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A note on the differential spectrum of a class of power mappings with Niho exponent

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Abstract

Let GF(q2) be the finite field containing q2 elements, where q is an odd prime power. In this paper, we study the differential properties of the power mapping F(x) = xd over GF(q2), where d = 2q − 1 is a Niho exponent [14]. The differential spectrum of F is given by

\(\mathbb {S}=\{\omega _{0}=\frac {q^{2}+q-2}2, \omega _{2}=\frac {q^{2}-q}2, \omega _{q}=1\}\).

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Acknowledgments

The authors are very grateful to the anonymous reviewers for their comments and suggestions which improved the presentation and quality of this paper. H. Yan’s research was supported by the National Natural Science Foundation of China (Grant No.11801468) and the Fundamental Research Funds for the Central Universities of China (Grant No.2682021ZTPY076).

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

    Haode Yan & Zhen Li

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  1. Haode Yan
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  2. Zhen Li
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Correspondence to Haode Yan.

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Yan, H., Li, Z. A note on the differential spectrum of a class of power mappings with Niho exponent. Cryptogr. Commun. 14, 1081–1089 (2022). https://doi.org/10.1007/s12095-022-00577-4

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  • DOI: https://doi.org/10.1007/s12095-022-00577-4

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