Eur. Phys. J. Plus (2022) 137: 619
https://doi.org/10.1140/epjp/s13360-022-02821-5

Regular Article

Circuit and microcontroller validation of the extreme multistable dynamics of a memristive Jerk system: application to image encryption

¹ Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O.Box 63, Buea, Cameroon
² Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
³ Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland
⁴ Research Unit of Condensed Matter, Department of Physics, Faculty of Sciences, Electronics and Signal Processing (URMACETS), University of Dschang, P.O. Box 67, Dschang, Cameroon
⁵ Research Centre for Nuclear Science and Technology, Institute of Geological and Mining Research, PO Box 4110, Yaounde, Cameroon
⁶ Research Unit of Laboratory of Energy and Artificial Intelligence (RU-LEAI), Electrical Engineering Department of ISTAMA, University of Douala, P.O. Box 3223, Douala, Cameroon

^a zerictabekoueng@yahoo.fr

Received: 30 January 2022
Accepted: 19 April 2022
Published online: 23 May 2022

Abstract

In this contribution, an image encryption technique jointly based on the contribution of chaotic behavior resulting from an extreme multistable system and DNA coding is proposed. The chaotic system used is based on a memristive model with quadratic memductance. This memductance is used to build the nonlinear term of a Jerk system. The investigation of the obtained system reveals that it is dissipative and deals with a line of equilibria. Using nonlinear analysis tools, including the two-parameter Lyapunov exponent, the graph of the Lyapunov spectrum, the bifurcation diagram, and phase portraits, to study the considered model, the results show that the considered system is able to exhibit the coexistence of an infinite number of stable states. Besides, the results of this work have been supported by using theoretical, numerical, and experimental approaches. Furthermore, the generated chaotic sequence by the proposed memristive Jerk system is used in the confusion and diffusion steps combined with DNA coding, thus enhancing the efficiency of the cryptosystem. The experimental results and the analyses (statistic, differential, and noise and data loss attacks) sufficiently show that the proposed cryptosystem is robust by the quality of the obtained results.