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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2016/143}},
      url = {https://eprint.iacr.org/2016/143}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.