Hyperchaotic Chen System Research Articles

An encryption algorithm for color images based on an improved dual-chaotic system combined with DNA encoding

This study improves the Logistic chaotic system and combines it with the hyperchaotic Chen system to create a dual chaotic system. The algorithm encrypts images in three stages. In the first stage, a plaintext-related key generation scheme is designed to generate the parameters and initial values of the dual chaotic system. In the second stage, the chaotic sequences generated by the dual chaotic system are used for dynamic DNA encoding and computation. In the third stage, the chaotic sequences generated by the improved Logistic chaotic system are used to perform row-column permutations, completing the scrambling. The security analysis of the encrypted images shows that the algorithm described in this paper is robust and secure, capable of resisting most known attacks. The algorithm is fast in encryption, provides high-quality image reconstruction, and is suitable for scenarios with high comprehensive performance and image quality requirements.

Control and synchronisation of an extended hyperchaotic system based on robust switching control

This paper introduces a new class of hyperchaotic systems developed based on Chen's hyperchaotic system. The hyperchaotic nature of the developed system is proven through the calculation of the positive Lyapunov exponent and simulation. A robust feedback control method is then introduced to stabilise the system. To enhance the security of telecommunication channels for information exchange, a switching structure comprising extended hyperchaotic systems is presented. The synchronisation problem of the proposed structure is addressed using a robust switched linear control method. The simulation results show the effectiveness of the proposed controller in guaranteeing system stability and solving the synchronisation problem thus increasing security in telecommunication networks.

New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption

<abstract> <p>With the popularization of digital image technology, image information has inevitably developed to involved the disclosure of personal privacy; in this study, a color image encryption algorithm was designed to encrypt and decrypt images by using chaotic sequences of a class of memristor-based hybrid delayed bidirectional associative memory neural networks (MHDBAMNNs) to protect images from illegal acquisition and use. Additionally, the discontinuity problem of the right-hand side of the Filippov system due to the hopping property of the memristor has been treated by using differential inclusion and set-valued mapping theories, and a sufficient criterion for guaranteeing the synchronization of finite-time projections derived based on the drive-response concept, Lyppunov stability theorem, and inequality technique. To improve the security performance, a color image encryption algorithm based on a combination of Chen's hyperchaotic system and a DNA codec operation was adopted, also, the robustness and validity of our proposed approach was demonstrated through image performance analysis. Furthermore, the potential application of the model in secure transmission has been explored.</p> </abstract>

Image Encryption Based on Fourier-DNA Coding for Hyperchaotic Chen System, Chen-Based Binary Quantization S-Box, and Variable-Base Modulo Operation

Image Encryption Based on Fourier-DNA Coding for Hyperchaotic Chen System, Chen-Based Binary Quantization S-Box, and Variable-Base Modulo Operation

Analytical Studies on Approximate Lag and Anticipating Synchronization in Two Unidirectionally Coupled Hyperchaotic Chen Systems without Time Delay

In this paper, approximate lag synchronization (LS) and anticipating synchronization (AS) between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling are analytically investigated. Firstly, the synchronization condition for exact LS in two unidirectionally coupled hyperchaotic Chen systems with time delay in signal transmission is analytically obtained. Under such conditions, approximate LS and AS are discussed by replacing the true time-delay terms with their Taylor expansions up to the third order.Differently from other research studies, the condition for exact LS is derived by regarding LS as a special type of generalized synchronization (GS), which has nothing to do with the value of the time delay. It is convenient to individually change the value of the lag and anticipation time of approximate LS and AS without considering the synchronization condition. Our study shows the power of a new method for recreating the past signals or predicting the future signals of a hyperchaotic Chen system by using its current signals. The results provide a simple way to eliminate the negative effects of time delay in the signal transmission between two hyperchaotic systems.

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.

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.

Visually meaningful image encryption combining with reversible data hiding in encrypted images

At present, most image encryption schemes directly change plaintext images into ciphertext images without visual significance, such ciphertext images can be detected and therefore subject to various attacks. To protect the content security and visual safety of images, a visually meaningful image encryption (VMIE) algorithm combining with Reversible Data Hiding in Encrypted Images (RDHEI) is proposed. First, the secret image is encrypted and additional information is embedded by Chen hyperchaotic system and prediction error expansion (PEE) method. Then the source image is encrypted by a Lorentz hyperchaotic system. Finally, bit-xor operation is performed on the resulting encrypted image and the result is saved in a cloud database to generate an indexing key using SHA-256,which enables the receiver to recover the secret image with the resource image and the key alone. The scheme combines with the RDHEI, improving the transmission efficiency and has no image quality problems.The experimental results and security analysis show that the image encryption scheme has sufficient key space, strong key sensitivity and wide applicability.

Dual Function Matrix Projective Synchronization for Fractional-order Hyperchaotic Systems

Abstract It is well known that the variability and complexity of projection proportionality factors of Dual Projective Synchronization (DPS) can effectively enhance signal confidentiality. However, in most literatures, the proportionality factors are some simple fixed constants, which can't ensure high security of information. For two pairs of fractional-order hyperchaotic systems (FOHS), how to expand the projection proportionality factors to increase its complexity? Then, our work will propose a new synchronization type, i.e., Dual Function Matrix Projective Synchronization (DFMPS) and realize the DFMPS for FOHS for the first time. Firstly, based on the traditional DPS, we generalize the proportionality factors to a general function matrix depending on time t, present the error functions and define the DFMPS. Then, for FOHS, the active controller and synchronization condition are designed and proved. At the same time, when the system is affected by parameter disturbance, the proposed active controller can eliminate the influence of parameter disturbance to the system's DFMPS, which indicates that the proposed control strategy has strong robustness. Finally, the DFMPS of two pairs of fractional-order hyperchaotic Chen and Rabinovich systems are realized, and synchronizing analysis and system robustness analysis are verified by numerical simulation. Particularly, the DFMPS can be degenerated to dual anti-synchronization, dual complete synchronization, DPS, modified DPS and dual matrix projective synchronization. This work extends the synchronization types for FOHS and offers a useful method to explore DFMPS for other fractional-order systems.

Double Encryption Algorithm for Massive Personal Biometric Authentication Images Based on Chaotic Mapping for Future Smart Cities

Abstract To address the problems of low encryption security, slow encryption speed, and small key space of personal biometric authentication image, a double encryption algorithm of image based on chaotic mapping is proposed. The global block-matching strategy of sparse clustering is used to remove the image noise, and the encrypted key information in the biometric authentication image is extracted by mathematical morphology. The logistic index is used to disrupt the image information distribution, bit scrambling is used to double scramble the image, and the Secure Hash Algorithm (SHA)-256 hash function is used to generate the initial value of the chaotic system to obtain the chaotic map and the random variable sequence of hyperchaotic Chen system, and the chaotic sequence is transformed into the ciphertext image matrix after exclusive OR (XOR) operation in order to realize the double encryption of personal biometric authentication image. The results show that the proposed method has large key space, high encryption accuracy, fast efficiency, and better security performance.

Synchronization of Hyperchaotic Systems Based on Intermittent Control and its Application in Secure Communication

The synchronization of master-slave hyperchaotic systems is investigated by intermittent control and proved by the Lyapunov stable theory. Meanwhile, a new secure communication scheme is designed for the continuous and digital information. The encrypted information is transmitted to receiver through the intermittent controller, which reduces the disturbance to the synchronization of master-slave systems and improves the security and reliability of secure communication. Before transmitting to the receiver, the continuous signal is firstly modulated and masked by the chaotic signals. Furthermore, an encryption algorithm for the digital information of color image is proposed by the pseudo-random sequences of Chen hyperchaotic system, and then the encrypted image is modulated and masked by the variables of the master system. The original image can be decrypted successfully at the receiving end after the slave system is synchronized with the master system. Finally, the feasibility and effectiveness of this scheme are verified by simulation experiments. In addition, the security analysis of the image encryption algorithm is also discussed, such as key sensitivity, correlation coefficient, NIST test, and return map.

Image Encryption Algorithm Based on Discrete Quantum Baker Map and Chen Hyperchaotic System

Image Encryption Algorithm Based on Discrete Quantum Baker Map and Chen Hyperchaotic System

A Novel Image Encryption Algorithm by Delay Induced Hyper-chaotic Chen System

A novel image encryption algorithm based on delay induced hyper-chaos (hyper-chaotic multi-attractors Chen system with time delay, HCMACS-TD), Arnold map and Multi-shift cipher function is proposed. To prevent private images from being stolen or used by unauthorized accesses, protecting images is very important. HCMACS-TD generating by linear time delay feedback, which possesses more than one positive Lyapunov exponent, the infinite dimensional, multi-attractors, and a wider chaotic parameter range is used in image encryption algorithm. Arnold map is used to complete the shuffle of the image and the multi-shift cipher function is used to encrypt the shuffled and confused image. In addition, the shuffled image except the first pixel as the initial element of the confusion process, enhances the relationship between the encrypted image and the original image. The performances of the proposed image encryption algorithm are evaluated, and the results show that the proposed image encryption algorithm has considerable advantages over some existing algorithms.

Three-Stage-Impulse Control of Memristor-Based Chen Hyper-Chaotic System

In this paper, on the basis of the three-dimensional Chen system, a smooth continuous nonlinear flux-controlled memristor model is used as the positive feedback term of this system, a hyper-chaotic circuit system is successfully constructed, and a simulated equivalent circuit is built for simulation using Multisim software, which agrees with the numerical simulation results by comparison. Meanwhile, a new impulsive control mode called the three-stage-impulse is put forward. It is a cyclic system with three components: continuous inputs are exerted in the first and third parts of the cycle while giving no input in the second part of the cycle, an impulse is exerted at the end of each continuous subsystem, the controller is simple in structure and effective in stabilizing most existing nonlinear systems. The Chen hyper-chaotic system will be controlled based on the three-stage-impulse control method combined with the Lyapunov stability principle. At the end of this paper, we have employed and simulated a numerical example; the experimental results show that the controller is effective for controlling and stabilizing the newly designed hyper-chaotic system.

Novel encryption for color images using fractional-order hyperchaotic system.

The fractional-order functions show better performance than their corresponding integer-order functions in various image processing applications. In this paper, the authors propose a novel utilization of fractional-order chaotic systems in color image encryption. The 4D hyperchaotic Chen system of fractional-order combined with the Fibonacci Q-matrix. The proposed encryption algorithm consists of three steps: in step#1, the input image decomposed into the primary color channels, R, G, & B. The confusion and diffusion operations are performed for each channel independently. In step#2, the 4D hyperchaotic Chen system of fractional orders generates random numbers to permit pixel positions. In step#3, we split the permitted image into 2times 2 blocks where the Fibonacci Q-matrix diffused each of them. Experiments performed where the obtained results ensure the efficiency of the proposed encryption algorithm and its ability to resist attacks.

Hyperchaotic Impulsive Synchronization and Digital Secure Communication

Based on chaos shift keying approach, impulsive signals from Hyperchaotic Chen system and Hyperchaotic Lü system are alternately emitted according to the transmission of binary signals “0” and “1”. In the receiver, these two hyperchaotic systems are adopted as response systems at the same time. The digital signals are recovered via comparing the discrete signals of the two error systems. Numerical simulations show the effectiveness of the method.

Development of a Novel Hyperchaos‐Based Image Encryption Algorithm Consisting of Two Scrambling‐Diffusion Operations

This paper proposes a hyperchaos‐based image encryption algorithm, which consists of two scrambling‐diffusion operations and one scrambling operation. In the proposed algorithm, the initial conditions of a hyperchaotic Chen system are first generated using the Message Digest 5 (MD5) value of digital images and given initial values, and then the images will be encrypted using the keystream created by the system. Since the initial values of hyperchaotic Chen systems are related to plaintext and the encryption process is related to the images, this algorithm is able to effectively protect images against selective plaintext attacks. Simulation results demonstrate that the present algorithm offers enhanced encryption performance, high security, and strong resistance to known attacks. Therefore, it may find wide application in image encryption transmission. Compared to other image encryption algorithms, the proposed algorithm uses different keystreams when encrypting different images and is capable of effectively resisting various plain image and differential attacks faster.

An image encryption algorithm based on hyperchaotic system and DNA coding

A chaotic image encryption scheme combining block scrambling and DNA coding is proposed. The chaotic sequences generated by Chen hyperchaotic system are used for inter-block index scrambling and intra-block Fisher-Yates scrambling. Then the index sequence is used to further scramble the image to further enhance the encryption effect. The pixel value of the image is initially changed by chaotic sequence, and diffused by different DNA coding rules and different operation rules corresponding to chaotic sequence. After decoding the DNA matrix, the final encrypted image is obtained. The initial values and parameters of the chaotic system are generated by SHA-512 hash function and plaintext image. The experimental results and various security analysis show that the algorithm has good encryption effect and can resist common attacks such as chosen-plaintext attacks, clipping attacks and noise attacks.

Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

Design of Adaptive-Robust Controller for Multi-State Synchronization of Chaotic Systems with Unknown and Time-Varying Delays and Its Application in Secure Communication.

In this paper, the multi-state synchronization of chaotic systems with non-identical, unknown, and time-varying delay in the presence of external perturbations and parametric uncertainties was studied. The presence of unknown delays, unknown bounds of disturbance and uncertainty, as well as changes in system parameters complicate the determination of control function and synchronization. During a synchronization scheme using a robust-adaptive control procedure with the help of the Lyapunov stability theorem, the errors converged to zero, and the updating rules were set to estimate the system parameters and delays. To investigate the performance of the proposed design, simulations have been carried out on two Chen hyper-chaotic systems as the slave and one Chua hyper-chaotic system as the master. Our results showed that the proposed controller outperformed the state-of-the-art techniques in terms of convergence speed of synchronization, parameter estimation, and delay estimation processes. The parameters and time delays were achieved with appropriate approximation. Finally, secure communication was realized with a chaotic masking method, and our results revealed the effectiveness of the proposed method in secure telecommunications.