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Math::Random::BlumBlumShub

Module Version: 0.02
Math::Random::BlumBlumShub - the Blum-Blum-Shub pseudorandom bit generator.

This module needs the GMP C library - available from: http://gmplib.org 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 $prime1 = Math::GMP->new($s1); my $prime2 = Math::GMP->new($s2); my $seed = Math::GMP->new(time + int(rand(10000))); my $bitstream = Math::GMP->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); # See the test script that ships with the Math::Random::BlumBlumShub # module source for other working demos (using both the Math::GMP and # Math::GMPz modules).

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. $bool = autocorrelation_20000($op, $offset); $op is a sequence (Math::GMPz/Math::GMP object) of 20000 + $offset bits. Returns true ("success") if the no. of bits in $op not equal to their $offset-leftshifts lies in the range [9655 .. 10345] (inclusive). Else returns 0 ("failure"). ($count, $x5val) = autocorrelation($op, $offset); $op is a sequence (Math::GMPz/Math::GMP object) of 20000 bits. Returns (resp.) the no. of bits in $op not equal to their $offset-leftshifts, and the X5 value as specified in section 5.4.4 of "Handbook of Applied Cryptography" (Menezes at al).

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 2006-2008, 2009, 2010, Sisyphus

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

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