Monomial bent functions

Abstract

In this correspondence, we focus on bent functions of the form F(2/sup n/) /spl rarr/ F(2) where x /spl rarr/ Tr(/spl alpha/x/sup d/). The main contribution of this correspondence is, that we prove that for n=4r, r odd, the exponent d=(2/sup r/+1)/sup 2/ allows the construction of bent functions. This open question has been posed by Canteaut based on computer experiments. As a consequence for each of the well understood families of bent functions, we now know an exponent d that yields to bent functions of the given type.