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**2007/379**

**Title:**

On The Inequivalence Of Ness-Helleseth APN Functions

**Authors:**
Xiangyong Zeng, Lei Hu, Yang Yang, Wenfeng Jiang

**Abstract:**

In this paper, the Ness-Helleseth functions over F_{p^n} defined by the form f(x)=ux^{\frac{p^n-1}{2}-1}+x^{p^n-2} are proven to be a new class of almost perfect nonlinear (APN) functions and they are CCZ-inequivalent with all other known APN functions when p\geq 7. The original method of Ness and Helleseth showing the functions are APN for p=3 and odd n\geq 3 is also suitable for showing their APN property for any prime p\geq 7 with p\equiv 3\,({\rm mod}\,4) and odd n.

**ePrint:**
https://eprint.iacr.org/2007/379

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