Period Lengths of Chaotic Pseudo-Random Number Generators

J. Keller and H. Wiese (Germany)

Keywords

Cryptographic protocols, pseudorandom number genera tors, random mappings, chaotic systems.

Abstract

Cryptographic communication protocols frequently em ploy random numbers to achieve desirable properties. Of ten, generators for pseudo-random numbers (PRNGs) are employed. A class of PRNGs that currently gains popular ity are chaotic PRNGs which are derived from chaotic sys tems in physics. While their mathematical properties make them promising, typical implementations of such genera tors use IEEE 754 floating point representations instead of real numbers. We show that this leads to periods that are much shorter than expected, and thus renders these PRNGs potentially insecure.

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