On a class of bent functions

Speaker: Petr Lisonek (Simon Fraser University)

Time: 12:00PM
Date: Wed 16th June 2010

Location: Mathematical Sciences Seminar Room

We look at the class of monomial and multinomial bent functions on GF(p^(2m)) for which each exponent in their trace representation is divisible by p^m-1. The study of these functions was initiated by Dillon's discovery of the monomial binary case in 1976. This is a distinguished class of bent functions that exhibit some properties desired in cryptographic applications (such as a high algebraic degree). We study both the binary case and the general odd characteristic case. The results are theoretical (constructions, characterizations,
necessary conditions) as well as algorithmic (polynomial time certification of bentness). The mathematical tools involve exponential sums (in particular Kloosterman sums), elliptic and hyperelliptic curves and spreads of m-dimensional subspaces of GF(p)^(2m).

(This talk is part of the Algebra/Claude Shannon Institute series.)