Differential spectrum of some power functions in odd prime characteristic

Upper bound on Δf of the power function in Fpn (Helleseth et al. (1999) [7]) is not tight, for example p=5, n=3, and k=2, which is the motivation of this work. In this paper, for an odd prime p, the differential spectrum of the power function in Fpn is calculated. For an odd prime p such that and odd n with m|n, the differential spectrum of the power function in Fpn is also derived. We also find some new power functions which are differentially 4 and 6-uniform.