The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers
Cryptography and Security
2011-01-25 v2 Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.cs/0607069,
title = {The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers},
author = {Mahesh C Shastry and Nithin Nagaraj and Prabhakar G Vaidya},
journal= {arXiv preprint arXiv:cs/0607069},
year = {2011}
}
Comments
25 pages, 15 figures