1 /* Originally written by Bodo Moeller for the OpenSSL project.
2 * ====================================================================
3 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in
14 * the documentation and/or other materials provided with the
17 * 3. All advertising materials mentioning features or use of this
18 * software must display the following acknowledgment:
19 * "This product includes software developed by the OpenSSL Project
20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 * endorse or promote products derived from this software without
24 * prior written permission. For written permission, please contact
25 * openssl-core@openssl.org.
27 * 5. Products derived from this software may not be called "OpenSSL"
28 * nor may "OpenSSL" appear in their names without prior written
29 * permission of the OpenSSL Project.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
55 /* ====================================================================
56 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
58 * Portions of the attached software ("Contribution") are developed by
59 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
61 * The Contribution is licensed pursuant to the OpenSSL open source
62 * license provided above.
64 * The elliptic curve binary polynomial software is originally written by
65 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
68 #ifndef OPENSSL_HEADER_EC_INTERNAL_H
69 #define OPENSSL_HEADER_EC_INTERNAL_H
71 #include <openssl/base.h>
73 #include <openssl/bn.h>
74 #include <openssl/ex_data.h>
75 #include <openssl/thread.h>
76 #include <openssl/type_check.h>
78 #include "../bn/internal.h"
80 #if defined(__cplusplus)
85 // Cap the size of all field elements and scalars, including custom curves, to
86 // 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to
87 // be the largest fields anyone plausibly uses.
88 #define EC_MAX_SCALAR_BYTES 66
89 #define EC_MAX_SCALAR_WORDS ((66 + BN_BYTES - 1) / BN_BYTES)
91 OPENSSL_COMPILE_ASSERT(EC_MAX_SCALAR_WORDS <= BN_SMALL_MAX_WORDS,
92 bn_small_functions_applicable);
94 // An EC_SCALAR is an integer fully reduced modulo the order. Only the first
95 // |order->width| words are used. An |EC_SCALAR| is specific to an |EC_GROUP|
96 // and must not be mixed between groups.
98 // bytes is the representation of the scalar in little-endian order.
99 uint8_t bytes[EC_MAX_SCALAR_BYTES];
100 BN_ULONG words[EC_MAX_SCALAR_WORDS];
103 struct ec_method_st {
104 int (*group_init)(EC_GROUP *);
105 void (*group_finish)(EC_GROUP *);
106 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
107 const BIGNUM *b, BN_CTX *);
108 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
109 BIGNUM *x, BIGNUM *y, BN_CTX *);
111 // Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar|
112 // are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null.
113 // Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar|
114 // and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is
116 int (*mul)(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
117 const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
118 // mul_public performs the same computation as mul. It further assumes that
119 // the inputs are public so there is no concern about leaking their values
121 int (*mul_public)(const EC_GROUP *group, EC_POINT *r,
122 const EC_SCALAR *g_scalar, const EC_POINT *p,
123 const EC_SCALAR *p_scalar, BN_CTX *ctx);
125 // 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the
126 // same implementations of point operations can be used with different
127 // optimized implementations of expensive field operations:
128 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
129 const BIGNUM *b, BN_CTX *);
130 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
132 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
133 BN_CTX *); // e.g. to Montgomery
134 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
135 BN_CTX *); // e.g. from Montgomery
138 const EC_METHOD *EC_GFp_mont_method(void);
141 const EC_METHOD *meth;
143 // Unlike all other |EC_POINT|s, |generator| does not own |generator->group|
144 // to avoid a reference cycle.
148 int curve_name; // optional NID for named curve
150 BN_MONT_CTX *order_mont; // data for ECDSA inverse
152 // The following members are handled by the method functions,
153 // even if they appear generic
155 BIGNUM field; // For curves over GF(p), this is the modulus.
157 BIGNUM a, b; // Curve coefficients.
159 int a_is_minus3; // enable optimized point arithmetics for special case
161 CRYPTO_refcount_t references;
163 BN_MONT_CTX *mont; // Montgomery structure.
165 BIGNUM one; // The value one.
169 // group is an owning reference to |group|, unless this is
170 // |group->generator|.
175 BIGNUM Z; // Jacobian projective coordinates:
176 // (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0
179 EC_GROUP *ec_group_new(const EC_METHOD *meth);
181 // ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to
182 // |*out|. It returns one on success and zero if |in| is out of range.
183 OPENSSL_EXPORT int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
186 // ec_bignum_to_scalar_unchecked behaves like |ec_bignum_to_scalar| but does not
187 // check |in| is fully reduced.
188 int ec_bignum_to_scalar_unchecked(const EC_GROUP *group, EC_SCALAR *out,
191 // ec_random_nonzero_scalar sets |out| to a uniformly selected random value from
192 // 1 to |group->order| - 1. It returns one on success and zero on error.
193 int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out,
194 const uint8_t additional_data[32]);
196 // ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| *
197 // |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and
198 // |p_scalar| need not be fully reduced. They need only contain as many bits as
200 int ec_point_mul_scalar(const EC_GROUP *group, EC_POINT *r,
201 const EC_SCALAR *g_scalar, const EC_POINT *p,
202 const EC_SCALAR *p_scalar, BN_CTX *ctx);
204 // ec_point_mul_scalar_public performs the same computation as
205 // ec_point_mul_scalar. It further assumes that the inputs are public so
206 // there is no concern about leaking their values through timing.
207 OPENSSL_EXPORT int ec_point_mul_scalar_public(
208 const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
209 const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
211 // ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of
212 // |scalar| to |out| and returns one on success or zero on internal error. |out|
213 // must have room for |bits| + 1 elements, each of which will be either zero or
214 // odd with an absolute value less than 2^w satisfying
215 // scalar = \sum_j out[j]*2^j
216 // where at most one of any w+1 consecutive digits is non-zero
217 // with the exception that the most significant digit may be only
218 // w-1 zeros away from that next non-zero digit.
219 int ec_compute_wNAF(const EC_GROUP *group, int8_t *out, const EC_SCALAR *scalar,
222 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
223 const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
225 // method functions in simple.c
226 int ec_GFp_simple_group_init(EC_GROUP *);
227 void ec_GFp_simple_group_finish(EC_GROUP *);
228 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
229 const BIGNUM *b, BN_CTX *);
230 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
231 BIGNUM *b, BN_CTX *);
232 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
233 int ec_GFp_simple_point_init(EC_POINT *);
234 void ec_GFp_simple_point_finish(EC_POINT *);
235 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
236 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
237 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
238 const BIGNUM *x, const BIGNUM *y,
240 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
241 const EC_POINT *b, BN_CTX *);
242 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
244 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
245 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
246 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
247 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
249 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
250 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
251 EC_POINT * [], BN_CTX *);
252 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
253 const BIGNUM *b, BN_CTX *);
254 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
257 // method functions in montgomery.c
258 int ec_GFp_mont_group_init(EC_GROUP *);
259 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
260 const BIGNUM *b, BN_CTX *);
261 void ec_GFp_mont_group_finish(EC_GROUP *);
262 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
263 const BIGNUM *b, BN_CTX *);
264 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
266 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
268 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
271 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
273 const EC_METHOD *EC_GFp_nistp224_method(void);
274 const EC_METHOD *EC_GFp_nistp256_method(void);
276 // EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
277 // x86-64 optimized P256. See http://eprint.iacr.org/2013/816.
278 const EC_METHOD *EC_GFp_nistz256_method(void);
280 // An EC_WRAPPED_SCALAR is an |EC_SCALAR| with a parallel |BIGNUM|
281 // representation. It exists to support the |EC_KEY_get0_private_key| API.
291 EC_WRAPPED_SCALAR *priv_key;
293 // fixed_k may contain a specific value of 'k', to be used in ECDSA signing.
294 // This is only for the FIPS power-on tests.
297 unsigned int enc_flag;
298 point_conversion_form_t conv_form;
300 CRYPTO_refcount_t references;
302 ECDSA_METHOD *ecdsa_meth;
304 CRYPTO_EX_DATA ex_data;
307 struct built_in_curve {
311 // comment is a human-readable string describing the curve.
313 // param_len is the number of bytes needed to store a field element.
315 // params points to an array of 6*|param_len| bytes which hold the field
316 // elements of the following (in big-endian order): prime, a, b, generator x,
317 // generator y, order.
318 const uint8_t *params;
319 const EC_METHOD *method;
322 #define OPENSSL_NUM_BUILT_IN_CURVES 4
324 struct built_in_curves {
325 struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES];
328 // OPENSSL_built_in_curves returns a pointer to static information about
329 // standard curves. The array is terminated with an entry where |nid| is
331 const struct built_in_curves *OPENSSL_built_in_curves(void);
333 #if defined(__cplusplus)
337 #endif // OPENSSL_HEADER_EC_INTERNAL_H