Key-dependent MDS matrices

Abstract

The linear optimal diffusion primitives, i.e. MDS matrices, are widely used in block ciphers. In this paper we studied some properties of MDS matrices over finite filed; particularly we proved that MDS matrix does not change the MDS property after multiplying to non-zero element or after permutation of rows/columns of matrices. We suggest a method of construction of key-dependent MDS matrices over finite field.