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A Framework to Optimize Implementations of Matrices

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Topics in Cryptology – CT-RSA 2021 (CT-RSA 2021)

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Abstract

In this paper, we propose several reduction rules to optimize the given implementation of a binary matrix over \(\mathbb {F}_{2}\). Moreover, we design a top-layer framework which can make use of the existing search algorithms for solving SLP problems as well as our proposed reduction rules. Thus, efficient implementations of matrices with fewer Xor gates can be expected with the framework. Our framework outperforms algorithms such as Paar1, RPaar1, BP, BFI, RNBP, A1 and A2 when tested on random matrices with various densities and those matrices designed in recent literature. Notably, we find an implementation of AES MixColumns using only 91 Xors, which is currently the shortest implementation to the best of our knowledge.

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Acknowledgments

We would like to thank the anonymous reviewers for their helpful comments and suggestions. This work was supported by the Application Foundation Frontier Project of Wuhan Science and Technology Bureau (Grant No. 2020010601012189) and the National Natural Science Foundation of China (Grant No. 61802119).

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, China

    Da Lin, Zejun Xiang, Xiangyong Zeng & Shasha Zhang

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  1. Da Lin
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  2. Zejun Xiang
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Correspondence to Zejun Xiang .

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  1. ETH Zürich, Zürich, Switzerland

    Kenneth G. Paterson

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Lin, D., Xiang, Z., Zeng, X., Zhang, S. (2021). A Framework to Optimize Implementations of Matrices. In: Paterson, K.G. (eds) Topics in Cryptology – CT-RSA 2021. CT-RSA 2021. Lecture Notes in Computer Science(), vol 12704. Springer, Cham. https://doi.org/10.1007/978-3-030-75539-3_25

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  • DOI: https://doi.org/10.1007/978-3-030-75539-3_25

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