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 F42
. In contrast to previous
constructions of MDS matrices, our constructions have achieved
fewer XORs.