On the Construction of Involutory MDS Matrices over $$\mathbb{F}_{2^{m}}$$

Abstract

This paper studies the problem of constructing lightweight involutory maximal distance separable (MDS) matrices. The authors find the exact lower bound of the XOR counts for 4 × 4 involutory MDS matrices over $$\mathbb{F}_{2^{4}}$$. Further, some new structures of 4 × 4 involutory MDS matrices over $$\mathbb{F}_{2^{m}}$$ are provided to construct involutory MDS matrices and the authors constructed the lightest 4 × 4 involutory MDS matrices over $$\mathbb{F}_{2^{8}}$$ so far by using these structures.