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;
306 size_t dirty_cnt; /* If any key material changes, increment this */
310 const EC_METHOD *meth;
311 /* NID for the curve if known */
314 * All members except 'meth' are handled by the method functions, even if
315 * they appear generic
319 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
320 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
321 int Z_is_one; /* enable optimized point arithmetics for
325 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
326 const EC_GROUP *group)
328 return group->meth == point->meth
329 && (group->curve_name == 0
330 || point->curve_name == 0
331 || group->curve_name == point->curve_name);
334 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
335 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
336 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
337 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
338 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
339 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
341 void EC_pre_comp_free(EC_GROUP *group);
342 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
343 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
344 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
345 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
346 void EC_ec_pre_comp_free(EC_PRE_COMP *);
349 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
350 * group->method->mul is 0)
352 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
353 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
355 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
356 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
358 /* method functions in ecp_smpl.c */
359 int ec_GFp_simple_group_init(EC_GROUP *);
360 void ec_GFp_simple_group_finish(EC_GROUP *);
361 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
362 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
363 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
364 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
365 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
366 BIGNUM *b, BN_CTX *);
367 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
368 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
369 int ec_GFp_simple_point_init(EC_POINT *);
370 void ec_GFp_simple_point_finish(EC_POINT *);
371 void ec_GFp_simple_point_clear_finish(EC_POINT *);
372 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
373 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
374 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
375 EC_POINT *, const BIGNUM *x,
377 const BIGNUM *z, BN_CTX *);
378 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
379 const EC_POINT *, BIGNUM *x,
380 BIGNUM *y, BIGNUM *z,
382 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
384 const BIGNUM *y, BN_CTX *);
385 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
386 const EC_POINT *, BIGNUM *x,
387 BIGNUM *y, BN_CTX *);
388 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
389 const BIGNUM *x, int y_bit,
391 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
392 point_conversion_form_t form,
393 unsigned char *buf, size_t len, BN_CTX *);
394 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
395 const unsigned char *buf, size_t len, BN_CTX *);
396 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
397 const EC_POINT *b, BN_CTX *);
398 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
400 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
401 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
402 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
403 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
405 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
406 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
407 EC_POINT *[], BN_CTX *);
408 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
409 const BIGNUM *b, BN_CTX *);
410 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
412 int ec_GFp_simple_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
414 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
416 int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
417 EC_POINT *r, EC_POINT *s,
418 EC_POINT *p, BN_CTX *ctx);
419 int ec_GFp_simple_ladder_step(const EC_GROUP *group,
420 EC_POINT *r, EC_POINT *s,
421 EC_POINT *p, BN_CTX *ctx);
422 int ec_GFp_simple_ladder_post(const EC_GROUP *group,
423 EC_POINT *r, EC_POINT *s,
424 EC_POINT *p, BN_CTX *ctx);
426 /* method functions in ecp_mont.c */
427 int ec_GFp_mont_group_init(EC_GROUP *);
428 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
429 const BIGNUM *b, BN_CTX *);
430 void ec_GFp_mont_group_finish(EC_GROUP *);
431 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
432 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
433 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
434 const BIGNUM *b, BN_CTX *);
435 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
437 int ec_GFp_mont_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
439 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
441 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
443 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
445 /* method functions in ecp_nist.c */
446 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
447 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
448 const BIGNUM *b, BN_CTX *);
449 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
450 const BIGNUM *b, BN_CTX *);
451 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
454 /* method functions in ec2_smpl.c */
455 int ec_GF2m_simple_group_init(EC_GROUP *);
456 void ec_GF2m_simple_group_finish(EC_GROUP *);
457 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
458 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
459 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
460 const BIGNUM *a, const BIGNUM *b,
462 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
463 BIGNUM *b, BN_CTX *);
464 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
465 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
466 int ec_GF2m_simple_point_init(EC_POINT *);
467 void ec_GF2m_simple_point_finish(EC_POINT *);
468 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
469 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
470 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
471 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
473 const BIGNUM *y, BN_CTX *);
474 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
475 const EC_POINT *, BIGNUM *x,
476 BIGNUM *y, BN_CTX *);
477 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
478 const BIGNUM *x, int y_bit,
480 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
481 point_conversion_form_t form,
482 unsigned char *buf, size_t len, BN_CTX *);
483 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
484 const unsigned char *buf, size_t len, BN_CTX *);
485 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
486 const EC_POINT *b, BN_CTX *);
487 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
489 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
490 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
491 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
492 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
494 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
495 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
496 EC_POINT *[], BN_CTX *);
497 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
498 const BIGNUM *b, BN_CTX *);
499 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
501 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
502 const BIGNUM *b, BN_CTX *);
504 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
505 /* method functions in ecp_nistp224.c */
506 int ec_GFp_nistp224_group_init(EC_GROUP *group);
507 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
508 const BIGNUM *a, const BIGNUM *n,
510 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
511 const EC_POINT *point,
512 BIGNUM *x, BIGNUM *y,
514 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
515 const BIGNUM *scalar, size_t num,
516 const EC_POINT *points[], const BIGNUM *scalars[],
518 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
519 const BIGNUM *scalar, size_t num,
520 const EC_POINT *points[],
521 const BIGNUM *scalars[], BN_CTX *ctx);
522 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
523 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
525 /* method functions in ecp_nistp256.c */
526 int ec_GFp_nistp256_group_init(EC_GROUP *group);
527 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
528 const BIGNUM *a, const BIGNUM *n,
530 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
531 const EC_POINT *point,
532 BIGNUM *x, BIGNUM *y,
534 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
535 const BIGNUM *scalar, size_t num,
536 const EC_POINT *points[], const BIGNUM *scalars[],
538 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
539 const BIGNUM *scalar, size_t num,
540 const EC_POINT *points[],
541 const BIGNUM *scalars[], BN_CTX *ctx);
542 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
543 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
545 /* method functions in ecp_nistp521.c */
546 int ec_GFp_nistp521_group_init(EC_GROUP *group);
547 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
548 const BIGNUM *a, const BIGNUM *n,
550 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
551 const EC_POINT *point,
552 BIGNUM *x, BIGNUM *y,
554 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
555 const BIGNUM *scalar, size_t num,
556 const EC_POINT *points[], const BIGNUM *scalars[],
558 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
559 const BIGNUM *scalar, size_t num,
560 const EC_POINT *points[],
561 const BIGNUM *scalars[], BN_CTX *ctx);
562 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
563 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
565 /* utility functions in ecp_nistputil.c */
566 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
569 void (*felem_one) (void *out),
570 int (*felem_is_zero) (const void
572 void (*felem_assign) (void *out,
575 void (*felem_square) (void *out,
578 void (*felem_mul) (void *out,
583 void (*felem_inv) (void *out,
586 void (*felem_contract) (void
591 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
592 unsigned char *digit, unsigned char in);
594 int ec_group_simple_order_bits(const EC_GROUP *group);
596 #ifdef ECP_NISTZ256_ASM
597 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
598 * P256. See http://eprint.iacr.org/2013/816.
599 * \return EC_METHOD object
601 const EC_METHOD *EC_GFp_nistz256_method(void);
604 const EC_METHOD *EC_GFp_s390x_nistp256_method(void);
605 const EC_METHOD *EC_GFp_s390x_nistp384_method(void);
606 const EC_METHOD *EC_GFp_s390x_nistp521_method(void);
609 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
610 unsigned char *buf, size_t len);
611 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
612 int ec_key_simple_generate_key(EC_KEY *eckey);
613 int ec_key_simple_generate_public_key(EC_KEY *eckey);
614 int ec_key_simple_check_key(const EC_KEY *eckey);
616 int ec_curve_nid_from_params(const EC_GROUP *group, BN_CTX *ctx);
618 /* EC_METHOD definitions */
620 struct ec_key_method_st {
623 int (*init)(EC_KEY *key);
624 void (*finish)(EC_KEY *key);
625 int (*copy)(EC_KEY *dest, const EC_KEY *src);
626 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
627 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
628 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
629 int (*keygen)(EC_KEY *key);
630 int (*compute_key)(unsigned char **pout, size_t *poutlen,
631 const EC_POINT *pub_key, const EC_KEY *ecdh);
632 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
633 *sig, unsigned int *siglen, const BIGNUM *kinv,
634 const BIGNUM *r, EC_KEY *eckey);
635 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
637 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
638 const BIGNUM *in_kinv, const BIGNUM *in_r,
641 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
642 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
643 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
644 const ECDSA_SIG *sig, EC_KEY *eckey);
647 #define EC_KEY_METHOD_DYNAMIC 1
649 EC_KEY *ec_key_new_method_int(OPENSSL_CTX *libctx, ENGINE *engine);
651 int ossl_ec_key_gen(EC_KEY *eckey);
652 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
653 const EC_POINT *pub_key, const EC_KEY *ecdh);
654 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
655 const EC_POINT *pub_key, const EC_KEY *ecdh);
657 struct ECDSA_SIG_st {
662 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
664 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
665 unsigned char *sig, unsigned int *siglen,
666 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
667 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
668 const BIGNUM *in_kinv, const BIGNUM *in_r,
670 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
671 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
672 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
673 const ECDSA_SIG *sig, EC_KEY *eckey);
674 int ecdsa_simple_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
676 ECDSA_SIG *ecdsa_simple_sign_sig(const unsigned char *dgst, int dgst_len,
677 const BIGNUM *in_kinv, const BIGNUM *in_r,
679 int ecdsa_simple_verify_sig(const unsigned char *dgst, int dgst_len,
680 const ECDSA_SIG *sig, EC_KEY *eckey);
682 void ED25519_public_from_private(uint8_t out_public_key[32],
683 const uint8_t private_key[32]);
686 * This functions computes a single point multiplication over the EC group,
687 * using, at a high level, a Montgomery ladder with conditional swaps, with
688 * various timing attack defenses.
690 * It performs either a fixed point multiplication
691 * (scalar * generator)
692 * when point is NULL, or a variable point multiplication
694 * when point is not NULL.
696 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
697 * constant time bets are off (where n is the cardinality of the EC group).
699 * This function expects `group->order` and `group->cardinality` to be well
700 * defined and non-zero: it fails with an error code otherwise.
702 * NB: This says nothing about the constant-timeness of the ladder step
703 * implementation (i.e., the default implementation is based on EC_POINT_add and
704 * EC_POINT_dbl, which of course are not constant time themselves) or the
705 * underlying multiprecision arithmetic.
707 * The product is stored in `r`.
709 * This is an internal function: callers are in charge of ensuring that the
710 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
712 * Returns 1 on success, 0 otherwise.
714 int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
715 const BIGNUM *scalar, const EC_POINT *point,
718 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
720 static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group,
721 EC_POINT *r, EC_POINT *s,
722 EC_POINT *p, BN_CTX *ctx)
724 if (group->meth->ladder_pre != NULL)
725 return group->meth->ladder_pre(group, r, s, p, ctx);
727 if (!EC_POINT_copy(s, p)
728 || !EC_POINT_dbl(group, r, s, ctx))
734 static ossl_inline int ec_point_ladder_step(const EC_GROUP *group,
735 EC_POINT *r, EC_POINT *s,
736 EC_POINT *p, BN_CTX *ctx)
738 if (group->meth->ladder_step != NULL)
739 return group->meth->ladder_step(group, r, s, p, ctx);
741 if (!EC_POINT_add(group, s, r, s, ctx)
742 || !EC_POINT_dbl(group, r, r, ctx))
749 static ossl_inline int ec_point_ladder_post(const EC_GROUP *group,
750 EC_POINT *r, EC_POINT *s,
751 EC_POINT *p, BN_CTX *ctx)
753 if (group->meth->ladder_post != NULL)
754 return group->meth->ladder_post(group, r, s, p, ctx);