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35b73a1f | 1 | /* |
da1c088f | 2 | * Copyright 2001-2023 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; |
3aef36ff | 48 | }; |
37c660ff BM |
49 | |
50 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) | |
0f113f3e MC |
51 | { |
52 | EC_PRE_COMP *ret = NULL; | |
53 | ||
54 | if (!group) | |
55 | return NULL; | |
56 | ||
64b25758 | 57 | ret = OPENSSL_zalloc(sizeof(*ret)); |
e077455e | 58 | if (ret == NULL) |
0f113f3e | 59 | return ret; |
9b398ef2 | 60 | |
0f113f3e MC |
61 | ret->group = group; |
62 | ret->blocksize = 8; /* default */ | |
0f113f3e | 63 | ret->w = 4; /* default */ |
9b398ef2 | 64 | |
1353736b | 65 | if (!CRYPTO_NEW_REF(&ret->references, 1)) { |
9b398ef2 AG |
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) |
1353736b | 76 | CRYPTO_UP_REF(&pre->references, &i); |
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 | ||
1353736b | 87 | CRYPTO_DOWN_REF(&pre->references, &i); |
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 | } | |
1353736b | 100 | CRYPTO_FREE_REF(&pre->references); |
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 | */ | |
32ab57cb SL |
139 | int ossl_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 | 155 | if (BN_is_zero(group->order)) { |
9311d0c4 | 156 | ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER); |
7d859d1c | 157 | return 0; |
01ad66f8 | 158 | } |
ac2b52c6 | 159 | if (BN_is_zero(group->cofactor)) { |
9311d0c4 | 160 | ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_COFACTOR); |
01ad66f8 NT |
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)) { | |
e077455e | 168 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
40e48e54 | 169 | goto err; |
37124360 | 170 | } |
40e48e54 BB |
171 | |
172 | if (point == NULL) { | |
37124360 | 173 | if (!EC_POINT_copy(p, group->generator)) { |
9311d0c4 | 174 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
40e48e54 | 175 | goto err; |
37124360 | 176 | } |
40e48e54 | 177 | } else { |
37124360 | 178 | if (!EC_POINT_copy(p, point)) { |
9311d0c4 | 179 | ERR_raise(ERR_LIB_EC, 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 | 191 | if (k == NULL) { |
e077455e | 192 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
37124360 NT |
193 | goto err; |
194 | } | |
195 | ||
196 | if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) { | |
9311d0c4 | 197 | ERR_raise(ERR_LIB_EC, 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); | |
99540ec7 P |
209 | if ((bn_wexpand(k, group_top + 2) == NULL) |
210 | || (bn_wexpand(lambda, group_top + 2) == NULL)) { | |
9311d0c4 | 211 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
40e48e54 | 212 | goto err; |
37124360 | 213 | } |
40e48e54 | 214 | |
37124360 | 215 | if (!BN_copy(k, scalar)) { |
9311d0c4 | 216 | ERR_raise(ERR_LIB_EC, 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 | 227 | if (!BN_nnmod(k, k, cardinality, ctx)) { |
9311d0c4 | 228 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
40e48e54 | 229 | goto err; |
37124360 | 230 | } |
40e48e54 BB |
231 | } |
232 | ||
37124360 | 233 | if (!BN_add(lambda, k, cardinality)) { |
9311d0c4 | 234 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
40e48e54 | 235 | goto err; |
37124360 | 236 | } |
40e48e54 | 237 | BN_set_flags(lambda, BN_FLG_CONSTTIME); |
37124360 | 238 | if (!BN_add(k, lambda, cardinality)) { |
9311d0c4 | 239 | ERR_raise(ERR_LIB_EC, 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); |
99540ec7 | 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)) { | |
9311d0c4 | 259 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
40e48e54 | 260 | goto err; |
37124360 | 261 | } |
40e48e54 | 262 | |
a4a93bbf | 263 | /* ensure input point is in affine coords for ladder step efficiency */ |
c2f2db9b BB |
264 | if (!p->Z_is_one && (group->meth->make_affine == NULL |
265 | || !group->meth->make_affine(group, p, ctx))) { | |
9311d0c4 | 266 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
a4a93bbf | 267 | goto err; |
37124360 | 268 | } |
40e48e54 | 269 | |
37124360 NT |
270 | /* Initialize the Montgomery ladder */ |
271 | if (!ec_point_ladder_pre(group, r, s, p, ctx)) { | |
9311d0c4 | 272 | ERR_raise(ERR_LIB_EC, EC_R_LADDER_PRE_FAILURE); |
40e48e54 | 273 | goto err; |
37124360 | 274 | } |
40e48e54 | 275 | |
37124360 NT |
276 | /* top bit is a 1, in a fixed pos */ |
277 | pbit = 1; | |
40e48e54 BB |
278 | |
279 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |
280 | BN_consttime_swap(c, (a)->X, (b)->X, w); \ | |
281 | BN_consttime_swap(c, (a)->Y, (b)->Y, w); \ | |
282 | BN_consttime_swap(c, (a)->Z, (b)->Z, w); \ | |
283 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |
284 | (a)->Z_is_one ^= (t); \ | |
285 | (b)->Z_is_one ^= (t); \ | |
286 | } while(0) | |
287 | ||
f4675379 | 288 | /*- |
a067a870 BB |
289 | * The ladder step, with branches, is |
290 | * | |
291 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
292 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
293 | * | |
294 | * Swapping R, S conditionally on k[i] leaves you with state | |
295 | * | |
296 | * k[i] == 0: T, U = R, S | |
297 | * k[i] == 1: T, U = S, R | |
298 | * | |
299 | * Then perform the ECC ops. | |
300 | * | |
301 | * U = add(T, U) | |
302 | * T = dbl(T) | |
303 | * | |
304 | * Which leaves you with state | |
305 | * | |
306 | * k[i] == 0: U = add(R, S), T = dbl(R) | |
307 | * k[i] == 1: U = add(S, R), T = dbl(S) | |
308 | * | |
309 | * Swapping T, U conditionally on k[i] leaves you with state | |
310 | * | |
311 | * k[i] == 0: R, S = T, U | |
312 | * k[i] == 1: R, S = U, T | |
313 | * | |
314 | * Which leaves you with state | |
315 | * | |
316 | * k[i] == 0: S = add(R, S), R = dbl(R) | |
317 | * k[i] == 1: R = add(S, R), S = dbl(S) | |
318 | * | |
319 | * So we get the same logic, but instead of a branch it's a | |
320 | * conditional swap, followed by ECC ops, then another conditional swap. | |
321 | * | |
322 | * Optimization: The end of iteration i and start of i-1 looks like | |
323 | * | |
324 | * ... | |
325 | * CSWAP(k[i], R, S) | |
326 | * ECC | |
327 | * CSWAP(k[i], R, S) | |
328 | * (next iteration) | |
329 | * CSWAP(k[i-1], R, S) | |
330 | * ECC | |
331 | * CSWAP(k[i-1], R, S) | |
332 | * ... | |
333 | * | |
334 | * So instead of two contiguous swaps, you can merge the condition | |
335 | * bits and do a single swap. | |
336 | * | |
f4675379 NT |
337 | * k[i] k[i-1] Outcome |
338 | * 0 0 No Swap | |
339 | * 0 1 Swap | |
340 | * 1 0 Swap | |
341 | * 1 1 No Swap | |
a067a870 BB |
342 | * |
343 | * This is XOR. pbit tracks the previous bit of k. | |
344 | */ | |
345 | ||
a766aab9 | 346 | for (i = cardinality_bits - 1; i >= 0; i--) { |
40e48e54 BB |
347 | kbit = BN_is_bit_set(k, i) ^ pbit; |
348 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |
37124360 NT |
349 | |
350 | /* Perform a single step of the Montgomery ladder */ | |
351 | if (!ec_point_ladder_step(group, r, s, p, ctx)) { | |
9311d0c4 | 352 | ERR_raise(ERR_LIB_EC, EC_R_LADDER_STEP_FAILURE); |
40e48e54 | 353 | goto err; |
37124360 | 354 | } |
40e48e54 BB |
355 | /* |
356 | * pbit logic merges this cswap with that of the | |
357 | * next iteration | |
358 | */ | |
359 | pbit ^= kbit; | |
360 | } | |
361 | /* one final cswap to move the right value into r */ | |
362 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |
363 | #undef EC_POINT_CSWAP | |
364 | ||
37124360 NT |
365 | /* Finalize ladder (and recover full point coordinates) */ |
366 | if (!ec_point_ladder_post(group, r, s, p, ctx)) { | |
9311d0c4 | 367 | ERR_raise(ERR_LIB_EC, EC_R_LADDER_POST_FAILURE); |
37124360 NT |
368 | goto err; |
369 | } | |
370 | ||
40e48e54 BB |
371 | ret = 1; |
372 | ||
f4675379 | 373 | err: |
37124360 | 374 | EC_POINT_free(p); |
8a74bb5c | 375 | EC_POINT_clear_free(s); |
40e48e54 | 376 | BN_CTX_end(ctx); |
40e48e54 BB |
377 | |
378 | return ret; | |
379 | } | |
f4675379 | 380 | |
36bed230 | 381 | #undef EC_POINT_BN_set_flags |
40e48e54 | 382 | |
0f113f3e | 383 | /* |
4656d9ec | 384 | * Table could be optimised for the wNAF-based implementation, |
0f113f3e MC |
385 | * sometimes smaller windows will give better performance (thus the |
386 | * boundaries should be increased) | |
c05940ed | 387 | */ |
3ba1f111 | 388 | #define EC_window_bits_for_scalar_size(b) \ |
0f113f3e MC |
389 | ((size_t) \ |
390 | ((b) >= 2000 ? 6 : \ | |
391 | (b) >= 800 ? 5 : \ | |
392 | (b) >= 300 ? 4 : \ | |
393 | (b) >= 70 ? 3 : \ | |
394 | (b) >= 20 ? 2 : \ | |
395 | 1)) | |
3ba1f111 | 396 | |
c80fd6b2 MC |
397 | /*- |
398 | * Compute | |
3ba1f111 BM |
399 | * \sum scalars[i]*points[i], |
400 | * also including | |
401 | * scalar*generator | |
402 | * in the addition if scalar != NULL | |
403 | */ | |
32ab57cb SL |
404 | int ossl_ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
405 | size_t num, const EC_POINT *points[], | |
406 | const BIGNUM *scalars[], BN_CTX *ctx) | |
0f113f3e | 407 | { |
0f113f3e MC |
408 | const EC_POINT *generator = NULL; |
409 | EC_POINT *tmp = NULL; | |
410 | size_t totalnum; | |
411 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ | |
412 | size_t pre_points_per_block = 0; | |
413 | size_t i, j; | |
414 | int k; | |
415 | int r_is_inverted = 0; | |
416 | int r_is_at_infinity = 1; | |
417 | size_t *wsize = NULL; /* individual window sizes */ | |
418 | signed char **wNAF = NULL; /* individual wNAFs */ | |
419 | size_t *wNAF_len = NULL; | |
420 | size_t max_len = 0; | |
421 | size_t num_val; | |
422 | EC_POINT **val = NULL; /* precomputation */ | |
423 | EC_POINT **v; | |
424 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or | |
425 | * 'pre_comp->points' */ | |
426 | const EC_PRE_COMP *pre_comp = NULL; | |
427 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be | |
428 | * treated like other scalars, i.e. | |
429 | * precomputation is not available */ | |
430 | int ret = 0; | |
431 | ||
de72274d | 432 | if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) { |
f4675379 | 433 | /*- |
37124360 NT |
434 | * Handle the common cases where the scalar is secret, enforcing a |
435 | * scalar multiplication implementation based on a Montgomery ladder, | |
436 | * with various timing attack defenses. | |
36bed230 | 437 | */ |
3051bf2a | 438 | if ((scalar != group->order) && (scalar != NULL) && (num == 0)) { |
de72274d BB |
439 | /*- |
440 | * In this case we want to compute scalar * GeneratorPoint: this | |
37124360 NT |
441 | * codepath is reached most prominently by (ephemeral) key |
442 | * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup, | |
443 | * ECDH keygen/first half), where the scalar is always secret. This | |
444 | * is why we ignore if BN_FLG_CONSTTIME is actually set and we | |
445 | * always call the ladder version. | |
de72274d | 446 | */ |
32ab57cb | 447 | return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); |
de72274d | 448 | } |
3051bf2a | 449 | if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) { |
de72274d | 450 | /*- |
37124360 NT |
451 | * In this case we want to compute scalar * VariablePoint: this |
452 | * codepath is reached most prominently by the second half of ECDH, | |
453 | * where the secret scalar is multiplied by the peer's public point. | |
454 | * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is | |
455 | * actually set and we always call the ladder version. | |
de72274d | 456 | */ |
32ab57cb SL |
457 | return ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0], |
458 | ctx); | |
de72274d | 459 | } |
36bed230 NT |
460 | } |
461 | ||
0f113f3e MC |
462 | if (scalar != NULL) { |
463 | generator = EC_GROUP_get0_generator(group); | |
464 | if (generator == NULL) { | |
9311d0c4 | 465 | ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR); |
0f113f3e MC |
466 | goto err; |
467 | } | |
468 | ||
469 | /* look if we can use precomputed multiples of generator */ | |
470 | ||
3aef36ff | 471 | pre_comp = group->pre_comp.ec; |
0f113f3e MC |
472 | if (pre_comp && pre_comp->numblocks |
473 | && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == | |
474 | 0)) { | |
475 | blocksize = pre_comp->blocksize; | |
476 | ||
477 | /* | |
478 | * determine maximum number of blocks that wNAF splitting may | |
479 | * yield (NB: maximum wNAF length is bit length plus one) | |
480 | */ | |
481 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; | |
482 | ||
483 | /* | |
484 | * we cannot use more blocks than we have precomputation for | |
485 | */ | |
486 | if (numblocks > pre_comp->numblocks) | |
487 | numblocks = pre_comp->numblocks; | |
488 | ||
489 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); | |
490 | ||
491 | /* check that pre_comp looks sane */ | |
492 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { | |
9311d0c4 | 493 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
494 | goto err; |
495 | } | |
496 | } else { | |
497 | /* can't use precomputation */ | |
498 | pre_comp = NULL; | |
499 | numblocks = 1; | |
500 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of | |
501 | * 'scalars' */ | |
502 | } | |
503 | } | |
504 | ||
505 | totalnum = num + numblocks; | |
506 | ||
cbe29648 RS |
507 | wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); |
508 | wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); | |
509 | /* include space for pivot */ | |
510 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); | |
511 | val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); | |
0f113f3e MC |
512 | |
513 | /* Ensure wNAF is initialised in case we end up going to err */ | |
90945fa3 | 514 | if (wNAF != NULL) |
0f113f3e MC |
515 | wNAF[0] = NULL; /* preliminary pivot */ |
516 | ||
e077455e | 517 | if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) |
0f113f3e | 518 | goto err; |
0f113f3e MC |
519 | |
520 | /* | |
521 | * num_val will be the total number of temporarily precomputed points | |
522 | */ | |
523 | num_val = 0; | |
524 | ||
525 | for (i = 0; i < num + num_scalar; i++) { | |
526 | size_t bits; | |
527 | ||
528 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); | |
529 | wsize[i] = EC_window_bits_for_scalar_size(bits); | |
530 | num_val += (size_t)1 << (wsize[i] - 1); | |
531 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ | |
532 | wNAF[i] = | |
533 | bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], | |
534 | &wNAF_len[i]); | |
535 | if (wNAF[i] == NULL) | |
536 | goto err; | |
537 | if (wNAF_len[i] > max_len) | |
538 | max_len = wNAF_len[i]; | |
539 | } | |
540 | ||
541 | if (numblocks) { | |
542 | /* we go here iff scalar != NULL */ | |
543 | ||
544 | if (pre_comp == NULL) { | |
545 | if (num_scalar != 1) { | |
9311d0c4 | 546 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
547 | goto err; |
548 | } | |
549 | /* we have already generated a wNAF for 'scalar' */ | |
550 | } else { | |
551 | signed char *tmp_wNAF = NULL; | |
552 | size_t tmp_len = 0; | |
553 | ||
554 | if (num_scalar != 0) { | |
9311d0c4 | 555 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
556 | goto err; |
557 | } | |
558 | ||
559 | /* | |
560 | * use the window size for which we have precomputation | |
561 | */ | |
562 | wsize[num] = pre_comp->w; | |
563 | tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); | |
564 | if (!tmp_wNAF) | |
565 | goto err; | |
566 | ||
567 | if (tmp_len <= max_len) { | |
568 | /* | |
569 | * One of the other wNAFs is at least as long as the wNAF | |
570 | * belonging to the generator, so wNAF splitting will not buy | |
571 | * us anything. | |
572 | */ | |
573 | ||
574 | numblocks = 1; | |
575 | totalnum = num + 1; /* don't use wNAF splitting */ | |
576 | wNAF[num] = tmp_wNAF; | |
577 | wNAF[num + 1] = NULL; | |
578 | wNAF_len[num] = tmp_len; | |
0f113f3e MC |
579 | /* |
580 | * pre_comp->points starts with the points that we need here: | |
581 | */ | |
582 | val_sub[num] = pre_comp->points; | |
583 | } else { | |
584 | /* | |
585 | * don't include tmp_wNAF directly into wNAF array - use wNAF | |
586 | * splitting and include the blocks | |
587 | */ | |
588 | ||
589 | signed char *pp; | |
590 | EC_POINT **tmp_points; | |
591 | ||
592 | if (tmp_len < numblocks * blocksize) { | |
593 | /* | |
594 | * possibly we can do with fewer blocks than estimated | |
595 | */ | |
596 | numblocks = (tmp_len + blocksize - 1) / blocksize; | |
597 | if (numblocks > pre_comp->numblocks) { | |
9311d0c4 | 598 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0e9eb1a5 | 599 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
600 | goto err; |
601 | } | |
602 | totalnum = num + numblocks; | |
603 | } | |
604 | ||
605 | /* split wNAF in 'numblocks' parts */ | |
606 | pp = tmp_wNAF; | |
607 | tmp_points = pre_comp->points; | |
608 | ||
609 | for (i = num; i < totalnum; i++) { | |
610 | if (i < totalnum - 1) { | |
611 | wNAF_len[i] = blocksize; | |
612 | if (tmp_len < blocksize) { | |
9311d0c4 | 613 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0e9eb1a5 | 614 | OPENSSL_free(tmp_wNAF); |
0f113f3e MC |
615 | goto err; |
616 | } | |
617 | tmp_len -= blocksize; | |
618 | } else | |
619 | /* | |
620 | * last block gets whatever is left (this could be | |
621 | * more or less than 'blocksize'!) | |
622 | */ | |
623 | wNAF_len[i] = tmp_len; | |
624 | ||
625 | wNAF[i + 1] = NULL; | |
626 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); | |
627 | if (wNAF[i] == NULL) { | |
0f113f3e MC |
628 | OPENSSL_free(tmp_wNAF); |
629 | goto err; | |
630 | } | |
631 | memcpy(wNAF[i], pp, wNAF_len[i]); | |
632 | if (wNAF_len[i] > max_len) | |
633 | max_len = wNAF_len[i]; | |
634 | ||
635 | if (*tmp_points == NULL) { | |
9311d0c4 | 636 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
637 | OPENSSL_free(tmp_wNAF); |
638 | goto err; | |
639 | } | |
640 | val_sub[i] = tmp_points; | |
641 | tmp_points += pre_points_per_block; | |
642 | pp += blocksize; | |
643 | } | |
644 | OPENSSL_free(tmp_wNAF); | |
645 | } | |
646 | } | |
647 | } | |
648 | ||
649 | /* | |
650 | * All points we precompute now go into a single array 'val'. | |
651 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a | |
652 | * subarray of 'pre_comp->points' if we already have precomputation. | |
653 | */ | |
cbe29648 | 654 | val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); |
e077455e | 655 | if (val == NULL) |
0f113f3e | 656 | goto err; |
0f113f3e MC |
657 | val[num_val] = NULL; /* pivot element */ |
658 | ||
659 | /* allocate points for precomputation */ | |
660 | v = val; | |
661 | for (i = 0; i < num + num_scalar; i++) { | |
662 | val_sub[i] = v; | |
663 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
664 | *v = EC_POINT_new(group); | |
665 | if (*v == NULL) | |
666 | goto err; | |
667 | v++; | |
668 | } | |
669 | } | |
670 | if (!(v == val + num_val)) { | |
9311d0c4 | 671 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
672 | goto err; |
673 | } | |
674 | ||
75ebbd9a | 675 | if ((tmp = EC_POINT_new(group)) == NULL) |
0f113f3e MC |
676 | goto err; |
677 | ||
50e735f9 MC |
678 | /*- |
679 | * prepare precomputed values: | |
680 | * val_sub[i][0] := points[i] | |
681 | * val_sub[i][1] := 3 * points[i] | |
682 | * val_sub[i][2] := 5 * points[i] | |
683 | * ... | |
684 | */ | |
0f113f3e MC |
685 | for (i = 0; i < num + num_scalar; i++) { |
686 | if (i < num) { | |
687 | if (!EC_POINT_copy(val_sub[i][0], points[i])) | |
688 | goto err; | |
689 | } else { | |
690 | if (!EC_POINT_copy(val_sub[i][0], generator)) | |
691 | goto err; | |
692 | } | |
693 | ||
694 | if (wsize[i] > 1) { | |
695 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) | |
696 | goto err; | |
697 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { | |
698 | if (!EC_POINT_add | |
699 | (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) | |
700 | goto err; | |
701 | } | |
702 | } | |
703 | } | |
704 | ||
c2f2db9b BB |
705 | if (group->meth->points_make_affine == NULL |
706 | || !group->meth->points_make_affine(group, num_val, val, ctx)) | |
0f113f3e | 707 | goto err; |
3ba1f111 | 708 | |
0f113f3e MC |
709 | r_is_at_infinity = 1; |
710 | ||
711 | for (k = max_len - 1; k >= 0; k--) { | |
712 | if (!r_is_at_infinity) { | |
713 | if (!EC_POINT_dbl(group, r, r, ctx)) | |
714 | goto err; | |
715 | } | |
716 | ||
717 | for (i = 0; i < totalnum; i++) { | |
718 | if (wNAF_len[i] > (size_t)k) { | |
719 | int digit = wNAF[i][k]; | |
720 | int is_neg; | |
721 | ||
722 | if (digit) { | |
723 | is_neg = digit < 0; | |
724 | ||
725 | if (is_neg) | |
726 | digit = -digit; | |
727 | ||
728 | if (is_neg != r_is_inverted) { | |
729 | if (!r_is_at_infinity) { | |
730 | if (!EC_POINT_invert(group, r, ctx)) | |
731 | goto err; | |
732 | } | |
733 | r_is_inverted = !r_is_inverted; | |
734 | } | |
735 | ||
736 | /* digit > 0 */ | |
737 | ||
738 | if (r_is_at_infinity) { | |
739 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) | |
740 | goto err; | |
c61ced5e BB |
741 | |
742 | /*- | |
743 | * Apply coordinate blinding for EC_POINT. | |
744 | * | |
745 | * The underlying EC_METHOD can optionally implement this function: | |
32ab57cb | 746 | * ossl_ec_point_blind_coordinates() returns 0 in case of errors or 1 on |
c61ced5e BB |
747 | * success or if coordinate blinding is not implemented for this |
748 | * group. | |
749 | */ | |
32ab57cb | 750 | if (!ossl_ec_point_blind_coordinates(group, r, ctx)) { |
9311d0c4 | 751 | ERR_raise(ERR_LIB_EC, EC_R_POINT_COORDINATES_BLIND_FAILURE); |
c61ced5e BB |
752 | goto err; |
753 | } | |
754 | ||
0f113f3e MC |
755 | r_is_at_infinity = 0; |
756 | } else { | |
757 | if (!EC_POINT_add | |
758 | (group, r, r, val_sub[i][digit >> 1], ctx)) | |
759 | goto err; | |
760 | } | |
761 | } | |
762 | } | |
763 | } | |
764 | } | |
765 | ||
766 | if (r_is_at_infinity) { | |
767 | if (!EC_POINT_set_to_infinity(group, r)) | |
768 | goto err; | |
769 | } else { | |
770 | if (r_is_inverted) | |
771 | if (!EC_POINT_invert(group, r, ctx)) | |
772 | goto err; | |
773 | } | |
774 | ||
775 | ret = 1; | |
3ba1f111 BM |
776 | |
777 | err: | |
8fdc3734 | 778 | EC_POINT_free(tmp); |
b548a1f1 RS |
779 | OPENSSL_free(wsize); |
780 | OPENSSL_free(wNAF_len); | |
0f113f3e MC |
781 | if (wNAF != NULL) { |
782 | signed char **w; | |
783 | ||
784 | for (w = wNAF; *w != NULL; w++) | |
785 | OPENSSL_free(*w); | |
786 | ||
787 | OPENSSL_free(wNAF); | |
788 | } | |
789 | if (val != NULL) { | |
790 | for (v = val; *v != NULL; v++) | |
791 | EC_POINT_clear_free(*v); | |
792 | ||
793 | OPENSSL_free(val); | |
794 | } | |
b548a1f1 | 795 | OPENSSL_free(val_sub); |
0f113f3e MC |
796 | return ret; |
797 | } | |
38374911 | 798 | |
1d97c843 | 799 | /*- |
32ab57cb | 800 | * ossl_ec_wNAF_precompute_mult() |
37c660ff | 801 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
32ab57cb | 802 | * for use with wNAF splitting as implemented in ossl_ec_wNAF_mul(). |
0f113f3e | 803 | * |
37c660ff BM |
804 | * 'pre_comp->points' is an array of multiples of the generator |
805 | * of the following form: | |
806 | * points[0] = generator; | |
807 | * points[1] = 3 * generator; | |
808 | * ... | |
809 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; | |
810 | * points[2^(w-1)] = 2^blocksize * generator; | |
811 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; | |
812 | * ... | |
813 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator | |
814 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator | |
815 | * ... | |
816 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator | |
817 | * points[2^(w-1)*numblocks] = NULL | |
7793f30e | 818 | */ |
32ab57cb | 819 | int ossl_ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
820 | { |
821 | const EC_POINT *generator; | |
822 | EC_POINT *tmp_point = NULL, *base = NULL, **var; | |
be2e334f | 823 | const BIGNUM *order; |
0f113f3e MC |
824 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
825 | EC_POINT **points = NULL; | |
826 | EC_PRE_COMP *pre_comp; | |
827 | int ret = 0; | |
48116c2d | 828 | int used_ctx = 0; |
f844f9eb | 829 | #ifndef FIPS_MODULE |
a9612d6c MC |
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) { | |
9311d0c4 | 840 | ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR); |
0f113f3e MC |
841 | goto err; |
842 | } | |
843 | ||
f844f9eb | 844 | #ifndef FIPS_MODULE |
a9612d6c | 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); | |
48116c2d | 852 | used_ctx = 1; |
0f113f3e | 853 | |
be2e334f DSH |
854 | order = EC_GROUP_get0_order(group); |
855 | if (order == NULL) | |
0f113f3e MC |
856 | goto err; |
857 | if (BN_is_zero(order)) { | |
9311d0c4 | 858 | ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER); |
0f113f3e MC |
859 | goto err; |
860 | } | |
861 | ||
862 | bits = BN_num_bits(order); | |
863 | /* | |
864 | * The following parameters mean we precompute (approximately) one point | |
865 | * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other | |
866 | * bit lengths, other parameter combinations might provide better | |
867 | * efficiency. | |
868 | */ | |
869 | blocksize = 8; | |
870 | w = 4; | |
871 | if (EC_window_bits_for_scalar_size(bits) > w) { | |
872 | /* let's not make the window too small ... */ | |
873 | w = EC_window_bits_for_scalar_size(bits); | |
874 | } | |
875 | ||
876 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks | |
877 | * to use for wNAF | |
878 | * splitting */ | |
879 | ||
880 | pre_points_per_block = (size_t)1 << (w - 1); | |
881 | num = pre_points_per_block * numblocks; /* number of points to compute | |
882 | * and store */ | |
883 | ||
b4faea50 | 884 | points = OPENSSL_malloc(sizeof(*points) * (num + 1)); |
e077455e | 885 | if (points == NULL) |
0f113f3e | 886 | goto err; |
0f113f3e MC |
887 | |
888 | var = points; | |
889 | var[num] = NULL; /* pivot */ | |
890 | for (i = 0; i < num; i++) { | |
891 | if ((var[i] = EC_POINT_new(group)) == NULL) { | |
e077455e | 892 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
0f113f3e MC |
893 | goto err; |
894 | } | |
895 | } | |
896 | ||
75ebbd9a RS |
897 | if ((tmp_point = EC_POINT_new(group)) == NULL |
898 | || (base = EC_POINT_new(group)) == NULL) { | |
e077455e | 899 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
0f113f3e MC |
900 | goto err; |
901 | } | |
902 | ||
903 | if (!EC_POINT_copy(base, generator)) | |
904 | goto err; | |
905 | ||
906 | /* do the precomputation */ | |
907 | for (i = 0; i < numblocks; i++) { | |
908 | size_t j; | |
909 | ||
910 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) | |
911 | goto err; | |
912 | ||
913 | if (!EC_POINT_copy(*var++, base)) | |
914 | goto err; | |
915 | ||
916 | for (j = 1; j < pre_points_per_block; j++, var++) { | |
917 | /* | |
918 | * calculate odd multiples of the current base point | |
919 | */ | |
920 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) | |
921 | goto err; | |
922 | } | |
923 | ||
924 | if (i < numblocks - 1) { | |
925 | /* | |
926 | * get the next base (multiply current one by 2^blocksize) | |
927 | */ | |
928 | size_t k; | |
929 | ||
930 | if (blocksize <= 2) { | |
9311d0c4 | 931 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
932 | goto err; |
933 | } | |
934 | ||
935 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) | |
936 | goto err; | |
937 | for (k = 2; k < blocksize; k++) { | |
938 | if (!EC_POINT_dbl(group, base, base, ctx)) | |
939 | goto err; | |
940 | } | |
941 | } | |
942 | } | |
943 | ||
c2f2db9b BB |
944 | if (group->meth->points_make_affine == NULL |
945 | || !group->meth->points_make_affine(group, num, points, ctx)) | |
0f113f3e MC |
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: |
48116c2d AG |
960 | if (used_ctx) |
961 | BN_CTX_end(ctx); | |
f844f9eb | 962 | #ifndef FIPS_MODULE |
23a1d5e9 | 963 | BN_CTX_free(new_ctx); |
a9612d6c | 964 | #endif |
3aef36ff | 965 | EC_ec_pre_comp_free(pre_comp); |
0f113f3e MC |
966 | if (points) { |
967 | EC_POINT **p; | |
968 | ||
969 | for (p = points; *p != NULL; p++) | |
970 | EC_POINT_free(*p); | |
971 | OPENSSL_free(points); | |
972 | } | |
8fdc3734 RS |
973 | EC_POINT_free(tmp_point); |
974 | EC_POINT_free(base); | |
0f113f3e MC |
975 | return ret; |
976 | } | |
7793f30e | 977 | |
32ab57cb | 978 | int ossl_ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
0f113f3e | 979 | { |
3aef36ff | 980 | return HAVEPRECOMP(group, ec); |
0f113f3e | 981 | } |