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EC_GROUP_COPY(3)		    OpenSSL		      EC_GROUP_COPY(3)

       EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor,
       EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of,
       EC_GROUP_set_generator, EC_GROUP_get0_generator,	EC_GROUP_get_order,
       EC_GROUP_get_cofactor, EC_GROUP_set_curve_name,
       EC_GROUP_get_curve_name,	EC_GROUP_set_asn1_flag,
       EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form,
       EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed,
       EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree,
       EC_GROUP_check, EC_GROUP_check_discriminant, EC_GROUP_cmp,
       EC_GROUP_get_basis_type,	EC_GROUP_get_trinomial_basis,
       EC_GROUP_get_pentanomial_basis -	Functions for manipulating EC_GROUP

	#include <openssl/ec.h>

	int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP	*src);
	EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);

	const EC_METHOD	*EC_GROUP_method_of(const EC_GROUP *group);

	int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
				   const BIGNUM	*order,	const BIGNUM *cofactor);
	const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);

	int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
	const BIGNUM *EC_GROUP_get0_order(const	EC_GROUP *group);
	int EC_GROUP_order_bits(const EC_GROUP *group);
	int EC_GROUP_get_cofactor(const	EC_GROUP *group, BIGNUM	*cofactor, BN_CTX *ctx);
	const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);

	void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
	int EC_GROUP_get_curve_name(const EC_GROUP *group);

	void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
	int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

	void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
	point_conversion_form_t	EC_GROUP_get_point_conversion_form(const EC_GROUP *);

	unsigned char *EC_GROUP_get0_seed(const	EC_GROUP *x);
	size_t EC_GROUP_get_seed_len(const EC_GROUP *);
	size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);

	int EC_GROUP_get_degree(const EC_GROUP *group);

	int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);

	int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);

	int EC_GROUP_cmp(const EC_GROUP	*a, const EC_GROUP *b, BN_CTX *ctx);

	int EC_GROUP_get_basis_type(const EC_GROUP *);
	int EC_GROUP_get_trinomial_basis(const EC_GROUP	*, unsigned int	*k);
	int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
					   unsigned int	*k2, unsigned int *k3);

       EC_GROUP_copy copies the	curve src into dst. Both src and dst must use
       the same	EC_METHOD.

       EC_GROUP_dup creates a new EC_GROUP object and copies the content from
       src to the newly	created	EC_GROUP object.

       EC_GROUP_method_of obtains the EC_METHOD	of group.

       EC_GROUP_set_generator sets curve parameters that must be agreed	by all
       participants using the curve. These parameters include the generator,
       the order and the cofactor. The generator is a well defined point on
       the curve chosen	for cryptographic operations. Integers used for	point
       multiplications will be between 0 and n-1 where n is the	order. The
       order multiplied	by the cofactor	gives the number of points on the

       EC_GROUP_get0_generator returns the generator for the identified	group.

       The functions EC_GROUP_get_order	and EC_GROUP_get_cofactor populate the
       provided	order and cofactor parameters with the respective order	and
       cofactors for the group.

       The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set
       and get the NID for the curve respectively (see EC_GROUP_new(3)). If a
       curve does not have a NID associated with it, then
       EC_GROUP_get_curve_name will return 0.

       The asn1_flag value is used to determine	whether	the curve encoding
       uses explicit parameters	or a named curve using an ASN1 OID: many
       applications only support the latter form. If asn1_flag is
       OPENSSL_EC_NAMED_CURVE then the named curve form	is used	and the
       parameters must have a corresponding named curve	NID set. If asn1_flags
       is OPENSSL_EC_EXPLICIT_CURVE the	parameters are explicitly encoded. The
       functions EC_GROUP_get_asn1_flag	and EC_GROUP_set_asn1_flag get and set
       the status of the asn1_flag for the curve.  Note:
       OPENSSL_EC_EXPLICIT_CURVE was added in OpenSSL 1.1.0, for previous
       versions	of OpenSSL the value 0 must be used instead. Before OpenSSL
       1.1.0 the default form was to use explicit parameters (meaning that
       applications would have to explicitly set the named curve form) in
       OpenSSL 1.1.0 and later the named curve form is the default.

       The point_conversion_form for a curve controls how EC_POINT data	is
       encoded as ASN1 as defined in X9.62 (ECDSA).  point_conversion_form_t
       is an enum defined as follows:

	typedef	enum {
	       /** the point is	encoded	as z||x, where the octet z specifies
		*   which solution of the quadratic equation y is  */
	       /** the point is	encoded	as z||x||y, where z is the octet 0x04  */
	       /** the point is	encoded	as z||x||y, where the octet z specifies
		*  which solution of the quadratic equation y is  */
	} point_conversion_form_t;

       For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet
       signifying the UNCOMPRESSED form	has been used followed by the octets
       for x, followed by the octets for y.

       For any given x co-ordinate for a point on a curve it is	possible to
       derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
       is encoded as an	octet signifying that the COMPRESSED form has been
       used AND	which of the two possible solutions for	y has been used,
       followed	by the octets for x.

       For POINT_CONVERSION_HYBRID the point is	encoded	as an octet signifying
       the HYBRID form has been	used AND which of the two possible solutions
       for y has been used, followed by	the octets for x, followed by the
       octets for y.

       The functions EC_GROUP_set_point_conversion_form	and
       EC_GROUP_get_point_conversion_form set and get the
       point_conversion_form for the curve respectively.

       ANSI X9.62 (ECDSA standard) defines a method of generating the curve
       parameter b from	a random number. This provides advantages in that a
       parameter obtained in this way is highly	unlikely to be susceptible to
       special purpose attacks,	or have	any trapdoors in it.  If the seed is
       present for a curve then	the b parameter	was generated in a verifiable
       fashion using that seed.	The OpenSSL EC library does not	use this seed
       value but does enable you to inspect it using EC_GROUP_get0_seed. This
       returns a pointer to a memory block containing the seed that was	used.
       The length of the memory	block can be obtained using
       EC_GROUP_get_seed_len. A	number of the builtin curves within the
       library provide seed values that	can be obtained. It is also possible
       to set a	custom seed using EC_GROUP_set_seed and	passing	a pointer to a
       memory block, along with	the length of the seed.	Again, the EC library
       will not	use this seed value, although it will be preserved in any ASN1
       based communications.

       EC_GROUP_get_degree gets	the degree of the field. For Fp	fields this
       will be the number of bits in p.	 For F2^m fields this will be the
       value m.

       The function EC_GROUP_check_discriminant	calculates the discriminant
       for the curve and verifies that it is valid.  For a curve defined over
       Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for
       F2^m curves the discriminant is simply b. In either case	for the	curve
       to be valid the discriminant must be non	zero.

       The function EC_GROUP_check performs a number of	checks on a curve to
       verify that it is valid.	Checks performed include verifying that	the
       discriminant is non zero; that a	generator has been defined; that the
       generator is on the curve and has the correct order.

       EC_GROUP_cmp compares a and b to	determine whether they represent the
       same curve or not.

       The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and
       EC_GROUP_get_pentanomial_basis should only be called for	curves defined
       over an F2^m field. Addition and	multiplication operations within an
       F2^m field are performed	using an irreducible polynomial	function f(x).
       This function is	either a trinomial of the form:

       f(x) = x^m + x^k	+ 1 with m > k >= 1

       or a pentanomial	of the form:

       f(x) = x^m + x^k3 + x^k2	+ x^k1 + 1 with	m > k3 > k2 > k1 >= 1

       The function EC_GROUP_get_basis_type returns a NID identifying whether
       a trinomial or pentanomial is in	use for	the field. The function
       EC_GROUP_get_trinomial_basis must only be called	where f(x) is of the
       trinomial form, and returns the value of	k. Similarly the function
       EC_GROUP_get_pentanomial_basis must only	be called where	f(x) is	of the
       pentanomial form, and returns the values	of k1, k2 and k3 respectively.

       The following functions return 1	on success or 0	on error:
       EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
       EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and

       EC_GROUP_dup returns a pointer to the duplicated	curve, or NULL on

       EC_GROUP_method_of returns the EC_METHOD	implementation in use for the
       given curve or NULL on error.

       EC_GROUP_get0_generator returns the generator for the given curve or
       NULL on error.

       EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name,
       EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form and
       EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1
       flag, point_conversion_form and degree for the specified	curve
       respectively. If	there is no curve name associated with a curve then
       EC_GROUP_get_curve_name will return 0.

       EC_GROUP_get0_order() returns an	internal pointer to the	group order.
       EC_GROUP_order_bits() returns the number	of bits	in the group order.
       EC_GROUP_get0_cofactor()	returns	an internal pointer to the group

       EC_GROUP_get0_seed returns a pointer to the seed	that was used to
       generate	the parameter b, or NULL if the	seed is	not specified.
       EC_GROUP_get_seed_len returns the length	of the seed or 0 if the	seed
       is not specified.

       EC_GROUP_set_seed returns the length of the seed	that has been set. If
       the supplied seed is NULL, or the supplied seed length is 0, the	return
       value will be 1.	On error 0 is returned.

       EC_GROUP_cmp returns 0 if the curves are	equal, 1 if they are not
       equal, or -1 on error.

       EC_GROUP_get_basis_type returns the values NID_X9_62_tpBasis or
       NID_X9_62_ppBasis (as defined in	<openssl/obj_mac.h>) for a trinomial
       or pentanomial respectively. Alternatively in the event of an error a 0
       is returned.

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

       Copyright 2013-2017 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

1.1.1d				  2019-09-10		      EC_GROUP_COPY(3)


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