Discrete Chaotic Systems Research Articles

A Class of Discrete Memristor Chaotic Maps Based on the Internal Perturbation

Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of chaotic maps with different discrete memristors, achieved through internal perturbation based on the Sine map. The I-V curve of the discrete memristor has a symmetrical structure. The dynamic characteristics of the designed system are analyzed using the chaotic attractor phase diagram, Lyapunov exponent (LE) spectrum, and bifurcation diagram. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map’s chaotic characteristics, expand the chaos range, and improve the ergodicity and LE value. Moreover, the type of discrete memristors has a significant impact on the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, in this paper, a direction for the design of a discrete memristor chaotic system is provided. Finally, a discrete memristor chaotic map with a simple structure and better performance is selected. Based on this, a pseudo-random sequence generator is designed, and the generated sequence passes the National Institute of Standards and Technology (NIST) test.

Optimization of data packet encryption algorithm in network link transport layer

ABSTRACT With the rapid development of information technology, huge data information is exchanged every moment in various types of networks, which contain information such as commercial secrets and personal privacy, and data security has a great impact on people’s lives. To address the issues of low efficiency and poor security in network link transmission layer database security encryption systems, a new system is studied and designed to strengthen the protection of data information from both hardware and software aspects. Then, a discrete chaotic system is introduced to ensure the stability of the dynamic grouping encryption algorithm. Finally, trajectory loop rotation is used to obtain address clusters using the discrete chaotic system, and dual address loop rotation is used to achieve the variability of the dynamic grouping algorithm. The experiment shows that for different file sizes, the encryption speed of the Dynamic Packet Encryption Optimization (DPEO) algorithm is stable between 5.84 and 5.98 mb/s. And after minor changes in the key, the NPCR of the ciphertext obtained by the DPEO algorithm exceeds 99.5%. In addition, its operation efficiency is excellent, reaching the stable entropy value in only 0. 52 s. In summary, the DPEO algorithm in the network link transport layer database security encryption system can combine high efficiency and excellent security performance.

Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption

This paper proposes a new two-dimensional discrete hyperchaotic system and utilizes it to design a pseudo-random number generator (PRNG) and an efficient color image encryption algorithm. This hyperchaotic system has very complex dynamic properties and can generate highly random chaotic sequences. The complex hyperchaotic characteristics of the system are confirmed via bifurcation diagram, chaotic attractor, Lyapunov exponents, correlation analysis, approximate entropy and permutation entropy. Compared with some traditional discrete chaotic systems, the new chaotic system has a larger range of chaotic parameters and more complex hyperchaotic characteristics, making it more suitable for application in information encryption. The proposed PRNG can generate highly random bit sequences that can fully pass all NIST testing items. The proposed color image encryption algorithm achieves cross-channel permutation and diffusion of pixels in parallel. These strategies not only greatly improve the encryption speed of color images, but also enhance the security level of cipher images. The simulation experiments and security analysis results show that the algorithm has strong robustness against differential attacks, statistical attacks and interference attacks, and has good application potential in real-time secure communication applications of color images.

Medical image encryption using multi chaotic maps

Over the last twenty years, chaos-based encryption has been an increasingly popular way to encrypt and decrypt data using nonlinear dynamics and deterministic chaos. Discrete chaotic systems based on iterative maps have gotten a lot of interest because of their simplicity and speed. In this paper, three kinds of chaotic maps are utilized to build a digital image encryption strategy depending on a chaotic system. These chaotic maps are the logistic map, Arnold Cat’s map, and Baker’s map. In addition to using the triple data encryption standard (3DES) encryption scheme with the chaotic maps mentioned. The results of the experiments revealed that the suggested digital image encryption technique is both efficient and secure, making it ideal for usage in insecure networks. The transmission control protocol (TCP)/internet protocol (IP) protocol was used for the purpose of transferring data from server to client through the network and vice versa.

Study of Generalized Chaotic Synchronization Method Incorporating Error-Feedback Coefficients.

In this paper, taking the generalized synchronization problem of discrete chaotic systems as a starting point, a generalized synchronization method incorporating error-feedback coefficients into the controller based on the generalized chaos synchronization theory and stability theorem for nonlinear systems is proposed. Two discrete chaotic systems with different dimensions are constructed in this paper, the dynamics of the proposed systems are analyzed, and finally, the phase diagrams, Lyapunov exponent diagrams, and bifurcation diagrams of these are shown and described. The experimental results show that the design of the adaptive generalized synchronization system is achievable in cases in which the error-feedback coefficient satisfies certain conditions. Finally, a chaotic hiding image encryption transmission system based on a generalized synchronization approach is proposed, in which an error-feedback coefficient is introduced into the controller.

Fully fixed-point integrated digital circuit design of discrete memristive systems

In this paper, the fully fixed-point digital integrated circuits of discrete memristive systems are designed with very low circuit area cost, where the two-stage pipeline and multi-cycle architecture is employed. Firstly, the mathematical models of the discrete memristor and a memristor chaotic map are presented and dynamics are analyzed. Secondly, data flow design is carried out and the feasibility of the fixed-point model is discussed, which provides a foundation for the further circuit design. Thirdly, different architectures are designed and we get the optimal results. As a result, gate area of the discrete memristor is 40288 μm2 and the equivalent gate counts are 4588, while gate area of the discrete memristor map is 40424 μm2 and the equivalent gate counts are 4604. Moreover, a chaotic pseudo random sequence generator is designed and the NIST test is passed. It provides the foundation for the further applications of the discrete memristor and discrete memristor chaotic systems.

TWO DISCRETE MEMRISTIVE CHAOTIC MAPS AND ITS DSP IMPLEMENTATION

In this paper, a discrete model of memristor is adopted and analyzed. The new discrete maps are built by introducing this discrete memristor model into a two-dimensional discrete map. Interestingly, introducing this discrete memristor model from different locations can lead to two new chaotic map models. The dynamical behaviors of the two maps are studied by means of bifurcation diagrams, phase diagrams and Lyapunov exponential spectra (LEs). The simulation results show that both chaotic systems have rich dynamical behaviors. In addition, they are experimentally found to have multi-stable properties, where the M-XM map has infinite attractors coexistence. Finally, we complete the hardware implementation of the two maps based on Digital Signal Processing (DSP) platform for the application of discrete chaotic systems.

Multistability Analysis of a Piecewise Map via Bifurcations

In this paper, we investigate the dynamical behavior of a one-dimensional piecewise map based on the logistic map, where generalized multistability can be observed. The proposed system has the unique property that the function is symmetric with respect to the origin but not its behavior, furthermore this system can display three types of multistability, and chaos for both, monostable and bistable behaviors. The stability analysis of the proposed system is presented. We describe the structure of bistable regions in the bifurcation diagram. Particular attention is paid to the chaotic regions. Corresponding to coexisting attractors, three scenarios of coexisting attractors, namely fixed points, periodic orbits, and chaotic attractors, can be found, which are unreported behaviors in discrete chaotic systems. The mechanism that leads to multistability phenomenon including pitchfork bifurcation, period-halving bifurcations, and the coexisting invariant sets is demonstrated. Furthermore, the Lyapunov exponent is analyzed with the type of multistability distinguished for a given set of parameters.

Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry

Multistability is an inherent property of many nonlinear dynamical systems. However, finding exact conditions where a certain nonlinear system is multistable, is a complex problem. In this study, we propose a novel approach for inducing multistability in a discrete system by applying the numerical integration method with variable symmetry to a continuous monostable system and finding a range of the symmetry coefficients for which multiple attractors coexist in its discrete model. We consider the well-known Chen system as an example, showing that multistability can be induced by discretization with variable symmetry. A special two-stage algorithm is proposed for a fast search for hidden attractors. Using the proposed algorithm, we found several multistable versions of the discrete Chen system and investigated their attractors and basins of attraction. By applying numerical backward error analysis, we discovered a generalized continuous Chen system with additional terms which were not present in the original system and have shown its approximate equivalence to the obtained discrete system. The results of this study can be used for inducing artificial multistability in a wide range of chaotic systems with possible applications in chaotic cryptography, communication, and chaos-based sensing.

Design and realization of discrete memristive hyperchaotic map with application in image encryption

The investigation of discrete memristive chaotic systems with complex dynamics has been an interesting and meaningful research work. This paper is devoted to constructing a hyperchaotic system with no fixed point and infinitely many coexisting attractors. The memristive Gaussian map (MGM) is coupled by a sinusoidal discrete memristor with the Gaussian map and induces extreme multistability associated with the initial state due to the import of sinusoidal nonlinearity. Creatively, the iterative number is imported into the system as a variable, which effectively boosts the complexity of its export. The most remarkable feature of the system is a large range of chaos and hyperchaos captured under multiple sets of parameters, and with various coexisting attractors. In addition, digital experiments are designed to verify the feasibility of the hardware implementation, an image encryption algorithm and PRNG are proposed based on the MGM chaotic sequence.

Memcapacitor-Coupled Chebyshev Hyperchaotic Map

The model of the consecutive memcapacitor has been widely used in chaotic circuits. However, the model of discrete memcapacitor and its application in chaotic systems have not been further studied. In this paper, a model of discrete memcapacitor is proposed. And the dynamical characteristics of the discrete memcapacitor model are analyzed. The memristive Chebyshev map is obtained by coupling the discrete memcapacitor with the Chebyshev map. Since memristive Chebyshev map has linear fixed points, the memristive Chebyshev map is unstable or critically stable, depending on the internal parameters and the initial condition of the chaotic map. The dynamical behavior of control parameter dependence of memristive Chebyshev map is studied by using several analysis methods, and its hyperchaotic attractor is found. The special phenomenon of coexistence of attractors is also found. Finally, the memristive Chebyshev map is realized by DSP. And the results of simulation are further verified. The results of this study supply a theoretical basis for the application of discrete memcapacitor in the design of discrete chaotic systems.

Memristor-Based Lozi Map with Hidden Hyperchaos

Recently, the application of memristors to improve chaos complexity in discrete chaotic systems has been paid more and more attention to. To enrich the application examples of discrete memristor-based chaotic systems, this article proposes a new three-dimensional (3-D) memristor-based Lozi map by introducing a discrete memristor into the original two-dimensional (2-D) Lozi map. The proposed map has no fixed points but can generate hidden hyperchaos, so it is a hidden hyperchaotic map. The dynamical effects of the discrete memristor on the memristor-based Lozi map and two types of coexisting hidden attractors boosted by the initial conditions are demonstrated using some numerical methods. The numerical results clearly show that the introduced discrete memristor allows the proposed map to have complicated hidden dynamics evolutions and also exhibit heterogeneous and homogeneous hidden multistability. Finally, a digital platform is used to realize the memristor-based Lozi map, and its experimental phase portraits are obtained to confirm the numerical ones.

A novel security and authentication method for infrared medical image with discrete time chaotic systems

Objective:Hand vein images have become important biometric signs used for identification systems. Also, dorsal hand vein images have noteworthy advantages in terms of reliability and contactless procedure. Surgically changing the vascular pattern under the skin is extremely difficult. Therefore, the use of such patterns in identity recognition applications is increasing day by day. In this context, many studies have been carried out in essential areas such as image acquisition for different textures, image preprocessing, data security, image feature extraction and recognition. Methods:In this article, a new dorsal hand vein identification application has been carried out with the chaos-based security mechanism to protect personal data and the Improved SURF method to reduce the error matches of traditional SURF method in the current application. There are two improvements in the presented system. The first one finds the features representing only the vein segments, not the remaining tissue or hairly parts. The second one eliminates the mismatching points to increase the accuracy. Results:Both encryption and data hiding techniques are preferred together to protect person data. In addition, dorsal hand vein images taken with a camera for matching and recorded in the database of the people have been improved with the newly developed I-SURF feature extraction method. Thereby, with the developed application, in addition to keeping the personal identity information securely in the database with chaos-based methods, higher accuracy rate has been achieved in matching the new image taken with the camera.

SM4 Chaotic Masking Scheme Against Power Analysis Based on FPGA

SCA is one of the biggest threats to the security of encryption chip. It can crack the unprotected encryption chip at lower cost and faster speed, which weakens the security of the SM4 encryption algorithm circuit without any protection. In this paper, the SM4 encryption algorithm is implemented on FPGA. The pseudo-random sequence generated by discrete chaotic system is used to randomly mask the intermediate value in the SM4 encryption process. This will disrupt the power consumption in the encryption process, thus preventing power analysis. Experimental results show that the proposed chaotic mask scheme can effectively prevent intermediate value leakage and protect the SM4 encryption system from power analysis attack.

Analogue circuit implementation of a new logistic‐like map

Discrete chaotic system has complex dynamics and becomes to be a present hot topic, but its analogue circuit implementation is rarely discussed. In this paper, by simplifying the logistic map, a new Logistic-like map is proposed. Its cobweb plots, bifurcations, Lyapunov exponents, and dynamic map are investigated theoretically and numerically. The results show that the Logistic-like map has complex dynamical behaviours. And then Psim simulation model is proposed to verify the feasibility of analogue circuit implementation. Finally, an analogue circuit experiment is performed and its results are consistent with the simulation results. The circuit designed is very simple and has less components, which can further broaden the applications of discrete chaotic map in applications.

High-security UFMC optical transmission system of seven-core fiber based on updating the 3D discrete chaotic model.

In this paper, we propose a high-security universal filtered multicarrier (UFMC) transmission system based on a novel, to the best of our knowledge, three-dimensional (3D) discrete chaotic model. The cascade of counters and the 3D discrete chaotic system is used to generate three masking factors and update these factors to encrypt the bitstream, constellation, and the information of the subcarriers. Using this structure, the key space is 10270 and the key is updated in a timely manner. In this work, the encryption scheme solves the dynamic degradation of chaotic cryptography. Experimental results show that there is no significant difference in error performance in comparison with before encryption. Compared with the orthogonal frequency division multiplexing (OFDM) system, the spectrum efficiency of the UFMC system is higher, which reduces out-of-band leakage and interference between services. Considering the complexity constraints of the receiver, the inter-symbol interference caused by fiber dispersion is alleviated by optimizing the distribution of data subbands, and the bit error rate (BER) performance is improved. It is shown that the UFMC system obtains 1.9 dB gain compared with the OFDM system in terms of receiver sensitivity when the BER is 10-3. This encryption scheme has a promising application prospect in short-distance optical access systems in the future.

Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems

This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. The system can be distributed uniformly by adjusting the parameters. In this paper, we propose an image encryption scheme based on a uniformly distributed discrete chaotic system and DNA encoding. DNA encoding and decoding rules are determined by plain text. The experimental results demonstrate that our encryption algorithm has a large key space, high key sensitivity, and fast encryption speed and can resist differential and statistical attacks.

Symmetry breaking bifurcation analysis and control of a cubic discrete chaotic system

Symmetry breaking bifurcation analysis and control of a cubic discrete chaotic system

Memristor-type chaotic mapping.

In this letter, a compact memristor structure unit is applied for constructing the discrete chaotic system and, consequently, a memristor-type chaotic mapping is designed. Two independent system parameters are proven to be partial and total amplitude controllers. Meanwhile, the internal memristor parameter returns the map a typical bifurcation. Finally, a hardware experiment based on STM32 is carried out by verifying the theoretical finding. To the best of our knowledge, the memristor-type chaotic mapping has not been previously reported.

Uniform non-degeneracy discrete chaotic system and its application in image encryption

Uniform non-degeneracy discrete chaotic system and its application in image encryption