Designing High-Order Lightweight Circulant MDS Matrices

Abstract

—MDS matrices are of great significance in the design of block ciphers and hash functions. In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency. We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware. Furthermore, we provide circulant MDS matrices with as few bit XOR operations as possible for the classical dimensions 4×4, 8×8 over the space of linear transformations over finite field . In contrast to previous constructions of MDS matrices, our constructions have achieved fewer XORs