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1 PAUSE user(s)
1 non-PAUSE user(s).

Jonathan Yu

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@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@cpan.org>

COPYRIGHT AND LICENSE

Legally speaking, this package and its contents are:

  Copyright (c) 2011 by Jonathan Yu <jawnsy@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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