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

A novel color image encryption algorithm based on a cross 2D hyperchaotic map is proposed in this paper. The cross 2D hyperchaotic map is constructed using one nonlinear function and two chaotic maps with a cross structure. Chaotic behaviors are illustrated using bifurcation diagrams, Lyapunov exponent spectra, phase portraits, etc. In the color image encryption algorithm, the keys are generated using hash function SHA-512 and the information of the plain color image. First, the color plain image is converted to a combined bit-level matrix and permuted by the chaos-based row and column combined cycle shift scrambling method. Then, the scrambled integer matrix is diffused according to the selecting sequence which depends on the chaotic sequence. Last, decompose the diffusion matrix to get the encrypted color image. Simulation experiments and security evaluations show that the algorithm can encrypt the color image effectively and has good security to resist various kinds of attacks.

In this paper, a cellular neural network (CNN) chaotic system is constructed and the multiple stability of the system and its rich chaotic properties are confirmed by studying the effect of parameters on the system, coexisting attractors, and offset boosting behavior. As linear feedback shift registers (LFSR) can be applied to cryptography, this paper applies LFSR to generate encrypted key matrices to enhance the randomness of encryption algorithms. Based on CNN and LFSR, a new color image encryption algorithm is designed by combining DNA coding and bit-plane decomposition with high bit-plane Zigzag dislocation changes. Experimental results and security tests show that the algorithm is highly secure and resistant to a variety of common attacks, such as differential attacks, cropping attacks, and noise attacks.

A color image encryption and decryption scheme based on extended DNA coding and fractional-order 5D hyper-chaotic system

A new three-dimensional chaotic system with fan-shaped Poincare maps is proposed. Based on merely six terms, the system is easy to implement. Its dynamic behaviors, such as equilibrium points, Poincare maps, power spectra, Lyapunov exponent spectra, bifurcation diagrams and forming mechanism, are analyzed theoretically and numerically. Results of theoretical analyses and numerical simulations indicate that the proposed system possesses complex chaotic attractors. Its equilibrium points are unstable, and the system can keep chaotic when its parameters vary in a wide domain. Furthermore, circuit simulations of the system are discussed. The results of numerical simulations and circuit simulations coincide very well. By virtue of its complex dynamic behaviors and wide-range parameters, the system can be adopted in some application fields where wide-range parameters and complex behaviors are usually preferred, such as secure communication, data encryption, information hiding.

Chaos is widely used in secure communication and cryptography due to its randomness, unpredictability, non-periodicity and high sensitivity to initial values and parameters. However, there are many risks in some existing chaotic image encryption algorithms because they use the the chaotic map without complex dynamic characteristics. To overcome these weaknesses, in this paper introduced an improved Hénon map, and the dynamic analysis results show that the improved Hénon map has more rich chaotic behaviors and better complexity. In addition, we designed a color image encryption scheme using the improved Hénon sequences. For this encryption algorithm, color image is divided into R, G, B primary colors, then R, G, B primary colors are scrambled and diffused by the improved Hénon sequences. The simulation results illustrate that color image encryption algorithm security is advanced by usingimproved Hénon map.

A color image encryption algorithm by combining the reality-preserving fractional DCT (RPFrDCT) with chaotic mapping in HSI space is presented, in which the generating sequence (GS) is introduced and produced by 2D chaotic mapping to ensure the uniqueness of the transform matrix and enlarge the cipher key space of the encryption system. In addition, the color image is converted from standard RGB space into HSI space and the nonlinearity of the spatial transform makes the proposed encryption algorithm more secure than linear ones. Three components, namely H, S and I, are encrypted by the RPFrDCT with fractional orders and GS as cipher keys. Three-dimensional (3D) scrambling is adopted to further enhance the security of the encryption algorithm. The nonlinearity of the spatial transform from RGB to HSI, the real-valued output and the high cipher key-sensitivity guarantee the security and the feasibility of the proposed encryption algorithm. Experimental results demonstrate that the proposed encryption algorithm is sensitive to cipher keys and, to some extent, robust to noise and occlusion attacks.

The bipolar pulse current can effectively mimic the external time-varying stimulus of neurons, and its effect of neuronal dynamics has rarely been reported. To this end, this paper reports the effects of bipolar pulses on a two-dimensional single inertial neuron model, showcasing the chaotic dynamics of hidden attractors and coexisting symmetric attractors, which is of significant importance for understanding the complex behaviors of neuron dynamics under time-varying external stimuli and its application. Firstly, the mathematical model of the single intertial neuron model with forced bipolar pulse is presented, and then the equilibrium states behaving as unstable saddle point (USP), stable node-focus (SNF), and stable node point (SNP) are analyzed. Additionally, by using multiple dynamical methods including bifurcation plots, basins of attraction, and phase plots, complex dynamics of interesting bifurcation behaviors and coexisting attractors are revealed, which are induced by the forced bipolar pulse current as well as initial values, both. In addition, such effets are well valideted via a simple multiplerless electronic neuron circuit. The implementation circuit of presented model is constructed on the analog level and executed using PSIM circuit platform. The measurement results verified the double-scroll chaotic attractors and the coexisting period/chaos behaviors. Finally, the chaotic sequences of the model are applied to color image encryption for the benefit of requirements on modern security field. The encryption effectiveness is demonstrated through various evaluation indexes, including histogram analysis, information entropy, correlation coefficient, plaintext sensitivity, and resistance to noise attacks.

A ring network with fractional-order bistable oscillators is proposed, and the relationship between synchronization and parameters, such as coupling modes and the initial structural conditions, etc., is investigated. Based on the bistable characteristics of P-R oscillator, the effects of the coupling strength and the structures in initial conditions on the dynamic behaviors of the ring network are investigated by analyzing the largest conditional Lyapunov exponents, the largest Lyapunov exponents and the bifurcation diagrams, etc. Further investigation reveals that the ring network can be controlled to form chaotic synchronization, chaotic non-synchronization, synchronous amplitude death, synchronous non-amplitude death, etc. by changing the initial conditions and the coupling strength. Furthermore, the contours of the largest conditional Lyapunov exponents and the largest Lyapunov exponents also show how the dynamic behaviors of the network are influenced by the competition between couplings along directions of y and z, strongly relies on the initial structural conditions of network.

Multi-wing chaotic systems are highly valued for their complexity and pseudo-randomness, making them promising in applications like secure communication and image encryption. However, existing chaotic systems face limitations in attractor diversity and system dimensions, which restrict their effectiveness in complex encryption applications. In this paper, we construct a four-dimensional multi-wing chaotic system based on the Sprott-A chaotic system by introducing linear feedback control and additional state variables. Furthermore, by incorporating piecewise linear functions and new state variables, a five-dimensional multi-wing chaotic system with the characteristic of odd and even numbers of hidden attractors are developed. Odd multi-wing attractors have centrally symmetric complex trajectories, while even multi-wing attractors possess axisymmetric trajectories through the introduction of offset terms. This system overcomes the limitations of existing chaotic systems and significantly improves complexity, controllability, and pseudo-randomness, making it more suitable for encryption applications. Based on this system, we design a new color image encryption algorithm that uses chaotic sequences for pixel permutation and diffusion operations. The security analysis indicates that the algorithm offers a large key space, high sensitivity to initial conditions, and strong resistance to various attacks, providing a novel solution for complex encryption applications.

This paper proposes a color image encryption algorithm based on a cloud model Fibonacci chaotic system, as well as a matrix convolution operation that can protect image content effectively and safely. The algorithm combines the cloud model with the generalized Fibonacci, creating a new complex chaotic system that realizes the dynamic random variation of chaotic sequences. The chaotic sequence is used to scramble the pixel coordinates of the mosaic images of the R, G, and B components of the color image. Then, the chaotic sequence value is used as a matrix convolution cloud algorithm that alternately updates the input value of the matrix convolution operation and the pixel value to obtain the permutation transformation of the original pixel value. Finally, the pixel values of the replacement and cloud model Fibonacci chaotic sequence and the pixel values of the front (rear) adjacent pixel points are subjected to a two-way exclusive XOR operation. Realizing the change of the arbitrary pixel value causes a chain transformation of the pixel values of all of the pixel points, and sequentially generates an encrypted image. Experiments show that the histogram of the encrypted image is smoother and adjacent pixels of the image have low correlation. In addition, this algorithm can resist attack experiments such as differential attack, select plaintext attack and noise attack and provides high encryption security, high anti-interference, and strong robustness. The dynamic chaotic system is used to realize the color image encryption of the dynamic key, and the encryption algorithm has higher security and the validity of the algorithm.

Audio encryption has gained popularity in a variety of fields including education, banking over the phone, military, and private audio conferences. Data encryption algorithms are necessary for processing and sending sensitive information in the context of secure speech conversations. In recent years, the importance of security in any communications system has increased. To transfer data securely, a variety of methods have been used. Chaotic system-based encryption is one of the most significant encryption methods used in the field of security. Chaos-based communication is a promising application of chaos theory and nonlinear dynamics. In this research, a chaotic algorithm for the new chaotic chameleon system was proposed, studied, and implemented. The chameleon chaotic system has been preferred to be employed because it has the property of changing from self-excited (SA) to hidden-attractor (HA) which increases the complexity of the system dynamics and gives strength to the encryption algorithm. A chaotic chameleon system is one in which, depending on the parameter values, the chaotic attractor alternates between being a hidden attractor and a self-excited attractor. This is an important feature, so it is preferable to use it in cryptography compared to other types of chaotic systems. This model was first implemented using a Field Programmable Gate Array (FPGA), which is the first time it has been implemented in practical applications. The chameleon system model was implemented using MATLAB Simulink and the Xilinx System Generator model. Self-excited, hidden, and coexisting attractors are shown in the proposed system. Vivado software was used to validate the designs, and Xilinx ZedBoard Zynq-7000 FPGA was used to implement them. The dynamic behavior of the proposed chaotic system was also studied and analysis methods, including phase portrait, bifurcation diagrams, and Lyapunov exponents. Assessing the quality of the suggested method by doing analyses of many quality measures, including correlation, differential signal-to-noise ratio (SNR), entropy, histogram analysis, and spectral density plot. The numerical analyses and simulation results demonstrate how well the suggested method performs in terms of security against different types of cryptographic assaults.

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application

Color image encryption and authentication algorithm integrating computational ghost imaging with quaternion multi-parameter discrete fractional angular transform

In this paper, a new three-dimensional autonomous chaotic system is proposed. However, the structural form of the new chaotic system is limited to a double-wing like most Lorenz-like systems. According to the equilibrium points and topological structure of this double-wing chaotic system we design some appropriate nonlinear functions for it. Then, the new double-wing chaotic system can be modified into a grid multi-wing chaotic system. Basic dynamical properties of the system are studied by theoretical analysis and numerical simulation, which proves the chaotic behaviors of this new grid multi-wing chaotic system. Finally, an oscillator circuit is designed for implementation. The circuit simulation results are in good agreement with the numerical simulation results.

A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincare maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.