Applying Horner's Rule to Optimize Lightweight MDS Matrices

Abstract

This article is concerned with the problem of constructing lightweight MDS matrices. The authors present a new construction of 4 × 4 MDS matrices over GL(F2, m) for any integer m. They give sufficient and necessary conditions to determine whether the construction is an MDS matrix. Further, for any even number m ≥ 4, they construct lightweight MDS matrices in this structure. Applying Horner's rule to implement MDS matrices, the authors constructions need only 8+4×3×m XOR operations.