Paper 2004/284 Original: eprint.iacr.org/2004/284 ↗
ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS
Abstract
It is well known that the degree of a $2m$-variable bent function is at most $m.$ However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree $m$ in $2m$ variables when $m>3;$ there is no homogenous bent function of degree $m-1$ in 2m variables when $m>4;$ Generally, for any nonnegative integer $k$, there exists a positive integer $N$ such that when $m>N$, there is no homogeneous bent functions of degree $m-k$ in $2m$ variables. In other words, we get a tighter upper bound on the degree of homogeneous bent functions. A conjecture is proposed that for any positive integer $k>1$, there exists a positive integer $N$ such that when $m>N$, there exists homogeneous bent function of degree $k$ in $2m$ variables.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2005-12-01: last updated
- 2004-11-03: published
- Short URL
- https://ia.cr/2004/284
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/284,
author = {Qingshu Meng and Huanguo Zhang and Min Yang and Jingsong Cui},
title = {ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/284},
year = {2004},
url = {https://eprint.iacr.org/2004/284}
}