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arXiv · 1207.1845

Differential Spectrum of Some Power Functions With Low Differential Uniformity

Sung-Tai Choi·Seokbeom Hong·Jong-Seon No·Habong Chung
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Abstract

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

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Sung-Tai Choi, Seokbeom Hong, Jong-Seon No, Habong Chung. 2012-07-08. Differential Spectrum of Some Power Functions With Low Differential Uniformity. https://arxiv.org/abs/1207.1845

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