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On the Construction of Involutory MDS Matrices over\(\mathbb{F}_{2^{m}}\)

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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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Author information

Authors and Affiliations

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Jian Bai & Dingkang Wang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Jian Bai & Dingkang Wang

  3. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Yao Sun

Authors
  1. Jian Bai

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  2. Yao Sun

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  3. Dingkang Wang

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Corresponding authors

Correspondence toJian Bai,Yao Sun orDingkang Wang.

Additional information

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 Complex33, 836–848 (2020). https://doi.org/10.1007/s11424-019-8125-0

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