TEXT MESSAGE ENCRYPTION AND DECRYPTION MODEL USING PERMUTATION MATRIX CONSTRUCTION OVER MAX-PLUS ALGEBRA

Abstract

This study addresses the weaknesses of cryptographic systems based on tropical circulant matrices, which still exhibit repetitive patterns and limited key spaces, making them vulnerable to pattern-based attacks. To overcome these issues, a text message encryption and decryption model is developed using permutation matrix constructions in Max-Plus algebra. This model is designed to consistently establish a shared secret key through a key exchange process and to ensure the security of text messages. The study's approach includes a literature review, the design of encryption and decryption algorithms within the Max-Plus semiring, and implementation through numerical simulations. Simulation processes are conducted to evaluate the model's resistance to attacks and its computational efficiency. The findings demonstrate that the use of permutation matrices effectively enhances system security by expanding the key search space and eliminating repetitive patterns commonly found in circulant models. The proposed model is capable of performing stable and accurate encryption and decryption processes across various matrix sizes. However, increasing matrix size leads to higher computational time, indicating the need for a balance between security and efficiency. Overall, this study demonstrates that permutation matrix constructions in Max-Plus algebra have significant potential to be developed as the foundation of modern cryptographic systems that are secure, efficient, and adaptive to future computational threats.