## Cryptology ePrint Archive: Report 2007/379

On The Inequivalence Of Ness-Helleseth APN Functions

Xiangyong Zeng and Lei Hu and Yang Yang and 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 $n$.

Category / Keywords: secret-key cryptography /Almost perfect nonlinear (APN) function, Ness-Helleseth function, CCZ-equivalence

Publication Info: Almost perfect nonlinear (APN), differential uniformity, EA-equivalence, CCZ-equivalence

Date: received 25 Sep 2007, last revised 13 Nov 2007

Contact author: xzeng at hubu edu cn

Available format(s): PDF | BibTeX Citation

Note: This is a full version of the original one.

[ Cryptology ePrint archive ]