Newer
Older
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
/* crypto/ec/ec_lcl.h */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2010 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.
*
*/
#include <stdlib.h>
#include <openssl/obj_mac.h>
#include <openssl/ec.h>
#include <openssl/bn.h>
#if defined(__SUNPRO_C)
# if __SUNPRO_C >= 0x520
# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
# endif
#endif
/* Use default functions for poin2oct, oct2point and compressed coordinates */
#define EC_FLAGS_DEFAULT_OCT 0x1
/* Structure details are not part of the exported interface,
* so all this may change in future versions. */
struct ec_method_st {
/* Various method flags */
int flags;
/* used by EC_METHOD_get_field_type: */
int field_type; /* a NID */
/* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
int (*group_init)(EC_GROUP *);
void (*group_finish)(EC_GROUP *);
void (*group_clear_finish)(EC_GROUP *);
int (*group_copy)(EC_GROUP *, const EC_GROUP *);
/* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
/* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
/* used by EC_GROUP_get_degree: */
int (*group_get_degree)(const EC_GROUP *);
/* used by EC_GROUP_check: */
int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
/* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
int (*point_init)(EC_POINT *);
void (*point_finish)(EC_POINT *);
void (*point_clear_finish)(EC_POINT *);
int (*point_copy)(EC_POINT *, const EC_POINT *);
/* used by EC_POINT_set_to_infinity,
* EC_POINT_set_Jprojective_coordinates_GFp,
* EC_POINT_get_Jprojective_coordinates_GFp,
* EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
* EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
* EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
*/
int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
/* used by EC_POINT_point2oct, EC_POINT_oct2point: */
size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *);
int (*oct2point)(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
/* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
/* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
/* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
* (default implementations are used if the 'mul' pointer is 0): */
int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
int (*have_precompute_mult)(const EC_GROUP *group);
/* internal functions */
/* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
* the same implementations of point operations can be used with different
* optimized implementations of expensive field operations: */
int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
} /* EC_METHOD */;
typedef struct ec_extra_data_st {
struct ec_extra_data_st *next;
void *data;
void *(*dup_func)(void *);
void (*free_func)(void *);
void (*clear_free_func)(void *);
} EC_EXTRA_DATA; /* used in EC_GROUP */
struct ec_group_st {
const EC_METHOD *meth;
EC_POINT *generator; /* optional */
BIGNUM order, cofactor;
int curve_name;/* optional NID for named curve */
int asn1_flag; /* flag to control the asn1 encoding */
point_conversion_form_t asn1_form;
unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
size_t seed_len;
EC_EXTRA_DATA *extra_data; /* linked list */
/* The following members are handled by the method functions,
* even if they appear generic */
BIGNUM field; /* Field specification.
* For curves over GF(p), this is the modulus;
* for curves over GF(2^m), this is the
* irreducible polynomial defining the field.
*/
int poly[6]; /* Field specification for curves over GF(2^m).
* The irreducible f(t) is then of the form:
* t^poly[0] + t^poly[1] + ... + t^poly[k]
* where m = poly[0] > poly[1] > ... > poly[k] = 0.
* The array is terminated with poly[k+1]=-1.
* All elliptic curve irreducibles have at most 5
* non-zero terms.
*/
BIGNUM a, b; /* Curve coefficients.
* (Here the assumption is that BIGNUMs can be used
* or abused for all kinds of fields, not just GF(p).)
* For characteristic > 3, the curve is defined
* by a Weierstrass equation of the form
* y^2 = x^3 + a*x + b.
* For characteristic 2, the curve is defined by
* an equation of the form
* y^2 + x*y = x^3 + a*x^2 + b.
*/
int a_is_minus3; /* enable optimized point arithmetics for special case */
void *field_data1; /* method-specific (e.g., Montgomery structure) */
void *field_data2; /* method-specific */
int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
} /* EC_GROUP */;
struct ec_key_st {
int version;
EC_GROUP *group;
EC_POINT *pub_key;
BIGNUM *priv_key;
unsigned int enc_flag;
point_conversion_form_t conv_form;
int references;
int flags;
EC_EXTRA_DATA *method_data;
} /* EC_KEY */;
/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
* (with visibility limited to 'package' level for now).
* We use the function pointers as index for retrieval; this obviates
* global ex_data-style index tables.
*/
int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
struct ec_point_st {
const EC_METHOD *meth;
/* All members except 'meth' are handled by the method functions,
* even if they appear generic */
BIGNUM X;
BIGNUM Y;
BIGNUM Z; /* Jacobian projective coordinates:
* (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
int Z_is_one; /* enable optimized point arithmetics for special case */
} /* EC_POINT */;
/* method functions in ec_mult.c
* (ec_lib.c uses these as defaults if group->method->mul is 0) */
int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
/* method functions in ecp_smpl.c */
int ec_GFp_simple_group_init(EC_GROUP *);
void ec_GFp_simple_group_finish(EC_GROUP *);
void ec_GFp_simple_group_clear_finish(EC_GROUP *);
int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
int ec_GFp_simple_group_get_degree(const EC_GROUP *);
int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
int ec_GFp_simple_point_init(EC_POINT *);
void ec_GFp_simple_point_finish(EC_POINT *);
void ec_GFp_simple_point_clear_finish(EC_POINT *);
int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *);
int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
/* method functions in ecp_mont.c */
int ec_GFp_mont_group_init(EC_GROUP *);
int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
void ec_GFp_mont_group_finish(EC_GROUP *);
void ec_GFp_mont_group_clear_finish(EC_GROUP *);
int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
/* method functions in ecp_nist.c */
int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
/* method functions in ec2_smpl.c */
int ec_GF2m_simple_group_init(EC_GROUP *);
void ec_GF2m_simple_group_finish(EC_GROUP *);
void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
int ec_GF2m_simple_point_init(EC_POINT *);
void ec_GF2m_simple_point_finish(EC_POINT *);
void ec_GF2m_simple_point_clear_finish(EC_POINT *);
int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, const BIGNUM *y, BN_CTX *);
int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
BIGNUM *x, BIGNUM *y, BN_CTX *);
int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
const BIGNUM *x, int y_bit, BN_CTX *);
size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *);
int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
/* method functions in ec2_mult.c */
int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
/* method functions in ec2_mult.c */
int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
/* method functions in ecp_nistp224.c */
int ec_GFp_nistp224_group_init(EC_GROUP *group);
int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
/* method functions in ecp_nistp256.c */
int ec_GFp_nistp256_group_init(EC_GROUP *group);
int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
/* method functions in ecp_nistp521.c */
int ec_GFp_nistp521_group_init(EC_GROUP *group);
int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
/* utility functions in ecp_nistputil.c */
void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
size_t felem_size, void *tmp_felems,
void (*felem_one)(void *out),
int (*felem_is_zero)(const void *in),
void (*felem_assign)(void *out, const void *in),
void (*felem_square)(void *out, const void *in),
void (*felem_mul)(void *out, const void *in1, const void *in2),
void (*felem_inv)(void *out, const void *in),
void (*felem_contract)(void *out, const void *in));
void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
#endif