Abstract
This paper studies the problem of constructing lightweight involutory maximal distance separable (MDS) matrices. The authors find the exact lower bound of the XOR counts for 4 × 4 involutory MDS matrices over \(\mathbb{F}_{2^{4}}\). Further, some new structures of 4 × 4 involutory MDS matrices over \(\mathbb{F}_{2^{m}}\) are provided to construct involutory MDS matrices and the authors constructed the lightest 4 × 4 involutory MDS matrices over \(\mathbb{F}_{2^{8}}\) so far by using these structures.
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This research was supported in part by the National Natural Science Foundation of China under Grant No. 11371356 & 61877058, CAS Project QYZDJ-SSW-SYS022 and the Strategy Cooperation Project AQ-1701.
This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.
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Bai, J., Sun, Y. & Wang, D. On the Construction of Involutory MDS Matrices over \(\mathbb{F}_{2^{m}}\). J Syst Sci Complex 33, 836–848 (2020). https://doi.org/10.1007/s11424-019-8125-0
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DOI: https://doi.org/10.1007/s11424-019-8125-0