Structural improvements of chaotic PRNG implementations

Abstract

Chaotic functions have been announced in the literature as promising for implementing low complexity pseudo-random number generators (PRNGs) required e.g. for RFID security applications. They combine good theoretical statistical properties with a computationally simple algorithm. Unfortunately, actual implementations with finite number precision show a disappointing behavior compared to the mathematical theory. This results for example in comparably short cycles in the state space graph, which lead to a repetition of the generated pseudo random values after a small number of iterations. This paper presents a simple way to improve the state space structure of chaotic PRNGs by using a different parametrization of the chaotic function at certain iterations and hereby breaking out of these cycles. This approach reduces this aspect of the weakness of such implementations, which we demonstrate with several examples.