Lorenz Chaotic Research Articles

Image Steganography Technique based on Lorenz Chaotic System and Bloom Filter

Image Steganography Technique based on Lorenz Chaotic System and Bloom Filter

A New Image Encryption Scheme Based on the Hybridization of Lorenz Chaotic Map and Fibonacci Q-Matrix

A New Image Encryption Scheme Based on the Hybridization of Lorenz Chaotic Map and Fibonacci Q-Matrix

An efficient and lightweight image encryption technique using Lorenz chaotic system

In the past few years, to store and transmit image data securely, numerous research initiatives on image encoding have been conducted. The primary objective of the image encryption technique is to safeguard the image by sabotaging the pixel pattern. Researchers suggested a safe, portable, and simple to use image encryption technique in this work. The encryption of the image is done using a bit-wise XOR operation, where the bit-wise operation is applied on each pixel of the plain image with a pseudo-random number that is created by the Lorenz chaotic system, to prevent unwanted access to confidential image data. The results of the experiments demonstrate that the suggested technique offers effective image encryption and decryption. The key stream of the encrypted image is made up of pseudo-random digits generated by the Lorenz Chaotic System. Several experimental tests have been performed, including histogram, correlation, information entropy, and differential analysis. The experimental findings reveal that the suggested approach performs image encryption and decryption efficiently.

Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption

Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaotic system and a 2D sinusoidally constrained polynomial hyper-chaotic map (2D-SCPM). Then, we elaborately developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM (MIEA-FCSM). The introduction of the fractional-order 3D Lorenz chaotic system with the fourth parameter not only enables MIEA-FCSM to have a significantly large key space but also enhances its overall security. Compared with recent alternatives, the structure of 2D-SCPM is simpler and more conducive to application implementation. In our proposed MIEA-FCSM, multi-channel fusion initially reduces the number of pixels to one-sixth of the original. Next, after two rounds of plaintext-related chaotic random substitution, dynamic diffusion, and fast scrambling, the fused 2D pixel matrix is eventually encrypted into the ciphertext one. According to numerous experiments and analyses, MIEA-FCSM obtained excellent scores for key space (2541), correlation coefficients (<0.004), information entropy (7.9994), NPCR (99.6098%), and UACI (33.4659%). Significantly, MIEA-FCSM also attained an average encryption rate as high as 168.5608 Mbps. Due to the superiority of the new fractional-order chaotic system, 2D-SCPM, and targeted designs, MIEA-FCSM outperforms many recently reported leading image encryption algorithms.

A Behavioural Model for Accurate Investigation of Noisy Lorenz Chaotic Synchronization Systems

A Behavioural Model for Accurate Investigation of Noisy Lorenz Chaotic Synchronization Systems

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative

Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of , , on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results of integer order are in good agreement with those of other methods. The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Time-Delay Fractional Variable Order Adaptive Synchronization and Anti-Synchronization between Chen and Lorenz Chaotic Systems Using Fractional Order PID Control

In this research work, time-delay adaptive synchronization and adaptive anti-synchronization of chaotic fractional order systems are analyzed via the Caputo fractional derivative, and the prob-lem of synchronization and anti-synchronization of chaotic systems of variable fractional order is solved by using the fractional order PID control law, the adaptive laws of variable-order frac-tional calculus, and a control law deduced from Lyapunov’s theory extended to systems of time-delay variable-order fractional calculus. In this research work, two important problems are solved in the control area: The first problem is described in which deals with syn-chro-nization of chaotic systems of adaptive fractional order with time delay, this problem is solved by using the fractional order PID control law and adaptative laws. The second problem is de-scribed in which deals with anti-synchronization of chaotic systems of adaptive frac-tional order with time delay, and this problem is solved by using the fractional order PID con-trol law and adaptative laws.

Internal synchronization using adaptive sliding mode

AbstractSynchronization of chaotic systems by means of the combination of drive‐response/master–slave systems have been widely utilized. In the current study, the author introduces the concept of internal synchronization (IS) that is based on the synchronization within the system among the subsystems. Furthermore, the two types of Internal Multi‐Switching Synchronization (IMSS): the first one based on single error while the other one is based on two errors, have been discussed. In order to demonstrate, the author chooses the Lorenz Chaotic System (LCS) and Lorenz Hyper Chaotic System (LHCS) together with the adaptive sliding mode control (SMC) technique in multi‐switching manner. In addition, the efficiency of the IMSS is illustrated using Mathematica. The computational part is the witness of the achievement of stability of the IS.

3D Textured Model Encryption Using 2D Logistic and 3D Lorenz Chaotic Map

The widespread of recent multimedia, including various 3D model applications in different domains of areas, may lead to 3D models being stolen and attacked by hackers. Moreover, 3D models must be protected from unauthorized users and when transmitting over the internet. Nowadays the 3D model protection is a very important issue. This paper proposed a scheme that provides high protection for the textured 3D model by implementing multiple levels of security. The first level of security is achieved by encrypting the texture map based on a key generated by a 2D Logistic chaotic map. The second level of security is implemented by modifying the vertices values of the 3D mesh based on keys generated by the 3D Lorenz chaotic map. The proposed scheme was implemented on various 3D textured models varying in the number of vertices and faces. The experimental results show that the proposed scheme has a good encryption and provides high security by completely deforms the whole texture and 3D mesh of the textured 3D model into the two levels. The encryption scheme has a large key space 10135 making the scheme resists violent attacks. The Hausdorff Distance (HD) and histogram metrics are adopted to calculate the matching degree between the original and extracted model. The results show that the original and extracted model are identical through the values of HD, which are approximate to zero, and the histogram visually is similar. Index Terms— 3D textured model, encryption, 2D Logistic map, 3D Lorenz map, chaotic map

Mathematical models of CBSC over wireless channels and their analysis by using the LeNN-WOA-NM algorithm

In recent studies, several chaos-based secure communication (CBSC) systems are developed and are assumed to be effective and promising tools for balancing communications in wireless applications. The reliability of a wireless communication system is dependent on the synchronization between receiving and transmitting nodes. Therefore, it is crucial to analyze the mathematical models for different enhancements through CBSC and avoid the difficulty in synchronization. We have designed a novel computational paradigm that uses weighted Legendre polynomials to construct series solutions for mathematical models of the Lorenz Chaotic Attractor (LCA) and Double Scroll Attractor (DSA) (with filter and without filter) by using Chua’s circuits. We design fitness functions for each system of differential equations. Two optimization techniques, the Whale Optimization Algorithm (WOA) and the Nelder–Mead (NM) algorithm are adopted to optimize the objective functions and calculate the best set of unknown weights. We name our soft computing paradigm, the LeNN-WOA-NM algorithm. We have compared our results with state-of-the-art, and we establish that the LeNN-WOA-NM algorithm is fast, accurate, and reliable. We present graphical and statistical analysis to further elaborate on the performance of our algorithm.

Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

3D Polygon Mesh Encryption Based on 3D Lorenz Chaotic Map

<p class="0abstract">The multimedia application developments in recent years lead to the widespread of 3D model applications. It becomes more popular in various fields as well as exchanging it over the internet. The security of the 3D models is a very important issue now a day, so the scheme for encrypting the 3D model will be proposed in this work. In this proposed scheme, the 3D polygon mesh model will be protected through the encrypting process based on a 3D Lorenz Chaotic map where the vertices value of the 3D polygon mesh model will be modified using 3D keys generated by 3D Lorenz Chaotic Map, which has excellent property and provides a good diffusion. The proposed scheme was implemented on various 3D models, which have a different number of vertices and faces. The experimental results show that the proposed scheme has good encryption results, which were noted through completely deforming and changing the whole shape of the 3D models. The Hausdorff Distance (HD) and histogram metrics are adopted to calculate the matching degree between the original and extracted model. The results show that the original and extracted model are identical through the values of HD, where they are approximately zero, and the histogram visually is identical. </p>

Bearing Fault Diagnosis Based on Chaotic Dynamic Errors in Key Components

Ball bearings are one of the most common components used in rotating machines. They reduce the rotational friction between the shaft and fixed components and maintain the center line of rotation of the shaft. A damaged bearing will cause abnormal vibration and noise, and often results in machine failure and loss of production. In this study the public database on ball bearings, provided by the Vibration Institute of Machinery Failure Prevention Technology (MFPT), was used for data retrieval and analysis, and a diagnosis model was created according to the data sets of the bearing in the database. Three different approaches were used for the extraction of features and a classifier was used to implement a diagnostic system. The aim of this study was a comparison of three approaches. The first was the Short-time Fourier Transform (STFT) where the time-frequency domain image is extracted as the feature used for status identification. The second and third approaches were based on the Chen-Lee Chaotic and the Lorenz Chaotic Systems and chaotic dynamic error maps were used in analysis and feature status identification. Chaotic systems are particularly sensitive to the slightest changes in input signals, and the time domain signals from bearings in different conditions were mapped onto individual images. The feature images extracted by the three different approaches were then used for training and verification in a Convolutional Neural Network (CNN). From the results of the experiments, it can be seen that all three approaches gave high identification rates. The interactive verification identification rate of the Chen-Lee chaotic system with CNN under three statuses reached 98.33%, and it also had the best computational efficiency in the condition without losing any classification accuracy. This will make a substantial contribution to real-time ball bearing fault diagnosis.

Parallel multi-layer selector S-Box based on lorenz chaotic system with FPGA implementation

<p><span>The substitution box (S-Box) is the main block in the encryption system, which replaces the non-encrypted data by dynamic secure and hidden data. S-Box can be designed based on complex nonlinear chaotic systems that presented in recent papers as a chaotic S-Box. The hardware implementation of these chaotic systems suffers from long processing time (low speed), and high-power consumption since it requires a large number of non-linear computational models. In this paper, we present a high-speed FPGA implementation of Parallel Multi-Layer Selector Substitution Boxes based on the Lorenz Chaotic System (PMLS S-Box). The proposed PMLS chaotic S-Box is modeled using Xilinx System Generator (XSG) in 32 bits fixed-point format, and the architecture implemented into Xilinx Spartan-6 X6SLX45 board. The maximum frequency of the proposed PMLS chaotic S-Box is 381.764 MHz, with dissipates of 77 mwatt. Compared to other S-Box chaotic systems, the proposed one achieves a higher frequency and lower power consumption. In addition, the proposed PMLS chaotic S-Box is analyzed based on S-Box standard tests such as; Bijectivity property, nonlinearity, strict avalanche criterion, differential probability, and bits independent criterion. The five different standard results for the proposed S-Box indicate that PMLSC can effectively resist crypto-analysis attacks, and is suitable for secure communications.</span></p>

A Novel Hybrid Secure Image Encryption Based on Julia Set of Fractals and 3D Lorenz Chaotic Map.

Chaos-based encryption schemes have attracted many researchers around the world in the digital image security domain. Digital images can be secured using existing chaotic maps, multiple chaotic maps, and several other hybrid dynamic systems that enhance the non-linearity of digital images. The combined property of confusion and diffusion was introduced by Claude Shannon which can be employed for digital image security. In this paper, we proposed a novel system that is computationally less expensive and provided a higher level of security. The system is based on a shuffling process with fractals key along with three-dimensional Lorenz chaotic map. The shuffling process added the confusion property and the pixels of the standard image is shuffled. Three-dimensional Lorenz chaotic map is used for a diffusion process which distorted all pixels of the image. In the statistical security test, means square error (MSE) evaluated error value was greater than the average value of 10000 for all standard images. The value of peak signal to noise (PSNR) was 7.69(dB) for the test image. Moreover, the calculated correlation coefficient values for each direction of the encrypted images was less than zero with a number of pixel change rate (NPCR) higher than 99%. During the security test, the entropy values were more than 7.9 for each grey channel which is almost equal to the ideal value of 8 for an 8-bit system. Numerous security tests and low computational complexity tests validate the security, robustness, and real-time implementation of the presented scheme.

Hybrid Image Encryption Technique Using Genetic Algorithm and Lorenz Chaotic System

One of the important application of image encryption is storing confidential and important images on a local device or a database in such a way that only the authorized party can view or perceive it. The current image encryption technique employs the genetic algorithm to increase confusion in the image, but compromises in time and space complexity. The other method employs chaos or pseudo random number generating systems which have fast and highly sensitive keys but fails to make the image sufficiently noisy and is risky due to its deterministic nature. We propose a technique which employs the non-deterministic, optimizing power of genetic algorithm and the space efficiency and key sensitivity of chaotic systems into a unified, efficient algorithm which will retain the merits of both the methods whereas tries to minimize their demerits in a software system. The encryption process proceeds in two steps, generating two keys. First, an encryption sequence is generated using Lorenz Chaotic system of differential equation. The seed values used are the user’s actual key having key sensitivity of 10-14. Second, the encrypted image’s genetic encryption sequence is generated which will result in an encrypted image with entropy value greater than 7.999 thus ensuring the image is very noisy. Proposed technique uses variations of Lorenz system seed sets to generate all random mutations and candidate solutions in Genetic encryption. Since only the seed sets leading to desired solution is stored, space efficiency is higher compared to storing the entire sequences. Using this image encryption technique we will ensure that the images are hidden securely under two layers of security, one chaotic and other non-deterministic.

Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization

In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm andC0algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process.

Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods

The Lorenz chaotic system is based on a nonlinear behavior and this causes the system to be unstable. Therefore, two different controller models were developed and named as the adaptive pole placement and sliding mode control (SMC) methods for the establishment of continuous time nonlinear Lorenz chaotic system. In order to achieve this, an improved controller structure was developed first theoretically for both the controller methods and then tested practically using the numerical samples. During the establishment of adaptive pole placement method for the Lorenz chaotic system, various stages were applied. The nonlinear chaotic system was also linearized by means of Taylor Series expansion processes. In addition, the feedback matrix of the adaptive pole placement method was determined using linear Jacobian matrix. The chaotic system reached an equilibrium point by using both the SMC and adaptive pole placement methods; however the simulation results of the SMC had better success than adaptive pole placement control technique.

Research on Image Encryption Based on Lorenz Chaotic Mapping in Finite Field

An image encryption method was built based on Lorenz chaotic mapping and finite field theory. First, original image information was divided into two image matrix by using Lorenz chaotic mapping. Second, five step calculations were finished about these two image matrix in the finite field. By combination of chaotic mapping and computing in the finite field, the new encryption method has a good effect and a fast speed. And the new encryption method realize the balance of speed and effect. Experimental results show that the proposed method has good encryption effect, attack resistance, the ideal speed of execution.

The Control of The Lorenz Chaotic System Blended With The Noise

In this study, the Lorenz chaotic system behavior is investigated according to the change in the noise of the system and measurement. The noise was emerged as an important impact on the Lorenz chaotic system. The discrete-time LQR ( Linear Quadratic Regulator) control method and discrete-time PI controller method have been used to the noisy system controls. Noise was accepted as a destructor that changes the output behavior of the chaotic system. Noisy system outputs were enforced to move to the equilibrium points by the support of controllers. Optimization of the controller parameters for noiseless system models was performed using a genetic algorithm method. Then, both control system algorithms determined as successful in transporting to the equilibrium point for state variables which are blended with the noise. Changes, associated with the noise conditions are given in the graphics and tables. Besides, the error performance criteria and the control performance criteria were obtained to evaluate the results. This study was performed by MATLAB-Simulink simulation program.