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NAME
Math::Random::ISAAC - Perl interface to the ISAAC PRNG algorithm
VERSION
version 1.004
SYNOPSIS
use Math::Random::ISAAC;
my $rng = Math::Random::ISAAC->new(@seeds);
for (0..30) {
print 'Result: ' . $rng->irand() . "\n";
}
DESCRIPTION
As with other Pseudo-Random Number Generator (PRNG) algorithms like the
Mersenne Twister (see Math::Random::MT), this algorithm is designed to
take some seed information and produce seemingly random results as
output.
However, ISAAC (Indirection, Shift, Accumulate, Add, and Count) has
different goals than these commonly used algorithms. In particular, it's
really fast - on average, it requires only 18.75 machine cycles to
generate a 32-bit value. This makes it suitable for applications where a
significant amount of random data needs to be produced quickly, such
solving using the Monte Carlo method or for games.
The results are uniformly distributed, unbiased, and unpredictable
unless you know the seed. The algorithm was published by Bob Jenkins in
the late 90s and despite the best efforts of many security researchers,
no feasible attacks have been found to date.
USAGE WARNING
There was no method supplied to provide the initial seed data by the
author. On his web site, Bob Jenkins writes:
Seeding a random number generator is essentially the same problem as
encrypting the seed with a block cipher.
In the same spirit, by default, this module does not seed the algorithm
at all -- it simply fills the state with zeroes -- if no seed is
provided. The idea is to remind users that selecting good seed data for
their purpose is important, and for the module to conveniently set it to
something like "localtime" behind-the-scenes hurts users in the long
run, since they don't understand the limitations of doing so.
The type of seed you might want to use depends entirely on the purpose
of using this algorithm in your program in the first place. Here are
some possible seeding methods:
1 Math::TrulyRandom
The Math::TrulyRandom module provides a way of obtaining truly
random data by using timing interrupts. This is probably one of the
better ways to seed the algorithm.
2 /dev/random
Using the system random device is, in principle, the best idea,
since it gathers entropy from various sources including interrupt
timing, other device interrupts, etc. However, it's not portable to
anything other than Unix-like platforms, and might not produce good
data on some systems.
3 localtime()
This works for basic things like simulations, but results in
not-so-random output, especially if you create new instances quickly
(as the seeds would be the same within per-second resolution).
4 Time::HiRes
In theory, using Time::HiRes is the same as option (2), but you get
a higher resolution time so you're less likely to have the same seed
twice. Note that you need to transform the output into an integer
somehow, perhaps by taking the least significant bits or using a
hash function. This would be less prone to duplicate instances, but
it's still not ideal.
METHODS
new
Math::Random::ISAAC->new( @seeds )
Creates a "Math::Random::ISAAC" object, based upon either the optimized
C/XS version of the algorithm, Math::Random::ISAAC::XS, or falls back to
the included Pure Perl module, Math::Random::ISAAC::PP.
Example code:
my $rng = Math::Random::ISAAC->new(time);
This method will return an appropriate Math::Random::ISAAC object or
throw an exception on error.
rand
$rng->rand()
Returns a random double-precision floating point number which is
normalized between 0 and 1 (inclusive; it's a closed interval).
Internally, this simply takes the uniformly distributed unsigned integer
from "$rng->irand()" and divides it by "2**32-1" (maximum unsigned
integer size)
Example code:
my $next = $rng->rand();
This method will return a double-precision floating point number or
throw an exception on error.
irand
$rng->irand()
Returns the next unsigned 32-bit random integer. It will return a value
with a value such that: 0 <= x <= 2**32-1.
Example code:
my $next = $rng->irand();
This method will return a 32-bit unsigned integer or throw an exception
on error.
PURPOSE
The intent of this module is to provide single simple interface to the
two compatible implementations of this module, namely,
Math::Random::ISAAC::XS and Math::Random::ISAAC::PP.
If, for some reason, you need to determine what version of the module is
actually being included by "Math::Random::ISAAC", then:
print 'Backend type: ', $Math::Random::ISAAC::DRIVER, "\n";
In order to force use of one or the other, simply load the appropriate
module:
use Math::Random::ISAAC::XS;
my $rng = Math::Random::ISAAC::XS->new();
# or
use Math::Random::ISAAC::PP;
my $rng = Math::Random::ISAAC::PP->new();
ACKNOWLEDGEMENTS
* Special thanks to Bob Jenkins <bob_jenkins AT burtleburtle.net> for
devising this very clever algorithm and releasing it into the public
domain.
* Thanks to John L. Allen (contact unknown) for providing a Perl port
of the original ISAAC code, upon which "Math::Random::ISAAC::PP" is
heavily based. His version is available on Bob's web site, in the
SEE ALSO section.
SEE ALSO
Math::Random::ISAAC::XS, the C/XS optimized version of this module,
which will be used automatically if available.
<http://burtleburtle.net/bob/rand/isaacafa.html>, Bob Jenkins' page
about ISAAC, which explains the algorithm as well as potential attacks.
<http://eprint.iacr.org/2006/438.pdf>, a paper entitled "On the
pseudo-random generator ISAAC," which claims there are many seeds which
will produce non-uniform results. The author, Jean-Philippe Aumasson,
argues ISAAC should be using rotations (circular shifts) instead of
normal shifts to increase diffusion of the state, among other things.
<http://eprint.iacr.org/2001/049.pdf>, a paper by Marina Pudovkina
discussing plaintext attacks on the ISAAC keystream generator. Among
other things, it notes that the time complexity is Tmet = 4.67*10^1240,
so it remains a secure cipher for practical applications.
CAVEATS
* There is no method that allows re-seeding of algorithms. This is not
really necessary because one can simply call "new" again with the
new seed data periodically.
But he also provides a simple workaround:
As ISAAC is intended to be a secure cipher, if you want to reseed it,
one way is to use some other cipher to seed some initial version of ISAAC,
then use ISAAC's output as a seed for other instances of ISAAC whenever
they need to be reseeded.
* There is no way to clone a PRNG instance. I'm not sure why this is
might even be necessary or useful. File a bug report with an
explanation why and I'll consider adding it to the next release.
BUGS
Please report any bugs or feature requests on the bugtracker website
http://rt.cpan.org/NoAuth/Bugs.html?Dist=Math-Random-ISAAC
When submitting a bug or request, please include a test-file or a patch
to an existing test-file that illustrates the bug or desired feature.
AUTHOR
Jonathan Yu <jawnsy AT cpan.org>
COPYRIGHT AND LICENSE
Legally speaking, this package and its contents are:
Copyright (c) 2011 by Jonathan Yu <jawnsy AT cpan.org>.
But this is really just a legal technicality that allows the author to
offer this package under the public domain and also a variety of
licensing options. For all intents and purposes, this is public domain
software, which means you can do whatever you want with it.
The software is provided "AS IS", without warranty of any kind, express
or implied, including but not limited to the warranties of
merchantability, fitness for a particular purpose and noninfringement.
In no event shall the authors or copyright holders be liable for any
claim, damages or other liability, whether in an action of contract,
tort or otherwise, arising from, out of or in connection with the
software or the use or other dealings in the software.
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