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On the c-differential uniformity of certain maps over finite fields

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Abstract

We give some classes of power maps with low c-differential uniformity over finite fields of odd characteristic, for \(c=-1\). Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect c-nonlinear function and investigate conditions when perturbations of perfect c-nonlinear (or not) function via an arbitrary Boolean or p-ary function is perfect c-nonlinear. In the process, we obtain a class of polynomials that are perfect c-nonlinear for all \(c\ne 1\), in every characteristic. The affine, extended affine and CCZ-equivalence is also looked at, as it relates to c-differential uniformity.

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Acknowledgements

The authors would like to express their sincere appreciation for the reviewers’ careful reading, beneficial comments and suggestions, and to the editors for the prompt handling of our paper. The research of Sartaj Ul Hasan is partially supported by Start-up Research Grant SRG/2019/000295 from the Science and Engineering Research Board, Government of India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Jammu, Jammu, 181221, India

    Sartaj Ul Hasan & Mohit Pal

  2. Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, 5020, Bergen, Norway

    Constanza Riera

  3. Applied Mathematics Department, Naval Postgraduate School, Monterey, 93943, USA

    Pantelimon  Stănică

Authors
  1. Sartaj Ul Hasan
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  2. Mohit Pal
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  3. Constanza Riera
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  4. Pantelimon  Stănică
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Correspondence to Pantelimon  Stănică.

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Communicated by G. Kyureghyan.

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Hasan, S.U., Pal, M., Riera, C. et al. On the c-differential uniformity of certain maps over finite fields. Des. Codes Cryptogr. 89, 221–239 (2021). https://doi.org/10.1007/s10623-020-00812-0

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  • DOI: https://doi.org/10.1007/s10623-020-00812-0

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