1 /* crypto/ec/ec_lcl.h */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2003 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 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
74 #include <openssl/obj_mac.h>
75 #include <openssl/ec.h>
76 #include <openssl/bn.h>
78 #if defined(__SUNPRO_C)
79 # if __SUNPRO_C >= 0x520
80 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
85 * Structure details are not part of the exported interface, so all this may
86 * change in future versions.
90 /* used by EC_METHOD_get_field_type: */
91 int field_type; /* a NID */
93 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
96 int (*group_init) (EC_GROUP *);
97 void (*group_finish) (EC_GROUP *);
98 void (*group_clear_finish) (EC_GROUP *);
99 int (*group_copy) (EC_GROUP *, const EC_GROUP *);
100 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
101 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
102 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
103 const BIGNUM *b, BN_CTX *);
104 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
106 /* used by EC_GROUP_get_degree: */
107 int (*group_get_degree) (const EC_GROUP *);
108 /* used by EC_GROUP_check: */
109 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
111 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
114 int (*point_init) (EC_POINT *);
115 void (*point_finish) (EC_POINT *);
116 void (*point_clear_finish) (EC_POINT *);
117 int (*point_copy) (EC_POINT *, const EC_POINT *);
119 * used by EC_POINT_set_to_infinity,
120 * EC_POINT_set_Jprojective_coordinates_GFp,
121 * EC_POINT_get_Jprojective_coordinates_GFp,
122 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
123 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
124 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
126 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
127 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
128 EC_POINT *, const BIGNUM *x,
130 const BIGNUM *z, BN_CTX *);
131 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
132 const EC_POINT *, BIGNUM *x,
133 BIGNUM *y, BIGNUM *z,
135 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
136 const BIGNUM *x, const BIGNUM *y,
138 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
139 BIGNUM *x, BIGNUM *y, BN_CTX *);
140 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
141 const BIGNUM *x, int y_bit,
143 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
144 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
145 point_conversion_form_t form, unsigned char *buf,
146 size_t len, BN_CTX *);
147 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
148 size_t len, BN_CTX *);
149 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
150 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
151 const EC_POINT *b, BN_CTX *);
152 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
153 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
155 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
157 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
158 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
159 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
161 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
162 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
163 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
166 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
167 * EC_POINT_have_precompute_mult (default implementations are used if the
168 * 'mul' pointer is 0):
170 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
171 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
173 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
174 int (*have_precompute_mult) (const EC_GROUP *group);
175 /* internal functions */
177 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
178 * 'dbl' so that the same implementations of point operations can be used
179 * with different optimized implementations of expensive field
182 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
183 const BIGNUM *b, BN_CTX *);
184 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
185 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
186 const BIGNUM *b, BN_CTX *);
187 /* e.g. to Montgomery */
188 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
190 /* e.g. from Montgomery */
191 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
193 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
196 typedef struct ec_extra_data_st {
197 struct ec_extra_data_st *next;
199 void *(*dup_func) (void *);
200 void (*free_func) (void *);
201 void (*clear_free_func) (void *);
202 } EC_EXTRA_DATA; /* used in EC_GROUP */
205 const EC_METHOD *meth;
206 EC_POINT *generator; /* optional */
207 BIGNUM order, cofactor;
208 int curve_name; /* optional NID for named curve */
209 int asn1_flag; /* flag to control the asn1 encoding */
210 point_conversion_form_t asn1_form;
211 unsigned char *seed; /* optional seed for parameters (appears in
214 EC_EXTRA_DATA *extra_data; /* linked list */
216 * The following members are handled by the method functions, even if
217 * they appear generic
220 * Field specification. For curves over GF(p), this is the modulus; for
221 * curves over GF(2^m), this is the irreducible polynomial defining the
226 * Field specification for curves over GF(2^m). The irreducible f(t) is
227 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
228 * poly[0] > poly[1] > ... > poly[k] = 0.
230 unsigned int poly[5];
232 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
233 * or abused for all kinds of fields, not just GF(p).) For characteristic
234 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
235 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
236 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
239 /* enable optimized point arithmetics for special case */
241 /* method-specific (e.g., Montgomery structure) */
243 /* method-specific */
245 /* method-specific */
246 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
255 unsigned int enc_flag;
256 point_conversion_form_t conv_form;
258 EC_EXTRA_DATA *method_data;
262 * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs
263 * only (with visibility limited to 'package' level for now). We use the
264 * function pointers as index for retrieval; this obviates global
265 * ex_data-style index tables.
267 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
268 void *(*dup_func) (void *),
269 void (*free_func) (void *),
270 void (*clear_free_func) (void *));
271 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *),
272 void (*free_func) (void *),
273 void (*clear_free_func) (void *));
274 void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
275 void (*free_func) (void *),
276 void (*clear_free_func) (void *));
277 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
278 void (*free_func) (void *),
279 void (*clear_free_func) (void *));
280 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
281 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
284 const EC_METHOD *meth;
286 * All members except 'meth' are handled by the method functions, even if
287 * they appear generic
291 BIGNUM Z; /* Jacobian projective coordinates: (X, Y, Z)
292 * represents (X/Z^2, Y/Z^3) if Z != 0 */
293 int Z_is_one; /* enable optimized point arithmetics for
298 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
299 * group->method->mul is 0)
301 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
302 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
304 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
305 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
307 /* method functions in ecp_smpl.c */
308 int ec_GFp_simple_group_init(EC_GROUP *);
309 void ec_GFp_simple_group_finish(EC_GROUP *);
310 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
311 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
312 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
313 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
314 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
315 BIGNUM *b, BN_CTX *);
316 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
317 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
318 int ec_GFp_simple_point_init(EC_POINT *);
319 void ec_GFp_simple_point_finish(EC_POINT *);
320 void ec_GFp_simple_point_clear_finish(EC_POINT *);
321 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
322 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
323 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
324 EC_POINT *, const BIGNUM *x,
326 const BIGNUM *z, BN_CTX *);
327 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
328 const EC_POINT *, BIGNUM *x,
329 BIGNUM *y, BIGNUM *z,
331 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
333 const BIGNUM *y, BN_CTX *);
334 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
335 const EC_POINT *, BIGNUM *x,
336 BIGNUM *y, BN_CTX *);
337 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
338 const BIGNUM *x, int y_bit,
340 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
341 point_conversion_form_t form,
342 unsigned char *buf, size_t len, BN_CTX *);
343 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
344 const unsigned char *buf, size_t len, BN_CTX *);
345 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
346 const EC_POINT *b, BN_CTX *);
347 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
349 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
350 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
351 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
352 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
354 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
355 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
356 EC_POINT *[], BN_CTX *);
357 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
358 const BIGNUM *b, BN_CTX *);
359 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
362 /* method functions in ecp_mont.c */
363 int ec_GFp_mont_group_init(EC_GROUP *);
364 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
365 const BIGNUM *b, BN_CTX *);
366 void ec_GFp_mont_group_finish(EC_GROUP *);
367 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
368 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
369 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
370 const BIGNUM *b, BN_CTX *);
371 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
373 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
375 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
377 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
379 /* method functions in ecp_nist.c */
380 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
381 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
382 const BIGNUM *b, BN_CTX *);
383 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
384 const BIGNUM *b, BN_CTX *);
385 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
388 /* method functions in ec2_smpl.c */
389 int ec_GF2m_simple_group_init(EC_GROUP *);
390 void ec_GF2m_simple_group_finish(EC_GROUP *);
391 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
392 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
393 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
394 const BIGNUM *a, const BIGNUM *b,
396 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
397 BIGNUM *b, BN_CTX *);
398 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
399 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
400 int ec_GF2m_simple_point_init(EC_POINT *);
401 void ec_GF2m_simple_point_finish(EC_POINT *);
402 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
403 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
404 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
405 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
407 const BIGNUM *y, BN_CTX *);
408 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
409 const EC_POINT *, BIGNUM *x,
410 BIGNUM *y, BN_CTX *);
411 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
412 const BIGNUM *x, int y_bit,
414 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
415 point_conversion_form_t form,
416 unsigned char *buf, size_t len, BN_CTX *);
417 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
418 const unsigned char *buf, size_t len, BN_CTX *);
419 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
420 const EC_POINT *b, BN_CTX *);
421 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
423 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
424 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
425 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
426 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
428 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
429 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
430 EC_POINT *[], BN_CTX *);
431 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
432 const BIGNUM *b, BN_CTX *);
433 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
435 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
436 const BIGNUM *b, BN_CTX *);
438 /* method functions in ec2_mult.c */
439 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
440 const BIGNUM *scalar, size_t num,
441 const EC_POINT *points[], const BIGNUM *scalars[],
443 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
444 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);