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Nonlinarity of Boolean functions and hyperelliptic curves

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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https://hal.archives-ouvertes.fr/hal-00145890
Contributor : François Rodier Connect in order to contact the contributor
Submitted on : Friday, May 11, 2007 - 10:45:36 PM
Last modification on : Monday, November 15, 2021 - 7:30:02 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 3:35:26 AM

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  • HAL Id : hal-00145890, version 1
  • ARXIV : 0705.1751

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Eric Férard, François Rodier. Nonlinarity of Boolean functions and hyperelliptic curves. {date}. ⟨hal-00145890⟩

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