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EC_GROUP_COPY(3)		    OpenSSL		      EC_GROUP_COPY(3)

NAME
       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
       objects

SYNOPSIS
	#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 *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);

DESCRIPTION
       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 curve.

       EC_GROUP_get0_generator() returns the generator for the identified
       group.

       EC_GROUP_get_order() retrieves the order	of group and copies its	value
       into order.  It fails in	case group is not fully	initialized (i.e., its
       order is	not set	or set to zero).

       EC_GROUP_get_cofactor() retrieves the cofactor of group and copies its
       value into cofactor. It fails in	case  group is not fully initialized
       or if the cofactor is not set (or set to	zero).

       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 NID_undef.

       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  */
	       POINT_CONVERSION_COMPRESSED = 2,
	       /** the point is	encoded	as z||x||y, where z is the octet 0x04  */
	       POINT_CONVERSION_UNCOMPRESSED = 4,
	       /** the point is	encoded	as z||x||y, where the octet z specifies
		*  which solution of the quadratic equation y is  */
	       POINT_CONVERSION_HYBRID = 6
	} 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	built-in 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.

RETURN VALUES
       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_get_pentanomial_basis().

       EC_GROUP_dup() returns a	pointer	to the duplicated curve, or NULL on
       error.

       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() returns 0 if the order is not set (or set to zero)
       for group or if copying into order fails, 1 otherwise.

       EC_GROUP_get_cofactor() returns 0 if the	cofactor is not	set (or	is set
       to zero)	for group or if	copying	into cofactor fails, 1 otherwise.

       EC_GROUP_get_curve_name() returns the curve name	(NID) for group	or
       will return NID_undef if	no curve name is associated.

       EC_GROUP_get_asn1_flag()	returns	the ASN1 flag for the specified	group
       .

       EC_GROUP_get_point_conversion_form() returns the	point_conversion_form
       for group.

       EC_GROUP_get_degree() returns the degree	for group or 0 if the
       operation is not	supported by the underlying group implementation.

       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
       cofactor.

       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.

SEE ALSO
       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
       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
       <https://www.openssl.org/source/license.html>.

1.1.1l				  2021-08-24		      EC_GROUP_COPY(3)

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

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