- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- SEE ALSO
- COPYRIGHT

# NAME

EC_GROUP_get_ecparameters, EC_GROUP_get_ecpkparameters, EC_GROUP_new, EC_GROUP_new_from_ecparameters, EC_GROUP_new_from_ecpkparameters, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, EC_GROUP_new_curve_GF2m, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m, EC_get_builtin_curves - Functions for creating and destroying EC_GROUP objects

# SYNOPSIS

     #include <openssl/ec.h>

     EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
     EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params)
     EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params)
     void EC_GROUP_free(EC_GROUP *group);
     void EC_GROUP_clear_free(EC_GROUP *group);

     EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
     EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
     EC_GROUP *EC_GROUP_new_by_curve_name(int nid);

     int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
     int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
     int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
     int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

     ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params)
     ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params)

     size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);

# DESCRIPTION

Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the 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 elliptic curve equation as follows:

y^2 mod p = x^3 +ax + b mod p

The second form is those defined over a binary field F2^m where the elements of the field are integers of length at most m bits. For this form the elliptic curve equation is modified to:

y^2 + xy = x^3 + ax^2 + b (where b != 0)

Operations in a binary field are performed relative to an irreducible polynomial. All such curves with OpenSSL use a trinomial or a pentanomial for this parameter.

A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by meth (see typedef struct { int nid; const char *comment; } EC_builtin_curve;

Each EC_builtin_curve item has a unique integer id (nid), and a human readable comment string describing the curve.

In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the nid of the curve to be constructed.

EC_GROUP_free frees the memory associated with the EC_GROUP. If group is NULL nothing is done.

EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory. If group is NULL nothing is done.

# RETURN VALUES

All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error.

EC_get_builtin_curves returns the number of builtin curves that are available.

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.

# SEE ALSO

ec(3), EC_POINT_new(3), EC_KEY_new(3), d2i_ECPKParameters(3)

# COPYRIGHT

Copyright 2013-2016 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the OpenSSL license (the "License"). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at https://www.openssl.org/source/license.html.