NAME

Crypt::ECDSA::Curve::Koblitz -- binary (F(2**N) curves for EC cryptography

DESCRIPTION

These are for use with Crypt::ECDSA, a Math::BigInt based cryptography module. These routines work most efficiently if the GMP math library is installed, and in particular the point multiply function may be quite tedious without the GMP math library, which enables Math::BigInt::GMP.

METHODS

<new>

Delegated to base class Crypt::ECDSA::Curve

reduce_F2m

Special binary field function--reduce the result of addition or multiplication on
the curve by the 'irreducible' basis polynomial.  Akin to modular addition, but slower :(.

multiply_F2m

Binary field multiplication

invert_F2m

Binary field inversion: used for binary field division, so that
  $x * $y             becomes 
  $x * invert_F2m($y)

is_on_curve

return 1 if (x, y) is on the curve, otherwise undef.

add_on_curve

Add a point on the curve to itself or another

subtract_on_curve

Subtract a point on the curve.  Same as addition.

double_on_curve

Double a point on the curve.   
Returns a new point, does NOT change the original.

inverse_on_curve

get a point's additive inverse

multiply_on_curve

my $Q = $G * n;

Multiply a curve point by a scalar.  
Note this should always be Point * scalar, not scalar * Point.

is_weak_curve

tests for known weak curve parameters

tau_point_multiply

Koblitz curve binary field point multiply algorithm from draft FIPS 186-3, pages 111-114  

FUNCTIONS

b<equation>

Return ascii string representation of the field equation

rounded_div

division with rounding

b<test_bit>

test if a bit in an integer is set

size_in_bits

binary size in bits of an integer

BUGS

Too slow for routine use with secure sizes at present.  This will likely be fixed
with XS code in a future release.  Use prime curves instead for now.

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.