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On the c-differential spectrum of power functions over finite fields

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Abstract

Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. Inspired by this pioneering work, power functions with low c-differential uniformity were constructed. Wang and Zheng (Several classes of PcN power functions over finite fields, arXiv:2104.12942) defined the c-differential spectrum of a power function. In this paper, we present some properties of the c-differential spectrum of a power function. Then we apply these properties to investigate the c-differential spectra of some power functions. A new class of APcN function is also obtained.

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Acknowledgements

The authors would like to thank the Associate Editor and 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 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 & Kun Zhang

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  1. Haode Yan
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Correspondence to Haode Yan.

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Communicated by K.-U. Schmidt.

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Yan, H., Zhang, K. On the c-differential spectrum of power functions over finite fields. Des. Codes Cryptogr. 90, 2385–2405 (2022). https://doi.org/10.1007/s10623-022-01086-4

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