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. The first form is those defined over the 61prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. This gives us a revised 62elliptic curve equation as follows: 63 64y^2 mod p = x^3 +ax + b mod p 65 66The second form is those defined over a binary field F2^m where the elements of the field are integers of length at 67most m bits. For this form the elliptic curve equation is modified to: 68 69y^2 + xy = x^3 + ax^2 + b (where b != 0) 70 71Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL 72use a trinomial or a pentanomial for this parameter. 73 74A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by B<meth> (see 75L<EC_GFp_simple_method(3)>). It is then necessary to call EC_GROUP_set_curve() to set the curve parameters. 76EC_GROUP_new_from_ecparameters() will create a group from the 77specified B<params> and 78EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK B<params>. 79 80EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve over Fp B<b> 81is the prime for the field. For a curve over F2^m B<p> represents the irreducible polynomial - each bit 82represents a term in the polynomial. Therefore there will either be three or five bits set dependent on whether 83the polynomial is a trinomial or a pentanomial. 84 85EC_group_get_curve() obtains the previously set curve parameters. 86 87EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for EC_GROUP_set_curve(). They are defined for 88backwards compatibility only and should not be used. 89 90EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for EC_GROUP_get_curve(). They are defined for 91backwards compatibility only and should not be used. 92 93The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and then the 94EC_GROUP_set_curve function. An appropriate default implementation method will be used. 95 96Whilst the library can be used to create any curve using the functions described above, there are also a number of 97predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function 98EC_get_builtin_curves. The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function 99will populate the B<r> array with information about the builtin curves. If B<nitems> is less than the total number of 100curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be 101provided. The return value is the total number of curves available (whether that number has been populated in B<r> or 102not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available. 103The EC_builtin_curve structure is defined as follows: 104 105 typedef struct { 106 int nid; 107 const char *comment; 108 } EC_builtin_curve; 109 110Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve. 111 112In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the B<nid> of the curve to 113be constructed. 114 115EC_GROUP_free frees the memory associated with the EC_GROUP. 116If B<group> is NULL nothing is done. 117 118EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory. 119If B<group> is NULL nothing is done. 120 121=head1 RETURN VALUES 122 123All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error. 124 125EC_get_builtin_curves returns the number of builtin curves that are available. 126 127EC_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. 128 129=head1 SEE ALSO 130 131L<crypto(7)>, L<EC_GROUP_copy(3)>, 132L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, 133L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> 134 135=head1 COPYRIGHT 136 137Copyright 2013-2018 The OpenSSL Project Authors. All Rights Reserved. 138 139Licensed under the OpenSSL license (the "License"). You may not use 140this file except in compliance with the License. You can obtain a copy 141in the file LICENSE in the source distribution or at 142L<https://www.openssl.org/source/license.html>. 143 144=cut 145