Exponential Sums and Boolean Functions

Julien Bringer (1) , Valérie Gillot (1) , Philippe Langevin (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

We study the nonlinearity of Boolean functions constructed by means of a subgroup of the multiplicative group of a finite field. The functions that we consider are constant over the non trivial cosets of a subgroup of small index. Classical properties of Gauss sums lead us to propose a new conjecture of the Patterson-Wiedemann type. One of the major steps of this approach consists in finding good estimations of exponential sums restricted over subgroup.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Julien Bringer, Valérie Gillot, Philippe Langevin. Exponential Sums and Boolean Functions. Proceedings of BFCA'05 Conference, March 7--8, 2005 Rouen, France, Mar 2005, Rouen, France. pp.177--186. ⟨hal-00993895⟩