NAME

       EC_GROUP_get_ecparameters, EC_GROUP_get_ecpkparameters, EC_GROUP_new_from_params,
       EC_GROUP_new_from_ecparameters, EC_GROUP_new_from_ecpkparameters, EC_GROUP_new,
       EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, EC_GROUP_new_curve_GF2m,
       EC_GROUP_new_by_curve_name_ex, 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,
       OSSL_EC_curve_nid2name - Functions for creating and destroying EC_GROUP objects

SYNOPSIS

        #include <openssl/ec.h>

        EC_GROUP *EC_GROUP_new_from_params(const OSSL_PARAM params[],
                                           OSSL_LIB_CTX *libctx, const char *propq);
        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);

        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_ex(OSSL_LIB_CTX *libctx, const char *propq,
                                                int nid);
        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);

        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);
        const char *OSSL_EC_curve_nid2name(int nid);

       The following functions have been deprecated since OpenSSL 3.0, and can be hidden entirely
       by defining OPENSSL_API_COMPAT with a suitable version value, see openssl_user_macros(7):

        EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
        void EC_GROUP_clear_free(EC_GROUP *group);

        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);

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.

       Although deprecated since OpenSSL 3.0 and should no longer be used, a new curve can be
       constructed by calling EC_GROUP_new(), using the implementation provided by meth (see
       EC_GFp_simple_method(3)) and associated with the library context ctx (see
       OSSL_LIB_CTX(3)).  The ctx parameter may be NULL in which case the default library context
       is used.  It is then necessary to call EC_GROUP_set_curve() to set the curve parameters.
       Applications should instead use one of the other EC_GROUP_new_* constructors.

       EC_GROUP_new_from_params() creates a group with parameters specified by params.  The
       library context libctx (see OSSL_LIB_CTX(3)) and property query string propq are used to
       fetch algorithms from providers.  params may be either a list of explicit params or a
       named group, The values for ctx and propq may be NULL.  The params that can be used are
       described in EVP_PKEY-EC(7).

       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 p 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.  In either
       case, a and b represents the coefficients a and b from the relevant equation introduced
       above.

       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 built-in 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 built-in curve use the function EC_GROUP_new_by_curve_name_ex()
       and provide the nid of the curve to be constructed, the associated library context to be
       used in ctx (see OSSL_LIB_CTX(3)) and any property query string in propq. The ctx value
       may be NULL in which case the default library context is used. The propq value may also be
       NULL.

       EC_GROUP_new_by_curve_name() is the same as EC_GROUP_new_by_curve_name_ex() except that
       the default library context is always used along with a NULL property query string.

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

       EC_GROUP_clear_free() is deprecated: it was meant to destroy any sensitive data held
       within the EC_GROUP and then free its memory, but since all the data stored in the
       EC_GROUP is public anyway, this function is unnecessary.  Its use can be safely replaced
       with EC_GROUP_free().  If group is NULL nothing is done.

       OSSL_EC_curve_nid2name() converts a curve nid into the corresponding name.

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 built-in 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.

       OSSL_EC_curve_nid2name() returns a character string constant, or NULL 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), OSSL_LIB_CTX(3), EVP_PKEY-EC(7)

HISTORY

       • EC_GROUP_new() was deprecated in OpenSSL 3.0.

         EC_GROUP_new_by_curve_name_ex() and EC_GROUP_new_from_params() were added in OpenSSL
         3.0.

       • EC_GROUP_clear_free() was deprecated in OpenSSL 3.0; use EC_GROUP_free() instead.

       •

          EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(),
          EC_GROUP_set_curve_GF2m() and EC_GROUP_get_curve_GF2m() were deprecated in
          OpenSSL 3.0; use EC_GROUP_set_curve() and EC_GROUP_get_curve() instead.

COPYRIGHT

       Copyright 2013-2021 The OpenSSL Project Authors. All Rights Reserved.

       Licensed under the Apache License 2.0 (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>.