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Evaluation of weil sums for some polynomials and associated quadratic forms

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Abstract

We study polynomials as quadratic forms over finite fields of odd characteristic. For these polynomials, we establish a connection between a kind of character sums, called Weil sums, and invariants of quadratic forms. A general method is presented to characterize quadratic forms based on coefficients of polynomials, which will be used for some special cases. The evaluation of some Weil sums will also help construct more bent functions or planar functions on finite fields.

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Acknowledgements

The second author was supported by the French Agence Nationale de la Recherche through ANR BARRACUDA (ANR-21-CE39-0009).

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No funding is available. There has been no financial support for this work.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris VIII, F-93526, Saint-Denis, France

    Ruikai Chen & Sihem Mesnager

  2. Laboratory Geometry, Analysis and Applications, LAGA, University Sorbonne Paris Nord, CNRS, UMR 7539, F-93430, Villetaneuse, France

    Ruikai Chen & Sihem Mesnager

  3. Telecom Paris, Polytechnic Institute of Paris, 91120, Palaiseau, France

    Sihem Mesnager

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  1. Ruikai Chen
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  2. Sihem Mesnager
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The authors confirm their responsibilities of the following: study conception and design, data collection, analysis and interpretation of results, and manuscript preparation.

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Correspondence to Ruikai Chen.

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Chen, R., Mesnager, S. Evaluation of weil sums for some polynomials and associated quadratic forms. Cryptogr. Commun. 15, 661–673 (2023). https://doi.org/10.1007/s12095-023-00628-4

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  • DOI: https://doi.org/10.1007/s12095-023-00628-4

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Mathematics Subject Classification (2010)