In today’s digital environment, a major amount of information is exchanged over insecure communication channels. In such an environment, cryptology plays a crucial role in ensuring that data is transmitted accurately and secure. Maximum distance separable (MDS) matrices which are derived from MDS codes, enhance the strength of cryptographic systems and contribute significantly to durability against different types of attacks. MDS matrices are widely used in the diffusion layers of lightweight block ciphers due to their easy usage and security. In addition, involutive MDS matrices with a minimum XOR number have lower costs and less memory because they allow the same matrix in encryption and decryption. For this reason, MDS matrices have been an area of interest. In this study, it is aimed to obtain 4x4 involutive
MDS matrices on F24, F26 and F27 finite fields that have not been studied before. After that, we have determined the matrices that have minimum XOR numbers. Thus, we have obtained 4x4 involutive MDS matrices with good properties to be used in block ciphers.