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A Note on Rotation Symmetric S-boxes

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Abstract

This paper is twofold. The first is devoted to study a class of quadratic rotation symmetric S-boxes (RSSBs) which was presented by Gao G, et al., Constructions of quadratic and cubic rotation symmetric bent functions, IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4908–4913, 2012, by decomposing a class of cubic rotation symmetric bent functions. The authors obtain its nonlinearity and differential uniformity of such class of S-boxes. In particular, the compositional inversion of the class of rotation symmetric S-boxes is also presented. Then the authors introduce a steepest-descent-like search algorithm for the generation of RSSBs. The algorithm finds 5,6,7,8-bit RSSBs with very good cryptographic properties which can be applied in designing cryptographical algorithms.

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Acknowledgement

The authors would like to thank the anonymous reviewers for detailed comments that improved both the presentation and editorial quality of this paper. Guangpu Gao would like to express his appreciation to Prof. T W Cusick for carefully reading the manuscript.

Author information

Authors and Affiliations

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450002, China

    Guangpu Gao

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Guangpu Gao & Dongdai Lin

  3. Guangxi Key Laboratory of Cryptogpraphy and Information Security, Guilin University of Electronic Technology, Guilin, 541004, China

    Wenfen Liu

Authors
  1. Guangpu Gao
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  2. Dongdai Lin
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  3. Wenfen Liu
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Corresponding authors

Correspondence to Guangpu Gao, Dongdai Lin or Wenfen Liu.

Additional information

This research was supported by the National Nature Science Foundation of China under Grant Nos. 61872381, 61872359, 61862011, and 61402522. The work of LIU Wenfen is also supported by Guangxi Key Laboratory of Cryptography and Information Security under Grant No. GCIS201704.

This paper was recommended for publication by Editor DENG Yingpu.

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Gao, G., Lin, D. & Liu, W. A Note on Rotation Symmetric S-boxes. J Syst Sci Complex 32, 1460–1472 (2019). https://doi.org/10.1007/s11424-019-7263-8

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  • DOI: https://doi.org/10.1007/s11424-019-7263-8

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