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EC_GROUP_NEW(3)			    OpenSSL		       EC_GROUP_NEW(3)

       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

	#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);

       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 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 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

       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.

       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

       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.

       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 2013-2020 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

1.1.1k				  2021-03-25		       EC_GROUP_NEW(3)


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