2 * Originally written by Bodo Moeller for the OpenSSL project.
4 /* ====================================================================
5 * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved.
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
33 * 6. Redistributions of any form whatsoever must retain the following
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
57 /* ====================================================================
58 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 * Portions of the attached software ("Contribution") are developed by
61 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 * The Contribution is licensed pursuant to the OpenSSL open source
64 * license provided above.
66 * The elliptic curve binary polynomial software is originally written by
67 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
73 #include <openssl/obj_mac.h>
74 #include <openssl/ec.h>
75 #include <openssl/bn.h>
77 #if defined(__SUNPRO_C)
78 # if __SUNPRO_C >= 0x520
79 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
83 /* Use default functions for poin2oct, oct2point and compressed coordinates */
84 #define EC_FLAGS_DEFAULT_OCT 0x1
86 /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */
87 #define EC_FLAGS_CUSTOM_CURVE 0x2
90 * Structure details are not part of the exported interface, so all this may
91 * change in future versions.
95 /* Various method flags */
97 /* used by EC_METHOD_get_field_type: */
98 int field_type; /* a NID */
100 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
103 int (*group_init) (EC_GROUP *);
104 void (*group_finish) (EC_GROUP *);
105 void (*group_clear_finish) (EC_GROUP *);
106 int (*group_copy) (EC_GROUP *, const EC_GROUP *);
107 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
108 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
109 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
110 const BIGNUM *b, BN_CTX *);
111 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
113 /* used by EC_GROUP_get_degree: */
114 int (*group_get_degree) (const EC_GROUP *);
115 int (*group_order_bits) (const EC_GROUP *);
116 /* used by EC_GROUP_check: */
117 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
119 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
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 *,
136 EC_POINT *, const BIGNUM *x,
138 const BIGNUM *z, BN_CTX *);
139 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
140 const EC_POINT *, BIGNUM *x,
141 BIGNUM *y, BIGNUM *z,
143 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
144 const BIGNUM *x, const BIGNUM *y,
146 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
147 BIGNUM *x, BIGNUM *y, BN_CTX *);
148 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
149 const BIGNUM *x, int y_bit,
151 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
152 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
153 point_conversion_form_t form, unsigned char *buf,
154 size_t len, BN_CTX *);
155 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
156 size_t len, BN_CTX *);
157 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
158 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
159 const EC_POINT *b, BN_CTX *);
160 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
161 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
163 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
165 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
166 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
167 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
169 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
170 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
171 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
174 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
175 * EC_POINT_have_precompute_mult (default implementations are used if the
176 * 'mul' pointer is 0):
178 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
179 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
181 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
182 int (*have_precompute_mult) (const EC_GROUP *group);
183 /* internal functions */
185 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
186 * 'dbl' so that the same implementations of point operations can be used
187 * with different optimized implementations of expensive field
190 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
191 const BIGNUM *b, BN_CTX *);
192 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
193 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
194 const BIGNUM *b, BN_CTX *);
195 /* e.g. to Montgomery */
196 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
198 /* e.g. from Montgomery */
199 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
201 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
202 /* private key operations */
203 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);
204 int (*oct2priv)(EC_KEY *eckey, unsigned char *buf, size_t len);
205 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);
206 int (*keygen)(EC_KEY *eckey);
207 int (*keycheck)(const EC_KEY *eckey);
208 int (*keygenpub)(EC_KEY *eckey);
209 int (*keycopy)(EC_KEY *dst, const EC_KEY *src);
210 void (*keyfinish)(EC_KEY *eckey);
211 /* custom ECDH operation */
212 int (*ecdh_compute_key)(void *out, size_t outlen, const EC_POINT *pub_key,
214 void *(*KDF) (const void *in, size_t inlen,
215 void *out, size_t *outlen));
219 * Types and functions to manipulate pre-computed values.
221 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
222 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
223 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
224 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
225 typedef struct ec_pre_comp_st EC_PRE_COMP;
228 const EC_METHOD *meth;
229 EC_POINT *generator; /* optional */
230 BIGNUM *order, *cofactor;
231 int curve_name; /* optional NID for named curve */
232 int asn1_flag; /* flag to control the asn1 encoding */
233 point_conversion_form_t asn1_form;
234 unsigned char *seed; /* optional seed for parameters (appears in
238 * The following members are handled by the method functions, even if
239 * they appear generic
242 * Field specification. For curves over GF(p), this is the modulus; for
243 * curves over GF(2^m), this is the irreducible polynomial defining the
248 * Field specification for curves over GF(2^m). The irreducible f(t) is
249 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
250 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
251 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
256 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
257 * or abused for all kinds of fields, not just GF(p).) For characteristic
258 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
259 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
260 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
263 /* enable optimized point arithmetics for special case */
265 /* method-specific (e.g., Montgomery structure) */
267 /* method-specific */
269 /* method-specific */
270 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
272 /* data for ECDSA inverse */
273 BN_MONT_CTX *mont_data;
275 /* precomputed values for speed. */
278 pct_nistp224, pct_nistp256, pct_nistp521, pct_nistz256,
279 pct_ec } pre_comp_type;
281 NISTP224_PRE_COMP *nistp224;
282 NISTP256_PRE_COMP *nistp256;
283 NISTP521_PRE_COMP *nistp521;
284 NISTZ256_PRE_COMP *nistz256;
289 #define SETPRECOMP(g, type, pre) \
290 g->pre_comp_type = pct_##type, g->pre_comp.type = pre
291 #define HAVEPRECOMP(g, type) \
292 g->pre_comp_type == pct_##type && g->pre_comp.type != NULL
295 const EC_KEY_METHOD *meth;
302 * Arbitrary extra data.
303 * For example in X25519 this contains the raw private key in a 32 byte
307 unsigned int enc_flag;
308 point_conversion_form_t conv_form;
311 CRYPTO_EX_DATA ex_data;
315 const EC_METHOD *meth;
317 * All members except 'meth' are handled by the method functions, even if
318 * they appear generic
322 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
323 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
324 int Z_is_one; /* enable optimized point arithmetics for
327 * Arbitrary extra data.
328 * For example in X25519 this contains the public key in a 32 byte buffer.
333 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
334 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
335 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
336 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
337 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
338 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
340 void EC_pre_comp_free(EC_GROUP *group);
341 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
342 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
343 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
344 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
345 void EC_ec_pre_comp_free(EC_PRE_COMP *);
348 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
349 * group->method->mul is 0)
351 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
352 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
354 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
355 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
357 /* method functions in ecp_smpl.c */
358 int ec_GFp_simple_group_init(EC_GROUP *);
359 void ec_GFp_simple_group_finish(EC_GROUP *);
360 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
361 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
362 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
363 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
364 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
365 BIGNUM *b, BN_CTX *);
366 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
367 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
368 int ec_GFp_simple_point_init(EC_POINT *);
369 void ec_GFp_simple_point_finish(EC_POINT *);
370 void ec_GFp_simple_point_clear_finish(EC_POINT *);
371 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
372 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
373 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
374 EC_POINT *, const BIGNUM *x,
376 const BIGNUM *z, BN_CTX *);
377 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
378 const EC_POINT *, BIGNUM *x,
379 BIGNUM *y, BIGNUM *z,
381 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
383 const BIGNUM *y, BN_CTX *);
384 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
385 const EC_POINT *, BIGNUM *x,
386 BIGNUM *y, BN_CTX *);
387 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
388 const BIGNUM *x, int y_bit,
390 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
391 point_conversion_form_t form,
392 unsigned char *buf, size_t len, BN_CTX *);
393 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
394 const unsigned char *buf, size_t len, BN_CTX *);
395 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
396 const EC_POINT *b, BN_CTX *);
397 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
399 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
400 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
401 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
402 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
404 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
405 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
406 EC_POINT *[], BN_CTX *);
407 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
408 const BIGNUM *b, BN_CTX *);
409 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
412 /* method functions in ecp_mont.c */
413 int ec_GFp_mont_group_init(EC_GROUP *);
414 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
415 const BIGNUM *b, BN_CTX *);
416 void ec_GFp_mont_group_finish(EC_GROUP *);
417 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
418 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
419 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
420 const BIGNUM *b, BN_CTX *);
421 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
423 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
425 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
427 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
429 /* method functions in ecp_nist.c */
430 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
431 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
432 const BIGNUM *b, BN_CTX *);
433 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
434 const BIGNUM *b, BN_CTX *);
435 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
438 /* method functions in ec2_smpl.c */
439 int ec_GF2m_simple_group_init(EC_GROUP *);
440 void ec_GF2m_simple_group_finish(EC_GROUP *);
441 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
442 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
443 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
444 const BIGNUM *a, const BIGNUM *b,
446 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
447 BIGNUM *b, BN_CTX *);
448 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
449 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
450 int ec_GF2m_simple_point_init(EC_POINT *);
451 void ec_GF2m_simple_point_finish(EC_POINT *);
452 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
453 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
454 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
455 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
457 const BIGNUM *y, BN_CTX *);
458 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
459 const EC_POINT *, BIGNUM *x,
460 BIGNUM *y, BN_CTX *);
461 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
462 const BIGNUM *x, int y_bit,
464 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
465 point_conversion_form_t form,
466 unsigned char *buf, size_t len, BN_CTX *);
467 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
468 const unsigned char *buf, size_t len, BN_CTX *);
469 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
470 const EC_POINT *b, BN_CTX *);
471 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
473 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
474 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
475 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
476 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
478 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
479 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
480 EC_POINT *[], BN_CTX *);
481 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
482 const BIGNUM *b, BN_CTX *);
483 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
485 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
486 const BIGNUM *b, BN_CTX *);
488 /* method functions in ec2_mult.c */
489 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
490 const BIGNUM *scalar, size_t num,
491 const EC_POINT *points[], const BIGNUM *scalars[],
493 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
494 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
496 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
497 /* method functions in ecp_nistp224.c */
498 int ec_GFp_nistp224_group_init(EC_GROUP *group);
499 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
500 const BIGNUM *a, const BIGNUM *n,
502 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
503 const EC_POINT *point,
504 BIGNUM *x, BIGNUM *y,
506 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
507 const BIGNUM *scalar, size_t num,
508 const EC_POINT *points[], const BIGNUM *scalars[],
510 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
511 const BIGNUM *scalar, size_t num,
512 const EC_POINT *points[],
513 const BIGNUM *scalars[], BN_CTX *ctx);
514 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
515 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
517 /* method functions in ecp_nistp256.c */
518 int ec_GFp_nistp256_group_init(EC_GROUP *group);
519 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
520 const BIGNUM *a, const BIGNUM *n,
522 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
523 const EC_POINT *point,
524 BIGNUM *x, BIGNUM *y,
526 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
527 const BIGNUM *scalar, size_t num,
528 const EC_POINT *points[], const BIGNUM *scalars[],
530 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
531 const BIGNUM *scalar, size_t num,
532 const EC_POINT *points[],
533 const BIGNUM *scalars[], BN_CTX *ctx);
534 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
535 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
537 /* method functions in ecp_nistp521.c */
538 int ec_GFp_nistp521_group_init(EC_GROUP *group);
539 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
540 const BIGNUM *a, const BIGNUM *n,
542 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
543 const EC_POINT *point,
544 BIGNUM *x, BIGNUM *y,
546 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
547 const BIGNUM *scalar, size_t num,
548 const EC_POINT *points[], const BIGNUM *scalars[],
550 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
551 const BIGNUM *scalar, size_t num,
552 const EC_POINT *points[],
553 const BIGNUM *scalars[], BN_CTX *ctx);
554 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
555 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
557 /* utility functions in ecp_nistputil.c */
558 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
561 void (*felem_one) (void *out),
562 int (*felem_is_zero) (const void
564 void (*felem_assign) (void *out,
567 void (*felem_square) (void *out,
570 void (*felem_mul) (void *out,
575 void (*felem_inv) (void *out,
578 void (*felem_contract) (void
583 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
584 unsigned char *digit, unsigned char in);
586 int ec_precompute_mont_data(EC_GROUP *);
588 #ifdef ECP_NISTZ256_ASM
589 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
590 * P256. See http://eprint.iacr.org/2013/816.
591 * \return EC_METHOD object
593 const EC_METHOD *EC_GFp_nistz256_method(void);
596 /* EC_METHOD definitions */
598 struct ec_key_method_st {
601 int (*init)(EC_KEY *key);
602 void (*finish)(EC_KEY *key);
603 int (*copy)(EC_KEY *dest, const EC_KEY *src);
604 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
605 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
606 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
607 int (*keygen)(EC_KEY *key);
608 int (*compute_key)(void *out, size_t outlen, const EC_POINT *pub_key,
610 void *(*KDF) (const void *in, size_t inlen,
611 void *out, size_t *outlen));
613 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
614 *sig, unsigned int *siglen, const BIGNUM *kinv,
615 const BIGNUM *r, EC_KEY *eckey);
616 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
618 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
619 const BIGNUM *in_kinv, const BIGNUM *in_r,
622 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
623 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
624 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
625 const ECDSA_SIG *sig, EC_KEY *eckey);
626 } /* EC_KEY_METHOD */ ;
628 #define EC_KEY_METHOD_DYNAMIC 1
630 int ossl_ec_key_gen(EC_KEY *eckey);
631 int ossl_ecdh_compute_key(void *out, size_t outlen, const EC_POINT *pub_key,
633 void *(*KDF) (const void *in, size_t inlen,
634 void *out, size_t *outlen));
636 struct ECDSA_SIG_st {
641 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
643 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
644 unsigned char *sig, unsigned int *siglen,
645 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
646 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
647 const BIGNUM *in_kinv, const BIGNUM *in_r,
649 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
650 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
651 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
652 const ECDSA_SIG *sig, EC_KEY *eckey);