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Robustification of a One-Dimensional Generic Sigmoidal Chaotic Map with Application of True Random Bit Generation

1
School of Systems Engineering, Electronic and Photonic Engineering, Kochi University of Technology, Tosayamada, Kami City, Kochi 782-8502, Japan
2
Center of Excellence in Intelligent Systems Integration, Faculty of Engineering, Thai-Nichi Institute of Technology (TNI), 1771/1, Pattanakarn Rd, Suan Luang, Bangkok 10250, Thailand
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(2), 136; https://doi.org/10.3390/e20020136
Received: 23 December 2017 / Revised: 7 February 2018 / Accepted: 16 February 2018 / Published: 20 February 2018
(This article belongs to the Special Issue Theoretical Aspect of Nonlinear Statistical Physics)
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Abstract

The search for generation approaches to robust chaos has received considerable attention due to potential applications in cryptography or secure communications. This paper is of interest regarding a 1-D sigmoidal chaotic map, which has never been distinctly investigated. This paper introduces a generic form of the sigmoidal chaotic map with three terms, i.e., xn+1 = ∓AfNL(Bxn) ± Cxn ± D, where A, B, C, and D are real constants. The unification of modified sigmoid and hyperbolic tangent (tanh) functions reveals the existence of a “unified sigmoidal chaotic map” generically fulfilling the three terms, with robust chaos partially appearing in some parameter ranges. A simplified generic form, i.e., xn+1 = ∓fNL(Bxn) ± Cxn, through various S-shaped functions, has recently led to the possibility of linearization using (i) hardtanh and (ii) signum functions. This study finds a linearized sigmoidal chaotic map that potentially offers robust chaos over an entire range of parameters. Chaos dynamics are described in terms of chaotic waveforms, histogram, cobweb plots, fixed point, Jacobian, and a bifurcation structure diagram based on Lyapunov exponents. As a practical example, a true random bit generator using the linearized sigmoidal chaotic map is demonstrated. The resulting output is evaluated using the NIST SP800-22 test suite and TestU01. View Full-Text
Keywords: robustification; unification; linearization; chaotic map; sigmoid; robust chaos; true random bit generator robustification; unification; linearization; chaotic map; sigmoid; robust chaos; true random bit generator
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Jiteurtragool, N.; Masayoshi, T.; San-Um, W. Robustification of a One-Dimensional Generic Sigmoidal Chaotic Map with Application of True Random Bit Generation. Entropy 2018, 20, 136.

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