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ec_lcl.h
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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) 1998-2010 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  * [email protected].
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  * ([email protected]). This product includes software written by Tim
55  * Hudson ([email protected]).
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 
91 struct 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 
181 typedef 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 
189 struct 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 
240 struct 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  */
262 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
263  void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
264 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
265  void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
266 void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
267  void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
268 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
269  void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
270 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
271 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
272 
273 
274 
275 struct 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) */
292 int 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 *);
294 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
295 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
296 
297 
298 /* method functions in ecp_smpl.c */
299 int ec_GFp_simple_group_init(EC_GROUP *);
300 void ec_GFp_simple_group_finish(EC_GROUP *);
301 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
302 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
303 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
304 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
305 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
306 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
307 int ec_GFp_simple_point_init(EC_POINT *);
308 void ec_GFp_simple_point_finish(EC_POINT *);
309 void ec_GFp_simple_point_clear_finish(EC_POINT *);
310 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
311 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
312 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
313  const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
314 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
315  BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
316 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
317  const BIGNUM *x, const BIGNUM *y, BN_CTX *);
318 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
319  BIGNUM *x, BIGNUM *y, BN_CTX *);
320 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
321  const BIGNUM *x, int y_bit, BN_CTX *);
322 size_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 *);
324 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
325  const unsigned char *buf, size_t len, BN_CTX *);
326 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
327 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
328 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
329 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
330 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
331 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
332 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
333 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
334 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
335 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
336 
337 
338 /* method functions in ecp_mont.c */
339 int ec_GFp_mont_group_init(EC_GROUP *);
340 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
341 void ec_GFp_mont_group_finish(EC_GROUP *);
342 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
343 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
344 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
345 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
346 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
347 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
348 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
349 
350 
351 /* method functions in ecp_nist.c */
352 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
353 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
354 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
355 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
356 
357 
358 /* method functions in ec2_smpl.c */
359 int ec_GF2m_simple_group_init(EC_GROUP *);
360 void ec_GF2m_simple_group_finish(EC_GROUP *);
361 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
362 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
363 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
364 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
365 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
366 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
367 int ec_GF2m_simple_point_init(EC_POINT *);
368 void ec_GF2m_simple_point_finish(EC_POINT *);
369 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
370 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
371 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
372 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
373  const BIGNUM *x, const BIGNUM *y, BN_CTX *);
374 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
375  BIGNUM *x, BIGNUM *y, BN_CTX *);
376 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
377  const BIGNUM *x, int y_bit, BN_CTX *);
378 size_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 *);
380 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
381  const unsigned char *buf, size_t len, BN_CTX *);
382 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
383 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
384 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
385 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
386 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
387 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
388 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
389 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
390 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
391 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
392 int 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 */
396 int 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 *);
398 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
399 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
400 
401 /* method functions in ec2_mult.c */
402 int 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 *);
404 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
405 int 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 */
409 int ec_GFp_nistp224_group_init(EC_GROUP *group);
410 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
411 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
412 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 *);
413 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);
414 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
415 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
416 
417 /* method functions in ecp_nistp256.c */
418 int ec_GFp_nistp256_group_init(EC_GROUP *group);
419 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
420 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
421 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 *);
422 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);
423 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
424 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
425 
426 /* method functions in ecp_nistp521.c */
427 int ec_GFp_nistp521_group_init(EC_GROUP *group);
428 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
429 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
430 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 *);
431 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);
432 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
433 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
434 
435 /* utility functions in ecp_nistputil.c */
436 void 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));
445 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
446 #endif
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