4D Hyperchaotic System Research Articles

A color image encryption algorithm based on a novel 4D hyperchaotic system and bit-level diffusion

As digital images are widely used in social media, medical, military and other fields, ensuring the privacy and security of image data has become a critical concern. Firstly, we propose a novel four-dimensional hyperchaotic system and validate that it exhibits a broad chaotic range, as demonstrated by bifurcation diagrams and Lyapunov exponent experiments. Additionally, simulated circuit diagrams verify the hardware feasibility of the proposed system. Secondly, we design a dynamic iterative scrambling (DIS) scheme that dynamically divides the image into multiple matrices for spatially indexed scrambling. Excellent substitution performance can be ensured by multiple iterations. In the diffusion stage, a multidirectional bit-level L-shaped (MDBL) scheme is proposed. Diffusion is conducted on the bit plane using a designed cross-multiplanar selection algorithm, which fuses the high and low bit planes, thereby enhancing the diffusion performance of MDBL. Thirdly, Based on the above concepts, a novel four-dimensional hyperchaotic system and an encryption algorithm based on bit-level diffusion are proposed. Finally, experimental results and security analyses demonstrate the effectiveness of the novel 4D hyperchaotic system and image encryption scheme. The proposed encryption scheme exhibits robust anti-interference capabilities and effectively safeguards image security.

Dynamics and Adaptive Control of a Novel 5D Hyperchaotic System: Either Hidden Attractor or Self-excited with Unusual Nature of Unstable Equilibria

In 2020, J. Sprott proposed a new three dimensional chaotic system with special features such like 1) dissipative and time-reversible; 2) no equilibrium point; 3) lien of initial conditions goes to the attractor. We observed that an extension of the so-called Sprott's 2020 system to four dimensional system with complex dynamics showed either chaotic or hyperchaotic with unbounded orbits. In this paper, a novel five dimensional hyperchaotic system based on Sprott's 2020 system has been proposed. The proposed system shows complex dynamics like hyperchaotic. The proposed system can be classified as a hidden attractor where no equilibrium point appeared or self-excited where an unusual nature of unstable equilibrium points connected to a very complicated function called Lambert W appeared. The dynamical properties of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Adaptive control to the proposed system was provided.

Dynamic analysis of a novel hyperchaotic system based on STM32 and application in image encryption

This paper presents a novel 4D hyperchaotic system derived from a modified 3D Lorenz chaotic system. A key aspect of this system is the presence of a single equilibrium point, and its stability is carefully analyzed. The dynamic properties, including the Lyapunov exponent spectrum, bifurcation diagram, and chaotic attractors, are investigated using MATLAB simulations. The results reveal that the system displays hyperchaotic behavior across a wide range of the parameter d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document}, with its chaotic attractor transitioning through four states: hyperchaotic, chaotic, periodic, and quasi-periodic, showcasing the system's complex dynamics. Experimental validation using STM32 embedded hardware successfully reproduces these four types of chaotic attractors, confirming the theoretical predictions. The proposed hyperchaotic system is then applied to image encryption, introducing a novel encryption method. The hyperchaotic key sequence generated by this system meets 15 tests of the NIST SP800-22 standard, and further experimental validation with STM32 hardware demonstrates the algorithm's effectiveness, simplicity, non-linearity, and high security. The encrypted images and sequences are rigorously tested key space analysis, histogram similarity analysis, information entropy analysis, statistical attack analysis, differential attack analysis, key sensitivity analysis, and correlation analysis, highlighting the robustness and reliability of the proposed system. This method is versatile and can be extended to various fields, including audio and video encryption, text encryption, IoT security, financial transaction security, and medical data protection.

Novel grayscale image encryption based on 4D fractional-order hyperchaotic system, 2D Henon map and knight tour algorithm

With the increasing frequency of data exchange, the security of transmitted information, especially images, has become paramount. This paper proposes a novel algorithm for encrypting grayscale images of any dimension by using a proposed fractional-order (FO) 4D hyperchaotic system, 2D Henon chaotic map permutation, and the knight tour algorithm. Initially, chaotic sequences are generated by utilizing the proposed FO 4D hyperchaotic system, which are later employed to rearrange and shuffle the entire image pixels to bolster the efficacy of image encryption. To introduce an additional layer of diffusion, 2D Henon chaotic map permutation is used. Furthermore, the knight tour algorithm is applied by starting from a chosen point and executing specified rounds on the scrambled image to increase the encryption’s robustness. The resultant image encryption algorithm undergoes thorough testing and evaluation. It exhibits high sensitivity to the encryption key and boasts a larger key space, rendering it more resistant to brute-force attacks. The proposed algorithm demonstrates an approximate correlation of 0 between adjacent pixels. Further, encryption of a grayscale image of size 256 × 256 takes approximately 0.4 seconds, rendering it more suitable for cryptographic purposes.

Dynamics, periodic orbits of a novel four-dimensional hyperchaotic system with hidden attractors

In recent years, the investigation of systems featuring hidden attractors and coexisting attractors has garnered significant attention. This paper presents a novel four-dimensional (4D) hyperchaotic system devoid of equilibrium points, achieved by formulating an equation without a solution or constructing a system without fixed points. Due to the complex shape of this attractor, a novel coding method is utilized to establish symbol dynamics using eight letters. The proposed system exhibits highly intricate dynamics, including variations in topological structure with alterations in system parameters, as well as an exploration and discussion of four types of coexisting attractors. Our extensive practice has led us to propose a new conjecture: hyperchaotic systems with parameters close to the bifurcation point frequently display multistable states. Furthermore, the unstable periodic orbits with different topological lengths in the hidden hyperchaotic attractor are calculated systematically using the variational method. Additionally, the DSP circuit implementation is employed to validate the numerical simulation results for this new 4D system. Finally, adaptive synchronization is successfully realized within the system, thereby confirming its feasibility.

A local encryption method for large-scale vector maps based on spatial hierarchical index and 4D hyperchaotic system

With the development of geographic information services, applications based on map data are increasing. Internet and mobile communication technologies have brought great convenience to the distribution, sharing, and acquisition of map data. Unfortunately, it also brings great challenges to protect the security and privacy of confidential map data. Although several encryption algorithms have been developed for map data, most of the existing methods are simple extensions of classical encryption algorithms for text data in cryptography, ignoring special structures and characteristics of geospatial data. Existing methods mainly take the entire map or layers as encryption units, which makes the encryption efficiency for large-scale map data low and limits the ability to perform local and incremental encryption for local areas, making it still challenging to meet the needs of map data in applications, such as autonomous driving. To solve the limitations, a local encryption approach for large-scale vector map data is proposed in this paper considering the structure characteristics of map data. Experiments on map data of different types (including points, lines, and polygons) demonstrate the effectiveness of the proposed method. With local and parallel encryption strategies, the proposed method has higher efficiency compared to available algorithms for large-scale map data.

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

Delayed self-feedback echo state network for long-term dynamics of hyperchaotic systems.

Analyzing the long-term behavior of hyperchaotic systems poses formidable challenges in the field of nonlinear science. This paper proposes a data-driven model called the delayed self-feedback echo state network (self-ESN) specifically designed for the evolution behavior of hyperchaotic systems. Self-ESN incorporates a delayed self-feedback term into the dynamic equationof a reservoir to reflect the finite transmission speed of neuron signals. Delayed self-feedback establishes a connection between the current and previous m time steps of the reservoir state and provides an effective means to capture the dynamic characteristics of the system, thereby significantly improving memory performance. In addition, the concept of local echo state property (ESP) is introduced to relax the conventional ESP condition, and theoretical analysis is conducted on guiding the selection of feedback delay and gain to ensure the local ESP. The judicious selection of feedback gain and delay in self-ESN improves prediction accuracy and overcomes the challenges associated with obtaining optimal parameters of the reservoir in conventional ESN models. Numerical experiments are conducted to assess the long-term prediction capabilities of the self-ESN across various scenarios, including a 4D hyperchaotic system, a hyperchaotic network, and an infinite-dimensional delayed chaotic system. The experiments involve reconstructing bifurcation diagrams, predicting the chaotic synchronization, examining spatiotemporal evolution patterns, and uncovering the hidden attractors. The results underscore the capability of the proposed self-ESN as a strategy for long-term prediction and analysis of the complex systems.

Physical Layer Encryption for CO-OFDM Systems Enabled by Camera Projection Scrambler

In this paper, we propose a camera projection approach to enhance the physical layer security of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The data are converted to the new location by the camera projection module in the encryption system, where the 5D hyperchaotic system provides the keys for the camera projection module. The simulated 16QAM CO-OFDM security system over 80 km SSMF is shown to provide a key space of about 9 × 1090 through the five-dimensional (5D) hyperchaotic system, making it impossible for eavesdroppers to obtain valid information, and the peak-to-average power ratio (PAPR) is reduced by about 0.8 dB.

A comprehensive study of the novel 4D hyperchaotic system with self-exited multistability and application in the voice encryption

This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

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

With the advancement of information technology, the security of digital images has become increasingly important. To ensure the integrity of images, this paper presents a novel color image encryption and decryption architecture. Firstly, a fractional-order five-dimensional hyper-chaotic system (F5DHS) is proposed and used to generate chaotic sequences for permutation and diffusion processes. Secondly, the extended DNA encoding scheme is employed to generate more DNA encoding rules and four DNA computation methods are used to improve the security of the encryption scheme. Thirdly, a blocked image encryption method is designed to divide the color image into sub-blocks and then determine the DNA encoding, DNA decoding and DNA arithmetic rules for each sub-block based on chaotic sequences. Finally, the results of simulation experiments and security analysis show that the color image encryption algorithm has good encryption performance, a large secret key space, and strong robustness to noise and data loss attacks, indicating that the proposed encryption algorithm can effectively protect the secure communication of digital images.

An efficient image encryption model based on 6D hyperchaotic system and symmetric matrix for color and gray images

The security of images is one of the predominant pivotal aspects in the mammoth and still expanding digital domain. Due to chaotic system properties i.e. randomness and unpredictability is very appropriate to encrypt the images. In this research article, we construct an encryption model via 6D hyperchaotic map and a symmetric matrix for both color and grayscale images. We utilize the 6D hyperchaotic map in the confusion stage to change the pixel location and the symmetric matrix is used for changing the pixel value in the diffusion step for each RGB channel extraction from plain or original image. The image encryption model is checked over differential attacks (NPCR and UACI). Histogram analysis, correlation coefficients, and entropy analysis are also performed as statistical attacks. In conclusion, the image pixels are uniformly distributed, and the average entropy value are 7.9992 and 7.9973 for color and grayscale images, subsequently. The average NPCR and UACI for color images are 99.5956 and 33.4061, correspondingly, while the values for grayscale images are 99.5934 and 33.3054, respectively. These values are in the vicinity of optimal ranges. The suggested scheme's great efficiency and the proposed algorithm's resilience to a wide range of cryptanalytic attacks are implied by experimental results, statistical analysis, and differential attacks.

New 4D hyperchaotic system’s application in image encryption

In order to protect sensitive information from unauthorized access and illegal copy during network transmission, storage and processing, we propose a new four-dimensional hyperchaotic system (4DHS) and apply it to encryption algorithm. Firstly, the dynamical properties of 4DHS are analyzed according to the structure, and the chaotic properties are verified by dissipation, equilibrium point and lyapunov exponent. Secondly, the chaotic sequence combined with Arnold scrambling method is adopted to scramble the pixel values of the plaintext image, and the scrambled pixel matrix is diffused into the ciphertext image matrix by XOR operation. Finally, we conduct the experiments to validate the effectiveness of the proposed encryption algorithm and achieve satisfactory results. At the same time, we compare the proposed encryption algorithm with other encryption algorithms, and the excellent encryption effect of our encryption algorithm can be proved.

Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm

In this paper, a synchronization study is proposed by using a 4D hyperchaotic system model to be used in secure data transfer applications. Active Disturbance Rejection Control (ADRC) method is used for synchronization process. To prove the success of ADRC method, it is compared with Proportional-Integral-Derivative (PID) control method. The coefficients of both control methods are optimized with Particle Swarm Optimization (PSO) algorithm. Synchronization system is modelled and tested in Matlab/Simulink environment. ADRC and PID methods are tested in simulation environment for the cases without disturbance and under disturbance. It can be seen from the test results that the ADRC method managed to keep the system synchronous without being affected by any disturbances. On the other hand, it is clearly seen that the PID method cannot maintain the synchronization of system under disturbance effects.

Qualitative analysis of a novel 4D hyperchaotic system and its chaos synchronization via active, adaptive, and sliding mode control

Qualitative analysis of a novel 4D hyperchaotic system and its chaos synchronization via active, adaptive, and sliding mode control

A fractional-order hyperchaotic system that is period in integer-order case and its application in a novel high-quality color image encryption algorithm

A new fractional-order 5D hyperchaotic system based on memristor is constructed in this paper, with the speciality that the system exists chaotic and hyperchaotic states in the fractional-order case, while in periodic state in the integer-order. In addition, it has a variety of special phenomena at fractional-order such as infinite initial value range, parameter-dependent offset-boosting and amplitude control, attractor coexistence, and fractional order complexity greater than integer order. The correctness and feasibility of the system is verified by analog circuit simulation and hardware circuit implementation. Combining this system with image encryption algorithms, two new scrambling algorithms and a diffusion algorithm are proposed. And a high-quality encryption scheme that can be applied to a wide range of color images is proposed. The scheme is found to have excellent security after verification by various security analyses and comparison with other literatures. This paper provides a basis for the superiority of fractional-order chaotic systems and provides new methods in the field of image encryption.

Advanced hybrid color image encryption utilizing novel chaotic neural network and 5D-hyperchaotic system

Advanced hybrid color image encryption utilizing novel chaotic neural network and 5D-hyperchaotic system

Securing Color Images with an Innovative Hybrid Method Combining DNA Computing and Chaotic Systems

Modern cryptography is a key element of data security, ensuring the confidentiality and integrity of information. In an increasingly digital world, cryptography remains crucial for the protection of sensitive data. In this context, we propose a novel hybrid security system for encrypted color images using a DNA model, chaotic systems, and SHA256-MD5 hash functions as a basis. The proposed hybrid system includes DNA permutation and diffusion. In DNA permutation, we unpredictably rearrange the location of DNA image elements by using the logistic map of low computational complexity. In DNA diffusion, we diffuse the permuted image of DNA with the DNA image key generated by a 5D hyper-chaotic system, using a variety of algebraic operators such as the circular offset in both directions. Considering the experimental outcomes and security evaluation, we can infer that the proposed hybrid security system demonstrates a high level of security, resistance to existing attacks, and practical application suitability while maintaining speed.

6D Hyperchaotic Encryption Model for Ensuring Security to 3D Printed Models and Medical Images

In the 6G era, where ultra-fast and reliable communication is expected to be ubiquitous, encryption shall continue to play a crucial role in ensuring the security and privacy of data. Encryption and decryption of medical images and 3D printed models using 6D hyperchaotic function is proposed in this research work for ensuring security in data transfer. Here we envisage using a six-dimensional hyperchaotic system for encryption purposes which shall offer a high level of security due to its complex and unpredictable dynamics with multiple positive Lyapunov exponents. This system can potentially enhance the encryption process for 3D objects and medical images, ensuring the protection of sensitive data and preventing unauthorized access. A hyperchaotic system is a type of dynamical system characterized by exhibiting more than one positive Lyapunov exponent, which indicates strong sensitivity to initial conditions. These systems have more degrees of freedom and complex and intricate dynamics compared to standard chaotic systems. The security of the encryption scheme depends on the complexity of the hyperchaotic system and the randomness of the secret key. The parameters of a 6D hyperchaotic system shall be used as an encryption key with six dimensions, each with its range of values, and shall provide many possible keys. In this work, we implemented a 6D hyperchaotic system for the encryption of the 3D printed model and medical images. The performance evaluation was done by metrics entropy, correlation, Number of Pixels Change Rate (NPCR), and Unified Averaged Changed Intensity (UACI) which revealed the robustness of the encryption model in ensuring security. Hyperchaotic systems can be efficiently implemented in parallel computing architectures, which allow faster encryption and decryption processes.

Color image ROI encryption algorithm based on a novel 4D hyperchaotic system

The significance of safeguarding the security of image information has escalated significantly, owing to the exponential proliferation of digital images containing sensitive information being disseminated on the Internet. In this paper, we first propose a novel 4D hyperchaotic system and design a new image encryption algorithm in conjunction with the hyperchaotic system. The algorithm uses a split random swap permutation method to permute the image and combines the S-box to diffuse the image. To improve the diffusivity of this encryption algorithm, a cross-random diffusion method is designed to diffuse the image again. Then, we propose a region of interest (ROI) encryption scheme for images. This scheme can automatically identify irregular privacy targets in images and encrypt them. To ensure the security of the region of interest location information during transmission, the scheme compresses the location information of the privacy target using a run-length encoding technique and then embeds the compressed data into the ciphertext image using reversible steganography based on histogram shift. The experimental results and security analysis unequivocally demonstrate that the image encryption algorithm proposed in this paper exhibits robust resistance against a wide array of attacks, thereby ensuring a high level of security. Additionally, the devised image ROI encryption scheme effectively safeguards diverse privacy targets.