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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)
- 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