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In this paper, for an odd prime $p$, the differential spectrum of the powerfunction $x^{\frac{p^k+1}{2}}$ in $\mathbb{F}_{p^n}$ is calculated. For an oddprime $p$ such that $p\equiv 3\bmod 4$ and odd $n$ with $k|n$, the differentialspectrum of the power function $x^{\frac{p^n+1}{p^k+1}+\frac{p^n-1}{2}}$ in$\mathbb{F}_{p^n}$ is also derived. From their differential spectrums, thedifferential uniformities of these two power functions are determined. We alsofind some new power functions having low differential uniformity.

Differential Spectrum of Some Power Functions With Low Differential Uniformity