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Nonlinarity of Boolean functions and hyperelliptic curves

Authors
  • Férard, Eric
  • Rodier, François
Publication Date
May 11, 2007
Source
HAL
Keywords
Language
English
License
Unknown
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Abstract

We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials of binary degree equal to 3. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersingular curves of genus 2. We give some criterion for a vectorial function not to be almost perfect nonlinear.

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