Paper 2016/143
On upper bounds for algebraic degrees of APN functions
Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li, and Bo Sun
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.
Note: This is an improved version of the paper.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- almost perfect nonlinearalmost bentBoolean functiondifferential uniformitynonlinearity
- Contact author(s)
- lilia b @ mail ru
- History
- 2016-07-08: last of 3 revisions
- 2016-02-16: received
- See all versions
- Short URL
- https://ia.cr/2016/143
- License
-
CC BY
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}
}
