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1/* crypto/ec/ec_lcl.h */
2/* ====================================================================
3 * Copyright (c) 1998-2001 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
57#include <stdlib.h>
58
59#include <openssl/ec.h>
60
61
62/* Structure details are not part of the exported interface,
63 * so all this may change in future versions. */
64
65struct ec_method_st {
66 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
67 int (*group_init)(EC_GROUP *);
68 void (*group_finish)(EC_GROUP *);
69 void (*group_clear_finish)(EC_GROUP *);
70 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
71
72 /* used by EC_GROUP_set_curve_GFp and EC_GROUP_get_curve_GFp: */
73 int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
74 int (*group_get_curve_GFp)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
75
76 /* used by EC_GROUP_set_generator, EC_GROUP_get0_generator,
77 * EC_GROUP_get_order, EC_GROUP_get_cofactor:
78 */
79 int (*group_set_generator)(EC_GROUP *, const EC_POINT *generator,
80 const BIGNUM *order, const BIGNUM *cofactor);
81 EC_POINT *(*group_get0_generator)(const EC_GROUP *);
82 int (*group_get_order)(const EC_GROUP *, BIGNUM *order, BN_CTX *);
83 int (*group_get_cofactor)(const EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
84
85 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
86 int (*point_init)(EC_POINT *);
87 void (*point_finish)(EC_POINT *);
88 void (*point_clear_finish)(EC_POINT *);
89 int (*point_copy)(EC_POINT *, const EC_POINT *);
90
91 /* used by EC_POINT_set_to_infinity,
92 * EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_get_Jprojective_coordinates_GFp,
93 * EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp,
94 * EC_POINT_set_compressed_coordinates_GFp:
95 */
96 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
97 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
98 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
99 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
100 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
101 int (*point_set_affine_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
102 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
103 int (*point_get_affine_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
104 BIGNUM *x, BIGNUM *y, BN_CTX *);
105 int (*point_set_compressed_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
106 const BIGNUM *x, int y_bit, BN_CTX *);
107
108 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
109 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
110 unsigned char *buf, size_t len, BN_CTX *);
111 int (*oct2point)(const EC_GROUP *, EC_POINT *,
112 const unsigned char *buf, size_t len, BN_CTX *);
113
114 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
115 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
116 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
117 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
118
119 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
120 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
121 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
122 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
123
124 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
125 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
126 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
127
128
129 /* internal functions */
130
131 /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that
132 * the same implementations of point operations can be used with different
133 * optimized implementations of expensive field operations: */
134 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
135 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
136
137 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
138 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
139 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
140} /* EC_METHOD */;
141
142
143struct ec_group_st {
144 const EC_METHOD *meth;
145
146 void *extra_data;
147 void *(*extra_data_dup_func)(void *);
148 void (*extra_data_free_func)(void *);
149 void (*extra_data_clear_free_func)(void *);
150
151 /* All members except 'meth' and 'extra_data...' are handled by
152 * the method functions, even if they appear generic */
153
154 BIGNUM field; /* Field specification.
155 * For curves over GF(p), this is the modulus. */
156
157 BIGNUM a, b; /* Curve coefficients.
158 * (Here the assumption is that BIGNUMs can be used
159 * or abused for all kinds of fields, not just GF(p).)
160 * For characteristic > 3, the curve is defined
161 * by a Weierstrass equation of the form
162 * y^2 = x^3 + a*x + b.
163 */
164 int a_is_minus3; /* enable optimized point arithmetics for special case */
165
166 EC_POINT *generator; /* optional */
167 BIGNUM order, cofactor;
168
169 void *field_data1; /* method-specific (e.g., Montgomery structure) */
170 void *field_data2; /* method-specific */
171} /* EC_GROUP */;
172
173
174/* Basically a 'mixin' for extra data, but available for EC_GROUPs only
175 * (with visibility limited to 'package' level for now).
176 * We use the function pointers as index for retrieval; this obviates
177 * global ex_data-style index tables.
178 * (Currently, we have one slot only, but is is possible to extend this
179 * if necessary.) */
180int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
181 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
182void *EC_GROUP_get_extra_data(const EC_GROUP *, void *(*extra_data_dup_func)(void *),
183 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
184void EC_GROUP_free_extra_data(EC_GROUP *);
185void EC_GROUP_clear_free_extra_data(EC_GROUP *);
186
187
188
189struct ec_point_st {
190 const EC_METHOD *meth;
191
192 /* All members except 'meth' are handled by the method functions,
193 * even if they appear generic */
194
195 BIGNUM X;
196 BIGNUM Y;
197 BIGNUM Z; /* Jacobian projective coordinates:
198 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
199 int Z_is_one; /* enable optimized point arithmetics for special case */
200} /* EC_POINT */;
201
202
203
204/* method functions in ecp_smpl.c */
205int ec_GFp_simple_group_init(EC_GROUP *);
206void ec_GFp_simple_group_finish(EC_GROUP *);
207void ec_GFp_simple_group_clear_finish(EC_GROUP *);
208int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
209int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
210int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
211int ec_GFp_simple_group_set_generator(EC_GROUP *, const EC_POINT *generator,
212 const BIGNUM *order, const BIGNUM *cofactor);
213EC_POINT *ec_GFp_simple_group_get0_generator(const EC_GROUP *);
214int ec_GFp_simple_group_get_order(const EC_GROUP *, BIGNUM *order, BN_CTX *);
215int ec_GFp_simple_group_get_cofactor(const EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
216int ec_GFp_simple_point_init(EC_POINT *);
217void ec_GFp_simple_point_finish(EC_POINT *);
218void ec_GFp_simple_point_clear_finish(EC_POINT *);
219int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
220int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
221int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
222 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
223int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
224 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
225int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *, EC_POINT *,
226 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
227int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
228 BIGNUM *x, BIGNUM *y, BN_CTX *);
229int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *, EC_POINT *,
230 const BIGNUM *x, int y_bit, BN_CTX *);
231size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
232 unsigned char *buf, size_t len, BN_CTX *);
233int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
234 const unsigned char *buf, size_t len, BN_CTX *);
235int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
236int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
237int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
238int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
239int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
240int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
241int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
242int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
243int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
244int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
245
246
247/* method functions in ecp_mont.c */
248int ec_GFp_mont_group_init(EC_GROUP *);
249int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
250void ec_GFp_mont_group_finish(EC_GROUP *);
251void ec_GFp_mont_group_clear_finish(EC_GROUP *);
252int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
253int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
254int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
255int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
256int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
257int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
258
259
260/* method functions in ecp_recp.c */
261int ec_GFp_recp_group_init(EC_GROUP *);
262int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
263void ec_GFp_recp_group_finish(EC_GROUP *);
264void ec_GFp_recp_group_clear_finish(EC_GROUP *);
265int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
266int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
267int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
268
269
270/* method functions in ecp_nist.c */
271int ec_GFp_nist_group_init(EC_GROUP *);
272int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
273void ec_GFp_nist_group_finish(EC_GROUP *);
274void ec_GFp_nist_group_clear_finish(EC_GROUP *);
275int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
276int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
277int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
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