Analyzing Logistic Map Pseudorandom Number Generators for Periodicity Induced by Finite Precision Floating-Point Representation

Authors

Kyle Persohn, Marquette UniversityFollow
Richard J. Povinelli, Marquette UniversityFollow

Document Type

Article

Language

eng

Format of Original

8 p.

Publication Date

3-2012

Publisher

Elsevier

Source Publication

Chaos, Solitons & Fractals

Source ISSN

0960-0779

Original Item ID

doi: 10.1016/j.chaos.2011.12.006

Abstract

Because of the mixing and aperiodic properties of chaotic maps, such maps have been used as the basis for pseudorandom number generators (PRNGs). However, when implemented on a finite precision computer, chaotic maps have finite and periodic orbits. This manuscript explores the consequences finite precision has on the periodicity of a PRNG based on the logistic map. A comparison is made with conventional methods of generating pseudorandom numbers. The approach used to determine the number, delay, and period of the orbits of the logistic map at varying degrees of precision (3 to 23 bits) is described in detail, including the use of the Condor high-throughput computing environment to parallelize independent tasks of analyzing a large initial seed space. Results demonstrate that in terms of pathological seeds and effective bit length, a PRNG based on the logistic map performs exponentially worse than conventional PRNGs.

Comments

Accepted version. Chaos, Solitons & Fractals, Vol. 45, No. 3 (March 2012): 238-245. DOI. © 2012 Elsevier. Used with permission.

Recommended Citation

Persohn, Kyle and Povinelli, Richard J., "Analyzing Logistic Map Pseudorandom Number Generators for Periodicity Induced by Finite Precision Floating-Point Representation" (2012). Electrical and Computer Engineering Faculty Research and Publications. 104.
https://epublications.marquette.edu/electric_fac/104