Hyperchaotic System Research Articles

2D compressed sensing of encrypted images based on complex‐valued measurement matrix

AbstractWhen using untrusted third parties to compress and transmit images in real‐life scenarios, it is vital to encrypt them before compression. In order to better address the issues of low security in the original image and poor reconstruction quality of the encrypted image during compressed sensing, this paper proposes a 2D compressed sensing scheme for encrypted images based on complex‐valued measurement matrix (2DCS‐CVM). Firstly, the SHA‐256 algorithm generates keys for the hyperchaotic Lorenz system, and then the chaotic sequences are used to create encrypted images with increased security through subtractive diffusion and global permutation. Secondly, the complex‐valued Vandermonde measurement matrix is utilized for 2D compressed sensing on the encrypted image, and the two‐dimensional projected gradient with embedding decryption algorithm is used to generate recovered images with improved reconstruction performance. Finally, the measurement matrix's computational complexity and transmission bandwidth are reduced through structural sparsification with sparse random matrices. Simulation results demonstrate that this scheme offers an optimal balance between storage, computational complexity, hardware implementation, and reconstruction performance while providing excellent security and robustness.

Reversibly selective encryption for medical images based on coupled chaotic maps and steganography

The security and confidentiality of medical images are of utmost importance due to frequent issues such as leakage, theft, and tampering during transmission and storage, which seriously impact patient privacy. Traditional encryption techniques applied to entire images have proven to be ineffective in guaranteeing timely encryption and preserving the privacy of organ regions separated from the background. In response, this study proposes a specialized and efficient local image encryption algorithm for the medical field. The proposed encryption algorithm focuses on the regions of interest (ROI) within massive medical images. Initially, the Laplacian of Gaussian operator and the outer boundary tracking algorithm are employed to extract the binary image and achieve ROI edge extraction. Subsequently, the image is divided into ROI and ROB (regions outside ROI). The ROI is transformed into a row vector and rearranged using the Lorenz hyperchaotic system. The rearranged sequence is XOR with the random sequence generated by the Henon chaotic map. Next, the encrypted sequence is arranged according to the location of the ROI region and recombined with the unencrypted ROB to obtain the complete encrypted image. Finally, the least significant bit algorithm controlled by the key is used to embed binary image into the encrypted image to ensure lossless decryption of the medical images. Experimental verification demonstrates that the proposed selective encryption algorithm for massive medical images offers relatively ideal security and higher encryption efficiency. This algorithm addresses the privacy concerns and challenges faced in the medical field and contributes to the secure transmission and storage of massive medical images.

General multi-switching synchronization using sliding mode control

Chaotic synchronization is a self-organizing phenomenon that occurs when two or more chaotic systems become synchronized. So far for multi-switching synchronization (MSS), only a homogeneous kind of switches have been discussed. This paper presents a generalized approach to MSS in which all possible heterogeneous combinations are presented. This generalization of MSS allows for greater flexibility and robustness in the MSS process. The switches are designed based on the order of the drive/response subsystems. The author also uses sliding mode control to achieve synchronization among various heterogeneous combinations during MSS. To demonstrate the effectiveness of the proposed approach, the author uses the Lorenz hyper chaotic system (LHCS) and the Chen hyper chaotic system (CHCS). The four different heterogeneous types of switches are designed and demonstrated for the chosen hyper chaotic systems. Mathematica is used for all numerical simulations. The results show that the proposed approach can achieve synchronization between two hyper chaotic systems with high accuracy. The author also shows that the proposed approach is robust to change in the parameters of the systems. This paper provides a new approach to chaotic synchronization that has potential applications in a variety of fields. The results presented in this paper are an important step towards the development of more robust and flexible synchronization schemes.

A novel color image encryption scheme using elliptic curve cryptography and hyperchaotic system

This paper develops an asymmetric color image encryption algorithm based on elliptic curve cryptography(ECC), five dimensions(5D) hyperchaotic system, and DNA dynamic coding. To embed the characteristics of original image in the image encryption algorithm, this algorithm builds a mathematical model to strengthen the connection between the original image, elliptic curve Diffie-Hellman(ECDH) algorithm and hyperchaotic system. The red, green and blue(RGB) channels of encrypted image is reshaped into a three dimensions(3D) matrix. Grouping and scrambling of 3D matrix is accomplished at pixel level, bit level and DNA level based on a 5D hyperchaotic system, which effectively enhances the cross-layer variation of images. Then, improved ECC is performed on the scrambled image where multiple elliptic curves and dynamic shared private keys can guarantee the forward secrecy of the image encryption algorithm. At last, the image is performed diffusion to obtain the final encrypted image. Simulation results and security analysis both indicate the image encryption algorithm has better performances in terms of key space, Shannon entropy, clipping attack resistance, etc.

Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic and Chaotic Systems in Presence of Uncertainties

Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master–slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov's concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.

Multi-stability analysis and energy control for 4D hyperchaotic system with hidden attractors

Multi-stability analysis and energy control for 4D hyperchaotic system with hidden attractors

Adaptive embedding combining LBE and IBBE for high-capacity reversible data hiding in encrypted images

Reversible data hiding in encrypted image (RDHEI) has received wide attention as an effective information protection technique, and most of the existing RDHEI schemes introduce pixel prediction technique to improve embedding performance. However, the high embedding capacity (EC) requirement is still not achieved because the redundancy of carrier medium is not fully utilized. Thus, a novel RDHEI based on pixel prediction and adaptively combining "L"-shaped block embedding (LBE) and improved binary-block embedding (IBBE) is presented, which maximizes the use of Laplacian-like distribution of prediction-errors to achieve higher EC. Specifically, the original image is first predicted to get the prediction-error image and then eight binary prediction-error bit-planes (PEBPs) are generated. Subsequently, the proposed LBE and IBBE are used to calculate the net EC to encode each PEBP. Also, a new bit-plane selection encryption is designed to ensure that the intra-block correlations of the IBBE-based PEBPs remain unchanged. Eventually, the data hider adaptively completes data embedding according to the PEBP coding. Moreover, the 4-D hyperchaotic system is exploited to encrypt the carrier image and the secret data to further enhance the security. Extensive experimental results verify that our strategy achieves more outstanding performance compared with some state-of-the-art schemes.

Quantum image encryption based on Baker map and DNA circular shift operation

Quantum computation can improve the efficiency of image processing by utilizing parallelism and superposition characteristics. In this paper, a quantum cryptosystem based on Baker map and deoxyribonucleic acid (DNA) circular shift operation is designed. Firstly, the digital image to be encrypted is firstly represented with a novel enhanced quantum representation model. Then quantum Baker map is used to permutate the position information of the prepared quantum image. Next, the designed DNA circular shift operation is performed to preliminarily change the color information of the scrambled image. Finally, the ciphertext image is obtained by implementing the exclusive OR (XOR) operation between the pseudo-random sequence generated by a four-dimensional (4D) hyper-chaotic system and the DNA shift operated image. Numerical experimental results and security analysis verify that the proposed scheme has good performance at securing information storage and transmission as the histograms of ciphertexts are uniform, the correlation coefficient values of three directions are very close to 0, the average information entropy is 7.9972, the key space is more than 1015×4 to resist brute-force attack. Furthermore, it has lower computational complexity compared with classical algorithms.

N-dimensional polynomial hyperchaotic systems with synchronization application

n-dimensional polynomial hyperchaotic systems with synchronization application

An image cipher based on bio-molecular hyper chaotic system with dual diffusion scheme

An image cipher based on bio-molecular hyper chaotic system with dual diffusion scheme

Circuit simulation and image encryption based on a six-dimensional cellular neural network hyperchaotic system

Circuit simulation and image encryption based on a six-dimensional cellular neural network hyperchaotic system

A Novel Memristor-Based Multi-Vortex Hyper-Chaotic Circuit Design and its Application in Image Encryption

This paper proposes a new four-dimensional hyper-chaotic system capable of generating multi-wing chaotic attractors by introducing active magnetron memristors, multi-segmented square functions and trigonometric functions. The dynamical properties of this new hyper-chaotic system, such as equilibrium point, dissipation, Lyapunov exponential spectrum, bifurcation diagram and Poincaré cross-section and attraction basin, are analyzed theoretically and simulated numerically, and the complexity of this system with different parameters is analyzed. It is observed that this hyper-chaotic system has periodic, chaotic and hyper-chaotic variations with an infinite number of equilibria and coexisting attractors under different parameter conditions. The circuit simulation was performed using Multisim and the results obtained were consistent with the numerical analysis of the dynamics, and the chaotic circuit system is designed by FPGA to verify the realizability of the system. Finally, an image encryption algorithm is designed in conjunction with the DNA algorithm to enable a new system chaotic sequence for image encryption. The results show that the hyper-chaotic system has rich dynamical behavior and has high-security performance when applied to image encryption with strong chaotic key and plaintext sensitivity and large key space in image encryption.

Image encryption algorithm based on hyperchaotic system and dynamic DNA encoding

Since the existing DNA encryption algorithms only have fixed DNA coding and decoding rules and a single algorithm that cannot meet more complex and more secure encryption requirements, an image encryption algorithm based on hyperchaotic system and dynamic DNA coding is proposed. The algorithm proposes two new operation methods in the DNA operation rules, namely the equal-additive column transformation and the equal-subtractive column transformation. which combine the SHA-256 function and the external key to generate the initial value of the chaotic system to ensure that key and plaintext of algorithm are correlated. In the encryption process, the plaintext image is firstly converted into a two-dimensional matrix for rotation and scrambling. Then the chaotic sequence generated by the hyperchaotic Chen system is used to perform DNA dynamic encoding, decoding and operation on the scrambled matrix and block matrix generated by logistic chaotic sequence. Finally, the encrypted matrix is scrambled in one dimension. Simulation results show that the improved encryption algorithm has a larger key space, breaks the strong correlation between image pixel layers, and can effectively resist multiple attacks.

Mixed Multi-Chaos Quantum Image Encryption Scheme Based on Quantum Cellular Automata (QCA)

The advent of quantum computers could enable the resolution of complex computational problems that conventional cryptographic protocols find challenging. As a result, the formidable computing capabilities of quantum computers may render all present-day cryptographic schemes that rely on computational complexity ineffectual. Inspired by these possibilities, the primary purpose of this paper is to suggest a quantum image encryption scheme based on quantum cellular automata with mixed multi-chaos hybrid maps and a hyperchaotic system with quantum operations. To achieve desirable encryption outcomes, we designed an encryption scheme involving two main operations: (1) pixel-level diffusion and (2) pixel-level permutation. Initially, the secret keys generated using the hyperchaotic system were closely tied to the original image. During the first phase, the establishment of correlations among the image pixels, in addition to the three chaotic sequences obtained from the hyperchaotic system, was achieved with the application of a quantum-state superposition and measurement principle, wherein the color information of a pixel is described using a single qubit. Therefore, the three channels of the plain image were subjected to quantum operations, which involve Hadamard transformation and the quantum-controlled NOT gate, before the diffusion of each color channel with the hyperchaotic system. Subsequently, a quantum ternary Toffoli gate was used to perform the diffusion operation. Next, the appropriate measurement was performed on the three diffused channels. To attain the confusion phase, a blend of mixed multi-chaos hybrid maps and a two-dimensional quantum cellular automaton was used to produce random and chaotic sequence keys. Subsequently, the circular shift was utilized to additionally shuffle the rows and columns of the three diffused components, in order to alter the positions of their pixel values, which significantly contributes to the permutation process. Lastly, the three encoding channels, R, G, and B, were merged to acquire the encrypted image. The experimental findings and security analyses established that the designed quantum image encryption scheme possesses excellent encryption efficiency, a high degree of security, and the ability to effectively withstand a diverse variety of statistical attacks.

Design and Dynamics of Multicavity Hyperchaotic Maps with Cylinder Attractors

Based on the mathematical model of the elliptical cylinder, we design a new hyperchaotic map with an elliptical cylinder or a cylinder attractor. The dynamical analysis results indicate the proposed system is globally hyperchaotic, and has large Lyapunov Exponents (LEs), and high Permutation Entropy (PE) complexity. Interestingly, the hyperchaotic system exhibits the offset boosting coexistence attractors with respect to the system parameters. In addition, three Multicavity Hyperchaotic Maps (MHCM) are constructed by introducing a symmetric staircase function, which expands greatly the phase space of the system. The MHCM have more complex topological structures and maintain the chaotic performance of the original map. To illustrate the feasibility of the hyperchaotic systems further, we apply them to design a Pseudo-Random Number Generator (PRNG), and implement them on the DSP platform.

A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption

With the advancement in information and communication technologies (ICTs), the widespread dissemination and sharing of digital images has raised concerns regarding privacy and security. Traditional methods of encrypting images often suffer from limitations such as a small key space and vulnerability to brute-force attacks. To address these issues, this paper proposes a novel eighth-order hyperchaotic system. This hyperchaotic system exhibits various dynamic behaviors, including hyperchaos, sub-hyperchaos, and chaos. The encryption scheme based on this system offers a key space larger than 22338. Through a comprehensive analysis involving histogram analysis, key space analysis, correlation analysis, entropy analysis, key sensitivity analysis, differential attack analysis, and cropping attack analysis, it is demonstrated that the proposed system is capable of resisting statistical attacks, brute force attacks, differential attacks, and cropping attacks, thereby providing excellent security performance.

Design of memristor hyperchaotic circuit with burst oscillation and infinite attractor coexistence and its application

A 4D hyperchaotic system with symmetry based on memristors is proposed and the chaotic properties of the circuit are verified by phase diagrams, Poincaré cross sections, bifurcation, Lyapunov exponents, and 0–1 tests. In addition, the system is found to have rich dynamical behaviors such as transient chaos, intermittent chaos, offset enhancement, burst oscillation, and infinite attractor coexistence. The complexity comparison analysis reveals that this hyperchaotic system has good symmetry as well as the initial values of the system that are more suitable for image encryption. Circuit simulation of the system using simulation software proved the usability of the system. A field programmable gate array (FPGA) is used to implement the actual digital circuit of the system. The final FPGA results agree with the numerical simulation and prove the practical value of the constructed memristor hyperchaotic system. Finally, chaotic circuits are applied to DNA image encryption. It is discovered to have a very large key space, strong key sensitivity, outstanding anti-cropping, noise immunity and high security performance. Thus, the proposed hyperchaotic system has good advantages for application in the field of image encryption.

Modeling method of a class of 5D Hamiltonian conservative hyperchaotic systems with adjustable signal amplitude

Compared to dissipative chaotic systems, conservative chaotic systems have gained attention because they can avoid reconstruction attacks due to the absence of attractors. This paper reports a general method for constructing 5D Hamiltonian conservative hyperchaotic systems, mainly by coupling three 5D sub-rigid bodies with two identical axes to obtain 5D Euler equations, and then combining Hamiltonian energy and Casimir energy analysis to obtain a 5D conservative hyperchaotic system. This method is general and convenient, and the constructed conservative hyperchaotic system has good performance. In addition, this paper investigates the impact of parameters and initial values on system performance using energy analysis and proposes a simple signal amplitude adjustment method. This method has no restrictions on the mathematical models of chaotic systems, can quickly adjust signal amplitudes, and enhances the hyperchaotic characteristics of the system based on this method. Finally, the correctness of the theoretical and simulation analysis is verified using a DSP hardware platform.

Characteristic analysis of 5D symmetric Hamiltonian conservative hyperchaotic system with hidden multiple stability

Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudo-randomness. In this work, a novel five-dimensional (5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology (NIST) test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor (DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.

A Robust Image Encryption Scheme Based on Block Compressive Sensing and Wavelet Transform

In this paper, a modified robust image encryption scheme is developed by combining block compressive sensing (BCS) and Wavelet Transform. It was achieved with a balanced performance of security, compression, robustness and running efficiency. First, the plain image is divided equally and sparsely represented in discrete wavelet transform (DWT) domain, and the coefficient vectors are confused using the coefficient random permutation strategy and encrypted into a secret image by compressive sensing. In pursuit of superior security, the hyper-chaotic Lorenz system is utilized to generate the updated secret code streams for encryption and embedding with assistance from the counter mode. This scheme is suitable for processing the medium and large images in parallel. Additionally, it exhibits superior robustness and efficiency compared with existing related schemes. Simulation results and comprehensive performance analyses are presented to demonstrate the effectiveness, secrecy and robustness of the proposed scheme. The compressive encryption model using BCS with Walsh transform as sensing matrix and WAM chaos system, the scrambling technique and diffusion succeeded in enhancement of secure performance.