The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers

Abstract

A 1-dimensional generalization of the well known Logistic Map is proposed. The proposed family of maps is referred to as the B-Exponential Map. The dynamics of this map are analyzed and found to have interesting properties. In particular, the B-Exponential Map exhibits robust chaos for all real values of the parameter B >= e^(-4). We then propose a pseudo-random number generator based on the B-Exponential Map by chaotically hopping between different trajectories for different values of B. We call this BEACH (B-Exponential All-Chaotic Map Hopping) pseudo-random number generator. BEACH successfully passes stringent statistical randomness tests such as ENT, NIST and Diehard. An implementation of BEACH is also outlined.

25 pages, 15 figures

References in corpus (1)

• Multi-Map Orbit Hopping Chaotic Stream Cipher

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