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1/* crypto/ec/ec_lcl.h */
2/*
3 * Originally written by Bodo Moeller for the OpenSSL project.
4 */
5/* ====================================================================
6 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 *
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 *
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
18 * distribution.
19 *
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 *
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
29 *
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
33 *
34 * 6. Redistributions of any form whatsoever must retain the following
35 * acknowledgment:
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 *
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
52 *
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
56 *
57 */
58/* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 *
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 *
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
66 *
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69 *
70 */
71
72
73#include <stdlib.h>
74
75#include <openssl/obj_mac.h>
76#include <openssl/ec.h>
77#include <openssl/bn.h>
78
79#if defined(__SUNPRO_C)
80# if __SUNPRO_C >= 0x520
81# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
82# endif
83#endif
84
85/* Structure details are not part of the exported interface,
86 * so all this may change in future versions. */
87
88struct ec_method_st {
89 /* used by EC_METHOD_get_field_type: */
90 int field_type; /* a NID */
91
92 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
93 int (*group_init)(EC_GROUP *);
94 void (*group_finish)(EC_GROUP *);
95 void (*group_clear_finish)(EC_GROUP *);
96 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
97
98 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
99 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
100 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
101 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
102
103 /* used by EC_GROUP_get_degree: */
104 int (*group_get_degree)(const EC_GROUP *);
105
106 /* used by EC_GROUP_check: */
107 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
108
109 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
110 int (*point_init)(EC_POINT *);
111 void (*point_finish)(EC_POINT *);
112 void (*point_clear_finish)(EC_POINT *);
113 int (*point_copy)(EC_POINT *, const EC_POINT *);
114
115 /* used by EC_POINT_set_to_infinity,
116 * EC_POINT_set_Jprojective_coordinates_GFp,
117 * EC_POINT_get_Jprojective_coordinates_GFp,
118 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
119 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
120 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
121 */
122 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
123 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
124 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
125 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
126 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
127 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
128 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
129 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
130 BIGNUM *x, BIGNUM *y, BN_CTX *);
131 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
132 const BIGNUM *x, int y_bit, BN_CTX *);
133
134 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
135 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
136 unsigned char *buf, size_t len, BN_CTX *);
137 int (*oct2point)(const EC_GROUP *, EC_POINT *,
138 const unsigned char *buf, size_t len, BN_CTX *);
139
140 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
141 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
142 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
143 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
144
145 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
146 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
147 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
148 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
149
150 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
151 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
152 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
153
154 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
155 * (default implementations are used if the 'mul' pointer is 0): */
156 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
157 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
158 int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
159 int (*have_precompute_mult)(const EC_GROUP *group);
160
161
162 /* internal functions */
163
164 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
165 * the same implementations of point operations can be used with different
166 * optimized implementations of expensive field operations: */
167 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
168 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
169 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
170
171 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
172 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
173 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
174} /* EC_METHOD */;
175
176typedef struct ec_extra_data_st {
177 struct ec_extra_data_st *next;
178 void *data;
179 void *(*dup_func)(void *);
180 void (*free_func)(void *);
181 void (*clear_free_func)(void *);
182} EC_EXTRA_DATA; /* used in EC_GROUP */
183
184struct ec_group_st {
185 const EC_METHOD *meth;
186
187 EC_POINT *generator; /* optional */
188 BIGNUM order, cofactor;
189
190 int curve_name;/* optional NID for named curve */
191 int asn1_flag; /* flag to control the asn1 encoding */
192 point_conversion_form_t asn1_form;
193
194 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
195 size_t seed_len;
196
197 EC_EXTRA_DATA *extra_data; /* linked list */
198
199 /* The following members are handled by the method functions,
200 * even if they appear generic */
201
202 BIGNUM field; /* Field specification.
203 * For curves over GF(p), this is the modulus;
204 * for curves over GF(2^m), this is the
205 * irreducible polynomial defining the field.
206 */
207
208 int poly[6]; /* Field specification for curves over GF(2^m).
209 * The irreducible f(t) is then of the form:
210 * t^poly[0] + t^poly[1] + ... + t^poly[k]
211 * where m = poly[0] > poly[1] > ... > poly[k] = 0.
212 * The array is terminated with poly[k+1]=-1.
213 * All elliptic curve irreducibles have at most 5
214 * non-zero terms.
215 */
216
217 BIGNUM a, b; /* Curve coefficients.
218 * (Here the assumption is that BIGNUMs can be used
219 * or abused for all kinds of fields, not just GF(p).)
220 * For characteristic > 3, the curve is defined
221 * by a Weierstrass equation of the form
222 * y^2 = x^3 + a*x + b.
223 * For characteristic 2, the curve is defined by
224 * an equation of the form
225 * y^2 + x*y = x^3 + a*x^2 + b.
226 */
227
228 int a_is_minus3; /* enable optimized point arithmetics for special case */
229
230 void *field_data1; /* method-specific (e.g., Montgomery structure) */
231 void *field_data2; /* method-specific */
232 int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
233} /* EC_GROUP */;
234
235struct ec_key_st {
236 int version;
237
238 EC_GROUP *group;
239
240 EC_POINT *pub_key;
241 BIGNUM *priv_key;
242
243 unsigned int enc_flag;
244 point_conversion_form_t conv_form;
245
246 int references;
247
248 EC_EXTRA_DATA *method_data;
249} /* EC_KEY */;
250
251/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
252 * (with visibility limited to 'package' level for now).
253 * We use the function pointers as index for retrieval; this obviates
254 * global ex_data-style index tables.
255 */
256int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
257 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
258void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
259 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
260void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
261 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
262void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
263 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
264void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
265void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
266
267
268
269struct ec_point_st {
270 const EC_METHOD *meth;
271
272 /* All members except 'meth' are handled by the method functions,
273 * even if they appear generic */
274
275 BIGNUM X;
276 BIGNUM Y;
277 BIGNUM Z; /* Jacobian projective coordinates:
278 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
279 int Z_is_one; /* enable optimized point arithmetics for special case */
280} /* EC_POINT */;
281
282
283
284/* method functions in ec_mult.c
285 * (ec_lib.c uses these as defaults if group->method->mul is 0) */
286int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
287 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
288int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
289int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
290
291
292/* method functions in ecp_smpl.c */
293int ec_GFp_simple_group_init(EC_GROUP *);
294void ec_GFp_simple_group_finish(EC_GROUP *);
295void ec_GFp_simple_group_clear_finish(EC_GROUP *);
296int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
297int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
298int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
299int ec_GFp_simple_group_get_degree(const EC_GROUP *);
300int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
301int ec_GFp_simple_point_init(EC_POINT *);
302void ec_GFp_simple_point_finish(EC_POINT *);
303void ec_GFp_simple_point_clear_finish(EC_POINT *);
304int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
305int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
306int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
307 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
308int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
309 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
310int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
311 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
312int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
313 BIGNUM *x, BIGNUM *y, BN_CTX *);
314int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
315 const BIGNUM *x, int y_bit, BN_CTX *);
316size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
317 unsigned char *buf, size_t len, BN_CTX *);
318int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
319 const unsigned char *buf, size_t len, BN_CTX *);
320int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
321int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
322int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
323int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
324int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
325int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
326int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
327int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
328int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
329int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
330
331
332/* method functions in ecp_mont.c */
333int ec_GFp_mont_group_init(EC_GROUP *);
334int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
335void ec_GFp_mont_group_finish(EC_GROUP *);
336void ec_GFp_mont_group_clear_finish(EC_GROUP *);
337int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
338int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
339int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
340int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
341int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
342int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
343
344
345/* method functions in ecp_nist.c */
346int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
347int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
348int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
349int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
350
351
352/* method functions in ec2_smpl.c */
353int ec_GF2m_simple_group_init(EC_GROUP *);
354void ec_GF2m_simple_group_finish(EC_GROUP *);
355void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
356int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
357int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
358int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
359int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
360int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
361int ec_GF2m_simple_point_init(EC_POINT *);
362void ec_GF2m_simple_point_finish(EC_POINT *);
363void ec_GF2m_simple_point_clear_finish(EC_POINT *);
364int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
365int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
366int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
367 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
368int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
369 BIGNUM *x, BIGNUM *y, BN_CTX *);
370int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
371 const BIGNUM *x, int y_bit, BN_CTX *);
372size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
373 unsigned char *buf, size_t len, BN_CTX *);
374int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
375 const unsigned char *buf, size_t len, BN_CTX *);
376int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
377int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
378int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
379int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
380int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
381int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
382int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
383int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
384int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
385int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
386int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
387
388
389/* method functions in ec2_mult.c */
390int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
391 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
392int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
393int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-03-20 17:45:10 +0000