Lyapunov Exponent Enhancement in Chaotic Maps with Uniform Distribution Modulo One Transformation


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ABLAY G.

Chaos Theory and Applications, vol.4, no.1, pp.45-58, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.51537/chaos.1069002
  • Journal Name: Chaos Theory and Applications
  • Journal Indexes: Scopus, International Bibliography of Art, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.45-58
  • Keywords: Chaos, Cryptography, Image encryption, Lyapunov exponent, Random numbers
  • Kayseri University Affiliated: No

Abstract

© Vascular and Endovascular Review 2021.Most of the chaotic maps are not suitable for chaos-based cryptosystems due to their narrow chaotic parameter range and lacking of strong unpredictability. This work presents a nonlinear transformation approach for Lyapunov exponent enhancement and robust chaotification in discrete-time chaotic systems for generating highly independent and uniformly distributed random chaotic sequences. The outcome of the new chaotic systems can directly be used in random number and random bit generators without any post-processing algorithms for various information technology applications. The proposed Lyapunov exponent enhancement based chaotic maps are analyzed with Lyapunov exponents, bifurcation diagrams, entropy, correlation and some other statistical tests. The results show that excellent random features can be accomplished even with one-dimensional chaotic maps with the proposed approach.