Semi-bent Functions with Multiple Trace Terms and Hyperelliptic Curves

  • Sihem Mesnager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7533)


Semi-bent functions with even number of variables are a class of important Boolean functions whose Hadamard transform takes three values. Semi-bent functions have been extensively studied due to their applications in cryptography and coding theory. In this paper we are interested in the property of semi-bentness of Boolean functions defined on the Galois field \({\mathbb F}_2^n\) (n even) with multiple trace terms obtained via Niho functions and two Dillon-like functions (the first one has been studied by the author and the second one has been studied very recently by Wang et al. using an approach introduced by the author). We subsequently give a connection between the property of semi-bentness and the number of rational points on some associated hyperelliptic curves. We use the hyperelliptic curve formalism to reduce the computational complexity in order to provide an efficient test of semi-bentness leading to substantial practical gain thanks to the current implementation of point counting over hyperelliptic curves.


Boolean function Symmetric cryptography Walsh-Hadamard transformation Semi-bent functions Dickson polynomial Hyperelliptic curves 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sihem Mesnager
    • 1
  1. 1.LAGA (Laboratoire Analyse, Géometrie et Applications), UMR 7539, CNRS, Department of MathematicsUniversity of Paris XIII and University of Paris VIIISaint-Denis CedexFrance

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