Memristor-based hyper-chaotic circuit for image encryption*

Abstract

The memristor is a kind of non-linear element with memory function, which can be applied to chaotic systems to increase signal randomness and complexity. In this paper, a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model, which can generate complex chaotic attractors. The basic dynamic theory analysis and numerical simulations of the system, such as the stability of equilibrium points, the Lyapunov exponents and dimension, Poincare maps, the power spectrum, and the waveform graph prove that it has rich dynamic behaviors. Then, the circuit implementation of this system is established. The consistency of simulation program with integrated circuit emphasis (SPICE) simulation and numerical analysis proves the ability to generate chaos. Finally, a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper. The scheme involves a total of two encryptions. By using different security analysis factors, the proposed algorithm is compared with other image encryption schemes, including correlation analysis, information entropy, etc. The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.

Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

“…The dynamic behaviors of the system are judged by observing the projection of phase diagram on the plane. This is the most direct way to observe the dynamic behaviors of a system [32]. For better analyzing its chaotic characteristics, we proceed a research about equilibrium points, Lyapunov exponent spectrum, bifurcation model and complexity.…”

“…The Lyapunov exponent spectrum is a useful tool for measuring whether the system is chaotic or hyperchaotic. In particular, systems with one positive Lyapunov exponent are chaotic, and those with two or more positive Lyapunov exponents are hyperchaotic [32]. The coexistence model of bifurcation is substantially the mapping of the coexistence attractors on the bifurcation plane [33].…”

Audio Encryption Algorithm Based on Chen Memristor Chaotic System

“…Compared with that of the traditional chaotic attractors, the circuit has rich dynamic characteristics and good application prospects in the field of secure communication. Chen J.J. [18] designed an image encryption algorithm of a new hyperchaotic system based on memristor, which can produce complex chaotic attractors. The experimental results show that the circuit simulation and numerical simulation results of the system always proved the feasibility, effectiveness, and ability to produce chaotic behavior of the system.…”

SPICE Behaviors of Double Memristor Circuits Using Cosine Window Function

“…No great progress was developed in the research field of memristor until the group of Williams at Hewlett-Packard (HP) lab successfully fabricated the first nanoscale memristive device based on titanium dioxide thin film in 2008 [2]. Since then, many researchers or scholars have focused on the memristor research [3][4][5][6][7] and its numerous potential applications in nonvolatile random access memories [8,9], neuromorphic systems [10,11], chaotic circuits [12], reconfigurable logics [13,14] and RF/microwave devices [15,16].…”