The Differential Spectrum of the Power Mapping x^pn^-3

Let n be a positive integer and p a prime. The power mapping x^{p^{n}-3} over {\mathbb {F}}-{p{n}} has desirable differential properties, and its differential spectra for p=2,\,3 have been determined. In this paper, for any odd prime p , by investigating certain quadratic character sums and some equations over {\mathbb {F}}-{p^{n}} , we determine the differential spectrum of x^{p^{n}-3} with a unified approach. The obtained result shows that for any given odd prime p , the differential spectrum can be expressed explicitly in terms of n. Compared with previous results, a special elliptic curve over {\mathbb {F}}-{p} plays an important role in our computation for the general case p \ge 5.