Hi,

According to section 5.4.4 of Handbook of Applied Cryptography (by Menezes, van Oorschot and Vanstone), FIPS 140-1 specified 4 statistical tests for randomness - namely "monobit", "runs", "long run", "poker".

I implemented those tests (undocumented and not exported) in Math::GMPz.
On Windows (whether randbits == 48 or randbits == 15, when I use rand() to generate the 20000-bit sequence that these tests require, I've always found the generated bit sequence to pass those tests.
Moreover, I can see no sign of any cycling - I take a 30-bit sequence from near the end of the string, and cannot find that same sub-string elsewhere within the 20000-bit sequence.

I've also added a fifth "autocorrelation" test from the same section of the book.
Here's the script I run:

use strict;
use warnings;
use Math::GMPz qw(:mpz);
use Test::More;

my $s;

# Create a string of 20000 bits
for(1..20000) {
 $s .= int(rand(2));
}

# Visually inspect the value
#open (my $fh, '>', 'val.txt') or warn "Open: $!";
#print $fh $s;
#close $fh;

# Vectorize that string into a
# Math::GMPz object
my $mpz = Math::GMPz->new($s, 2);

# Check that the no. of set bits is in
# the range 9655..10345
cmp_ok(Math::GMPz::Rmonobit($mpz), '==', 1,
                           'monobit test');

# Check that the longest run of the same bit is
# shorter than 34 
cmp_ok(Math::GMPz::Rlong_run($mpz), '==', 1,
                           'long run test');

# Check that the numbers of 1-bit runs, 2-bit runs,
# 3-bit runs 4-bit runs, 5-bit runs and 6-bit runs
# (of both zeros and ones) meet expectations. 
cmp_ok(Math::GMPz::Rruns($mpz), '==', 1,
                           'runs test');

# Check that the no. of occurrences of the various
# 4-bit sequences meets expectations.
cmp_ok(Math::GMPz::Rpoker($mpz), '==', 1,
                           'poker test');

# Check that the number of times that
# bit[pos] == bit[pos + 2] is in the
# range 9655..10345.
my @ret = Math::GMPz::autocorrelation($mpz, 2);
cmp_ok($ret[0], '>', 9654, 'autocorrelation count > lower limit');
cmp_ok($ret[0], '<', 10346, 'autocorrelation count < upper limit');

done_testing();
[download]

Cheers,
Rob