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1/* $OpenBSD: ec_lcl.h,v 1.5 2014/06/12 15:49:29 deraadt Exp $ */
2/*
3 * Originally written by Bodo Moeller for the OpenSSL project.
4 */
5/* ====================================================================
6 * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 *
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 *
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
18 * distribution.
19 *
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 *
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
29 *
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
33 *
34 * 6. Redistributions of any form whatsoever must retain the following
35 * acknowledgment:
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 *
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
52 *
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
56 *
57 */
58/* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 *
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 *
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
66 *
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69 *
70 */
71
72
73#include <stdlib.h>
74
75#include <openssl/obj_mac.h>
76#include <openssl/ec.h>
77#include <openssl/bn.h>
78
79#if defined(__SUNPRO_C)
80# if __SUNPRO_C >= 0x520
81# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
82# endif
83#endif
84
85/* Use default functions for poin2oct, oct2point and compressed coordinates */
86#define EC_FLAGS_DEFAULT_OCT 0x1
87
88/* Structure details are not part of the exported interface,
89 * so all this may change in future versions. */
90
91struct ec_method_st {
92 /* Various method flags */
93 int flags;
94 /* used by EC_METHOD_get_field_type: */
95 int field_type; /* a NID */
96
97 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
98 int (*group_init)(EC_GROUP *);
99 void (*group_finish)(EC_GROUP *);
100 void (*group_clear_finish)(EC_GROUP *);
101 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
102
103 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
104 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
105 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
106 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
107
108 /* used by EC_GROUP_get_degree: */
109 int (*group_get_degree)(const EC_GROUP *);
110
111 /* used by EC_GROUP_check: */
112 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
113
114 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
115 int (*point_init)(EC_POINT *);
116 void (*point_finish)(EC_POINT *);
117 void (*point_clear_finish)(EC_POINT *);
118 int (*point_copy)(EC_POINT *, const EC_POINT *);
119
120 /* used by EC_POINT_set_to_infinity,
121 * EC_POINT_set_Jprojective_coordinates_GFp,
122 * EC_POINT_get_Jprojective_coordinates_GFp,
123 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
124 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
125 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
126 */
127 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
128 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
129 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
130 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
131 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
132 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
133 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
134 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
135 BIGNUM *x, BIGNUM *y, BN_CTX *);
136 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
137 const BIGNUM *x, int y_bit, BN_CTX *);
138
139 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
140 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
141 unsigned char *buf, size_t len, BN_CTX *);
142 int (*oct2point)(const EC_GROUP *, EC_POINT *,
143 const unsigned char *buf, size_t len, BN_CTX *);
144
145 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
146 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
147 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
148 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
149
150 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
151 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
152 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
153 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
154
155 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
156 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
157 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
158
159 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
160 * (default implementations are used if the 'mul' pointer is 0): */
161 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
162 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
163 int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
164 int (*have_precompute_mult)(const EC_GROUP *group);
165
166
167 /* internal functions */
168
169 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
170 * the same implementations of point operations can be used with different
171 * optimized implementations of expensive field operations: */
172 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
173 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
174 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
175
176 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
177 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
178 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
179} /* EC_METHOD */;
180
181typedef struct ec_extra_data_st {
182 struct ec_extra_data_st *next;
183 void *data;
184 void *(*dup_func)(void *);
185 void (*free_func)(void *);
186 void (*clear_free_func)(void *);
187} EC_EXTRA_DATA; /* used in EC_GROUP */
188
189struct ec_group_st {
190 const EC_METHOD *meth;
191
192 EC_POINT *generator; /* optional */
193 BIGNUM order, cofactor;
194
195 int curve_name;/* optional NID for named curve */
196 int asn1_flag; /* flag to control the asn1 encoding */
197 point_conversion_form_t asn1_form;
198
199 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
200 size_t seed_len;
201
202 EC_EXTRA_DATA *extra_data; /* linked list */
203
204 /* The following members are handled by the method functions,
205 * even if they appear generic */
206
207 BIGNUM field; /* Field specification.
208 * For curves over GF(p), this is the modulus;
209 * for curves over GF(2^m), this is the
210 * irreducible polynomial defining the field.
211 */
212
213 int poly[6]; /* Field specification for curves over GF(2^m).
214 * The irreducible f(t) is then of the form:
215 * t^poly[0] + t^poly[1] + ... + t^poly[k]
216 * where m = poly[0] > poly[1] > ... > poly[k] = 0.
217 * The array is terminated with poly[k+1]=-1.
218 * All elliptic curve irreducibles have at most 5
219 * non-zero terms.
220 */
221
222 BIGNUM a, b; /* Curve coefficients.
223 * (Here the assumption is that BIGNUMs can be used
224 * or abused for all kinds of fields, not just GF(p).)
225 * For characteristic > 3, the curve is defined
226 * by a Weierstrass equation of the form
227 * y^2 = x^3 + a*x + b.
228 * For characteristic 2, the curve is defined by
229 * an equation of the form
230 * y^2 + x*y = x^3 + a*x^2 + b.
231 */
232
233 int a_is_minus3; /* enable optimized point arithmetics for special case */
234
235 void *field_data1; /* method-specific (e.g., Montgomery structure) */
236 void *field_data2; /* method-specific */
237 int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
238} /* EC_GROUP */;
239
240struct ec_key_st {
241 int version;
242
243 EC_GROUP *group;
244
245 EC_POINT *pub_key;
246 BIGNUM *priv_key;
247
248 unsigned int enc_flag;
249 point_conversion_form_t conv_form;
250
251 int references;
252 int flags;
253
254 EC_EXTRA_DATA *method_data;
255} /* EC_KEY */;
256
257/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
258 * (with visibility limited to 'package' level for now).
259 * We use the function pointers as index for retrieval; this obviates
260 * global ex_data-style index tables.
261 */
262int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
263 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
264void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
265 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
266void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
267 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
268void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
269 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
270void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
271void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
272
273
274
275struct ec_point_st {
276 const EC_METHOD *meth;
277
278 /* All members except 'meth' are handled by the method functions,
279 * even if they appear generic */
280
281 BIGNUM X;
282 BIGNUM Y;
283 BIGNUM Z; /* Jacobian projective coordinates:
284 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
285 int Z_is_one; /* enable optimized point arithmetics for special case */
286} /* EC_POINT */;
287
288
289
290/* method functions in ec_mult.c
291 * (ec_lib.c uses these as defaults if group->method->mul is 0) */
292int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
293 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
294int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
295int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
296
297
298/* method functions in ecp_smpl.c */
299int ec_GFp_simple_group_init(EC_GROUP *);
300void ec_GFp_simple_group_finish(EC_GROUP *);
301void ec_GFp_simple_group_clear_finish(EC_GROUP *);
302int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
303int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
304int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
305int ec_GFp_simple_group_get_degree(const EC_GROUP *);
306int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
307int ec_GFp_simple_point_init(EC_POINT *);
308void ec_GFp_simple_point_finish(EC_POINT *);
309void ec_GFp_simple_point_clear_finish(EC_POINT *);
310int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
311int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
312int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
313 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
314int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
315 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
316int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
317 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
318int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
319 BIGNUM *x, BIGNUM *y, BN_CTX *);
320int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
321 const BIGNUM *x, int y_bit, BN_CTX *);
322size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
323 unsigned char *buf, size_t len, BN_CTX *);
324int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
325 const unsigned char *buf, size_t len, BN_CTX *);
326int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
327int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
328int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
329int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
330int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
331int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
332int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
333int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
334int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
335int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
336
337
338/* method functions in ecp_mont.c */
339int ec_GFp_mont_group_init(EC_GROUP *);
340int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
341void ec_GFp_mont_group_finish(EC_GROUP *);
342void ec_GFp_mont_group_clear_finish(EC_GROUP *);
343int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
344int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
345int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
346int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
347int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
348int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
349
350
351/* method functions in ecp_nist.c */
352int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
353int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
354int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
355int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
356
357
358/* method functions in ec2_smpl.c */
359int ec_GF2m_simple_group_init(EC_GROUP *);
360void ec_GF2m_simple_group_finish(EC_GROUP *);
361void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
362int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
363int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
364int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
365int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
366int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
367int ec_GF2m_simple_point_init(EC_POINT *);
368void ec_GF2m_simple_point_finish(EC_POINT *);
369void ec_GF2m_simple_point_clear_finish(EC_POINT *);
370int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
371int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
372int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
373 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
374int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
375 BIGNUM *x, BIGNUM *y, BN_CTX *);
376int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
377 const BIGNUM *x, int y_bit, BN_CTX *);
378size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
379 unsigned char *buf, size_t len, BN_CTX *);
380int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
381 const unsigned char *buf, size_t len, BN_CTX *);
382int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
383int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
384int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
385int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
386int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
387int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
388int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
389int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
390int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
391int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
392int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
393
394
395/* method functions in ec2_mult.c */
396int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
397 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
398int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
399int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
400
401/* method functions in ec2_mult.c */
402int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
403 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
404int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
405int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
406
407#ifndef OPENSSL_EC_NISTP_64_GCC_128
408/* method functions in ecp_nistp224.c */
409int ec_GFp_nistp224_group_init(EC_GROUP *group);
410int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
411int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
412int 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 *);
413int 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);
414int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
415int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
416
417/* method functions in ecp_nistp256.c */
418int ec_GFp_nistp256_group_init(EC_GROUP *group);
419int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
420int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
421int 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 *);
422int 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);
423int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
424int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
425
426/* method functions in ecp_nistp521.c */
427int ec_GFp_nistp521_group_init(EC_GROUP *group);
428int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
429int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
430int 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 *);
431int 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);
432int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
433int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
434
435/* utility functions in ecp_nistputil.c */
436void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
437 size_t felem_size, void *tmp_felems,
438 void (*felem_one)(void *out),
439 int (*felem_is_zero)(const void *in),
440 void (*felem_assign)(void *out, const void *in),
441 void (*felem_square)(void *out, const void *in),
442 void (*felem_mul)(void *out, const void *in1, const void *in2),
443 void (*felem_inv)(void *out, const void *in),
444 void (*felem_contract)(void *out, const void *in));
445void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
446#endif
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