NAME¶
Math::Random::ISAAC - Perl interface to the ISAAC PRNG algorithm
VERSION¶
version 1.003
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.