Quantifiers for randomness of chaotic pseudo random number generators

TL;DR

This paper investigates how various statistical quantifiers can distinguish chaos in pseudo random number generators, emphasizing the roles of invariant measures and mixing constants in assessing and improving PRNG quality.

Contribution

It provides a comparative analysis of different chaos quantifiers, highlighting their relevance in evaluating and enhancing the randomness of chaotic PRNGs.

Findings

Invariant measure and mixing constant are key to chaos detection.

Certain quantifiers effectively distinguish chaotic from non-chaotic sequences.

The analysis guides the selection and improvement of PRNGs.

Abstract

We deal with randomness-quantifiers and concentrate on their ability do discern the hallmark of chaos in time-series used in connection with pseudo random number generators (PRNG). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely, i) its invariant measure and ii) the mixing constant. This is of help in answering two questions that arise in applications, that is, (1) which is the best PRNG among the available ones? and (2) If a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure?. Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.