
13 | ||
9b398ef2 | 14 | #include "internal/cryptlib.h" |
0c994d54 | 15 | #include "crypto/bn.h" |
b5acbf91 | 16 | #include "ec_local.h" |
cd420b0b | 17 | #include "internal/refcount.h" |
48fe4d62 | 18 | |
37c660ff | 19 | /* |
0d4fb843 | 20 | * This file implements the wNAF-based interleaving multi-exponentiation method |
dea0eb2c RS |
21 | * Formerly at: |
22 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp | |
23 | * You might now find it here: | |
24 | * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 | |
25 | * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf | |
26 | * For multiplication with precomputation, we use wNAF splitting, formerly at: | |
27 | * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp | |
37c660ff | 28 | */ |
48fe4d62 | 29 | |
37c660ff | 30 | /* structure for precomputed multiples of the generator */ |
3aef36ff | 31 | struct ec_pre_comp_st { |
0f113f3e MC |
32 | const EC_GROUP *group; /* parent EC_GROUP object */ |
33 | size_t blocksize; /* block size for wNAF splitting */ | |
34 | size_t numblocks; /* max. number of blocks for which we have | |
35 | * precomputation */ | |
36 | size_t w; /* window size */ | |
37 | EC_POINT **points; /* array with pre-calculated multiples of | |
38 | * generator: 'num' pointers to EC_POINT | |
39 | * objects followed by a NULL */ | |
40 | size_t num; /* numblocks * 2^(w-1) */ | |
2f545ae4 | 41 | CRYPTO_REF_COUNT references; |
9b398ef2 | 42 | CRYPTO_RWLOCK *lock; |
3aef36ff | 43 | }; |
37c660ff BM |
44 | |
45 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
0f113f3e MC |
46 | { |
47 | EC_PRE_COMP *ret = NULL; | |
48 | ||
49 | if (!group) | |
50 | return NULL; | |
51 | ||
64b25758 | 52 | ret = OPENSSL_zalloc(sizeof(*ret)); |
90945fa3 | 53 | if (ret == NULL) { |
0f113f3e MC |
54 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
55 | return ret; | |
56 | } | |
9b398ef2 | 57 | |
0f113f3e MC |
58 | ret->group = group; |
59 | ret->blocksize = 8; /* default */ | |
0f113f3e | 60 | ret->w = 4; /* default */ |
0f113f3e | 61 | ret->references = 1; |
9b398ef2 AG |
62 | |
63 | ret->lock = CRYPTO_THREAD_lock_new(); | |
64 | if (ret->lock == NULL) { | |
65 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
66 | OPENSSL_free(ret); | |
67 | return NULL; | |
68 | } | |
0f113f3e MC |
69 | return ret; |
70 | } | |
37c660ff | 71 | |
3aef36ff | 72 | EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) |
0f113f3e | 73 | { |
9b398ef2 | 74 | int i; |
3aef36ff | 75 | if (pre != NULL) |
2f545ae4 | 76 | CRYPTO_UP_REF(&pre->references, &i, pre->lock); |
3aef36ff | 77 | return pre; |
0f113f3e | 78 | } |
37c660ff | 79 | |
3aef36ff | 80 | void EC_ec_pre_comp_free(EC_PRE_COMP *pre) |
0f113f3e | 81 | { |
9b398ef2 AG |
82 | int i; |
83 | ||
84 | if (pre == NULL) | |
85 | return; | |
86 | ||
2f545ae4 | 87 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
9b398ef2 AG |
88 | REF_PRINT_COUNT("EC_ec", pre); |
89 | if (i > 0) | |
0f113f3e | 90 | return; |
9b398ef2 | 91 | REF_ASSERT_ISNT(i < 0); |
ba729265 | 92 | |
3aef36ff RS |
93 | if (pre->points != NULL) { |
94 | EC_POINT **pts; | |
37c660ff | 95 | |
3aef36ff RS |
96 | for (pts = pre->points; *pts != NULL; pts++) |
97 | EC_POINT_free(*pts); | |
0f113f3e MC |
98 | OPENSSL_free(pre->points); |
99 | } | |
9b398ef2 | 100 | CRYPTO_THREAD_lock_free(pre->lock); |
0f113f3e MC |
101 | OPENSSL_free(pre); |
102 | } | |
37c660ff | 103 | |
36bed230 | 104 | #define EC_POINT_BN_set_flags(P, flags) do { \ |
40e48e54 BB |
105 | BN_set_flags((P)->X, (flags)); \ |
106 | BN_set_flags((P)->Y, (flags)); \ | |
107 | BN_set_flags((P)->Z, (flags)); \ | |
108 | } while(0) | |
109 | ||
f4675379 | 110 | /*- |
37124360 NT |
111 | * This functions computes a single point multiplication over the EC group, |
112 | * using, at a high level, a Montgomery ladder with conditional swaps, with | |
113 | * various timing attack defenses. | |
a067a870 | 114 | * |
fe2d3975 | 115 | * It performs either a fixed point multiplication |
40e48e54 | 116 | * (scalar * generator) |
fe2d3975 | 117 | * when point is NULL, or a variable point multiplication |
40e48e54 BB |
118 | * (scalar * point) |
119 | * when point is not NULL. | |
120 | * | |
37124360 NT |
121 | * `scalar` cannot be NULL and should be in the range [0,n) otherwise all |
122 | * constant time bets are off (where n is the cardinality of the EC group). | |
40e48e54 | 123 | * |
01ad66f8 NT |
124 | * This function expects `group->order` and `group->cardinality` to be well |
125 | * defined and non-zero: it fails with an error code otherwise. | |
126 | * | |
37124360 NT |
127 | * NB: This says nothing about the constant-timeness of the ladder step |
128 | * implementation (i.e., the default implementation is based on EC_POINT_add and | |
129 | * EC_POINT_dbl, which of course are not constant time themselves) or the | |
130 | * underlying multiprecision arithmetic. | |
40e48e54 | 131 | * |
37124360 | 132 | * The product is stored in `r`. |
40e48e54 | 133 | * |
01ad66f8 NT |
134 | * This is an internal function: callers are in charge of ensuring that the |
135 | * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. | |
136 | * | |
40e48e54 BB |
137 | * Returns 1 on success, 0 otherwise. |
138 | */ | |
37124360 NT |
139 | int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, |
140 | const BIGNUM *scalar, const EC_POINT *point, | |
141 | BN_CTX *ctx) | |
40e48e54 | 142 | { |
a766aab9 | 143 | int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; |
37124360 | 144 | EC_POINT *p = NULL; |
40e48e54 BB |
145 | EC_POINT *s = NULL; |
146 | BIGNUM *k = NULL; | |
147 | BIGNUM *lambda = NULL; | |
a766aab9 | 148 | BIGNUM *cardinality = NULL; |
36bed230 | 149 | int ret = 0; |
40e48e54 | 150 | |
37124360 NT |
151 | /* early exit if the input point is the point at infinity */ |
152 | if (point != NULL && EC_POINT_is_at_infinity(group, point)) | |
153 | return EC_POINT_set_to_infinity(group, r); | |
154 | ||
01ad66f8 NT |
155 | if (BN_is_zero(group->order)) { |
156 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER); | |
7d859d1c | 157 | return 0; |
01ad66f8 NT |
158 | } |
159 | if (BN_is_zero(group->cofactor)) { | |
160 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR); | |
161 | return 0; | |
162 | } | |
7d859d1c AP |
163 | |
164 | BN_CTX_start(ctx); | |
40e48e54 | 165 | |
37124360 NT |
166 | if (((p = EC_POINT_new(group)) == NULL) |
167 | || ((s = EC_POINT_new(group)) == NULL)) { | |
168 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); | |
40e48e54 | 169 | goto err; |
37124360 | 170 | } |
40e48e54 BB |
171 | |
172 | if (point == NULL) { | |
37124360 NT |
173 | if (!EC_POINT_copy(p, group->generator)) { |
174 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); | |
40e48e54 | 175 | goto err; |
37124360 | 176 | } |
40e48e54 | 177 | } else { |
37124360 NT |
178 | if (!EC_POINT_copy(p, point)) { |
179 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); | |
40e48e54 | 180 | goto err; |
37124360 | 181 | } |
40e48e54 BB |
182 | } |
183 | ||
37124360 NT |
184 | EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME); |
185 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME); | |
36bed230 | 186 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME); |
40e48e54 | 187 | |
a766aab9 | 188 | cardinality = BN_CTX_get(ctx); |
40e48e54 BB |
189 | lambda = BN_CTX_get(ctx); |
190 | k = BN_CTX_get(ctx); | |
37124360 NT |
191 | if (k == NULL) { |
192 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE); | |
193 | goto err; | |
194 | } | |
195 | ||
196 | if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) { | |
197 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 198 | goto err; |
37124360 | 199 | } |
40e48e54 BB |
200 | |
201 | /* | |
a766aab9 | 202 | * Group cardinalities are often on a word boundary. |
40e48e54 BB |
203 | * So when we pad the scalar, some timing diff might |
204 | * pop if it needs to be expanded due to carries. | |
205 | * So expand ahead of time. | |
206 | */ | |
a766aab9 BB |
207 | cardinality_bits = BN_num_bits(cardinality); |
208 | group_top = bn_get_top(cardinality); | |
b1d6d55e P |
209 | if ((bn_wexpand(k, group_top + 2) == NULL) |
210 | || (bn_wexpand(lambda, group_top + 2) == NULL)) { | |
37124360 | 211 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); |
40e48e54 | 212 | goto err; |
37124360 | 213 | } |
40e48e54 | 214 | |
37124360 NT |
215 | if (!BN_copy(k, scalar)) { |
216 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 217 | goto err; |
37124360 | 218 | } |
40e48e54 BB |
219 | |
220 | BN_set_flags(k, BN_FLG_CONSTTIME); | |
221 | ||
a766aab9 | 222 | if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) { |
f4675379 | 223 | /*- |
40e48e54 BB |
224 | * this is an unusual input, and we don't guarantee |
225 | * constant-timeness | |
226 | */ | |
37124360 NT |
227 | if (!BN_nnmod(k, k, cardinality, ctx)) { |
228 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 229 | goto err; |
37124360 | 230 | } |
40e48e54 BB |
231 | } |
232 | ||
37124360 NT |
233 | if (!BN_add(lambda, k, cardinality)) { |
234 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 235 | goto err; |
37124360 | 236 | } |
40e48e54 | 237 | BN_set_flags(lambda, BN_FLG_CONSTTIME); |
37124360 NT |
238 | if (!BN_add(k, lambda, cardinality)) { |
239 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 240 | goto err; |
37124360 | 241 | } |
40e48e54 | 242 | /* |
a766aab9 BB |
243 | * lambda := scalar + cardinality |
244 | * k := scalar + 2*cardinality | |
40e48e54 | 245 | */ |
a766aab9 | 246 | kbit = BN_is_bit_set(lambda, cardinality_bits); |
b1d6d55e | 247 | BN_consttime_swap(kbit, k, lambda, group_top + 2); |
40e48e54 BB |
248 | |
249 | group_top = bn_get_top(group->field); | |
250 | if ((bn_wexpand(s->X, group_top) == NULL) | |
251 | || (bn_wexpand(s->Y, group_top) == NULL) | |
252 | || (bn_wexpand(s->Z, group_top) == NULL) | |
253 | || (bn_wexpand(r->X, group_top) == NULL) | |
254 | || (bn_wexpand(r->Y, group_top) == NULL) | |
37124360 NT |
255 | || (bn_wexpand(r->Z, group_top) == NULL) |
256 | || (bn_wexpand(p->X, group_top) == NULL) | |
257 | || (bn_wexpand(p->Y, group_top) == NULL) | |
258 | || (bn_wexpand(p->Z, group_top) == NULL)) { | |
259 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB); | |
40e48e54 | 260 | goto err; |
37124360 | 261 | } |
40e48e54 | 262 | |
f667820c SH |
263 | /*- |
264 | * Apply coordinate blinding for EC_POINT. | |
265 | * | |
266 | * The underlying EC_METHOD can optionally implement this function: | |
267 | * ec_point_blind_coordinates() returns 0 in case of errors or 1 on | |
268 | * success or if coordinate blinding is not implemented for this | |
269 | * group. | |
270 | */ | |
37124360 NT |
271 | if (!ec_point_blind_coordinates(group, p, ctx)) { |
272 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE); | |
40e48e54 | 273 | goto err; |
37124360 | 274 | } |
40e48e54 | 275 | |
37124360 NT |
276 | /* Initialize the Montgomery ladder */ |
277 | if (!ec_point_ladder_pre(group, r, s, p, ctx)) { | |
278 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE); | |
40e48e54 | 279 | goto err; |
37124360 | 280 | } |
40e48e54 | 281 | |
37124360 NT |
282 | /* top bit is a 1, in a fixed pos */ |
283 | pbit = 1; | |
40e48e54 BB |
284 | |
285 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |
286 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ | |
287 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ | |
288 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ | |
289 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |
290 | (a)->Z_is_one ^= (t); \ | |
291 | (b)->Z_is_one ^= (t); \ | |
292 | } while(0) | |
293 | ||
f4675379 | 294 | /*- |
a067a870 BB |
295 | * The ladder step, with branches, is |
296 | * | |
297 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
298 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
299 | * | |
300 | * Swapping R, S conditionally on k[i] leaves you with state | |
301 | * | |
302 | * k[i] == 0: T, U = R, S | |
303 | * k[i] == 1: T, U = S, R | |
304 | * | |
305 | * Then perform the ECC ops. | |
306 | * | |
307 | * U = add(T, U) | |
308 | * T = dbl(T) | |
309 | * | |
310 | * Which leaves you with state | |
311 | * | |
312 | * k[i] == 0: U = add(R, S), T = dbl(R) | |
313 | * k[i] == 1: U = add(S, R), T = dbl(S) | |
314 | * | |
315 | * Swapping T, U conditionally on k[i] leaves you with state | |
316 | * | |
317 | * k[i] == 0: R, S = T, U | |
318 | * k[i] == 1: R, S = U, T | |
319 | * | |
320 | * Which leaves you with state | |
321 | * | |
322 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
323 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
324 | * | |
325 | * So we get the same logic, but instead of a branch it's a | |
326 | * conditional swap, followed by ECC ops, then another conditional swap. | |
327 | * | |
328 | * Optimization: The end of iteration i and start of i-1 looks like | |
329 | * | |
330 | * ... | |
331 | * CSWAP(k[i], R, S) | |
332 | * ECC | |
333 | * CSWAP(k[i], R, S) | |
334 | * (next iteration) | |
335 | * CSWAP(k[i-1], R, S) | |
336 | * ECC | |
337 | * CSWAP(k[i-1], R, S) | |
338 | * ... | |
339 | * | |
340 | * So instead of two contiguous swaps, you can merge the condition | |
341 | * bits and do a single swap. | |
342 | * | |
f4675379 NT |
343 | * k[i] k[i-1] Outcome |
344 | * 0 0 No Swap | |
345 | * 0 1 Swap | |
346 | * 1 0 Swap | |
347 | * 1 1 No Swap | |
a067a870 BB |
348 | * |
349 | * This is XOR. pbit tracks the previous bit of k. | |
350 | */ | |
351 | ||
a766aab9 | 352 | for (i = cardinality_bits - 1; i >= 0; i--) { |
40e48e54 BB |
353 | kbit = BN_is_bit_set(k, i) ^ pbit; |
354 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |
37124360 NT |
355 | |
356 | /* Perform a single step of the Montgomery ladder */ | |
357 | if (!ec_point_ladder_step(group, r, s, p, ctx)) { | |
358 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE); | |
40e48e54 | 359 | goto err; |
37124360 | 360 | } |
40e48e54 BB |
361 | /* |
362 | * pbit logic merges this cswap with that of the | |
363 | * next iteration | |
364 | */ | |
365 | pbit ^= kbit; | |
366 | } | |
367 | /* one final cswap to move the right value into r */ | |
368 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |
369 | #undef EC_POINT_CSWAP | |
370 | ||
37124360 NT |
371 | /* Finalize ladder (and recover full point coordinates) */ |
372 | if (!ec_point_ladder_post(group, r, s, p, ctx)) { | |
373 | ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE); | |
374 | goto err; | |
375 | } | |
376 | ||
40e48e54 BB |
377 | ret = 1; |
378 | ||
f4675379 | 379 | err: |
37124360 | 380 | EC_POINT_free(p); |
202f7c56 | 381 | EC_POINT_clear_free(s); |
40e48e54 | 382 | BN_CTX_end(ctx); |
40e48e54 BB |
383 | |
384 | return ret; | |
385 | } | |
f4675379 | 386 | |
36bed230 | 387 | #undef EC_POINT_BN_set_flags |
40e48e54 | 388 | |
0f113f3e MC |
389 | /* |
390 | * TODO: table should be optimised for the wNAF-based implementation, | |
391 | * sometimes smaller windows will give better performance (thus the | |
392 | * boundaries should be increased) | |
c05940ed | 393 | */ |
3ba1f111 | 394 | #define EC_window_bits_for_scalar_size(b) \ |
0f113f3e MC |
395 | ((size_t) \ |
396 | ((b) >= 2000 ? 6 : \ | |
397 | (b) >= 800 ? 5 : \ | |
398 | (b) >= 300 ? 4 : \ | |
399 | (b) >= 70 ? 3 : \ | |
400 | (b) >= 20 ? 2 : \ | |
401 | 1)) | |
3ba1f111 | 402 | |
c80fd6b2 MC |
403 | /*- |
404 | * Compute | |
3ba1f111 BM |
405 | * \sum scalars[i]*points[i], |
406 | * also including | |
407 | * scalar*generator | |
408 | * in the addition if scalar != NULL | |
409 | */ | |
7793f30e | 410 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
0f113f3e MC |
411 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
412 | BN_CTX *ctx) | |
413 | { | |
0f113f3e MC |
414 | const EC_POINT *generator = NULL; |
415 | EC_POINT *tmp = NULL; | |
416 | size_t totalnum; | |
417 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
418 | size_t pre_points_per_block = 0; | |
419 | size_t i, j; | |
420 | int k; | |
421 | int r_is_inverted = 0; | |
422 | int r_is_at_infinity = 1; | |
423 | size_t *wsize = NULL; /* individual window sizes */ | |
424 | signed char **wNAF = NULL; /* individual wNAFs */ | |
425 | size_t *wNAF_len = NULL; | |
426 | size_t max_len = 0; | |
427 | size_t num_val; | |
428 | EC_POINT **val = NULL; /* precomputation */ | |
429 | EC_POINT **v; | |
430 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
431 | * 'pre_comp->points' */ | |
432 | const EC_PRE_COMP *pre_comp = NULL; | |
433 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be | |
434 | * treated like other scalars, i.e. | |
435 | * precomputation is not available */ | |
436 | int ret = 0; | |
437 | ||
de72274d | 438 | if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) { |
f4675379 | 439 | /*- |
37124360 NT |
440 | * Handle the common cases where the scalar is secret, enforcing a |
441 | * scalar multiplication implementation based on a Montgomery ladder, | |
442 | * with various timing attack defenses. | |
36bed230 | 443 | */ |
e861d659 | 444 | if ((scalar != group->order) && (scalar != NULL) && (num == 0)) { |
de72274d BB |
445 | /*- |
446 | * In this case we want to compute scalar * GeneratorPoint: this | |
37124360 NT |
447 | * codepath is reached most prominently by (ephemeral) key |
448 | * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, | |
449 | * ECDH keygen/first half), where the scalar is always secret. This | |
450 | * is why we ignore if BN_FLG_CONSTTIME is actually set and we | |
451 | * always call the ladder version. | |
de72274d | 452 | */ |
37124360 | 453 | return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); |
de72274d | 454 | } |
e861d659 | 455 | if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) { |
de72274d | 456 | /*- |
37124360 NT |
457 | * In this case we want to compute scalar * VariablePoint: this |
458 | * codepath is reached most prominently by the second half of ECDH, | |
459 | * where the secret scalar is multiplied by the peer's public point. | |
460 | * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is | |
461 | * actually set and we always call the ladder version. | |
de72274d | 462 | */ |
37124360 | 463 | return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); |
de72274d | 464 | } |
36bed230 NT |
465 | } |
466 | ||
0f113f3e MC |
467 | if (scalar != NULL) { |
468 | generator = EC_GROUP_get0_generator(group); | |
469 | if (generator == NULL) { | |
470 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); | |
471 | goto err; | |
472 | } | |
473 | ||
474 | /* look if we can use precomputed multiples of generator */ | |
475 | ||
3aef36ff | 476 | pre_comp = group->pre_comp.ec; |
0f113f3e MC |
477 | if (pre_comp && pre_comp->numblocks |
478 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
479 | 0)) { | |
480 | blocksize = pre_comp->blocksize; | |
481 | ||
482 | /* | |
483 | * determine maximum number of blocks that wNAF splitting may | |
484 | * yield (NB: maximum wNAF length is bit length plus one) | |
485 | */ | |
486 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
487 | ||
488 | /* | |
489 | * we cannot use more blocks than we have precomputation for | |
490 | */ | |
491 | if (numblocks > pre_comp->numblocks) | |
492 | numblocks = pre_comp->numblocks; | |
493 | ||
494 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
495 | ||
496 | /* check that pre_comp looks sane */ | |
497 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
498 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
499 | goto err; | |
500 | } | |
501 | } else { | |
502 | /* can't use precomputation */ | |
503 | pre_comp = NULL; | |
504 | numblocks = 1; | |
505 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
506 | * 'scalars' */ | |
507 | } | |
508 | } | |
509 | ||
510 | totalnum = num + numblocks; | |
511 | ||
cbe29648 RS |
512 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
513 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); | |
514 | /* include space for pivot */ | |
515 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); | |
516 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); | |
0f113f3e MC |
517 | |
518 | /* Ensure wNAF is initialised in case we end up going to err */ | |
90945fa3 | 519 | if (wNAF != NULL) |
0f113f3e MC |
520 | wNAF[0] = NULL; /* preliminary pivot */ |
521 | ||
90945fa3 | 522 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { |
0f113f3e MC |
523 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
524 | goto err; | |
525 | } | |
526 | ||
527 | /* | |
528 | * num_val will be the total number of temporarily precomputed points | |
529 | */ | |
530 | num_val = 0; | |
531 | ||
532 | for (i = 0; i < num + num_scalar; i++) { | |
533 | size_t bits; | |
534 | ||
535 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
536 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
537 | num_val += (size_t)1 << (wsize[i] - 1); | |
538 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
539 | wNAF[i] = | |
540 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
541 | &wNAF_len[i]); | |
542 | if (wNAF[i] == NULL) | |
543 | goto err; | |
544 | if (wNAF_len[i] > max_len) | |
545 | max_len = wNAF_len[i]; | |
546 | } | |
547 | ||
548 | if (numblocks) { | |
549 | /* we go here iff scalar != NULL */ | |
550 | ||
551 | if (pre_comp == NULL) { | |
552 | if (num_scalar != 1) { | |
553 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
554 | goto err; | |
555 | } | |
556 | /* we have already generated a wNAF for 'scalar' */ | |
557 | } else { | |
558 | signed char *tmp_wNAF = NULL; | |
559 | size_t tmp_len = 0; | |
560 | ||
561 | if (num_scalar != 0) { | |
562 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
563 | goto err; | |
564 | } | |
565 | ||
566 | /* | |
567 | * use the window size for which we have precomputation | |
568 | */ | |
569 | wsize[num] = pre_comp->w; | |
570 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
571 | if (!tmp_wNAF) | |
572 | goto err; | |
573 | ||
574 | if (tmp_len <= max_len) { | |
575 | /* | |
576 | * One of the other wNAFs is at least as long as the wNAF | |
577 | * belonging to the generator, so wNAF splitting will not buy | |
578 | * us anything. | |
579 | */ | |
580 | ||
581 | numblocks = 1; | |
582 | totalnum = num + 1; /* don't use wNAF splitting */ | |
583 | wNAF[num] = tmp_wNAF; | |
584 | wNAF[num + 1] = NULL; | |
585 | wNAF_len[num] = tmp_len; | |
0f113f3e MC |
586 | /* |
587 | * pre_comp->points starts with the points that we need here: | |
588 | */ | |
589 | val_sub[num] = pre_comp->points; | |
590 | } else { | |
591 | /* | |
592 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
593 | * splitting and include the blocks | |
594 | */ | |
595 | ||
596 | signed char *pp; | |
597 | EC_POINT **tmp_points; | |
598 | ||
599 | if (tmp_len < numblocks * blocksize) { | |
600 | /* | |
601 | * possibly we can do with fewer blocks than estimated | |
602 | */ | |
603 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
604 | if (numblocks > pre_comp->numblocks) { | |
605 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 606 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
607 | goto err; |
608 | } | |
609 | totalnum = num + numblocks; | |
610 | } | |
611 | ||
612 | /* split wNAF in 'numblocks' parts */ | |
613 | pp = tmp_wNAF; | |
614 | tmp_points = pre_comp->points; | |
615 | ||
616 | for (i = num; i < totalnum; i++) { | |
617 | if (i < totalnum - 1) { | |
618 | wNAF_len[i] = blocksize; | |
619 | if (tmp_len < blocksize) { | |
620 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
0e9eb1a5 | 621 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
622 | goto err; |
623 | } | |
624 | tmp_len -= blocksize; | |
625 | } else | |
626 | /* | |
627 | * last block gets whatever is left (this could be | |
628 | * more or less than 'blocksize'!) | |
629 | */ | |
630 | wNAF_len[i] = tmp_len; | |
631 | ||
632 | wNAF[i + 1] = NULL; | |
633 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
634 | if (wNAF[i] == NULL) { | |
635 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
636 | OPENSSL_free(tmp_wNAF); | |
637 | goto err; | |
638 | } | |
639 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
640 | if (wNAF_len[i] > max_len) | |
641 | max_len = wNAF_len[i]; | |
642 | ||
643 | if (*tmp_points == NULL) { | |
644 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
645 | OPENSSL_free(tmp_wNAF); | |
646 | goto err; | |
647 | } | |
648 | val_sub[i] = tmp_points; | |
649 | tmp_points += pre_points_per_block; | |
650 | pp += blocksize; | |
651 | } | |
652 | OPENSSL_free(tmp_wNAF); | |
653 | } | |
654 | } | |
655 | } | |
656 | ||
657 | /* | |
658 | * All points we precompute now go into a single array 'val'. | |
659 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
660 | * subarray of 'pre_comp->points' if we already have precomputation. | |
661 | */ | |
cbe29648 | 662 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
0f113f3e MC |
663 | if (val == NULL) { |
664 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); | |
665 | goto err; | |
666 | } | |
667 | val[num_val] = NULL; /* pivot element */ | |
668 | ||
669 | /* allocate points for precomputation */ | |
670 | v = val; | |
671 | for (i = 0; i < num + num_scalar; i++) { | |
672 | val_sub[i] = v; | |
673 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
674 | *v = EC_POINT_new(group); | |
675 | if (*v == NULL) | |
676 | goto err; | |
677 | v++; | |
678 | } | |
679 | } | |
680 | if (!(v == val + num_val)) { | |
681 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); | |
682 | goto err; | |
683 | } | |
684 | ||
75ebbd9a | 685 | if ((tmp = EC_POINT_new(group)) == NULL) |
0f113f3e MC |
686 | goto err; |
687 | ||
50e735f9 MC |
688 | /*- |
689 | * prepare precomputed values: | |
690 | * val_sub[i][0] := points[i] | |
691 | * val_sub[i][1] := 3 * points[i] | |
692 | * val_sub[i][2] := 5 * points[i] | |
693 | * ... | |
694 | */ | |
0f113f3e MC |
695 | for (i = 0; i < num + num_scalar; i++) { |
696 | if (i < num) { | |
697 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
698 | goto err; | |
699 | } else { | |
700 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
701 | goto err; | |
702 | } | |
703 | ||
704 | if (wsize[i] > 1) { | |
705 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
706 | goto err; | |
707 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
708 | if (!EC_POINT_add | |
709 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
710 | goto err; | |
711 | } | |
712 | } | |
713 | } | |
714 | ||
0f113f3e MC |
715 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
716 | goto err; | |
3ba1f111 | 717 | |
0f113f3e MC |
718 | r_is_at_infinity = 1; |
719 | ||
720 | for (k = max_len - 1; k >= 0; k--) { | |
721 | if (!r_is_at_infinity) { | |
722 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
723 | goto err; | |
724 | } | |
725 | ||
726 | for (i = 0; i < totalnum; i++) { | |
727 | if (wNAF_len[i] > (size_t)k) { | |
728 | int digit = wNAF[i][k]; | |
729 | int is_neg; | |
730 | ||
731 | if (digit) { | |
732 | is_neg = digit < 0; | |
733 | ||
734 | if (is_neg) | |
735 | digit = -digit; | |
736 | ||
737 | if (is_neg != r_is_inverted) { | |
738 | if (!r_is_at_infinity) { | |
739 | if (!EC_POINT_invert(group, r, ctx)) | |
740 | goto err; | |
741 | } | |
742 | r_is_inverted = !r_is_inverted; | |
743 | } | |
744 | ||
745 | /* digit > 0 */ | |
746 | ||
747 | if (r_is_at_infinity) { | |
748 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
749 | goto err; | |
750 | r_is_at_infinity = 0; | |
751 | } else { | |
752 | if (!EC_POINT_add | |
753 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
754 | goto err; | |
755 | } | |
756 | } | |
757 | } | |
758 | } | |
759 | } | |
760 | ||
761 | if (r_is_at_infinity) { | |
762 | if (!EC_POINT_set_to_infinity(group, r)) | |
763 | goto err; | |
764 | } else { | |
765 | if (r_is_inverted) | |
766 | if (!EC_POINT_invert(group, r, ctx)) | |
767 | goto err; | |
768 | } | |
769 | ||
770 | ret = 1; | |
3ba1f111 BM |
771 | |
772 | err: | |
8fdc3734 | 773 | EC_POINT_free(tmp); |
b548a1f1 RS |
774 | OPENSSL_free(wsize); |
775 | OPENSSL_free(wNAF_len); | |
0f113f3e MC |
776 | if (wNAF != NULL) { |
777 | signed char **w; | |
778 | ||
779 | for (w = wNAF; *w != NULL; w++) | |
780 | OPENSSL_free(*w); | |
781 | ||
782 | OPENSSL_free(wNAF); | |
783 | } | |
784 | if (val != NULL) { | |
785 | for (v = val; *v != NULL; v++) | |
786 | EC_POINT_clear_free(*v); | |
787 | ||
788 | OPENSSL_free(val); | |
789 | } | |
b548a1f1 | 790 | OPENSSL_free(val_sub); |
0f113f3e MC |
791 | return ret; |
792 | } | |
38374911 | 793 | |
1d97c843 TH |
794 | /*- |
795 | * ec_wNAF_precompute_mult() | |
37c660ff BM |
796 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
797 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). | |
0f113f3e | 798 | * |
37c660ff BM |
799 | * 'pre_comp->points' is an array of multiples of the generator |
800 | * of the following form: | |
801 | * points[0] = generator; | |
802 | * points[1] = 3 * generator; | |
803 | * ... | |
804 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
805 | * points[2^(w-1)] = 2^blocksize * generator; | |
806 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
807 | * ... | |
808 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
809 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
810 | * ... | |
811 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
812 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 813 | */ |
7793f30e | 814 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
815 | { |
816 | const EC_POINT *generator; | |
817 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
818 | BN_CTX *new_ctx = NULL; | |
be2e334f | 819 | const BIGNUM *order; |
0f113f3e MC |
820 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
821 | EC_POINT **points = NULL; | |
822 | EC_PRE_COMP *pre_comp; | |
823 | int ret = 0; | |
824 | ||
825 | /* if there is an old EC_PRE_COMP object, throw it away */ | |
2c52ac9b | 826 | EC_pre_comp_free(group); |
0f113f3e MC |
827 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
828 | return 0; | |
829 | ||
830 | generator = EC_GROUP_get0_generator(group); | |
831 | if (generator == NULL) { | |
832 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); | |
833 | goto err; | |
834 | } | |
835 | ||
836 | if (ctx == NULL) { | |
837 | ctx = new_ctx = BN_CTX_new(); | |
838 | if (ctx == NULL) | |
839 | goto err; | |
840 | } | |
841 | ||
842 | BN_CTX_start(ctx); | |
0f113f3e | 843 | |
be2e334f DSH |
844 | order = EC_GROUP_get0_order(group); |
845 | if (order == NULL) | |
0f113f3e MC |
846 | goto err; |
847 | if (BN_is_zero(order)) { | |
848 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); | |
849 | goto err; | |
850 | } | |
851 | ||
852 | bits = BN_num_bits(order); | |
853 | /* | |
854 | * The following parameters mean we precompute (approximately) one point | |
855 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
856 | * bit lengths, other parameter combinations might provide better | |
857 | * efficiency. | |
858 | */ | |
859 | blocksize = 8; | |
860 | w = 4; | |
861 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
862 | /* let's not make the window too small ... */ | |
863 | w = EC_window_bits_for_scalar_size(bits); | |
864 | } | |
865 | ||
866 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
867 | * to use for wNAF | |
868 | * splitting */ | |
869 | ||
870 | pre_points_per_block = (size_t)1 << (w - 1); | |
871 | num = pre_points_per_block * numblocks; /* number of points to compute | |
872 | * and store */ | |
873 | ||
b4faea50 | 874 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
90945fa3 | 875 | if (points == NULL) { |
0f113f3e MC |
876 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
877 | goto err; | |
878 | } | |
879 | ||
880 | var = points; | |
881 | var[num] = NULL; /* pivot */ | |
882 | for (i = 0; i < num; i++) { | |
883 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
884 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); | |
885 | goto err; | |
886 | } | |
887 | } | |
888 | ||
75ebbd9a RS |
889 | if ((tmp_point = EC_POINT_new(group)) == NULL |
890 | || (base = EC_POINT_new(group)) == NULL) { | |
0f113f3e MC |
891 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
892 | goto err; | |
893 | } | |
894 | ||
895 | if (!EC_POINT_copy(base, generator)) | |
896 | goto err; | |
897 | ||
898 | /* do the precomputation */ | |
899 | for (i = 0; i < numblocks; i++) { | |
900 | size_t j; | |
901 | ||
902 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
903 | goto err; | |
904 | ||
905 | if (!EC_POINT_copy(*var++, base)) | |
906 | goto err; | |
907 | ||
908 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
909 | /* | |
910 | * calculate odd multiples of the current base point | |
911 | */ | |
912 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
913 | goto err; | |
914 | } | |
915 | ||
916 | if (i < numblocks - 1) { | |
917 | /* | |
918 | * get the next base (multiply current one by 2^blocksize) | |
919 | */ | |
920 | size_t k; | |
921 | ||
922 | if (blocksize <= 2) { | |
923 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); | |
924 | goto err; | |
925 | } | |
926 | ||
927 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
928 | goto err; | |
929 | for (k = 2; k < blocksize; k++) { | |
930 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
931 | goto err; | |
932 | } | |
933 | } | |
934 | } | |
935 | ||
936 | if (!EC_POINTs_make_affine(group, num, points, ctx)) | |
937 | goto err; | |
938 | ||
939 | pre_comp->group = group; | |
940 | pre_comp->blocksize = blocksize; | |
941 | pre_comp->numblocks = numblocks; | |
942 | pre_comp->w = w; | |
943 | pre_comp->points = points; | |
944 | points = NULL; | |
945 | pre_comp->num = num; | |
3aef36ff | 946 | SETPRECOMP(group, ec, pre_comp); |
0f113f3e | 947 | pre_comp = NULL; |
0f113f3e | 948 | ret = 1; |
3aef36ff | 949 | |
38374911 | 950 | err: |
c8a9fa69 | 951 | BN_CTX_end(ctx); |
23a1d5e9 | 952 | BN_CTX_free(new_ctx); |
3aef36ff | 953 | EC_ec_pre_comp_free(pre_comp); |
0f113f3e MC |
954 | if (points) { |
955 | EC_POINT **p; | |
956 | ||
957 | for (p = points; *p != NULL; p++) | |
958 | EC_POINT_free(*p); | |
959 | OPENSSL_free(points); | |
960 | } | |
8fdc3734 RS |
961 | EC_POINT_free(tmp_point); |
962 | EC_POINT_free(base); | |
0f113f3e MC |
963 | return ret; |
964 | } | |
7793f30e | 965 | |
37c660ff | 966 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
0f113f3e | 967 | { |
3aef36ff | 968 | return HAVEPRECOMP(group, ec); |
0f113f3e | 969 | } |