A Novel Method of Computing Quadratic Weil Sum

Let χ be an additive character of F q and let L(x) be a linearized polynomial over F qn. In this paper, we consider the Weil sums of quadratic functions, namely, ∑x∈Fqnχ(Tr(χL(χ)) . Quadratic Weil sum is a critical topic in number theory and has applications in sequence design, coding, and cryptography. The computation of a quadratic Weil sum is complicated and sometimes impractical. This paper introduces a novel and generic way of computing quadratic Weil sums, which allows us to deal with the computation more efficiently compared with previous methods. As a result, we give a formula for computing ∑x∈Pqnχ(Tr(∑i,j≤naijχqi+qj)) explicitly in the case aij ∈ Fq . We also incorporate our results to obtain the condition for a class of Boolean functions to be bent, which are highly non-linear and widely applied in cryptography.