Research on Image Encryption Algorithm Based on Matrix Scrambling and Matrix Product Transformation

Shu Qin; Chunming Xu

doi:10.47709/cnahpc.v7i2.5643

Authors

Shu Qin Yancheng Teachers University
Chunming Xu Yancheng Teachers University

DOI:

https://doi.org/10.47709/cnahpc.v7i2.5643

Keywords:

Image encryption, matrix scrambling, matrix product transformation, chaotic systems, network security

Abstract

This study introduces an innovative image encryption algorithm that leverages multiple rounds of matrix scrambling and matrix product transformation. Each round of encryption integrates cross-scrambling operations within the image matrix and invertible matrix product transformations, thereby effectively disrupting pixel positions and values. By iteratively adjusting pixel positions and transforming pixel values, the algorithm significantly enhances the security and robustness of the encryption process. The experimental results demonstrate that the proposed algorithm exhibits excellent resistance to statistical analysis, differential attacks, and other potential threats, thereby ensuring high security and practical applicability.

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References

In the wake of the rapid advancement of information technology, digital images have proliferated across military, commercial, medical, and personal domains. However, their susceptibility to replication and widespread dissemination exposes them to a range of security vulnerabilities, such as unauthorized access, tampering, and data leakage. To safeguard the privacy and security of digital images, image encryption technology has emerged as a crucial solution (Liang et al., 2022; Malik et al., 2020; Wang et al., 2021). This technology employs specific algorithms to process image data, rendering it unintelligible without proper authorization and thereby effectively protecting the security of image information. Its significance extends beyond military, commercial, and medical applications to everyday information security (Wang et al., 2023; Xiong et al., 2023).

At present, the predominant image encryption methods encompass symmetric encryption algorithms (e.g., DES, AES) (Muhajer, 2020), chaotic encryption algorithms (Tao et al., 2022), the Arnold transform (Qu et al., 2022), and matrix transformation-based encryption methods (Aqel et al., 2018), among others. Symmetric encryption algorithms are widely adopted for their rapid encryption speed and robust security. However, their relatively short key lengths render them susceptible to brute-force attacks. Chaotic encryption algorithms capitalize on the inherent randomness of chaotic systems and their sensitivity to initial conditions to generate pseudo-random sequences as encryption keys, thereby offering enhanced security and a broader key space. The Arnold transform, a classical image scrambling technique, disrupts pixel * Corresponding author, ycxcm@126.com

positions to eliminate correlations between adjacent pixels and achieve encryption.

Matrix-based encryption methods, such as Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) (Liu et al., 2020), apply specific matrix operations to the image for encryption. While these methods provide a certain degree of security, their effectiveness is increasingly challenged by advancements in decryption technologies. Thus, the development of more secure and efficient image encryption algorithms is of utmost importance.

This study proposes an innovative image encryption algorithm that integrates multiple rounds of scrambling and matrix transformations to enhance the security and efficiency of image encryption. The algorithm executes multiple rounds of encryption, combining internal cross-scrambling of the image matrix with invertible matrix product transformations to disrupt both pixel positions and values. By innovatively integrating these techniques, the proposed method significantly strengthens encryption and increases the complexity and attack resistance of the encrypted image data.