1 /* crypto/ec/ec_lcl.h */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2010 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)
84 /* Use default functions for poin2oct, oct2point and compressed coordinates */
85 #define EC_FLAGS_DEFAULT_OCT 0x1
88 * Structure details are not part of the exported interface, so all this may
89 * change in future versions.
93 /* Various method flags */
95 /* used by EC_METHOD_get_field_type: */
96 int field_type
; /* a NID */
98 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
101 int (*group_init
) (EC_GROUP
*);
102 void (*group_finish
) (EC_GROUP
*);
103 void (*group_clear_finish
) (EC_GROUP
*);
104 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
,
108 const BIGNUM
*b
, BN_CTX
*);
109 int (*group_get_curve
) (const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
,
111 /* used by EC_GROUP_get_degree: */
112 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,
119 int (*point_init
) (EC_POINT
*);
120 void (*point_finish
) (EC_POINT
*);
121 void (*point_clear_finish
) (EC_POINT
*);
122 int (*point_copy
) (EC_POINT
*, const EC_POINT
*);
124 * used by EC_POINT_set_to_infinity,
125 * EC_POINT_set_Jprojective_coordinates_GFp,
126 * EC_POINT_get_Jprojective_coordinates_GFp,
127 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
128 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
129 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
131 int (*point_set_to_infinity
) (const EC_GROUP
*, EC_POINT
*);
132 int (*point_set_Jprojective_coordinates_GFp
) (const EC_GROUP
*,
133 EC_POINT
*, const BIGNUM
*x
,
135 const BIGNUM
*z
, BN_CTX
*);
136 int (*point_get_Jprojective_coordinates_GFp
) (const EC_GROUP
*,
137 const EC_POINT
*, BIGNUM
*x
,
138 BIGNUM
*y
, BIGNUM
*z
,
140 int (*point_set_affine_coordinates
) (const EC_GROUP
*, EC_POINT
*,
141 const BIGNUM
*x
, const BIGNUM
*y
,
143 int (*point_get_affine_coordinates
) (const EC_GROUP
*, const EC_POINT
*,
144 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*);
145 int (*point_set_compressed_coordinates
) (const EC_GROUP
*, EC_POINT
*,
146 const BIGNUM
*x
, int y_bit
,
148 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
149 size_t (*point2oct
) (const EC_GROUP
*, const EC_POINT
*,
150 point_conversion_form_t form
, unsigned char *buf
,
151 size_t len
, BN_CTX
*);
152 int (*oct2point
) (const EC_GROUP
*, EC_POINT
*, const unsigned char *buf
,
153 size_t len
, BN_CTX
*);
154 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
155 int (*add
) (const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
156 const EC_POINT
*b
, BN_CTX
*);
157 int (*dbl
) (const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
, BN_CTX
*);
158 int (*invert
) (const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
160 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
162 int (*is_at_infinity
) (const EC_GROUP
*, const EC_POINT
*);
163 int (*is_on_curve
) (const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
164 int (*point_cmp
) (const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
166 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
167 int (*make_affine
) (const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
168 int (*points_make_affine
) (const EC_GROUP
*, size_t num
, EC_POINT
*[],
171 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
172 * EC_POINT_have_precompute_mult (default implementations are used if the
173 * 'mul' pointer is 0):
175 int (*mul
) (const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
176 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
178 int (*precompute_mult
) (EC_GROUP
*group
, BN_CTX
*);
179 int (*have_precompute_mult
) (const EC_GROUP
*group
);
180 /* internal functions */
182 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
183 * 'dbl' so that the same implementations of point operations can be used
184 * with different optimized implementations of expensive field
187 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
188 const BIGNUM
*b
, BN_CTX
*);
189 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*);
190 int (*field_div
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
191 const BIGNUM
*b
, BN_CTX
*);
192 /* e.g. to Montgomery */
193 int (*field_encode
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
195 /* e.g. from Montgomery */
196 int (*field_decode
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
198 int (*field_set_to_one
) (const EC_GROUP
*, BIGNUM
*r
, BN_CTX
*);
202 * Types and functions to manipulate pre-computed values.
204 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP
;
205 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP
;
206 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP
;
207 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP
;
208 typedef struct ec_pre_comp_st EC_PRE_COMP
;
211 const EC_METHOD
*meth
;
212 EC_POINT
*generator
; /* optional */
213 BIGNUM
*order
, *cofactor
;
214 int curve_name
; /* optional NID for named curve */
215 int asn1_flag
; /* flag to control the asn1 encoding */
216 point_conversion_form_t asn1_form
;
217 unsigned char *seed
; /* optional seed for parameters (appears in
221 * The following members are handled by the method functions, even if
222 * they appear generic
225 * Field specification. For curves over GF(p), this is the modulus; for
226 * curves over GF(2^m), this is the irreducible polynomial defining the
231 * Field specification for curves over GF(2^m). The irreducible f(t) is
232 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
233 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
234 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
239 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
240 * or abused for all kinds of fields, not just GF(p).) For characteristic
241 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
242 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
243 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
246 /* enable optimized point arithmetics for special case */
248 /* method-specific (e.g., Montgomery structure) */
250 /* method-specific */
252 /* method-specific */
253 int (*field_mod_func
) (BIGNUM
*, const BIGNUM
*, const BIGNUM
*,
255 /* data for ECDSA inverse */
256 BN_MONT_CTX
*mont_data
;
258 /* precomputed values for speed. */
261 pct_nistp224
, pct_nistp256
, pct_nistp521
, pct_nistz256
,
262 pct_ec
} pre_comp_type
;
264 NISTP224_PRE_COMP
*nistp224
;
265 NISTP256_PRE_COMP
*nistp256
;
266 NISTP521_PRE_COMP
*nistp521
;
267 NISTZ256_PRE_COMP
*nistz256
;
272 #define SETPRECOMP(g, type, pre) \
273 g->pre_comp_type = pct_##type, g->pre_comp.type = pre
274 #define HAVEPRECOMP(g, type) \
275 g->pre_comp_type == pct_##type && g->pre_comp.type != NULL
278 const EC_KEY_METHOD
*meth
;
284 unsigned int enc_flag
;
285 point_conversion_form_t conv_form
;
288 CRYPTO_EX_DATA ex_data
;
292 const EC_METHOD
*meth
;
294 * All members except 'meth' are handled by the method functions, even if
295 * they appear generic
299 BIGNUM
*Z
; /* Jacobian projective coordinates: * (X, Y,
300 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
301 int Z_is_one
; /* enable optimized point arithmetics for
305 NISTP224_PRE_COMP
*EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP
*);
306 NISTP256_PRE_COMP
*EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP
*);
307 NISTP521_PRE_COMP
*EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP
*);
308 NISTZ256_PRE_COMP
*EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP
*);
309 NISTP256_PRE_COMP
*EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP
*);
310 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*);
312 void EC_pre_comp_free(EC_GROUP
*group
);
313 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP
*);
314 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP
*);
315 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP
*);
316 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP
*);
317 void EC_ec_pre_comp_free(EC_PRE_COMP
*);
320 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
321 * group->method->mul is 0)
323 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
324 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
326 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*);
327 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
);
329 /* method functions in ecp_smpl.c */
330 int ec_GFp_simple_group_init(EC_GROUP
*);
331 void ec_GFp_simple_group_finish(EC_GROUP
*);
332 void ec_GFp_simple_group_clear_finish(EC_GROUP
*);
333 int ec_GFp_simple_group_copy(EC_GROUP
*, const EC_GROUP
*);
334 int ec_GFp_simple_group_set_curve(EC_GROUP
*, const BIGNUM
*p
,
335 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*);
336 int ec_GFp_simple_group_get_curve(const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
,
337 BIGNUM
*b
, BN_CTX
*);
338 int ec_GFp_simple_group_get_degree(const EC_GROUP
*);
339 int ec_GFp_simple_group_check_discriminant(const EC_GROUP
*, BN_CTX
*);
340 int ec_GFp_simple_point_init(EC_POINT
*);
341 void ec_GFp_simple_point_finish(EC_POINT
*);
342 void ec_GFp_simple_point_clear_finish(EC_POINT
*);
343 int ec_GFp_simple_point_copy(EC_POINT
*, const EC_POINT
*);
344 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP
*, EC_POINT
*);
345 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP
*,
346 EC_POINT
*, const BIGNUM
*x
,
348 const BIGNUM
*z
, BN_CTX
*);
349 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP
*,
350 const EC_POINT
*, BIGNUM
*x
,
351 BIGNUM
*y
, BIGNUM
*z
,
353 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP
*, EC_POINT
*,
355 const BIGNUM
*y
, BN_CTX
*);
356 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP
*,
357 const EC_POINT
*, BIGNUM
*x
,
358 BIGNUM
*y
, BN_CTX
*);
359 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP
*, EC_POINT
*,
360 const BIGNUM
*x
, int y_bit
,
362 size_t ec_GFp_simple_point2oct(const EC_GROUP
*, const EC_POINT
*,
363 point_conversion_form_t form
,
364 unsigned char *buf
, size_t len
, BN_CTX
*);
365 int ec_GFp_simple_oct2point(const EC_GROUP
*, EC_POINT
*,
366 const unsigned char *buf
, size_t len
, BN_CTX
*);
367 int ec_GFp_simple_add(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
368 const EC_POINT
*b
, BN_CTX
*);
369 int ec_GFp_simple_dbl(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
371 int ec_GFp_simple_invert(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
372 int ec_GFp_simple_is_at_infinity(const EC_GROUP
*, const EC_POINT
*);
373 int ec_GFp_simple_is_on_curve(const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
374 int ec_GFp_simple_cmp(const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
376 int ec_GFp_simple_make_affine(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
377 int ec_GFp_simple_points_make_affine(const EC_GROUP
*, size_t num
,
378 EC_POINT
*[], BN_CTX
*);
379 int ec_GFp_simple_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
380 const BIGNUM
*b
, BN_CTX
*);
381 int ec_GFp_simple_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
384 /* method functions in ecp_mont.c */
385 int ec_GFp_mont_group_init(EC_GROUP
*);
386 int ec_GFp_mont_group_set_curve(EC_GROUP
*, const BIGNUM
*p
, const BIGNUM
*a
,
387 const BIGNUM
*b
, BN_CTX
*);
388 void ec_GFp_mont_group_finish(EC_GROUP
*);
389 void ec_GFp_mont_group_clear_finish(EC_GROUP
*);
390 int ec_GFp_mont_group_copy(EC_GROUP
*, const EC_GROUP
*);
391 int ec_GFp_mont_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
392 const BIGNUM
*b
, BN_CTX
*);
393 int ec_GFp_mont_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
395 int ec_GFp_mont_field_encode(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
397 int ec_GFp_mont_field_decode(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
399 int ec_GFp_mont_field_set_to_one(const EC_GROUP
*, BIGNUM
*r
, BN_CTX
*);
401 /* method functions in ecp_nist.c */
402 int ec_GFp_nist_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
);
403 int ec_GFp_nist_group_set_curve(EC_GROUP
*, const BIGNUM
*p
, const BIGNUM
*a
,
404 const BIGNUM
*b
, BN_CTX
*);
405 int ec_GFp_nist_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
406 const BIGNUM
*b
, BN_CTX
*);
407 int ec_GFp_nist_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
410 /* method functions in ec2_smpl.c */
411 int ec_GF2m_simple_group_init(EC_GROUP
*);
412 void ec_GF2m_simple_group_finish(EC_GROUP
*);
413 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*);
414 int ec_GF2m_simple_group_copy(EC_GROUP
*, const EC_GROUP
*);
415 int ec_GF2m_simple_group_set_curve(EC_GROUP
*, const BIGNUM
*p
,
416 const BIGNUM
*a
, const BIGNUM
*b
,
418 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
,
419 BIGNUM
*b
, BN_CTX
*);
420 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*);
421 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*, BN_CTX
*);
422 int ec_GF2m_simple_point_init(EC_POINT
*);
423 void ec_GF2m_simple_point_finish(EC_POINT
*);
424 void ec_GF2m_simple_point_clear_finish(EC_POINT
*);
425 int ec_GF2m_simple_point_copy(EC_POINT
*, const EC_POINT
*);
426 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*, EC_POINT
*);
427 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*, EC_POINT
*,
429 const BIGNUM
*y
, BN_CTX
*);
430 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*,
431 const EC_POINT
*, BIGNUM
*x
,
432 BIGNUM
*y
, BN_CTX
*);
433 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP
*, EC_POINT
*,
434 const BIGNUM
*x
, int y_bit
,
436 size_t ec_GF2m_simple_point2oct(const EC_GROUP
*, const EC_POINT
*,
437 point_conversion_form_t form
,
438 unsigned char *buf
, size_t len
, BN_CTX
*);
439 int ec_GF2m_simple_oct2point(const EC_GROUP
*, EC_POINT
*,
440 const unsigned char *buf
, size_t len
, BN_CTX
*);
441 int ec_GF2m_simple_add(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
442 const EC_POINT
*b
, BN_CTX
*);
443 int ec_GF2m_simple_dbl(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
445 int ec_GF2m_simple_invert(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
446 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*, const EC_POINT
*);
447 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
448 int ec_GF2m_simple_cmp(const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
450 int ec_GF2m_simple_make_affine(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
451 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*, size_t num
,
452 EC_POINT
*[], BN_CTX
*);
453 int ec_GF2m_simple_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
454 const BIGNUM
*b
, BN_CTX
*);
455 int ec_GF2m_simple_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
457 int ec_GF2m_simple_field_div(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
458 const BIGNUM
*b
, BN_CTX
*);
460 /* method functions in ec2_mult.c */
461 int ec_GF2m_simple_mul(const EC_GROUP
*group
, EC_POINT
*r
,
462 const BIGNUM
*scalar
, size_t num
,
463 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
465 int ec_GF2m_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
466 int ec_GF2m_have_precompute_mult(const EC_GROUP
*group
);
468 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
469 /* method functions in ecp_nistp224.c */
470 int ec_GFp_nistp224_group_init(EC_GROUP
*group
);
471 int ec_GFp_nistp224_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
472 const BIGNUM
*a
, const BIGNUM
*n
,
474 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP
*group
,
475 const EC_POINT
*point
,
476 BIGNUM
*x
, BIGNUM
*y
,
478 int ec_GFp_nistp224_mul(const EC_GROUP
*group
, EC_POINT
*r
,
479 const BIGNUM
*scalar
, size_t num
,
480 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
482 int ec_GFp_nistp224_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
483 const BIGNUM
*scalar
, size_t num
,
484 const EC_POINT
*points
[],
485 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
486 int ec_GFp_nistp224_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
487 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP
*group
);
489 /* method functions in ecp_nistp256.c */
490 int ec_GFp_nistp256_group_init(EC_GROUP
*group
);
491 int ec_GFp_nistp256_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
492 const BIGNUM
*a
, const BIGNUM
*n
,
494 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP
*group
,
495 const EC_POINT
*point
,
496 BIGNUM
*x
, BIGNUM
*y
,
498 int ec_GFp_nistp256_mul(const EC_GROUP
*group
, EC_POINT
*r
,
499 const BIGNUM
*scalar
, size_t num
,
500 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
502 int ec_GFp_nistp256_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
503 const BIGNUM
*scalar
, size_t num
,
504 const EC_POINT
*points
[],
505 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
506 int ec_GFp_nistp256_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
507 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP
*group
);
509 /* method functions in ecp_nistp521.c */
510 int ec_GFp_nistp521_group_init(EC_GROUP
*group
);
511 int ec_GFp_nistp521_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
512 const BIGNUM
*a
, const BIGNUM
*n
,
514 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP
*group
,
515 const EC_POINT
*point
,
516 BIGNUM
*x
, BIGNUM
*y
,
518 int ec_GFp_nistp521_mul(const EC_GROUP
*group
, EC_POINT
*r
,
519 const BIGNUM
*scalar
, size_t num
,
520 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
522 int ec_GFp_nistp521_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
523 const BIGNUM
*scalar
, size_t num
,
524 const EC_POINT
*points
[],
525 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
526 int ec_GFp_nistp521_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
527 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP
*group
);
529 /* utility functions in ecp_nistputil.c */
530 void ec_GFp_nistp_points_make_affine_internal(size_t num
, void *point_array
,
533 void (*felem_one
) (void *out
),
534 int (*felem_is_zero
) (const void
536 void (*felem_assign
) (void *out
,
539 void (*felem_square
) (void *out
,
542 void (*felem_mul
) (void *out
,
547 void (*felem_inv
) (void *out
,
550 void (*felem_contract
) (void
555 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign
,
556 unsigned char *digit
, unsigned char in
);
558 int ec_precompute_mont_data(EC_GROUP
*);
560 #ifdef ECP_NISTZ256_ASM
561 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
562 * P256. See http://eprint.iacr.org/2013/816.
563 * \return EC_METHOD object
565 const EC_METHOD
*EC_GFp_nistz256_method(void);
568 /* EC_METHOD definitions */
570 struct ec_key_method_st
{
573 int (*init
)(EC_KEY
*key
);
574 void (*finish
)(EC_KEY
*key
);
575 int (*copy
)(EC_KEY
*dest
, const EC_KEY
*src
);
576 int (*set_group
)(EC_KEY
*key
, const EC_GROUP
*grp
);
577 int (*set_private
)(EC_KEY
*key
, const BIGNUM
*priv_key
);
578 int (*set_public
)(EC_KEY
*key
, const EC_POINT
*pub_key
);
579 int (*keygen
)(EC_KEY
*key
);
580 int (*compute_key
)(void *out
, size_t outlen
, const EC_POINT
*pub_key
,
582 void *(*KDF
) (const void *in
, size_t inlen
,
583 void *out
, size_t *outlen
));
585 int (*sign
)(int type
, const unsigned char *dgst
, int dlen
, unsigned char
586 *sig
, unsigned int *siglen
, const BIGNUM
*kinv
,
587 const BIGNUM
*r
, EC_KEY
*eckey
);
588 int (*sign_setup
)(EC_KEY
*eckey
, BN_CTX
*ctx_in
, BIGNUM
**kinvp
,
590 ECDSA_SIG
*(*sign_sig
)(const unsigned char *dgst
, int dgst_len
,
591 const BIGNUM
*in_kinv
, const BIGNUM
*in_r
,
594 int (*verify
)(int type
, const unsigned char *dgst
, int dgst_len
,
595 const unsigned char *sigbuf
, int sig_len
, EC_KEY
*eckey
);
596 int (*verify_sig
)(const unsigned char *dgst
, int dgst_len
,
597 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);
598 } /* EC_KEY_METHOD */ ;
600 #define EC_KEY_METHOD_DYNAMIC 1
602 int ossl_ec_key_gen(EC_KEY
*eckey
);
603 int ossl_ecdh_compute_key(void *out
, size_t outlen
, const EC_POINT
*pub_key
,
605 void *(*KDF
) (const void *in
, size_t inlen
,
606 void *out
, size_t *outlen
));
608 struct ECDSA_SIG_st
{
613 int ossl_ecdsa_sign_setup(EC_KEY
*eckey
, BN_CTX
*ctx_in
, BIGNUM
**kinvp
,
615 int ossl_ecdsa_sign(int type
, const unsigned char *dgst
, int dlen
,
616 unsigned char *sig
, unsigned int *siglen
,
617 const BIGNUM
*kinv
, const BIGNUM
*r
, EC_KEY
*eckey
);
618 ECDSA_SIG
*ossl_ecdsa_sign_sig(const unsigned char *dgst
, int dgst_len
,
619 const BIGNUM
*in_kinv
, const BIGNUM
*in_r
,
621 int ossl_ecdsa_verify(int type
, const unsigned char *dgst
, int dgst_len
,
622 const unsigned char *sigbuf
, int sig_len
, EC_KEY
*eckey
);
623 int ossl_ecdsa_verify_sig(const unsigned char *dgst
, int dgst_len
,
624 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);