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Differential spectra of a class of power permutations with characteristic 5

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Abstract

Let n be a positive integer and \(F(x)=x^d\) over \({\mathbb {F}}_{5^n}\), where \(d=\frac{5^n-3}{2}\). In this paper, we study the differential properties of the power permutation F(x). It is shown that F(x) is differentially 4-uniform when n is even, and differentially 5-uniform when n is odd. Based on some knowledge on elliptic curves over finite fields, the differential spectrum of F(x) is also determined.

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Acknowledgements

The authors are very grateful to the editor and the reviewers for their detailed comments and suggestions that much improved the presentation and quality of this paper. H. Yan’s research was supported by the National Natural Science Foundation of China (No. 11801468), the Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS201814), and the Fundamental Research Funds for the Central Universities of China (No. 2682018CX61). C. Li’s research was supported by the National Natural Science Foundation of China (12071138), the Shanghai Chenguang Program (18CG22), and the Foundation of State Key Laboratory of Integrated Services Networks (ISN20-02).

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Authors and Affiliations

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

    Haode Yan

  2. Guangxi Key Laboratory of Cryptography and Information Security, Guilin, 541000, China

    Haode Yan

  3. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Chengju Li

  4. State Key Laboratory of Integrated Services and Networks, Xi’an, 710071, China

    Chengju Li

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

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Communicated by P. Charpin.

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Yan, H., Li, C. Differential spectra of a class of power permutations with characteristic 5. Des. Codes Cryptogr. 89, 1181–1191 (2021). https://doi.org/10.1007/s10623-021-00865-9

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  • DOI: https://doi.org/10.1007/s10623-021-00865-9

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