High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

Abstract

Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

Cap like Trajectories in 5D Chaotic Tangent Hyperbolic Memristive Model: Fractional Calculus and Encryption

“…Several papers have been published on modeling chaotic and hyperchaotic systems, with widespread application across diverse fields, including electrical circuits, mathematics, and physics [1][2][3][4][5][6]. It has emerged as a prominent trend in recent years.…”

Fractional-Order sliding mode control of a 4D memristive chaotic system

“…Furthermore, the fact that chaotic systems are based on flux-controlled memristor makes this type of circuit easier to implement (Bao et al, 2018; Gokyildirim, Yesil and Babacan, 2022a). Recently, researchers have investigated fractional-order memristive systems with a single unstable equilibrium point (Rahman et al, 2021), bursting and boosting phenomena (Borah and Roy, 2021), and multiple coexisting analyses (Hu et al, 2021). However, most of the studied fractional-order chaotic systems do not provide dynamic analyses which include bifurcation diagrams and Lyapunov exponents.…”

Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients

“…Owing to their broad importance in many fields and their numerous engineering applications, nonlinear oscillators have recently attracted the attention of a large number of researchers due to their extremely rich dynamics ( Joshi, 2021 ; Dashkovskiy and Pavlichkov, 2020 ; Ahmed et al, 2017 ; Cheng and Zhan, 2020 ; Kudryashov, 2018 ; Tang et al, 2020 ; Dashkovskiy and Pavlichkov, 2020 ; Fonkou et al, 2022 ; Han et al, 2019 ; Ramirez et al, 2020 ; FitzHugh, 1961 ; Rahman et al, 2021a , Rahman et al, 2021b , Rahman et al, 2021c , Rahman et al, 2021d ). Their fields of application are between others: seismology, communication and neurophysiology ( Rahman et al, 2021a , Rahman et al, 2021b , Rahman et al, 2021c , Rahman et al, 2021d ; Lucero and Schoentgen, 2013 ; Rowat and Selverston, 1993 ; Balachandran and Kandiban, 2009 ). These oscillators exhibit rich dynamics among which limit cycle oscillations of sinusoidal and relaxation nature, since one of their important characteristic is their capacity to present limit cycle behaviors which is an important criterion in the characterization of the artificial pacemaker ( Steeb, 1977 ; Hochstadt and Stephan, 1967 ; D'Heedene, 1996 ; Steeb and Kunick, 1987 ; Steeb et al, 1983 ).…”

“…When subjected to an external periodic excitation, numerical studies and singular point analysis have revealed chaotic behaviors, allowing the analysis of phenomena such as control and cardiac activity with numerous technological applications. ( Steeb and Kunick, 1982 ; Steeb and Kunick, 1983 ; Forger, 1999 ; Enrique et al, 2020 ; Rahman et al, 2019 ; Kai and Tomita, 1979 ; Rahman et al, 2021a , Rahman et al, 2021b , Rahman et al, 2021c , Rahman et al, 2021d ; Van der Pol and Van der Mark, 1926 ; Van der Pol and Van der Mark, 1928 ; Alhasnawi et al, 2021 ).…”