Constructions of Lightweight MDS Diffusion Layers from Hankel Matrices

Maximal distance separable (MDS) matrices are used as optimal diffusion layers in many block ciphers and hash functions. Recently, the designers paid more attention to the lightweight MDS matrices because it can reduce the hardware resource. In this paper, we give a new method to construct the lightweight MDS matrices. We provide some theoretical results and two kinds of 4 × 4 lightweight Hankel MDS matrices. We also prove that the 2s × 2s involution Hankel MDS matrix does not exist in finite field. Furthermore, we searched the 4 × 4 Hankel MDS matrices over GL(4, F2) and GL(8, F2) that have the better s-XOR counts until now.