2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
13 #include <openssl/obj_mac.h>
14 #include <openssl/ec.h>
15 #include <openssl/bn.h>
16 #include "internal/refcount.h"
17 #include "internal/ec_int.h"
18 #include "curve448/curve448_lcl.h"
20 #if defined(__SUNPRO_C)
21 # if __SUNPRO_C >= 0x520
22 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
26 /* Use default functions for poin2oct, oct2point and compressed coordinates */
27 #define EC_FLAGS_DEFAULT_OCT 0x1
29 /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */
30 #define EC_FLAGS_CUSTOM_CURVE 0x2
32 /* Curve does not support signing operations */
33 #define EC_FLAGS_NO_SIGN 0x4
36 * Structure details are not part of the exported interface, so all this may
37 * change in future versions.
41 /* Various method flags */
43 /* used by EC_METHOD_get_field_type: */
44 int field_type; /* a NID */
46 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
49 int (*group_init) (EC_GROUP *);
50 void (*group_finish) (EC_GROUP *);
51 void (*group_clear_finish) (EC_GROUP *);
52 int (*group_copy) (EC_GROUP *, const EC_GROUP *);
53 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
54 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
55 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
56 const BIGNUM *b, BN_CTX *);
57 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
59 /* used by EC_GROUP_get_degree: */
60 int (*group_get_degree) (const EC_GROUP *);
61 int (*group_order_bits) (const EC_GROUP *);
62 /* used by EC_GROUP_check: */
63 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
65 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
68 int (*point_init) (EC_POINT *);
69 void (*point_finish) (EC_POINT *);
70 void (*point_clear_finish) (EC_POINT *);
71 int (*point_copy) (EC_POINT *, const EC_POINT *);
73 * used by EC_POINT_set_to_infinity,
74 * EC_POINT_set_Jprojective_coordinates_GFp,
75 * EC_POINT_get_Jprojective_coordinates_GFp,
76 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
77 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
78 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
80 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
81 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
82 EC_POINT *, const BIGNUM *x,
84 const BIGNUM *z, BN_CTX *);
85 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
86 const EC_POINT *, BIGNUM *x,
89 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
90 const BIGNUM *x, const BIGNUM *y,
92 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
93 BIGNUM *x, BIGNUM *y, BN_CTX *);
94 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
95 const BIGNUM *x, int y_bit,
97 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
98 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
99 point_conversion_form_t form, unsigned char *buf,
100 size_t len, BN_CTX *);
101 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
102 size_t len, BN_CTX *);
103 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
104 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
105 const EC_POINT *b, BN_CTX *);
106 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
107 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
109 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
111 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
112 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
113 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
115 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
116 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
117 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
120 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
121 * EC_POINT_have_precompute_mult (default implementations are used if the
122 * 'mul' pointer is 0):
125 * mul() calculates the value
127 * r := generator * scalar
128 * + points[0] * scalars[0]
130 * + points[num-1] * scalars[num-1].
132 * For a fixed point multiplication (scalar != NULL, num == 0)
133 * or a variable point multiplication (scalar == NULL, num == 1),
134 * mul() must use a constant time algorithm: in both cases callers
135 * should provide an input scalar (either scalar or scalars[0])
136 * in the range [0, ec_group_order); for robustness, implementers
137 * should handle the case when the scalar has not been reduced, but
138 * may treat it as an unusual input, without any constant-timeness
141 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
142 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
144 int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
145 int (*have_precompute_mult) (const EC_GROUP *group);
146 /* internal functions */
148 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
149 * 'dbl' so that the same implementations of point operations can be used
150 * with different optimized implementations of expensive field
153 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
154 const BIGNUM *b, BN_CTX *);
155 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
156 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
157 const BIGNUM *b, BN_CTX *);
158 /* e.g. to Montgomery */
159 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
161 /* e.g. from Montgomery */
162 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
164 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
165 /* private key operations */
166 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len);
167 int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len);
168 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key);
169 int (*keygen)(EC_KEY *eckey);
170 int (*keycheck)(const EC_KEY *eckey);
171 int (*keygenpub)(EC_KEY *eckey);
172 int (*keycopy)(EC_KEY *dst, const EC_KEY *src);
173 void (*keyfinish)(EC_KEY *eckey);
174 /* custom ECDH operation */
175 int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,
176 const EC_POINT *pub_key, const EC_KEY *ecdh);
177 /* Inverse modulo order */
178 int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r,
179 const BIGNUM *x, BN_CTX *);
180 int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
181 int (*ladder_pre)(const EC_GROUP *group,
182 EC_POINT *r, EC_POINT *s,
183 EC_POINT *p, BN_CTX *ctx);
184 int (*ladder_step)(const EC_GROUP *group,
185 EC_POINT *r, EC_POINT *s,
186 EC_POINT *p, BN_CTX *ctx);
187 int (*ladder_post)(const EC_GROUP *group,
188 EC_POINT *r, EC_POINT *s,
189 EC_POINT *p, BN_CTX *ctx);
193 * Types and functions to manipulate pre-computed values.
195 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP;
196 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP;
197 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP;
198 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP;
199 typedef struct ec_pre_comp_st EC_PRE_COMP;
202 const EC_METHOD *meth;
203 EC_POINT *generator; /* optional */
204 BIGNUM *order, *cofactor;
205 int curve_name; /* optional NID for named curve */
206 int asn1_flag; /* flag to control the asn1 encoding */
207 point_conversion_form_t asn1_form;
208 unsigned char *seed; /* optional seed for parameters (appears in
212 * The following members are handled by the method functions, even if
213 * they appear generic
216 * Field specification. For curves over GF(p), this is the modulus; for
217 * curves over GF(2^m), this is the irreducible polynomial defining the
222 * Field specification for curves over GF(2^m). The irreducible f(t) is
223 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
224 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
225 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
230 * Curve coefficients. (Here the assumption is that BIGNUMs can be used
231 * or abused for all kinds of fields, not just GF(p).) For characteristic
232 * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
233 * x^3 + a*x + b. For characteristic 2, the curve is defined by an
234 * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
237 /* enable optimized point arithmetics for special case */
239 /* method-specific (e.g., Montgomery structure) */
241 /* method-specific */
243 /* method-specific */
244 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
246 /* data for ECDSA inverse */
247 BN_MONT_CTX *mont_data;
250 * Precomputed values for speed. The PCT_xxx names match the
251 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP
256 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256,
260 NISTP224_PRE_COMP *nistp224;
261 NISTP256_PRE_COMP *nistp256;
262 NISTP521_PRE_COMP *nistp521;
263 NISTZ256_PRE_COMP *nistz256;
268 #define SETPRECOMP(g, type, pre) \
269 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre
270 #define HAVEPRECOMP(g, type) \
271 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL
274 const EC_KEY_METHOD *meth;
280 unsigned int enc_flag;
281 point_conversion_form_t conv_form;
282 CRYPTO_REF_COUNT references;
284 CRYPTO_EX_DATA ex_data;
289 const EC_METHOD *meth;
290 /* NID for the curve if known */
293 * All members except 'meth' are handled by the method functions, even if
294 * they appear generic
298 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y,
299 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
300 int Z_is_one; /* enable optimized point arithmetics for
304 static ossl_inline int ec_point_is_compat(const EC_POINT *point,
305 const EC_GROUP *group)
307 if (group->meth != point->meth
308 || (group->curve_name != 0
309 && point->curve_name != 0
310 && group->curve_name != point->curve_name))
316 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *);
317 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
318 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *);
319 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *);
320 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *);
321 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *);
323 void EC_pre_comp_free(EC_GROUP *group);
324 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *);
325 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *);
326 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *);
327 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *);
328 void EC_ec_pre_comp_free(EC_PRE_COMP *);
331 * method functions in ec_mult.c (ec_lib.c uses these as defaults if
332 * group->method->mul is 0)
334 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
335 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
337 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
338 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
340 /* method functions in ecp_smpl.c */
341 int ec_GFp_simple_group_init(EC_GROUP *);
342 void ec_GFp_simple_group_finish(EC_GROUP *);
343 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
344 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
345 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
346 const BIGNUM *a, const BIGNUM *b, BN_CTX *);
347 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
348 BIGNUM *b, BN_CTX *);
349 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
350 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
351 int ec_GFp_simple_point_init(EC_POINT *);
352 void ec_GFp_simple_point_finish(EC_POINT *);
353 void ec_GFp_simple_point_clear_finish(EC_POINT *);
354 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
355 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
356 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
357 EC_POINT *, const BIGNUM *x,
359 const BIGNUM *z, BN_CTX *);
360 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
361 const EC_POINT *, BIGNUM *x,
362 BIGNUM *y, BIGNUM *z,
364 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
366 const BIGNUM *y, BN_CTX *);
367 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
368 const EC_POINT *, BIGNUM *x,
369 BIGNUM *y, BN_CTX *);
370 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
371 const BIGNUM *x, int y_bit,
373 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
374 point_conversion_form_t form,
375 unsigned char *buf, size_t len, BN_CTX *);
376 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
377 const unsigned char *buf, size_t len, BN_CTX *);
378 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
379 const EC_POINT *b, BN_CTX *);
380 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
382 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
383 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
384 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
385 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
387 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
388 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
389 EC_POINT *[], BN_CTX *);
390 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
391 const BIGNUM *b, BN_CTX *);
392 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
394 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
396 int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
397 EC_POINT *r, EC_POINT *s,
398 EC_POINT *p, BN_CTX *ctx);
399 int ec_GFp_simple_ladder_step(const EC_GROUP *group,
400 EC_POINT *r, EC_POINT *s,
401 EC_POINT *p, BN_CTX *ctx);
402 int ec_GFp_simple_ladder_post(const EC_GROUP *group,
403 EC_POINT *r, EC_POINT *s,
404 EC_POINT *p, BN_CTX *ctx);
406 /* method functions in ecp_mont.c */
407 int ec_GFp_mont_group_init(EC_GROUP *);
408 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
409 const BIGNUM *b, BN_CTX *);
410 void ec_GFp_mont_group_finish(EC_GROUP *);
411 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
412 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
413 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
414 const BIGNUM *b, BN_CTX *);
415 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
417 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
419 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
421 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
423 /* method functions in ecp_nist.c */
424 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
425 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
426 const BIGNUM *b, BN_CTX *);
427 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
428 const BIGNUM *b, BN_CTX *);
429 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
432 /* method functions in ec2_smpl.c */
433 int ec_GF2m_simple_group_init(EC_GROUP *);
434 void ec_GF2m_simple_group_finish(EC_GROUP *);
435 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
436 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
437 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
438 const BIGNUM *a, const BIGNUM *b,
440 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
441 BIGNUM *b, BN_CTX *);
442 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
443 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
444 int ec_GF2m_simple_point_init(EC_POINT *);
445 void ec_GF2m_simple_point_finish(EC_POINT *);
446 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
447 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
448 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
449 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
451 const BIGNUM *y, BN_CTX *);
452 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
453 const EC_POINT *, BIGNUM *x,
454 BIGNUM *y, BN_CTX *);
455 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
456 const BIGNUM *x, int y_bit,
458 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
459 point_conversion_form_t form,
460 unsigned char *buf, size_t len, BN_CTX *);
461 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
462 const unsigned char *buf, size_t len, BN_CTX *);
463 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
464 const EC_POINT *b, BN_CTX *);
465 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
467 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
468 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
469 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
470 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
472 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
473 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
474 EC_POINT *[], BN_CTX *);
475 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
476 const BIGNUM *b, BN_CTX *);
477 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
479 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
480 const BIGNUM *b, BN_CTX *);
482 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
483 /* method functions in ecp_nistp224.c */
484 int ec_GFp_nistp224_group_init(EC_GROUP *group);
485 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
486 const BIGNUM *a, const BIGNUM *n,
488 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
489 const EC_POINT *point,
490 BIGNUM *x, BIGNUM *y,
492 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
493 const BIGNUM *scalar, size_t num,
494 const EC_POINT *points[], const BIGNUM *scalars[],
496 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
497 const BIGNUM *scalar, size_t num,
498 const EC_POINT *points[],
499 const BIGNUM *scalars[], BN_CTX *ctx);
500 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
501 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
503 /* method functions in ecp_nistp256.c */
504 int ec_GFp_nistp256_group_init(EC_GROUP *group);
505 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
506 const BIGNUM *a, const BIGNUM *n,
508 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
509 const EC_POINT *point,
510 BIGNUM *x, BIGNUM *y,
512 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
513 const BIGNUM *scalar, size_t num,
514 const EC_POINT *points[], const BIGNUM *scalars[],
516 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
517 const BIGNUM *scalar, size_t num,
518 const EC_POINT *points[],
519 const BIGNUM *scalars[], BN_CTX *ctx);
520 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
521 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
523 /* method functions in ecp_nistp521.c */
524 int ec_GFp_nistp521_group_init(EC_GROUP *group);
525 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
526 const BIGNUM *a, const BIGNUM *n,
528 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
529 const EC_POINT *point,
530 BIGNUM *x, BIGNUM *y,
532 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
533 const BIGNUM *scalar, size_t num,
534 const EC_POINT *points[], const BIGNUM *scalars[],
536 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
537 const BIGNUM *scalar, size_t num,
538 const EC_POINT *points[],
539 const BIGNUM *scalars[], BN_CTX *ctx);
540 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
541 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
543 /* utility functions in ecp_nistputil.c */
544 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
547 void (*felem_one) (void *out),
548 int (*felem_is_zero) (const void
550 void (*felem_assign) (void *out,
553 void (*felem_square) (void *out,
556 void (*felem_mul) (void *out,
561 void (*felem_inv) (void *out,
564 void (*felem_contract) (void
569 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
570 unsigned char *digit, unsigned char in);
572 int ec_group_simple_order_bits(const EC_GROUP *group);
574 #ifdef ECP_NISTZ256_ASM
575 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
576 * P256. See http://eprint.iacr.org/2013/816.
577 * \return EC_METHOD object
579 const EC_METHOD *EC_GFp_nistz256_method(void);
582 size_t ec_key_simple_priv2oct(const EC_KEY *eckey,
583 unsigned char *buf, size_t len);
584 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len);
585 int ec_key_simple_generate_key(EC_KEY *eckey);
586 int ec_key_simple_generate_public_key(EC_KEY *eckey);
587 int ec_key_simple_check_key(const EC_KEY *eckey);
589 /* EC_METHOD definitions */
591 struct ec_key_method_st {
594 int (*init)(EC_KEY *key);
595 void (*finish)(EC_KEY *key);
596 int (*copy)(EC_KEY *dest, const EC_KEY *src);
597 int (*set_group)(EC_KEY *key, const EC_GROUP *grp);
598 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key);
599 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key);
600 int (*keygen)(EC_KEY *key);
601 int (*compute_key)(unsigned char **pout, size_t *poutlen,
602 const EC_POINT *pub_key, const EC_KEY *ecdh);
603 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char
604 *sig, unsigned int *siglen, const BIGNUM *kinv,
605 const BIGNUM *r, EC_KEY *eckey);
606 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
608 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len,
609 const BIGNUM *in_kinv, const BIGNUM *in_r,
612 int (*verify)(int type, const unsigned char *dgst, int dgst_len,
613 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
614 int (*verify_sig)(const unsigned char *dgst, int dgst_len,
615 const ECDSA_SIG *sig, EC_KEY *eckey);
618 #define EC_KEY_METHOD_DYNAMIC 1
620 int ossl_ec_key_gen(EC_KEY *eckey);
621 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen,
622 const EC_POINT *pub_key, const EC_KEY *ecdh);
623 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen,
624 const EC_POINT *pub_key, const EC_KEY *ecdh);
626 struct ECDSA_SIG_st {
631 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp,
633 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen,
634 unsigned char *sig, unsigned int *siglen,
635 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey);
636 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
637 const BIGNUM *in_kinv, const BIGNUM *in_r,
639 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len,
640 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey);
641 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
642 const ECDSA_SIG *sig, EC_KEY *eckey);
644 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
645 const uint8_t public_key[32], const uint8_t private_key[32]);
646 int ED25519_verify(const uint8_t *message, size_t message_len,
647 const uint8_t signature[64], const uint8_t public_key[32]);
648 void ED25519_public_from_private(uint8_t out_public_key[32],
649 const uint8_t private_key[32]);
651 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
652 const uint8_t peer_public_value[32]);
653 void X25519_public_from_private(uint8_t out_public_value[32],
654 const uint8_t private_key[32]);
657 * This functions computes a single point multiplication over the EC group,
658 * using, at a high level, a Montgomery ladder with conditional swaps, with
659 * various timing attack defenses.
661 * It performs either a fixed point multiplication
662 * (scalar * generator)
663 * when point is NULL, or a variable point multiplication
665 * when point is not NULL.
667 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
668 * constant time bets are off (where n is the cardinality of the EC group).
670 * This function expects `group->order` and `group->cardinality` to be well
671 * defined and non-zero: it fails with an error code otherwise.
673 * NB: This says nothing about the constant-timeness of the ladder step
674 * implementation (i.e., the default implementation is based on EC_POINT_add and
675 * EC_POINT_dbl, which of course are not constant time themselves) or the
676 * underlying multiprecision arithmetic.
678 * The product is stored in `r`.
680 * This is an internal function: callers are in charge of ensuring that the
681 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
683 * Returns 1 on success, 0 otherwise.
685 int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
686 const BIGNUM *scalar, const EC_POINT *point,
689 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
691 static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group,
692 EC_POINT *r, EC_POINT *s,
693 EC_POINT *p, BN_CTX *ctx)
695 if (group->meth->ladder_pre != NULL)
696 return group->meth->ladder_pre(group, r, s, p, ctx);
698 if (!EC_POINT_copy(s, p)
699 || !EC_POINT_dbl(group, r, s, ctx))
705 static ossl_inline int ec_point_ladder_step(const EC_GROUP *group,
706 EC_POINT *r, EC_POINT *s,
707 EC_POINT *p, BN_CTX *ctx)
709 if (group->meth->ladder_step != NULL)
710 return group->meth->ladder_step(group, r, s, p, ctx);
712 if (!EC_POINT_add(group, s, r, s, ctx)
713 || !EC_POINT_dbl(group, r, r, ctx))
720 static ossl_inline int ec_point_ladder_post(const EC_GROUP *group,
721 EC_POINT *r, EC_POINT *s,
722 EC_POINT *p, BN_CTX *ctx)
724 if (group->meth->ladder_post != NULL)
725 return group->meth->ladder_post(group, r, s, p, ctx);