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Math::Random::BlumBlumShub

Module Version: 0.01
Math::Random::BlumBlumShub - the Blum-Blum-Shub pseudorandom bit generator.

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.)

An implementation of the Blum-Blum-Shub pseudorandom bit generator.

use warnings; use Math::Random::BlumBlumShub qw(bbs bbs_seedgen); use Math::GMP; # and/or: use Math::GMPz; my $s1 = '615389388455725613122981570401989286707'; my $s2 = '8936277569639798554773638405675965349567'; my $prime1 = Math::GMPz->new($s1); my $prime2 = Math::GMPz->new($s2); my $seed = Math::GMPz->new(time + int(rand(10000))); my $bitstream = Math::GMPz->new(); my $bits_out = 500; # Generate the seed value bbs_seedgen($seed, $prime1, $prime2); # Fill $bitstream with 500 random bits using $seed, $prime1 and $prime2 bbs($bitstream, $prime1, $prime2, $seed, $bits_out);

bbs($o, $p, $q, $seed, $bits); "$o", "$p", "$q", and "$seed" are all Math::GMP or Math::GMPz objects. $p and $q must be large primes congruent to 3 modulus 4. (The bbs function checks $p and $q for congruence to 3 modulus 4, but does not verify that $p and $q are, in fact, prime.) Output a $bits-bit random bitstream to $o - calculated using the Blum-Blum-Shub algorithm, based on the inputs $p, $q, and $seed. See the bbs_seedgen documentation below for the requirements that $seed needs to meet. bbs_seedgen($seed, $p, $q); "$seed", "$p", and "$q" are all Math::GMP or Math::GMPz objects. $p and $q are the 2 large primes being used by the BlumBlumShub PRBG. The seed needs to be less than N = $p * $q, and gcd(seed, N) must be 1. This routine uses the mpz_urandomm() function to pseudorandomly generate a seed less than N. (The supplied value of $seed is used to seed mpz_urandomm.) If gcd(seed, N) != 1, then the seed is decremented until gcd(seed, N) == 1. $seed is then set to that seed value. You can, of course, write your own routine to create the 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.

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.

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

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

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