/src/openssl/crypto/ec/ecp_smpl.c
Line | Count | Source (jump to first uncovered line) |
1 | | /* |
2 | | * Copyright 2001-2022 The OpenSSL Project Authors. All Rights Reserved. |
3 | | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
4 | | * |
5 | | * Licensed under the Apache License 2.0 (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 |
9 | | */ |
10 | | |
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 | | |
17 | | #include <openssl/err.h> |
18 | | #include <openssl/symhacks.h> |
19 | | |
20 | | #include "ec_local.h" |
21 | | |
22 | | const EC_METHOD *EC_GFp_simple_method(void) |
23 | 0 | { |
24 | 0 | static const EC_METHOD ret = { |
25 | 0 | EC_FLAGS_DEFAULT_OCT, |
26 | 0 | NID_X9_62_prime_field, |
27 | 0 | ossl_ec_GFp_simple_group_init, |
28 | 0 | ossl_ec_GFp_simple_group_finish, |
29 | 0 | ossl_ec_GFp_simple_group_clear_finish, |
30 | 0 | ossl_ec_GFp_simple_group_copy, |
31 | 0 | ossl_ec_GFp_simple_group_set_curve, |
32 | 0 | ossl_ec_GFp_simple_group_get_curve, |
33 | 0 | ossl_ec_GFp_simple_group_get_degree, |
34 | 0 | ossl_ec_group_simple_order_bits, |
35 | 0 | ossl_ec_GFp_simple_group_check_discriminant, |
36 | 0 | ossl_ec_GFp_simple_point_init, |
37 | 0 | ossl_ec_GFp_simple_point_finish, |
38 | 0 | ossl_ec_GFp_simple_point_clear_finish, |
39 | 0 | ossl_ec_GFp_simple_point_copy, |
40 | 0 | ossl_ec_GFp_simple_point_set_to_infinity, |
41 | 0 | ossl_ec_GFp_simple_point_set_affine_coordinates, |
42 | 0 | ossl_ec_GFp_simple_point_get_affine_coordinates, |
43 | 0 | 0, 0, 0, |
44 | 0 | ossl_ec_GFp_simple_add, |
45 | 0 | ossl_ec_GFp_simple_dbl, |
46 | 0 | ossl_ec_GFp_simple_invert, |
47 | 0 | ossl_ec_GFp_simple_is_at_infinity, |
48 | 0 | ossl_ec_GFp_simple_is_on_curve, |
49 | 0 | ossl_ec_GFp_simple_cmp, |
50 | 0 | ossl_ec_GFp_simple_make_affine, |
51 | 0 | ossl_ec_GFp_simple_points_make_affine, |
52 | 0 | 0 /* mul */ , |
53 | 0 | 0 /* precompute_mult */ , |
54 | 0 | 0 /* have_precompute_mult */ , |
55 | 0 | ossl_ec_GFp_simple_field_mul, |
56 | 0 | ossl_ec_GFp_simple_field_sqr, |
57 | 0 | 0 /* field_div */ , |
58 | 0 | ossl_ec_GFp_simple_field_inv, |
59 | 0 | 0 /* field_encode */ , |
60 | 0 | 0 /* field_decode */ , |
61 | 0 | 0, /* field_set_to_one */ |
62 | 0 | ossl_ec_key_simple_priv2oct, |
63 | 0 | ossl_ec_key_simple_oct2priv, |
64 | 0 | 0, /* set private */ |
65 | 0 | ossl_ec_key_simple_generate_key, |
66 | 0 | ossl_ec_key_simple_check_key, |
67 | 0 | ossl_ec_key_simple_generate_public_key, |
68 | 0 | 0, /* keycopy */ |
69 | 0 | 0, /* keyfinish */ |
70 | 0 | ossl_ecdh_simple_compute_key, |
71 | 0 | ossl_ecdsa_simple_sign_setup, |
72 | 0 | ossl_ecdsa_simple_sign_sig, |
73 | 0 | ossl_ecdsa_simple_verify_sig, |
74 | 0 | 0, /* field_inverse_mod_ord */ |
75 | 0 | ossl_ec_GFp_simple_blind_coordinates, |
76 | 0 | ossl_ec_GFp_simple_ladder_pre, |
77 | 0 | ossl_ec_GFp_simple_ladder_step, |
78 | 0 | ossl_ec_GFp_simple_ladder_post |
79 | 0 | }; |
80 | |
|
81 | 0 | return &ret; |
82 | 0 | } |
83 | | |
84 | | /* |
85 | | * Most method functions in this file are designed to work with |
86 | | * non-trivial representations of field elements if necessary |
87 | | * (see ecp_mont.c): while standard modular addition and subtraction |
88 | | * are used, the field_mul and field_sqr methods will be used for |
89 | | * multiplication, and field_encode and field_decode (if defined) |
90 | | * will be used for converting between representations. |
91 | | * |
92 | | * Functions ec_GFp_simple_points_make_affine() and |
93 | | * ec_GFp_simple_point_get_affine_coordinates() specifically assume |
94 | | * that if a non-trivial representation is used, it is a Montgomery |
95 | | * representation (i.e. 'encoding' means multiplying by some factor R). |
96 | | */ |
97 | | |
98 | | int ossl_ec_GFp_simple_group_init(EC_GROUP *group) |
99 | 4.68k | { |
100 | 4.68k | group->field = BN_new(); |
101 | 4.68k | group->a = BN_new(); |
102 | 4.68k | group->b = BN_new(); |
103 | 4.68k | if (group->field == NULL || group->a == NULL || group->b == NULL) { |
104 | 0 | BN_free(group->field); |
105 | 0 | BN_free(group->a); |
106 | 0 | BN_free(group->b); |
107 | 0 | return 0; |
108 | 0 | } |
109 | 4.68k | group->a_is_minus3 = 0; |
110 | 4.68k | return 1; |
111 | 4.68k | } |
112 | | |
113 | | void ossl_ec_GFp_simple_group_finish(EC_GROUP *group) |
114 | 4.68k | { |
115 | 4.68k | BN_free(group->field); |
116 | 4.68k | BN_free(group->a); |
117 | 4.68k | BN_free(group->b); |
118 | 4.68k | } |
119 | | |
120 | | void ossl_ec_GFp_simple_group_clear_finish(EC_GROUP *group) |
121 | 0 | { |
122 | 0 | BN_clear_free(group->field); |
123 | 0 | BN_clear_free(group->a); |
124 | 0 | BN_clear_free(group->b); |
125 | 0 | } |
126 | | |
127 | | int ossl_ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) |
128 | 2.35k | { |
129 | 2.35k | if (!BN_copy(dest->field, src->field)) |
130 | 0 | return 0; |
131 | 2.35k | if (!BN_copy(dest->a, src->a)) |
132 | 0 | return 0; |
133 | 2.35k | if (!BN_copy(dest->b, src->b)) |
134 | 0 | return 0; |
135 | | |
136 | 2.35k | dest->a_is_minus3 = src->a_is_minus3; |
137 | | |
138 | 2.35k | return 1; |
139 | 2.35k | } |
140 | | |
141 | | int ossl_ec_GFp_simple_group_set_curve(EC_GROUP *group, |
142 | | const BIGNUM *p, const BIGNUM *a, |
143 | | const BIGNUM *b, BN_CTX *ctx) |
144 | 2.33k | { |
145 | 2.33k | int ret = 0; |
146 | 2.33k | BN_CTX *new_ctx = NULL; |
147 | 2.33k | BIGNUM *tmp_a; |
148 | | |
149 | | /* p must be a prime > 3 */ |
150 | 2.33k | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { |
151 | 0 | ERR_raise(ERR_LIB_EC, EC_R_INVALID_FIELD); |
152 | 0 | return 0; |
153 | 0 | } |
154 | | |
155 | 2.33k | if (ctx == NULL) { |
156 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
157 | 0 | if (ctx == NULL) |
158 | 0 | return 0; |
159 | 0 | } |
160 | | |
161 | 2.33k | BN_CTX_start(ctx); |
162 | 2.33k | tmp_a = BN_CTX_get(ctx); |
163 | 2.33k | if (tmp_a == NULL) |
164 | 0 | goto err; |
165 | | |
166 | | /* group->field */ |
167 | 2.33k | if (!BN_copy(group->field, p)) |
168 | 0 | goto err; |
169 | 2.33k | BN_set_negative(group->field, 0); |
170 | | |
171 | | /* group->a */ |
172 | 2.33k | if (!BN_nnmod(tmp_a, a, p, ctx)) |
173 | 0 | goto err; |
174 | 2.33k | if (group->meth->field_encode != NULL) { |
175 | 1.80k | if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) |
176 | 0 | goto err; |
177 | 1.80k | } else if (!BN_copy(group->a, tmp_a)) |
178 | 0 | goto err; |
179 | | |
180 | | /* group->b */ |
181 | 2.33k | if (!BN_nnmod(group->b, b, p, ctx)) |
182 | 0 | goto err; |
183 | 2.33k | if (group->meth->field_encode != NULL) |
184 | 1.80k | if (!group->meth->field_encode(group, group->b, group->b, ctx)) |
185 | 0 | goto err; |
186 | | |
187 | | /* group->a_is_minus3 */ |
188 | 2.33k | if (!BN_add_word(tmp_a, 3)) |
189 | 0 | goto err; |
190 | 2.33k | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); |
191 | | |
192 | 2.33k | ret = 1; |
193 | | |
194 | 2.33k | err: |
195 | 2.33k | BN_CTX_end(ctx); |
196 | 2.33k | BN_CTX_free(new_ctx); |
197 | 2.33k | return ret; |
198 | 2.33k | } |
199 | | |
200 | | int ossl_ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, |
201 | | BIGNUM *a, BIGNUM *b, BN_CTX *ctx) |
202 | 0 | { |
203 | 0 | int ret = 0; |
204 | 0 | BN_CTX *new_ctx = NULL; |
205 | |
|
206 | 0 | if (p != NULL) { |
207 | 0 | if (!BN_copy(p, group->field)) |
208 | 0 | return 0; |
209 | 0 | } |
210 | | |
211 | 0 | if (a != NULL || b != NULL) { |
212 | 0 | if (group->meth->field_decode != NULL) { |
213 | 0 | if (ctx == NULL) { |
214 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
215 | 0 | if (ctx == NULL) |
216 | 0 | return 0; |
217 | 0 | } |
218 | 0 | if (a != NULL) { |
219 | 0 | if (!group->meth->field_decode(group, a, group->a, ctx)) |
220 | 0 | goto err; |
221 | 0 | } |
222 | 0 | if (b != NULL) { |
223 | 0 | if (!group->meth->field_decode(group, b, group->b, ctx)) |
224 | 0 | goto err; |
225 | 0 | } |
226 | 0 | } else { |
227 | 0 | if (a != NULL) { |
228 | 0 | if (!BN_copy(a, group->a)) |
229 | 0 | goto err; |
230 | 0 | } |
231 | 0 | if (b != NULL) { |
232 | 0 | if (!BN_copy(b, group->b)) |
233 | 0 | goto err; |
234 | 0 | } |
235 | 0 | } |
236 | 0 | } |
237 | | |
238 | 0 | ret = 1; |
239 | |
|
240 | 0 | err: |
241 | 0 | BN_CTX_free(new_ctx); |
242 | 0 | return ret; |
243 | 0 | } |
244 | | |
245 | | int ossl_ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
246 | 11 | { |
247 | 11 | return BN_num_bits(group->field); |
248 | 11 | } |
249 | | |
250 | | int ossl_ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, |
251 | | BN_CTX *ctx) |
252 | 0 | { |
253 | 0 | int ret = 0; |
254 | 0 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; |
255 | 0 | const BIGNUM *p = group->field; |
256 | 0 | BN_CTX *new_ctx = NULL; |
257 | |
|
258 | 0 | if (ctx == NULL) { |
259 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
260 | 0 | if (ctx == NULL) { |
261 | 0 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
262 | 0 | goto err; |
263 | 0 | } |
264 | 0 | } |
265 | 0 | BN_CTX_start(ctx); |
266 | 0 | a = BN_CTX_get(ctx); |
267 | 0 | b = BN_CTX_get(ctx); |
268 | 0 | tmp_1 = BN_CTX_get(ctx); |
269 | 0 | tmp_2 = BN_CTX_get(ctx); |
270 | 0 | order = BN_CTX_get(ctx); |
271 | 0 | if (order == NULL) |
272 | 0 | goto err; |
273 | | |
274 | 0 | if (group->meth->field_decode != NULL) { |
275 | 0 | if (!group->meth->field_decode(group, a, group->a, ctx)) |
276 | 0 | goto err; |
277 | 0 | if (!group->meth->field_decode(group, b, group->b, ctx)) |
278 | 0 | goto err; |
279 | 0 | } else { |
280 | 0 | if (!BN_copy(a, group->a)) |
281 | 0 | goto err; |
282 | 0 | if (!BN_copy(b, group->b)) |
283 | 0 | goto err; |
284 | 0 | } |
285 | | |
286 | | /*- |
287 | | * check the discriminant: |
288 | | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) |
289 | | * 0 =< a, b < p |
290 | | */ |
291 | 0 | if (BN_is_zero(a)) { |
292 | 0 | if (BN_is_zero(b)) |
293 | 0 | goto err; |
294 | 0 | } else if (!BN_is_zero(b)) { |
295 | 0 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) |
296 | 0 | goto err; |
297 | 0 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) |
298 | 0 | goto err; |
299 | 0 | if (!BN_lshift(tmp_1, tmp_2, 2)) |
300 | 0 | goto err; |
301 | | /* tmp_1 = 4*a^3 */ |
302 | | |
303 | 0 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) |
304 | 0 | goto err; |
305 | 0 | if (!BN_mul_word(tmp_2, 27)) |
306 | 0 | goto err; |
307 | | /* tmp_2 = 27*b^2 */ |
308 | | |
309 | 0 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) |
310 | 0 | goto err; |
311 | 0 | if (BN_is_zero(a)) |
312 | 0 | goto err; |
313 | 0 | } |
314 | 0 | ret = 1; |
315 | |
|
316 | 0 | err: |
317 | 0 | BN_CTX_end(ctx); |
318 | 0 | BN_CTX_free(new_ctx); |
319 | 0 | return ret; |
320 | 0 | } |
321 | | |
322 | | int ossl_ec_GFp_simple_point_init(EC_POINT *point) |
323 | 34.4k | { |
324 | 34.4k | point->X = BN_new(); |
325 | 34.4k | point->Y = BN_new(); |
326 | 34.4k | point->Z = BN_new(); |
327 | 34.4k | point->Z_is_one = 0; |
328 | | |
329 | 34.4k | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
330 | 0 | BN_free(point->X); |
331 | 0 | BN_free(point->Y); |
332 | 0 | BN_free(point->Z); |
333 | 0 | return 0; |
334 | 0 | } |
335 | 34.4k | return 1; |
336 | 34.4k | } |
337 | | |
338 | | void ossl_ec_GFp_simple_point_finish(EC_POINT *point) |
339 | 31.6k | { |
340 | 31.6k | BN_free(point->X); |
341 | 31.6k | BN_free(point->Y); |
342 | 31.6k | BN_free(point->Z); |
343 | 31.6k | } |
344 | | |
345 | | void ossl_ec_GFp_simple_point_clear_finish(EC_POINT *point) |
346 | 2.77k | { |
347 | 2.77k | BN_clear_free(point->X); |
348 | 2.77k | BN_clear_free(point->Y); |
349 | 2.77k | BN_clear_free(point->Z); |
350 | 2.77k | point->Z_is_one = 0; |
351 | 2.77k | } |
352 | | |
353 | | int ossl_ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
354 | 12.5k | { |
355 | 12.5k | if (!BN_copy(dest->X, src->X)) |
356 | 0 | return 0; |
357 | 12.5k | if (!BN_copy(dest->Y, src->Y)) |
358 | 0 | return 0; |
359 | 12.5k | if (!BN_copy(dest->Z, src->Z)) |
360 | 0 | return 0; |
361 | 12.5k | dest->Z_is_one = src->Z_is_one; |
362 | 12.5k | dest->curve_name = src->curve_name; |
363 | | |
364 | 12.5k | return 1; |
365 | 12.5k | } |
366 | | |
367 | | int ossl_ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, |
368 | | EC_POINT *point) |
369 | 11 | { |
370 | 11 | point->Z_is_one = 0; |
371 | 11 | BN_zero(point->Z); |
372 | 11 | return 1; |
373 | 11 | } |
374 | | |
375 | | int ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, |
376 | | EC_POINT *point, |
377 | | const BIGNUM *x, |
378 | | const BIGNUM *y, |
379 | | const BIGNUM *z, |
380 | | BN_CTX *ctx) |
381 | 3.87k | { |
382 | 3.87k | BN_CTX *new_ctx = NULL; |
383 | 3.87k | int ret = 0; |
384 | | |
385 | 3.87k | if (ctx == NULL) { |
386 | 1.49k | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
387 | 1.49k | if (ctx == NULL) |
388 | 0 | return 0; |
389 | 1.49k | } |
390 | | |
391 | 3.87k | if (x != NULL) { |
392 | 3.87k | if (!BN_nnmod(point->X, x, group->field, ctx)) |
393 | 0 | goto err; |
394 | 3.87k | if (group->meth->field_encode) { |
395 | 2.99k | if (!group->meth->field_encode(group, point->X, point->X, ctx)) |
396 | 0 | goto err; |
397 | 2.99k | } |
398 | 3.87k | } |
399 | | |
400 | 3.87k | if (y != NULL) { |
401 | 3.87k | if (!BN_nnmod(point->Y, y, group->field, ctx)) |
402 | 0 | goto err; |
403 | 3.87k | if (group->meth->field_encode) { |
404 | 2.99k | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) |
405 | 0 | goto err; |
406 | 2.99k | } |
407 | 3.87k | } |
408 | | |
409 | 3.87k | if (z != NULL) { |
410 | 3.87k | int Z_is_one; |
411 | | |
412 | 3.87k | if (!BN_nnmod(point->Z, z, group->field, ctx)) |
413 | 0 | goto err; |
414 | 3.87k | Z_is_one = BN_is_one(point->Z); |
415 | 3.87k | if (group->meth->field_encode) { |
416 | 2.99k | if (Z_is_one && (group->meth->field_set_to_one != 0)) { |
417 | 2.77k | if (!group->meth->field_set_to_one(group, point->Z, ctx)) |
418 | 0 | goto err; |
419 | 2.77k | } else { |
420 | 221 | if (!group-> |
421 | 221 | meth->field_encode(group, point->Z, point->Z, ctx)) |
422 | 0 | goto err; |
423 | 221 | } |
424 | 2.99k | } |
425 | 3.87k | point->Z_is_one = Z_is_one; |
426 | 3.87k | } |
427 | | |
428 | 3.87k | ret = 1; |
429 | | |
430 | 3.87k | err: |
431 | 3.87k | BN_CTX_free(new_ctx); |
432 | 3.87k | return ret; |
433 | 3.87k | } |
434 | | |
435 | | int ossl_ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, |
436 | | const EC_POINT *point, |
437 | | BIGNUM *x, BIGNUM *y, |
438 | | BIGNUM *z, BN_CTX *ctx) |
439 | 0 | { |
440 | 0 | BN_CTX *new_ctx = NULL; |
441 | 0 | int ret = 0; |
442 | |
|
443 | 0 | if (group->meth->field_decode != NULL) { |
444 | 0 | if (ctx == NULL) { |
445 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
446 | 0 | if (ctx == NULL) |
447 | 0 | return 0; |
448 | 0 | } |
449 | | |
450 | 0 | if (x != NULL) { |
451 | 0 | if (!group->meth->field_decode(group, x, point->X, ctx)) |
452 | 0 | goto err; |
453 | 0 | } |
454 | 0 | if (y != NULL) { |
455 | 0 | if (!group->meth->field_decode(group, y, point->Y, ctx)) |
456 | 0 | goto err; |
457 | 0 | } |
458 | 0 | if (z != NULL) { |
459 | 0 | if (!group->meth->field_decode(group, z, point->Z, ctx)) |
460 | 0 | goto err; |
461 | 0 | } |
462 | 0 | } else { |
463 | 0 | if (x != NULL) { |
464 | 0 | if (!BN_copy(x, point->X)) |
465 | 0 | goto err; |
466 | 0 | } |
467 | 0 | if (y != NULL) { |
468 | 0 | if (!BN_copy(y, point->Y)) |
469 | 0 | goto err; |
470 | 0 | } |
471 | 0 | if (z != NULL) { |
472 | 0 | if (!BN_copy(z, point->Z)) |
473 | 0 | goto err; |
474 | 0 | } |
475 | 0 | } |
476 | | |
477 | 0 | ret = 1; |
478 | |
|
479 | 0 | err: |
480 | 0 | BN_CTX_free(new_ctx); |
481 | 0 | return ret; |
482 | 0 | } |
483 | | |
484 | | int ossl_ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, |
485 | | EC_POINT *point, |
486 | | const BIGNUM *x, |
487 | | const BIGNUM *y, BN_CTX *ctx) |
488 | 3.37k | { |
489 | 3.37k | if (x == NULL || y == NULL) { |
490 | | /* |
491 | | * unlike for projective coordinates, we do not tolerate this |
492 | | */ |
493 | 0 | ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER); |
494 | 0 | return 0; |
495 | 0 | } |
496 | | |
497 | 3.37k | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, |
498 | 3.37k | BN_value_one(), ctx); |
499 | 3.37k | } |
500 | | |
501 | | int ossl_ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, |
502 | | const EC_POINT *point, |
503 | | BIGNUM *x, BIGNUM *y, |
504 | | BN_CTX *ctx) |
505 | 1.13k | { |
506 | 1.13k | BN_CTX *new_ctx = NULL; |
507 | 1.13k | BIGNUM *Z, *Z_1, *Z_2, *Z_3; |
508 | 1.13k | const BIGNUM *Z_; |
509 | 1.13k | int ret = 0; |
510 | | |
511 | 1.13k | if (EC_POINT_is_at_infinity(group, point)) { |
512 | 0 | ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); |
513 | 0 | return 0; |
514 | 0 | } |
515 | | |
516 | 1.13k | if (ctx == NULL) { |
517 | 814 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
518 | 814 | if (ctx == NULL) |
519 | 0 | return 0; |
520 | 814 | } |
521 | | |
522 | 1.13k | BN_CTX_start(ctx); |
523 | 1.13k | Z = BN_CTX_get(ctx); |
524 | 1.13k | Z_1 = BN_CTX_get(ctx); |
525 | 1.13k | Z_2 = BN_CTX_get(ctx); |
526 | 1.13k | Z_3 = BN_CTX_get(ctx); |
527 | 1.13k | if (Z_3 == NULL) |
528 | 0 | goto err; |
529 | | |
530 | | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ |
531 | | |
532 | 1.13k | if (group->meth->field_decode != NULL) { |
533 | 816 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) |
534 | 0 | goto err; |
535 | 816 | Z_ = Z; |
536 | 816 | } else { |
537 | 318 | Z_ = point->Z; |
538 | 318 | } |
539 | | |
540 | 1.13k | if (BN_is_one(Z_)) { |
541 | 900 | if (group->meth->field_decode != NULL) { |
542 | 647 | if (x != NULL) { |
543 | 647 | if (!group->meth->field_decode(group, x, point->X, ctx)) |
544 | 0 | goto err; |
545 | 647 | } |
546 | 647 | if (y != NULL) { |
547 | 551 | if (!group->meth->field_decode(group, y, point->Y, ctx)) |
548 | 0 | goto err; |
549 | 551 | } |
550 | 647 | } else { |
551 | 253 | if (x != NULL) { |
552 | 253 | if (!BN_copy(x, point->X)) |
553 | 0 | goto err; |
554 | 253 | } |
555 | 253 | if (y != NULL) { |
556 | 217 | if (!BN_copy(y, point->Y)) |
557 | 0 | goto err; |
558 | 217 | } |
559 | 253 | } |
560 | 900 | } else { |
561 | 234 | if (!group->meth->field_inv(group, Z_1, Z_, ctx)) { |
562 | 1 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
563 | 1 | goto err; |
564 | 1 | } |
565 | | |
566 | 233 | if (group->meth->field_encode == NULL) { |
567 | | /* field_sqr works on standard representation */ |
568 | 64 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) |
569 | 0 | goto err; |
570 | 169 | } else { |
571 | 169 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) |
572 | 0 | goto err; |
573 | 169 | } |
574 | | |
575 | 233 | if (x != NULL) { |
576 | | /* |
577 | | * in the Montgomery case, field_mul will cancel out Montgomery |
578 | | * factor in X: |
579 | | */ |
580 | 233 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) |
581 | 0 | goto err; |
582 | 233 | } |
583 | | |
584 | 233 | if (y != NULL) { |
585 | 103 | if (group->meth->field_encode == NULL) { |
586 | | /* |
587 | | * field_mul works on standard representation |
588 | | */ |
589 | 27 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) |
590 | 0 | goto err; |
591 | 76 | } else { |
592 | 76 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) |
593 | 0 | goto err; |
594 | 76 | } |
595 | | |
596 | | /* |
597 | | * in the Montgomery case, field_mul will cancel out Montgomery |
598 | | * factor in Y: |
599 | | */ |
600 | 103 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) |
601 | 0 | goto err; |
602 | 103 | } |
603 | 233 | } |
604 | | |
605 | 1.13k | ret = 1; |
606 | | |
607 | 1.13k | err: |
608 | 1.13k | BN_CTX_end(ctx); |
609 | 1.13k | BN_CTX_free(new_ctx); |
610 | 1.13k | return ret; |
611 | 1.13k | } |
612 | | |
613 | | int ossl_ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
614 | | const EC_POINT *b, BN_CTX *ctx) |
615 | 30.4k | { |
616 | 30.4k | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
617 | 30.4k | const BIGNUM *, BN_CTX *); |
618 | 30.4k | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
619 | 30.4k | const BIGNUM *p; |
620 | 30.4k | BN_CTX *new_ctx = NULL; |
621 | 30.4k | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; |
622 | 30.4k | int ret = 0; |
623 | | |
624 | 30.4k | if (a == b) |
625 | 0 | return EC_POINT_dbl(group, r, a, ctx); |
626 | 30.4k | if (EC_POINT_is_at_infinity(group, a)) |
627 | 1 | return EC_POINT_copy(r, b); |
628 | 30.4k | if (EC_POINT_is_at_infinity(group, b)) |
629 | 0 | return EC_POINT_copy(r, a); |
630 | | |
631 | 30.4k | field_mul = group->meth->field_mul; |
632 | 30.4k | field_sqr = group->meth->field_sqr; |
633 | 30.4k | p = group->field; |
634 | | |
635 | 30.4k | if (ctx == NULL) { |
636 | 23 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
637 | 23 | if (ctx == NULL) |
638 | 0 | return 0; |
639 | 23 | } |
640 | | |
641 | 30.4k | BN_CTX_start(ctx); |
642 | 30.4k | n0 = BN_CTX_get(ctx); |
643 | 30.4k | n1 = BN_CTX_get(ctx); |
644 | 30.4k | n2 = BN_CTX_get(ctx); |
645 | 30.4k | n3 = BN_CTX_get(ctx); |
646 | 30.4k | n4 = BN_CTX_get(ctx); |
647 | 30.4k | n5 = BN_CTX_get(ctx); |
648 | 30.4k | n6 = BN_CTX_get(ctx); |
649 | 30.4k | if (n6 == NULL) |
650 | 0 | goto end; |
651 | | |
652 | | /* |
653 | | * Note that in this function we must not read components of 'a' or 'b' |
654 | | * once we have written the corresponding components of 'r'. ('r' might |
655 | | * be one of 'a' or 'b'.) |
656 | | */ |
657 | | |
658 | | /* n1, n2 */ |
659 | 30.4k | if (b->Z_is_one) { |
660 | 15.0k | if (!BN_copy(n1, a->X)) |
661 | 0 | goto end; |
662 | 15.0k | if (!BN_copy(n2, a->Y)) |
663 | 0 | goto end; |
664 | | /* n1 = X_a */ |
665 | | /* n2 = Y_a */ |
666 | 15.3k | } else { |
667 | 15.3k | if (!field_sqr(group, n0, b->Z, ctx)) |
668 | 0 | goto end; |
669 | 15.3k | if (!field_mul(group, n1, a->X, n0, ctx)) |
670 | 0 | goto end; |
671 | | /* n1 = X_a * Z_b^2 */ |
672 | | |
673 | 15.3k | if (!field_mul(group, n0, n0, b->Z, ctx)) |
674 | 0 | goto end; |
675 | 15.3k | if (!field_mul(group, n2, a->Y, n0, ctx)) |
676 | 0 | goto end; |
677 | | /* n2 = Y_a * Z_b^3 */ |
678 | 15.3k | } |
679 | | |
680 | | /* n3, n4 */ |
681 | 30.4k | if (a->Z_is_one) { |
682 | 266 | if (!BN_copy(n3, b->X)) |
683 | 0 | goto end; |
684 | 266 | if (!BN_copy(n4, b->Y)) |
685 | 0 | goto end; |
686 | | /* n3 = X_b */ |
687 | | /* n4 = Y_b */ |
688 | 30.2k | } else { |
689 | 30.2k | if (!field_sqr(group, n0, a->Z, ctx)) |
690 | 0 | goto end; |
691 | 30.2k | if (!field_mul(group, n3, b->X, n0, ctx)) |
692 | 0 | goto end; |
693 | | /* n3 = X_b * Z_a^2 */ |
694 | | |
695 | 30.2k | if (!field_mul(group, n0, n0, a->Z, ctx)) |
696 | 0 | goto end; |
697 | 30.2k | if (!field_mul(group, n4, b->Y, n0, ctx)) |
698 | 0 | goto end; |
699 | | /* n4 = Y_b * Z_a^3 */ |
700 | 30.2k | } |
701 | | |
702 | | /* n5, n6 */ |
703 | 30.4k | if (!BN_mod_sub_quick(n5, n1, n3, p)) |
704 | 0 | goto end; |
705 | 30.4k | if (!BN_mod_sub_quick(n6, n2, n4, p)) |
706 | 0 | goto end; |
707 | | /* n5 = n1 - n3 */ |
708 | | /* n6 = n2 - n4 */ |
709 | | |
710 | 30.4k | if (BN_is_zero(n5)) { |
711 | 20 | if (BN_is_zero(n6)) { |
712 | | /* a is the same point as b */ |
713 | 15 | BN_CTX_end(ctx); |
714 | 15 | ret = EC_POINT_dbl(group, r, a, ctx); |
715 | 15 | ctx = NULL; |
716 | 15 | goto end; |
717 | 15 | } else { |
718 | | /* a is the inverse of b */ |
719 | 5 | BN_zero(r->Z); |
720 | 5 | r->Z_is_one = 0; |
721 | 5 | ret = 1; |
722 | 5 | goto end; |
723 | 5 | } |
724 | 20 | } |
725 | | |
726 | | /* 'n7', 'n8' */ |
727 | 30.4k | if (!BN_mod_add_quick(n1, n1, n3, p)) |
728 | 0 | goto end; |
729 | 30.4k | if (!BN_mod_add_quick(n2, n2, n4, p)) |
730 | 0 | goto end; |
731 | | /* 'n7' = n1 + n3 */ |
732 | | /* 'n8' = n2 + n4 */ |
733 | | |
734 | | /* Z_r */ |
735 | 30.4k | if (a->Z_is_one && b->Z_is_one) { |
736 | 5 | if (!BN_copy(r->Z, n5)) |
737 | 0 | goto end; |
738 | 30.4k | } else { |
739 | 30.4k | if (a->Z_is_one) { |
740 | 254 | if (!BN_copy(n0, b->Z)) |
741 | 0 | goto end; |
742 | 30.1k | } else if (b->Z_is_one) { |
743 | 15.0k | if (!BN_copy(n0, a->Z)) |
744 | 0 | goto end; |
745 | 15.1k | } else { |
746 | 15.1k | if (!field_mul(group, n0, a->Z, b->Z, ctx)) |
747 | 0 | goto end; |
748 | 15.1k | } |
749 | 30.4k | if (!field_mul(group, r->Z, n0, n5, ctx)) |
750 | 0 | goto end; |
751 | 30.4k | } |
752 | 30.4k | r->Z_is_one = 0; |
753 | | /* Z_r = Z_a * Z_b * n5 */ |
754 | | |
755 | | /* X_r */ |
756 | 30.4k | if (!field_sqr(group, n0, n6, ctx)) |
757 | 0 | goto end; |
758 | 30.4k | if (!field_sqr(group, n4, n5, ctx)) |
759 | 0 | goto end; |
760 | 30.4k | if (!field_mul(group, n3, n1, n4, ctx)) |
761 | 0 | goto end; |
762 | 30.4k | if (!BN_mod_sub_quick(r->X, n0, n3, p)) |
763 | 0 | goto end; |
764 | | /* X_r = n6^2 - n5^2 * 'n7' */ |
765 | | |
766 | | /* 'n9' */ |
767 | 30.4k | if (!BN_mod_lshift1_quick(n0, r->X, p)) |
768 | 0 | goto end; |
769 | 30.4k | if (!BN_mod_sub_quick(n0, n3, n0, p)) |
770 | 0 | goto end; |
771 | | /* n9 = n5^2 * 'n7' - 2 * X_r */ |
772 | | |
773 | | /* Y_r */ |
774 | 30.4k | if (!field_mul(group, n0, n0, n6, ctx)) |
775 | 0 | goto end; |
776 | 30.4k | if (!field_mul(group, n5, n4, n5, ctx)) |
777 | 0 | goto end; /* now n5 is n5^3 */ |
778 | 30.4k | if (!field_mul(group, n1, n2, n5, ctx)) |
779 | 0 | goto end; |
780 | 30.4k | if (!BN_mod_sub_quick(n0, n0, n1, p)) |
781 | 0 | goto end; |
782 | 30.4k | if (BN_is_odd(n0)) |
783 | 15.0k | if (!BN_add(n0, n0, p)) |
784 | 0 | goto end; |
785 | | /* now 0 <= n0 < 2*p, and n0 is even */ |
786 | 30.4k | if (!BN_rshift1(r->Y, n0)) |
787 | 0 | goto end; |
788 | | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
789 | | |
790 | 30.4k | ret = 1; |
791 | | |
792 | 30.4k | end: |
793 | 30.4k | BN_CTX_end(ctx); |
794 | 30.4k | BN_CTX_free(new_ctx); |
795 | 30.4k | return ret; |
796 | 30.4k | } |
797 | | |
798 | | int ossl_ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
799 | | BN_CTX *ctx) |
800 | 59.4k | { |
801 | 59.4k | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
802 | 59.4k | const BIGNUM *, BN_CTX *); |
803 | 59.4k | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
804 | 59.4k | const BIGNUM *p; |
805 | 59.4k | BN_CTX *new_ctx = NULL; |
806 | 59.4k | BIGNUM *n0, *n1, *n2, *n3; |
807 | 59.4k | int ret = 0; |
808 | | |
809 | 59.4k | if (EC_POINT_is_at_infinity(group, a)) { |
810 | 6 | BN_zero(r->Z); |
811 | 6 | r->Z_is_one = 0; |
812 | 6 | return 1; |
813 | 6 | } |
814 | | |
815 | 59.4k | field_mul = group->meth->field_mul; |
816 | 59.4k | field_sqr = group->meth->field_sqr; |
817 | 59.4k | p = group->field; |
818 | | |
819 | 59.4k | if (ctx == NULL) { |
820 | 27 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
821 | 27 | if (ctx == NULL) |
822 | 0 | return 0; |
823 | 27 | } |
824 | | |
825 | 59.4k | BN_CTX_start(ctx); |
826 | 59.4k | n0 = BN_CTX_get(ctx); |
827 | 59.4k | n1 = BN_CTX_get(ctx); |
828 | 59.4k | n2 = BN_CTX_get(ctx); |
829 | 59.4k | n3 = BN_CTX_get(ctx); |
830 | 59.4k | if (n3 == NULL) |
831 | 0 | goto err; |
832 | | |
833 | | /* |
834 | | * Note that in this function we must not read components of 'a' once we |
835 | | * have written the corresponding components of 'r'. ('r' might the same |
836 | | * as 'a'.) |
837 | | */ |
838 | | |
839 | | /* n1 */ |
840 | 59.4k | if (a->Z_is_one) { |
841 | 329 | if (!field_sqr(group, n0, a->X, ctx)) |
842 | 0 | goto err; |
843 | 329 | if (!BN_mod_lshift1_quick(n1, n0, p)) |
844 | 0 | goto err; |
845 | 329 | if (!BN_mod_add_quick(n0, n0, n1, p)) |
846 | 0 | goto err; |
847 | 329 | if (!BN_mod_add_quick(n1, n0, group->a, p)) |
848 | 0 | goto err; |
849 | | /* n1 = 3 * X_a^2 + a_curve */ |
850 | 59.1k | } else if (group->a_is_minus3) { |
851 | 45.0k | if (!field_sqr(group, n1, a->Z, ctx)) |
852 | 0 | goto err; |
853 | 45.0k | if (!BN_mod_add_quick(n0, a->X, n1, p)) |
854 | 0 | goto err; |
855 | 45.0k | if (!BN_mod_sub_quick(n2, a->X, n1, p)) |
856 | 0 | goto err; |
857 | 45.0k | if (!field_mul(group, n1, n0, n2, ctx)) |
858 | 0 | goto err; |
859 | 45.0k | if (!BN_mod_lshift1_quick(n0, n1, p)) |
860 | 0 | goto err; |
861 | 45.0k | if (!BN_mod_add_quick(n1, n0, n1, p)) |
862 | 0 | goto err; |
863 | | /*- |
864 | | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) |
865 | | * = 3 * X_a^2 - 3 * Z_a^4 |
866 | | */ |
867 | 45.0k | } else { |
868 | 14.0k | if (!field_sqr(group, n0, a->X, ctx)) |
869 | 0 | goto err; |
870 | 14.0k | if (!BN_mod_lshift1_quick(n1, n0, p)) |
871 | 0 | goto err; |
872 | 14.0k | if (!BN_mod_add_quick(n0, n0, n1, p)) |
873 | 0 | goto err; |
874 | 14.0k | if (!field_sqr(group, n1, a->Z, ctx)) |
875 | 0 | goto err; |
876 | 14.0k | if (!field_sqr(group, n1, n1, ctx)) |
877 | 0 | goto err; |
878 | 14.0k | if (!field_mul(group, n1, n1, group->a, ctx)) |
879 | 0 | goto err; |
880 | 14.0k | if (!BN_mod_add_quick(n1, n1, n0, p)) |
881 | 0 | goto err; |
882 | | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ |
883 | 14.0k | } |
884 | | |
885 | | /* Z_r */ |
886 | 59.4k | if (a->Z_is_one) { |
887 | 329 | if (!BN_copy(n0, a->Y)) |
888 | 0 | goto err; |
889 | 59.1k | } else { |
890 | 59.1k | if (!field_mul(group, n0, a->Y, a->Z, ctx)) |
891 | 0 | goto err; |
892 | 59.1k | } |
893 | 59.4k | if (!BN_mod_lshift1_quick(r->Z, n0, p)) |
894 | 0 | goto err; |
895 | 59.4k | r->Z_is_one = 0; |
896 | | /* Z_r = 2 * Y_a * Z_a */ |
897 | | |
898 | | /* n2 */ |
899 | 59.4k | if (!field_sqr(group, n3, a->Y, ctx)) |
900 | 0 | goto err; |
901 | 59.4k | if (!field_mul(group, n2, a->X, n3, ctx)) |
902 | 0 | goto err; |
903 | 59.4k | if (!BN_mod_lshift_quick(n2, n2, 2, p)) |
904 | 0 | goto err; |
905 | | /* n2 = 4 * X_a * Y_a^2 */ |
906 | | |
907 | | /* X_r */ |
908 | 59.4k | if (!BN_mod_lshift1_quick(n0, n2, p)) |
909 | 0 | goto err; |
910 | 59.4k | if (!field_sqr(group, r->X, n1, ctx)) |
911 | 0 | goto err; |
912 | 59.4k | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) |
913 | 0 | goto err; |
914 | | /* X_r = n1^2 - 2 * n2 */ |
915 | | |
916 | | /* n3 */ |
917 | 59.4k | if (!field_sqr(group, n0, n3, ctx)) |
918 | 0 | goto err; |
919 | 59.4k | if (!BN_mod_lshift_quick(n3, n0, 3, p)) |
920 | 0 | goto err; |
921 | | /* n3 = 8 * Y_a^4 */ |
922 | | |
923 | | /* Y_r */ |
924 | 59.4k | if (!BN_mod_sub_quick(n0, n2, r->X, p)) |
925 | 0 | goto err; |
926 | 59.4k | if (!field_mul(group, n0, n1, n0, ctx)) |
927 | 0 | goto err; |
928 | 59.4k | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) |
929 | 0 | goto err; |
930 | | /* Y_r = n1 * (n2 - X_r) - n3 */ |
931 | | |
932 | 59.4k | ret = 1; |
933 | | |
934 | 59.4k | err: |
935 | 59.4k | BN_CTX_end(ctx); |
936 | 59.4k | BN_CTX_free(new_ctx); |
937 | 59.4k | return ret; |
938 | 59.4k | } |
939 | | |
940 | | int ossl_ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, |
941 | | BN_CTX *ctx) |
942 | 7.57k | { |
943 | 7.57k | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) |
944 | | /* point is its own inverse */ |
945 | 6 | return 1; |
946 | | |
947 | 7.56k | return BN_usub(point->Y, group->field, point->Y); |
948 | 7.57k | } |
949 | | |
950 | | int ossl_ec_GFp_simple_is_at_infinity(const EC_GROUP *group, |
951 | | const EC_POINT *point) |
952 | 135k | { |
953 | 135k | return BN_is_zero(point->Z); |
954 | 135k | } |
955 | | |
956 | | int ossl_ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
957 | | BN_CTX *ctx) |
958 | 4.09k | { |
959 | 4.09k | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
960 | 4.09k | const BIGNUM *, BN_CTX *); |
961 | 4.09k | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
962 | 4.09k | const BIGNUM *p; |
963 | 4.09k | BN_CTX *new_ctx = NULL; |
964 | 4.09k | BIGNUM *rh, *tmp, *Z4, *Z6; |
965 | 4.09k | int ret = -1; |
966 | | |
967 | 4.09k | if (EC_POINT_is_at_infinity(group, point)) |
968 | 0 | return 1; |
969 | | |
970 | 4.09k | field_mul = group->meth->field_mul; |
971 | 4.09k | field_sqr = group->meth->field_sqr; |
972 | 4.09k | p = group->field; |
973 | | |
974 | 4.09k | if (ctx == NULL) { |
975 | 1.49k | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
976 | 1.49k | if (ctx == NULL) |
977 | 0 | return -1; |
978 | 1.49k | } |
979 | | |
980 | 4.09k | BN_CTX_start(ctx); |
981 | 4.09k | rh = BN_CTX_get(ctx); |
982 | 4.09k | tmp = BN_CTX_get(ctx); |
983 | 4.09k | Z4 = BN_CTX_get(ctx); |
984 | 4.09k | Z6 = BN_CTX_get(ctx); |
985 | 4.09k | if (Z6 == NULL) |
986 | 0 | goto err; |
987 | | |
988 | | /*- |
989 | | * We have a curve defined by a Weierstrass equation |
990 | | * y^2 = x^3 + a*x + b. |
991 | | * The point to consider is given in Jacobian projective coordinates |
992 | | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). |
993 | | * Substituting this and multiplying by Z^6 transforms the above equation into |
994 | | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. |
995 | | * To test this, we add up the right-hand side in 'rh'. |
996 | | */ |
997 | | |
998 | | /* rh := X^2 */ |
999 | 4.09k | if (!field_sqr(group, rh, point->X, ctx)) |
1000 | 0 | goto err; |
1001 | | |
1002 | 4.09k | if (!point->Z_is_one) { |
1003 | 369 | if (!field_sqr(group, tmp, point->Z, ctx)) |
1004 | 0 | goto err; |
1005 | 369 | if (!field_sqr(group, Z4, tmp, ctx)) |
1006 | 0 | goto err; |
1007 | 369 | if (!field_mul(group, Z6, Z4, tmp, ctx)) |
1008 | 0 | goto err; |
1009 | | |
1010 | | /* rh := (rh + a*Z^4)*X */ |
1011 | 369 | if (group->a_is_minus3) { |
1012 | 237 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) |
1013 | 0 | goto err; |
1014 | 237 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) |
1015 | 0 | goto err; |
1016 | 237 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) |
1017 | 0 | goto err; |
1018 | 237 | if (!field_mul(group, rh, rh, point->X, ctx)) |
1019 | 0 | goto err; |
1020 | 237 | } else { |
1021 | 132 | if (!field_mul(group, tmp, Z4, group->a, ctx)) |
1022 | 0 | goto err; |
1023 | 132 | if (!BN_mod_add_quick(rh, rh, tmp, p)) |
1024 | 0 | goto err; |
1025 | 132 | if (!field_mul(group, rh, rh, point->X, ctx)) |
1026 | 0 | goto err; |
1027 | 132 | } |
1028 | | |
1029 | | /* rh := rh + b*Z^6 */ |
1030 | 369 | if (!field_mul(group, tmp, group->b, Z6, ctx)) |
1031 | 0 | goto err; |
1032 | 369 | if (!BN_mod_add_quick(rh, rh, tmp, p)) |
1033 | 0 | goto err; |
1034 | 3.72k | } else { |
1035 | | /* point->Z_is_one */ |
1036 | | |
1037 | | /* rh := (rh + a)*X */ |
1038 | 3.72k | if (!BN_mod_add_quick(rh, rh, group->a, p)) |
1039 | 0 | goto err; |
1040 | 3.72k | if (!field_mul(group, rh, rh, point->X, ctx)) |
1041 | 0 | goto err; |
1042 | | /* rh := rh + b */ |
1043 | 3.72k | if (!BN_mod_add_quick(rh, rh, group->b, p)) |
1044 | 0 | goto err; |
1045 | 3.72k | } |
1046 | | |
1047 | | /* 'lh' := Y^2 */ |
1048 | 4.09k | if (!field_sqr(group, tmp, point->Y, ctx)) |
1049 | 0 | goto err; |
1050 | | |
1051 | 4.09k | ret = (0 == BN_ucmp(tmp, rh)); |
1052 | | |
1053 | 4.09k | err: |
1054 | 4.09k | BN_CTX_end(ctx); |
1055 | 4.09k | BN_CTX_free(new_ctx); |
1056 | 4.09k | return ret; |
1057 | 4.09k | } |
1058 | | |
1059 | | int ossl_ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
1060 | | const EC_POINT *b, BN_CTX *ctx) |
1061 | 11 | { |
1062 | | /*- |
1063 | | * return values: |
1064 | | * -1 error |
1065 | | * 0 equal (in affine coordinates) |
1066 | | * 1 not equal |
1067 | | */ |
1068 | | |
1069 | 11 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
1070 | 11 | const BIGNUM *, BN_CTX *); |
1071 | 11 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
1072 | 11 | BN_CTX *new_ctx = NULL; |
1073 | 11 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; |
1074 | 11 | const BIGNUM *tmp1_, *tmp2_; |
1075 | 11 | int ret = -1; |
1076 | | |
1077 | 11 | if (EC_POINT_is_at_infinity(group, a)) { |
1078 | 0 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; |
1079 | 0 | } |
1080 | | |
1081 | 11 | if (EC_POINT_is_at_infinity(group, b)) |
1082 | 0 | return 1; |
1083 | | |
1084 | 11 | if (a->Z_is_one && b->Z_is_one) { |
1085 | 6 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; |
1086 | 6 | } |
1087 | | |
1088 | 5 | field_mul = group->meth->field_mul; |
1089 | 5 | field_sqr = group->meth->field_sqr; |
1090 | | |
1091 | 5 | if (ctx == NULL) { |
1092 | 5 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
1093 | 5 | if (ctx == NULL) |
1094 | 0 | return -1; |
1095 | 5 | } |
1096 | | |
1097 | 5 | BN_CTX_start(ctx); |
1098 | 5 | tmp1 = BN_CTX_get(ctx); |
1099 | 5 | tmp2 = BN_CTX_get(ctx); |
1100 | 5 | Za23 = BN_CTX_get(ctx); |
1101 | 5 | Zb23 = BN_CTX_get(ctx); |
1102 | 5 | if (Zb23 == NULL) |
1103 | 0 | goto end; |
1104 | | |
1105 | | /*- |
1106 | | * We have to decide whether |
1107 | | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), |
1108 | | * or equivalently, whether |
1109 | | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). |
1110 | | */ |
1111 | | |
1112 | 5 | if (!b->Z_is_one) { |
1113 | 3 | if (!field_sqr(group, Zb23, b->Z, ctx)) |
1114 | 0 | goto end; |
1115 | 3 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) |
1116 | 0 | goto end; |
1117 | 3 | tmp1_ = tmp1; |
1118 | 3 | } else |
1119 | 2 | tmp1_ = a->X; |
1120 | 5 | if (!a->Z_is_one) { |
1121 | 3 | if (!field_sqr(group, Za23, a->Z, ctx)) |
1122 | 0 | goto end; |
1123 | 3 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) |
1124 | 0 | goto end; |
1125 | 3 | tmp2_ = tmp2; |
1126 | 3 | } else |
1127 | 2 | tmp2_ = b->X; |
1128 | | |
1129 | | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ |
1130 | 5 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
1131 | 1 | ret = 1; /* points differ */ |
1132 | 1 | goto end; |
1133 | 1 | } |
1134 | | |
1135 | 4 | if (!b->Z_is_one) { |
1136 | 2 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) |
1137 | 0 | goto end; |
1138 | 2 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) |
1139 | 0 | goto end; |
1140 | | /* tmp1_ = tmp1 */ |
1141 | 2 | } else |
1142 | 2 | tmp1_ = a->Y; |
1143 | 4 | if (!a->Z_is_one) { |
1144 | 3 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) |
1145 | 0 | goto end; |
1146 | 3 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) |
1147 | 0 | goto end; |
1148 | | /* tmp2_ = tmp2 */ |
1149 | 3 | } else |
1150 | 1 | tmp2_ = b->Y; |
1151 | | |
1152 | | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ |
1153 | 4 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
1154 | 0 | ret = 1; /* points differ */ |
1155 | 0 | goto end; |
1156 | 0 | } |
1157 | | |
1158 | | /* points are equal */ |
1159 | 4 | ret = 0; |
1160 | | |
1161 | 5 | end: |
1162 | 5 | BN_CTX_end(ctx); |
1163 | 5 | BN_CTX_free(new_ctx); |
1164 | 5 | return ret; |
1165 | 4 | } |
1166 | | |
1167 | | int ossl_ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
1168 | | BN_CTX *ctx) |
1169 | 52 | { |
1170 | 52 | BN_CTX *new_ctx = NULL; |
1171 | 52 | BIGNUM *x, *y; |
1172 | 52 | int ret = 0; |
1173 | | |
1174 | 52 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) |
1175 | 0 | return 1; |
1176 | | |
1177 | 52 | if (ctx == NULL) { |
1178 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
1179 | 0 | if (ctx == NULL) |
1180 | 0 | return 0; |
1181 | 0 | } |
1182 | | |
1183 | 52 | BN_CTX_start(ctx); |
1184 | 52 | x = BN_CTX_get(ctx); |
1185 | 52 | y = BN_CTX_get(ctx); |
1186 | 52 | if (y == NULL) |
1187 | 0 | goto err; |
1188 | | |
1189 | 52 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) |
1190 | 1 | goto err; |
1191 | 51 | if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) |
1192 | 0 | goto err; |
1193 | 51 | if (!point->Z_is_one) { |
1194 | 0 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
1195 | 0 | goto err; |
1196 | 0 | } |
1197 | | |
1198 | 51 | ret = 1; |
1199 | | |
1200 | 52 | err: |
1201 | 52 | BN_CTX_end(ctx); |
1202 | 52 | BN_CTX_free(new_ctx); |
1203 | 52 | return ret; |
1204 | 51 | } |
1205 | | |
1206 | | int ossl_ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, |
1207 | | EC_POINT *points[], BN_CTX *ctx) |
1208 | 186 | { |
1209 | 186 | BN_CTX *new_ctx = NULL; |
1210 | 186 | BIGNUM *tmp, *tmp_Z; |
1211 | 186 | BIGNUM **prod_Z = NULL; |
1212 | 186 | size_t i; |
1213 | 186 | int ret = 0; |
1214 | | |
1215 | 186 | if (num == 0) |
1216 | 0 | return 1; |
1217 | | |
1218 | 186 | if (ctx == NULL) { |
1219 | 0 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
1220 | 0 | if (ctx == NULL) |
1221 | 0 | return 0; |
1222 | 0 | } |
1223 | | |
1224 | 186 | BN_CTX_start(ctx); |
1225 | 186 | tmp = BN_CTX_get(ctx); |
1226 | 186 | tmp_Z = BN_CTX_get(ctx); |
1227 | 186 | if (tmp_Z == NULL) |
1228 | 0 | goto err; |
1229 | | |
1230 | 186 | prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); |
1231 | 186 | if (prod_Z == NULL) |
1232 | 0 | goto err; |
1233 | 17.8k | for (i = 0; i < num; i++) { |
1234 | 17.7k | prod_Z[i] = BN_new(); |
1235 | 17.7k | if (prod_Z[i] == NULL) |
1236 | 0 | goto err; |
1237 | 17.7k | } |
1238 | | |
1239 | | /* |
1240 | | * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, |
1241 | | * skipping any zero-valued inputs (pretend that they're 1). |
1242 | | */ |
1243 | | |
1244 | 186 | if (!BN_is_zero(points[0]->Z)) { |
1245 | 186 | if (!BN_copy(prod_Z[0], points[0]->Z)) |
1246 | 0 | goto err; |
1247 | 186 | } else { |
1248 | 0 | if (group->meth->field_set_to_one != 0) { |
1249 | 0 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) |
1250 | 0 | goto err; |
1251 | 0 | } else { |
1252 | 0 | if (!BN_one(prod_Z[0])) |
1253 | 0 | goto err; |
1254 | 0 | } |
1255 | 0 | } |
1256 | | |
1257 | 17.7k | for (i = 1; i < num; i++) { |
1258 | 17.5k | if (!BN_is_zero(points[i]->Z)) { |
1259 | 17.5k | if (!group-> |
1260 | 17.5k | meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, |
1261 | 17.5k | ctx)) |
1262 | 0 | goto err; |
1263 | 17.5k | } else { |
1264 | 0 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) |
1265 | 0 | goto err; |
1266 | 0 | } |
1267 | 17.5k | } |
1268 | | |
1269 | | /* |
1270 | | * Now use a single explicit inversion to replace every non-zero |
1271 | | * points[i]->Z by its inverse. |
1272 | | */ |
1273 | | |
1274 | 186 | if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) { |
1275 | 0 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
1276 | 0 | goto err; |
1277 | 0 | } |
1278 | 186 | if (group->meth->field_encode != NULL) { |
1279 | | /* |
1280 | | * In the Montgomery case, we just turned R*H (representing H) into |
1281 | | * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to |
1282 | | * multiply by the Montgomery factor twice. |
1283 | | */ |
1284 | 134 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
1285 | 0 | goto err; |
1286 | 134 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
1287 | 0 | goto err; |
1288 | 134 | } |
1289 | | |
1290 | 17.7k | for (i = num - 1; i > 0; --i) { |
1291 | | /* |
1292 | | * Loop invariant: tmp is the product of the inverses of points[0]->Z |
1293 | | * .. points[i]->Z (zero-valued inputs skipped). |
1294 | | */ |
1295 | 17.5k | if (!BN_is_zero(points[i]->Z)) { |
1296 | | /* |
1297 | | * Set tmp_Z to the inverse of points[i]->Z (as product of Z |
1298 | | * inverses 0 .. i, Z values 0 .. i - 1). |
1299 | | */ |
1300 | 17.5k | if (!group-> |
1301 | 17.5k | meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) |
1302 | 0 | goto err; |
1303 | | /* |
1304 | | * Update tmp to satisfy the loop invariant for i - 1. |
1305 | | */ |
1306 | 17.5k | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) |
1307 | 0 | goto err; |
1308 | | /* Replace points[i]->Z by its inverse. */ |
1309 | 17.5k | if (!BN_copy(points[i]->Z, tmp_Z)) |
1310 | 0 | goto err; |
1311 | 17.5k | } |
1312 | 17.5k | } |
1313 | | |
1314 | 186 | if (!BN_is_zero(points[0]->Z)) { |
1315 | | /* Replace points[0]->Z by its inverse. */ |
1316 | 186 | if (!BN_copy(points[0]->Z, tmp)) |
1317 | 0 | goto err; |
1318 | 186 | } |
1319 | | |
1320 | | /* Finally, fix up the X and Y coordinates for all points. */ |
1321 | | |
1322 | 17.8k | for (i = 0; i < num; i++) { |
1323 | 17.7k | EC_POINT *p = points[i]; |
1324 | | |
1325 | 17.7k | if (!BN_is_zero(p->Z)) { |
1326 | | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ |
1327 | | |
1328 | 17.7k | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) |
1329 | 0 | goto err; |
1330 | 17.7k | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) |
1331 | 0 | goto err; |
1332 | | |
1333 | 17.7k | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) |
1334 | 0 | goto err; |
1335 | 17.7k | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) |
1336 | 0 | goto err; |
1337 | | |
1338 | 17.7k | if (group->meth->field_set_to_one != 0) { |
1339 | 11.8k | if (!group->meth->field_set_to_one(group, p->Z, ctx)) |
1340 | 0 | goto err; |
1341 | 11.8k | } else { |
1342 | 5.89k | if (!BN_one(p->Z)) |
1343 | 0 | goto err; |
1344 | 5.89k | } |
1345 | 17.7k | p->Z_is_one = 1; |
1346 | 17.7k | } |
1347 | 17.7k | } |
1348 | | |
1349 | 186 | ret = 1; |
1350 | | |
1351 | 186 | err: |
1352 | 186 | BN_CTX_end(ctx); |
1353 | 186 | BN_CTX_free(new_ctx); |
1354 | 186 | if (prod_Z != NULL) { |
1355 | 17.8k | for (i = 0; i < num; i++) { |
1356 | 17.7k | if (prod_Z[i] == NULL) |
1357 | 0 | break; |
1358 | 17.7k | BN_clear_free(prod_Z[i]); |
1359 | 17.7k | } |
1360 | 186 | OPENSSL_free(prod_Z); |
1361 | 186 | } |
1362 | 186 | return ret; |
1363 | 186 | } |
1364 | | |
1365 | | int ossl_ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
1366 | | const BIGNUM *b, BN_CTX *ctx) |
1367 | 0 | { |
1368 | 0 | return BN_mod_mul(r, a, b, group->field, ctx); |
1369 | 0 | } |
1370 | | |
1371 | | int ossl_ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
1372 | | BN_CTX *ctx) |
1373 | 0 | { |
1374 | 0 | return BN_mod_sqr(r, a, group->field, ctx); |
1375 | 0 | } |
1376 | | |
1377 | | /*- |
1378 | | * Computes the multiplicative inverse of a in GF(p), storing the result in r. |
1379 | | * If a is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error. |
1380 | | * Since we don't have a Mont structure here, SCA hardening is with blinding. |
1381 | | * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.) |
1382 | | */ |
1383 | | int ossl_ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, |
1384 | | const BIGNUM *a, BN_CTX *ctx) |
1385 | 378 | { |
1386 | 378 | BIGNUM *e = NULL; |
1387 | 378 | BN_CTX *new_ctx = NULL; |
1388 | 378 | int ret = 0; |
1389 | | |
1390 | 378 | if (ctx == NULL |
1391 | 378 | && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL) |
1392 | 0 | return 0; |
1393 | | |
1394 | 378 | BN_CTX_start(ctx); |
1395 | 378 | if ((e = BN_CTX_get(ctx)) == NULL) |
1396 | 0 | goto err; |
1397 | | |
1398 | 378 | do { |
1399 | 378 | if (!BN_priv_rand_range_ex(e, group->field, 0, ctx)) |
1400 | 7 | goto err; |
1401 | 378 | } while (BN_is_zero(e)); |
1402 | | |
1403 | | /* r := a * e */ |
1404 | 371 | if (!group->meth->field_mul(group, r, a, e, ctx)) |
1405 | 0 | goto err; |
1406 | | /* r := 1/(a * e) */ |
1407 | 371 | if (!BN_mod_inverse(r, r, group->field, ctx)) { |
1408 | 0 | ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT); |
1409 | 0 | goto err; |
1410 | 0 | } |
1411 | | /* r := e/(a * e) = 1/a */ |
1412 | 371 | if (!group->meth->field_mul(group, r, r, e, ctx)) |
1413 | 0 | goto err; |
1414 | | |
1415 | 371 | ret = 1; |
1416 | | |
1417 | 378 | err: |
1418 | 378 | BN_CTX_end(ctx); |
1419 | 378 | BN_CTX_free(new_ctx); |
1420 | 378 | return ret; |
1421 | 371 | } |
1422 | | |
1423 | | /*- |
1424 | | * Apply randomization of EC point projective coordinates: |
1425 | | * |
1426 | | * (X, Y, Z) = (lambda^2*X, lambda^3*Y, lambda*Z) |
1427 | | * lambda = [1, group->field) |
1428 | | * |
1429 | | */ |
1430 | | int ossl_ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, |
1431 | | BN_CTX *ctx) |
1432 | 136 | { |
1433 | 136 | int ret = 0; |
1434 | 136 | BIGNUM *lambda = NULL; |
1435 | 136 | BIGNUM *temp = NULL; |
1436 | | |
1437 | 136 | BN_CTX_start(ctx); |
1438 | 136 | lambda = BN_CTX_get(ctx); |
1439 | 136 | temp = BN_CTX_get(ctx); |
1440 | 136 | if (temp == NULL) { |
1441 | 0 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
1442 | 0 | goto end; |
1443 | 0 | } |
1444 | | |
1445 | | /*- |
1446 | | * Make sure lambda is not zero. |
1447 | | * If the RNG fails, we cannot blind but nevertheless want |
1448 | | * code to continue smoothly and not clobber the error stack. |
1449 | | */ |
1450 | 136 | do { |
1451 | 136 | ERR_set_mark(); |
1452 | 136 | ret = BN_priv_rand_range_ex(lambda, group->field, 0, ctx); |
1453 | 136 | ERR_pop_to_mark(); |
1454 | 136 | if (ret == 0) { |
1455 | 0 | ret = 1; |
1456 | 0 | goto end; |
1457 | 0 | } |
1458 | 136 | } while (BN_is_zero(lambda)); |
1459 | | |
1460 | | /* if field_encode defined convert between representations */ |
1461 | 136 | if ((group->meth->field_encode != NULL |
1462 | 136 | && !group->meth->field_encode(group, lambda, lambda, ctx)) |
1463 | 136 | || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx) |
1464 | 136 | || !group->meth->field_sqr(group, temp, lambda, ctx) |
1465 | 136 | || !group->meth->field_mul(group, p->X, p->X, temp, ctx) |
1466 | 136 | || !group->meth->field_mul(group, temp, temp, lambda, ctx) |
1467 | 136 | || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx)) |
1468 | 0 | goto end; |
1469 | | |
1470 | 136 | p->Z_is_one = 0; |
1471 | 136 | ret = 1; |
1472 | | |
1473 | 136 | end: |
1474 | 136 | BN_CTX_end(ctx); |
1475 | 136 | return ret; |
1476 | 136 | } |
1477 | | |
1478 | | /*- |
1479 | | * Input: |
1480 | | * - p: affine coordinates |
1481 | | * |
1482 | | * Output: |
1483 | | * - s := p, r := 2p: blinded projective (homogeneous) coordinates |
1484 | | * |
1485 | | * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve |
1486 | | * multiplication resistant against side channel attacks" appendix, described at |
1487 | | * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 |
1488 | | * simplified for Z1=1. |
1489 | | * |
1490 | | * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z) |
1491 | | * for any non-zero \lambda that holds for projective (homogeneous) coords. |
1492 | | */ |
1493 | | int ossl_ec_GFp_simple_ladder_pre(const EC_GROUP *group, |
1494 | | EC_POINT *r, EC_POINT *s, |
1495 | | EC_POINT *p, BN_CTX *ctx) |
1496 | 1.09k | { |
1497 | 1.09k | BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL; |
1498 | | |
1499 | 1.09k | t1 = s->Z; |
1500 | 1.09k | t2 = r->Z; |
1501 | 1.09k | t3 = s->X; |
1502 | 1.09k | t4 = r->X; |
1503 | 1.09k | t5 = s->Y; |
1504 | | |
1505 | 1.09k | if (!p->Z_is_one /* r := 2p */ |
1506 | 1.09k | || !group->meth->field_sqr(group, t3, p->X, ctx) |
1507 | 1.09k | || !BN_mod_sub_quick(t4, t3, group->a, group->field) |
1508 | 1.09k | || !group->meth->field_sqr(group, t4, t4, ctx) |
1509 | 1.09k | || !group->meth->field_mul(group, t5, p->X, group->b, ctx) |
1510 | 1.09k | || !BN_mod_lshift_quick(t5, t5, 3, group->field) |
1511 | | /* r->X coord output */ |
1512 | 1.09k | || !BN_mod_sub_quick(r->X, t4, t5, group->field) |
1513 | 1.09k | || !BN_mod_add_quick(t1, t3, group->a, group->field) |
1514 | 1.09k | || !group->meth->field_mul(group, t2, p->X, t1, ctx) |
1515 | 1.09k | || !BN_mod_add_quick(t2, group->b, t2, group->field) |
1516 | | /* r->Z coord output */ |
1517 | 1.09k | || !BN_mod_lshift_quick(r->Z, t2, 2, group->field)) |
1518 | 0 | return 0; |
1519 | | |
1520 | | /* make sure lambda (r->Y here for storage) is not zero */ |
1521 | 1.09k | do { |
1522 | 1.09k | if (!BN_priv_rand_range_ex(r->Y, group->field, 0, ctx)) |
1523 | 24 | return 0; |
1524 | 1.09k | } while (BN_is_zero(r->Y)); |
1525 | | |
1526 | | /* make sure lambda (s->Z here for storage) is not zero */ |
1527 | 1.07k | do { |
1528 | 1.07k | if (!BN_priv_rand_range_ex(s->Z, group->field, 0, ctx)) |
1529 | 38 | return 0; |
1530 | 1.07k | } while (BN_is_zero(s->Z)); |
1531 | | |
1532 | | /* if field_encode defined convert between representations */ |
1533 | 1.03k | if (group->meth->field_encode != NULL |
1534 | 1.03k | && (!group->meth->field_encode(group, r->Y, r->Y, ctx) |
1535 | 756 | || !group->meth->field_encode(group, s->Z, s->Z, ctx))) |
1536 | 0 | return 0; |
1537 | | |
1538 | | /* blind r and s independently */ |
1539 | 1.03k | if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) |
1540 | 1.03k | || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx) |
1541 | 1.03k | || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */ |
1542 | 0 | return 0; |
1543 | | |
1544 | 1.03k | r->Z_is_one = 0; |
1545 | 1.03k | s->Z_is_one = 0; |
1546 | | |
1547 | 1.03k | return 1; |
1548 | 1.03k | } |
1549 | | |
1550 | | /*- |
1551 | | * Input: |
1552 | | * - s, r: projective (homogeneous) coordinates |
1553 | | * - p: affine coordinates |
1554 | | * |
1555 | | * Output: |
1556 | | * - s := r + s, r := 2r: projective (homogeneous) coordinates |
1557 | | * |
1558 | | * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi |
1559 | | * "A fast parallel elliptic curve multiplication resistant against side channel |
1560 | | * attacks", as described at |
1561 | | * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4 |
1562 | | */ |
1563 | | int ossl_ec_GFp_simple_ladder_step(const EC_GROUP *group, |
1564 | | EC_POINT *r, EC_POINT *s, |
1565 | | EC_POINT *p, BN_CTX *ctx) |
1566 | 320k | { |
1567 | 320k | int ret = 0; |
1568 | 320k | BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; |
1569 | | |
1570 | 320k | BN_CTX_start(ctx); |
1571 | 320k | t0 = BN_CTX_get(ctx); |
1572 | 320k | t1 = BN_CTX_get(ctx); |
1573 | 320k | t2 = BN_CTX_get(ctx); |
1574 | 320k | t3 = BN_CTX_get(ctx); |
1575 | 320k | t4 = BN_CTX_get(ctx); |
1576 | 320k | t5 = BN_CTX_get(ctx); |
1577 | 320k | t6 = BN_CTX_get(ctx); |
1578 | | |
1579 | 320k | if (t6 == NULL |
1580 | 320k | || !group->meth->field_mul(group, t6, r->X, s->X, ctx) |
1581 | 320k | || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx) |
1582 | 320k | || !group->meth->field_mul(group, t4, r->X, s->Z, ctx) |
1583 | 320k | || !group->meth->field_mul(group, t3, r->Z, s->X, ctx) |
1584 | 320k | || !group->meth->field_mul(group, t5, group->a, t0, ctx) |
1585 | 320k | || !BN_mod_add_quick(t5, t6, t5, group->field) |
1586 | 320k | || !BN_mod_add_quick(t6, t3, t4, group->field) |
1587 | 320k | || !group->meth->field_mul(group, t5, t6, t5, ctx) |
1588 | 320k | || !group->meth->field_sqr(group, t0, t0, ctx) |
1589 | 320k | || !BN_mod_lshift_quick(t2, group->b, 2, group->field) |
1590 | 320k | || !group->meth->field_mul(group, t0, t2, t0, ctx) |
1591 | 320k | || !BN_mod_lshift1_quick(t5, t5, group->field) |
1592 | 320k | || !BN_mod_sub_quick(t3, t4, t3, group->field) |
1593 | | /* s->Z coord output */ |
1594 | 320k | || !group->meth->field_sqr(group, s->Z, t3, ctx) |
1595 | 320k | || !group->meth->field_mul(group, t4, s->Z, p->X, ctx) |
1596 | 320k | || !BN_mod_add_quick(t0, t0, t5, group->field) |
1597 | | /* s->X coord output */ |
1598 | 320k | || !BN_mod_sub_quick(s->X, t0, t4, group->field) |
1599 | 320k | || !group->meth->field_sqr(group, t4, r->X, ctx) |
1600 | 320k | || !group->meth->field_sqr(group, t5, r->Z, ctx) |
1601 | 320k | || !group->meth->field_mul(group, t6, t5, group->a, ctx) |
1602 | 320k | || !BN_mod_add_quick(t1, r->X, r->Z, group->field) |
1603 | 320k | || !group->meth->field_sqr(group, t1, t1, ctx) |
1604 | 320k | || !BN_mod_sub_quick(t1, t1, t4, group->field) |
1605 | 320k | || !BN_mod_sub_quick(t1, t1, t5, group->field) |
1606 | 320k | || !BN_mod_sub_quick(t3, t4, t6, group->field) |
1607 | 320k | || !group->meth->field_sqr(group, t3, t3, ctx) |
1608 | 320k | || !group->meth->field_mul(group, t0, t5, t1, ctx) |
1609 | 320k | || !group->meth->field_mul(group, t0, t2, t0, ctx) |
1610 | | /* r->X coord output */ |
1611 | 320k | || !BN_mod_sub_quick(r->X, t3, t0, group->field) |
1612 | 320k | || !BN_mod_add_quick(t3, t4, t6, group->field) |
1613 | 320k | || !group->meth->field_sqr(group, t4, t5, ctx) |
1614 | 320k | || !group->meth->field_mul(group, t4, t4, t2, ctx) |
1615 | 320k | || !group->meth->field_mul(group, t1, t1, t3, ctx) |
1616 | 320k | || !BN_mod_lshift1_quick(t1, t1, group->field) |
1617 | | /* r->Z coord output */ |
1618 | 320k | || !BN_mod_add_quick(r->Z, t4, t1, group->field)) |
1619 | 0 | goto err; |
1620 | | |
1621 | 320k | ret = 1; |
1622 | | |
1623 | 320k | err: |
1624 | 320k | BN_CTX_end(ctx); |
1625 | 320k | return ret; |
1626 | 320k | } |
1627 | | |
1628 | | /*- |
1629 | | * Input: |
1630 | | * - s, r: projective (homogeneous) coordinates |
1631 | | * - p: affine coordinates |
1632 | | * |
1633 | | * Output: |
1634 | | * - r := (x,y): affine coordinates |
1635 | | * |
1636 | | * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass |
1637 | | * Elliptic Curves and Side-Channel Attacks", modified to work in mixed |
1638 | | * projective coords, i.e. p is affine and (r,s) in projective (homogeneous) |
1639 | | * coords, and return r in affine coordinates. |
1640 | | * |
1641 | | * X4 = two*Y1*X2*Z3*Z2; |
1642 | | * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2); |
1643 | | * Z4 = two*Y1*Z3*SQR(Z2); |
1644 | | * |
1645 | | * Z4 != 0 because: |
1646 | | * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch); |
1647 | | * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch); |
1648 | | * - Y1==0 implies p has order 2, so either r or s are infinity and handled by |
1649 | | * one of the BN_is_zero(...) branches. |
1650 | | */ |
1651 | | int ossl_ec_GFp_simple_ladder_post(const EC_GROUP *group, |
1652 | | EC_POINT *r, EC_POINT *s, |
1653 | | EC_POINT *p, BN_CTX *ctx) |
1654 | 1.03k | { |
1655 | 1.03k | int ret = 0; |
1656 | 1.03k | BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; |
1657 | | |
1658 | 1.03k | if (BN_is_zero(r->Z)) |
1659 | 11 | return EC_POINT_set_to_infinity(group, r); |
1660 | | |
1661 | 1.02k | if (BN_is_zero(s->Z)) { |
1662 | 74 | if (!EC_POINT_copy(r, p) |
1663 | 74 | || !EC_POINT_invert(group, r, ctx)) |
1664 | 0 | return 0; |
1665 | 74 | return 1; |
1666 | 74 | } |
1667 | | |
1668 | 948 | BN_CTX_start(ctx); |
1669 | 948 | t0 = BN_CTX_get(ctx); |
1670 | 948 | t1 = BN_CTX_get(ctx); |
1671 | 948 | t2 = BN_CTX_get(ctx); |
1672 | 948 | t3 = BN_CTX_get(ctx); |
1673 | 948 | t4 = BN_CTX_get(ctx); |
1674 | 948 | t5 = BN_CTX_get(ctx); |
1675 | 948 | t6 = BN_CTX_get(ctx); |
1676 | | |
1677 | 948 | if (t6 == NULL |
1678 | 948 | || !BN_mod_lshift1_quick(t4, p->Y, group->field) |
1679 | 948 | || !group->meth->field_mul(group, t6, r->X, t4, ctx) |
1680 | 948 | || !group->meth->field_mul(group, t6, s->Z, t6, ctx) |
1681 | 948 | || !group->meth->field_mul(group, t5, r->Z, t6, ctx) |
1682 | 948 | || !BN_mod_lshift1_quick(t1, group->b, group->field) |
1683 | 948 | || !group->meth->field_mul(group, t1, s->Z, t1, ctx) |
1684 | 948 | || !group->meth->field_sqr(group, t3, r->Z, ctx) |
1685 | 948 | || !group->meth->field_mul(group, t2, t3, t1, ctx) |
1686 | 948 | || !group->meth->field_mul(group, t6, r->Z, group->a, ctx) |
1687 | 948 | || !group->meth->field_mul(group, t1, p->X, r->X, ctx) |
1688 | 948 | || !BN_mod_add_quick(t1, t1, t6, group->field) |
1689 | 948 | || !group->meth->field_mul(group, t1, s->Z, t1, ctx) |
1690 | 948 | || !group->meth->field_mul(group, t0, p->X, r->Z, ctx) |
1691 | 948 | || !BN_mod_add_quick(t6, r->X, t0, group->field) |
1692 | 948 | || !group->meth->field_mul(group, t6, t6, t1, ctx) |
1693 | 948 | || !BN_mod_add_quick(t6, t6, t2, group->field) |
1694 | 948 | || !BN_mod_sub_quick(t0, t0, r->X, group->field) |
1695 | 948 | || !group->meth->field_sqr(group, t0, t0, ctx) |
1696 | 948 | || !group->meth->field_mul(group, t0, t0, s->X, ctx) |
1697 | 948 | || !BN_mod_sub_quick(t0, t6, t0, group->field) |
1698 | 948 | || !group->meth->field_mul(group, t1, s->Z, t4, ctx) |
1699 | 948 | || !group->meth->field_mul(group, t1, t3, t1, ctx) |
1700 | 948 | || (group->meth->field_decode != NULL |
1701 | 948 | && !group->meth->field_decode(group, t1, t1, ctx)) |
1702 | 948 | || !group->meth->field_inv(group, t1, t1, ctx) |
1703 | 948 | || (group->meth->field_encode != NULL |
1704 | 942 | && !group->meth->field_encode(group, t1, t1, ctx)) |
1705 | 948 | || !group->meth->field_mul(group, r->X, t5, t1, ctx) |
1706 | 948 | || !group->meth->field_mul(group, r->Y, t0, t1, ctx)) |
1707 | 6 | goto err; |
1708 | | |
1709 | 942 | if (group->meth->field_set_to_one != NULL) { |
1710 | 687 | if (!group->meth->field_set_to_one(group, r->Z, ctx)) |
1711 | 0 | goto err; |
1712 | 687 | } else { |
1713 | 255 | if (!BN_one(r->Z)) |
1714 | 0 | goto err; |
1715 | 255 | } |
1716 | | |
1717 | 942 | r->Z_is_one = 1; |
1718 | 942 | ret = 1; |
1719 | | |
1720 | 948 | err: |
1721 | 948 | BN_CTX_end(ctx); |
1722 | 948 | return ret; |
1723 | 942 | } |