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A family of crooked functions

Designs, Codes and Cryptography volume 50, pages 235–241 (2009)Cite this article

Abstract

It has been proved in Bierbrauer and Kyureghyan (Des. Codes Cryptogr. 46:269–301, 2008) that a binomial function aX i + bX j can be crooked only if both exponents i, j have 2-weight  ≤2. In the present paper we give a brief construction for all known examples of crooked binomial functions. These consist of an infinite family and one sporadic example. The construction of the sporadic example uses the properties of an algebraic curve of genus 3. Computer experiments support the conjecture that each crooked binomial is equivalent either to a member of the family or to the sporadic example.

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References

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan, 49931, USA

    Jürgen Bierbrauer

Authors
  1. Jürgen Bierbrauer
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Correspondence to Jürgen Bierbrauer.

Additional information

Communicated by A. Pott.

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Bierbrauer, J. A family of crooked functions. Des. Codes Cryptogr. 50, 235–241 (2009). https://doi.org/10.1007/s10623-008-9227-1

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  • DOI: https://doi.org/10.1007/s10623-008-9227-1

Keywords

  • Crooked functions
  • APN functions
  • Codes
  • Algebraic curve

Mathematics Subject Classifications (2000)

  • 11T06
  • 11T71

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