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An innovative approach based on optimization for the determination of initial conditions of continuous-time chaotic system as a random number generator

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  • Yildirim, Gokce
  • Tanyildizi, Erkan

Abstract

Security has been one of the important problems in the processing, storage and transmission of information. The transfer of information to virtual environments with technological developments has made it necessary to examine the concept of security with different dimensions. Data security can be achieved to a great extent by using randomly generated unpredictable bit sequences in encryption. In this study, approximately 1,000,000 random bits were generated for use in computer science. The Mode2(x) method and the unpredictable nature of chaotic systems are used for random number generation. With this hybrid structure used in the study, it is aimed to gain a different perspective to future studies. However, it is known that the sensitivity of chaotic systems to initial conditions is very high. The most important contribution of the study to the literature is that the initial conditions were determined using optimization algorithms. In this study, Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) were used to calculate the initial conditions. To the authors' knowledge, this is the first study to use optimization to determine initial conditions for continuous-time chaotic systems. NIST SP 800-22 Statistical Test Suite was used to analyze the reliability of the generated random bits. It was seen that the proposed method passed all statistical tests successfully (100 %). Histogram and floating frequency analysis were used for the analysis of random numbers obtained from the generated bits. Histogram plots showed uniform distribution. It is seen that there is a homogeneous distribution in the sliding frequency analysis.

Suggested Citation

  • Yildirim, Gokce & Tanyildizi, Erkan, 2023. "An innovative approach based on optimization for the determination of initial conditions of continuous-time chaotic system as a random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004496
    DOI: 10.1016/j.chaos.2023.113548
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    References listed on IDEAS

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    1. Çavuşoğlu, Ünal & Kaçar, Sezgin & Pehlivan, Ihsan & Zengin, Ahmet, 2017. "Secure image encryption algorithm design using a novel chaos based S-Box," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 92-101.
    2. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
    3. Ying Sun & Yuelin Gao & Xudong Shi, 2019. "Chaotic Multi-Objective Particle Swarm Optimization Algorithm Incorporating Clone Immunity," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2023. "Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part," Mathematics, MDPI, vol. 11(23), pages 1-26, November.

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