The Differential Spectrum of the Power Mapping x pn −3

Let [Formula Omitted] be a positive integer and [Formula Omitted] a prime. The power mapping [Formula Omitted] over [Formula Omitted] has desirable differential properties, and its differential spectra for [Formula Omitted] have been determined. In this paper, for any odd prime [Formula Omitted], by investigating certain quadratic character sums and some equations over [Formula Omitted], we determine the differential spectrum of [Formula Omitted] with a unified approach. The obtained result shows that for any given odd prime [Formula Omitted], the differential spectrum can be expressed explicitly in terms of [Formula Omitted]. Compared with previous results, a special elliptic curve over [Formula Omitted] plays an important role in our computation for the general case [Formula Omitted].