1/* Originally written by Bodo Moeller for the OpenSSL project.
2 * ====================================================================
3 * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 *
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in
14 *    the documentation and/or other materials provided with the
15 *    distribution.
16 *
17 * 3. All advertising materials mentioning features or use of this
18 *    software must display the following acknowledgment:
19 *    "This product includes software developed by the OpenSSL Project
20 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
21 *
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 *    endorse or promote products derived from this software without
24 *    prior written permission. For written permission, please contact
25 *    openssl-core@openssl.org.
26 *
27 * 5. Products derived from this software may not be called "OpenSSL"
28 *    nor may "OpenSSL" appear in their names without prior written
29 *    permission of the OpenSSL Project.
30 *
31 * 6. Redistributions of any form whatsoever must retain the following
32 *    acknowledgment:
33 *    "This product includes software developed by the OpenSSL Project
34 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
35 *
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
49 *
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com).  This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
53 *
54 */
55/* ====================================================================
56 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
57 *
58 * Portions of the attached software ("Contribution") are developed by
59 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
60 *
61 * The Contribution is licensed pursuant to the OpenSSL open source
62 * license provided above.
63 *
64 * The elliptic curve binary polynomial software is originally written by
65 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
66 * Laboratories. */
67
68#ifndef OPENSSL_HEADER_EC_INTERNAL_H
69#define OPENSSL_HEADER_EC_INTERNAL_H
70
71#include <openssl/base.h>
72
73#include <openssl/bn.h>
74#include <openssl/ex_data.h>
75#include <openssl/thread.h>
76
77#if defined(__cplusplus)
78extern "C" {
79#endif
80
81
82/* Use default functions for poin2oct, oct2point and compressed coordinates */
83#define EC_FLAGS_DEFAULT_OCT 0x1
84
85struct ec_method_st {
86  /* Various method flags */
87  int flags;
88
89  /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
90  int (*group_init)(EC_GROUP *);
91  void (*group_finish)(EC_GROUP *);
92  void (*group_clear_finish)(EC_GROUP *);
93  int (*group_copy)(EC_GROUP *, const EC_GROUP *);
94
95  /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
96  /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
97  int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
98                         const BIGNUM *b, BN_CTX *);
99  int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
100                         BN_CTX *);
101
102  /* used by EC_GROUP_get_degree: */
103  int (*group_get_degree)(const EC_GROUP *);
104
105  /* used by EC_GROUP_check: */
106  int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
107
108  /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
109  int (*point_init)(EC_POINT *);
110  void (*point_finish)(EC_POINT *);
111  void (*point_clear_finish)(EC_POINT *);
112  int (*point_copy)(EC_POINT *, const EC_POINT *);
113
114  /* used by EC_POINT_set_to_infinity,
115   * EC_POINT_set_Jprojective_coordinates_GFp,
116   * EC_POINT_get_Jprojective_coordinates_GFp,
117   * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
118   * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
119   * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
120   */
121  int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
122  int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
123                                               const BIGNUM *x, const BIGNUM *y,
124                                               const BIGNUM *z, BN_CTX *);
125  int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *,
126                                               const EC_POINT *, BIGNUM *x,
127                                               BIGNUM *y, BIGNUM *z, BN_CTX *);
128  int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
129                                      const BIGNUM *x, const BIGNUM *y,
130                                      BN_CTX *);
131  int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
132                                      BIGNUM *x, BIGNUM *y, BN_CTX *);
133  int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
134                                          const BIGNUM *x, int y_bit, BN_CTX *);
135
136  /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
137  size_t (*point2oct)(const EC_GROUP *, const EC_POINT *,
138                      point_conversion_form_t form, unsigned char *buf,
139                      size_t len, BN_CTX *);
140  int (*oct2point)(const EC_GROUP *, EC_POINT *, const unsigned char *buf,
141                   size_t len, BN_CTX *);
142
143  /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
144  int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
145             const EC_POINT *b, BN_CTX *);
146  int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
147  int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
148
149  /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
150  int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
151  int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
152  int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
153                   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 * [],
158                            BN_CTX *);
159
160  /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
161   * EC_POINT_have_precompute_mult
162   * (default implementations are used if the 'mul' pointer is 0): */
163  int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
164             size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
165             BN_CTX *);
166  int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
167  int (*have_precompute_mult)(const EC_GROUP *group);
168
169
170  /* internal functions */
171
172  /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl'
173   * so that the same implementations of point operations can be used with
174   * different optimized implementations of expensive field operations: */
175  int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
176                   const BIGNUM *b, BN_CTX *);
177  int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
178  int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
179                   const BIGNUM *b, BN_CTX *);
180
181  int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
182                      BN_CTX *); /* e.g. to Montgomery */
183  int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
184                      BN_CTX *); /* e.g. from Montgomery */
185  int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
186} /* EC_METHOD */;
187
188const EC_METHOD* EC_GFp_mont_method(void);
189
190struct ec_pre_comp_st;
191void ec_pre_comp_free(struct ec_pre_comp_st *pre_comp);
192void *ec_pre_comp_dup(struct ec_pre_comp_st *pre_comp);
193
194struct ec_group_st {
195  const EC_METHOD *meth;
196
197  EC_POINT *generator; /* optional */
198  BIGNUM order, cofactor;
199
200  int curve_name; /* optional NID for named curve */
201
202  struct ec_pre_comp_st *pre_comp;
203
204  /* The following members are handled by the method functions,
205   * even if they appear generic */
206
207  BIGNUM field; /* For curves over GF(p), this is the modulus. */
208
209  BIGNUM a, b; /* Curve coefficients. */
210
211  int a_is_minus3; /* enable optimized point arithmetics for special case */
212
213  BN_MONT_CTX *mont; /* Montgomery structure. */
214  BIGNUM *one; /* The value one */
215} /* EC_GROUP */;
216
217struct ec_point_st {
218  const EC_METHOD *meth;
219
220  /* All members except 'meth' are handled by the method functions,
221   * even if they appear generic */
222
223  BIGNUM X;
224  BIGNUM Y;
225  BIGNUM Z; /* Jacobian projective coordinates:
226             * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
227  int Z_is_one; /* enable optimized point arithmetics for special case */
228} /* EC_POINT */;
229
230EC_GROUP *ec_group_new(const EC_METHOD *meth);
231int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src);
232
233int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
234                size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
235                BN_CTX *);
236int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
237int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
238
239/* method functions in simple.c */
240int ec_GFp_simple_group_init(EC_GROUP *);
241void ec_GFp_simple_group_finish(EC_GROUP *);
242void ec_GFp_simple_group_clear_finish(EC_GROUP *);
243int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
244int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
245                                  const BIGNUM *b, BN_CTX *);
246int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
247                                  BIGNUM *b, BN_CTX *);
248int ec_GFp_simple_group_get_degree(const EC_GROUP *);
249int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
250int ec_GFp_simple_point_init(EC_POINT *);
251void ec_GFp_simple_point_finish(EC_POINT *);
252void ec_GFp_simple_point_clear_finish(EC_POINT *);
253int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
254int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
255int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
256                                                  const BIGNUM *x,
257                                                  const BIGNUM *y,
258                                                  const BIGNUM *z, BN_CTX *);
259int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
260                                                  const EC_POINT *, BIGNUM *x,
261                                                  BIGNUM *y, BIGNUM *z,
262                                                  BN_CTX *);
263int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
264                                               const BIGNUM *x, const BIGNUM *y,
265                                               BN_CTX *);
266int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
267                                               const EC_POINT *, BIGNUM *x,
268                                               BIGNUM *y, BN_CTX *);
269int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
270                                             const BIGNUM *x, int y_bit,
271                                             BN_CTX *);
272int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
273                      const EC_POINT *b, BN_CTX *);
274int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
275                      BN_CTX *);
276int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
277int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
278int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
279int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
280                      BN_CTX *);
281int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
282int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
283                                     EC_POINT * [], BN_CTX *);
284int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
285                            const BIGNUM *b, BN_CTX *);
286int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
287                            BN_CTX *);
288
289/* method functions in montgomery.c */
290int ec_GFp_mont_group_init(EC_GROUP *);
291int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
292                                const BIGNUM *b, BN_CTX *);
293void ec_GFp_mont_group_finish(EC_GROUP *);
294void ec_GFp_mont_group_clear_finish(EC_GROUP *);
295int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
296int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
297                          const BIGNUM *b, BN_CTX *);
298int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
299                          BN_CTX *);
300int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
301                             BN_CTX *);
302int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
303                             BN_CTX *);
304int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
305
306int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
307                                             EC_POINT *point, const BIGNUM *x,
308                                             const BIGNUM *y, const BIGNUM *z,
309                                             BN_CTX *ctx);
310
311void ec_GFp_nistp_points_make_affine_internal(
312    size_t num, void *point_array, size_t felem_size, void *tmp_felems,
313    void (*felem_one)(void *out), int (*felem_is_zero)(const void *in),
314    void (*felem_assign)(void *out, const void *in),
315    void (*felem_square)(void *out, const void *in),
316    void (*felem_mul)(void *out, const void *in1, const void *in2),
317    void (*felem_inv)(void *out, const void *in),
318    void (*felem_contract)(void *out, const void *in));
319
320void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
321
322const EC_METHOD *EC_GFp_nistp256_method(void);
323
324struct ec_key_st {
325  int version;
326
327  EC_GROUP *group;
328
329  EC_POINT *pub_key;
330  BIGNUM *priv_key;
331
332  unsigned int enc_flag;
333  point_conversion_form_t conv_form;
334
335  CRYPTO_refcount_t references;
336  int flags;
337
338  ECDSA_METHOD *ecdsa_meth;
339
340  CRYPTO_EX_DATA ex_data;
341} /* EC_KEY */;
342
343/* curve_data contains data about a built-in elliptic curve. */
344struct curve_data {
345  /* comment is a human-readable string describing the curve. */
346  const char *comment;
347  /* param_len is the number of bytes needed to store a field element. */
348  uint8_t param_len;
349  /* cofactor is the cofactor of the group (i.e. the number of elements in the
350   * group divided by the size of the main subgroup. */
351  uint8_t cofactor; /* promoted to BN_ULONG */
352  /* data points to an array of 6*|param_len| bytes which hold the field
353   * elements of the following (in big-endian order): prime, a, b, generator x,
354   * generator y, order. */
355  const uint8_t data[];
356};
357
358struct built_in_curve {
359  int nid;
360  const struct curve_data *data;
361  const EC_METHOD *(*method)(void);
362};
363
364/* OPENSSL_built_in_curves is terminated with an entry where |nid| is
365 * |NID_undef|. */
366extern const struct built_in_curve OPENSSL_built_in_curves[];
367
368#if defined(__cplusplus)
369}  /* extern C */
370#endif
371
372#endif  /* OPENSSL_HEADER_EC_INTERNAL_H */
373