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1 | =pod |
2 | ||
3 | =head1 NAME | |
4 | ||
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5 | EC_GROUP_get_ecparameters, |
6 | EC_GROUP_get_ecpkparameters, | |
7 | EC_GROUP_new, | |
8 | EC_GROUP_new_from_ecparameters, | |
60b350a3 | 9 | EC_GROUP_new_from_ecpkparameters, |
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10 | EC_GROUP_free, |
11 | EC_GROUP_clear_free, | |
12 | EC_GROUP_new_curve_GFp, | |
13 | EC_GROUP_new_curve_GF2m, | |
14 | EC_GROUP_new_by_curve_name, | |
15 | EC_GROUP_set_curve, | |
16 | EC_GROUP_get_curve, | |
17 | EC_GROUP_set_curve_GFp, | |
18 | EC_GROUP_get_curve_GFp, | |
19 | EC_GROUP_set_curve_GF2m, | |
20 | EC_GROUP_get_curve_GF2m, | |
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21 | EC_get_builtin_curves - Functions for creating and destroying EC_GROUP |
22 | objects | |
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23 | |
24 | =head1 SYNOPSIS | |
25 | ||
26 | #include <openssl/ec.h> | |
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27 | |
28 | EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); | |
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29 | EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params) |
30 | EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params) | |
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31 | void EC_GROUP_free(EC_GROUP *group); |
32 | void EC_GROUP_clear_free(EC_GROUP *group); | |
33 | ||
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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); | |
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38 | EC_GROUP *EC_GROUP_new_by_curve_name(int nid); |
39 | ||
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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); | |
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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); | |
aafbe1cc | 52 | |
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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 | ||
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56 | size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems); |
57 | ||
58 | =head1 DESCRIPTION | |
59 | ||
60 | Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the | |
61 | 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 | |
62 | elliptic curve equation as follows: | |
63 | ||
64 | y^2 mod p = x^3 +ax + b mod p | |
65 | ||
66 | The second form is those defined over a binary field F2^m where the elements of the field are integers of length at | |
67 | most m bits. For this form the elliptic curve equation is modified to: | |
68 | ||
69 | y^2 + xy = x^3 + ax^2 + b (where b != 0) | |
70 | ||
71 | Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL | |
72 | use a trinomial or a pentanomial for this parameter. | |
73 | ||
74 | A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by B<meth> (see | |
de34e45a | 75 | L<EC_GFp_simple_method(3)>). It is then necessary to call EC_GROUP_set_curve() to set the curve parameters. |
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76 | EC_GROUP_new_from_ecparameters() will create a group from the |
77 | specified B<params> and | |
78 | EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK B<params>. | |
aafbe1cc | 79 | |
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80 | EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve over Fp B<b> |
81 | is the prime for the field. For a curve over F2^m B<p> represents the irreducible polynomial - each bit | |
82 | represents a term in the polynomial. Therefore there will either be three or five bits set dependent on whether | |
83 | the polynomial is a trinomial or a pentanomial. | |
aafbe1cc | 84 | |
de34e45a | 85 | EC_group_get_curve() obtains the previously set curve parameters. |
aafbe1cc | 86 | |
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87 | EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m are synonyms for EC_GROUP_set_curve(). |
88 | ||
89 | EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m are synonyms for EC_GROUP_get_curve(). | |
90 | ||
91 | The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and then the | |
92 | EC_GROUP_set_curve function. An appropriate default implementation method will be used. | |
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93 | |
94 | Whilst the library can be used to create any curve using the functions described above, there are also a number of | |
95 | predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function | |
96 | EC_get_builtin_curves. The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function | |
97 | will populate the B<r> array with information about the builtin curves. If B<nitems> is less than the total number of | |
98 | curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be | |
99 | provided. The return value is the total number of curves available (whether that number has been populated in B<r> or | |
100 | not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available. | |
101 | The EC_builtin_curve structure is defined as follows: | |
102 | ||
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103 | typedef struct { |
104 | int nid; | |
105 | const char *comment; | |
106 | } EC_builtin_curve; | |
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107 | |
108 | Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve. | |
109 | ||
110 | 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 | |
111 | be constructed. | |
112 | ||
113 | EC_GROUP_free frees the memory associated with the EC_GROUP. | |
8fdc3734 | 114 | If B<group> is NULL nothing is done. |
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115 | |
116 | EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory. | |
8fdc3734 | 117 | If B<group> is NULL nothing is done. |
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118 | |
119 | =head1 RETURN VALUES | |
120 | ||
121 | All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error. | |
122 | ||
123 | EC_get_builtin_curves returns the number of builtin curves that are available. | |
124 | ||
125 | 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. | |
126 | ||
127 | =head1 SEE ALSO | |
128 | ||
9e183d22 | 129 | L<crypto(7)>, L<EC_GROUP_copy(3)>, |
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130 | L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, |
131 | L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> | |
aafbe1cc | 132 | |
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133 | =head1 COPYRIGHT |
134 | ||
9e183d22 | 135 | Copyright 2013-2017 The OpenSSL Project Authors. All Rights Reserved. |
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136 | |
137 | Licensed under the OpenSSL license (the "License"). You may not use | |
138 | this file except in compliance with the License. You can obtain a copy | |
139 | in the file LICENSE in the source distribution or at | |
140 | L<https://www.openssl.org/source/license.html>. | |
141 | ||
142 | =cut |