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A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption

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  • Louzzani, Noura
  • Boukabou, Abdelkrim
  • Bahi, Halima
  • Boussayoud, Ali

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.

Suggested Citation

  • Louzzani, Noura & Boukabou, Abdelkrim & Bahi, Halima & Boussayoud, Ali, 2021. "A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s096007792100669x
    DOI: 10.1016/j.chaos.2021.111315
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    References listed on IDEAS

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    1. de Carvalho, R. Egydio & Leonel, Edson D., 2016. "Squared sine logistic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 37-44.
    2. García-Guerrero, E.E. & Inzunza-González, E. & López-Bonilla, O.R. & Cárdenas-Valdez, J.R. & Tlelo-Cuautle, E., 2020. "Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    4. Özer, Mehmet & Čenys, Antanas & Polatoglu, Yasar & Hacibekiroglu, Gürsel & Akat, Ercument & Valaristos, A. & Anagnostopoulos, A.N., 2007. "Bifurcations of Fibonacci generating functions," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1240-1247.
    5. Esteban Tlelo-Cuautle & Antonio de Jesus Quintas-Valles & Luis Gerardo de la Fraga & Jose de Jesus Rangel-Magdaleno, 2016. "VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-32, December.
    6. Saba, Nabiha & Boussayoud, Ali, 2021. "On the bivariate Mersenne Lucas polynomials and their properties," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    Cited by:

    1. Kavuran, Gürkan, 2022. "When machine learning meets fractional-order chaotic signals: detecting dynamical variations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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