Quantifiers for randomness of chaotic pseudo random number generators

L. DE MICCO; H. A. LARRONDO; A. PLASTINO; O. A. ROSSO

Philosophical Transactions of the Royal Society A

The Royal Society

Año: 2009 vol. 367 p. 3281 - 3296

1471-2962

We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). 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: (i) which is the best PRNG among the available ones? and (ii) 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.which is the best PRNG among the available ones? and (ii) 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.