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-.\" $OpenBSD: EC_GROUP_copy.3,v 1.16 2025/03/08 16:40:59 tb Exp $
-.\" full merge up to: OpenSSL d900a015 Oct 8 14:40:42 2015 +0200
-.\" selective merge up to: OpenSSL 24c23e1f Aug 22 10:51:25 2019 +0530
-.\"
-.\" This file was written by Matt Caswell <matt@openssl.org>,
-.\" Dr. Stephen Henson <steve@openssl.org>,
-.\" and Jayaram X Matta <jayaramx.matta@intel.com>.
-.\" Copyright (c) 2013, 2015, 2019 The OpenSSL Project.  All rights reserved.
-.\"
-.\" Redistribution and use in source and binary forms, with or without
-.\" modification, are permitted provided that the following conditions
-.\" are met:
-.\"
-.\" 1. Redistributions of source code must retain the above copyright
-.\"    notice, this list of conditions and the following disclaimer.
-.\"
-.\" 2. Redistributions in binary form must reproduce the above copyright
-.\"    notice, this list of conditions and the following disclaimer in
-.\"    the documentation and/or other materials provided with the
-.\"    distribution.
-.\"
-.\" 3. All advertising materials mentioning features or use of this
-.\"    software must display the following acknowledgment:
-.\"    "This product includes software developed by the OpenSSL Project
-.\"    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
-.\"
-.\" 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
-.\"    endorse or promote products derived from this software without
-.\"    prior written permission. For written permission, please contact
-.\"    openssl-core@openssl.org.
-.\"
-.\" 5. Products derived from this software may not be called "OpenSSL"
-.\"    nor may "OpenSSL" appear in their names without prior written
-.\"    permission of the OpenSSL Project.
-.\"
-.\" 6. Redistributions of any form whatsoever must retain the following
-.\"    acknowledgment:
-.\"    "This product includes software developed by the OpenSSL Project
-.\"    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
-.\"
-.\" THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
-.\" EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-.\" PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
-.\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-.\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
-.\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-.\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
-.\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
-.\" OF THE POSSIBILITY OF SUCH DAMAGE.
-.\"
-.Dd $Mdocdate: March 8 2025 $
-.Dt EC_GROUP_COPY 3
-.Os
-.Sh NAME
-.Nm EC_GROUP_copy ,
-.Nm EC_GROUP_dup ,
-.Nm EC_GROUP_set_generator ,
-.Nm EC_GROUP_get0_generator ,
-.Nm EC_GROUP_get_order ,
-.Nm EC_GROUP_order_bits ,
-.Nm EC_GROUP_get_cofactor ,
-.Nm EC_GROUP_set_curve_name ,
-.Nm EC_GROUP_get_curve_name ,
-.Nm EC_GROUP_set_asn1_flag ,
-.Nm EC_GROUP_get_asn1_flag ,
-.Nm EC_GROUP_set_point_conversion_form ,
-.Nm EC_GROUP_get_point_conversion_form ,
-.Nm EC_GROUP_get0_seed ,
-.Nm EC_GROUP_get_seed_len ,
-.Nm EC_GROUP_set_seed ,
-.Nm EC_GROUP_get_degree ,
-.Nm EC_GROUP_check ,
-.Nm EC_GROUP_check_discriminant ,
-.Nm EC_GROUP_cmp ,
-.Nm EC_GROUP_get_basis_type
-.Nd manipulate EC_GROUP objects
-.Sh SYNOPSIS
-.In openssl/ec.h
-.In openssl/bn.h
-.Ft int
-.Fo EC_GROUP_copy
-.Fa "EC_GROUP *dst"
-.Fa "const EC_GROUP *src"
-.Fc
-.Ft EC_GROUP *
-.Fo EC_GROUP_dup
-.Fa "const EC_GROUP *src"
-.Fc
-.Ft int
-.Fo EC_GROUP_set_generator
-.Fa "EC_GROUP *group"
-.Fa "const EC_POINT *generator"
-.Fa "const BIGNUM *order"
-.Fa "const BIGNUM *cofactor"
-.Fc
-.Ft const EC_POINT *
-.Fo EC_GROUP_get0_generator
-.Fa "const EC_GROUP *group"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_order
-.Fa "const EC_GROUP *group"
-.Fa "BIGNUM *order"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo EC_GROUP_order_bits
-.Fa "const EC_GROUP *group"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_cofactor
-.Fa "const EC_GROUP *group"
-.Fa "BIGNUM *cofactor"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft void
-.Fo EC_GROUP_set_curve_name
-.Fa "EC_GROUP *group"
-.Fa "int nid"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_curve_name
-.Fa "const EC_GROUP *group"
-.Fc
-.Ft void
-.Fo EC_GROUP_set_asn1_flag
-.Fa "EC_GROUP *group"
-.Fa "int flag"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_asn1_flag
-.Fa "const EC_GROUP *group"
-.Fc
-.Ft void
-.Fo EC_GROUP_set_point_conversion_form
-.Fa "EC_GROUP *group"
-.Fa "point_conversion_form_t form"
-.Fc
-.Ft point_conversion_form_t
-.Fo EC_GROUP_get_point_conversion_form
-.Fa "const EC_GROUP *"
-.Fc
-.Ft unsigned char *
-.Fo EC_GROUP_get0_seed
-.Fa "const EC_GROUP *x"
-.Fc
-.Ft size_t
-.Fo EC_GROUP_get_seed_len
-.Fa "const EC_GROUP *"
-.Fc
-.Ft size_t
-.Fo EC_GROUP_set_seed
-.Fa "EC_GROUP *"
-.Fa "const unsigned char *"
-.Fa "size_t len"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_degree
-.Fa "const EC_GROUP *group"
-.Fc
-.Ft int
-.Fo EC_GROUP_check
-.Fa "const EC_GROUP *group"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo EC_GROUP_check_discriminant
-.Fa "const EC_GROUP *group"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo EC_GROUP_cmp
-.Fa "const EC_GROUP *a"
-.Fa "const EC_GROUP *b"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo EC_GROUP_get_basis_type
-.Fa "const EC_GROUP *"
-.Fc
-.Sh DESCRIPTION
-These functions operate on
-.Vt EC_GROUP
-objects created by the functions described in
-.Xr EC_GROUP_new 3 .
-.Pp
-.Fn EC_GROUP_copy
-copies the curve
-.Fa src
-into
-.Fa dst .
-Both
-.Fa src
-and
-.Fa dst
-must use the same
-.Vt EC_METHOD .
-.Pp
-.Fn EC_GROUP_dup
-creates a new
-.Vt EC_GROUP
-object and copies the content from
-.Fa src
-to the newly created
-.Vt EC_GROUP
-object.
-.Pp
-.Fn EC_GROUP_set_generator
-sets curve parameters that must be agreed by all participants using
-the curve.
-These parameters include the
-.Fa generator ,
-the
-.Fa order
-and the
-.Fa cofactor .
-The
-.Fa generator
-is a well defined point on the curve chosen for cryptographic
-operations.
-Integers used for point multiplications will be between 0 and
-.Fa order No - 1 .
-The
-.Fa order
-multiplied by the
-.Fa cofactor
-gives the number of points on the curve.
-.Pp
-.Fn EC_GROUP_get0_generator
-returns the generator for the identified
-.Fa group .
-.Pp
-.Fn EC_GROUP_get_order
-retrieves the order of the
-.Fa group
-and copies its value into
-.Fa order .
-It fails if the order of the
-.Fa group
-is not set or set to zero.
-.Pp
-.Fn EC_GROUP_get_cofactor
-retrieves the cofactor of the
-.Fa group
-and copies its value into
-.Fa cofactor .
-It fails if the cofactor of the
-.Fa group
-is not set or set to zero.
-.Pp
-The functions
-.Fn EC_GROUP_set_curve_name
-and
-.Fn EC_GROUP_get_curve_name
-set and get the NID for the curve, respectively (see
-.Xr EC_GROUP_new 3 ) .
-If a curve does not have a NID associated with it, then
-.Fn EC_GROUP_get_curve_name
-will return
-.Dv NID_undef .
-.Pp
-The asn1_flag value is used to determine whether the curve encoding
-uses explicit parameters or a named curve using an ASN.1 OID:
-many applications only support the latter form.
-If asn1_flag is the default value
-.Dv 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
-.Dv OPENSSL_EC_EXPLICIT_CURVE ,
-the parameters are explicitly encoded.
-The functions
-.Fn EC_GROUP_get_asn1_flag
-and
-.Fn EC_GROUP_set_asn1_flag
-get and set the status of the asn1_flag for the curve.
-.Pp
-The point_conversion_form for a curve controls how
-.Vt EC_POINT
-data is encoded as ASN.1 as defined in X9.62 (ECDSA).
-.Vt point_conversion_form_t
-is an enum defined as follows:
-.Bd -literal
-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;
-.Ed
-.Pp
-For
-.Dv 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.
-.Pp
-For any given x coordinate for a point on a curve it is possible to
-derive two possible y values.
-For
-.Dv 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.
-.Pp
-For
-.Dv 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.
-.Pp
-The functions
-.Fn EC_GROUP_set_point_conversion_form
-and
-.Fn EC_GROUP_get_point_conversion_form
-set and get the point_conversion_form for the curve, respectively.
-.Pp
-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
-.Fn 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
-.Fn 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
-.Fn 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 ASN.1 based communications.
-.Pp
-.Fn 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.
-.Pp
-The function
-.Fn 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.
-.Pp
-The function
-.Fn 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.
-.Pp
-.Fn EC_GROUP_cmp
-compares
-.Fa a
-and
-.Fa b
-to determine whether they represent the same curve or not.
-.Pp
-.Fn EC_GROUP_get_basis_type
-always returns 0 and is only provided for compatibility.
-.Sh RETURN VALUES
-The following functions return 1 on success or 0 on error:
-.Fn EC_GROUP_copy ,
-.Fn EC_GROUP_set_generator ,
-.Fn EC_GROUP_check ,
-and
-.Fn EC_GROUP_check_discriminant .
-.Pp
-.Fn EC_GROUP_dup
-returns a pointer to the duplicated curve or
-.Dv NULL
-on error.
-.Pp
-.Fn EC_GROUP_get0_generator
-returns the generator for the given curve or
-.Dv NULL
-on error.
-.Pp
-.Fn EC_GROUP_get_order
-returns 0 if the order is not set or set to zero for the
-.Fa group
-or if copying into
-.Fa order
-fails, or 1 otherwise.
-.Pp
-.Fn EC_GROUP_order_bits
-returns the number of bits in the group order.
-.Pp
-.Fn EC_GROUP_get_cofactor
-returns 0 if the cofactor is not set or set to zero for the
-.Fa group
-or if copying into
-.Fa cofactor
-fails, or 1 otherwise.
-.Pp
-.Fn EC_GROUP_get_curve_name
-returns the curve name (NID) for the
-.Fa group
-or
-.Dv NID_undef
-if no curve name is associated.
-.Pp
-.Fn EC_GROUP_get_asn1_flag
-returns the ASN.1 flag for the specified
-.Fa group .
-.Pp
-.Fn EC_GROUP_get_point_conversion_form
-returns the point_conversion_form for the
-.Fa group .
-.Pp
-.Fn EC_GROUP_get_degree
-returns the degree for the
-.Fa group
-or 0 if the operation is not supported
-by the underlying group implementation.
-.Pp
-.Fn EC_GROUP_get0_seed
-returns a pointer to the seed that was used to generate the parameter
-b, or
-.Dv NULL
-if the seed is not specified.
-.Fn EC_GROUP_get_seed_len
-returns the length of the seed or 0 if the seed is not specified.
-.Pp
-.Fn EC_GROUP_set_seed
-returns the length of the seed that has been set.
-If the supplied seed is
-.Dv NULL
-or the supplied seed length is 0, the return value will be 1.
-On error 0 is returned.
-.Pp
-.Fn EC_GROUP_cmp
-returns 0 if the curves are equal, 1 if they are not equal,
-or -1 on error.
-.Pp
-.Fn EC_GROUP_get_basis_type
-always returns 0.
-.Sh SEE ALSO
-.Xr d2i_ECPKParameters 3 ,
-.Xr EC_GROUP_new 3 ,
-.Xr EC_KEY_new 3 ,
-.Xr EC_POINT_add 3 ,
-.Xr EC_POINT_new 3
-.Sh HISTORY
-.Fn EC_GROUP_copy ,
-.Fn EC_GROUP_set_generator ,
-.Fn EC_GROUP_get0_generator ,
-.Fn EC_GROUP_get_order ,
-and
-.Fn EC_GROUP_get_cofactor
-first appeared in OpenSSL 0.9.7 and have been available since
-.Ox 3.2 .
-.Pp
-.Fn EC_GROUP_dup ,
-.Fn EC_GROUP_set_curve_name ,
-.Fn EC_GROUP_get_curve_name ,
-.Fn EC_GROUP_set_asn1_flag ,
-.Fn EC_GROUP_get_asn1_flag ,
-.Fn EC_GROUP_set_point_conversion_form ,
-.Fn EC_GROUP_get_point_conversion_form ,
-.Fn EC_GROUP_get0_seed ,
-.Fn EC_GROUP_get_seed_len ,
-.Fn EC_GROUP_set_seed ,
-.Fn EC_GROUP_get_degree ,
-.Fn EC_GROUP_check ,
-.Fn EC_GROUP_check_discriminant ,
-.Fn EC_GROUP_cmp ,
-and
-.Fn EC_GROUP_get_basis_type
-first appeared in OpenSSL 0.9.8 and have been available since
-.Ox 4.5 .
-.Pp
-.Fn EC_GROUP_order_bits
-first appeared in OpenSSL 1.1.0 and has been available since
-.Ox 7.0 .