Paper 2007/379
On The Inequivalence Of Ness-Helleseth APN Functions
Xiangyong Zeng, Lei Hu, 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 $n$.
Note: This is a full version of the original one.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Almost perfect nonlinear (APN), differential uniformity, EA-equivalence, CCZ-equivalence
- Keywords
- Almost perfect nonlinear (APN) functionNess-Helleseth functionCCZ-equivalence
- Contact author(s)
- xzeng @ hubu edu cn
- History
- 2007-11-13: last of 2 revisions
- 2007-09-27: received
- See all versions
- Short URL
- https://ia.cr/2007/379
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/379,
author = {Xiangyong Zeng and Lei Hu and Yang Yang and Wenfeng Jiang},
title = {On The Inequivalence Of Ness-Helleseth {APN} Functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/379},
year = {2007},
url = {https://eprint.iacr.org/2007/379}
}
