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  *    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 #include <stdlib.h>
73 
74 #include <openssl/obj_mac.h>
75 #include <openssl/ec.h>
76 #include <openssl/bn.h>
77 
78 #if defined(__SUNPRO_C)
79 # if __SUNPRO_C >= 0x520
80 #  pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
81 # endif
82 #endif
83 
84 /* Use default functions for poin2oct, oct2point and compressed coordinates */
85 #define EC_FLAGS_DEFAULT_OCT    0x1
86 
87 /*
88  * Structure details are not part of the exported interface, so all this may
89  * change in future versions.
90  */
91 
92 struct ec_method_st {
93     /* Various method flags */
94     int flags;
95     /* used by EC_METHOD_get_field_type: */
96     int field_type;             /* a NID */
97     /*
98      * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
99      * EC_GROUP_copy:
100      */
101     int (*group_init) (EC_GROUP *);
102     void (*group_finish) (EC_GROUP *);
103     void (*group_clear_finish) (EC_GROUP *);
104     int (*group_copy) (EC_GROUP *, const EC_GROUP *);
105     /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
106     /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
107     int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
108                             const BIGNUM *b, BN_CTX *);
109     int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
110                             BN_CTX *);
111     /* used by EC_GROUP_get_degree: */
112     int (*group_get_degree) (const EC_GROUP *);
113     /* used by EC_GROUP_check: */
114     int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
115     /*
116      * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
117      * EC_POINT_copy:
118      */
119     int (*point_init) (EC_POINT *);
120     void (*point_finish) (EC_POINT *);
121     void (*point_clear_finish) (EC_POINT *);
122     int (*point_copy) (EC_POINT *, const EC_POINT *);
123     /*-
124      * used by EC_POINT_set_to_infinity,
125      * EC_POINT_set_Jprojective_coordinates_GFp,
126      * EC_POINT_get_Jprojective_coordinates_GFp,
127      * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
128      * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
129      * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
130      */
131     int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
132     int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
133                                                   EC_POINT *, const BIGNUM *x,
134                                                   const BIGNUM *y,
135                                                   const BIGNUM *z, BN_CTX *);
136     int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
137                                                   const EC_POINT *, BIGNUM *x,
138                                                   BIGNUM *y, BIGNUM *z,
139                                                   BN_CTX *);
140     int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
141                                          const BIGNUM *x, const BIGNUM *y,
142                                          BN_CTX *);
143     int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
144                                          BIGNUM *x, BIGNUM *y, BN_CTX *);
145     int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
146                                              const BIGNUM *x, int y_bit,
147                                              BN_CTX *);
148     /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
149     size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
150                          point_conversion_form_t form, unsigned char *buf,
151                          size_t len, BN_CTX *);
152     int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
153                       size_t len, BN_CTX *);
154     /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
155     int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
156                 const EC_POINT *b, BN_CTX *);
157     int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
158     int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
159     /*
160      * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
161      */
162     int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
163     int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
164     int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
165                       BN_CTX *);
166     /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
167     int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
168     int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
169                                BN_CTX *);
170     /*
171      * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
172      * EC_POINT_have_precompute_mult (default implementations are used if the
173      * 'mul' pointer is 0):
174      */
175     int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
176                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
177                 BN_CTX *);
178     int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
179     int (*have_precompute_mult) (const EC_GROUP *group);
180     /* internal functions */
181     /*
182      * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
183      * 'dbl' so that the same implementations of point operations can be used
184      * with different optimized implementations of expensive field
185      * operations:
186      */
187     int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
188                       const BIGNUM *b, BN_CTX *);
189     int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
190     int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
191                       const BIGNUM *b, BN_CTX *);
192     /* e.g. to Montgomery */
193     int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
194                          BN_CTX *);
195     /* e.g. from Montgomery */
196     int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
197                          BN_CTX *);
198     int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
199 } /* EC_METHOD */ ;
200 
201 typedef struct ec_extra_data_st {
202     struct ec_extra_data_st *next;
203     void *data;
204     void *(*dup_func) (void *);
205     void (*free_func) (void *);
206     void (*clear_free_func) (void *);
207 } EC_EXTRA_DATA;                /* used in EC_GROUP */
208 
209 struct ec_group_st {
210     const EC_METHOD *meth;
211     EC_POINT *generator;        /* optional */
212     BIGNUM order, cofactor;
213     int curve_name;             /* optional NID for named curve */
214     int asn1_flag;              /* flag to control the asn1 encoding */
215     point_conversion_form_t asn1_form;
216     unsigned char *seed;        /* optional seed for parameters (appears in
217                                  * ASN1) */
218     size_t seed_len;
219     EC_EXTRA_DATA *extra_data;  /* linked list */
220     /*
221      * The following members are handled by the method functions, even if
222      * they appear generic
223      */
224     /*
225      * Field specification. For curves over GF(p), this is the modulus; for
226      * curves over GF(2^m), this is the irreducible polynomial defining the
227      * field.
228      */
229     BIGNUM field;
230     /*
231      * Field specification for curves over GF(2^m). The irreducible f(t) is
232      * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
233      * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
234      * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
235      * terms.
236      */
237     int poly[6];
238     /*
239      * Curve coefficients. (Here the assumption is that BIGNUMs can be used
240      * or abused for all kinds of fields, not just GF(p).) For characteristic
241      * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
242      * x^3 + a*x + b. For characteristic 2, the curve is defined by an
243      * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
244      */
245     BIGNUM a, b;
246     /* enable optimized point arithmetics for special case */
247     int a_is_minus3;
248     /* method-specific (e.g., Montgomery structure) */
249     void *field_data1;
250     /* method-specific */
251     void *field_data2;
252     /* method-specific */
253     int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
254                            BN_CTX *);
255 } /* EC_GROUP */ ;
256 
257 struct ec_key_st {
258     int version;
259     EC_GROUP *group;
260     EC_POINT *pub_key;
261     BIGNUM *priv_key;
262     unsigned int enc_flag;
263     point_conversion_form_t conv_form;
264     int references;
265     int flags;
266     EC_EXTRA_DATA *method_data;
267 } /* EC_KEY */ ;
268 
269 /*
270  * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs
271  * only (with visibility limited to 'package' level for now). We use the
272  * function pointers as index for retrieval; this obviates global
273  * ex_data-style index tables.
274  */
275 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
276                         void *(*dup_func) (void *),
277                         void (*free_func) (void *),
278                         void (*clear_free_func) (void *));
279 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *),
280                           void (*free_func) (void *),
281                           void (*clear_free_func) (void *));
282 void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
283                           void (*free_func) (void *),
284                           void (*clear_free_func) (void *));
285 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
286                                 void (*free_func) (void *),
287                                 void (*clear_free_func) (void *));
288 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
289 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
290 
291 struct ec_point_st {
292     const EC_METHOD *meth;
293     /*
294      * All members except 'meth' are handled by the method functions, even if
295      * they appear generic
296      */
297     BIGNUM X;
298     BIGNUM Y;
299     BIGNUM Z;                   /* Jacobian projective coordinates: (X, Y, Z)
300                                  * represents (X/Z^2, Y/Z^3) if Z != 0 */
301     int Z_is_one;               /* enable optimized point arithmetics for
302                                  * special case */
303 } /* EC_POINT */ ;
304 
305 /*
306  * method functions in ec_mult.c (ec_lib.c uses these as defaults if
307  * group->method->mul is 0)
308  */
309 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
310                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
311                 BN_CTX *);
312 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
313 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
314 
315 /* method functions in ecp_smpl.c */
316 int ec_GFp_simple_group_init(EC_GROUP *);
317 void ec_GFp_simple_group_finish(EC_GROUP *);
318 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
319 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
320 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
321                                   const BIGNUM *a, const BIGNUM *b, BN_CTX *);
322 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
323                                   BIGNUM *b, BN_CTX *);
324 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
325 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
326 int ec_GFp_simple_point_init(EC_POINT *);
327 void ec_GFp_simple_point_finish(EC_POINT *);
328 void ec_GFp_simple_point_clear_finish(EC_POINT *);
329 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
330 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
331 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
332                                                   EC_POINT *, const BIGNUM *x,
333                                                   const BIGNUM *y,
334                                                   const BIGNUM *z, BN_CTX *);
335 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
336                                                   const EC_POINT *, BIGNUM *x,
337                                                   BIGNUM *y, BIGNUM *z,
338                                                   BN_CTX *);
339 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
340                                                const BIGNUM *x,
341                                                const BIGNUM *y, BN_CTX *);
342 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
343                                                const EC_POINT *, BIGNUM *x,
344                                                BIGNUM *y, BN_CTX *);
345 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
346                                              const BIGNUM *x, int y_bit,
347                                              BN_CTX *);
348 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
349                                point_conversion_form_t form,
350                                unsigned char *buf, size_t len, BN_CTX *);
351 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
352                             const unsigned char *buf, size_t len, BN_CTX *);
353 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
354                       const EC_POINT *b, BN_CTX *);
355 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
356                       BN_CTX *);
357 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
358 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
359 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
360 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
361                       BN_CTX *);
362 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
363 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
364                                      EC_POINT *[], BN_CTX *);
365 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
366                             const BIGNUM *b, BN_CTX *);
367 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
368                             BN_CTX *);
369 
370 /* method functions in ecp_mont.c */
371 int ec_GFp_mont_group_init(EC_GROUP *);
372 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
373                                 const BIGNUM *b, BN_CTX *);
374 void ec_GFp_mont_group_finish(EC_GROUP *);
375 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
376 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
377 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
378                           const BIGNUM *b, BN_CTX *);
379 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
380                           BN_CTX *);
381 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
382                              BN_CTX *);
383 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
384                              BN_CTX *);
385 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
386 
387 /* method functions in ecp_nist.c */
388 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
389 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
390                                 const BIGNUM *b, BN_CTX *);
391 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
392                           const BIGNUM *b, BN_CTX *);
393 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
394                           BN_CTX *);
395 
396 /* method functions in ec2_smpl.c */
397 int ec_GF2m_simple_group_init(EC_GROUP *);
398 void ec_GF2m_simple_group_finish(EC_GROUP *);
399 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
400 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
401 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
402                                    const BIGNUM *a, const BIGNUM *b,
403                                    BN_CTX *);
404 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
405                                    BIGNUM *b, BN_CTX *);
406 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
407 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
408 int ec_GF2m_simple_point_init(EC_POINT *);
409 void ec_GF2m_simple_point_finish(EC_POINT *);
410 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
411 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
412 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
413 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
414                                                 const BIGNUM *x,
415                                                 const BIGNUM *y, BN_CTX *);
416 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
417                                                 const EC_POINT *, BIGNUM *x,
418                                                 BIGNUM *y, BN_CTX *);
419 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
420                                               const BIGNUM *x, int y_bit,
421                                               BN_CTX *);
422 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
423                                 point_conversion_form_t form,
424                                 unsigned char *buf, size_t len, BN_CTX *);
425 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
426                              const unsigned char *buf, size_t len, BN_CTX *);
427 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
428                        const EC_POINT *b, BN_CTX *);
429 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
430                        BN_CTX *);
431 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
432 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
433 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
434 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
435                        BN_CTX *);
436 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
437 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
438                                       EC_POINT *[], BN_CTX *);
439 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
440                              const BIGNUM *b, BN_CTX *);
441 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
442                              BN_CTX *);
443 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
444                              const BIGNUM *b, BN_CTX *);
445 
446 /* method functions in ec2_mult.c */
447 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
448                        const BIGNUM *scalar, size_t num,
449                        const EC_POINT *points[], const BIGNUM *scalars[],
450                        BN_CTX *);
451 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
452 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
453 
454 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
455 /* method functions in ecp_nistp224.c */
456 int ec_GFp_nistp224_group_init(EC_GROUP *group);
457 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
458                                     const BIGNUM *a, const BIGNUM *n,
459                                     BN_CTX *);
460 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
461                                                  const EC_POINT *point,
462                                                  BIGNUM *x, BIGNUM *y,
463                                                  BN_CTX *ctx);
464 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
465                         const BIGNUM *scalar, size_t num,
466                         const EC_POINT *points[], const BIGNUM *scalars[],
467                         BN_CTX *);
468 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
469                                const BIGNUM *scalar, size_t num,
470                                const EC_POINT *points[],
471                                const BIGNUM *scalars[], BN_CTX *ctx);
472 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
473 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
474 
475 /* method functions in ecp_nistp256.c */
476 int ec_GFp_nistp256_group_init(EC_GROUP *group);
477 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
478                                     const BIGNUM *a, const BIGNUM *n,
479                                     BN_CTX *);
480 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
481                                                  const EC_POINT *point,
482                                                  BIGNUM *x, BIGNUM *y,
483                                                  BN_CTX *ctx);
484 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
485                         const BIGNUM *scalar, size_t num,
486                         const EC_POINT *points[], const BIGNUM *scalars[],
487                         BN_CTX *);
488 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
489                                const BIGNUM *scalar, size_t num,
490                                const EC_POINT *points[],
491                                const BIGNUM *scalars[], BN_CTX *ctx);
492 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
493 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
494 
495 /* method functions in ecp_nistp521.c */
496 int ec_GFp_nistp521_group_init(EC_GROUP *group);
497 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
498                                     const BIGNUM *a, const BIGNUM *n,
499                                     BN_CTX *);
500 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
501                                                  const EC_POINT *point,
502                                                  BIGNUM *x, BIGNUM *y,
503                                                  BN_CTX *ctx);
504 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
505                         const BIGNUM *scalar, size_t num,
506                         const EC_POINT *points[], const BIGNUM *scalars[],
507                         BN_CTX *);
508 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
509                                const BIGNUM *scalar, size_t num,
510                                const EC_POINT *points[],
511                                const BIGNUM *scalars[], BN_CTX *ctx);
512 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
513 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
514 
515 /* utility functions in ecp_nistputil.c */
516 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
517                                               size_t felem_size,
518                                               void *tmp_felems,
519                                               void (*felem_one) (void *out),
520                                               int (*felem_is_zero) (const void
521                                                                     *in),
522                                               void (*felem_assign) (void *out,
523                                                                     const void
524                                                                     *in),
525                                               void (*felem_square) (void *out,
526                                                                     const void
527                                                                     *in),
528                                               void (*felem_mul) (void *out,
529                                                                  const void
530                                                                  *in1,
531                                                                  const void
532                                                                  *in2),
533                                               void (*felem_inv) (void *out,
534                                                                  const void
535                                                                  *in),
536                                               void (*felem_contract) (void
537                                                                       *out,
538                                                                       const
539                                                                       void
540                                                                       *in));
541 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
542                                      unsigned char *digit, unsigned char in);
543 #endif
544