1 /* crypto/ec/ec_lcl.h */
2 /* ====================================================================
3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
59 #include <openssl/obj_mac.h>
60 #include <openssl/ec.h>
63 /* Structure details are not part of the exported interface,
64 * so all this may change in future versions. */
67 /* used by EC_METHOD_get_field_type: */
68 int field_type; /* a NID */
70 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
71 int (*group_init)(EC_GROUP *);
72 void (*group_finish)(EC_GROUP *);
73 void (*group_clear_finish)(EC_GROUP *);
74 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
76 /* used by EC_GROUP_set_curve_GFp and EC_GROUP_get_curve_GFp: */
77 int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
78 int (*group_get_curve_GFp)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
80 /* used by EC_GROUP_check: */
81 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
83 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
84 int (*point_init)(EC_POINT *);
85 void (*point_finish)(EC_POINT *);
86 void (*point_clear_finish)(EC_POINT *);
87 int (*point_copy)(EC_POINT *, const EC_POINT *);
89 /* used by EC_POINT_set_to_infinity,
90 * EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_get_Jprojective_coordinates_GFp,
91 * EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp,
92 * EC_POINT_set_compressed_coordinates_GFp:
94 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
95 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
96 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
97 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
98 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
99 int (*point_set_affine_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
100 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
101 int (*point_get_affine_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
102 BIGNUM *x, BIGNUM *y, BN_CTX *);
103 int (*point_set_compressed_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
104 const BIGNUM *x, int y_bit, BN_CTX *);
106 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
107 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
108 unsigned char *buf, size_t len, BN_CTX *);
109 int (*oct2point)(const EC_GROUP *, EC_POINT *,
110 const unsigned char *buf, size_t len, BN_CTX *);
112 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
113 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
114 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
115 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
117 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
118 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
119 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
120 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
122 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
123 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
124 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
127 /* internal functions */
129 /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that
130 * the same implementations of point operations can be used with different
131 * optimized implementations of expensive field operations: */
132 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
133 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
135 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
136 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
137 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
142 const EC_METHOD *meth;
144 EC_POINT *generator; /* optional */
145 BIGNUM order, cofactor;
147 int curve_name;/* optional NID for named curve */
148 int asn1_flag; /* flag to control the asn1 encoding */
149 point_conversion_form_t asn1_form;
152 void *(*extra_data_dup_func)(void *);
153 void (*extra_data_free_func)(void *);
154 void (*extra_data_clear_free_func)(void *);
156 unsigned char *seed; /* XXX */
157 size_t seed_len; /* XXX */
159 /* The following members are handled by the method functions,
160 * even if they appear generic */
162 BIGNUM field; /* Field specification.
163 * For curves over GF(p), this is the modulus;
164 * for curves over GF(2^m), this is the
165 * irreducible polynomial defining the field.
168 BIGNUM a, b; /* Curve coefficients.
169 * (Here the assumption is that BIGNUMs can be used
170 * or abused for all kinds of fields, not just GF(p).)
171 * For characteristic > 3, the curve is defined
172 * by a Weierstrass equation of the form
173 * y^2 = x^3 + a*x + b.
174 * For characteristic 2, the curve is defined by
175 * an equation of the form
176 * y^2 + x*y = x^3 + a*x^2 + b.
179 int a_is_minus3; /* enable optimized point arithmetics for special case */
181 void *field_data1; /* method-specific (e.g., Montgomery structure) */
182 void *field_data2; /* method-specific */
186 /* Basically a 'mixin' for extra data, but available for EC_GROUPs only
187 * (with visibility limited to 'package' level for now).
188 * We use the function pointers as index for retrieval; this obviates
189 * global ex_data-style index tables.
190 * (Currently, we have one slot only, but is is possible to extend this
192 int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
193 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
194 void *EC_GROUP_get_extra_data(const EC_GROUP *, void *(*extra_data_dup_func)(void *),
195 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
196 void EC_GROUP_free_extra_data(EC_GROUP *);
197 void EC_GROUP_clear_free_extra_data(EC_GROUP *);
202 const EC_METHOD *meth;
204 /* All members except 'meth' are handled by the method functions,
205 * even if they appear generic */
209 BIGNUM Z; /* Jacobian projective coordinates:
210 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
211 int Z_is_one; /* enable optimized point arithmetics for special case */
216 /* method functions in ecp_smpl.c */
217 int ec_GFp_simple_group_init(EC_GROUP *);
218 void ec_GFp_simple_group_finish(EC_GROUP *);
219 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
220 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
221 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
222 int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
223 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
224 int ec_GFp_simple_point_init(EC_POINT *);
225 void ec_GFp_simple_point_finish(EC_POINT *);
226 void ec_GFp_simple_point_clear_finish(EC_POINT *);
227 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
228 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
229 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
230 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
231 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
232 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
233 int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *, EC_POINT *,
234 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
235 int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
236 BIGNUM *x, BIGNUM *y, BN_CTX *);
237 int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *, EC_POINT *,
238 const BIGNUM *x, int y_bit, BN_CTX *);
239 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
240 unsigned char *buf, size_t len, BN_CTX *);
241 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
242 const unsigned char *buf, size_t len, BN_CTX *);
243 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
244 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
245 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
246 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
247 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
248 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
249 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
250 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
251 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
252 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
255 /* method functions in ecp_mont.c */
256 int ec_GFp_mont_group_init(EC_GROUP *);
257 int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
258 void ec_GFp_mont_group_finish(EC_GROUP *);
259 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
260 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
261 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
262 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
263 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
264 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
265 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
268 /* method functions in ecp_recp.c */
269 int ec_GFp_recp_group_init(EC_GROUP *);
270 int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
271 void ec_GFp_recp_group_finish(EC_GROUP *);
272 void ec_GFp_recp_group_clear_finish(EC_GROUP *);
273 int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
274 int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
275 int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
278 /* method functions in ecp_nist.c */
279 int ec_GFp_nist_group_init(EC_GROUP *);
280 int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
281 void ec_GFp_nist_group_finish(EC_GROUP *);
282 void ec_GFp_nist_group_clear_finish(EC_GROUP *);
283 int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
284 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
285 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);