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Discrete Time Chaotic Maps With Application to Random Bit Generation

Discrete Time Chaotic Maps With Application to Random Bit Generation
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Author(s): Lazaros Moysis (Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece), Ahmad Taher Azar (Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh, Saudi Arabia), Aleksandra Tutueva (Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, Russia), Denis N. Butusov (Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, Russia)and Christos Volos (Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece)
Copyright: 2021
Pages: 41
Source title: Handbook of Research on Modeling, Analysis, and Control of Complex Systems
Source Author(s)/Editor(s): Ahmad Taher Azar (Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt & College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia)and Nashwa Ahmad Kamal (Faculty of Engineering, Cairo University, Giza, Egypt)
DOI: 10.4018/978-1-7998-5788-4.ch022

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Abstract

Chaotic behavior is a term that is attributed to dynamical systems whose solutions are highly sensitive to initial conditions. This means that small perturbations in the initial conditions can lead to completely different trajectories in the solution space. These types of chaotic dynamical systems arise in various natural or artificial systems in biology, circuits, engineering, computer science, and more. This chapter reports on some new chaotic discrete time two-dimensional maps that are derived from simple modifications to the well-known Hénon, Lozi, Sine-Sine, and Tinkerbell maps. Numerical simulations are carried out for different parameter values and initial conditions, and it is shown that the mappings either diverge to infinity or converge to attractors of many different shapes. The application to random bit generation is then considered using a collection of the proposed maps by applying a simple rule. The resulting bit generator successfully passes all statistical tests performed.

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