A nonlinear conjugate gradient method for solving quaternion matrix equation and its application in color image encryption and decryption

This paper investigates the anticontrol of the fractional-order chaotic system. The necessary condition of the anticontrol of the fractional-order chaotic system is proposed, and based on this necessary condition, a 3D fractional-order chaotic system is driven to two new 4D fractional-order hyperchaotic systems, respectively, without changing the parameters and fractional order. Hyperchaotic properties of these new fractional dynamic systems are confirmed by Lyapunov exponents and bifurcation diagrams. Furthermore, a color image encryption algorithm is designed based on these fractional hyperchaotic systems. The effectiveness of their application in image encryption is verified.

Quaternion discrete fractional Krawtchouk transform and its application in color image encryption and watermarking

This paper traces the process of constructing a new one-dimensional chaotic map, and will provide a simple application in color image encryption. The use of Sarkovskii’s theorem will make it possible to determine the existence of chaos and restrict all conditions to ensure the existence of this new sequence. In addition, the sensitivity to initial conditions will be proved by Lyapunov’s index value. Similarly, the performance of this new chaotic map will be illustrated graphically and compared with other chaotic maps most commonly used in cryptography. Finally, a humble color image encryption application will show the power of this new chaotic map.

For the sake of better removing dependence of color image pixel values, this paper designs a color image encryption algorithm based on a new four-dimensional chaos. Firstly, a new four-dimension chaos is built through feedback control, which has three equilibrium points. In comparison with the original, this system is of more complex topology and better randomness. Secondly, the image channel R, G, B are combined into one matrix. Finally, the encrypted image is the result of scrambling the matrix on the bit. The experiment shows that the algorithm applies to color image encryption because of its large key space, good key sensitivity, high encryption and decryption efficiency, and was suitable for color image encryption.

This paper proposes a novel exponential hyper-chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan-Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper-chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high-order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper-chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper-chaotic system to increase the security of image encryption.

Infinite lines of equilibria exist in a new memristive system when a tangent function is introduced for attractor self-reproducing. Lyapunov exponent spectra and bifurcation diagram shows that the newly proposed chaotic system exhibits intermittent chaos and hypermultistability characterized for the coexistence of infinite countable and uncountable attractors. The physical feasibility of the new memristive chaotic system is confirmed by PSpice circuit simulation. Finally, the system is applied in color image encryption, where the performance in the process is evaluated. Numerical simulation proves that the new memristive chaotic system has high security in image encryption.

In this paper, a color image encryption algorithm based on the fractional-order multi-scroll Chen chaotic system and DNA mutation principle is proposed. The dynamical performances of the fractional-order multi-scroll Chen chaotic system are analyzed by phase diagram, Lyapunov exponential spectrum and bifurcation diagram. Meanwhile, we realized the hardware circuit simulation of the chaotic system on the DSP platform. Based on comprehensive analysis, an image encryption algorithm is designed. In particular, a DNA algorithm with mutation effect has been introduced into the encryption algorithm. Finally, the performances of the designed encryption scheme are analyzed by key space, correlation coefficients, information entropy, histogram, differential attacks and robustness analysis. The experimental results prove that the algorithm has strong encryption capabilities and can withstand multiple decryption methods. The new color image encryption scheme proposed in this paper can realize the secure communication of digital images.

This paper proposes a new two-dimensional discrete hyperchaotic system and utilizes it to design a pseudo-random number generator (PRNG) and an efficient color image encryption algorithm. This hyperchaotic system has very complex dynamic properties and can generate highly random chaotic sequences. The complex hyperchaotic characteristics of the system are confirmed via bifurcation diagram, chaotic attractor, Lyapunov exponents, correlation analysis, approximate entropy and permutation entropy. Compared with some traditional discrete chaotic systems, the new chaotic system has a larger range of chaotic parameters and more complex hyperchaotic characteristics, making it more suitable for application in information encryption. The proposed PRNG can generate highly random bit sequences that can fully pass all NIST testing items. The proposed color image encryption algorithm achieves cross-channel permutation and diffusion of pixels in parallel. These strategies not only greatly improve the encryption speed of color images, but also enhance the security level of cipher images. The simulation experiments and security analysis results show that the algorithm has strong robustness against differential attacks, statistical attacks and interference attacks, and has good application potential in real-time secure communication applications of color images.

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.

An overview of encryption algorithms in color images

An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption

Design of a new multi-wing chaotic system and its application in color image encryption

The time delay caused by transmission in neurons is often ignored, but it is demonstrated by theories and practices that time delay is unavoidable. A new chaotic neuron model with time delay self‐feedback is proposed based on Chen’s chaotic neuron. The bifurcation diagram and Lyapunov exponential diagram are used to analyze the chaotic characteristics of neurons in the model when they receive the output signals at different times. The experimental results exhibit that it has a rich dynamic behavior. In addition, the randomness of chaotic series generated by chaotic neurons with time delay self‐feedback under different conditions is verified. In order to investigate the application of this model in image encryption, an image encryption scheme is proposed. The security analysis of the simulation results shows that the encryption algorithm has an excellent anti‐attack ability. Therefore, it is necessary and practical to study chaotic neurons with time delay self‐feedback.

Spatiotemporal chaos in multiple coupled mapping lattices with multi-dynamic coupling coefficient and its application in color image encryption

A color image encryption scheme based on 1D cubic map