Paper 2016/143 Original: eprint.iacr.org/2016/143 ↗
On upper bounds for algebraic degrees of APN functions
Abstract
We study the problem of existence of APN functions of algebraic degree $n$ over $\ftwon$. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions $F$ over $\ftwon$ the function $x^{2^n-1}+F(x)$ is not APN, and changing a value of $F$ in a single point results in non-APN functions.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2016-07-08: last updated
- 2016-02-16: published
- Short URL
- https://ia.cr/2016/143
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2016/143,
author = {Lilya Budaghyan and Claude Carlet and Tor Helleseth and Nian Li and Bo Sun},
title = {On upper bounds for algebraic degrees of APN functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/143},
year = {2016},
url = {https://eprint.iacr.org/2016/143}
}