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1 /* crypto/ec/ec_lcl.h */
2 /*
3  * Originally written by Bodo Moeller for the OpenSSL project.
4  */
5 /* ====================================================================
6  * Copyright (c) 1998-2003 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 /* Structure details are not part of the exported interface,
86  * so all this may change in future versions. */
87 
88 struct ec_method_st {
89 	/* used by EC_METHOD_get_field_type: */
90 	int field_type; /* a NID */
91 
92 	/* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
93 	int (*group_init)(EC_GROUP *);
94 	void (*group_finish)(EC_GROUP *);
95 	void (*group_clear_finish)(EC_GROUP *);
96 	int (*group_copy)(EC_GROUP *, const EC_GROUP *);
97 
98 	/* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
99 	/* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
100 	int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
101 	int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
102 
103 	/* used by EC_GROUP_get_degree: */
104 	int (*group_get_degree)(const EC_GROUP *);
105 
106 	/* used by EC_GROUP_check: */
107 	int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
108 
109 	/* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
110 	int (*point_init)(EC_POINT *);
111 	void (*point_finish)(EC_POINT *);
112 	void (*point_clear_finish)(EC_POINT *);
113 	int (*point_copy)(EC_POINT *, const EC_POINT *);
114 
115 	/* used by EC_POINT_set_to_infinity,
116 	 * EC_POINT_set_Jprojective_coordinates_GFp,
117 	 * EC_POINT_get_Jprojective_coordinates_GFp,
118 	 * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
119 	 * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
120 	 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
121 	 */
122 	int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
123 	int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
124 		const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
125 	int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
126 		BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
127 	int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
128 		const BIGNUM *x, const BIGNUM *y, BN_CTX *);
129 	int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
130 		BIGNUM *x, BIGNUM *y, BN_CTX *);
131 	int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
132 		const BIGNUM *x, int y_bit, BN_CTX *);
133 
134 	/* used by EC_POINT_point2oct, EC_POINT_oct2point: */
135 	size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
136 	        unsigned char *buf, size_t len, BN_CTX *);
137 	int (*oct2point)(const EC_GROUP *, EC_POINT *,
138 	        const unsigned char *buf, size_t len, BN_CTX *);
139 
140 	/* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
141 	int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
142 	int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
143 	int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
144 
145 	/* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
146 	int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
147 	int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
148 	int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
149 
150 	/* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
151 	int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
152 	int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
153 
154 	/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
155 	 * (default implementations are used if the 'mul' pointer is 0): */
156 	int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
157 		size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
158 	int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
159 	int (*have_precompute_mult)(const EC_GROUP *group);
160 
161 
162 	/* internal functions */
163 
164 	/* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
165 	 * the same implementations of point operations can be used with different
166 	 * optimized implementations of expensive field operations: */
167 	int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
168 	int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
169 	int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
170 
171 	int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
172 	int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
173 	int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
174 } /* EC_METHOD */;
175 
176 typedef struct ec_extra_data_st {
177 	struct ec_extra_data_st *next;
178 	void *data;
179 	void *(*dup_func)(void *);
180 	void (*free_func)(void *);
181 	void (*clear_free_func)(void *);
182 } EC_EXTRA_DATA; /* used in EC_GROUP */
183 
184 struct ec_group_st {
185 	const EC_METHOD *meth;
186 
187 	EC_POINT *generator; /* optional */
188 	BIGNUM order, cofactor;
189 
190 	int curve_name;/* optional NID for named curve */
191 	int asn1_flag; /* flag to control the asn1 encoding */
192 	point_conversion_form_t asn1_form;
193 
194 	unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
195 	size_t seed_len;
196 
197 	EC_EXTRA_DATA *extra_data; /* linked list */
198 
199 	/* The following members are handled by the method functions,
200 	 * even if they appear generic */
201 
202 	BIGNUM field; /* Field specification.
203 	               * For curves over GF(p), this is the modulus;
204 	               * for curves over GF(2^m), this is the
205 	               * irreducible polynomial defining the field.
206 	               */
207 
208 	unsigned int poly[5]; /* Field specification for curves over GF(2^m).
209 	                       * The irreducible f(t) is then of the form:
210 	                       *     t^poly[0] + t^poly[1] + ... + t^poly[k]
211 	                       * where m = poly[0] > poly[1] > ... > poly[k] = 0.
212 	                       */
213 
214 	BIGNUM a, b; /* Curve coefficients.
215 	              * (Here the assumption is that BIGNUMs can be used
216 	              * or abused for all kinds of fields, not just GF(p).)
217 	              * For characteristic  > 3,  the curve is defined
218 	              * by a Weierstrass equation of the form
219 	              *     y^2 = x^3 + a*x + b.
220 	              * For characteristic  2,  the curve is defined by
221 	              * an equation of the form
222 	              *     y^2 + x*y = x^3 + a*x^2 + b.
223 	              */
224 
225 	int a_is_minus3; /* enable optimized point arithmetics for special case */
226 
227 	void *field_data1; /* method-specific (e.g., Montgomery structure) */
228 	void *field_data2; /* method-specific */
229 	int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *,	BN_CTX *); /* method-specific */
230 } /* EC_GROUP */;
231 
232 struct ec_key_st {
233 	int version;
234 
235 	EC_GROUP *group;
236 
237 	EC_POINT *pub_key;
238 	BIGNUM	 *priv_key;
239 
240 	unsigned int enc_flag;
241 	point_conversion_form_t conv_form;
242 
243 	int 	references;
244 
245 	EC_EXTRA_DATA *method_data;
246 } /* EC_KEY */;
247 
248 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
249  * (with visibility limited to 'package' level for now).
250  * We use the function pointers as index for retrieval; this obviates
251  * global ex_data-style index tables.
252  */
253 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
254 	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
255 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
256 	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
257 void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
258 	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
259 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
260 	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
261 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
262 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
263 
264 
265 
266 struct ec_point_st {
267 	const EC_METHOD *meth;
268 
269 	/* All members except 'meth' are handled by the method functions,
270 	 * even if they appear generic */
271 
272 	BIGNUM X;
273 	BIGNUM Y;
274 	BIGNUM Z; /* Jacobian projective coordinates:
275 	           * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
276 	int Z_is_one; /* enable optimized point arithmetics for special case */
277 } /* EC_POINT */;
278 
279 
280 
281 /* method functions in ec_mult.c
282  * (ec_lib.c uses these as defaults if group->method->mul is 0) */
283 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
284 	size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
285 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
286 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
287 
288 
289 /* method functions in ecp_smpl.c */
290 int ec_GFp_simple_group_init(EC_GROUP *);
291 void ec_GFp_simple_group_finish(EC_GROUP *);
292 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
293 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
294 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
295 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
296 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
297 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
298 int ec_GFp_simple_point_init(EC_POINT *);
299 void ec_GFp_simple_point_finish(EC_POINT *);
300 void ec_GFp_simple_point_clear_finish(EC_POINT *);
301 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
302 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
303 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
304 	const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
305 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
306 	BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
307 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
308 	const BIGNUM *x, const BIGNUM *y, BN_CTX *);
309 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
310 	BIGNUM *x, BIGNUM *y, BN_CTX *);
311 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
312 	const BIGNUM *x, int y_bit, BN_CTX *);
313 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
314 	unsigned char *buf, size_t len, BN_CTX *);
315 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
316 	const unsigned char *buf, size_t len, BN_CTX *);
317 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
318 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
319 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
320 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
321 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
322 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
323 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
324 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
325 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
326 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
327 
328 
329 /* method functions in ecp_mont.c */
330 int ec_GFp_mont_group_init(EC_GROUP *);
331 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
332 void ec_GFp_mont_group_finish(EC_GROUP *);
333 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
334 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
335 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
336 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
337 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
338 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
339 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
340 
341 
342 /* method functions in ecp_nist.c */
343 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
344 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
345 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
346 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
347 
348 
349 /* method functions in ec2_smpl.c */
350 int ec_GF2m_simple_group_init(EC_GROUP *);
351 void ec_GF2m_simple_group_finish(EC_GROUP *);
352 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
353 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
354 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
355 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
356 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
357 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
358 int ec_GF2m_simple_point_init(EC_POINT *);
359 void ec_GF2m_simple_point_finish(EC_POINT *);
360 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
361 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
362 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
363 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
364 	const BIGNUM *x, const BIGNUM *y, BN_CTX *);
365 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
366 	BIGNUM *x, BIGNUM *y, BN_CTX *);
367 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
368 	const BIGNUM *x, int y_bit, BN_CTX *);
369 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
370 	unsigned char *buf, size_t len, BN_CTX *);
371 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
372 	const unsigned char *buf, size_t len, BN_CTX *);
373 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
374 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
375 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
376 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
377 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
378 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
379 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
380 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
381 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
382 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
383 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
384 
385 
386 /* method functions in ec2_mult.c */
387 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
388 	size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
389 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
390 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
391