A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption. (October 2021)

• Record Type: Journal Article
• Authors: Louzzani, Noura; Boukabou, Abdelkrim; Bahi, Halima; Boussayoud, Ali
• Is Part Of: Chaos, solitons and fractals. Volume 151(2021)
• Publication Date: 2021-10
• Subjects: Generating function -- Chebyshev polynomials of the second kind -- Chaos -- Lyapunov exponent -- Bifurcation diagram -- Cryptosystem; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111315
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Analytic derivation of the generating function of the generalized Chebyshev polynomials of the second kind. Explore the typical period-doubling cascade to chaos using the bifurcation diagram and the Lyapunov exponent. Application of the proposed chaos based generating function for image encryption. Abstract: In this paper, we propose a generating function for Chebyshev polynomials with typical period-doubling to chaos. In this context, the bifurcation diagram and Lyapunov exponent proved that the proposed generating function is a deterministic system that exhibits chaotic behavior for specific values of the control parameters. As an application, this proposed generating function is used as a chaos-based cryptosystem to encrypt different images. Security analysis demonstrated that the proposed generating function of the Chebyshev polynomials presents an excellent performance in image encryption against various attacks.