Properties making a chaotic system a good pseudo random number generator

Abstract

We discuss the properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy, high dimensionality of the parent dynamical system, and very large period of the generated sequence. We propose the multidimensional Anosov symplectic (cat) map as a pseudo random number generator. We show what chaotic features of this map are useful for generating pseudo random numbers and investigate numerically which of them survive in the discrete state version of the map. Testing and comparisons with other generators are performed.