Information Entropy Analysis Research Articles

Investigation of Laser Ablation Quality Based upon Entropy Analysis of Data Science

Laser ablation is a vital material removal technique, but current methods lack a data-driven approach to assess quality. This study proposes a novel method, employing information entropy, a concept from data science, to evaluate laser ablation quality. By analyzing the randomness associated with the ablation process through the distribution of a probability value (reb), we quantify the uncertainty (entropy) of the ablation. Our research reveals that higher energy levels lead to lower entropy, signifying a more controlled and predictable ablation process. Furthermore, using an interval time closer to the baseline value improves the ablation consistency. Additionally, the analysis suggests that the energy level has a stronger correlation with entropy than the baseline interval time (bit). The entropy decreased by 6.32 from 12.94 at 0.258 mJ to 6.62 at 0.378 mJ, while the change due to the bit was only 2.12 (from 10.84 at bit/2 to 8.72 at bit). This indicates that energy is a more dominant factor for predicting ablation quality. Overall, this work demonstrates the feasibility of information entropy analysis for evaluating laser ablation, paving the way for optimizing laser parameters and achieving a more precise material removal process.

Image encryption algorithm based on matrix projective combination-combination synchronization of an 11-dimensional time delayed hyperchaotic system

Abstract Secure image transmission is critical to protect sensitive data from unauthorized access, especially in an era of increasing digital threats. Chaotic systems with their inherent complexity and unpredictability, provide a promising solution for enhancing encryption security. To contribute to this field, we investigate a new 11-dimensional hyperchaotic system by taking advantage of its complex dynamical properties to strengthen security. The high dimensional of the system intensifies chaotic behaviors such as stability, attractors and sensitive to initial conditions, making it particularly suitable for encrypted transmission.
 Time delay is an important factor to be considered affecting the control and synchronization in nonlinear system. Additionally, time delays include the effects of past states, further increasing the unpredictability of the system. To explore these dynamics, we analyze the Lyapunov exponents, stability of equilibrium points, symmetry and dissipation. A matrix projective combination-combination synchronization scheme is proposed to synchronize four identical 11-dimensional hyperchaotic systems with time delay. Nonlinear active controllers designed based on Lyapunov stability theory are used to achieve this synchronization. This work advances an important idea for encryption and decryption algorithms, which is the secure transmission of images using affine encryption. In the affine encryption algorithm, the key is based on the solution of synchronized chaotic delayed systems and the private message of the sender and receiver. This proposed encryption and decryption algorithms have been applied on plain images. Numerical simulations and security analysis including key space, histogram, information entropy and correlation analysis are conducted to validate the theoretical results and encryption algorithm. Experimental analysis and comparisons with existing literature confirm the effectiveness and security of the proposed approach for cryptographic purposes.

Dynamic analysis of a novel hyperchaotic system based on STM32 and application in image encryption

This paper presents a novel 4D hyperchaotic system derived from a modified 3D Lorenz chaotic system. A key aspect of this system is the presence of a single equilibrium point, and its stability is carefully analyzed. The dynamic properties, including the Lyapunov exponent spectrum, bifurcation diagram, and chaotic attractors, are investigated using MATLAB simulations. The results reveal that the system displays hyperchaotic behavior across a wide range of the parameter d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document}, with its chaotic attractor transitioning through four states: hyperchaotic, chaotic, periodic, and quasi-periodic, showcasing the system's complex dynamics. Experimental validation using STM32 embedded hardware successfully reproduces these four types of chaotic attractors, confirming the theoretical predictions. The proposed hyperchaotic system is then applied to image encryption, introducing a novel encryption method. The hyperchaotic key sequence generated by this system meets 15 tests of the NIST SP800-22 standard, and further experimental validation with STM32 hardware demonstrates the algorithm's effectiveness, simplicity, non-linearity, and high security. The encrypted images and sequences are rigorously tested key space analysis, histogram similarity analysis, information entropy analysis, statistical attack analysis, differential attack analysis, key sensitivity analysis, and correlation analysis, highlighting the robustness and reliability of the proposed system. This method is versatile and can be extended to various fields, including audio and video encryption, text encryption, IoT security, financial transaction security, and medical data protection.

Information Entropy Analysis of a PIV Image Based on Wavelet Decomposition and Reconstruction.

In particle image velocimetry (PIV) experiments, background noise inevitably exists in the particle images when a particle image is being captured or transmitted, which blurs the particle image, reduces the information entropy of the image, and finally makes the obtained flow field inaccurate. Taking a low-quality original particle image as the research object in this research, a frequency domain processing method based on wavelet decomposition and reconstruction was applied to perform particle image pre-processing. Information entropy analysis was used to evaluate the effect of image processing. The results showed that useful high-frequency particle information representing particle image details in the original particle image was effectively extracted and enhanced, and the image background noise was significantly weakened. Then, information entropy analysis of the image revealed that compared with the unprocessed original particle image, the reconstructed particle image contained more effective details of the particles with higher information entropy. Based on reconstructed particle images, a more accurate flow field can be obtained within a lower error range.

A two-dimensional chaotic model and its application in image encryption

In this paper, we propose a rule that follows a time-varying delay construction method and construct a time-varying delay scheme based on it. This construction scheme is also combined with a polynomial to obtain a novel two-dimensional chaotic model. Both mathematical analysis and experimental results show that the model satisfies the chaos condition. Good experimental results have been achieved in complexity analysis, information entropy analysis, and Auto-correlation analysis, and have certain competitiveness. The obtained chaotic model is also applied to the image encryption algorithm. The experimental results show that the encryption algorithm has high security and can effectively resist noise attacks, shear attacks, differential attacks.

Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

Information entropy analysis of the relation between climate and thermal adaptation: A case study in hot summer and cold winter region of China

The shift of paradigm from reductionist to holism in the field of thermal adaptation promoted a boom in thermal adaptation theory and provided a systemic perspective on this issue. The thermal adaptation theory confronts twin difficulties of scale and complexity. The complexity and entropy of occupants' thermal adaptation emerging. This paper aims to investigate the information entropy exchange in the coupled climate-building-occupants system. First, we justified that the building-occupants system is an open system and exchanges energy, matter, and entropy with its surrounding climate system. Then, correlation analysis results suggested that climate entropy could influence thermal adaptation entropy. Thermal adaptation entropy fluctuated with climate entropy and the difference varied between −0.5 and 0.5 below 31 °C. A generalized entropy balance model was proposed for quantifying the entropy exchange among coupled climate-building-occupants systems for both free-running and air-conditioning buildings. The quantitative relation between the entropy of thermal adaptation and H_DTR reveals the dynamic occupant's thermal adaptation under the process of entropy exchange with the climate system. The H_DTR and entropy relation models provide a new perspective on thermal adaptation coupled with climate beyond outdoor daily mean temperatures. Control strategies that integrate the dynamic characteristics of DTR can bring more economical, energy-efficient and comfortable effects to the operation of air conditioning or heating systems. Our findings shed some light on the dynamical and complex thermal adaptation. In further studies, more results and methods from meteorological research could be used for thermal adaptation research and interdisciplinary theories could be adopted to help us better understand occupants' thermal adaptation.

A real-time measurement and analysis method for gas holdup in a wet scrubber with the use of image information entropy

Wet scrubbers are often used in various types of industrial workshops to separate dust particles from the air. Non-uniform gas–liquid flow patterns above the sieve plate can result in significant losses in purification efficiency for particles. To improve the flow pattern via sieve plate design and to more accurately predict purification efficiency, a better understanding of the gas holdup is required. Various methods have been developed to measure and analyze the gas holdup from local and global perspectives. However, for guiding the operation and design of reactors, it is obviously insufficient to obtain the phase holdup characteristics under a steady state. The spatial and temporal characteristics of gas holdup in a wet scrubber are rather difficult to measure in real time with the current techniques. In this study, a fast real-time method for measurement of gas holdup characteristics was proposed, based on image information entropy analysis. The axial and radial profiles of gas holdup under different bubble washing operation statuses were obtained and are discussed here. More detailed information about the gas holdup above the sieve plate under various operation conditions has been attained. Sieve plate resistance and bubbling state were analyzed with the use of image information entropy.

FAM: Improving columnar vision transformer with feature attention mechanism

Vision Transformer has garnered outstanding performance in visual tasks due to its capability for global modeling of image information. However, during the self-attention computation of image tokens, a common issue of attention map homogenization arises, impacting the final performance of the model as attention maps propagate through feature maps layer by layer. In this research, we propose a token-based approach to adjust the output of attention sub-layer, focusing on the feature dimensions, to address the homogenization problem. Furthermore, different network architectures exhibit variations in their approaches to modeling image features. Specifically, Vision Transformers excel at modeling long-range relationships, while convolutional neural networks possess local receptive fields. Therefore, this paper introduces a plug-and-play convolutional operator-based component, integrated into the Vision Transformer, to validate the impact of structural enhancements on model performance. Experimental results on image recognition and adversarial attack tasks respectively demonstrate the effectiveness and robustness of the two proposed methods. Additionally, the analysis of information entropy on the feature maps of the model’s final layer indicates that the improved model exhibits higher information richness, making it more conducive to the classifier’s discriminative capabilities.

Quantum image encryption algorithm based on four-dimensional chaos

Background: Quantum image processing is rapidly developing in the field of quantum computing, and it can be successfully implemented on the Noisy Intermediate-Scale Quantum (NISQ) device. Quantum image encryption holds a pivotal position in this domain. However, the encryption process often encounters security vulnerabilities and entails complex computational complexities, thereby consuming substantial quantum resources. To address this, the present study proposes a quantum image encryption algorithm based on four-dimensional chaos.Methods: The classical image is first encoded into quantum information using the Generalized Quantum Image Representation (GQIR) method. Subsequently, the trajectory of the four-dimensional chaotic system is randomized, and multi-dimensional chaotic keys are generated to initially encrypt the pixel values of the image. Then, the Arnold transformation is applied to randomly encrypt the pixel positions, resulting in the encrypted image. During the decryption process, the inverse process of encryption is employed to restore the original image.Results: We simulated this process in the Python environment, and the information entropy analysis experiment showed that the information entropy of the three encrypted images reached above 7.999, so the system has good encryption. At the same time, the correlation of the pixel distribution after the encryption algorithm is weak, which proves that the control parameters of the chaotic system can effectively reduce the correlation between pixels in the image. In the final key space analysis, the key space issued by our encryption can reach $10140\gg 2128$.Conclusion: Our method is resistant to destructive attacks and can produce scrambled images with higher encryption and usability. This algorithm solves the problems of general encryption algorithms such as periodicity, small key space, and vulnerability to statistical analysis, and proposes a reliable and effective encryption scheme. By making full use of the characteristics of Arnold transformation permutation, ergodicity and the randomness of the four-dimensional chaotic system, the encryption algorithm uses the larger key space provided by the four-dimensional Lorenz system.

Fast and Lightweight Image Cryptosystem for IoMT Applications

This paper presents a fast and lightweight image encryption technique founded on a new concept of progressive and selective diffusion. We make use of modified chaotic systems like the sine-logistic system, sine-tangent system, and tent-logistic system to generate key blocks for diffusion. The encryption procedure comprises three stages: column diffusion, permutation, and row diffusion, which collectively contribute to the overall encryption mechanism. In the first stage, progressive and selective column substitution of the input image is conducted employing key-blocks D1 and D2, in a manner that each substituted column data is a function of previously diffused data. In the second stage, the column-substituted image goes through an adaptive permutation operation realized using an improved sin-logistic system. The last stage incorporates two distinct mappings based on key arrays and key blocks to ensure selective and progressive inter-row substitution/diffusion. The experimental results suggest that the proposed image system exhibits rapid performance as it reports an average encryption time of 0.03 seconds for an image of the size 256×256. Besides, the use of 1-D chaotic maps together with simple yet effective confusion and diffusion processes make it lightweight. Furthermore, it provides better security performance shown by various parameters like Information Entropy Analysis (IE), Correlation Coefficient analysis (CC), Histogram analysis, Differential Attacks Analysis (NPCR and UACI), key sensitivity assessment, and fidelity analysis. The suggested system has the capability to meet the cryptographic objectives as it reports average values of IE = 7.9974, CC =0.0035, NPCR =99.61%, UACI = 33.48%, and an enormously large key space compared to the state-of-art. The proposed technique offers enhanced data security, preserving patient privacy and preventing unauthorized access, while ensuring efficient encryption performance to assure the security and immediate transmission and storage of medical images. The better security performance together with computational efficiency and lightweight nature makes it an ideal candidate to be used in IoMT systems.

Research on Chaotic Image Encryption Based on Fibonacci-ILogistic-IHenon

To further improve the security of image encryption, we propose an image encryption algorithm that combines Fibonacci with improved logistic and improved Henon chaotic mapping, i.e., the Fibonacci-ILogistic-IHenon algorithm. The algorithm addresses that the existing logistic chaotic algorithm is controlled by the parameter resulting in an uneven distribution, and the Henon chaotic algorithm may have the problem of periodic orbits. Using the mode-taking and sinusoidal functions for optimization, the output sequence region generated by the logistic chaotic mapping is adjusted to the input of the Henon chaotic mapping, which enables the construction of a new chaotic system (ILogistic-IHenon). In the image encryption implementation, Fibonacci is used to cure the chaos, and ILogistic-IHenon is utilized to generate chaotic sequences to complete the encryption. In the simulation experiments, we choose the improved logistic encryption algorithm, the improved Henon encryption algorithm, and the improved logistic-ent encryption algorithm as the comparison algorithms, and the results illustrate that the Fibonacci-ILogistic-IHenon algorithm has better performance in image encryption statistical analysis, encryption speed, pixel correlation analysis, information entropy analysis, differential attack analysis and other metrics.

The Effect of Information Entropy Analysis in Computer-Assisted English Translation on Improving Translation Naturalness

Abstract This paper borrows the concept of entropy and refers the information entropy to the computer-aided English translation to build up the information entropy assessment and evaluation model and the information entropy-based English translation optimization model. The information entropy operation formula is used to calculate the fuzziness between the original text and the target translated text, and at the same time, the segmentation function is utilized to find the approximation value of the information entropy value obtained in a sufficiently fine segmentation of the translated text. Obtain the rectangular window function of semantic Gaussian marginalization, project the information entropy data, add the semantic correlation factors of words, identify the features of semantic information, and realize the optimization of English translation. Simulation experiments are carried out to verify the performance of the model. The information entropy evaluation and analysis model in this paper can achieve convergence after 45 iterations. In contrast, the word error rate and the cut-off error rate of the English translation optimization model are both lower than 10%, and the feature recognition and classification are higher than 80%. The fuzzy statements in Chinese writer Lao She’s work “Teahouse” are selected to explore the naturalness of translation. The information entropy value of the translation optimization model in this paper is closer to the original text, and the English translation’s naturalness is better than that of the GLR model.

Information Entropy Analysis of Classroom Teaching Process under the New Curriculum Reform

Information Entropy Analysis of Classroom Teaching Process under the New Curriculum Reform

Chaotic Multiple-Image Encryption Algorithm Based on Block Scrambling and Dynamic DNA Coding

In this paper, a chaotic multiple-image encryption algorithm using block scrambling and dynamic DNA coding is designed. The algorithm can achieve simultaneous encryption of many different types of images. Firstly, a new block scrambling algorithm is proposed, which is divided into two scrambling modes according to the size of the initial block. And it combines with the cyclic shift operation to achieve scrambling. Secondly, dynamic DNA coding is utilized to diffuse images, which enhances the complexity and security of the proposed multiple-image encryption algorithm. Through the analysis of key space, correlation, information entropy, histogram, differential attacks and robustness, it is verified that the algorithm is safe and effective. Experimental results show that the new multiple-image encryption algorithm is suitable for multiple color and gray images encryption. The algorithm has excellent encryption performance, and can be applied in secure communication.

Chaos-based Image Encryption in Embedded Systems using Lorenz-Rossler System

Digital data is increasing rapidly in the world day by day. Information security is important during data exchange over the Internet. The way to securely transmit images over the network is through the image encryption technique. In the proposed cryptography system, the hybridization of Lorenz-Rossler chaotic systems is used, and a random number sequence is generated. The security analyses such as histogram, correlation, differential attack, information entropy, and duration analysis of the study are performed. It is seen that the proposed system performs well, especially in terms of correlation. Additionally, the performance of the developed embedded system platforms is compared after testing on Nvidia Jetson Nano and Xilinx PYNQ Z1 boards. The Nvidia Jetson Nano board is more performant than the Xilinx PYNQ Z1 board. The safety and feasibility of the proposed system have been demonstrated.

A Color Image-Encryption Algorithm Using Extended DNA Coding and Zig-Zag Transform Based on a Fractional-Order Laser System

With the advancement of information technology, the security of digital images has become increasingly important. To ensure the integrity of images, a novel color image-encryption algorithm based on extended DNA coding, Zig-Zag transform, and a fractional-order laser system is proposed in this paper. First, the dynamic characteristics of the fractional-order laser chaotic system (FLCS) were analyzed using a phase diagram and Lyapunov exponent spectra. The chaotic sequences generated by the system were used to design image-encryption algorithms. Second, a modified Zig-Zag confusing method was adopted to confuse the image. Finally, in the diffusion link, the DNA encoding scheme was extended to allow for a greater number of DNA encoding rules, increasing the randomness of the matrix and improving the security of the encryption scheme. The performance of the designed encryption algorithm is analyzed using key space, a histogram, information entropy, correlation coefficients, differential attack, and robustness analysis. The experimental results demonstrate that the algorithm can withstand multiple decryption methods and has strong encryption capability. The proposed novel color image-encryption scheme enables secure communication of digital images.

A physical memristor-based chaotic system and its application in colour image encryption scheme

This work proposes a physical memristor (TaOx) based new 4D chaotic system with 3D multi-scroll, no equilibrium point, spiking behaviour, coexistence bursting oscillation and multistability. Using this physical memristor-based chaotic system, a novel and efficient colour image encryption algorithm has been developed using a unique box scrambling method and bit-wise XOR operations. Many interesting and new dynamics of a material-based memristive chaotic system are reported here, like 3D multi-scroll chaotic attractors, bursting characteristics, multistability, a neuronal system like spiking behaviours etc using Lyapunov spectrum and bifurcation plots. It is observed that the number of scrolls is changed with the total simulation time. This novel memristive chaotic system has limit cycles with controllable spikes and bursting oscillation. In addition, the system shows chaotic bursting oscillation under a different set of parameters and initial conditions. The coexistence of the bursting phenomena is studied here. The bursting and spiking characteristic is important for material-based memristors in neuromorphic applications. 3D Chaotic multi-scroll and multistability properties make the image encryption method more efficient and secure. Such characteristics are rare in physical memristor-based chaotic systems and using this, the image encryption algorithm is also rare in recent findings. Therefore, a new secure image encryption algorithm for colour images is proposed here, based on the unique box scrambling method, bitwise XOR operation and pseudo-random number generation using the proposed memristive chaotic system. Various tests like NPCR, UACI, histogram analysis, correlation study, information entropy analysis, robustness against external noise, etc have been performed to check the algorithm’s robustness and efficiency and test the capability to resist statistical and differential attacks.

Competitiveness Evaluation of Express Delivery Enterprises Based on the Information Entropy and Gray Correlation Analysis

With the rise of e-commerce in China, the express delivery industry has developed rapidly; however, in this stage of rapid growth, the development of express delivery enterprises is uneven. There are problems such as high loss, damage rates, and poor service attitudes. An evaluation of the competitiveness of express delivery enterprises can help these companies understand their shortcomings and learn from each other’s strengths, which can promote the long-term development of express delivery enterprises. In this study, the information entropy method and the gray prediction method were used to establish an index system and analyze the core competitiveness of four listed express delivery companies in China, using indicators such as service quality, price level, market position, guarantee ability, and comprehensive strength; the purpose was to study the competitive advantages of these express companies. By using the gray correlation analysis to calculate the degree of correlation and comparing the size of the degree of correlation, it can be concluded that among the four express delivery companies, ZTO Express shows the strongest competitiveness and that Shentong Express is the weakest. Through the evaluation and analysis of the competitiveness of express delivery enterprises, this study provides a reference basis for operation development and competitiveness improvement of express delivery enterprises in China.

A Novel Image Encryption Scheme Using Chaotic Maps and Fuzzy Numbers for Secure Transmission of Information

The complexity of chaotic systems, if used in information encryption, can determine the status of security. The paper proposes a novel image encryption scheme that uses chaotic maps and fuzzy numbers for the secure transmission of information. The encryption method combines logistic and sine maps to form the logistic sine map, as well as the fuzzy concept and the Hénon map to form the fuzzy Hénon map, in which these maps are used to generate secure secret keys, respectively. Additionally, a fuzzy triangular membership function is used to modify the initial conditions of the maps during the diffusion process. The encryption process involves scrambling the image pixels, summing adjacent row values, and XORing the result with randomly generated numbers from the chaotic maps. The proposed method is tested against various attacks, including statistical attack analysis, local entropy analysis, differential attack analysis, signal-to-noise ratio, signal-to-noise distortion ratio, mean error square, brute force attack analysis, and information entropy analysis, while the randomness number has been evaluated using the NIST test. This scheme also has a high key sensitivity, which means that a small change in the secret keys can result in a significant change in the encrypted image The results demonstrate the effectiveness of the proposed scheme in ensuring the secure transmission of information.