**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
**DOI: **10.1007/s11432-017-9320-8

**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)

**Short URL: **ia.cr/2016/686

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