The Differential Spectrum of the Power Mapping xpn−3

Abstract

Let n be a positive integer and p a prime. The power mapping xpn−3 over Fpn 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 Fpn , we determine the differential spectrum of xpn−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 Fp plays an important role in our computation for the general case p≥5.