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>
79 #if defined(__SUNPRO_C)
80 # if __SUNPRO_C >= 0x520
81 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
85 /* Use default functions for poin2oct, oct2point and compressed coordinates */
86 #define EC_FLAGS_DEFAULT_OCT 0x1
88 /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */
89 #define EC_FLAGS_CUSTOM_CURVE 0x2
91 /* Curve does not support signing operations */
92 #define EC_FLAGS_NO_SIGN 0x4
95 * Structure details are not part of the exported interface, so all this may
96 * change in future versions.
100 /* Various method flags */
102 /* used by EC_METHOD_get_field_type: */
103 int field_type; /* a NID */
105 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
108 int (*group_init) (EC_GROUP *);
109 void (*group_finish) (EC_GROUP *);
110 void (*group_clear_finish) (EC_GROUP *);
111 int (*group_copy) (EC_GROUP *, const EC_GROUP *);
112 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
113 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
114 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
115 const BIGNUM *b, BN_CTX *);
116 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
118 /* used by EC_GROUP_get_degree: */
119 int (*group_get_degree) (const EC_GROUP *);
120 int (*group_order_bits) (const EC_GROUP *);
121 /* used by EC_GROUP_check: */
122 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
124 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
127 int (*point_init) (EC_POINT *);
128 void (*point_finish) (EC_POINT *);
129 void (*point_clear_finish) (EC_POINT *);
130 int (*point_copy) (EC_POINT *, const EC_POINT *);
132 * used by EC_POINT_set_to_infinity,
133 * EC_POINT_set_Jprojective_coordinates_GFp,
134 * EC_POINT_get_Jprojective_coordinates_GFp,
135 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
136 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
137 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
139 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
140 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
141 EC_POINT *, const BIGNUM *x,
143 const BIGNUM *z, BN_CTX *);
144 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
145 const EC_POINT *, BIGNUM *x,
146 BIGNUM *y, BIGNUM *z,
148 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
149 const BIGNUM *x, const BIGNUM *y,
151 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
152 BIGNUM *x, BIGNUM *y, BN_CTX *);
153 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
154 const BIGNUM *x, int y_bit,
156 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
157 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
158 point_conversion_form_t form, unsigned char *buf,
159 size_t len, BN_CTX *);
160 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
161 size_t len, BN_CTX *);
162 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
163 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
164 const EC_POINT *b, BN_CTX *);
165 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
166 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
168 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
170 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
171 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
172 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
174 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
175 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
176 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
179 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
180 * EC_POINT_have_precompute_mult (default implementations are used if the
181 * 'mul' pointer is 0):
183 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
184 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
186 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
187 int (*have_precompute_mult) (const EC_GROUP *group);
188 /* internal functions */
190 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
191 * 'dbl' so that the same implementations of point operations can be used
192 * with different optimized implementations of expensive field
195 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
196 const BIGNUM *b, BN_CTX *);
197 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
198 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
199 const BIGNUM *b, BN_CTX *);
200 /* e.g. to Montgomery */
201 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
203 /* e.g. from Montgomery */
204 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
206 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
207 /* private key operations */
208 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);
209 int (*oct2priv)(EC_KEY *eckey, unsigned char *buf, size_t len);
210 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);
211 int (*keygen)(EC_KEY *eckey);
212 int (*keycheck)(const EC_KEY *eckey);
213 int (*keygenpub)(EC_KEY *eckey);
214 int (*keycopy)(EC_KEY *dst, const EC_KEY *src);
215 void (*keyfinish)(EC_KEY *eckey);
216 /* custom ECDH operation */
217 int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,
218 const EC_POINT *pub_key, const EC_KEY *ecdh);
222 * Types and functions to manipulate pre-computed values.
224 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
225 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
226 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
227 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
228 typedef struct ec_pre_comp_st EC_PRE_COMP;
231 const EC_METHOD *meth;
232 EC_POINT *generator; /* optional */
233 BIGNUM *order, *cofactor;
234 int curve_name; /* optional NID for named curve */
235 int asn1_flag; /* flag to control the asn1 encoding */
236 point_conversion_form_t asn1_form;
237 unsigned char *seed; /* optional seed for parameters (appears in
241 * The following members are handled by the method functions, even if
242 * they appear generic
245 * Field specification. For curves over GF(p), this is the modulus; for
246 * curves over GF(2^m), this is the irreducible polynomial defining the
251 * Field specification for curves over GF(2^m). The irreducible f(t) is
252 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
253 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
254 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
259 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
260 * or abused for all kinds of fields, not just GF(p).) For characteristic
261 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
262 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
263 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
266 /* enable optimized point arithmetics for special case */
268 /* method-specific (e.g., Montgomery structure) */
270 /* method-specific */
272 /* method-specific */
273 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
275 /* data for ECDSA inverse */
276 BN_MONT_CTX *mont_data;
278 /* precomputed values for speed. */
281 pct_nistp224, pct_nistp256, pct_nistp521, pct_nistz256,
282 pct_ec } pre_comp_type;
284 NISTP224_PRE_COMP *nistp224;
285 NISTP256_PRE_COMP *nistp256;
286 NISTP521_PRE_COMP *nistp521;
287 NISTZ256_PRE_COMP *nistz256;
292 #define SETPRECOMP(g, type, pre) \
293 g->pre_comp_type = pct_##type, g->pre_comp.type = pre
294 #define HAVEPRECOMP(g, type) \
295 g->pre_comp_type == pct_##type && g->pre_comp.type != NULL
298 const EC_KEY_METHOD *meth;
305 * Arbitrary extra data.
306 * For example in X25519 this contains the raw private key in a 32 byte
310 unsigned int enc_flag;
311 point_conversion_form_t conv_form;
314 CRYPTO_EX_DATA ex_data;
319 const EC_METHOD *meth;
321 * All members except 'meth' are handled by the method functions, even if
322 * they appear generic
326 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
327 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
328 int Z_is_one; /* enable optimized point arithmetics for
331 * Arbitrary extra data.
332 * For example in X25519 this contains the public key in a 32 byte buffer.
337 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
338 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
339 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
340 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
341 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
342 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
344 void EC_pre_comp_free(EC_GROUP *group);
345 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
346 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
347 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
348 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
349 void EC_ec_pre_comp_free(EC_PRE_COMP *);
352 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
353 * group->method->mul is 0)
355 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
356 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
358 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
359 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
361 /* method functions in ecp_smpl.c */
362 int ec_GFp_simple_group_init(EC_GROUP *);
363 void ec_GFp_simple_group_finish(EC_GROUP *);
364 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
365 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
366 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
367 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
368 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
369 BIGNUM *b, BN_CTX *);
370 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
371 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
372 int ec_GFp_simple_point_init(EC_POINT *);
373 void ec_GFp_simple_point_finish(EC_POINT *);
374 void ec_GFp_simple_point_clear_finish(EC_POINT *);
375 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
376 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
377 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
378 EC_POINT *, const BIGNUM *x,
380 const BIGNUM *z, BN_CTX *);
381 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
382 const EC_POINT *, BIGNUM *x,
383 BIGNUM *y, BIGNUM *z,
385 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
387 const BIGNUM *y, BN_CTX *);
388 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
389 const EC_POINT *, BIGNUM *x,
390 BIGNUM *y, BN_CTX *);
391 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
392 const BIGNUM *x, int y_bit,
394 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
395 point_conversion_form_t form,
396 unsigned char *buf, size_t len, BN_CTX *);
397 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
398 const unsigned char *buf, size_t len, BN_CTX *);
399 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
400 const EC_POINT *b, BN_CTX *);
401 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
403 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
404 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
405 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
406 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
408 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
409 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
410 EC_POINT *[], BN_CTX *);
411 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
412 const BIGNUM *b, BN_CTX *);
413 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
416 /* method functions in ecp_mont.c */
417 int ec_GFp_mont_group_init(EC_GROUP *);
418 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
419 const BIGNUM *b, BN_CTX *);
420 void ec_GFp_mont_group_finish(EC_GROUP *);
421 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
422 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
423 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
424 const BIGNUM *b, BN_CTX *);
425 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
427 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
429 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
431 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
433 /* method functions in ecp_nist.c */
434 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
435 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
436 const BIGNUM *b, BN_CTX *);
437 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
438 const BIGNUM *b, BN_CTX *);
439 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
442 /* method functions in ec2_smpl.c */
443 int ec_GF2m_simple_group_init(EC_GROUP *);
444 void ec_GF2m_simple_group_finish(EC_GROUP *);
445 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
446 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
447 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
448 const BIGNUM *a, const BIGNUM *b,
450 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
451 BIGNUM *b, BN_CTX *);
452 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
453 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
454 int ec_GF2m_simple_point_init(EC_POINT *);
455 void ec_GF2m_simple_point_finish(EC_POINT *);
456 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
457 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
458 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
459 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
461 const BIGNUM *y, BN_CTX *);
462 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
463 const EC_POINT *, BIGNUM *x,
464 BIGNUM *y, BN_CTX *);
465 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
466 const BIGNUM *x, int y_bit,
468 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
469 point_conversion_form_t form,
470 unsigned char *buf, size_t len, BN_CTX *);
471 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
472 const unsigned char *buf, size_t len, BN_CTX *);
473 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
474 const EC_POINT *b, BN_CTX *);
475 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
477 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
478 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
479 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
480 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
482 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
483 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
484 EC_POINT *[], BN_CTX *);
485 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
486 const BIGNUM *b, BN_CTX *);
487 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
489 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
490 const BIGNUM *b, BN_CTX *);
492 /* method functions in ec2_mult.c */
493 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
494 const BIGNUM *scalar, size_t num,
495 const EC_POINT *points[], const BIGNUM *scalars[],
497 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
498 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
500 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
501 /* method functions in ecp_nistp224.c */
502 int ec_GFp_nistp224_group_init(EC_GROUP *group);
503 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
504 const BIGNUM *a, const BIGNUM *n,
506 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
507 const EC_POINT *point,
508 BIGNUM *x, BIGNUM *y,
510 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
511 const BIGNUM *scalar, size_t num,
512 const EC_POINT *points[], const BIGNUM *scalars[],
514 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
515 const BIGNUM *scalar, size_t num,
516 const EC_POINT *points[],
517 const BIGNUM *scalars[], BN_CTX *ctx);
518 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
519 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
521 /* method functions in ecp_nistp256.c */
522 int ec_GFp_nistp256_group_init(EC_GROUP *group);
523 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
524 const BIGNUM *a, const BIGNUM *n,
526 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
527 const EC_POINT *point,
528 BIGNUM *x, BIGNUM *y,
530 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
531 const BIGNUM *scalar, size_t num,
532 const EC_POINT *points[], const BIGNUM *scalars[],
534 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
535 const BIGNUM *scalar, size_t num,
536 const EC_POINT *points[],
537 const BIGNUM *scalars[], BN_CTX *ctx);
538 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
539 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
541 /* method functions in ecp_nistp521.c */
542 int ec_GFp_nistp521_group_init(EC_GROUP *group);
543 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
544 const BIGNUM *a, const BIGNUM *n,
546 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
547 const EC_POINT *point,
548 BIGNUM *x, BIGNUM *y,
550 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
551 const BIGNUM *scalar, size_t num,
552 const EC_POINT *points[], const BIGNUM *scalars[],
554 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
555 const BIGNUM *scalar, size_t num,
556 const EC_POINT *points[],
557 const BIGNUM *scalars[], BN_CTX *ctx);
558 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
559 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
561 /* utility functions in ecp_nistputil.c */
562 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
565 void (*felem_one) (void *out),
566 int (*felem_is_zero) (const void
568 void (*felem_assign) (void *out,
571 void (*felem_square) (void *out,
574 void (*felem_mul) (void *out,
579 void (*felem_inv) (void *out,
582 void (*felem_contract) (void
587 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
588 unsigned char *digit, unsigned char in);
590 int ec_precompute_mont_data(EC_GROUP *);
591 int ec_group_simple_order_bits(const EC_GROUP *group);
593 #ifdef ECP_NISTZ256_ASM
594 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
595 * P256. See http://eprint.iacr.org/2013/816.
596 * \return EC_METHOD object
598 const EC_METHOD *EC_GFp_nistz256_method(void);
601 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
602 unsigned char *buf, size_t len);
603 int ec_key_simple_oct2priv(EC_KEY *eckey, unsigned char *buf, size_t len);
604 int ec_key_simple_generate_key(EC_KEY *eckey);
605 int ec_key_simple_generate_public_key(EC_KEY *eckey);
606 int ec_key_simple_check_key(const EC_KEY *eckey);
608 /* EC_METHOD definitions */
610 struct ec_key_method_st {
613 int (*init)(EC_KEY *key);
614 void (*finish)(EC_KEY *key);
615 int (*copy)(EC_KEY *dest, const EC_KEY *src);
616 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
617 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
618 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
619 int (*keygen)(EC_KEY *key);
620 int (*compute_key)(unsigned char **pout, size_t *poutlen,
621 const EC_POINT *pub_key, const EC_KEY *ecdh);
622 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
623 *sig, unsigned int *siglen, const BIGNUM *kinv,
624 const BIGNUM *r, EC_KEY *eckey);
625 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
627 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
628 const BIGNUM *in_kinv, const BIGNUM *in_r,
631 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
632 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
633 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
634 const ECDSA_SIG *sig, EC_KEY *eckey);
635 } /* EC_KEY_METHOD */ ;
637 #define EC_KEY_METHOD_DYNAMIC 1
639 int ossl_ec_key_gen(EC_KEY *eckey);
640 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
641 const EC_POINT *pub_key, const EC_KEY *ecdh);
642 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
643 const EC_POINT *pub_key, const EC_KEY *ecdh);
645 struct ECDSA_SIG_st {
650 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
652 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
653 unsigned char *sig, unsigned int *siglen,
654 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
655 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
656 const BIGNUM *in_kinv, const BIGNUM *in_r,
658 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
659 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
660 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
661 const ECDSA_SIG *sig, EC_KEY *eckey);
663 const EC_METHOD *ec_x25519_meth(void);
665 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
666 const uint8_t peer_public_value[32]);
667 void X25519_public_from_private(uint8_t out_public_value[32],
668 const uint8_t private_key[32]);