1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
|
/* crypto/ec/ec.h */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
#ifndef HEADER_EC_H
#define HEADER_EC_H
#include <openssl/opensslconf.h>
#ifdef OPENSSL_NO_EC
#error EC is disabled.
#endif
#include <openssl/asn1.h>
#include <openssl/symhacks.h>
#ifndef OPENSSL_NO_DEPRECATED
#include <openssl/bn.h>
#endif
#ifdef __cplusplus
extern "C" {
#elif defined(__SUNPRO_C)
# if __SUNPRO_C >= 0x520
# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
# endif
#endif
typedef enum {
/* values as defined in X9.62 (ECDSA) and elsewhere */
POINT_CONVERSION_COMPRESSED = 2,
POINT_CONVERSION_UNCOMPRESSED = 4,
POINT_CONVERSION_HYBRID = 6
} point_conversion_form_t;
typedef struct ec_method_st EC_METHOD;
typedef struct ec_group_st
/*
EC_METHOD *meth;
-- field definition
-- curve coefficients
-- optional generator with associated information (order, cofactor)
-- optional extra data (precomputed table for fast computation of multiples of generator)
-- ASN1 stuff
*/
EC_GROUP;
typedef struct ec_point_st EC_POINT;
/* EC_METHODs for curves over GF(p).
* EC_GFp_simple_method provides the basis for the optimized methods.
*/
const EC_METHOD *EC_GFp_simple_method(void);
const EC_METHOD *EC_GFp_mont_method(void);
const EC_METHOD *EC_GFp_nist_method(void);
/* EC_METHOD for curves over GF(2^m).
*/
const EC_METHOD *EC_GF2m_simple_method(void);
EC_GROUP *EC_GROUP_new(const EC_METHOD *);
void EC_GROUP_free(EC_GROUP *);
void EC_GROUP_clear_free(EC_GROUP *);
int EC_GROUP_copy(EC_GROUP *, const EC_GROUP *);
EC_GROUP *EC_GROUP_dup(const EC_GROUP *);
const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *);
int EC_METHOD_get_field_type(const EC_METHOD *);
int EC_GROUP_set_generator(EC_GROUP *, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *);
int EC_GROUP_get_order(const EC_GROUP *, BIGNUM *order, BN_CTX *);
int EC_GROUP_get_cofactor(const EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
void EC_GROUP_set_curve_name(EC_GROUP *, int nid);
int EC_GROUP_get_curve_name(const EC_GROUP *);
void EC_GROUP_set_asn1_flag(EC_GROUP *, int flag);
int EC_GROUP_get_asn1_flag(const EC_GROUP *);
void EC_GROUP_set_point_conversion_form(EC_GROUP *, point_conversion_form_t);
point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
unsigned char *EC_GROUP_get0_seed(const EC_GROUP *);
size_t EC_GROUP_get_seed_len(const EC_GROUP *);
size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
int EC_GROUP_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int EC_GROUP_get_curve_GFp(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
int EC_GROUP_set_curve_GF2m(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int EC_GROUP_get_curve_GF2m(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
/* returns the number of bits needed to represent a field element */
int EC_GROUP_get_degree(const EC_GROUP *);
/* EC_GROUP_check() returns 1 if 'group' defines a valid group, 0 otherwise */
int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
/* EC_GROUP_check_discriminant() returns 1 if the discriminant of the
* elliptic curve is not zero, 0 otherwise */
int EC_GROUP_check_discriminant(const EC_GROUP *, BN_CTX *);
/* EC_GROUP_cmp() returns 0 if both groups are equal and 1 otherwise */
int EC_GROUP_cmp(const EC_GROUP *, const EC_GROUP *, BN_CTX *);
/* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*()
* after choosing an appropriate EC_METHOD */
EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
/* EC_GROUP_new_by_curve_name() creates a EC_GROUP structure
* specified by a curve name (in form of a NID) */
EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
/* handling of internal curves */
typedef struct {
int nid;
const char *comment;
} EC_builtin_curve;
/* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number
* of all available curves or zero if a error occurred.
* In case r ist not zero nitems EC_builtin_curve structures
* are filled with the data of the first nitems internal groups */
size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
/* EC_POINT functions */
EC_POINT *EC_POINT_new(const EC_GROUP *);
void EC_POINT_free(EC_POINT *);
void EC_POINT_clear_free(EC_POINT *);
int EC_POINT_copy(EC_POINT *, const EC_POINT *);
EC_POINT *EC_POINT_dup(const EC_POINT *, const EC_GROUP *);
const EC_METHOD *EC_POINT_method_of(const EC_POINT *);
int EC_POINT_set_to_infinity(const EC_GROUP *, EC_POINT *);
int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
size_t EC_POINT_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX
|