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1 | =pod |
2 | ||
3 | =head1 NAME | |
4 | ||
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5 | EC_GROUP_new, EC_GROUP_new_from_ecparameters, |
6 | EC_GROUP_new_from_ecpkparameters, | |
7 | EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, | |
8 | EC_GROUP_new_curve_GF2m, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve_GFp, | |
9 | EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m, | |
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10 | EC_get_builtin_curves - Functions for creating and destroying EC_GROUP |
11 | objects | |
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12 | |
13 | =head1 SYNOPSIS | |
14 | ||
15 | #include <openssl/ec.h> | |
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16 | |
17 | EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); | |
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18 | EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params) |
19 | EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params) | |
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20 | void EC_GROUP_free(EC_GROUP *group); |
21 | void EC_GROUP_clear_free(EC_GROUP *group); | |
22 | ||
23 | EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | |
24 | EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | |
25 | EC_GROUP *EC_GROUP_new_by_curve_name(int nid); | |
26 | ||
27 | int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | |
28 | int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | |
29 | int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | |
30 | int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | |
31 | ||
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32 | ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params) |
33 | ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params) | |
34 | ||
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35 | size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems); |
36 | ||
37 | =head1 DESCRIPTION | |
38 | ||
39 | Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the | |
40 | prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. This gives us a revised | |
41 | elliptic curve equation as follows: | |
42 | ||
43 | y^2 mod p = x^3 +ax + b mod p | |
44 | ||
45 | The second form is those defined over a binary field F2^m where the elements of the field are integers of length at | |
46 | most m bits. For this form the elliptic curve equation is modified to: | |
47 | ||
48 | y^2 + xy = x^3 + ax^2 + b (where b != 0) | |
49 | ||
50 | Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL | |
51 | use a trinomial or a pentanomial for this parameter. | |
52 | ||
53 | A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by B<meth> (see | |
9b86974e | 54 | L<EC_GFp_simple_method(3)>). It is then necessary to call either EC_GROUP_set_curve_GFp or |
186bb907 | 55 | EC_GROUP_set_curve_GF2m as appropriate to create a curve defined over Fp or over F2^m respectively. |
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56 | EC_GROUP_new_from_ecparameters() will create a group from the |
57 | specified B<params> and | |
58 | EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK B<params>. | |
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59 | |
60 | EC_GROUP_set_curve_GFp sets the curve parameters B<p>, B<a> and B<b> for a curve over Fp stored in B<group>. | |
61 | EC_group_get_curve_GFp obtains the previously set curve parameters. | |
62 | ||
63 | EC_GROUP_set_curve_GF2m sets the equivalent curve parameters for a curve over F2^m. In this case B<p> represents | |
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64 | the irreducible polynomial - each bit represents a term in the polynomial. Therefore there will either be three |
65 | or five bits set dependent on whether the polynomial is a trinomial or a pentanomial. | |
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66 | EC_group_get_curve_GF2m obtains the previously set curve parameters. |
67 | ||
68 | The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and the | |
69 | appropriate EC_group_set_curve function. An appropriate default implementation method will be used. | |
70 | ||
71 | Whilst the library can be used to create any curve using the functions described above, there are also a number of | |
72 | predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function | |
73 | EC_get_builtin_curves. The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function | |
74 | will populate the B<r> array with information about the builtin curves. If B<nitems> is less than the total number of | |
75 | curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be | |
76 | provided. The return value is the total number of curves available (whether that number has been populated in B<r> or | |
77 | not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available. | |
78 | The EC_builtin_curve structure is defined as follows: | |
79 | ||
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80 | typedef struct { |
81 | int nid; | |
82 | const char *comment; | |
83 | } EC_builtin_curve; | |
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84 | |
85 | Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve. | |
86 | ||
87 | In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the B<nid> of the curve to | |
88 | be constructed. | |
89 | ||
90 | EC_GROUP_free frees the memory associated with the EC_GROUP. | |
8fdc3734 | 91 | If B<group> is NULL nothing is done. |
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92 | |
93 | EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory. | |
8fdc3734 | 94 | If B<group> is NULL nothing is done. |
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95 | |
96 | =head1 RETURN VALUES | |
97 | ||
98 | All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error. | |
99 | ||
100 | EC_get_builtin_curves returns the number of builtin curves that are available. | |
101 | ||
102 | EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m return 1 on success or 0 on error. | |
103 | ||
104 | =head1 SEE ALSO | |
105 | ||
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106 | L<crypto(3)>, L<ec(3)>, L<EC_GROUP_copy(3)>, |
107 | L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, | |
108 | L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> | |
aafbe1cc | 109 | |
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110 | =head1 COPYRIGHT |
111 | ||
112 | Copyright 2013-2016 The OpenSSL Project Authors. All Rights Reserved. | |
113 | ||
114 | Licensed under the OpenSSL license (the "License"). You may not use | |
115 | this file except in compliance with the License. You can obtain a copy | |
116 | in the file LICENSE in the source distribution or at | |
117 | L<https://www.openssl.org/source/license.html>. | |
118 | ||
119 | =cut |