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 "internal/ec_int.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 multipicative 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);
182 /* Inverse modulo order */
183 int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r,
184 const BIGNUM *x, BN_CTX *);
185 int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
186 int (*ladder_pre)(const EC_GROUP *group,
187 EC_POINT *r, EC_POINT *s,
188 EC_POINT *p, BN_CTX *ctx);
189 int (*ladder_step)(const EC_GROUP *group,
190 EC_POINT *r, EC_POINT *s,
191 EC_POINT *p, BN_CTX *ctx);
192 int (*ladder_post)(const EC_GROUP *group,
193 EC_POINT *r, EC_POINT *s,
194 EC_POINT *p, BN_CTX *ctx);
198 * Types and functions to manipulate pre-computed values.
200 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
201 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
202 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
203 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
204 typedef struct ec_pre_comp_st EC_PRE_COMP;
207 const EC_METHOD *meth;
208 EC_POINT *generator; /* optional */
209 BIGNUM *order, *cofactor;
210 int curve_name; /* optional NID for named curve */
211 int asn1_flag; /* flag to control the asn1 encoding */
212 point_conversion_form_t asn1_form;
213 unsigned char *seed; /* optional seed for parameters (appears in
217 * The following members are handled by the method functions, even if
218 * they appear generic
221 * Field specification. For curves over GF(p), this is the modulus; for
222 * curves over GF(2^m), this is the irreducible polynomial defining the
227 * Field specification for curves over GF(2^m). The irreducible f(t) is
228 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
229 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
230 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
235 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
236 * or abused for all kinds of fields, not just GF(p).) For characteristic
237 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
238 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
239 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
242 /* enable optimized point arithmetics for special case */
244 /* method-specific (e.g., Montgomery structure) */
246 /* method-specific */
248 /* method-specific */
249 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
251 /* data for ECDSA inverse */
252 BN_MONT_CTX *mont_data;
255 * Precomputed values for speed. The PCT_xxx names match the
256 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
261 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,
265 NISTP224_PRE_COMP *nistp224;
266 NISTP256_PRE_COMP *nistp256;
267 NISTP521_PRE_COMP *nistp521;
268 NISTZ256_PRE_COMP *nistz256;
273 #define SETPRECOMP(g, type, pre) \
274 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
275 #define HAVEPRECOMP(g, type) \
276 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
279 const EC_KEY_METHOD *meth;
285 unsigned int enc_flag;
286 point_conversion_form_t conv_form;
287 CRYPTO_REF_COUNT references;
289 CRYPTO_EX_DATA ex_data;
294 const EC_METHOD *meth;
295 /* NID for the curve if known */
298 * All members except 'meth' are handled by the method functions, even if
299 * they appear generic
303 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
304 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
305 int Z_is_one; /* enable optimized point arithmetics for
309 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
310 const EC_GROUP *group)
312 return group->meth == point->meth
313 && (group->curve_name == 0
314 || point->curve_name == 0
315 || group->curve_name == point->curve_name);
318 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
319 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
320 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
321 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
322 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
323 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
325 void EC_pre_comp_free(EC_GROUP *group);
326 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
327 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
328 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
329 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
330 void EC_ec_pre_comp_free(EC_PRE_COMP *);
333 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
334 * group->method->mul is 0)
336 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
337 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
339 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
340 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
342 /* method functions in ecp_smpl.c */
343 int ec_GFp_simple_group_init(EC_GROUP *);
344 void ec_GFp_simple_group_finish(EC_GROUP *);
345 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
346 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
347 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
348 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
349 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
350 BIGNUM *b, BN_CTX *);
351 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
352 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
353 int ec_GFp_simple_point_init(EC_POINT *);
354 void ec_GFp_simple_point_finish(EC_POINT *);
355 void ec_GFp_simple_point_clear_finish(EC_POINT *);
356 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
357 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
358 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
359 EC_POINT *, const BIGNUM *x,
361 const BIGNUM *z, BN_CTX *);
362 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
363 const EC_POINT *, BIGNUM *x,
364 BIGNUM *y, BIGNUM *z,
366 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
368 const BIGNUM *y, BN_CTX *);
369 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
370 const EC_POINT *, BIGNUM *x,
371 BIGNUM *y, BN_CTX *);
372 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
373 const BIGNUM *x, int y_bit,
375 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
376 point_conversion_form_t form,
377 unsigned char *buf, size_t len, BN_CTX *);
378 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
379 const unsigned char *buf, size_t len, BN_CTX *);
380 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
381 const EC_POINT *b, BN_CTX *);
382 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
384 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
385 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
386 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
387 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
389 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
390 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
391 EC_POINT *[], BN_CTX *);
392 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
393 const BIGNUM *b, BN_CTX *);
394 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
396 int ec_GFp_simple_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
398 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
400 int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
401 EC_POINT *r, EC_POINT *s,
402 EC_POINT *p, BN_CTX *ctx);
403 int ec_GFp_simple_ladder_step(const EC_GROUP *group,
404 EC_POINT *r, EC_POINT *s,
405 EC_POINT *p, BN_CTX *ctx);
406 int ec_GFp_simple_ladder_post(const EC_GROUP *group,
407 EC_POINT *r, EC_POINT *s,
408 EC_POINT *p, BN_CTX *ctx);
410 /* method functions in ecp_mont.c */
411 int ec_GFp_mont_group_init(EC_GROUP *);
412 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
413 const BIGNUM *b, BN_CTX *);
414 void ec_GFp_mont_group_finish(EC_GROUP *);
415 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
416 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
417 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
418 const BIGNUM *b, BN_CTX *);
419 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
421 int ec_GFp_mont_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
423 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
425 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
427 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
429 /* method functions in ecp_nist.c */
430 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
431 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
432 const BIGNUM *b, BN_CTX *);
433 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
434 const BIGNUM *b, BN_CTX *);
435 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
438 /* method functions in ec2_smpl.c */
439 int ec_GF2m_simple_group_init(EC_GROUP *);
440 void ec_GF2m_simple_group_finish(EC_GROUP *);
441 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
442 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
443 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
444 const BIGNUM *a, const BIGNUM *b,
446 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
447 BIGNUM *b, BN_CTX *);
448 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
449 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
450 int ec_GF2m_simple_point_init(EC_POINT *);
451 void ec_GF2m_simple_point_finish(EC_POINT *);
452 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
453 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
454 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
455 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
457 const BIGNUM *y, BN_CTX *);
458 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
459 const EC_POINT *, BIGNUM *x,
460 BIGNUM *y, BN_CTX *);
461 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
462 const BIGNUM *x, int y_bit,
464 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
465 point_conversion_form_t form,
466 unsigned char *buf, size_t len, BN_CTX *);
467 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
468 const unsigned char *buf, size_t len, BN_CTX *);
469 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
470 const EC_POINT *b, BN_CTX *);
471 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
473 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
474 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
475 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
476 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
478 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
479 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
480 EC_POINT *[], BN_CTX *);
481 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
482 const BIGNUM *b, BN_CTX *);
483 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
485 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
486 const BIGNUM *b, BN_CTX *);
488 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
489 /* method functions in ecp_nistp224.c */
490 int ec_GFp_nistp224_group_init(EC_GROUP *group);
491 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
492 const BIGNUM *a, const BIGNUM *n,
494 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
495 const EC_POINT *point,
496 BIGNUM *x, BIGNUM *y,
498 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
499 const BIGNUM *scalar, size_t num,
500 const EC_POINT *points[], const BIGNUM *scalars[],
502 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
503 const BIGNUM *scalar, size_t num,
504 const EC_POINT *points[],
505 const BIGNUM *scalars[], BN_CTX *ctx);
506 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
507 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
509 /* method functions in ecp_nistp256.c */
510 int ec_GFp_nistp256_group_init(EC_GROUP *group);
511 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
512 const BIGNUM *a, const BIGNUM *n,
514 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
515 const EC_POINT *point,
516 BIGNUM *x, BIGNUM *y,
518 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
519 const BIGNUM *scalar, size_t num,
520 const EC_POINT *points[], const BIGNUM *scalars[],
522 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
523 const BIGNUM *scalar, size_t num,
524 const EC_POINT *points[],
525 const BIGNUM *scalars[], BN_CTX *ctx);
526 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
527 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
529 /* method functions in ecp_nistp521.c */
530 int ec_GFp_nistp521_group_init(EC_GROUP *group);
531 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
532 const BIGNUM *a, const BIGNUM *n,
534 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
535 const EC_POINT *point,
536 BIGNUM *x, BIGNUM *y,
538 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
539 const BIGNUM *scalar, size_t num,
540 const EC_POINT *points[], const BIGNUM *scalars[],
542 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
543 const BIGNUM *scalar, size_t num,
544 const EC_POINT *points[],
545 const BIGNUM *scalars[], BN_CTX *ctx);
546 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
547 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
549 /* utility functions in ecp_nistputil.c */
550 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
553 void (*felem_one) (void *out),
554 int (*felem_is_zero) (const void
556 void (*felem_assign) (void *out,
559 void (*felem_square) (void *out,
562 void (*felem_mul) (void *out,
567 void (*felem_inv) (void *out,
570 void (*felem_contract) (void
575 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
576 unsigned char *digit, unsigned char in);
578 int ec_group_simple_order_bits(const EC_GROUP *group);
580 #ifdef ECP_NISTZ256_ASM
581 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
582 * P256. See http://eprint.iacr.org/2013/816.
583 * \return EC_METHOD object
585 const EC_METHOD *EC_GFp_nistz256_method(void);
588 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
589 unsigned char *buf, size_t len);
590 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
591 int ec_key_simple_generate_key(EC_KEY *eckey);
592 int ec_key_simple_generate_public_key(EC_KEY *eckey);
593 int ec_key_simple_check_key(const EC_KEY *eckey);
595 int ec_curve_nid_from_params(const EC_GROUP *group);
597 /* EC_METHOD definitions */
599 struct ec_key_method_st {
602 int (*init)(EC_KEY *key);
603 void (*finish)(EC_KEY *key);
604 int (*copy)(EC_KEY *dest, const EC_KEY *src);
605 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
606 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
607 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
608 int (*keygen)(EC_KEY *key);
609 int (*compute_key)(unsigned char **pout, size_t *poutlen,
610 const EC_POINT *pub_key, const EC_KEY *ecdh);
611 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
612 *sig, unsigned int *siglen, const BIGNUM *kinv,
613 const BIGNUM *r, EC_KEY *eckey);
614 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
616 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
617 const BIGNUM *in_kinv, const BIGNUM *in_r,
620 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
621 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
622 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
623 const ECDSA_SIG *sig, EC_KEY *eckey);
626 #define EC_KEY_METHOD_DYNAMIC 1
628 int ossl_ec_key_gen(EC_KEY *eckey);
629 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
630 const EC_POINT *pub_key, const EC_KEY *ecdh);
631 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
632 const EC_POINT *pub_key, const EC_KEY *ecdh);
634 struct ECDSA_SIG_st {
639 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
641 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
642 unsigned char *sig, unsigned int *siglen,
643 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
644 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
645 const BIGNUM *in_kinv, const BIGNUM *in_r,
647 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
648 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
649 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
650 const ECDSA_SIG *sig, EC_KEY *eckey);
652 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
653 const uint8_t public_key[32], const uint8_t private_key[32]);
654 int ED25519_verify(const uint8_t *message, size_t message_len,
655 const uint8_t signature[64], const uint8_t public_key[32]);
656 void ED25519_public_from_private(uint8_t out_public_key[32],
657 const uint8_t private_key[32]);
659 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
660 const uint8_t peer_public_value[32]);
661 void X25519_public_from_private(uint8_t out_public_value[32],
662 const uint8_t private_key[32]);
665 * This functions computes a single point multiplication over the EC group,
666 * using, at a high level, a Montgomery ladder with conditional swaps, with
667 * various timing attack defenses.
669 * It performs either a fixed point multiplication
670 * (scalar * generator)
671 * when point is NULL, or a variable point multiplication
673 * when point is not NULL.
675 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
676 * constant time bets are off (where n is the cardinality of the EC group).
678 * This function expects `group->order` and `group->cardinality` to be well
679 * defined and non-zero: it fails with an error code otherwise.
681 * NB: This says nothing about the constant-timeness of the ladder step
682 * implementation (i.e., the default implementation is based on EC_POINT_add and
683 * EC_POINT_dbl, which of course are not constant time themselves) or the
684 * underlying multiprecision arithmetic.
686 * The product is stored in `r`.
688 * This is an internal function: callers are in charge of ensuring that the
689 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
691 * Returns 1 on success, 0 otherwise.
693 int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
694 const BIGNUM *scalar, const EC_POINT *point,
697 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
699 static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group,
700 EC_POINT *r, EC_POINT *s,
701 EC_POINT *p, BN_CTX *ctx)
703 if (group->meth->ladder_pre != NULL)
704 return group->meth->ladder_pre(group, r, s, p, ctx);
706 if (!EC_POINT_copy(s, p)
707 || !EC_POINT_dbl(group, r, s, ctx))
713 static ossl_inline int ec_point_ladder_step(const EC_GROUP *group,
714 EC_POINT *r, EC_POINT *s,
715 EC_POINT *p, BN_CTX *ctx)
717 if (group->meth->ladder_step != NULL)
718 return group->meth->ladder_step(group, r, s, p, ctx);
720 if (!EC_POINT_add(group, s, r, s, ctx)
721 || !EC_POINT_dbl(group, r, r, ctx))
728 static ossl_inline int ec_point_ladder_post(const EC_GROUP *group,
729 EC_POINT *r, EC_POINT *s,
730 EC_POINT *p, BN_CTX *ctx)
732 if (group->meth->ladder_post != NULL)
733 return group->meth->ladder_post(group, r, s, p, ctx);