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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, EC_GROUP_get_curve,
       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(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
                               const BIGNUM *b, BN_CTX *ctx);
        int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
                               BN_CTX *ctx);
        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 EC_GFp_simple_method(3)). It is then necessary to call EC_GROUP_set_curve()
       to set the curve parameters.  EC_GROUP_new_from_ecparameters() will create a group from
       the specified params and EC_GROUP_new_from_ecpkparameters() will create a group from the
       specific PK params.

       EC_GROUP_set_curve() sets the curve parameters p, a and b. For a curve over Fp b is the
       prime for the field. For a curve over F2^m p represents the irreducible polynomial - each
       bit represents a term in the polynomial. Therefore there will either be three or five bits
       set dependent on whether the polynomial is a trinomial or a pentanomial.

       EC_group_get_curve() obtains the previously set curve parameters.

       EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for
       EC_GROUP_set_curve(). They are defined for backwards compatibility only and should not be
       used.

       EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for
       EC_GROUP_get_curve(). They are defined for backwards compatibility only and should not be
       used.

       The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling
       EC_GROUP_new and then the EC_GROUP_set_curve function. An appropriate default
       implementation method will be used.

       Whilst the library can be used to create any curve using the functions described above,
       there are also a number of predefined curves that are available. In order to obtain a list
       of all of the predefined curves, call the function EC_get_builtin_curves. The parameter r
       should be an array of EC_builtin_curve structures of size nitems. The function will
       populate the r array with information about the builtin curves. If nitems is less than the
       total number of curves available, then the first nitems curves will be returned. Otherwise
       the total number of curves will be provided. The return value is the total number of
       curves available (whether that number has been populated in r or not). Passing a NULL r,
       or setting nitems to 0 will do nothing other than return the total number of curves
       available.  The EC_builtin_curve structure is defined as follows:

        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

       crypto(7), EC_GROUP_copy(3), EC_POINT_new(3), EC_POINT_add(3), EC_KEY_new(3),
       EC_GFp_simple_method(3), d2i_ECPKParameters(3)

COPYRIGHT

       Copyright 2013-2018 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>.