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 OpenSSL license (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 "internal/ec_int.h"
18 #include "curve448/curve448_lcl.h"
20 #if defined(__SUNPRO_C)
21 # if __SUNPRO_C >= 0x520
22 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
26 /* Use default functions for poin2oct, oct2point and compressed coordinates */
27 #define EC_FLAGS_DEFAULT_OCT 0x1
29 /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */
30 #define EC_FLAGS_CUSTOM_CURVE 0x2
32 /* Curve does not support signing operations */
33 #define EC_FLAGS_NO_SIGN 0x4
36 * Structure details are not part of the exported interface, so all this may
37 * change in future versions.
41 /* Various method flags */
43 /* used by EC_METHOD_get_field_type: */
44 int field_type; /* a NID */
46 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
49 int (*group_init) (EC_GROUP *);
50 void (*group_finish) (EC_GROUP *);
51 void (*group_clear_finish) (EC_GROUP *);
52 int (*group_copy) (EC_GROUP *, const EC_GROUP *);
53 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
54 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
55 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
56 const BIGNUM *b, BN_CTX *);
57 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
59 /* used by EC_GROUP_get_degree: */
60 int (*group_get_degree) (const EC_GROUP *);
61 int (*group_order_bits) (const EC_GROUP *);
62 /* used by EC_GROUP_check: */
63 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
65 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
68 int (*point_init) (EC_POINT *);
69 void (*point_finish) (EC_POINT *);
70 void (*point_clear_finish) (EC_POINT *);
71 int (*point_copy) (EC_POINT *, const EC_POINT *);
73 * used by EC_POINT_set_to_infinity,
74 * EC_POINT_set_Jprojective_coordinates_GFp,
75 * EC_POINT_get_Jprojective_coordinates_GFp,
76 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
77 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
78 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
80 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
81 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
82 EC_POINT *, const BIGNUM *x,
84 const BIGNUM *z, BN_CTX *);
85 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
86 const EC_POINT *, BIGNUM *x,
89 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
90 const BIGNUM *x, const BIGNUM *y,
92 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
93 BIGNUM *x, BIGNUM *y, BN_CTX *);
94 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
95 const BIGNUM *x, int y_bit,
97 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
98 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
99 point_conversion_form_t form, unsigned char *buf,
100 size_t len, BN_CTX *);
101 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
102 size_t len, BN_CTX *);
103 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
104 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
105 const EC_POINT *b, BN_CTX *);
106 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
107 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
109 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
111 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
112 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
113 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
115 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
116 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
117 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
120 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
121 * EC_POINT_have_precompute_mult (default implementations are used if the
122 * 'mul' pointer is 0):
125 * mul() calculates the value
127 * r := generator * scalar
128 * + points[0] * scalars[0]
130 * + points[num-1] * scalars[num-1].
132 * For a fixed point multiplication (scalar != NULL, num == 0)
133 * or a variable point multiplication (scalar == NULL, num == 1),
134 * mul() must use a constant time algorithm: in both cases callers
135 * should provide an input scalar (either scalar or scalars[0])
136 * in the range [0, ec_group_order); for robustness, implementers
137 * should handle the case when the scalar has not been reduced, but
138 * may treat it as an unusual input, without any constant-timeness
141 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
142 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
144 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
145 int (*have_precompute_mult) (const EC_GROUP *group);
146 /* internal functions */
148 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
149 * 'dbl' so that the same implementations of point operations can be used
150 * with different optimized implementations of expensive field
153 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
154 const BIGNUM *b, BN_CTX *);
155 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
156 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
157 const BIGNUM *b, BN_CTX *);
158 /* e.g. to Montgomery */
159 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
161 /* e.g. from Montgomery */
162 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
164 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
165 /* private key operations */
166 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);
167 int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len);
168 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);
169 int (*keygen)(EC_KEY *eckey);
170 int (*keycheck)(const EC_KEY *eckey);
171 int (*keygenpub)(EC_KEY *eckey);
172 int (*keycopy)(EC_KEY *dst, const EC_KEY *src);
173 void (*keyfinish)(EC_KEY *eckey);
174 /* custom ECDH operation */
175 int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,
176 const EC_POINT *pub_key, const EC_KEY *ecdh);
177 /* Inverse modulo order */
178 int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r,
179 const BIGNUM *x, BN_CTX *);
180 int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
184 * Types and functions to manipulate pre-computed values.
186 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
187 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
188 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
189 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
190 typedef struct ec_pre_comp_st EC_PRE_COMP;
193 const EC_METHOD *meth;
194 EC_POINT *generator; /* optional */
195 BIGNUM *order, *cofactor;
196 int curve_name; /* optional NID for named curve */
197 int asn1_flag; /* flag to control the asn1 encoding */
198 point_conversion_form_t asn1_form;
199 unsigned char *seed; /* optional seed for parameters (appears in
203 * The following members are handled by the method functions, even if
204 * they appear generic
207 * Field specification. For curves over GF(p), this is the modulus; for
208 * curves over GF(2^m), this is the irreducible polynomial defining the
213 * Field specification for curves over GF(2^m). The irreducible f(t) is
214 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
215 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
216 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
221 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
222 * or abused for all kinds of fields, not just GF(p).) For characteristic
223 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
224 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
225 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
228 /* enable optimized point arithmetics for special case */
230 /* method-specific (e.g., Montgomery structure) */
232 /* method-specific */
234 /* method-specific */
235 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
237 /* data for ECDSA inverse */
238 BN_MONT_CTX *mont_data;
241 * Precomputed values for speed. The PCT_xxx names match the
242 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
247 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,
251 NISTP224_PRE_COMP *nistp224;
252 NISTP256_PRE_COMP *nistp256;
253 NISTP521_PRE_COMP *nistp521;
254 NISTZ256_PRE_COMP *nistz256;
259 #define SETPRECOMP(g, type, pre) \
260 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
261 #define HAVEPRECOMP(g, type) \
262 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
265 const EC_KEY_METHOD *meth;
271 unsigned int enc_flag;
272 point_conversion_form_t conv_form;
273 CRYPTO_REF_COUNT references;
275 CRYPTO_EX_DATA ex_data;
280 const EC_METHOD *meth;
281 /* NID for the curve if known */
284 * All members except 'meth' are handled by the method functions, even if
285 * they appear generic
289 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
290 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
291 int Z_is_one; /* enable optimized point arithmetics for
296 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
297 const EC_GROUP *group)
299 if (group->meth != point->meth
300 || (group->curve_name != 0
301 && point->curve_name != 0
302 && group->curve_name != point->curve_name))
309 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
310 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
311 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
312 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
313 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
314 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
316 void EC_pre_comp_free(EC_GROUP *group);
317 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
318 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
319 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
320 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
321 void EC_ec_pre_comp_free(EC_PRE_COMP *);
324 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
325 * group->method->mul is 0)
327 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
328 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
330 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
331 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
333 /* method functions in ecp_smpl.c */
334 int ec_GFp_simple_group_init(EC_GROUP *);
335 void ec_GFp_simple_group_finish(EC_GROUP *);
336 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
337 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
338 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
339 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
340 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
341 BIGNUM *b, BN_CTX *);
342 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
343 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
344 int ec_GFp_simple_point_init(EC_POINT *);
345 void ec_GFp_simple_point_finish(EC_POINT *);
346 void ec_GFp_simple_point_clear_finish(EC_POINT *);
347 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
348 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
349 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
350 EC_POINT *, const BIGNUM *x,
352 const BIGNUM *z, BN_CTX *);
353 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
354 const EC_POINT *, BIGNUM *x,
355 BIGNUM *y, BIGNUM *z,
357 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
359 const BIGNUM *y, BN_CTX *);
360 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
361 const EC_POINT *, BIGNUM *x,
362 BIGNUM *y, BN_CTX *);
363 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
364 const BIGNUM *x, int y_bit,
366 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
367 point_conversion_form_t form,
368 unsigned char *buf, size_t len, BN_CTX *);
369 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
370 const unsigned char *buf, size_t len, BN_CTX *);
371 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
372 const EC_POINT *b, BN_CTX *);
373 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
375 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
376 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
377 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
378 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
380 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
381 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
382 EC_POINT *[], BN_CTX *);
383 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
384 const BIGNUM *b, BN_CTX *);
385 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
387 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
390 /* method functions in ecp_mont.c */
391 int ec_GFp_mont_group_init(EC_GROUP *);
392 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
393 const BIGNUM *b, BN_CTX *);
394 void ec_GFp_mont_group_finish(EC_GROUP *);
395 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
396 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
397 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
398 const BIGNUM *b, BN_CTX *);
399 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
401 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
403 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
405 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
407 /* method functions in ecp_nist.c */
408 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
409 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
410 const BIGNUM *b, BN_CTX *);
411 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
412 const BIGNUM *b, BN_CTX *);
413 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
416 /* method functions in ec2_smpl.c */
417 int ec_GF2m_simple_group_init(EC_GROUP *);
418 void ec_GF2m_simple_group_finish(EC_GROUP *);
419 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
420 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
421 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
422 const BIGNUM *a, const BIGNUM *b,
424 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
425 BIGNUM *b, BN_CTX *);
426 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
427 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
428 int ec_GF2m_simple_point_init(EC_POINT *);
429 void ec_GF2m_simple_point_finish(EC_POINT *);
430 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
431 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
432 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
433 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
435 const BIGNUM *y, BN_CTX *);
436 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
437 const EC_POINT *, BIGNUM *x,
438 BIGNUM *y, BN_CTX *);
439 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
440 const BIGNUM *x, int y_bit,
442 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
443 point_conversion_form_t form,
444 unsigned char *buf, size_t len, BN_CTX *);
445 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
446 const unsigned char *buf, size_t len, BN_CTX *);
447 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
448 const EC_POINT *b, BN_CTX *);
449 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
451 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
452 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
453 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
454 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
456 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
457 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
458 EC_POINT *[], BN_CTX *);
459 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
460 const BIGNUM *b, BN_CTX *);
461 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
463 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
464 const BIGNUM *b, BN_CTX *);
466 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
467 /* method functions in ecp_nistp224.c */
468 int ec_GFp_nistp224_group_init(EC_GROUP *group);
469 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
470 const BIGNUM *a, const BIGNUM *n,
472 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
473 const EC_POINT *point,
474 BIGNUM *x, BIGNUM *y,
476 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
477 const BIGNUM *scalar, size_t num,
478 const EC_POINT *points[], const BIGNUM *scalars[],
480 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
481 const BIGNUM *scalar, size_t num,
482 const EC_POINT *points[],
483 const BIGNUM *scalars[], BN_CTX *ctx);
484 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
485 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
487 /* method functions in ecp_nistp256.c */
488 int ec_GFp_nistp256_group_init(EC_GROUP *group);
489 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
490 const BIGNUM *a, const BIGNUM *n,
492 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
493 const EC_POINT *point,
494 BIGNUM *x, BIGNUM *y,
496 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
497 const BIGNUM *scalar, size_t num,
498 const EC_POINT *points[], const BIGNUM *scalars[],
500 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
501 const BIGNUM *scalar, size_t num,
502 const EC_POINT *points[],
503 const BIGNUM *scalars[], BN_CTX *ctx);
504 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
505 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
507 /* method functions in ecp_nistp521.c */
508 int ec_GFp_nistp521_group_init(EC_GROUP *group);
509 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
510 const BIGNUM *a, const BIGNUM *n,
512 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
513 const EC_POINT *point,
514 BIGNUM *x, BIGNUM *y,
516 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
517 const BIGNUM *scalar, size_t num,
518 const EC_POINT *points[], const BIGNUM *scalars[],
520 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
521 const BIGNUM *scalar, size_t num,
522 const EC_POINT *points[],
523 const BIGNUM *scalars[], BN_CTX *ctx);
524 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
525 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
527 /* utility functions in ecp_nistputil.c */
528 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
531 void (*felem_one) (void *out),
532 int (*felem_is_zero) (const void
534 void (*felem_assign) (void *out,
537 void (*felem_square) (void *out,
540 void (*felem_mul) (void *out,
545 void (*felem_inv) (void *out,
548 void (*felem_contract) (void
553 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
554 unsigned char *digit, unsigned char in);
556 int ec_group_simple_order_bits(const EC_GROUP *group);
558 #ifdef ECP_NISTZ256_ASM
559 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
560 * P256. See http://eprint.iacr.org/2013/816.
561 * \return EC_METHOD object
563 const EC_METHOD *EC_GFp_nistz256_method(void);
566 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
567 unsigned char *buf, size_t len);
568 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
569 int ec_key_simple_generate_key(EC_KEY *eckey);
570 int ec_key_simple_generate_public_key(EC_KEY *eckey);
571 int ec_key_simple_check_key(const EC_KEY *eckey);
573 /* EC_METHOD definitions */
575 struct ec_key_method_st {
578 int (*init)(EC_KEY *key);
579 void (*finish)(EC_KEY *key);
580 int (*copy)(EC_KEY *dest, const EC_KEY *src);
581 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
582 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
583 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
584 int (*keygen)(EC_KEY *key);
585 int (*compute_key)(unsigned char **pout, size_t *poutlen,
586 const EC_POINT *pub_key, const EC_KEY *ecdh);
587 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
588 *sig, unsigned int *siglen, const BIGNUM *kinv,
589 const BIGNUM *r, EC_KEY *eckey);
590 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
592 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
593 const BIGNUM *in_kinv, const BIGNUM *in_r,
596 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
597 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
598 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
599 const ECDSA_SIG *sig, EC_KEY *eckey);
602 #define EC_KEY_METHOD_DYNAMIC 1
604 int ossl_ec_key_gen(EC_KEY *eckey);
605 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
606 const EC_POINT *pub_key, const EC_KEY *ecdh);
607 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
608 const EC_POINT *pub_key, const EC_KEY *ecdh);
610 struct ECDSA_SIG_st {
615 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
617 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
618 unsigned char *sig, unsigned int *siglen,
619 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
620 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
621 const BIGNUM *in_kinv, const BIGNUM *in_r,
623 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
624 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
625 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
626 const ECDSA_SIG *sig, EC_KEY *eckey);
628 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
629 const uint8_t public_key[32], const uint8_t private_key[32]);
630 int ED25519_verify(const uint8_t *message, size_t message_len,
631 const uint8_t signature[64], const uint8_t public_key[32]);
632 void ED25519_public_from_private(uint8_t out_public_key[32],
633 const uint8_t private_key[32]);
635 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
636 const uint8_t peer_public_value[32]);
637 void X25519_public_from_private(uint8_t out_public_value[32],
638 const uint8_t private_key[32]);
640 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);