Dynamics analysis of a four-dimensional hyperchaotic hidden system and its application in image encryption

It is known that chaotic, especially hyperchaotic system can be suitable for the application in image encryption owing to itself characteristics. While currently, certain improved chaotic or hyperchaotic systems are confronted with the security issue of encryption due to their less complex dynamical behaviors. To address the problem well, we introduce a novel two-dimensional (2D) crossed hyperchaotic map which is based on the logistic map and the infinite collapse map. The analysis of phase diagram and Lyapunov exponential spectrum demonstrate that the given system can exhibit extensive hyperchaotic behavior and good traversal properties. Moreover, the growing use of digital images has prompted demand for multi-image encryption scheme. For this reason, based on the given 2D crossed hyperchaotic map, a multiple image encryption (MIE) scheme that employs a cross-plane with the operation of simultaneous permutation and diffusion to modify the values of its positions and pixels across multiple images is proposed. A pixel blur preprocessing technique is introduced such that the efficiency of key calculation and the speed and safety of information encryption are greatly improved. Eventually, some simulation examples and security analysis reveal that the put forward encryption scheme is able to keep out kinds of attacks such as the selective plaintext attacks and data loss.

Nonlinear analysis, circuit implementation, and application in image encryption of a four-dimensional multi-scroll hyper-chaotic system

Memristors exhibit controllable nonlinear characteristics, generating chaotic signals that are characterized by randomness, sensitivity, and unpredictability, thereby demonstrating significant potential applications in information encryption and signal processing. With the integration of chaos theory and electronic technology, constructing memristive hyperchaotic systems has become a hot topic in nonlinear science and information security. To overcome the limitation of monotonic dynamic characteristics in traditional chaotic systems, we design a novel memristor-based hyperchaotic system with richer dynamic behavior and higher application value in this paper. Moreover, the characteristic analysis, theoretical verification, application exploration, and hardware implementation are conducted to support the engineering applications of the system. Building upon the classical Chen system, this work is innovatively combined with a cubic nonlinear magnetically controlled memristor model as a feedback element. By establishing a mathematical model of the memristor and coupling it with the state equations of the Chen system, we design a four-dimensional memristor-based hyperchaotic system. First, by integrating numerical computation with differential equation theory, a comprehensive mathematical model is established to analyze fundamental properties, such as symmetry and dissipativity, thereby validating the system’s rationality. Second, the system’s dynamical behaviors are analyzed, including attractor phase diagrams, Lyapunov exponents, power spectra, parameter effects, transient dynamics, and coexisting attractors. Simultaneously, variational methods are utilized to analyze unstable periodic orbits within the system. A symbolic coding approach based on orbital characteristics is established to convert orbital information into symbolic sequences, and orbital pruning rules are explored to provide a basis for optimal orbital control. Furthermore, a digital image encryption method is proposed based on this system. Using chaotic sequences as keys, image pixels are scrambled and diffused. The effectiveness of encryption is validated through histogram analysis, correlation analysis, information entropy evaluation, and testing of anti-attack capabilities. Finally, a DSP-based digital circuit hardware platform is constructed to run the system, and the hardware experimental results are compared with software simulation outcomes. These findings reveal that the introduction of memristors induces linearly distributed equilibrium points in phase space, generating hidden attractors that enrich the chaotic behavior of the system. The simulation of dynamic behavior confirms the rich dynamics of this four-dimensional memristor-based hyperchaotic system. The proposed digital image encryption method demonstrates robust security performance. The DSP hardware experiments and software simulations yield highly consistent attractor phase diagrams, validating the correctness and feasibility of the system.

In this paper, a four-dimensional hyperchaotic system is constructed by adding a state feedback controller into a chaotic system. Numerical simulations and theoretical analysis show that this four-dimensional system will take on periodic,complex periodic, quasi-periodic chaotic hyperchaotic dynamical behaviours as parameters vary. Moreover, an electronic circuit diagram is designed for demonstrating the existence of the hyperchaos. Finally, an adaptive tracking controller is proposed to acquire adaptive tracking control for this hyperchaotic system.

A new hyperchaotic system and its generalized synchronization

Generating grid double-scroll attractors from magnetized SC-CNN and its application in image encryption

Compared with integer order chaotic systems, fractional order chaotic systems can reflect natural phenomena more accurately, which are more suitable for chaotic cryptosystems. In order to explore the application of fractional order chaotic system in cryptography, a novel fractional order hyperchaotic system is constructed and implemented on DSP platform. More progressively, based on Adomian decomposition method, the dynamic behavior is studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum and spectral entropy (SE) complexity. It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state. Therefore, the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system have sufficient randomness and are well suited for applications in secure communications. In addition, a color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA dynamic coding. Firstly, the improved Arnold algorithm is used to scramble the original image, then the column cyclic shift method is applied for secondary scrambling, and finally the pixel value is diffused by DNA sequence operation. The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively, but also has high security and can resist various common attacks.

Mirror symmetry multi-wing attractors generated from a novel four-dimensional hyperchaotic system

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviors by varying parameter k are studied. Numerical simulations are presented to show these results.

The widespread adoption of consumer electronics (CE), particularly in smart home ecosystems, has led to the proliferation of intelligent devices such as smart cameras, video doorbells, and smart door locks. While these devices enhance convenience and automation, they generate massive amounts of visual data containing sensitive personal information, thereby increasing the risk of privacy leakage and challenging traditional encryption methods in consumer IoT networks. To address this issue, a cryptanalysis-driven image encryption scheme via a chaos-based 3D S-box and genetic code is proposed, specifically designed to safeguard visual privacy in consumer applications. First, a novel dynamical architecture, formally termed 3D Non-degenerate Hyperchaos (3D-NDHC), is constructed to serve as a robust entropy source. Explicitly defined as a globally bounded volume-expanding hyperchaotic system, 3D-NDHC distinguishes itself from traditional dissipative maps by exhibiting global robust hyperchaos and scalable complexity, where the Lyapunov exponents grow logarithmically with control parameters, ensuring high unpredictability. Next, a dynamically generated three-dimensional S-box driven by these chaotic sequences is introduced to perform efficient image permutation. Subsequently, a genetic code method enhanced by cryptanalysis is applied to confuse the permuted image matrix, specifically addressing the security vulnerabilities often inherent in lightweight encryption algorithms. Finally, under the control of pseudo-chaotic sequences, a lightweight wave diffusion process is employed to spread the pixel values and produce the final ciphertext image. In contrast to conventional algorithms that rely on standard encryption techniques, the proposed approach integrates a chaos-driven 3D S-box with a cryptanalysis-enhanced genetic code scheme. This combination introduces a high level of confusion and diffusion, significantly increasing the difficulty for attackers attempting to illegally decrypt sensitive images from smart devices. Experimental results and security analyses demonstrate that the scheme effectively resists various cryptographic attacks and outperforms several recently proposed image encryption algorithms, offering a robust solution for protecting digital image privacy in smart home environments.

The investigation of chaotic systems containing hidden and coexisting attractors has attracted extensive attention. This paper presents a four-dimensional (4D) novel hyperchaotic system, evolved by adding a linear state feedback controller to a 3D chaotic system with two stable node-focus points. The proposed system has no equilibrium point or two lines of equilibria, depending on the value of the constant term. Complex dynamical behaviors such as hidden chaotic and hyperchaotic attractors and five types of coexisting attractors of the simple 4D autonomous system are investigated and discussed, and are numerically verified by analyzing phase diagrams, Poincaré maps, the Lyapunov exponent spectrum, and its bifurcation diagram. The short unstable cycles in the hyperchaotic system are systematically explored via the variational method, and symbol codings of the cycles with four letters are realized based on the topological properties of the trajectory projection on the 2D phase space. The bifurcations of the cycles are explored through a homotopy evolution approach. Finally, the novel 4D system is implemented by an analog electronic circuit and is found to be consistent with the numerical simulation results.

The multi-scroll hyper-chaotic coexistence attractors and its application

Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic system

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

A new four-dimensional hyperchaotic system with three quadratic nonlinearities is proposed in this paper. The dynamical properties of the new hyperchaotic system are explored in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. Also, a detailed dynamical analysis of the new hyperchaotic system has been carried out with bifurcation diagram and Lyapunov exponents. As an engineering application, an electronic circuit realization of the new hyperchaotic system is designed via MultiSIM to confirm the feasibility of the theoretical hyperchaotic model.