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Control of multistability with selection of chaotic attractor: application to image encryption

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Abstract

Dynamic systems exhibiting chaos with periodic windows and multistability are not recommended for cryptography due to the lack of security in these regimes. In this work, we use a linear augmentation control scheme to control a periodic attractor in the windows of multistability to a final chaotic attractor which survives to the variation of initial seed useful for image encryption. The empirical Chua’s system with piecewise linear nonlinearity is used as a sample dynamical system but the idea can be applied using any other dynamical system. First, this system is analyzed to reveal multistability dynamics. Second, the technique of linear augmentation combined with the nonlinear system invariant sets like equilibrium points is used to choose a desired survive attractor among the coexisting ones. It is found that annihilation of multistability in the Chua’s system when varying the coupling strength is obtained through several crises among which interior crisis and border collision. Finally, a survived chaotic attractor is jointly used with SHA-512 for image encryption algorithm using a simple diffusion-confusion structure. Security analysis shows that the encryption process based on control theory can resist various forms of attack.

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My manuscript has no associated data or the data will not be deposited.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon

    Zeric Tabekoueng Njitacke, Michael Ekonde Sone & Christian Tchito Tchapga

  2. Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, Cameroon

    Thophile Fonzin Fozin

  3. Research Unit of Condensed Matter, Electronics and Signal Processing (UR-MACETS), Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Nestor Tsafack & Gervais Dolvis Leutcho

  4. Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Zeric Tabekoueng Njitacke, Nestor Tsafack & Gervais Dolvis Leutcho

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  1. Zeric Tabekoueng Njitacke
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  2. Michael Ekonde Sone
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  3. Thophile Fonzin Fozin
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Correspondence to Zeric Tabekoueng Njitacke.

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Njitacke, Z.T., Sone, M.E., Fozin, T.F. et al. Control of multistability with selection of chaotic attractor: application to image encryption. Eur. Phys. J. Spec. Top. 230, 1839–1854 (2021). https://doi.org/10.1140/epjs/s11734-021-00137-6

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