/ 
Math-Random-MicaliSchnorr-0.01
River stage zero No dependents
/ Math::Random::MicaliSchnorr

NAME

Math::Random::MicaliSchnorr - the Micali-Schnorr pseudorandom bit generator.

DEPENDENCIES

This module needs the GMP C library - available from:
http://swox.com/gmp

The functions in this module take either Math::GMP or Math::GMPz objects
as their arguments - so you'll need either Math::GMP or Math::GMPz as
well. (Actually, *any* perl scalar that's a reference to a GMP mpz
structure will suffice - it doesn't *have* to be a Math::GMP or
Math::GMPz object.)

DESCRIPTION

An implementation of the Micali-Schnorr pseudorandom bit generator.

SYNOPSIS

use warnings;
use Math::Random::MicaliSchnorr qw(ms ms_seedgen);

use Math::GMP;
# and/or:
use Math::GMPz;

my $s1 = '1255031698703398971890886237939563492533';
my $s2 = '10512667662093824763131998324796018248471';
my $prime1    = Math::GMPz->new($s1);
my $prime2    = Math::GMPz->new($s2);
my $seed      = Math::GMPz->new(time + int(rand(10000)));
my $exp;
my $bitstream = Math::GMPz->new();
my $bits_out  = 500;

# Generate the seed value
ms_seedgen($seed, $exp, $prime1, $prime2);

# Fill $bitstream with 500 random bits using $seed, $prime1 and $prime2
ms($bitstream, $prime1, $prime2, $seed, $exp, $bits_out);

FUNCTIONS

ms($o, $prime1, $prime2, $seed, $exp, $bits);

 "$o", "$p", "$q", and "$seed" are all Math::GMP or Math::GMPz objects.
 $p and $q are large primes. (The ms function does not check that they
 are, in fact, prime.)
 Output a $bits-bit random bitstream to $o - calculated using the 
 Micali-Schnorr algorithm, based on the inputs $p, $q, $seed and $exp.
 See the ms_seedgen documentation (below) for the requirements regarding
 $seed and $exp.

ms_seedgen($seed, $exp, $prime1, $prime2);
 $seed is a Math::GMP or Math::GMPz object. $exp is just a normal perl
 scalar (that will have an unsigned integer value assigned to it). The
 ms_seedgen function assigns suitable values to both $seed and $exp. You
 can, of course, write your own routine for determining these values.
 (The ms function checks that $seed and $exp are in the allowed range.)
 Here are the rules for determining those values:
 Let N be the bitlength of n = $prime1 * $prime2.
 Let phi = ($prime1 - 1) * ($prime2 - 1). $exp must satisfy all 3 of the 
 following conditions:
  i) 2 < $exp < phi
  ii) The greatest common denominator of $exp and phi is 1
  iii) $exp * 80 <= N
 Conditions i) and iii) mean that N has to be at least 340 (80 * 3).
 The ms_seedgen function selects the largest value for $exp that
 satisfies those 3 conditions. Having found a suitable value for $exp, we
 then need to calculate the integer value k = int(N *(1 - (2 / $exp))).
 Then calculate r = N - k.
 $seed is a random number of bitlength r. The ms_seedgen function uses
 the GMP library's mpz_urandomb function to select $seed.
 The mpz_urandomb function is seeded by the value supplied in $seed.

$bool = monobit($op);
$bool = longrun($op);
$bool = runs($op);
$bool = poker($op);

 These are the 4 standard FIPS-140 statistical tests for testing
 prbg's. They return '1' for success and '0' for failure.
 They test 20000-bit pseudorandom sequences, stored in the
 Math::GMPz/Math::GMP object $op.

BUGS

You can get segfaults if you pass the wrong type of argument to the
functions - so if you get a segfault, the first thing to do is to check
that the argument types you have supplied are appropriate.

LICENSE

This program is free software; you may redistribute it and/or 
modify it under the same terms as Perl itself.

AUTHOR

Copyright Sisyhpus <sisyphus at(@) cpan dot (.) org>