Abstract
Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In this paper we study and construct efficient d ×d circulant MDS matrices for d up to 8 and consider their inverses, which are essential for SPN networks. We explore some interesting and useful properties of circulant matrices which are prevalent in many parts of mathematics and computer science. We prove that circulant MDS matrix can not be involutory. We also prove that 2 d ×2 d circulant matrix can not be both orthogonal and MDS.
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