2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
13 #include <openssl/obj_mac.h>
14 #include <openssl/ec.h>
15 #include <openssl/bn.h>
16 #include "internal/refcount.h"
17 #include "crypto/ec.h"
19 #if defined(__SUNPRO_C)
20 # if __SUNPRO_C >= 0x520
21 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
25 /* Use default functions for poin2oct, oct2point and compressed coordinates */
26 #define EC_FLAGS_DEFAULT_OCT 0x1
28 /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */
29 #define EC_FLAGS_CUSTOM_CURVE 0x2
31 /* Curve does not support signing operations */
32 #define EC_FLAGS_NO_SIGN 0x4
35 * Structure details are not part of the exported interface, so all this may
36 * change in future versions.
40 /* Various method flags */
42 /* used by EC_METHOD_get_field_type: */
43 int field_type
; /* a NID */
45 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
48 int (*group_init
) (EC_GROUP
*);
49 void (*group_finish
) (EC_GROUP
*);
50 void (*group_clear_finish
) (EC_GROUP
*);
51 int (*group_copy
) (EC_GROUP
*, const EC_GROUP
*);
52 /* used by EC_GROUP_set_curve, EC_GROUP_get_curve: */
53 int (*group_set_curve
) (EC_GROUP
*, const BIGNUM
*p
, const BIGNUM
*a
,
54 const BIGNUM
*b
, BN_CTX
*);
55 int (*group_get_curve
) (const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
, BIGNUM
*b
,
57 /* used by EC_GROUP_get_degree: */
58 int (*group_get_degree
) (const EC_GROUP
*);
59 int (*group_order_bits
) (const EC_GROUP
*);
60 /* used by EC_GROUP_check: */
61 int (*group_check_discriminant
) (const EC_GROUP
*, BN_CTX
*);
63 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
66 int (*point_init
) (EC_POINT
*);
67 void (*point_finish
) (EC_POINT
*);
68 void (*point_clear_finish
) (EC_POINT
*);
69 int (*point_copy
) (EC_POINT
*, const EC_POINT
*);
71 * used by EC_POINT_set_to_infinity,
72 * EC_POINT_set_Jprojective_coordinates_GFp,
73 * EC_POINT_get_Jprojective_coordinates_GFp,
74 * EC_POINT_set_affine_coordinates,
75 * EC_POINT_get_affine_coordinates,
76 * EC_POINT_set_compressed_coordinates:
78 int (*point_set_to_infinity
) (const EC_GROUP
*, EC_POINT
*);
79 int (*point_set_Jprojective_coordinates_GFp
) (const EC_GROUP
*,
80 EC_POINT
*, const BIGNUM
*x
,
82 const BIGNUM
*z
, BN_CTX
*);
83 int (*point_get_Jprojective_coordinates_GFp
) (const EC_GROUP
*,
84 const EC_POINT
*, BIGNUM
*x
,
87 int (*point_set_affine_coordinates
) (const EC_GROUP
*, EC_POINT
*,
88 const BIGNUM
*x
, const BIGNUM
*y
,
90 int (*point_get_affine_coordinates
) (const EC_GROUP
*, const EC_POINT
*,
91 BIGNUM
*x
, BIGNUM
*y
, BN_CTX
*);
92 int (*point_set_compressed_coordinates
) (const EC_GROUP
*, EC_POINT
*,
93 const BIGNUM
*x
, int y_bit
,
95 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
96 size_t (*point2oct
) (const EC_GROUP
*, const EC_POINT
*,
97 point_conversion_form_t form
, unsigned char *buf
,
98 size_t len
, BN_CTX
*);
99 int (*oct2point
) (const EC_GROUP
*, EC_POINT
*, const unsigned char *buf
,
100 size_t len
, BN_CTX
*);
101 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
102 int (*add
) (const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
103 const EC_POINT
*b
, BN_CTX
*);
104 int (*dbl
) (const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
, BN_CTX
*);
105 int (*invert
) (const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
107 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
109 int (*is_at_infinity
) (const EC_GROUP
*, const EC_POINT
*);
110 int (*is_on_curve
) (const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
111 int (*point_cmp
) (const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
113 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
114 int (*make_affine
) (const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
115 int (*points_make_affine
) (const EC_GROUP
*, size_t num
, EC_POINT
*[],
118 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
119 * EC_POINT_have_precompute_mult (default implementations are used if the
120 * 'mul' pointer is 0):
123 * mul() calculates the value
125 * r := generator * scalar
126 * + points[0] * scalars[0]
128 * + points[num-1] * scalars[num-1].
130 * For a fixed point multiplication (scalar != NULL, num == 0)
131 * or a variable point multiplication (scalar == NULL, num == 1),
132 * mul() must use a constant time algorithm: in both cases callers
133 * should provide an input scalar (either scalar or scalars[0])
134 * in the range [0, ec_group_order); for robustness, implementers
135 * should handle the case when the scalar has not been reduced, but
136 * may treat it as an unusual input, without any constant-timeness
139 int (*mul
) (const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
140 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
142 int (*precompute_mult
) (EC_GROUP
*group
, BN_CTX
*);
143 int (*have_precompute_mult
) (const EC_GROUP
*group
);
144 /* internal functions */
146 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
147 * 'dbl' so that the same implementations of point operations can be used
148 * with different optimized implementations of expensive field
151 int (*field_mul
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
152 const BIGNUM
*b
, BN_CTX
*);
153 int (*field_sqr
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*);
154 int (*field_div
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
155 const BIGNUM
*b
, BN_CTX
*);
157 * 'field_inv' computes the multiplicative inverse of a in the field,
158 * storing the result in r.
160 * If 'a' is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error.
162 int (*field_inv
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*);
163 /* e.g. to Montgomery */
164 int (*field_encode
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
166 /* e.g. from Montgomery */
167 int (*field_decode
) (const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
169 int (*field_set_to_one
) (const EC_GROUP
*, BIGNUM
*r
, BN_CTX
*);
170 /* private key operations */
171 size_t (*priv2oct
)(const EC_KEY
*eckey
, unsigned char *buf
, size_t len
);
172 int (*oct2priv
)(EC_KEY
*eckey
, const unsigned char *buf
, size_t len
);
173 int (*set_private
)(EC_KEY
*eckey
, const BIGNUM
*priv_key
);
174 int (*keygen
)(EC_KEY
*eckey
);
175 int (*keycheck
)(const EC_KEY
*eckey
);
176 int (*keygenpub
)(EC_KEY
*eckey
);
177 int (*keycopy
)(EC_KEY
*dst
, const EC_KEY
*src
);
178 void (*keyfinish
)(EC_KEY
*eckey
);
179 /* custom ECDH operation */
180 int (*ecdh_compute_key
)(unsigned char **pout
, size_t *poutlen
,
181 const EC_POINT
*pub_key
, const EC_KEY
*ecdh
);
183 int (*ecdsa_sign_setup
)(EC_KEY
*eckey
, BN_CTX
*ctx
, BIGNUM
**kinvp
,
185 ECDSA_SIG
*(*ecdsa_sign_sig
)(const unsigned char *dgst
, int dgstlen
,
186 const BIGNUM
*kinv
, const BIGNUM
*r
,
188 int (*ecdsa_verify_sig
)(const unsigned char *dgst
, int dgstlen
,
189 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);
190 /* Inverse modulo order */
191 int (*field_inverse_mod_ord
)(const EC_GROUP
*, BIGNUM
*r
,
192 const BIGNUM
*x
, BN_CTX
*);
193 int (*blind_coordinates
)(const EC_GROUP
*group
, EC_POINT
*p
, BN_CTX
*ctx
);
194 int (*ladder_pre
)(const EC_GROUP
*group
,
195 EC_POINT
*r
, EC_POINT
*s
,
196 EC_POINT
*p
, BN_CTX
*ctx
);
197 int (*ladder_step
)(const EC_GROUP
*group
,
198 EC_POINT
*r
, EC_POINT
*s
,
199 EC_POINT
*p
, BN_CTX
*ctx
);
200 int (*ladder_post
)(const EC_GROUP
*group
,
201 EC_POINT
*r
, EC_POINT
*s
,
202 EC_POINT
*p
, BN_CTX
*ctx
);
206 * Types and functions to manipulate pre-computed values.
208 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP
;
209 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP
;
210 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP
;
211 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP
;
212 typedef struct ec_pre_comp_st EC_PRE_COMP
;
215 const EC_METHOD
*meth
;
216 EC_POINT
*generator
; /* optional */
217 BIGNUM
*order
, *cofactor
;
218 int curve_name
; /* optional NID for named curve */
219 int asn1_flag
; /* flag to control the asn1 encoding */
220 point_conversion_form_t asn1_form
;
221 unsigned char *seed
; /* optional seed for parameters (appears in
225 * The following members are handled by the method functions, even if
226 * they appear generic
229 * Field specification. For curves over GF(p), this is the modulus; for
230 * curves over GF(2^m), this is the irreducible polynomial defining the
235 * Field specification for curves over GF(2^m). The irreducible f(t) is
236 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
237 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
238 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
243 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
244 * or abused for all kinds of fields, not just GF(p).) For characteristic
245 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
246 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
247 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
250 /* enable optimized point arithmetics for special case */
252 /* method-specific (e.g., Montgomery structure) */
254 /* method-specific */
256 /* method-specific */
257 int (*field_mod_func
) (BIGNUM
*, const BIGNUM
*, const BIGNUM
*,
259 /* data for ECDSA inverse */
260 BN_MONT_CTX
*mont_data
;
263 * Precomputed values for speed. The PCT_xxx names match the
264 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
269 PCT_nistp224
, PCT_nistp256
, PCT_nistp521
, PCT_nistz256
,
273 NISTP224_PRE_COMP
*nistp224
;
274 NISTP256_PRE_COMP
*nistp256
;
275 NISTP521_PRE_COMP
*nistp521
;
276 NISTZ256_PRE_COMP
*nistz256
;
283 #define SETPRECOMP(g, type, pre) \
284 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
285 #define HAVEPRECOMP(g, type) \
286 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
289 const EC_KEY_METHOD
*meth
;
295 unsigned int enc_flag
;
296 point_conversion_form_t conv_form
;
297 CRYPTO_REF_COUNT references
;
300 CRYPTO_EX_DATA ex_data
;
307 const EC_METHOD
*meth
;
308 /* NID for the curve if known */
311 * All members except 'meth' are handled by the method functions, even if
312 * they appear generic
316 BIGNUM
*Z
; /* Jacobian projective coordinates: * (X, Y,
317 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
318 int Z_is_one
; /* enable optimized point arithmetics for
322 static ossl_inline
int ec_point_is_compat(const EC_POINT
*point
,
323 const EC_GROUP
*group
)
325 return group
->meth
== point
->meth
326 && (group
->curve_name
== 0
327 || point
->curve_name
== 0
328 || group
->curve_name
== point
->curve_name
);
331 NISTP224_PRE_COMP
*EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP
*);
332 NISTP256_PRE_COMP
*EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP
*);
333 NISTP521_PRE_COMP
*EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP
*);
334 NISTZ256_PRE_COMP
*EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP
*);
335 NISTP256_PRE_COMP
*EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP
*);
336 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*);
338 void EC_pre_comp_free(EC_GROUP
*group
);
339 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP
*);
340 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP
*);
341 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP
*);
342 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP
*);
343 void EC_ec_pre_comp_free(EC_PRE_COMP
*);
346 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
347 * group->method->mul is 0)
349 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
350 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
352 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*);
353 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
);
355 /* method functions in ecp_smpl.c */
356 int ec_GFp_simple_group_init(EC_GROUP
*);
357 void ec_GFp_simple_group_finish(EC_GROUP
*);
358 void ec_GFp_simple_group_clear_finish(EC_GROUP
*);
359 int ec_GFp_simple_group_copy(EC_GROUP
*, const EC_GROUP
*);
360 int ec_GFp_simple_group_set_curve(EC_GROUP
*, const BIGNUM
*p
,
361 const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*);
362 int ec_GFp_simple_group_get_curve(const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
,
363 BIGNUM
*b
, BN_CTX
*);
364 int ec_GFp_simple_group_get_degree(const EC_GROUP
*);
365 int ec_GFp_simple_group_check_discriminant(const EC_GROUP
*, BN_CTX
*);
366 int ec_GFp_simple_point_init(EC_POINT
*);
367 void ec_GFp_simple_point_finish(EC_POINT
*);
368 void ec_GFp_simple_point_clear_finish(EC_POINT
*);
369 int ec_GFp_simple_point_copy(EC_POINT
*, const EC_POINT
*);
370 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP
*, EC_POINT
*);
371 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP
*,
372 EC_POINT
*, const BIGNUM
*x
,
374 const BIGNUM
*z
, BN_CTX
*);
375 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP
*,
376 const EC_POINT
*, BIGNUM
*x
,
377 BIGNUM
*y
, BIGNUM
*z
,
379 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP
*, EC_POINT
*,
381 const BIGNUM
*y
, BN_CTX
*);
382 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP
*,
383 const EC_POINT
*, BIGNUM
*x
,
384 BIGNUM
*y
, BN_CTX
*);
385 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP
*, EC_POINT
*,
386 const BIGNUM
*x
, int y_bit
,
388 size_t ec_GFp_simple_point2oct(const EC_GROUP
*, const EC_POINT
*,
389 point_conversion_form_t form
,
390 unsigned char *buf
, size_t len
, BN_CTX
*);
391 int ec_GFp_simple_oct2point(const EC_GROUP
*, EC_POINT
*,
392 const unsigned char *buf
, size_t len
, BN_CTX
*);
393 int ec_GFp_simple_add(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
394 const EC_POINT
*b
, BN_CTX
*);
395 int ec_GFp_simple_dbl(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
397 int ec_GFp_simple_invert(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
398 int ec_GFp_simple_is_at_infinity(const EC_GROUP
*, const EC_POINT
*);
399 int ec_GFp_simple_is_on_curve(const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
400 int ec_GFp_simple_cmp(const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
402 int ec_GFp_simple_make_affine(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
403 int ec_GFp_simple_points_make_affine(const EC_GROUP
*, size_t num
,
404 EC_POINT
*[], BN_CTX
*);
405 int ec_GFp_simple_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
406 const BIGNUM
*b
, BN_CTX
*);
407 int ec_GFp_simple_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
409 int ec_GFp_simple_field_inv(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
411 int ec_GFp_simple_blind_coordinates(const EC_GROUP
*group
, EC_POINT
*p
,
413 int ec_GFp_simple_ladder_pre(const EC_GROUP
*group
,
414 EC_POINT
*r
, EC_POINT
*s
,
415 EC_POINT
*p
, BN_CTX
*ctx
);
416 int ec_GFp_simple_ladder_step(const EC_GROUP
*group
,
417 EC_POINT
*r
, EC_POINT
*s
,
418 EC_POINT
*p
, BN_CTX
*ctx
);
419 int ec_GFp_simple_ladder_post(const EC_GROUP
*group
,
420 EC_POINT
*r
, EC_POINT
*s
,
421 EC_POINT
*p
, BN_CTX
*ctx
);
423 /* method functions in ecp_mont.c */
424 int ec_GFp_mont_group_init(EC_GROUP
*);
425 int ec_GFp_mont_group_set_curve(EC_GROUP
*, const BIGNUM
*p
, const BIGNUM
*a
,
426 const BIGNUM
*b
, BN_CTX
*);
427 void ec_GFp_mont_group_finish(EC_GROUP
*);
428 void ec_GFp_mont_group_clear_finish(EC_GROUP
*);
429 int ec_GFp_mont_group_copy(EC_GROUP
*, const EC_GROUP
*);
430 int ec_GFp_mont_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
431 const BIGNUM
*b
, BN_CTX
*);
432 int ec_GFp_mont_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
434 int ec_GFp_mont_field_inv(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
436 int ec_GFp_mont_field_encode(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
438 int ec_GFp_mont_field_decode(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
440 int ec_GFp_mont_field_set_to_one(const EC_GROUP
*, BIGNUM
*r
, BN_CTX
*);
442 /* method functions in ecp_nist.c */
443 int ec_GFp_nist_group_copy(EC_GROUP
*dest
, const EC_GROUP
*src
);
444 int ec_GFp_nist_group_set_curve(EC_GROUP
*, const BIGNUM
*p
, const BIGNUM
*a
,
445 const BIGNUM
*b
, BN_CTX
*);
446 int ec_GFp_nist_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
447 const BIGNUM
*b
, BN_CTX
*);
448 int ec_GFp_nist_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
451 /* method functions in ec2_smpl.c */
452 int ec_GF2m_simple_group_init(EC_GROUP
*);
453 void ec_GF2m_simple_group_finish(EC_GROUP
*);
454 void ec_GF2m_simple_group_clear_finish(EC_GROUP
*);
455 int ec_GF2m_simple_group_copy(EC_GROUP
*, const EC_GROUP
*);
456 int ec_GF2m_simple_group_set_curve(EC_GROUP
*, const BIGNUM
*p
,
457 const BIGNUM
*a
, const BIGNUM
*b
,
459 int ec_GF2m_simple_group_get_curve(const EC_GROUP
*, BIGNUM
*p
, BIGNUM
*a
,
460 BIGNUM
*b
, BN_CTX
*);
461 int ec_GF2m_simple_group_get_degree(const EC_GROUP
*);
462 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP
*, BN_CTX
*);
463 int ec_GF2m_simple_point_init(EC_POINT
*);
464 void ec_GF2m_simple_point_finish(EC_POINT
*);
465 void ec_GF2m_simple_point_clear_finish(EC_POINT
*);
466 int ec_GF2m_simple_point_copy(EC_POINT
*, const EC_POINT
*);
467 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP
*, EC_POINT
*);
468 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP
*, EC_POINT
*,
470 const BIGNUM
*y
, BN_CTX
*);
471 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP
*,
472 const EC_POINT
*, BIGNUM
*x
,
473 BIGNUM
*y
, BN_CTX
*);
474 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP
*, EC_POINT
*,
475 const BIGNUM
*x
, int y_bit
,
477 size_t ec_GF2m_simple_point2oct(const EC_GROUP
*, const EC_POINT
*,
478 point_conversion_form_t form
,
479 unsigned char *buf
, size_t len
, BN_CTX
*);
480 int ec_GF2m_simple_oct2point(const EC_GROUP
*, EC_POINT
*,
481 const unsigned char *buf
, size_t len
, BN_CTX
*);
482 int ec_GF2m_simple_add(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
483 const EC_POINT
*b
, BN_CTX
*);
484 int ec_GF2m_simple_dbl(const EC_GROUP
*, EC_POINT
*r
, const EC_POINT
*a
,
486 int ec_GF2m_simple_invert(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
487 int ec_GF2m_simple_is_at_infinity(const EC_GROUP
*, const EC_POINT
*);
488 int ec_GF2m_simple_is_on_curve(const EC_GROUP
*, const EC_POINT
*, BN_CTX
*);
489 int ec_GF2m_simple_cmp(const EC_GROUP
*, const EC_POINT
*a
, const EC_POINT
*b
,
491 int ec_GF2m_simple_make_affine(const EC_GROUP
*, EC_POINT
*, BN_CTX
*);
492 int ec_GF2m_simple_points_make_affine(const EC_GROUP
*, size_t num
,
493 EC_POINT
*[], BN_CTX
*);
494 int ec_GF2m_simple_field_mul(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
495 const BIGNUM
*b
, BN_CTX
*);
496 int ec_GF2m_simple_field_sqr(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
498 int ec_GF2m_simple_field_div(const EC_GROUP
*, BIGNUM
*r
, const BIGNUM
*a
,
499 const BIGNUM
*b
, BN_CTX
*);
501 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
502 /* method functions in ecp_nistp224.c */
503 int ec_GFp_nistp224_group_init(EC_GROUP
*group
);
504 int ec_GFp_nistp224_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
505 const BIGNUM
*a
, const BIGNUM
*n
,
507 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP
*group
,
508 const EC_POINT
*point
,
509 BIGNUM
*x
, BIGNUM
*y
,
511 int ec_GFp_nistp224_mul(const EC_GROUP
*group
, EC_POINT
*r
,
512 const BIGNUM
*scalar
, size_t num
,
513 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
515 int ec_GFp_nistp224_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
516 const BIGNUM
*scalar
, size_t num
,
517 const EC_POINT
*points
[],
518 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
519 int ec_GFp_nistp224_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
520 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP
*group
);
522 /* method functions in ecp_nistp256.c */
523 int ec_GFp_nistp256_group_init(EC_GROUP
*group
);
524 int ec_GFp_nistp256_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
525 const BIGNUM
*a
, const BIGNUM
*n
,
527 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP
*group
,
528 const EC_POINT
*point
,
529 BIGNUM
*x
, BIGNUM
*y
,
531 int ec_GFp_nistp256_mul(const EC_GROUP
*group
, EC_POINT
*r
,
532 const BIGNUM
*scalar
, size_t num
,
533 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
535 int ec_GFp_nistp256_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
536 const BIGNUM
*scalar
, size_t num
,
537 const EC_POINT
*points
[],
538 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
539 int ec_GFp_nistp256_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
540 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP
*group
);
542 /* method functions in ecp_nistp521.c */
543 int ec_GFp_nistp521_group_init(EC_GROUP
*group
);
544 int ec_GFp_nistp521_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
545 const BIGNUM
*a
, const BIGNUM
*n
,
547 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP
*group
,
548 const EC_POINT
*point
,
549 BIGNUM
*x
, BIGNUM
*y
,
551 int ec_GFp_nistp521_mul(const EC_GROUP
*group
, EC_POINT
*r
,
552 const BIGNUM
*scalar
, size_t num
,
553 const EC_POINT
*points
[], const BIGNUM
*scalars
[],
555 int ec_GFp_nistp521_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
556 const BIGNUM
*scalar
, size_t num
,
557 const EC_POINT
*points
[],
558 const BIGNUM
*scalars
[], BN_CTX
*ctx
);
559 int ec_GFp_nistp521_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
);
560 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP
*group
);
562 /* utility functions in ecp_nistputil.c */
563 void ec_GFp_nistp_points_make_affine_internal(size_t num
, void *point_array
,
566 void (*felem_one
) (void *out
),
567 int (*felem_is_zero
) (const void
569 void (*felem_assign
) (void *out
,
572 void (*felem_square
) (void *out
,
575 void (*felem_mul
) (void *out
,
580 void (*felem_inv
) (void *out
,
583 void (*felem_contract
) (void
588 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign
,
589 unsigned char *digit
, unsigned char in
);
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 const EC_METHOD
*EC_GFp_s390x_nistp256_method(void);
602 const EC_METHOD
*EC_GFp_s390x_nistp384_method(void);
603 const EC_METHOD
*EC_GFp_s390x_nistp521_method(void);
606 size_t ec_key_simple_priv2oct(const EC_KEY
*eckey
,
607 unsigned char *buf
, size_t len
);
608 int ec_key_simple_oct2priv(EC_KEY
*eckey
, const unsigned char *buf
, size_t len
);
609 int ec_key_simple_generate_key(EC_KEY
*eckey
);
610 int ec_key_simple_generate_public_key(EC_KEY
*eckey
);
611 int ec_key_simple_check_key(const EC_KEY
*eckey
);
613 int ec_curve_nid_from_params(const EC_GROUP
*group
, BN_CTX
*ctx
);
615 /* EC_METHOD definitions */
617 struct ec_key_method_st
{
620 int (*init
)(EC_KEY
*key
);
621 void (*finish
)(EC_KEY
*key
);
622 int (*copy
)(EC_KEY
*dest
, const EC_KEY
*src
);
623 int (*set_group
)(EC_KEY
*key
, const EC_GROUP
*grp
);
624 int (*set_private
)(EC_KEY
*key
, const BIGNUM
*priv_key
);
625 int (*set_public
)(EC_KEY
*key
, const EC_POINT
*pub_key
);
626 int (*keygen
)(EC_KEY
*key
);
627 int (*compute_key
)(unsigned char **pout
, size_t *poutlen
,
628 const EC_POINT
*pub_key
, const EC_KEY
*ecdh
);
629 int (*sign
)(int type
, const unsigned char *dgst
, int dlen
, unsigned char
630 *sig
, unsigned int *siglen
, const BIGNUM
*kinv
,
631 const BIGNUM
*r
, EC_KEY
*eckey
);
632 int (*sign_setup
)(EC_KEY
*eckey
, BN_CTX
*ctx_in
, BIGNUM
**kinvp
,
634 ECDSA_SIG
*(*sign_sig
)(const unsigned char *dgst
, int dgst_len
,
635 const BIGNUM
*in_kinv
, const BIGNUM
*in_r
,
638 int (*verify
)(int type
, const unsigned char *dgst
, int dgst_len
,
639 const unsigned char *sigbuf
, int sig_len
, EC_KEY
*eckey
);
640 int (*verify_sig
)(const unsigned char *dgst
, int dgst_len
,
641 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);
644 #define EC_KEY_METHOD_DYNAMIC 1
646 EC_KEY
*ec_key_new_method_int(OPENSSL_CTX
*libctx
, ENGINE
*engine
);
648 int ossl_ec_key_gen(EC_KEY
*eckey
);
649 int ossl_ecdh_compute_key(unsigned char **pout
, size_t *poutlen
,
650 const EC_POINT
*pub_key
, const EC_KEY
*ecdh
);
651 int ecdh_simple_compute_key(unsigned char **pout
, size_t *poutlen
,
652 const EC_POINT
*pub_key
, const EC_KEY
*ecdh
);
654 struct ECDSA_SIG_st
{
659 int ossl_ecdsa_sign_setup(EC_KEY
*eckey
, BN_CTX
*ctx_in
, BIGNUM
**kinvp
,
661 int ossl_ecdsa_sign(int type
, const unsigned char *dgst
, int dlen
,
662 unsigned char *sig
, unsigned int *siglen
,
663 const BIGNUM
*kinv
, const BIGNUM
*r
, EC_KEY
*eckey
);
664 ECDSA_SIG
*ossl_ecdsa_sign_sig(const unsigned char *dgst
, int dgst_len
,
665 const BIGNUM
*in_kinv
, const BIGNUM
*in_r
,
667 int ossl_ecdsa_verify(int type
, const unsigned char *dgst
, int dgst_len
,
668 const unsigned char *sigbuf
, int sig_len
, EC_KEY
*eckey
);
669 int ossl_ecdsa_verify_sig(const unsigned char *dgst
, int dgst_len
,
670 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);
671 int ecdsa_simple_sign_setup(EC_KEY
*eckey
, BN_CTX
*ctx_in
, BIGNUM
**kinvp
,
673 ECDSA_SIG
*ecdsa_simple_sign_sig(const unsigned char *dgst
, int dgst_len
,
674 const BIGNUM
*in_kinv
, const BIGNUM
*in_r
,
676 int ecdsa_simple_verify_sig(const unsigned char *dgst
, int dgst_len
,
677 const ECDSA_SIG
*sig
, EC_KEY
*eckey
);
679 int ED25519_sign(uint8_t *out_sig
, const uint8_t *message
, size_t message_len
,
680 const uint8_t public_key
[32], const uint8_t private_key
[32]);
681 int ED25519_verify(const uint8_t *message
, size_t message_len
,
682 const uint8_t signature
[64], const uint8_t public_key
[32]);
683 void ED25519_public_from_private(uint8_t out_public_key
[32],
684 const uint8_t private_key
[32]);
686 int X25519(uint8_t out_shared_key
[32], const uint8_t private_key
[32],
687 const uint8_t peer_public_value
[32]);
688 void X25519_public_from_private(uint8_t out_public_value
[32],
689 const uint8_t private_key
[32]);
692 * This functions computes a single point multiplication over the EC group,
693 * using, at a high level, a Montgomery ladder with conditional swaps, with
694 * various timing attack defenses.
696 * It performs either a fixed point multiplication
697 * (scalar * generator)
698 * when point is NULL, or a variable point multiplication
700 * when point is not NULL.
702 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
703 * constant time bets are off (where n is the cardinality of the EC group).
705 * This function expects `group->order` and `group->cardinality` to be well
706 * defined and non-zero: it fails with an error code otherwise.
708 * NB: This says nothing about the constant-timeness of the ladder step
709 * implementation (i.e., the default implementation is based on EC_POINT_add and
710 * EC_POINT_dbl, which of course are not constant time themselves) or the
711 * underlying multiprecision arithmetic.
713 * The product is stored in `r`.
715 * This is an internal function: callers are in charge of ensuring that the
716 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
718 * Returns 1 on success, 0 otherwise.
720 int ec_scalar_mul_ladder(const EC_GROUP
*group
, EC_POINT
*r
,
721 const BIGNUM
*scalar
, const EC_POINT
*point
,
724 int ec_point_blind_coordinates(const EC_GROUP
*group
, EC_POINT
*p
, BN_CTX
*ctx
);
726 static ossl_inline
int ec_point_ladder_pre(const EC_GROUP
*group
,
727 EC_POINT
*r
, EC_POINT
*s
,
728 EC_POINT
*p
, BN_CTX
*ctx
)
730 if (group
->meth
->ladder_pre
!= NULL
)
731 return group
->meth
->ladder_pre(group
, r
, s
, p
, ctx
);
733 if (!EC_POINT_copy(s
, p
)
734 || !EC_POINT_dbl(group
, r
, s
, ctx
))
740 static ossl_inline
int ec_point_ladder_step(const EC_GROUP
*group
,
741 EC_POINT
*r
, EC_POINT
*s
,
742 EC_POINT
*p
, BN_CTX
*ctx
)
744 if (group
->meth
->ladder_step
!= NULL
)
745 return group
->meth
->ladder_step(group
, r
, s
, p
, ctx
);
747 if (!EC_POINT_add(group
, s
, r
, s
, ctx
)
748 || !EC_POINT_dbl(group
, r
, r
, ctx
))
755 static ossl_inline
int ec_point_ladder_post(const EC_GROUP
*group
,
756 EC_POINT
*r
, EC_POINT
*s
,
757 EC_POINT
*p
, BN_CTX
*ctx
)
759 if (group
->meth
->ladder_post
!= NULL
)
760 return group
->meth
->ladder_post(group
, r
, s
, p
, ctx
);