Generalized hyper-bent functions over GF(p)GF(p)

In this paper, we extend the concept of binary hyper-bent functions introduced by Carlet to functions defined over GF(p)GF(p). We show that such functions must be quadratic. We also provide the necessary and sufficient conditions on the symmetric coefficient matrix corresponding to the quadratic form of f:Zpn→Zp that guarantee that f is a hyper-bent function.