A novel 4D chaotic system with nonhyperbolic hyperbolic shape equilibrium points: Analysis, circuit implementation and color image encryption

Abstract

This paper presents a new 4D chaotic system by extending a 3D system to investigate chaotic systems2 with hidden attractors further and explore their engineering applications in color image encryption. The system has hyperbolic shape equilibriums and the equilibriums are nonhyperbolic which is interesting and rarely mentioned before. The system has been investigated deeply by phase plot, time series, the largest Lyapunov exponent, bifurcation diagram, Poincaré map and 0–1 test. A coexisting hidden attractor has been found in this new system and the circuit simulation model of the system is built by Power Simulation (PSIM). Circuit simulation results are consistent with results of numerical simulations which verify its dynamic behavior further. Then, by combining the generalized Arnold transform with the new chaotic system, a new color image encryption algorithm has been proposed which has large key space and can encrypt either square images or nonsquare images with different size. Finally, the results of encryption experiment and security analysis prove the effectiveness of the algorithm.

A Novel Conservative Chaotic System Involved in Hyperbolic Functions and Its Application to Design an Efficient Colour Image Encryption Scheme

“…In this paper, we used the suggested approach to encrypt colour images and determine the entropy values of the cyphered images, as shown in Table 3. In a second experiment, we used our technique and some other existing methods [2,9,12,18,23] to encrypt Lena's colour image. Table 4 displays the computed entropy values.…”

“…Many image encryption techniques have been suggested and developed by researchers, such as Arnold transformation-based [1][2][3], quantum system-based [4][5][6], compression sensing-based [7][8][9], cellular automata-based [10][11][12], DNA computing-based [13][14][15], elliptic curves-based [16][17][18], and chaotic system-based [19][20][21][22][23] approaches. The approach of digital image encryption based on chaotic systems is considered to be more effective than other approaches due to their ability to improve unpredictability, which makes encryption more resistant to attacks.…”

A new image encryption algorithm based on optimized Lorenz chaotic system

“…To further express the difference between the decrypted image and the plaintext image quantitatively and exactly, the concept of mean squared error 4 of image grayscale value is introduced to better analyze the key sensitivity of the algorithm. Let P = { p i , j } the pixel grayscale value matrix of original image, and P ' = { p ' i , j } the pixel grayscale value matrix of decrypted image, resolution ratio of both original image and decrypted image is m × n , of which i = 1, 2, 3, …, m , j = 1, 2, 3, …, n , then the mean squared error E p , p ' of grayscale of two images can be expressed by Equation ): …”

“…Matthews first proposed to apply the chaos in cryptology in his paper published in 1989, and in which the chaotic stream ciphers plan based on deformed Logistic map was also proposed 2 . Since, chaotic cryptography attracted broad attention, especially since 2010, a new research trend was created by digitalized chaotic ciphers research 3‐5 . For example, in 1997, Fridrich applied chaos in encryption of digital images for the first time, 6 then chaos‐based image encryption methods are researched for years 7 .…”

“…2 Since, chaotic cryptography attracted broad attention, especially since 2010, a new research trend was created by digitalized chaotic ciphers research. [3][4][5] For example, in 1997, Fridrich applied chaos in encryption of digital images for the first time, 6 then chaos-based image encryption methods are researched for years. 7 Some of these methods are flawed in treating pixel bytes still in the form of the bit stream and thus inefficient.…”