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 matrixlightweight
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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2016/686}},
      url = {https://eprint.iacr.org/2016/686}
}
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