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 "curve448/curve448_lcl.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_GFp, EC_GROUP_get_curve_GFp, */
53 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
54 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
55 const BIGNUM *b, BN_CTX *);
56 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
58 /* used by EC_GROUP_get_degree: */
59 int (*group_get_degree) (const EC_GROUP *);
60 int (*group_order_bits) (const EC_GROUP *);
61 /* used by EC_GROUP_check: */
62 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
64 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
67 int (*point_init) (EC_POINT *);
68 void (*point_finish) (EC_POINT *);
69 void (*point_clear_finish) (EC_POINT *);
70 int (*point_copy) (EC_POINT *, const EC_POINT *);
72 * used by EC_POINT_set_to_infinity,
73 * EC_POINT_set_Jprojective_coordinates_GFp,
74 * EC_POINT_get_Jprojective_coordinates_GFp,
75 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
76 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
77 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
79 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
80 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
81 EC_POINT *, const BIGNUM *x,
83 const BIGNUM *z, BN_CTX *);
84 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
85 const EC_POINT *, BIGNUM *x,
88 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
89 const BIGNUM *x, const BIGNUM *y,
91 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
92 BIGNUM *x, BIGNUM *y, BN_CTX *);
93 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
94 const BIGNUM *x, int y_bit,
96 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
97 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
98 point_conversion_form_t form, unsigned char *buf,
99 size_t len, BN_CTX *);
100 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
101 size_t len, BN_CTX *);
102 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
103 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
104 const EC_POINT *b, BN_CTX *);
105 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
106 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
108 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
110 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
111 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
112 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
114 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
115 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
116 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
119 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
120 * EC_POINT_have_precompute_mult (default implementations are used if the
121 * 'mul' pointer is 0):
124 * mul() calculates the value
126 * r := generator * scalar
127 * + points[0] * scalars[0]
129 * + points[num-1] * scalars[num-1].
131 * For a fixed point multiplication (scalar != NULL, num == 0)
132 * or a variable point multiplication (scalar == NULL, num == 1),
133 * mul() must use a constant time algorithm: in both cases callers
134 * should provide an input scalar (either scalar or scalars[0])
135 * in the range [0, ec_group_order); for robustness, implementers
136 * should handle the case when the scalar has not been reduced, but
137 * may treat it as an unusual input, without any constant-timeness
140 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
141 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
143 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
144 int (*have_precompute_mult) (const EC_GROUP *group);
145 /* internal functions */
147 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
148 * 'dbl' so that the same implementations of point operations can be used
149 * with different optimized implementations of expensive field
152 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
153 const BIGNUM *b, BN_CTX *);
154 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
155 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
156 const BIGNUM *b, BN_CTX *);
157 /* e.g. to Montgomery */
158 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
160 /* e.g. from Montgomery */
161 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
163 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
164 /* private key operations */
165 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);
166 int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len);
167 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);
168 int (*keygen)(EC_KEY *eckey);
169 int (*keycheck)(const EC_KEY *eckey);
170 int (*keygenpub)(EC_KEY *eckey);
171 int (*keycopy)(EC_KEY *dst, const EC_KEY *src);
172 void (*keyfinish)(EC_KEY *eckey);
173 /* custom ECDH operation */
174 int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,
175 const EC_POINT *pub_key, const EC_KEY *ecdh);
176 /* Inverse modulo order */
177 int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r,
178 const BIGNUM *x, BN_CTX *);
179 int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
183 * Types and functions to manipulate pre-computed values.
185 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
186 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
187 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
188 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
189 typedef struct ec_pre_comp_st EC_PRE_COMP;
192 const EC_METHOD *meth;
193 EC_POINT *generator; /* optional */
194 BIGNUM *order, *cofactor;
195 int curve_name; /* optional NID for named curve */
196 int asn1_flag; /* flag to control the asn1 encoding */
197 point_conversion_form_t asn1_form;
198 unsigned char *seed; /* optional seed for parameters (appears in
202 * The following members are handled by the method functions, even if
203 * they appear generic
206 * Field specification. For curves over GF(p), this is the modulus; for
207 * curves over GF(2^m), this is the irreducible polynomial defining the
212 * Field specification for curves over GF(2^m). The irreducible f(t) is
213 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
214 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
215 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
220 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
221 * or abused for all kinds of fields, not just GF(p).) For characteristic
222 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
223 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
224 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
227 /* enable optimized point arithmetics for special case */
229 /* method-specific (e.g., Montgomery structure) */
231 /* method-specific */
233 /* method-specific */
234 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
236 /* data for ECDSA inverse */
237 BN_MONT_CTX *mont_data;
240 * Precomputed values for speed. The PCT_xxx names match the
241 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
246 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,
250 NISTP224_PRE_COMP *nistp224;
251 NISTP256_PRE_COMP *nistp256;
252 NISTP521_PRE_COMP *nistp521;
253 NISTZ256_PRE_COMP *nistz256;
258 #define SETPRECOMP(g, type, pre) \
259 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
260 #define HAVEPRECOMP(g, type) \
261 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
264 const EC_KEY_METHOD *meth;
270 unsigned int enc_flag;
271 point_conversion_form_t conv_form;
272 CRYPTO_REF_COUNT references;
274 CRYPTO_EX_DATA ex_data;
279 const EC_METHOD *meth;
280 /* NID for the curve if known */
283 * All members except 'meth' are handled by the method functions, even if
284 * they appear generic
288 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
289 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
290 int Z_is_one; /* enable optimized point arithmetics for
295 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
296 const EC_GROUP *group)
298 if (group->meth != point->meth
299 || (group->curve_name != 0
300 && point->curve_name != 0
301 && group->curve_name != point->curve_name))
308 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
309 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
310 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
311 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
312 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
313 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
315 void EC_pre_comp_free(EC_GROUP *group);
316 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
317 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
318 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
319 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
320 void EC_ec_pre_comp_free(EC_PRE_COMP *);
323 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
324 * group->method->mul is 0)
326 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
327 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
329 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
330 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
332 /* method functions in ecp_smpl.c */
333 int ec_GFp_simple_group_init(EC_GROUP *);
334 void ec_GFp_simple_group_finish(EC_GROUP *);
335 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
336 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
337 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
338 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
339 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
340 BIGNUM *b, BN_CTX *);
341 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
342 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
343 int ec_GFp_simple_point_init(EC_POINT *);
344 void ec_GFp_simple_point_finish(EC_POINT *);
345 void ec_GFp_simple_point_clear_finish(EC_POINT *);
346 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
347 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
348 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
349 EC_POINT *, const BIGNUM *x,
351 const BIGNUM *z, BN_CTX *);
352 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
353 const EC_POINT *, BIGNUM *x,
354 BIGNUM *y, BIGNUM *z,
356 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
358 const BIGNUM *y, BN_CTX *);
359 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
360 const EC_POINT *, BIGNUM *x,
361 BIGNUM *y, BN_CTX *);
362 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
363 const BIGNUM *x, int y_bit,
365 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
366 point_conversion_form_t form,
367 unsigned char *buf, size_t len, BN_CTX *);
368 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
369 const unsigned char *buf, size_t len, BN_CTX *);
370 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
371 const EC_POINT *b, BN_CTX *);
372 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
374 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
375 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
376 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
377 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
379 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
380 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
381 EC_POINT *[], BN_CTX *);
382 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
383 const BIGNUM *b, BN_CTX *);
384 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
386 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
389 /* method functions in ecp_mont.c */
390 int ec_GFp_mont_group_init(EC_GROUP *);
391 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
392 const BIGNUM *b, BN_CTX *);
393 void ec_GFp_mont_group_finish(EC_GROUP *);
394 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
395 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
396 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
397 const BIGNUM *b, BN_CTX *);
398 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
400 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
402 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
404 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
406 /* method functions in ecp_nist.c */
407 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
408 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
409 const BIGNUM *b, BN_CTX *);
410 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
411 const BIGNUM *b, BN_CTX *);
412 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
415 /* method functions in ec2_smpl.c */
416 int ec_GF2m_simple_group_init(EC_GROUP *);
417 void ec_GF2m_simple_group_finish(EC_GROUP *);
418 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
419 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
420 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
421 const BIGNUM *a, const BIGNUM *b,
423 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
424 BIGNUM *b, BN_CTX *);
425 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
426 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
427 int ec_GF2m_simple_point_init(EC_POINT *);
428 void ec_GF2m_simple_point_finish(EC_POINT *);
429 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
430 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
431 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
432 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
434 const BIGNUM *y, BN_CTX *);
435 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
436 const EC_POINT *, BIGNUM *x,
437 BIGNUM *y, BN_CTX *);
438 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
439 const BIGNUM *x, int y_bit,
441 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
442 point_conversion_form_t form,
443 unsigned char *buf, size_t len, BN_CTX *);
444 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
445 const unsigned char *buf, size_t len, BN_CTX *);
446 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
447 const EC_POINT *b, BN_CTX *);
448 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
450 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
451 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
452 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
453 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
455 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
456 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
457 EC_POINT *[], BN_CTX *);
458 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
459 const BIGNUM *b, BN_CTX *);
460 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
462 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
463 const BIGNUM *b, BN_CTX *);
465 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
466 /* method functions in ecp_nistp224.c */
467 int ec_GFp_nistp224_group_init(EC_GROUP *group);
468 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
469 const BIGNUM *a, const BIGNUM *n,
471 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
472 const EC_POINT *point,
473 BIGNUM *x, BIGNUM *y,
475 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
476 const BIGNUM *scalar, size_t num,
477 const EC_POINT *points[], const BIGNUM *scalars[],
479 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
480 const BIGNUM *scalar, size_t num,
481 const EC_POINT *points[],
482 const BIGNUM *scalars[], BN_CTX *ctx);
483 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
484 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
486 /* method functions in ecp_nistp256.c */
487 int ec_GFp_nistp256_group_init(EC_GROUP *group);
488 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
489 const BIGNUM *a, const BIGNUM *n,
491 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
492 const EC_POINT *point,
493 BIGNUM *x, BIGNUM *y,
495 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
496 const BIGNUM *scalar, size_t num,
497 const EC_POINT *points[], const BIGNUM *scalars[],
499 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
500 const BIGNUM *scalar, size_t num,
501 const EC_POINT *points[],
502 const BIGNUM *scalars[], BN_CTX *ctx);
503 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
504 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
506 /* method functions in ecp_nistp521.c */
507 int ec_GFp_nistp521_group_init(EC_GROUP *group);
508 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
509 const BIGNUM *a, const BIGNUM *n,
511 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
512 const EC_POINT *point,
513 BIGNUM *x, BIGNUM *y,
515 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
516 const BIGNUM *scalar, size_t num,
517 const EC_POINT *points[], const BIGNUM *scalars[],
519 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
520 const BIGNUM *scalar, size_t num,
521 const EC_POINT *points[],
522 const BIGNUM *scalars[], BN_CTX *ctx);
523 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
524 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
526 /* utility functions in ecp_nistputil.c */
527 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
530 void (*felem_one) (void *out),
531 int (*felem_is_zero) (const void
533 void (*felem_assign) (void *out,
536 void (*felem_square) (void *out,
539 void (*felem_mul) (void *out,
544 void (*felem_inv) (void *out,
547 void (*felem_contract) (void
552 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
553 unsigned char *digit, unsigned char in);
555 int ec_group_simple_order_bits(const EC_GROUP *group);
557 #ifdef ECP_NISTZ256_ASM
558 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
559 * P256. See http://eprint.iacr.org/2013/816.
560 * \return EC_METHOD object
562 const EC_METHOD *EC_GFp_nistz256_method(void);
565 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
566 unsigned char *buf, size_t len);
567 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
568 int ec_key_simple_generate_key(EC_KEY *eckey);
569 int ec_key_simple_generate_public_key(EC_KEY *eckey);
570 int ec_key_simple_check_key(const EC_KEY *eckey);
572 /* EC_METHOD definitions */
574 struct ec_key_method_st {
577 int (*init)(EC_KEY *key);
578 void (*finish)(EC_KEY *key);
579 int (*copy)(EC_KEY *dest, const EC_KEY *src);
580 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
581 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
582 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
583 int (*keygen)(EC_KEY *key);
584 int (*compute_key)(unsigned char **pout, size_t *poutlen,
585 const EC_POINT *pub_key, const EC_KEY *ecdh);
586 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
587 *sig, unsigned int *siglen, const BIGNUM *kinv,
588 const BIGNUM *r, EC_KEY *eckey);
589 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
591 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
592 const BIGNUM *in_kinv, const BIGNUM *in_r,
595 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
596 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
597 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
598 const ECDSA_SIG *sig, EC_KEY *eckey);
601 #define EC_KEY_METHOD_DYNAMIC 1
603 int ossl_ec_key_gen(EC_KEY *eckey);
604 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
605 const EC_POINT *pub_key, const EC_KEY *ecdh);
606 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
607 const EC_POINT *pub_key, const EC_KEY *ecdh);
609 struct ECDSA_SIG_st {
614 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
616 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
617 unsigned char *sig, unsigned int *siglen,
618 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
619 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
620 const BIGNUM *in_kinv, const BIGNUM *in_r,
622 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
623 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
624 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
625 const ECDSA_SIG *sig, EC_KEY *eckey);
627 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
628 const uint8_t public_key[32], const uint8_t private_key[32]);
629 int ED25519_verify(const uint8_t *message, size_t message_len,
630 const uint8_t signature[64], const uint8_t public_key[32]);
631 void ED25519_public_from_private(uint8_t out_public_key[32],
632 const uint8_t private_key[32]);
634 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
635 const uint8_t peer_public_value[32]);
636 void X25519_public_from_private(uint8_t out_public_value[32],
637 const uint8_t private_key[32]);
639 int ec_group_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
640 const BIGNUM *x, BN_CTX *ctx);
642 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);