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A Class of Power Mappings with Low Boomerang Uniformity

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

Let \(f(x)=x^{\frac{q-3}{2}}\) be a power mapping over \({\mathbb {F}}_{q}\), where q is an odd prime power. The differential uniformity of f was determined by Helleseth and Sandberg [14] in 1997. In this paper, we study the boomerang uniformity of f via its differential properties. It is shown that f has low boomerang uniformity when \(q \equiv 3 \pmod 4\).

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Acknowledgements

The authors would like to thank the anonymous reviewers for giving us invaluable comments and suggestions that greatly improved the quality of this paper. H. Yan’s research was supported by the Natural Science Foundation of Sichuan (Grant No. 2022NSFSC1805) and the Fundamental Research Funds for the Central Universities of China (Grant No. 2682021ZTPY076).

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Haode Yan & Ziying Zhang

  2. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Zhengchun Zhou

Authors
  1. Haode Yan
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  2. Ziying Zhang
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  3. Zhengchun Zhou
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Correspondence to Ziying Zhang .

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Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Yan, H., Zhang, Z., Zhou, Z. (2023). A Class of Power Mappings with Low Boomerang Uniformity. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22943-5

  • Online ISBN: 978-3-031-22944-2

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