Paper 2017/368

Analysis of Toeplitz MDS Matrices

Sumanta Sarkar and Habeeb Syed

Abstract

This work considers the problem of constructing efficient MDS matrices over the field ${\text{F}}_{2^m}$. Efficiency is measured by the metric XOR count which was introduced by Khoo et al. in CHES 2014. Recently Sarkar and Syed (ToSC Vol. 1, 2016) have shown the existence of $4\times 4$ Toeplitz MDS matrices with optimal XOR counts. In this paper, we present some characterizations of Toeplitz matrices in light of MDS property. Our study leads to improving the known bounds of XOR counts of $8\times 8$ MDS matrices by obtaining Toeplitz MDS matrices with lower XOR counts over ${\text{F}}_{2^4}$ and ${\text{F}}_{2^8}$.