Chaos Map Research Articles

Pixel Permutation Using Chaotic Perfect Shuffle Technique for Image Encryption

A proposed algorithm for digital image encryption is presented in this paper. It combines permutation and substitution techniques. Logistic map which is a chaos function is used in both techniques. Before encrypting, the keystream is generated first from the logistics map. Then, the plain image’s pixel positions are shuffled with perfect shuffle permutation based on ascending keystream order, thereby executing the permutation process. Next, the pixel values are substituted using the XOR operation with a keystream which is also generated from the logistic map. Pixels are operated in cipher block chain mode. This research aim is to develop an image encryption algorithm, especially in the permutation process, that has high resistance to attacks by crackers. The attack types observed in this research include statistical attacks, permutation matrix attacks, differential attacks, as well as brute force attacks. From the experimental results and analysis of the proposed algorithm indicate that it has high resistance from all those attacks.

Constructive approach and randomization of a two-parameter chaos system for securing data

Secure communication techniques are important due to the increase in the number of technology users across the world. Likewise, a more random encryption algorithm suitable to secure data from unauthorised users is highly expected. This paper proposes a two-parameter nonlinear chaos map that is sensitive to the trio seed (s0, \alpha, \lambda) and has better information encryption. We introduce the parameter \alpha to linearise the conventional chaos system, which in turn brings a delay in the cryptosystems. The delay is a phenomenon that changes the chaotic features of a system. A small delay in the system leads to more aperiodicity and the unpredictability of the chaotic attractions. We normalise the new chaos map and use the Lipschitz and pseudo-contractive operators to obtain its irregularity region in Hilbert spaces. We also analyse the chaos map in terms of trajectory, Lyapunov exponent, complexity, and information entropy. Results obtained show that the new chaos map has a wide chaotic range and better statistical properties. It also maintains low complexity due to its linearity and produces more key spaces than most existing chaotic maps.

IDG-SemiAD: An Immune Detector Generation-Based Collaborative Learning Scheme for Semi-supervised Anomaly Detection in Industrial Cyber-physical Systems

Anomaly detection is a critical line of defense to ensure the network security of industrial cyber-physical systems. However, a significant issue in the anomaly detection is the insufficient labels of anomaly classes. With emergence of the new and unknown network attacks, accurately labeling these attacks can be a costly task. The issue of inadequate labeling may negatively impact the detection performance of many existing anomaly detection methods. To meet this gap, this paper proposes a semi-supervised collaborative learning paradigm called IDG-SemiAD, based on an immune detector generation algorithm. First, we design an immune detector generation algorithm based on a chaos map to generate abnormal samples from self-samples. Then, these abnormal samples are combined with self-samples and given specific labels to form a new training set. Finally, the LightGBM classifier is used for training and detection. Experiments on the widely used public dataset BATADAL show that the proposed IDG-SemiAD outperforms the classical v-detector method in terms of recall and f-score, with improvements of 8.2% and 8%, respectively, and outperforms deep learning-based anomaly detection methods, with a maximum improvements of up to 89.7% and 59.5% respectively.

Enhanced Whale Optimization Algorithm for Fuzzy Proportional–Integral–Derivative Control Optimization in Unmanned Aerial Vehicles

The traditional PID controller in quadrotor UAVs has poor performance, a large overshoot, and a long adjustment time, which limit its stability and accuracy in practical applications. In order to solve this problem, an improved whale optimization fuzzy PID control strategy based on CRICLE chaos map initialization is proposed, and a detailed simulation analysis was carried out using MATLAB software (MATLAB R2022B). Firstly, to more realistically reflect quadrotor UAVs’ flight behavior, a dynamic simulation model was established, and the dynamics and kinematic characteristics of the aircraft were considered. Then, CRICLE chaotic mapping initialization was introduced to improve the global search ability of the whale optimization algorithm and to effectively initialize the parameters of the fuzzy PID controller. This improved initialization method helped to speed up the convergence process and improve the stability of the control system. In the simulation experiments, we compared the performance indicators of the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID controller to the traditional PID and fuzzy PID controllers, including overshoot, adjustment time, etc. The results show that the proposed control strategy has better performance than the traditional PID and fuzzy PID controllers, significantly reduces overshoot, and achieves a significant improvement in adjustment time. Therefore, the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID control strategy proposed in this study provides an effective solution for improving the performance of the quadrotor control system and has practical application potential.

Migration time prediction and assessment of toxic fumes under forced ventilation in underground mines

This study aims to predict the migration time of toxic fumes induced by excavation blasting in underground mines. To reduce numerical simulation time and optimize ventilation design, several back propagation neural network (BPNN) models optimized by honey badger algorithm (HBA) with four chaos mapping (CM) functions (i.e., Chebyshev (Che) map, Circle (Cir) map, Logistic (Log) map, and Piecewise (Pie) map) are developed to predict the migration time. 125 simulations by the computational fluid dynamics (CFD) method are used to train and test the developed models. The determination coefficient (R2), the variance accounted for (VAF), the Willmott’s index (WI), the root mean square error (RMSE), the mean absolute percentage error (MAPE), and the sum of squares error (SSE) are utilized to evaluate the model performance. The evaluation results indicate that the CirHBA-BPNN model has achieved the most satisfactory performance by reaching the highest values of R2 (0.9945), WI (0.9986), VAF (99.4811%), and the lowest values of RMSE (15.7600), MAPE (0.0343) and SSE (6209.4), respectively. The wind velocity in roadway (Wv) is the most important feature for predicting the migration time of toxic fumes. Furthermore, the intrinsic response characteristic of the optimal model is implemented to enhance the model interpretability and provide reference for the relationship between features and migration time of toxic fumes in ventilation design.

Multi-Strategy Improved Particle Swarm Optimization Algorithm and Gazelle Optimization Algorithm and Application

In addressing the challenges associated with low convergence accuracy and unstable optimization results in the original gazelle optimization algorithm (GOA), this paper proposes a novel approach incorporating chaos mapping termed multi-strategy particle swarm optimization with gazelle optimization algorithm (MPSOGOA). In the population initialization stage, segmented mapping is integrated to generate a uniformly distributed high-quality population which enhances diversity, and global perturbation of the population is added to improve the convergence speed in the early iteration and the convergence accuracy in the late iteration. By combining particle swarm optimization (PSO) and GOA, the algorithm leverages individual experiences of gazelles, which improves convergence accuracy and stability. Tested on 35 benchmark functions, MPSOGOA demonstrates superior performance in convergence accuracy and stability through Friedman tests and Wilcoxon signed-rank tests, surpassing other metaheuristic algorithms. Applied to engineering optimization problems, including constrained implementations, MPSOGOA exhibits excellent optimization performance.

Layout of Detection Array Based on Multi-Strategy Fusion Improved Adaptive Mayfly Algorithm in Bearing-Only Sensor Network.

The various applications of bearing-only sensor networks for detection and localization are becoming increasingly widespread and important. The array layout of the bearing-only sensor network seriously impacts the detection performance. This paper proposes a multi-strategy fusion improved adaptive mayfly algorithm (MIAMA) in a bearing-only sensor network to perform layout planning on the geometric configuration of the optimal detection. Firstly, the system model of a bearing-only sensor network was constructed, and the observability of the system was analyzed based on the Cramer-Rao Lower Bound and Fisher Information Matrix. Then, in view of the limitations of the traditional mayfly algorithm, which has a single initial population and no adaptability and poor global search capabilities, multi-strategy fusion improvements were carried out by introducing Tent chaos mapping, the adaptive inertia weight factor, and Random Opposition-based Learning. Finally, three simulation experiments were conducted. Through comparison with the Particle Swarm Optimization (PSO) algorithm, Mayfly Algorithm (MA), and Genetic Algorithm (GA), the effectiveness and superiority of the proposed MIAMA were validated.

Prediction of Physical and Mechanical Properties of Heat-Treated Wood Based on the Improved Beluga Whale Optimisation Back Propagation (IBWO-BP) Neural Network

The physical and mechanical properties of heat-treated wood are essential factors in assessing its appropriateness for different applications. While back-propagation (BP) neural networks are widely used for predicting wood properties, their accuracy often falls short of expectations. This paper introduces an improved Beluga Whale Optimisation (IBWO)-BP model as a solution to this challenge. We improved the standard Beluga Whale Optimisation (BWO) algorithm in three ways: (1) use Bernoulli chaos mapping to explore the entire search space during population initialization; (2) incorporate the position update formula of the Firefly Algorithm (FA) to improve the position update strategy and convergence speed; (3) apply the opposition-based learning based on the lens imaging (lensOBL) mechanism to the optimal individual, which prevents the algorithm from getting stuck in local optima during each iteration. Subsequently, we adjusted the weights and thresholds of the BP model, deploying the IBWO approach. Ultimately, we employ the IBWO-BP model to predict the swelling and shrinkage ratio of air-dry volume, as well as the modulus of elasticity (MOE) and bending strength (MOR) of heat-treated wood. The benefit of IBWO is demonstrated through comparison with other meta-heuristic algorithms (MHAs). When compared to earlier prediction models, the results revealed that the mean square error (MSE) decreased by 39.7%, the root mean square error (RMSE) by 22.4%, the mean absolute percentage error (MAPE) by 9.8%, the mean absolute error (MAE) by 31.5%, and the standard deviation (STD) by 18.9%. Therefore, this model has excellent generalisation ability and relatively good prediction accuracy.

Enhancing copyright protection with Hadamard transform-based blind digital watermarking using the cycling chaos system

The network's ease of use has brought a copyright dilemma for some multimedia works. It is consequently necessary to develop a safe digital watermarking technology to guarantee the protection of digital work's copyright. The proposed method addresses the pressing need for robust blind digital watermarking technology to safeguard the copyrights of multimedia works in the face of the accessibility provided by modern networks. Two approaches are presented in our research paper. First, a blind Hadamard transform-based method is proposed, leveraging the energy concentration concept inherent in the transform. This technique embeds watermarks into the highest energy coefficients of color host images in the transform domain. Notably, watermark extraction is achieved without accessing the original data. Extensive simulation tests validate the efficacy of this method. Second, we have explored the burgeoning field of chaotic systems in watermarking. An LSB-based strategy, termed the cycling chaos algorithm, is introduced. This approach seamlessly integrates data, into color images using the least significant bits. It employs a cycling chaos function to generate a key for a pseudorandom number generator, which, in turn, determines the intensity and pixel positions for storing privileged data in the original image. Through simulation trials, the significant impact of this method on various performance metrics is demonstrated. These contributions aim to not only address immediate copyright protection challenges but also inspire further exploration and advancement in digital watermarking.

Railway wagon bearing fault diagnosis method based on improved sparrow search algorithm optimizing variational mode decomposition and multi-level convolutional neural network.

Ensuring the safe operation of trains hinges on precise bearing condition monitoring, given the pivotal role bearings play in railway wagons. The status and maintenance of wagon bearings are of paramount concern, necessitating a shift from traditional maintenance approaches reliant on schedules and experience, which often lack real-time precision and efficiency. To address this challenge, our research focuses on enhancing the sparrow search algorithm by incorporating logistic chaos mapping and the levy flight strategy. This enhanced algorithm optimizes variational mode decomposition parameters, utilizing intrinsic mode components' average dispersion entropy as the fitness function. This optimization is integrated with a multi-level convolutional neural network for bearing fault diagnosis. Our findings demonstrate the improved algorithm's enhanced spatial search capabilities and reduced modal aliasing in the frequency components. Experimental validation on public datasets and the group's experimental platform for railway wagons shows that multi-level convolutional neural networks have higher diagnostic accuracy and faster convergence speeds than traditional models such as LeNet-5, AlexNet, and convolutional neural network. Our research introduces a highly accurate and widely applicable methodology for mechanical equipment fault diagnosis, aligning with the requirements of the "smart" era.

Security and privacy protection protocol based on edge computing in smart campus

AbstractWith the continuous emergence of modern Internet of Things, mobile Internet and other new generation of campus information technology and its extensive application in professional campus education, the development of college professional campus education information construction has entered a new stage of development. In view of higher requirements on data storage and network transmission delay of core business system in smart campus and more prominent wireless network security problems, this paper proposes a privacy protection protocol for smart campus based on chaotic mapping and edge computing. The protocol uses chaos mapping algorithm to protect user identity and negotiate session keys, and introduces edge computing to process authentication information on the edge server, which reduces the pressure of the core network and improves the authentication efficiency. This paper proves the security of the protocol by using BAN logic and Scyther, and verifies that the protocol can resist known attacks by analysing informal security. Through performance analysis and comparison, the proposed protocol has obvious advantages in computation and communication overhead.

Parameter extraction of solar cell models using improved war strategy algorithm

A study proposed an improved war strategy algorithm called the chaos genetic manifestation war strategy algorithm (CGM-WSO) to extract parameters of solar cell model. The CGM-WSO algorithm incorporates three improvement measures. First, it introduces the logistic–tent chaos map to enable random perturbation during initialization. Second, it utilizes the crossover and mutation operators of the genetic algorithm to enhance the algorithm’s ability to escape local optima. Finally, the Lambert W function is employed to obtain explicit analytic expressions of single and double diode models. The performance of the CGM-WSO algorithm was validated using several cell’s models, and the results demonstrated significantly improved accuracy, reliability, and convergence speed compared to other algorithms.

A novel hybrid swarm intelligence algorithm for solving TSP and desired-path-based online obstacle avoidance strategy for AUV

Aiming at the problem that Ant Colony Optimization (ACO) is subject primarily to the parameters, we propose a hybrid algorithm SOA-ACO-2Opt to optimize the ACO parameter combination through Seagull Optimization Algorithm (SOA) to strengthen ACO’s search capability. To obtain a uniform initial distribution of the ACO parameter combination, we incorporated the Kent Chaos Map (KCM) to randomly initialize the seagull’s position, reducing the tendency of SOA to fall into the local optimum. To avoid slow calculation speed and premature convergence of ACO, we improved the adaptive multi-population mechanism to reduce repeated redundant calculations and used the ϵ−greedy and default strategy, respectively, to update the ants’ position. 2Opt is applied to find shorter paths in each iteration. In addition, when AUV navigates on the planned path, it may encounter obstacles. Therefore, this paper proposes an autonomous obstacle avoidance algorithm based on forward-looking sonar to ensure safety during tasks. SOA-ACO-2Opt is verified against twelve different problems extracted from TSPLIB and compared with some state-of-the-art algorithms. Furthermore, sea trials were carried out for several representative marine engineering applications of TSP and obstacle avoidance. Experimental results show that this work can significantly improve AUV’s work efficiency and intelligence and protect the AUV’s safety.

Reliability model for key components of urban rail transit train based on improved hunter-prey optimization

The reliability of key components of urban rail transit (URT) plays an important role in the maintenance plans of URT. It is necessary to establish the reliability model of URT trains. In the current research, the reliability model has a limited scope of application and fails to accurately depict the reliability of key components in URT trains. To solve the above problem, a multi-peak type mixture Weibull distribution model is established using several three-parameter Weibull distributions based on fault modes of components sourced from historical lifetime data. Due to the complexity of this model, parameter estimation is challenging. For this purpose, an improved hunter-prey optimization (IHPO) was proposed to improve parameter estimation accuracy. Firstly, an improved Hénon chaos map was introduced to improve the distribution of the initial population. Secondly, the Lévy flight was introduced to increase the probability of the individual spreading to the whole range at the late stage. Lastly, a nonlinear balance factor was proposed to enhance the algorithm’s global search capability. The simulation experiment was carried out with examples of the balanced pressing wheel and the wheelset. The IHPO algorithm-based parameter estimation method shows the highest R-square with values of 0.996 and 0.999, respectively, and the lowest root mean square error with values of 0.019 and 0.008, respectively. The simulation results demonstrate that the stability and optimization of the HPO are improved, and the multi-peak mixture Weibull distribution model based on the IHPO can accurately depict URT trains’ reliability.

Intelligent Path Planning with an Improved Sparrow Search Algorithm for Workshop UAV Inspection.

Intelligent workshop UAV inspection path planning is a typical indoor UAV path planning technology. The UAV can conduct intelligent inspection on each work area of the workshop to solve or provide timely feedback on problems in the work area. The sparrow search algorithm (SSA), as a novel swarm intelligence optimization algorithm, has been proven to have good optimization performance. However, the reduction in the SSA's search capability in the middle or late stage of iterations reduces population diversity, leading to shortcomings of the algorithm, including low convergence speed, low solution accuracy and an increased risk of falling into local optima. To overcome these difficulties, an improved sparrow search algorithm (namely the chaotic mapping-firefly sparrow search algorithm (CFSSA)) is proposed by integrating chaotic cube mapping initialization, firefly algorithm disturbance search and tent chaos mapping perturbation search. First, chaotic cube mapping was used to initialize the population to improve the distribution quality and diversity of the population. Then, after the sparrow search, the firefly algorithm disturbance and tent chaos mapping perturbation were employed to update the positions of all individuals in the population to enable a full search of the algorithm in the solution space. This technique can effectively avoid falling into local optima and improve the convergence speed and solution accuracy. The simulation results showed that, compared with the traditional intelligent bionic algorithms, the optimized algorithm provided a greatly improved convergence capability. The feasibility of the proposed algorithm was validated with a final simulation test. Compared with other SSA optimization algorithms, the results show that the CFSSA has the best efficiency. In an inspection path planning problem, the CFSSA has its advantages and applicability and is an applicable algorithm compared to SSA optimization algorithms.

Secure authentication protocols to resist off-line attacks on authentication data table

In text-based authentication, the passwords along with user names are maintained in the Authentication Data Table (ADT). It is necessary to preserve the privacy of passwords in ADT to avoid offline attacks like brute force attacks, lookup table attacks, etc. In this paper, three password protection schemes, namely Encrypted Image Password (EIP), Dynamic Authentication Data Table (D-ADT), and Extended Encrypted Image Password (EEIP) are proposed for secure authentication. In EIP, the input passwords are first converted to hashed passwords and then transformed into images. Next, these image passwords are encrypted using a novel image password encryption system using chaos functions and confusion-diffusion mechanisms. In D-ADT, the hashed passwords are encrypted using a random key. The major highlight of this scheme is that during every log, the hashed password is encrypted with a new random key while keeping the plain password same as it is. So, during each login of the user, the old encrypted password is replaced with a new encrypted password in the authentication data table. The EEIP scheme combines both approaches. Passwords are converted to images and image passwords are encrypted with the new random key at every login. Performance and security analysis are carried out for the proposed algorithm concerning correlation analysis, differential analysis, entropy analysis, computation time, keyspace, and offline attack analysis.

Parameter extraction of photovoltaic model based on butterfly optimization algorithm with chaos learning strategy

Accurate extraction of photovoltaic (PV) model parameter is significant for the evaluation of PV system. Most of existing methods for extracting the PV parameters suffer from low extraction accuracy and are prone to fall into local optima. To solve these shortcomings, a chaos learning butterfly optimization algorithm (CLBOA) is proposed. First, the introduced Cauchy mutation increases the perturbation to butterflies and helps the algorithm to jump out of local optima. Second, a chaos learning strategy is proposed to lead the butterflies within the population to learn from the optimal individual using the improved Tent chaos mapping, which strengthens the learning exchange of the population, enhances the ability of global exploration and local exploitation, and optimizes the convergence speed and accuracy. Third, the three worst individual positions were randomly initialized using a terminal elimination mechanism to increase population diversity. After evaluating CLBOA through the CEC2022 benchmark suite, it was used to extract parameters for a total of 12 PV cell and module models for 5 materials. Compared with 9 well-known algorithms, CLBOA performs excellent in terms of convergence performance, parameters extraction accuracy, running time and improvement index. Finally, CLBOA was applied on YL PV power station model of Guizhou Power Grid in China under different irradiations and temperatures. The I-V and P-V curves reconstructed by CLBOA are highly fit to the synthesized curves, and the individual absolute error (IAE) and relative error (RE) also confirm the satisfactory accuracy of parameters extraction. Comprehensive analysis shows that CLBOA can extract parameters better than the comparison algorithms, demonstrating its strong potential for PV parameters extraction.

An optimized chaotic S-box for real-time image encryption scheme based on 4-dimensional memristive hyperchaotic map

As digital products communicate over public networks, digital image security becomes essential. Despite advancements in encryption technology, protecting data from secure images remains a complex computational issue that necessitates using an encrypted environment to protect data transmitted from devices over networks. Encryption is critical for protecting sensitive information, especially images, from unauthorized access or failure. Image encryption is distinct from text encryption. Images contain extensive data with high redundancy and a high correlation between nearby pixels, making them difficult to process with traditional technology. In recent decades, chaos maps have become popular in the crypto community. This work proposes a new encryption technology based on chaotic map substitution boxes (S-box) and cellular automata (CA) to address the frequent challenges in chaotic encryption methods. To address the inadequate randomness provided by the 1D chaotic map, this work presented a 4D memristive hyperchaos with a more excellent chaotic range, increased uncertainty, and ergodicity as an alternative to the software-based approach, which is vulnerable and offers low throughput. The suggested encryption technique was implemented on an Intel Cyclone IV EP4CE115F29C7 FPGA. It is less prone to tampering and has a better throughput. This suggested encryption scheme employs 1384 LEs. In comparison to traditional algorithms, the suggested Number of Pixels Change Rate (NPCR) (99.9706%), unified averaged changed intensity (UACI) (33.3956%), and information entropy (IE) (7.984) accomplish more effective. Statistical studies such as IE, histogram, correlation, peak signal-to-noise ratio (PSNR), differential analysis such as NPCR and UACI, and noise attack analyses are employed to validate the suggested encryption design. Regarding security, the suggested hybrid method outperforms conventional algorithms while protecting image quality.

New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption

Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α < 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests).

A new chaos function development through the combination of Circle map and MS map

Digital data protection is very important to prevent manipulation of digital data by unauthorized parties. Reliable techniques for securing digital data are needed, safe and fast. One technique is to use cryptography. One of the cryptographic techniques that can be used to encode digital data is to use the chaos function. We propose in this paper a new chaos function which is a composition of Circle map and MS map functions. This function has chaotic nature and the result of which is named the MSI-Circle map. The sensitivity and randomness tests of the MSI-Circle map function are carried out using a bifurcation diagram, Lyapunov exponent, and NIST test suites. The analysis result of the bifurcation diagram shows that the MSI-Circle map has a good density at the value of r ∈ (−∞,−3] ∪ [3,−∞]. Lyapunov exponent has a non-negative value at x0 = 0.4, r = 3.8, Ω = 0.5, λ = 2.1, K = 4 which is the domain xn ∈ (0, 1) and parameter values r, Ω, λ and K are any real numbers. The results of the NIST randomness level test show that the MSI-Circle map function passed all the randomness test of 16 NIST tests.