Construction of MDS matrices from minors of an MDS matrix

Diffusion layers are an important part of most symmetric ciphers and MDS matrices can be used to construct perfect diffusion layers. However, there are few techniques for constructing these matrices with low implementation cost in software/hardware. Conventional MDS matrices are constructed on finite fields and MDS matrices over commutative rings acting on modules have been characterized by Dong Dong et. al. in 1998. In this paper, we consider MDS matrices over commutative rings acting on corresponding modules and using the minors of such matrices, we construct new MDS diffusion layers.