1=pod
2
3=head1 NAME
4
5EC_GROUP_get_ecparameters,
6EC_GROUP_get_ecpkparameters,
7EC_GROUP_new,
8EC_GROUP_new_from_ecparameters,
9EC_GROUP_new_from_ecpkparameters,
10EC_GROUP_free,
11EC_GROUP_clear_free,
12EC_GROUP_new_curve_GFp,
13EC_GROUP_new_curve_GF2m,
14EC_GROUP_new_by_curve_name,
15EC_GROUP_set_curve,
16EC_GROUP_get_curve,
17EC_GROUP_set_curve_GFp,
18EC_GROUP_get_curve_GFp,
19EC_GROUP_set_curve_GF2m,
20EC_GROUP_get_curve_GF2m,
21EC_get_builtin_curves - Functions for creating and destroying EC_GROUP
22objects
23
24=head1 SYNOPSIS
25
26 #include <openssl/ec.h>
27
28 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
29 EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params)
30 EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params)
31 void EC_GROUP_free(EC_GROUP *group);
32 void EC_GROUP_clear_free(EC_GROUP *group);
33
34 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
35                                  const BIGNUM *b, BN_CTX *ctx);
36 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
37                                   const BIGNUM *b, BN_CTX *ctx);
38 EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
39
40 int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
41                        const BIGNUM *b, BN_CTX *ctx);
42 int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
43                        BN_CTX *ctx);
44 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p,
45                            const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
46 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p,
47                            BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
48 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p,
49                             const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
50 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p,
51                             BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
52
53 ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params)
54 ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params)
55
56 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
57
58=head1 DESCRIPTION
59
60Within the library there are two forms of elliptic curve that are of interest.
61The first form is those defined over the prime field Fp. The elements of Fp are
62the integers 0 to p-1, where p is a prime number. This gives us a revised
63elliptic curve equation as follows:
64
65y^2 mod p = x^3 +ax + b mod p
66
67The second form is those defined over a binary field F2^m where the elements of
68the field are integers of length at most m bits. For this form the elliptic
69curve equation is modified to:
70
71y^2 + xy = x^3 + ax^2 + b (where b != 0)
72
73Operations in a binary field are performed relative to an B<irreducible
74polynomial>. All such curves with OpenSSL use a trinomial or a pentanomial for
75this parameter.
76
77A new curve can be constructed by calling EC_GROUP_new(), using the
78implementation provided by B<meth> (see L<EC_GFp_simple_method(3)>). It is then
79necessary to call EC_GROUP_set_curve() to set the curve parameters.
80EC_GROUP_new_from_ecparameters() will create a group from the specified
81B<params> and EC_GROUP_new_from_ecpkparameters() will create a group from the
82specific PK B<params>.
83
84EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve
85over Fp B<p> is the prime for the field. For a curve over F2^m B<p> represents
86the irreducible polynomial - each bit represents a term in the polynomial.
87Therefore there will either be three or five bits set dependent on whether the
88polynomial is a trinomial or a pentanomial.
89In either case, B<a> and B<b> represents the coefficients a and b from the
90relevant equation introduced above.
91
92EC_group_get_curve() obtains the previously set curve parameters.
93
94EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for
95EC_GROUP_set_curve(). They are defined for backwards compatibility only and
96should not be used.
97
98EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for
99EC_GROUP_get_curve(). They are defined for backwards compatibility only and
100should not be used.
101
102The functions EC_GROUP_new_curve_GFp() and EC_GROUP_new_curve_GF2m() are
103shortcuts for calling EC_GROUP_new() and then the EC_GROUP_set_curve() function.
104An appropriate default implementation method will be used.
105
106Whilst the library can be used to create any curve using the functions described
107above, there are also a number of predefined curves that are available. In order
108to obtain a list of all of the predefined curves, call the function
109EC_get_builtin_curves(). The parameter B<r> should be an array of
110EC_builtin_curve structures of size B<nitems>. The function will populate the
111B<r> array with information about the builtin curves. If B<nitems> is less than
112the total number of curves available, then the first B<nitems> curves will be
113returned. Otherwise the total number of curves will be provided. The return
114value is the total number of curves available (whether that number has been
115populated in B<r> or not). Passing a NULL B<r>, or setting B<nitems> to 0 will
116do nothing other than return the total number of curves available.
117The EC_builtin_curve structure is defined as follows:
118
119 typedef struct {
120        int nid;
121        const char *comment;
122        } EC_builtin_curve;
123
124Each EC_builtin_curve item has a unique integer id (B<nid>), and a human
125readable comment string describing the curve.
126
127In order to construct a builtin curve use the function
128EC_GROUP_new_by_curve_name() and provide the B<nid> of the curve to
129be constructed.
130
131EC_GROUP_free() frees the memory associated with the EC_GROUP.
132If B<group> is NULL nothing is done.
133
134EC_GROUP_clear_free() destroys any sensitive data held within the EC_GROUP and
135then frees its memory. If B<group> is NULL nothing is done.
136
137=head1 RETURN VALUES
138
139All EC_GROUP_new* functions return a pointer to the newly constructed group, or
140NULL on error.
141
142EC_get_builtin_curves() returns the number of builtin curves that are available.
143
144EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(), EC_GROUP_set_curve_GF2m(),
145EC_GROUP_get_curve_GF2m() return 1 on success or 0 on error.
146
147=head1 SEE ALSO
148
149L<crypto(7)>, L<EC_GROUP_copy(3)>,
150L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
151L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
152
153=head1 COPYRIGHT
154
155Copyright 2013-2019 The OpenSSL Project Authors. All Rights Reserved.
156
157Licensed under the OpenSSL license (the "License").  You may not use
158this file except in compliance with the License.  You can obtain a copy
159in the file LICENSE in the source distribution or at
160L<https://www.openssl.org/source/license.html>.
161
162=cut
163