Paper 2017/197
A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group
Wenying Zhang, Zhaohui Xing, and Keqin Feng
Abstract
We present a construction of bent function $f_{a,S}$ with $n=2m$ variables for any nonzero vector $a\in \mathbb{F}_{2}^{m}$ and subset $S$ of $\mathbb{F}_{2}^{m}$ satisfying $a+S=S$. We give the simple expression of the dual bent function of $f_{a,S}$. We prove that $f_{a,S}$ has optimal algebraic degree $m$ if and only if $|S|\equiv 2 (\bmod 4) $. This construction provides series of bent functions with optimal algebraic degree and large symmetric group if $a$ and $S$ are chosen properly.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint.
- Contact author(s)
- wzhang @ esat kuleuven be
- History
- 2017-02-28: received
- Short URL
- https://ia.cr/2017/197
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/197,
author = {Wenying Zhang and Zhaohui Xing and Keqin Feng},
title = {A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/197},
year = {2017},
url = {https://eprint.iacr.org/2017/197}
}
