Hyperchaotic System Research Articles

Color image encryption based on discrete memristor logistic map and DNA encoding

This paper proposes a color image encryption scheme with new features based on two-dimensional discrete memristor logistic map (2D-MLM), Deoxyribonucleic acid (DNA) encoding and multi-wing hyperchaotic systems. Firstly, the discrete memristor map and four-wing hyperchaotic system are used to generate various pseudo-random sequences. Secondly, the original image is processed in blocks, and DNA encoding and operation are performed on the sub-block image using multiple pseudo-random sequences. Finally, combining the pseudo-random sequence to diffuse the sub-block image and DNA decoding, we can get the encrypted image. The scheme generates a one-time key for each image, and uses multiple different sub-keys to increase the key space. The use of diverse pseudo-random sequences for image scrambling effectively avoids the security risks associated with using a single chaotic sequence. The key space of this algorithm reaches 2425, the information entropy of the ciphertext image is 7.9993, the number of pixels change rate (NPCR) and the uniformed average change intensity (UACI) reach 99.6095 % and 33.5089 %, and the inter-pixel correlation is close to zero. The simulation results prove that the proposed algorithm has good security against many potential attacks.

Generalized time-delay reverse synchronization with error feedback coefficients

To enhance the application of discrete chaotic systems in secure communication, we introduce a novel generalized time-delay inverse synchronization method with error feedback coefficient. This paper outlines the derivation of an inverse master-slave time-delay generalized synchronization system using the Lyapunov theory with error feedback coefficient design, which is proposed for the first time. To verify the efficacy of the synchronization method, we constructed a new 4D discrete hyperchaotic system. The dynamic properties of the novel system, such as the phase diagram and Lyapunov exponents, are investigated. Empirical outcomes reveal that generalized discrete time-delay synchronization can be accomplished under certain conditions for the error feedback coefficient. The study utilizes the chaotic masking technique to encrypt and decrypt messages in the secure communication system. The experimental findings reveal that by integrating the synchronization approach with the time-delay context of secure communication, the applicable design of the synchronization procedure is adaptable and trustworthy, catering to the pertinent requirements of engineering, and has the capacity to attain instantaneous chaotic synchronization requisites.

Image encryption algorithm based on DNA network and hyperchaotic system

Image encryption algorithm based on DNA network and hyperchaotic system

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.

An Image Double Encryption Based on Improved GAN and Hyper Chaotic System

An Image Double Encryption Based on Improved GAN and Hyper Chaotic System

Color Image Compression and Encryption Algorithm Based on 2D Compressed Sensing and Hyperchaotic System

Color Image Compression and Encryption Algorithm Based on 2D Compressed Sensing and Hyperchaotic System

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>

Triple Layer RGB Image Encryption Algorithm Utilizing Three Hyperchaotic Systems and Its FPGA Implementation

Triple Layer RGB Image Encryption Algorithm Utilizing Three Hyperchaotic Systems and Its FPGA Implementation

Controllable multistability of fractional-order memristive Henon map and its application in video encryption

In recent years, the use of discrete memristors to enhance chaotic maps has received increasing attention. The introduction of memristors increases the complexity of chaotic maps, making them suitable for engineering applications based on chaotic systems. In this work, a fractional-order discrete memristor exhibiting local activity and controllable asymptotic stability points is constructed by using multiband nonlinear functions. The locally active property of this memristor is demonstrated by using the power-off plot and DC <i> <b>v</b> </i> -<i> <b>i</b> </i> plot. It is then introduced into the Henon map to construct a fractional-order memristive Henon map that can generate any number of coexisting attractors. Simulation results show that the number of fixed points in the system is controlled by the memristor parameters and related to the number of coexisting attractors, thus achieving controllable homogeneous multistability. The complex dynamical behaviors of this map are analyzed by using phase portraits, bifurcation diagrams, maximum Lyapunov exponent (MLE), and attractor basins. Numerical simulations show that the fractional-order map can generate various periodic orbits, chaotic attractors, and period-doubling bifurcations. The system is then implemented on an ARM digital platform. The experimental results are consistent with the simulation results, confirming the accuracy of the theoretical analysis and its physical feasibility. Finally, a parallel video encryption algorithm is designed by using the chaotic sequence iteratively generated by fraction-order memory Henon mapping, which mainly includes frame pixel scrambling and diffusion. Comprehensive security analyses are conducted, proving the robustness and reliability of the proposed encryption scheme. The results show that the encryption algorithm can effectively protect video information. In the future, we will explore other methods of constructing chaotic or hyperchaotic systems with controllable multistability and study their circuit implementation, synchronization control, and chaos-based engineering applications.

Design and analysis of a novel self-excited 5-D hyperchaotic system with maximum (n-2) positive lyapunov exponents

In this work, analytic and designed a new self -existed 5-D with thirteen terms nine of the term exhibit linearity, while the remaining one demonstrates nonlinearity. It has the highest Lyapunov Exponent with three positive ones to leverage the sequence in data security, encryption, and other related aspects, it’s advantageous to utilize a complex system where the key remains unbreakable It contains fifteen keys sensitive ICs and parameters. The system is a highly intricate dynamical system characterized by two equilibrium points, as demonstrated through examinations such as observation of phase plane trajectories, the investigation into eigenvalue structure, and assessment of dissipative stability. These analyses provide evidence supporting the existence of chaotic and hyperchaotic attractors within the system. The results of the simulations are derived from MATLAB 2021b, and Mathematica 11. A detailed and comprehensive evaluation of the recommended techniques has been carried out, offering insights into their effectiveness and suitability for theoretical computation and numerical simulation.

A new image encryption based on hybrid heterogeneous time-delay chaotic systems

<abstract><p>Chaos theory has been widely utilized in password design, resulting in an encryption algorithm that exhibits strong security and high efficiency. However, rapid advancements in cryptanalysis technology have rendered single system generated sequences susceptible to tracking and simulation, compromising encryption algorithm security. To address this issue, we propose an image encryption algorithm based on hybrid heterogeneous time-delay chaotic systems. Our algorithm utilizes a collection of sequences generated by multiple heterogeneous time-delay chaotic systems, rather than sequences from a single chaotic system. Specifically, three sequences are randomly assigned to image pixel scrambling and diffusion operations. Furthermore, the time-delay chaotic system comprises multiple hyperchaotic systems with positive Lyapunov exponents, exhibiting a more complex dynamic behavior than non-delay chaotic systems. Our encryption algorithm is developed by a plurality of time-delay chaotic systems, thereby increasing the key space, enhancing security, and making the encrypted image more difficult to crack. Simulation experiment results verify that our algorithm exhibits superior encryption efficiency and security compared to other encryption algorithms.</p></abstract>

<i>N</i>-dimensional discrete hyperchaotic system and its application in audio encryption

Discrete chaotic system, as a pseudo-random signal source, plays a very important role in secure communication. However, many low-dimensional chaotic systems are prone to chaos degradation. Therefore, many scholars have studied the construction of high-dimensional chaotic systems. However, many existing algorithms for constructing high-dimensional chaotic systems have relatively high time complexity and relatively complex structures. To solve this problem, this paper explores an <i>n</i>-dimensional discrete hyperchaotic system with a simple structure. Firstly, the <i>n</i>-dimensional discrete hyperchaotic system is constructed by using sine function and power function and simple operations. Then, it is theoretically analyzed that the system can be through parameter settings the positive Lyapunov exponents based on Jacobian matrix method. Next, the algorithm time complexity, sample entropy, correlation dimension and other indexes are compared with the existing methods. The experimental results show that our system has a simple structure, high complexity and good algorithm time complexity. Therewith, a six-dimensional chaotic system is chosen as an example, the phase diagram, bifurcation diagram, Lyapunov expnonents, complexity and other characteristics of the system are analyzed, and the results show that the proposed system has good chaotic characteristics. Moreover, to show the application of the proposed system, we apply it to audio encryption. Based on this system, we combine it with the XOR operation and true random numbers to explore a novel method of one-cipher audio encryption. Through experimental simulation, compared with some existing audio encryption algorithms, this algorithm can satisfy various statistical tests and resists various common attacks. It also proves that the proposed system can be effectively applied in the field of audio encryption.

A 4D Entangled Memristor Hyperchaotic System and Its New Predefined-Time Sliding Mode Synchronization Control

A 4D Entangled Memristor Hyperchaotic System and Its New Predefined-Time Sliding Mode Synchronization Control

A Novel Four-Dimensional Hyperchaotic System: Design, Dynamic Analysis, Synchronization, and Image Encryption

A Novel Four-Dimensional Hyperchaotic System: Design, Dynamic Analysis, Synchronization, and Image Encryption

Secure Image Encryption using E-Fractal-Based Non-Commutative Group and Hash Function

Due to the importance of data security at present, an encryption algorithm based on the principle of non-commutative group, hash function, and E-fractal has been proposed. Key generation depends on the array values generated by the braid group and using them as input to the SHA-3 (256) which increases the strength of the key because it generates values in one direction only. The results of the hash function are determined by the Lorenz hyper-chaotic system initial values, and four image-size arrays are generated as the final image-encryption keys using the RC4 algorithm. Then the use of the E-fractal diffusion method. To bolster the security of the encryption, it is employed to disperse the pixel values., adopting the control word that increases the randomness of the data. The security analysis of the proposed encryption algorithm demonstrates that it is difficult to decipher due to the presence of the hash function in addition to its easy implementation within seconds, and the efficiency scale was calculated that showed its strength in effectively resisting attacks by others.

A New 6D Hyperchaos-Based Medical Image Encryption Scheme Using k-Fibonacci Numbers

In the era of information technology, hospitals, medical centers, doctors and health specialists share millions of images. Securing these images is essential to maintaining patients’ privacy. Several cryptographic algorithms are implemented to meet the increasing demands of transmission systems. As a contribution to securing these data, we propose a novel robust and efficient algorithm. We randomly generate numbers from a six-dimensional hyperchaotic system and Arnold’s cat map to confuse the original images. The confused images are then diffused using a k-Fibonacci matrix. The performance of the proposed algorithm was evaluated using several parameters tested on a set of reference images of different sizes and modalities. The obtained results are conclusive and the performances are excellent, sometimes exceeding those found by other recent algorithms proposed in the literature.

Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method.

Offset boosting in a memristive hyperchaotic system

In this article, an autonomous memristive hyperchaotic system with multi-dimensional offset boosting is constructed and analyzed. Besides this, the oscillation can be rescaled by an independent controller in the memristor. Two independent constants are obtained for offset boosting with one or two variables, which provide two modes of offset boosting, including single control and synchronous reverse control. In addition, the offset of the variables is also modified by the system bifurcation parameters or combined with amplitude control. The multistability can also be identified according to the offset boosting. Finally, circuit implementation based on PCB is proposed to confirm the numerical simulations.

A universal method for constructing n-dimensional polynomial hyperchaotic systems with any desired positive Lyapunov exponents

Most existing chaotic maps have many defects in engineering applications, such as discontinuous parameter range, uneven output of chaotic sequences and dynamic degradation. Based on this, a generalized n-dimensional polynomial chaotic map is proposed in this paper. By setting the coefficient of the linear term and the order of the highest order term of the polynomial, a series of n-dimensional polynomial chaotic maps of specific Lyapunov exponents can be obtained. The system solves the defects of the above system well, in addition, one can get the desired number of positive Lyapunov exponents, and one can get the desired value of positive Lyapunov exponents. Then, the effectiveness of the map is verified by a specific numerical example, and its dynamic analysis shows that the map has complex dynamic behavior. Finally, the map is applied to secure communication technology. Compared with other chaotic maps of the same dimension, the maps can obtain a smaller bit error rate, indicating that the chaotic map is more suitable for chaotic secure communication applications.

Enhancing Key Exchange Security: Leveraging RSA Protocol in Encryption Algorithm Based on Hyperchaotic System

Enhancing Key Exchange Security: Leveraging RSA Protocol in Encryption Algorithm Based on Hyperchaotic System