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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)
78 extern "C" {
79 #endif
80 
81 
82 struct ec_method_st {
83   int (*group_init)(EC_GROUP *);
84   void (*group_finish)(EC_GROUP *);
85   int (*group_copy)(EC_GROUP *, const EC_GROUP *);
86   int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
87                          const BIGNUM *b, BN_CTX *);
88   int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
89                                       BIGNUM *x, BIGNUM *y, BN_CTX *);
90 
91   /* Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar|
92    * are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null.
93    * Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar|
94    * and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is
95    * non-null. */
96   int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
97              const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx);
98 
99   /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the
100    * same implementations of point operations can be used with different
101    * optimized implementations of expensive field operations: */
102   int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
103                    const BIGNUM *b, BN_CTX *);
104   int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
105 
106   int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
107                       BN_CTX *); /* e.g. to Montgomery */
108   int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
109                       BN_CTX *); /* e.g. from Montgomery */
110 } /* EC_METHOD */;
111 
112 const EC_METHOD *EC_GFp_mont_method(void);
113 
114 struct ec_group_st {
115   const EC_METHOD *meth;
116 
117   EC_POINT *generator;
118   BIGNUM order;
119 
120   int curve_name; /* optional NID for named curve */
121 
122   const BN_MONT_CTX *mont_data; /* data for ECDSA inverse */
123 
124   /* The following members are handled by the method functions,
125    * even if they appear generic */
126 
127   BIGNUM field; /* For curves over GF(p), this is the modulus. */
128 
129   BIGNUM a, b; /* Curve coefficients. */
130 
131   int a_is_minus3; /* enable optimized point arithmetics for special case */
132 
133   BN_MONT_CTX *mont; /* Montgomery structure. */
134 
135   BIGNUM one; /* The value one. */
136 } /* EC_GROUP */;
137 
138 struct ec_point_st {
139   const EC_METHOD *meth;
140 
141   BIGNUM X;
142   BIGNUM Y;
143   BIGNUM Z; /* Jacobian projective coordinates:
144              * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
145 } /* EC_POINT */;
146 
147 EC_GROUP *ec_group_new(const EC_METHOD *meth);
148 int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src);
149 
150 /* ec_group_get_mont_data returns a Montgomery context for operations in the
151  * scalar field of |group|. It may return NULL in the case that |group| is not
152  * a built-in group. */
153 const BN_MONT_CTX *ec_group_get_mont_data(const EC_GROUP *group);
154 
155 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
156                 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx);
157 
158 /* method functions in simple.c */
159 int ec_GFp_simple_group_init(EC_GROUP *);
160 void ec_GFp_simple_group_finish(EC_GROUP *);
161 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
162 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
163                                   const BIGNUM *b, BN_CTX *);
164 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
165                                   BIGNUM *b, BN_CTX *);
166 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
167 int ec_GFp_simple_point_init(EC_POINT *);
168 void ec_GFp_simple_point_finish(EC_POINT *);
169 void ec_GFp_simple_point_clear_finish(EC_POINT *);
170 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
171 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
172 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
173                                                   const BIGNUM *x,
174                                                   const BIGNUM *y,
175                                                   const BIGNUM *z, BN_CTX *);
176 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
177                                                   const EC_POINT *, BIGNUM *x,
178                                                   BIGNUM *y, BIGNUM *z,
179                                                   BN_CTX *);
180 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
181                                                const BIGNUM *x, const BIGNUM *y,
182                                                BN_CTX *);
183 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
184                                              const BIGNUM *x, int y_bit,
185                                              BN_CTX *);
186 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
187                       const EC_POINT *b, BN_CTX *);
188 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
189                       BN_CTX *);
190 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
191 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
192 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
193 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
194                       BN_CTX *);
195 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
196 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
197                                      EC_POINT * [], BN_CTX *);
198 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
199                             const BIGNUM *b, BN_CTX *);
200 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
201                             BN_CTX *);
202 
203 /* method functions in montgomery.c */
204 int ec_GFp_mont_group_init(EC_GROUP *);
205 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
206                                 const BIGNUM *b, BN_CTX *);
207 void ec_GFp_mont_group_finish(EC_GROUP *);
208 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
209 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
210                           const BIGNUM *b, BN_CTX *);
211 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
212                           BN_CTX *);
213 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
214                              BN_CTX *);
215 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
216                              BN_CTX *);
217 
218 int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
219                                              EC_POINT *point, const BIGNUM *x,
220                                              const BIGNUM *y, const BIGNUM *z,
221                                              BN_CTX *ctx);
222 
223 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
224 
225 const EC_METHOD *EC_GFp_nistp224_method(void);
226 const EC_METHOD *EC_GFp_nistp256_method(void);
227 
228 /* EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
229  * x86-64 optimized P256. See http://eprint.iacr.org/2013/816. */
230 const EC_METHOD *EC_GFp_nistz256_method(void);
231 
232 struct ec_key_st {
233   EC_GROUP *group;
234 
235   EC_POINT *pub_key;
236   BIGNUM *priv_key;
237 
238   /* fixed_k may contain a specific value of 'k', to be used in ECDSA signing.
239    * This is only for the FIPS power-on tests. */
240   BIGNUM *fixed_k;
241 
242   unsigned int enc_flag;
243   point_conversion_form_t conv_form;
244 
245   CRYPTO_refcount_t references;
246 
247   ECDSA_METHOD *ecdsa_meth;
248 
249   CRYPTO_EX_DATA ex_data;
250 } /* EC_KEY */;
251 
252 struct built_in_curve {
253   int nid;
254   const uint8_t *oid;
255   uint8_t oid_len;
256   /* comment is a human-readable string describing the curve. */
257   const char *comment;
258   /* param_len is the number of bytes needed to store a field element. */
259   uint8_t param_len;
260   /* params points to an array of 6*|param_len| bytes which hold the field
261    * elements of the following (in big-endian order): prime, a, b, generator x,
262    * generator y, order. */
263   const uint8_t *params;
264   const EC_METHOD *method;
265 };
266 
267 #define OPENSSL_NUM_BUILT_IN_CURVES 4
268 
269 struct built_in_curves {
270   struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES];
271 };
272 
273 /* OPENSSL_built_in_curves returns a pointer to static information about
274  * standard curves. The array is terminated with an entry where |nid| is
275  * |NID_undef|. */
276 const struct built_in_curves *OPENSSL_built_in_curves(void);
277 
278 #if defined(__cplusplus)
279 }  /* extern C */
280 #endif
281 
282 #endif  /* OPENSSL_HEADER_EC_INTERNAL_H */
283