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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 /* Use default functions for poin2oct, oct2point and compressed coordinates */
83 #define EC_FLAGS_DEFAULT_OCT 0x1
84 
85 struct 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 
188 const EC_METHOD* EC_GFp_mont_method(void);
189 
190 struct ec_pre_comp_st;
191 void ec_pre_comp_free(struct ec_pre_comp_st *pre_comp);
192 void *ec_pre_comp_dup(struct ec_pre_comp_st *pre_comp);
193 
194 struct 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 
217 struct 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 
230 EC_GROUP *ec_group_new(const EC_METHOD *meth);
231 int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src);
232 
233 int 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 *);
236 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
237 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
238 
239 /* method functions in simple.c */
240 int ec_GFp_simple_group_init(EC_GROUP *);
241 void ec_GFp_simple_group_finish(EC_GROUP *);
242 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
243 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
244 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
245                                   const BIGNUM *b, BN_CTX *);
246 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
247                                   BIGNUM *b, BN_CTX *);
248 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
249 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
250 int ec_GFp_simple_point_init(EC_POINT *);
251 void ec_GFp_simple_point_finish(EC_POINT *);
252 void ec_GFp_simple_point_clear_finish(EC_POINT *);
253 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
254 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
255 int 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 *);
259 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
260                                                   const EC_POINT *, BIGNUM *x,
261                                                   BIGNUM *y, BIGNUM *z,
262                                                   BN_CTX *);
263 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
264                                                const BIGNUM *x, const BIGNUM *y,
265                                                BN_CTX *);
266 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
267                                                const EC_POINT *, BIGNUM *x,
268                                                BIGNUM *y, BN_CTX *);
269 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
270                                              const BIGNUM *x, int y_bit,
271                                              BN_CTX *);
272 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
273                       const EC_POINT *b, BN_CTX *);
274 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
275                       BN_CTX *);
276 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
277 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
278 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
279 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
280                       BN_CTX *);
281 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
282 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
283                                      EC_POINT * [], BN_CTX *);
284 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
285                             const BIGNUM *b, BN_CTX *);
286 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
287                             BN_CTX *);
288 
289 /* method functions in montgomery.c */
290 int ec_GFp_mont_group_init(EC_GROUP *);
291 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
292                                 const BIGNUM *b, BN_CTX *);
293 void ec_GFp_mont_group_finish(EC_GROUP *);
294 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
295 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
296 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
297                           const BIGNUM *b, BN_CTX *);
298 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
299                           BN_CTX *);
300 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
301                              BN_CTX *);
302 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
303                              BN_CTX *);
304 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
305 
306 int 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 
311 void 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 
320 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
321 
322 const EC_METHOD *EC_GFp_nistp256_method(void);
323 
324 struct 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. */
344 struct 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 
358 struct 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|. */
366 extern 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