On the Non-linearity and Sparsity of Boolean Functions Related to the Discrete Logarithm in Finite Fields of Characteristic Two

  • Nina Brandstätter
  • Tanja Lange
  • Arne Winterhof
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)


In public-key cryptography the discrete logarithm has gained increasing interest as a one-way function. This paper deals with the particularly interesting case of the discrete logarithm in finite fields of characteristic two.

We obtain bounds on the maximal Fourier coefficient, i.e., on the non-linearity, on the degree and the sparsity of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic.

The proofs of the results for odd characteristic involve quadratic character sums and are not directly extendable to characteristic two. Here we use a compensation for dealing with the quadratic character.


Discrete logarithm Boolean functions non-linearity degree sparsity maximal Fourier coefficient 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nina Brandstätter
    • 1
  • Tanja Lange
    • 2
  • Arne Winterhof
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

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