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
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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 /* internal function: ec_group_index2nid() returns the NID of curve
93 * with the given index i from the internal curve list */
94 int ec_group_index2nid(int i);
97 /* Structure details are not part of the exported interface,
98 * so all this may change in future versions. */
100 struct ec_method_st {
101 /* used by EC_METHOD_get_field_type: */
102 int field_type; /* a NID */
104 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
105 int (*group_init)(EC_GROUP *);
106 void (*group_finish)(EC_GROUP *);
107 void (*group_clear_finish)(EC_GROUP *);
108 int (*group_copy)(EC_GROUP *, const EC_GROUP *);
110 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
111 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
112 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
113 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
115 /* used by EC_GROUP_get_degree: */
116 int (*group_get_degree)(const EC_GROUP *);
118 /* used by EC_GROUP_check: */
119 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
121 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
122 int (*point_init)(EC_POINT *);
123 void (*point_finish)(EC_POINT *);
124 void (*point_clear_finish)(EC_POINT *);
125 int (*point_copy)(EC_POINT *, const EC_POINT *);
127 /* used by EC_POINT_set_to_infinity,
128 * EC_POINT_set_Jprojective_coordinates_GFp,
129 * EC_POINT_get_Jprojective_coordinates_GFp,
130 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
131 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
132 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
134 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
135 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
136 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
137 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
138 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
139 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
140 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
141 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
142 BIGNUM *x, BIGNUM *y, BN_CTX *);
143 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
144 const BIGNUM *x, int y_bit, BN_CTX *);
146 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
147 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
148 unsigned char *buf, size_t len, BN_CTX *);
149 int (*oct2point)(const EC_GROUP *, EC_POINT *,
150 const unsigned char *buf, size_t len, BN_CTX *);
152 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
153 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
154 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
155 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
157 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult: */
158 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
159 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
160 int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
162 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
163 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
164 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
165 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
167 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
168 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
169 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
172 /* internal functions */
174 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
175 * the same implementations of point operations can be used with different
176 * optimized implementations of expensive field operations: */
177 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
178 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
179 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
181 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
182 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
183 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
188 const EC_METHOD *meth;
190 EC_POINT *generator; /* optional */
191 BIGNUM order, cofactor;
193 int curve_name;/* optional NID for named curve */
194 int asn1_flag; /* flag to control the asn1 encoding */
195 point_conversion_form_t asn1_form;
197 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
201 void *(*extra_data_dup_func)(void *);
202 void (*extra_data_free_func)(void *);
203 void (*extra_data_clear_free_func)(void *);
205 /* The following members are handled by the method functions,
206 * even if they appear generic */
208 BIGNUM field; /* Field specification.
209 * For curves over GF(p), this is the modulus;
210 * for curves over GF(2^m), this is the
211 * irreducible polynomial defining the field.
214 unsigned int poly[5]; /* Field specification for curves over GF(2^m).
215 * The irreducible f(t) is then of the form:
216 * t^poly[0] + t^poly[1] + ... + t^poly[k]
217 * where m = poly[0] > poly[1] > ... > poly[k] = 0.
220 BIGNUM a, b; /* Curve coefficients.
221 * (Here the assumption is that BIGNUMs can be used
222 * or abused for all kinds of fields, not just GF(p).)
223 * For characteristic > 3, the curve is defined
224 * by a Weierstrass equation of the form
225 * y^2 = x^3 + a*x + b.
226 * For characteristic 2, the curve is defined by
227 * an equation of the form
228 * y^2 + x*y = x^3 + a*x^2 + b.
231 int a_is_minus3; /* enable optimized point arithmetics for special case */
233 void *field_data1; /* method-specific (e.g., Montgomery structure) */
234 void *field_data2; /* method-specific */
238 /* Basically a 'mixin' for extra data, but available for EC_GROUPs only
239 * (with visibility limited to 'package' level for now).
240 * We use the function pointers as index for retrieval; this obviates
241 * global ex_data-style index tables.
242 * (Currently, we have one slot only, but is is possible to extend this
244 int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
245 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
246 void *EC_GROUP_get_extra_data(const EC_GROUP *, void *(*extra_data_dup_func)(void *),
247 void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
248 void EC_GROUP_free_extra_data(EC_GROUP *);
249 void EC_GROUP_clear_free_extra_data(EC_GROUP *);
254 const EC_METHOD *meth;
256 /* All members except 'meth' are handled by the method functions,
257 * even if they appear generic */
261 BIGNUM Z; /* Jacobian projective coordinates:
262 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
263 int Z_is_one; /* enable optimized point arithmetics for special case */
268 /* method functions in ec_mult.c */
269 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
270 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
271 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
273 /* method functions in ecp_smpl.c */
274 int ec_GFp_simple_group_init(EC_GROUP *);
275 void ec_GFp_simple_group_finish(EC_GROUP *);
276 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
277 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
278 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
279 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
280 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
281 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
282 int ec_GFp_simple_point_init(EC_POINT *);
283 void ec_GFp_simple_point_finish(EC_POINT *);
284 void ec_GFp_simple_point_clear_finish(EC_POINT *);
285 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
286 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
287 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
288 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
289 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
290 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
291 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
292 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
293 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
294 BIGNUM *x, BIGNUM *y, BN_CTX *);
295 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
296 const BIGNUM *x, int y_bit, BN_CTX *);
297 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
298 unsigned char *buf, size_t len, BN_CTX *);
299 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
300 const unsigned char *buf, size_t len, BN_CTX *);
301 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
302 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
303 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
304 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
305 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
306 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
307 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
308 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
309 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
310 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
313 /* method functions in ecp_mont.c */
314 int ec_GFp_mont_group_init(EC_GROUP *);
315 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
316 void ec_GFp_mont_group_finish(EC_GROUP *);
317 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
318 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
319 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
320 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
321 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
322 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
323 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
326 /* method functions in ecp_recp.c */
327 int ec_GFp_recp_group_init(EC_GROUP *);
328 int ec_GFp_recp_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
329 void ec_GFp_recp_group_finish(EC_GROUP *);
330 void ec_GFp_recp_group_clear_finish(EC_GROUP *);
331 int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
332 int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
333 int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
336 /* method functions in ecp_nist.c */
337 int ec_GFp_nist_group_init(EC_GROUP *);
338 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
339 void ec_GFp_nist_group_finish(EC_GROUP *);
340 void ec_GFp_nist_group_clear_finish(EC_GROUP *);
341 int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
342 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
343 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
346 /* method functions in ec2_smpl.c */
347 int ec_GF2m_simple_group_init(EC_GROUP *);
348 void ec_GF2m_simple_group_finish(EC_GROUP *);
349 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
350 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
351 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
352 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
353 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
354 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
355 int ec_GF2m_simple_point_init(EC_POINT *);
356 void ec_GF2m_simple_point_finish(EC_POINT *);
357 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
358 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
359 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
360 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
361 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
362 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
363 BIGNUM *x, BIGNUM *y, BN_CTX *);
364 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
365 const BIGNUM *x, int y_bit, BN_CTX *);
366 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
367 unsigned char *buf, size_t len, BN_CTX *);
368 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
369 const unsigned char *buf, size_t len, BN_CTX *);
370 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
371 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
372 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
373 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
374 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
375 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
376 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
377 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
378 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
379 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
380 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
383 /* method functions in ec2_mult.c */
384 int ec_GF2m_mont_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
385 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
386 int ec_GF2m_mont_precompute_mult(EC_GROUP *group, BN_CTX *ctx);