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Paper: On The Inequivalence Of Ness-Helleseth APN Functions

Authors:
Xiangyong Zeng
Lei Hu
Yang Yang
Wenfeng Jiang
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URL: http://eprint.iacr.org/2007/379
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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 $n$.
BibTeX
@misc{eprint-2007-13659,
  title={On The Inequivalence Of Ness-Helleseth APN Functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography /Almost perfect nonlinear (APN) function, Ness-Helleseth function, CCZ-equivalence},
  url={http://eprint.iacr.org/2007/379},
  note={Almost perfect nonlinear (APN), differential uniformity, EA-equivalence, CCZ-equivalence xzeng@hubu.edu.cn 13830 received 25 Sep 2007, last revised 13 Nov 2007},
  author={Xiangyong Zeng and Lei Hu and Yang Yang and Wenfeng Jiang},
  year=2007
}