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

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

Paper 2016/686

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

Jian Bai, Ting Li, Yao Sun, 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.

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

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Major revision. SCIENCE CHINA Information Sciences
DOI: 10.1007/s11432-017-9320-8
Keywords: MDS matrix lightweight
Contact author(s): baijian @ amss ac cn
History: 2017-12-25: last of 4 revisions; 2016-07-12: received; See all versions
Short URL: https://ia.cr/2016/686
License: CC BY

BibTeX

@misc{cryptoeprint:2016/686,
      author = {Jian Bai and Ting Li and Yao Sun and Dingkang Wang and Dongdai Lin},
      title = {The Lightest 4x4 {MDS} Matrices over ${GL}(4,\mathbb{F}_2)$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/686},
      year = {2016},
      doi = {10.1007/s11432-017-9320-8},
      url = {https://eprint.iacr.org/2016/686}
}