Non-linearity of the Carlet-Feng function, and repartition of Gauss sums

François Rodier

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arXiv · 2003.12491

Non-linearity of the Carlet-Feng function, and repartition of Gauss sums

François Rodier

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Abstract

The search for Boolean functions that can withstand the main crypyographic attacks is essential. In 2008, Carlet and Feng studied a class of functions which have optimal cryptographic properties with the exception of nonlinearity for which they give a good but not optimal bound. Carlet and some people who have also worked on this problem of nonlinearity have asked for a new answer to this problem. We provide a new solution to improve the evaluation of the nonlinearity of the Carlet-Feng function, by means of the estimation of the distribution of Gauss sums. This work is in progress and we give some suggestions to improve this work.

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François Rodier. 2020-03-27. Non-linearity of the Carlet-Feng function, and repartition of Gauss sums. https://arxiv.org/abs/2003.12491

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