Research on Image Steganography Based on Sudoku Matrix

Summary. It is known that if M is a 3 × 3 magic matrix then every positive, odd power of M is a magic matrix, while an even power need not be. Given any n × n magic matrix M, we find all polynomials f such that f(M) is a magic matrix.

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.

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.

Data hiding is a technique used for embedding secret messages in a carrier medium which cannot be perceived by human eye. In the data hiding scheme based on the magic matrix, previous methods exploited a magic matrix with various shapes to carry secret messages, but the embedding capacity was often limited. Inspired by the magic matrix scheme using magic signet proposed by Lee et al., the proposed method develops a double-layer magic matrix scheme to enhance the embedding capacity. Under the framework of a double-layer matrix, we tested many combinations of different signet sizes which can carry secret data in various notational number systems. The experimental results show that the proposed scheme had a higher embedding capacity and good image quality compared to the previous methods.

Digital image steganography algorithms usually suffer from a lossy restoration of the cover content after extraction of a secret message. When a cover object and confidential information are both utilised, the reversible property of the cover is inevitable. With this objective, several reversible data hiding (RDH) algorithms are available in the literature. Conversely, because both are diametrically related parameters, existing RDH algorithms focus on either a good embedding capacity (EC) or better stego-image quality. In this paper, a pixel expansion reversible data hiding (PE-RDH) method with a high EC and good stego-image quality are proposed. The proposed PE-RDH method was based on three typical RDH schemes, namely difference expansion, histogram shifting, and pixel value ordering. The PE-RDH method has an average EC of 0.75 bpp, with an average peak signal-to-noise ratio (PSNR) of 30.89 dB. It offers 100% recovery of the original image and confidential hidden messages. To protect secret as well as cover the proposed PE-RDH is also implemented on the encrypted image by using homomorphic encryption. The strength of the proposed method on the encrypted image was verified based on a comparison with several existing methods, and the approach achieved better results than these methods in terms of its EC, location map size and imperceptibility of directly decrypted images.

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.

Complex and robust tissue self-organization requires defined initial conditions and dynamic boundaries-neighbouring tissues and extracellular matrix that actively evolve to guide morphogenesis. A major challenge in tissue engineering is identifying material properties that are compatible with controlling initial culture conditions while mimicking dynamic tissue boundaries. Here we describe a highly tunable granular biomaterial, MAGIC matrix, that supports both long-term bioprinting and gold-standard tissue self-organization. We identify that significant stress relaxation at the long timescales and large deformation magnitudes relevant to self-organization is required for optimal morphogenesis. We apply optimized MAGIC matrices toward precise extrusion bioprinting of saturated cell suspensions directly into three-dimensional culture. Carefully controlling initial conditions for tissue growth yields dramatic increases in organoid reproducibility and complexity across multiple tissue types, enabling high-throughput generation of organoid arrays and perfusable three-dimensional microphysiological systems. Our results identify key biomaterial parameters for optimal organoid morphogenesis and lay the foundation for fabricating more complex and reproducible self-organized tissues.

Data hiding is a technology designed for safely transmitting secret data through open communication channels, in which the secret data are embedded into a cover carrier imperceptibly. Among the existing data hiding schemes, the exploiting-modification-direction (EMD) based schemes draw considerable attentions due to large embedding capacity. The proposed scheme improves the EMD-2 scheme by constructing an extended squared magic matrix, resulting in a larger embedding capacity high up to 3.15 bits per pixel (bpp). Experimental results show that the proposed scheme outperforms state-of-the-art reference matrix based schemes in terms of embedding capacity, meanwhile, maintains good image quality.

Reversible watermarking methods have drawn attention of many researchers in recent years because original cover objects can be completely restored upon extraction of embedded information. The prediction error expansion (PEE) embedding proposed by Thodi and Rodriguez can embed one information bit into one cover pixel and achieve good visual quality of watermarked images. However, the PEE method is not a generalised scheme and its embedding capacity measured by bit per pixel (bpp) and visual quality measured by peak signal-to-noise ratio (PSNR) can be improved. Thus, we propose two novel schemes based on the PEE method by using pixel partition strategies to improve embedding capacity and/or visual quality. The first proposed scheme makes the PEE method be generalised and the second proposed scheme can embed more than 1 bpp. Experimental results show that the proposed schemes can significantly improve visual quality of the watermarked images produced by the PEE method when embedding capacity falls within the range [0·1, 1]. In particular, when an embedding capacity belongs to the range [0·1, 0·5], in average, the first proposed scheme with K = 1 can improve the PSNR of the PEE method at least 13 dB for test images. In addition, when embedding capacity falls within the range [0·1, 1], in average, the second proposed scheme with K = 1 can improve the PSNR of the PEE method at least 14 dB for test images.

Image Steganography is a covert communication to hide the existence of messages into images from a third party. High embedding capacity, good visual quality and security are three significant essentials. In the proposed method, every secret digit is embedded into each cover pixel pair based on a magic matrix with pencil-shaped patterns to obtain higher embedding capacity while preserving good image quality. Experimental results show that the proposed scheme ensures higher embedding capacity of 2 bits per pixel and PSNR of 44.7 dB on average compared with existing schemes, while ensuring security by scrambling the secret message with a secure key.

A high stego-image quality steganographic scheme with reversibility and high payload using multiple embedding strategy

Data embedding is one of the important issues for securely conveying secrets from senders to receivers without arousing any notices to attackers. Wet paper coding (WPC) is one of the data embedding schemes which embeds secrets into a subset of pixels of an image. The pixels in the subset are also called dry pixels. Inspired by wet paper coding, a novel data embedding scheme with a magic matrix is presented in this paper. Before data embedding, pixels are randomly chosen to define which pixels are dry and wet. Later on, two pixels are treated as a group and each group is judged as embeddable if at least one pixel is a dry pixel in the group. The experimental results show that our proposed scheme can achieve not only good visual quality but also high embedding rate.

Optimized reversible data hiding technique based on multidirectional prediction error histogram and fluctuation-based adaptation

Image steganography aims to conceal confidential information within digital images in an undetectable manner. However, many existing techniques face a trade‐off between embedding capacity, imperceptibility, and computational efficiency, especially transform‐domain approaches based on floating‐point operations. This paper proposes a novel image steganographic method based on an enhanced Pyramid Integer Wavelet Transform (PIWT) combined with a Modified Optimal Pixel Adjustment Process (MOPAP). The PIWT enables integer‐to‐integer transformation, avoiding floating‐point computations and improving its suitability for efficient implementation. Secret data are embedded into transform coefficients using a linear feedback shift register (LFSR) to introduce randomness in the embedding locations, while the proposed MOPAP is employed to reduce embedding distortion and enhance imperceptibility. Experimental results demonstrate that the proposed method achieves an average Peak Signal to Noise Ratio (PSNR) of 50.1 dB at an embedding capacity of 1 bpp, outperforming conventional Least Significant Bit (LSB) and Lifting Wavelet Transform (LWT) steganographic methods in terms of imperceptibility and embedding capacity. In addition, statistical evaluation indicates improved resistance against classical steganalysis compared to baseline approaches. These results confirm that the proposed method provides an effective balance between embedding capacity, imperceptibility, and computational efficiency, making it a promising solution for secure image‐based data hiding applications.

Multi-directional block based PVD and modulus function image steganography to avoid FOBP and IEP