Software and Hardware Implementation Sensitivity of Chaotic Systems and Impact on Encryption Applications
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Software and Hardware Implementation Sensitivity of Chaotic Systems and Impact on Encryption Applications Wafaa S. Sayed1 · Ahmed G. Radwan1,2 · Hossam A. H. Fahmy3 · AbdelLatif El-Sedeek1 Received: 3 October 2019 / Revised: 8 April 2020 / Accepted: 11 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper discusses the implementation sensitivity of chaotic systems added to their widely discussed sensitivities to initial conditions and parameter variation. This sensitivity can cause mismatches in some applications, which require an exact duplication of the system, e.g., chaos-based cryptography, synchronization and communication. Specifically, different implementation cases of three discretized jerk-based chaotic systems and a discrete-time logistic map are presented corresponding to different orders of additions and multiplications. The cases exhibit roughly similar attractor shapes, bifurcation behavior and Lyapunov exponents. However, mismatches between the time series corresponding to these cases in software double-precision, single-precision floating-point and hardware fixed-point implementations are reported. The number of time units after which the mismatch starts to become noticeable, and the effects of the discretization step and precision are discussed. Experimental results on Artix7 XC7A100T FPGA and oscilloscope validate the presence of mismatch reported through simulations. The wrong decryption effect of this mismatch is demonstrated for a software image encryption application, where one case is used for encryption and the other(s) for decryption. Pseudo-Random Number Generation and image encryption application using the mismatch signal as a chaotic generator are proposed and show good results using several well-established performance metrics. Keywords Chaotic systems · Digital implementation · Fixed-point arithmetic · Floating-point arithmetic · Image encryption
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Wafaa S. Sayed [email protected]
Extended author information available on the last page of the article
Circuits, Systems, and Signal Processing
1 Introduction Chaos theory studies the aperiodic random-like behavior generated from deterministic relations, which exhibit increased sensitivity to initial conditions and parameter variation. Chaotic systems are classified into discrete-time difference equations and continuous-time differential equations. Chaotic behavior can be visualized and quantified through time series, strange attractor and positive Maximum Lyapunov Exponent (MLE). Applications of chaotic systems include modeling [26] and Pseudo-Random Number Generators (PRNGs) for chaos-based communication and cryptography [15,17,19,20,24,28,29]. Utilizing chaotic systems in encryption, synchronization or other communication applications requires the duplication, i.e., having exact implementations of the system in the transmitter and the receiver. Consequently, any mismatches due to implementation sensitivity can cause unexpected results. Sensitivity to initial conditions property
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