The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers
<|reference_start|>The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers: 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.<|reference_end|>
@article{shastry2006the,
    title={The B-Exponential Map: A Generalization of the Logistic Map, and Its
  Applications In Generating Pseudo-random Numbers},
    author={Mahesh C Shastry, Nithin Nagaraj, Prabhakar G Vaidya},
    journal={arXiv preprint arXiv:cs/0607069},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0607069},
    primaryClass={cs.CR nlin.CD}
}