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

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.

Automated summary

In this paper, an image encryption technique based on chaotic behavior and DNA coding is proposed. The system used can exhibit the coexistence of an infinite number of stable states, and the efficiency of the cryptosystem is enhanced by using DNA coding. The experimental results and analyses demonstrate the robustness of the proposed cryptosystem.