NAME

Crypt::ECDSA::Curve -- Base class for ECC curves

DESCRIPTION

These are for use with Crypt::ECDSA and require Math::BigInt::GMP.

METHODS

new

Constructor.  Takes the following named pair arguments:

standard => 'standard-curve-name'

Used for named standard curves such as the NIST standard curves.  
Preferentially, these are invoked by classes which inherit
from Crypt::ECDSA::Curve, such as Crypt::ECDSA::Curve::Prime, 
Crypt::ECDSA::Curve::Binary, or Crypt::ECDSA::Curve::Koblitz.

See US govenment standard publications FIPS 186-2 or FIPS 186-3.

used as:

new(standard => 'standard curve name'), where curve name is one of:

Crypt::ECDSA::Curve::Prime->new( standard => 
 [ one of 'ECP-192', 'ECP-224', 'ECP-256', 'ECP-384', 'ECP-521' ] )
 
Crypt::ECDSA::Curve::Koblitz->new( standard => 
 [ one of 'EC2N-163', 'EC2N-233', 'EC2N-283', 'EC2N-409', 'EC2N-571' ] )
 
Koblitz curves are a special case of binary curves, with a simpler equation.

Non-standard curve types are supported either via specifying parameters and algorithm,
or by specifying a generic "standard" via specifying in new the pair:
   standard => 'generic_prime' or standard => 'generic_binary'.

The following are used mainly for non-standard curve types.  They are 
gotten from pre-defined values for named curves:

p => $p , sets curve modulus  ( for prime curve over F(p) )

a => $a, sets curve param a

b => $b, sets curve param b

N  =>  the exponent in 2**N, where 2**N is a binary curve modulus
  ( for binary or Koblitz curve over F(2**N) )

h    => curve cofactor for the point order

r    =>  base point G order for prime curves

n   =>   base point G order for binary curves

G_x  => $x,  a base point x coordinate

G_y  =>  $y, a base point y coordinate

irreducible => binary curve irreducible basis polynimial in binary integer 
  format, so that x**233 + x**74 + 1 becomes
     polynomial => [ 233, 74, 0 ] and irreducible =>           
       '0x20000000000000000000000000000000000000004000000000000000001'

a

my $param = $curve->a;

Returns parameter a in the elliptic equation.

b

my $param = $curve->b;

Returns parameter b in the elliptic equation.

p

my $param = $curve->p;

returns parameter p in the equation-- this is the field modulus parameter for prime curves

order

my $param = $curve->order;

Returns the curve base point G order if known.

curve_order

my $param = $curve->curve_order;

Returns the curve order if known. This might calculate the order some day.
It does not in this version.

modulus

my $divisor = $curve->modulus;

Returns the mathmetical divisor used to reduce numbers in the field.  This is either the 
prime of an Fp field curve or the irreducible polynomial of a binary field curve.

infinity

my $inf = $curve->infinity;

Returns a valid point at infinity for the curve.

standard

my $param = $curve->standard;

Returns the 'standard' type of the curve, if defined for the instance.

Class Internal Functions

q

AUTHOR

William Herrera B<wherrera@skylightview.com>. 

SUPPORT

Questions, feature requests and bug reports should go to <wherrera@skylightview.com>.

COPYRIGHT

Copyright (c) 2007 William Herrera. All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.