A proper Euler’s magic matrix is an integer n×n matrix M∈Zn×n such that M⋅Mt=γ⋅I for some nonzero constant γ, the sum of the squares of the entries along each of the two main diagonals equals γ, and the squares of all entries in M are pairwise distinct. Euler constructed such matrices for n=4. In this work, we use multiplication matrices of the octonions to construct examples for n=8, and prove that no such matrix exists for n=3.

Image steganography is the process of hiding information, which can be text, image, or video inside a cover image. Recent steganography literature hasn't addressed the problem of loss of secret information during extraction and reliability. Hence, to reduce information loss and provide reliability between in the basic criteria, Herein, we proposed a hybrid method that utilizes the least significant bit (LSB) substitution, transppsition, magic matrix, key and Advance Encrytion Standard (AES) algorithm. The LSB method decreases embedding errors by implementing a new value difference algorithm. In addition, to improves the reliability between the basic criterion for image steganography we used transposition, magic matrix, key and AES. The proposed method ensures a high-quality image format in the RGB color model to conceal the hidden message within the cover image which is jpeg. The proposed hybrid method performed several experiments and these are mainly based on quality assessment metrics such as PSNR, SSIM, RMSE, NCC, etc. which showed better results. The proposed method also analyzed with different perspectives in terms of different dimensions of images and different sizes of message text which showed better results. In addition, the performance of the proposed method showed better results based on (regular and singular) steganalysis, noise, and cropping attacks. The security analyses such as key space, differential, and statistical attacks show that the proposed scheme is secure and robust against channel noise and JPEG compression.

Complex and robust self-organization requires defined initial conditions and dynamic boundaries – neighboring tissues and extracellular matrix (ECM) that actively evolve to guide morphogenesis. A major challenge in tissue engineering is identifying material properties that mimic dynamic tissue boundaries but that are compatible with the engineering tools necessary for controlling the initial conditions of culture. Here we describe a highly tunable granular biomaterial, MAGIC matrix, that supports long-term bioprinting and gold-standard tissue self-organization. MAGIC matrix is designed for two temperature regimes: at 4 °C it exhibits reversible yield-stress behavior to support hours-long high-fidelity 3D printing without compromising cell viability; when transferred to cell culture at 37 °C, the material cross-links and exhibits viscoelasticity and stress relaxation that can be tuned to match numerous conditions, including that of reconstituted basement membrane matrices like Matrigel. We demonstrate that the timescale of stress relaxation and loss tangent are decoupled in MAGIC matrices, allowing us to test the role of stress relaxation rate and strain-dependence across formulations with identical storage and loss moduli. We find that fast absolute stress relaxation rates and large relative deformation magnitudes are required to optimize for morphogenesis. We apply optimized MAGIC matrices toward precise extrusion bioprinting of saturated cell suspensions directly into 3D culture. The ability to carefully control initial conditions for tissue growth yields dramatic increases in organoid reproducibility and complexity across multiple tissue types. We also fabricate perfusable 3D microphysiological systems that experience large strains in response to pressurization due to the compliant and dynamic tissue boundaries. Combined, our results both identify key parameters for optimal organoid morphogenesis in an engineered material and lay the foundation for fabricating more complex and reproducible tissue morphologies by canalizing their self-organization in both space and time.

n the age of pervasive digital communication, ensuring the confidentiality of sensitive information has become increasingly vital. Image steganography, particularly techniques based on Least Significant Bit (LSB) manipulation, offers a covert channel for data hiding. However, classical LSB methods lack robustness and are vulnerable to various attacks. This research presents a comparative and consolidated study of advanced LSB-based image steganography techniques enhanced with cryptographic mechanisms such as Huffman Coding, Triple DES (3DES), Multi-Level Encryption (MLE), and MD5 hashing. A novel approach—Huffman Code LSB-based Image Steganography using Multi-Level Encryption and the achromatic component (HC-LSBIS-MLE-AC)—is reviewed for its use of the HSI color model, Magic Matrix scrambling, and Huffman encoding, significantly improving security, payload capacity, and visual imperceptibility. Additionally, a hybrid technique employing 3DES with LSB embedding and MD5 key hashing is evaluated for its simplicity and effectiveness in secure communication. Key Words: Image Steganography, Data Hiding ,Encryption ,Huffman Coding, Multi-Level Encryption (MLE) ,3DES (Triple DES) ,MD5 Hashing ,Achromatic Component (Intensity Channel) ,HSI Color Model , Steganalysis Resistance, Imperceptibility ,Hybrid Security Systems , Robustness ,CovertCommunication,Digital Forensics

MATADOR: a magic matrix-based framework for tamper detection and image recovery

Hardware Implementation of Sudoku, Optimal Sudoku, Sky-Scrapper, Novel Shade Dispersion and Magic Matrix Shifting PV Reconfiguration Techniques With MPPT Algorithm to Enhance Maximum Power

Abstract This paper proposes a novel image encryption algorithm to enhance the security and privacy of image data shared across various channels. The algorithm integrates an Iteratively Compounded Magic Matrix (ICMM) and a modified differential encoding approach. A method to generate a novel ICMM of order 3 ×2 m ( m ∈ N ) using iterative matrix compounding is introduced. The modified differential encoding technique generates a single random sequence from two input sequences. The encryption process begins with pixel and ICMM element randomization using a 2D Arnold map. The diffusion phase involves two security layers: the first modifies pixel values using ICMM row matrix and Fast Fourier Transform, mitigating potential attacks; the second minimizes confidentiality risks using modified differential encoding and a 3D Bernoulli map at the bit level. Additional security is achieved by XORing cipher image components with unitary matrices derived from the ICMM via singular value decomposition. Numerical and graphical simulations validate the algorithm’s security and complexity, and comparative analysis confirms its effectiveness in meeting security standards.

Steganography is used to hide sensitive types of data including images, audio, text, and videos in an invisible way so that no one can detect it. Image-based steganography is a technique that uses images as a cover media for hiding and transmitting sensitive information over the internet. However, image-based steganography is a challenging task due to transparency, security, computational efficiency, tamper protection, payload, etc. Recently, different image steganography methods have been proposed but most of them have reliability issues. Therefore, to solve this issue, we propose an efficient technique based on the Least Significant Bit (LSB). The LSB substitution method minimizes the error rate in the embedding process and is used to achieve greater reliability. Our proposed image-based steganography algorithm incorporates LSB substitution with Magic Matrix, Multi-Level Encryption Algorithm (MLEA), Secret Key (SK), and transposition, flipping. We performed several experiments and the results show that our proposed technique is efficient and achieves efficient results. We tested a total of 165 different RGB images of various dimensions and sizes of hidden information, using various Quality Assessment Metrics (QAMs); A name of few are; Normalized Cross Correlation (NCC), Image Fidelity (IF), Peak Signal Noise Ratio (PSNR), Root Mean Square Error (RMSE), Quality Index (QI), Correlation Coefficient (CC), Structural Similarity Index (SSIM), Mean Square Error (MSE), Entropy, Contrast, and Homogeneity, Image Histogram (IH). We also conducted a comparative analysis with some existing methods as well as security analysis which showed better results. The achieved result demonstrates significant improvements over the current state-of-the-art methods.

Watermark Tampering Detection based on Magic Matrix

In the recent couple of years, due to the accelerated popularity of the internet, various organizations such as government offices, military, private companies, etc. use different transferring methods for exchanging their information. The Internet has various benefits and some demerits, but the primary bad mark is security of information transmission over an unreliable network, and widely uses of images. So, Steganography is the state of the art of implanting a message in the cover objects, that nobody can suspect or identify it. Therefore, in the field of cover steganography, it is very critical to track down a mechanism for concealing data by utilizing different blends of compression strategies. Amplifying the payload limit, and robustness, and working on the visual quality are the vital factors of this research to make a reliable mechanism. Different cover steganography research strategies have been recommended, and each adores its benefits and impediments but there is a need to foster some better cover steganography implements to accomplish dependability between the essential model of cover steganography. To handle these issues, in this paper we proposed a method in view of Huffman code, Least Significant Bits (LSB) based cover steganography utilizing Multi-Level Encryption (MLE) and colorless part (HC-LSBIS-MLE-AC) of the picture. It also used different substitution and flicking concepts, MLE, Magic matrix, and achromatic concepts for proving the proficiency, and significance of the method. The algorithm was also statistically investigated based on some Statistical Assessment Metrics (SAM) such as Mean Square Error (MSE), Peak Signal Noise Ratio (PSNR), Normalized Cross Correlation (NCC), Structural Similarity Index Metric (SSIM), etc. and different perspectives. The observational outcomes show the likelihood of the proposed algorithm and the capacity to give unwavering quality between security, payload, perception, computation, and temper protection.

Motivated by current experiments on searching for neutrinoless double beta decays, we study the phenomenological consequences and testability of the constraint relation “Mii=Mjj+Meμ+Meτ”, for i,j=e,μ,τ, on the magic neutrino mass matrix elements. This hypothesis is inspired by the μ−τ symmetry and gives rise to six different Majorana neutrino mass textures, including two textures one-zero. These obtained textures are diagonalized by the well-known trimaximal mixing which provides nonzero and nonmaximal reactor and atmospheric angles, respectively. Depending on the predominance of the e-row or μ-τ block, the preferred neutrino mass hierarchy and the lower limits on the |Mii| effective Majorana masses for each magic matrix are determined. Furthermore, in light of the global-fit results of neutrino oscillation parameters as reported by NuFIT 5.1, we also study the testability of these textures at the proposed neutrinoless double beta decay experiments such as KamLAND-Zen, GERDA Phase-II and nEXO, by incorporating the effective Majorana neutrino masses |Mij| that are generated through these neutrino mass matrices.

SummaryThe unpredictability of partial shadowing impacts the solar photovoltaic system's performance. This results in mismatch losses, reducing the healthy PV module's power output. This paper proposes a new reconfiguration method to increase the power generation of an array by lowering the power losses. A new physical relocation technique named the magic matrix shifting (MMS) method has been introduced in this paper. This work uses MATLAB/Simulink to model a 36, 213w, 6 × 6 PV array construction. Under six different partial shading situations, the performance has been examined based on P‐V, I‐V characteristics, maximum power extraction, power loss, and percentage. For comparison purposes, conventional total‐cross‐tide (TCT) and six other reconfigurations, including sudoku (SK), optimum sudoku (OSK), zig‐zag (ZZ), magic square (MS), sky‐scraper (SS), and novel shade dispersion (NSD) have been considered.

A novel 4-D hyperchaotic system that have seven positive parameters in third order with thirteen terms is proposed,in this paper, the proposed chaotic behavior is proved by analysis of the Lyapunov's exponent, fractional dimension, zero-one test, sensitivity dependent on initial condition (SDIC), phase portraits, and waveform analysis, this study offers an innovative designed image encryption algorithm depending on a 4-D chaotic system using fast discrete Walsh-Hadamard transform and magic matrix that is both effective and simple for image encryption and gives it a higher level of security. This new 4-D hyperchaotic system is used to produce a random key in this algorithm. The implemented and simulated results using mathematica programs and MATLAB programs were supplied qualitatively and in figures. The proposed system is hyperchaotic, according to testing results, because it possesses two Lyapunov positive exponents.

Multi-level image security using elliptic curve and magic matrix with advanced encryption standard

Adaptive data hiding scheme based on magic matrix of flexible dimension

In a wireless cellular system, resource allocation among active users is a challenging task. The cellular systems with nonorthogonal multiple access (NOMA) solve the problem of bandwidth and time allocation. All the active users in the same NOMA cluster are allowed to access the complete cluster bandwidth at the same time. However, power allocation in NOMA is a multiconstraint optimization problem. The complexity of power allocation increases with the increase in the number of users inside the cluster. This article presents a novel technique for power allocation in a NOMA downlink cluster, using the magic sum of the magic matrix. The sum throughput (SUMTP) and the min–max fairness index (MMFI) are calculated and compared with an existing method for the downlink NOMA system. The proposed method shows comparable SUMTP performance to the conventional optimized method while ensuring better MMFI. We observed an inverse association between SUMTP and MMFI. In addition, the execution time of the proposed method is much lesser than that of the conventional optimized method owing to lower number of flops required for magic-matrix-based power allocation.

Data hiding is a technique that embeds a secret message into a cover medium and transfers the hidden information in the secret message to the recipient. In the past, several data hiding methods based on magic matrix have used various geometrical shapes to transmit secret data. The embedding capacity achieved in these methods was often limited due to simple geometrical layouts. This paper proposes a data hiding scheme based on a double-layer octagon-shaped shell matrix. Compared to previous octagon-shaped data hiding methods, the proposed method embeds a total of 7 bits in each pixel pair, reaching an embedding capacity of 3.5 bits per pixel (bpp). Experimental results show that the proposed scheme has a higher embedding capacity compared to other irreversible data hiding schemes. Using the proposed method, it is possible to maintain the Peak Signal to Noise Ratio (PSNR) within an acceptable range with the embedding time less than 2 s.

At present, the Sudoku matrix, turtle shell matrix, and octagonal matrix have been put forward according to the magic matrix-based data hiding methods. Moreover, the magic matrices to be designed depend on the size of the embedding capacity. In addition, by determining the classification of points of pixel pairs after applying a magic matrix and by determining the traversal area, the average peak signal-to-noise ratio (PSNR) can be improved. Therefore, this topic intends to propose a data hiding method based on a 16 × 16 Sudoku matrix by using the 16 × 16 Sudoku matrix and extending it to a double-layer magic matrix. Low-cost data embedding methods are also studied, in order to improve the PSNR and maintain good image quality with the same embedding capacity.

Reversible data hiding based on three shadow images using rhombus magic matrix

Information hiding in motion data of virtual characters