On the direct building of 8 x 8 self-reciprocal recursive MDS Matrices effective for implementation over GF(q) using Reed-Solomon codes

MDS matrices are from the MDS codes in coding theory that are being used widely in cryptographic applications. Recursive MDS matrix is an matrix that is a power of some simple companion matrix. These matrices are so convenient for execution especially for hardware implementation using LFSRs. Therefore, these matrices have attracted the interest of many scientists. In this paper, we give a way to directly build 8 x 8 self-reciprocal recursive MDS matrices efficient for execution over the field GF(q), (q = p(r), pis a prime number) using the Reed-Solomon codes. These matrices are significant in practice because they have the potential to be used in lightweight cryptographic algorithms.