.\"	$OpenBSD: ec.3,v 1.3 2016/11/06 15:57:38 schwarze Exp $
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.Dd $Mdocdate: November 6 2016 $
.Dt EC 3
.Os
.Sh NAME
.Nm ec
.Nd Elliptic Curve functions
.Sh SYNOPSIS
.In openssl/ec.h
.Sh DESCRIPTION
This library provides an extensive set of functions for performing
operations on elliptic curves over finite fields.
In general an elliptic curve is one with an equation of the form:
.Pp
.Dl y^2 = x^3 + ax + b
.Pp
An
.Vt EC_GROUP
structure is used to represent the definition of an elliptic curve.
Points on a curve are stored using an
.Vt EC_POINT
structure.
An
.Vt EC_KEY
is used to hold a private/public key pair, where a private key is simply a
.Vt BIGNUM
and a public key is a point on a curve represented by an
.Vt EC_POINT .
.Pp
The library contains a number of alternative implementations of the
different functions.
Each implementation is optimised for different scenarios.
No matter which implementation is being used, the interface remains the
same.
The library handles calling the correct implementation when an interface
function is invoked.
An implementation is represented by an
.Vt EC_METHOD
structure.
.Pp
The creation and destruction of
.Vt EC_GROUP
objects is described in
.Xr EC_GROUP_new 3 .
Functions for manipulating
.Vt EC_GROUP
objects are described in
.Xr EC_GROUP_copy 3 .
.Pp
Functions for creating, destroying and manipulating
.Vt EC_POINT
objects are explained in
.Xr EC_POINT_new 3 ,
whilst functions for performing mathematical operations and tests on
.Vt EC_POINT Ns s
are coverd in
.Xr EC_POINT_add 3 .
.Pp
For working with private and public keys refer to
.Xr EC_KEY_new 3 .
Implementations are covered in
.Xr EC_GFp_simple_method 3 .
.Pp
For information on encoding and decoding curve parameters to and
from ASN.1 see
.Xr d2i_ECPKParameters 3 .
.Sh SEE ALSO
.Xr crypto 3 ,
.Xr d2i_ECPKParameters 3 ,
.Xr EC_GFp_simple_method 3 ,
.Xr EC_GROUP_copy 3 ,
.Xr EC_GROUP_new 3 ,
.Xr EC_KEY_new 3 ,
.Xr EC_POINT_add 3 ,
.Xr EC_POINT_new 3 ,
.Xr EVP_PKEY_CTX_set_ec_paramgen_curve_nid 3