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

François Rodier (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Carlet-Feng function; nonlinearity; Gaussian sums; equidistribution; discrep- ancy

Domaines: Théorie des nombres [math.NT]; Théorie de l'information et codage [math.IT]

François Rodier. Non-linearity of the Carlet-Feng function, and repartition of Gauss sums. 2020. ⟨hal-02521875⟩