<p>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.</p>
M. C. Shastry, Nagaraj, N., and Vaidya, P. G., “The B-Exponential Map: A Generalization of the Logistic Map, and its Applications in Generating Pseudo-Random Numbers”, arXiv preprint cs/0607069, 2006.