Efficient MDS Diffusion Layers Through Decomposition of Matrices

Diffusion layers are critical components of symmetric ciphers. MDS matrices are diffusion layers of maximal branch number which have been used in various symmetric ciphers. In this article, we examine decomposition of cyclic matrices from mathematical viewpoint and based on that, we present new cyclic MDS matrices. From the aspect of implementation, the proposed matrices have lower implementations costs both in software and hardware, compared to what is presented in cryptographic literature, up to our knowledge.