A Graph-Based Framework for Recursive Self-Invertible Matrix Cryptography Using Complete Graphs K_4

Résumé

This paper proposes a novel symmetric encryption scheme that integrates algebraic graph theory with recursive matrix transformations. The method encodes plaintext into weighted complete graphs K_4 and encrypts the resulting adjacency matrices using a dynamic sequence of self-invertible keys. Unlike static Hill ciphers, this approach utilizes a recursive function to generate unique keys for each data block, significantly enhancing security against cryptanalysis. We define the algebraic structure over a modular arithmetic system (mod 29), detail the recursive key generation algorithm, and provide three distinct numerical illustrations of the encryption and decryption protocols.