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Title:
The Lightest 4x4 MDS Matrices over GL(4,\mathbb{F}_2)
Authors: Jian Bai, Ting Li, Yao Sun, Dingkang Wang, 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.
ePrint: https://eprint.iacr.org/2016/686
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