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"
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, EC_GROUP_get_curve: */
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,
76 * EC_POINT_get_affine_coordinates,
77 * EC_POINT_set_compressed_coordinates:
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);
180 int (*ladder_pre)(const EC_GROUP *group,
181 EC_POINT *r, EC_POINT *s,
182 EC_POINT *p, BN_CTX *ctx);
183 int (*ladder_step)(const EC_GROUP *group,
184 EC_POINT *r, EC_POINT *s,
185 EC_POINT *p, BN_CTX *ctx);
186 int (*ladder_post)(const EC_GROUP *group,
187 EC_POINT *r, EC_POINT *s,
188 EC_POINT *p, BN_CTX *ctx);
192 * Types and functions to manipulate pre-computed values.
194 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
195 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
196 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
197 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
198 typedef struct ec_pre_comp_st EC_PRE_COMP;
201 const EC_METHOD *meth;
202 EC_POINT *generator; /* optional */
203 BIGNUM *order, *cofactor;
204 int curve_name; /* optional NID for named curve */
205 int asn1_flag; /* flag to control the asn1 encoding */
206 point_conversion_form_t asn1_form;
207 unsigned char *seed; /* optional seed for parameters (appears in
211 * The following members are handled by the method functions, even if
212 * they appear generic
215 * Field specification. For curves over GF(p), this is the modulus; for
216 * curves over GF(2^m), this is the irreducible polynomial defining the
221 * Field specification for curves over GF(2^m). The irreducible f(t) is
222 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
223 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
224 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
229 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
230 * or abused for all kinds of fields, not just GF(p).) For characteristic
231 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
232 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
233 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
236 /* enable optimized point arithmetics for special case */
238 /* method-specific (e.g., Montgomery structure) */
240 /* method-specific */
242 /* method-specific */
243 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
245 /* data for ECDSA inverse */
246 BN_MONT_CTX *mont_data;
249 * Precomputed values for speed. The PCT_xxx names match the
250 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
255 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,
259 NISTP224_PRE_COMP *nistp224;
260 NISTP256_PRE_COMP *nistp256;
261 NISTP521_PRE_COMP *nistp521;
262 NISTZ256_PRE_COMP *nistz256;
267 #define SETPRECOMP(g, type, pre) \
268 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
269 #define HAVEPRECOMP(g, type) \
270 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
273 const EC_KEY_METHOD *meth;
279 unsigned int enc_flag;
280 point_conversion_form_t conv_form;
281 CRYPTO_REF_COUNT references;
283 CRYPTO_EX_DATA ex_data;
288 const EC_METHOD *meth;
289 /* NID for the curve if known */
292 * All members except 'meth' are handled by the method functions, even if
293 * they appear generic
297 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
298 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
299 int Z_is_one; /* enable optimized point arithmetics for
303 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
304 const EC_GROUP *group)
306 if (group->meth != point->meth
307 || (group->curve_name != 0
308 && point->curve_name != 0
309 && group->curve_name != point->curve_name))
315 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
316 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
317 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
318 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
319 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
320 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
322 void EC_pre_comp_free(EC_GROUP *group);
323 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
324 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
325 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
326 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
327 void EC_ec_pre_comp_free(EC_PRE_COMP *);
330 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
331 * group->method->mul is 0)
333 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
334 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
336 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
337 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
339 /* method functions in ecp_smpl.c */
340 int ec_GFp_simple_group_init(EC_GROUP *);
341 void ec_GFp_simple_group_finish(EC_GROUP *);
342 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
343 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
344 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
345 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
346 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
347 BIGNUM *b, BN_CTX *);
348 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
349 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
350 int ec_GFp_simple_point_init(EC_POINT *);
351 void ec_GFp_simple_point_finish(EC_POINT *);
352 void ec_GFp_simple_point_clear_finish(EC_POINT *);
353 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
354 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
355 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
356 EC_POINT *, const BIGNUM *x,
358 const BIGNUM *z, BN_CTX *);
359 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
360 const EC_POINT *, BIGNUM *x,
361 BIGNUM *y, BIGNUM *z,
363 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
365 const BIGNUM *y, BN_CTX *);
366 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
367 const EC_POINT *, BIGNUM *x,
368 BIGNUM *y, BN_CTX *);
369 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
370 const BIGNUM *x, int y_bit,
372 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
373 point_conversion_form_t form,
374 unsigned char *buf, size_t len, BN_CTX *);
375 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
376 const unsigned char *buf, size_t len, BN_CTX *);
377 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
378 const EC_POINT *b, BN_CTX *);
379 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
381 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
382 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
383 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
384 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
386 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
387 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
388 EC_POINT *[], BN_CTX *);
389 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
390 const BIGNUM *b, BN_CTX *);
391 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
393 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
395 int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
396 EC_POINT *r, EC_POINT *s,
397 EC_POINT *p, BN_CTX *ctx);
398 int ec_GFp_simple_ladder_step(const EC_GROUP *group,
399 EC_POINT *r, EC_POINT *s,
400 EC_POINT *p, BN_CTX *ctx);
401 int ec_GFp_simple_ladder_post(const EC_GROUP *group,
402 EC_POINT *r, EC_POINT *s,
403 EC_POINT *p, BN_CTX *ctx);
405 /* method functions in ecp_mont.c */
406 int ec_GFp_mont_group_init(EC_GROUP *);
407 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
408 const BIGNUM *b, BN_CTX *);
409 void ec_GFp_mont_group_finish(EC_GROUP *);
410 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
411 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
412 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
413 const BIGNUM *b, BN_CTX *);
414 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
416 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
418 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
420 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
422 /* method functions in ecp_nist.c */
423 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
424 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
425 const BIGNUM *b, BN_CTX *);
426 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
427 const BIGNUM *b, BN_CTX *);
428 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
431 /* method functions in ec2_smpl.c */
432 int ec_GF2m_simple_group_init(EC_GROUP *);
433 void ec_GF2m_simple_group_finish(EC_GROUP *);
434 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
435 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
436 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
437 const BIGNUM *a, const BIGNUM *b,
439 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
440 BIGNUM *b, BN_CTX *);
441 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
442 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
443 int ec_GF2m_simple_point_init(EC_POINT *);
444 void ec_GF2m_simple_point_finish(EC_POINT *);
445 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
446 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
447 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
448 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
450 const BIGNUM *y, BN_CTX *);
451 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
452 const EC_POINT *, BIGNUM *x,
453 BIGNUM *y, BN_CTX *);
454 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
455 const BIGNUM *x, int y_bit,
457 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
458 point_conversion_form_t form,
459 unsigned char *buf, size_t len, BN_CTX *);
460 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
461 const unsigned char *buf, size_t len, BN_CTX *);
462 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
463 const EC_POINT *b, BN_CTX *);
464 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
466 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
467 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
468 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
469 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
471 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
472 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
473 EC_POINT *[], BN_CTX *);
474 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
475 const BIGNUM *b, BN_CTX *);
476 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
478 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
479 const BIGNUM *b, BN_CTX *);
481 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
482 /* method functions in ecp_nistp224.c */
483 int ec_GFp_nistp224_group_init(EC_GROUP *group);
484 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
485 const BIGNUM *a, const BIGNUM *n,
487 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
488 const EC_POINT *point,
489 BIGNUM *x, BIGNUM *y,
491 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
492 const BIGNUM *scalar, size_t num,
493 const EC_POINT *points[], const BIGNUM *scalars[],
495 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
496 const BIGNUM *scalar, size_t num,
497 const EC_POINT *points[],
498 const BIGNUM *scalars[], BN_CTX *ctx);
499 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
500 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
502 /* method functions in ecp_nistp256.c */
503 int ec_GFp_nistp256_group_init(EC_GROUP *group);
504 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
505 const BIGNUM *a, const BIGNUM *n,
507 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
508 const EC_POINT *point,
509 BIGNUM *x, BIGNUM *y,
511 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
512 const BIGNUM *scalar, size_t num,
513 const EC_POINT *points[], const BIGNUM *scalars[],
515 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
516 const BIGNUM *scalar, size_t num,
517 const EC_POINT *points[],
518 const BIGNUM *scalars[], BN_CTX *ctx);
519 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
520 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
522 /* method functions in ecp_nistp521.c */
523 int ec_GFp_nistp521_group_init(EC_GROUP *group);
524 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
525 const BIGNUM *a, const BIGNUM *n,
527 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
528 const EC_POINT *point,
529 BIGNUM *x, BIGNUM *y,
531 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
532 const BIGNUM *scalar, size_t num,
533 const EC_POINT *points[], const BIGNUM *scalars[],
535 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
536 const BIGNUM *scalar, size_t num,
537 const EC_POINT *points[],
538 const BIGNUM *scalars[], BN_CTX *ctx);
539 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
540 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
542 /* utility functions in ecp_nistputil.c */
543 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
546 void (*felem_one) (void *out),
547 int (*felem_is_zero) (const void
549 void (*felem_assign) (void *out,
552 void (*felem_square) (void *out,
555 void (*felem_mul) (void *out,
560 void (*felem_inv) (void *out,
563 void (*felem_contract) (void
568 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
569 unsigned char *digit, unsigned char in);
571 int ec_group_simple_order_bits(const EC_GROUP *group);
573 #ifdef ECP_NISTZ256_ASM
574 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
575 * P256. See http://eprint.iacr.org/2013/816.
576 * \return EC_METHOD object
578 const EC_METHOD *EC_GFp_nistz256_method(void);
581 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
582 unsigned char *buf, size_t len);
583 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
584 int ec_key_simple_generate_key(EC_KEY *eckey);
585 int ec_key_simple_generate_public_key(EC_KEY *eckey);
586 int ec_key_simple_check_key(const EC_KEY *eckey);
588 /* EC_METHOD definitions */
590 struct ec_key_method_st {
593 int (*init)(EC_KEY *key);
594 void (*finish)(EC_KEY *key);
595 int (*copy)(EC_KEY *dest, const EC_KEY *src);
596 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
597 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
598 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
599 int (*keygen)(EC_KEY *key);
600 int (*compute_key)(unsigned char **pout, size_t *poutlen,
601 const EC_POINT *pub_key, const EC_KEY *ecdh);
602 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
603 *sig, unsigned int *siglen, const BIGNUM *kinv,
604 const BIGNUM *r, EC_KEY *eckey);
605 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
607 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
608 const BIGNUM *in_kinv, const BIGNUM *in_r,
611 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
612 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
613 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
614 const ECDSA_SIG *sig, EC_KEY *eckey);
617 #define EC_KEY_METHOD_DYNAMIC 1
619 int ossl_ec_key_gen(EC_KEY *eckey);
620 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
621 const EC_POINT *pub_key, const EC_KEY *ecdh);
622 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
623 const EC_POINT *pub_key, const EC_KEY *ecdh);
625 struct ECDSA_SIG_st {
630 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
632 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
633 unsigned char *sig, unsigned int *siglen,
634 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
635 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
636 const BIGNUM *in_kinv, const BIGNUM *in_r,
638 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
639 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
640 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
641 const ECDSA_SIG *sig, EC_KEY *eckey);
643 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
644 const uint8_t public_key[32], const uint8_t private_key[32]);
645 int ED25519_verify(const uint8_t *message, size_t message_len,
646 const uint8_t signature[64], const uint8_t public_key[32]);
647 void ED25519_public_from_private(uint8_t out_public_key[32],
648 const uint8_t private_key[32]);
650 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
651 const uint8_t peer_public_value[32]);
652 void X25519_public_from_private(uint8_t out_public_value[32],
653 const uint8_t private_key[32]);
656 * This functions computes a single point multiplication over the EC group,
657 * using, at a high level, a Montgomery ladder with conditional swaps, with
658 * various timing attack defenses.
660 * It performs either a fixed point multiplication
661 * (scalar * generator)
662 * when point is NULL, or a variable point multiplication
664 * when point is not NULL.
666 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
667 * constant time bets are off (where n is the cardinality of the EC group).
669 * This function expects `group->order` and `group->cardinality` to be well
670 * defined and non-zero: it fails with an error code otherwise.
672 * NB: This says nothing about the constant-timeness of the ladder step
673 * implementation (i.e., the default implementation is based on EC_POINT_add and
674 * EC_POINT_dbl, which of course are not constant time themselves) or the
675 * underlying multiprecision arithmetic.
677 * The product is stored in `r`.
679 * This is an internal function: callers are in charge of ensuring that the
680 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
682 * Returns 1 on success, 0 otherwise.
684 int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
685 const BIGNUM *scalar, const EC_POINT *point,
688 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
690 static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group,
691 EC_POINT *r, EC_POINT *s,
692 EC_POINT *p, BN_CTX *ctx)
694 if (group->meth->ladder_pre != NULL)
695 return group->meth->ladder_pre(group, r, s, p, ctx);
697 if (!EC_POINT_copy(s, p)
698 || !EC_POINT_dbl(group, r, s, ctx))
704 static ossl_inline int ec_point_ladder_step(const EC_GROUP *group,
705 EC_POINT *r, EC_POINT *s,
706 EC_POINT *p, BN_CTX *ctx)
708 if (group->meth->ladder_step != NULL)
709 return group->meth->ladder_step(group, r, s, p, ctx);
711 if (!EC_POINT_add(group, s, r, s, ctx)
712 || !EC_POINT_dbl(group, r, r, ctx))
719 static ossl_inline int ec_point_ladder_post(const EC_GROUP *group,
720 EC_POINT *r, EC_POINT *s,
721 EC_POINT *p, BN_CTX *ctx)
723 if (group->meth->ladder_post != NULL)
724 return group->meth->ladder_post(group, r, s, p, ctx);