On Compact Cauchy Matrices for Substitution-Permutation Networks

Maximum distance separable (MDS) matrices are widely used in the design of block ciphers. However, it is highly nontrival to find MDS matrices which could be used in practice. This paper focuses on the design of efficient MDS matrices for substitution-permutation networks (SPNs). We provide a new method to construct and count these MDS matrices. Moreover, we identified an interesting class of Cauchy matrices (named compact Cauchy matrices) which has the fewest different entries and is thus more favorable for implementation. Finally, we prove that all compact Cauchy matrices could be modified into an involution compact Cauchy matrix, and show how to maximize the occurrences of entry “1” in a compact Cauchy matrix.