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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 itsdifferential spectra for $p=2,\,3$ have been determined. In this paper, for anyodd prime $p$, by investigating certain quadratic character sums and someequations 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 anygiven odd prime $p$, the differential spectrum can be expressed explicitly interms of $n$. Compared with previous results, a special elliptic curve over$\mathbb{F}_{p}$ plays an important role in our computation for the generalcase $p \ge 5$.

The Differential Spectrum of the Power Mapping $x^{p^n-3}$