Cryptology ePrint Archive: Report 2016/686

The Lightest 4x4 MDS Matrices over $GL(4,\mathbb{F}_2)$

Jian Bai and Ting Li and Yao Sun and Dingkang Wang and Dongdai Lin

Abstract: Maximal distance separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching $4\times 4$ MDS matrices over GL(4, $\mathbb{F}_2$). By this algorithm, we find all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices are classified to 3 types, and some necessary and sufficient conditions are presented for them as well. Some theoretical results can be generalized to the case $GL(m,\mathbb{F}_2)$ easily, and $4 \times 4$ MDS matrices with 10 XOR counts can be constructed directly.

Category / Keywords: MDS matrix, lightweight

Original Publication (with major differences): SCIENCE CHINA Information Sciences

Date: received 7 Jul 2016, last revised 24 Dec 2017

Contact author: baijian at amss ac cn

Available format(s): PDF | BibTeX Citation

Note: The early version is only a display of the most important result.

Version: 20171225:054123 (All versions of this report)

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