Quantifiers for randomness of chaotic pseudo-random number generators

• Autores: De Micco, L.; Larrondo, H.A.; Plastino, A.; Rosso, O.A.
• Año de publicación: 2009
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2009;367(1901):3281-3296
• Materia: Excess entropy; Permutation entropy; Random number; Rate entropy; Recurrence plots; Statistical complexity; Chaotic systems; Entropy; Number theory; Time series; Excess entropy; Permutation entropy; Random number; Rate entropy; Recurrence plots; Statistical complexity; Random number generation; article; nonlinear system; time; Nonlinear Dynamics; Time Factors
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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. © 2009 The Royal Society.