Construction of MDS matrices combining the Feistel, Misty and Lai-Massey schemes

In cryptography maximum distance separable (MDS) matrices are an important structural element to provide the diffusion property in the block ciphers, stream ciphers and hash functions. To discover new kind of transformations that may generate a series of new MDS matrices which could be used in practice is not a trivial task. In this paper we propose new methods for constructing MDS matrices of size $4\times 4$ combining the well-known Feistel, Misty and Lai-Massey structures which are very attractive for the so-called lightweight schemes.