1 /* crypto/ec/ec_lcl.h */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
67 * In addition, Sun covenants to all licensees who provide a reciprocal
68 * covenant with respect to their own patents if any, not to sue under
69 * current and future patent claims necessarily infringed by the making,
70 * using, practicing, selling, offering for sale and/or otherwise
71 * disposing of the Contribution as delivered hereunder
72 * (or portions thereof), provided that such covenant shall not apply:
73 * 1) for code that a licensee deletes from the Contribution;
74 * 2) separates from the Contribution; or
75 * 3) for infringements caused by:
76 * i) the modification of the Contribution or
77 * ii) the combination of the Contribution with other software or
78 * devices where such combination causes the infringement.
80 * The elliptic curve binary polynomial software is originally written by
81 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
88 #include <openssl/obj_mac.h>
89 #include <openssl/ec.h>
92 /* Structure details are not part of the exported interface,
93 * so all this may change in future versions. */
96 /* used by EC_METHOD_get_field_type: */
97 int field_type; /* a NID */
99 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
100 int (*group_init)(EC_GROUP *);
101 void (*group_finish)(EC_GROUP *);
102 void (*group_clear_finish)(EC_GROUP *);
103 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
105 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
106 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
107 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
108 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
110 /* used by EC_GROUP_get_degree: */
111 int (*group_get_degree)(const EC_GROUP *);
113 /* used by EC_GROUP_check: */
114 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
116 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
117 int (*point_init)(EC_POINT *);
118 void (*point_finish)(EC_POINT *);
119 void (*point_clear_finish)(EC_POINT *);
120 int (*point_copy)(EC_POINT *, const EC_POINT *);
122 /* used by EC_POINT_set_to_infinity,
123 * EC_POINT_set_Jprojective_coordinates_GFp,
124 * EC_POINT_get_Jprojective_coordinates_GFp,
125 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
126 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
127 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
129 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
130 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
131 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
132 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
133 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
134 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
135 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
136 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
137 BIGNUM *x, BIGNUM *y, BN_CTX *);
138 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
139 const BIGNUM *x, int y_bit, BN_CTX *);
141 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
142 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
143 unsigned char *buf, size_t len, BN_CTX *);
144 int (*oct2point)(const EC_GROUP *, EC_POINT *,
145 const unsigned char *buf, size_t len, BN_CTX *);
147 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
148 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
149 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
150 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
152 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult: */
153 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
154 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
155 int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
157 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
158 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
159 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
160 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
162 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
163 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
164 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
167 /* internal functions */
169 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
170 * the same implementations of point operations can be used with different
171 * optimized implementations of expensive field operations: */
172 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
173 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
174 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
176 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
177 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
178 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
183 const EC_METHOD *meth;
185 EC_POINT *generator; /* optional */
186 BIGNUM order, cofactor;
188 int curve_name;/* optional NID for named curve */
189 int asn1_flag; /* flag to control the asn1 encoding */
190 point_conversion_form_t asn1_form;
192 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
196 void *(*extra_data_dup_func)(void *);
197 void (*extra_data_free_func)(void *);
198 void (*extra_data_clear_free_func)(void *);
200 /* The following members are handled by the method functions,
201 * even if they appear generic */
203 BIGNUM field; /* Field specification.
204 * For curves over GF(p), this is the modulus;
205 * for curves over GF(2^m), this is the
206 * irreducible polynomial defining the field.
209 unsigned int poly[5]; /* Field specification for curves over GF(2^m).
210 * The irreducible f(t) is then of the form:
211 * t^poly[0] + t^poly[1] + ... + t^poly[k]
212 * where m = poly[0] > poly[1] > ... > poly[k] = 0.
215 BIGNUM a, b; /* Curve coefficients.
216 * (Here the assumption is that BIGNUMs can be used
217 * or abused for all kinds of fields, not just GF(p).)
218 * For characteristic > 3, the curve is defined
219 * by a Weierstrass equation of the form
220 * y^2 = x^3 + a*x + b.
221 * For characteristic 2, the curve is defined by
222 * an equation of the form
223 * y^2 + x*y = x^3 + a*x^2 + b.
226 int a_is_minus3; /* enable optimized point arithmetics for special case */
228 void *field_data1; /* method-specific (e.g., Montgomery structure) */
229 void *field_data2; /* method-specific */
233 /* Basically a 'mixin' for extra data, but available for EC_GROUPs only
234 * (with visibility limited to 'package' level for now).
235 * We use the function pointers as index for retrieval; this obviates
236 * global ex_data-style index tables.
237 * (Currently, we have one slot only, but is is possible to extend this
239 int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
240 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
241 void *EC_GROUP_get_extra_data(const EC_GROUP *, void *(*extra_data_dup_func)(void *),
242 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
243 void EC_GROUP_free_extra_data(EC_GROUP *);
244 void EC_GROUP_clear_free_extra_data(EC_GROUP *);
249 const EC_METHOD *meth;
251 /* All members except 'meth' are handled by the method functions,
252 * even if they appear generic */
256 BIGNUM Z; /* Jacobian projective coordinates:
257 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
258 int Z_is_one; /* enable optimized point arithmetics for special case */
263 /* method functions in ec_mult.c */
264 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
265 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
266 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
268 /* method functions in ecp_smpl.c */
269 int ec_GFp_simple_group_init(EC_GROUP *);
270 void ec_GFp_simple_group_finish(EC_GROUP *);
271 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
272 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
273 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
274 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
275 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
276 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
277 int ec_GFp_simple_point_init(EC_POINT *);
278 void ec_GFp_simple_point_finish(EC_POINT *);
279 void ec_GFp_simple_point_clear_finish(EC_POINT *);
280 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
281 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
282 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
283 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
284 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
285 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
286 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
287 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
288 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
289 BIGNUM *x, BIGNUM *y, BN_CTX *);
290 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
291 const BIGNUM *x, int y_bit, BN_CTX *);
292 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
293 unsigned char *buf, size_t len, BN_CTX *);
294 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
295 const unsigned char *buf, size_t len, BN_CTX *);
296 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
297 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
298 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
299 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
300 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
301 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
302 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
303 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
304 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
305 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
308 /* method functions in ecp_mont.c */
309 int ec_GFp_mont_group_init(EC_GROUP *);
310 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
311 void ec_GFp_mont_group_finish(EC_GROUP *);
312 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
313 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
314 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
315 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
316 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
317 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
318 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
321 /* method functions in ecp_recp.c */
322 int ec_GFp_recp_group_init(EC_GROUP *);
323 int ec_GFp_recp_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
324 void ec_GFp_recp_group_finish(EC_GROUP *);
325 void ec_GFp_recp_group_clear_finish(EC_GROUP *);
326 int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
327 int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
328 int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
331 /* method functions in ecp_nist.c */
332 int ec_GFp_nist_group_init(EC_GROUP *);
333 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
334 void ec_GFp_nist_group_finish(EC_GROUP *);
335 void ec_GFp_nist_group_clear_finish(EC_GROUP *);
336 int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
337 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
338 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
341 /* method functions in ec2_smpl.c */
342 int ec_GF2m_simple_group_init(EC_GROUP *);
343 void ec_GF2m_simple_group_finish(EC_GROUP *);
344 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
345 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
346 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
347 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
348 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
349 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
350 int ec_GF2m_simple_point_init(EC_POINT *);
351 void ec_GF2m_simple_point_finish(EC_POINT *);
352 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
353 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
354 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
355 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
356 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
357 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
358 BIGNUM *x, BIGNUM *y, BN_CTX *);
359 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
360 const BIGNUM *x, int y_bit, BN_CTX *);
361 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
362 unsigned char *buf, size_t len, BN_CTX *);
363 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
364 const unsigned char *buf, size_t len, BN_CTX *);
365 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
366 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
367 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
368 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
369 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
370 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
371 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
372 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
373 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
374 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
375 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
378 /* method functions in ec2_mult.c */
379 int ec_GF2m_mont_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
380 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
381 int ec_GF2m_mont_precompute_mult(EC_GROUP *group, BN_CTX *ctx);