A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption. (October 2021) - Louzzani, Noura; Boukabou, Abdelkrim; Bahi, Halima; Boussayoud, Ali
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.