Contribution to the Study of Linear Cryptosystems: An Analysis of Non-Invertible Matrix-Based Techniques Beyond the Hill Cipherer

Abstract

Linear cryptosystem, such as the Hill cipher, are foundational in symmetric-key encryption but are limited by the requirement of invertible key matrices, reducing key space and security. This study investigates the use of non-invertible matrices to enhance cryptographic complexity and resilience. We analyze the mathematical principles, design optimized encryption and decryption algorithms, and evaluate their performance against known attacks. Experimental results show that non-invertible matrix-based methods provide stronger data protection than conventional approaches while remaining practically feasible. This proposed symmetric encryption algorithm advances matrix-based cryptography, offering a robust framework for secure communication and guiding future cryptosystem development.