**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.

**Category / Keywords: **secret-key cryptography /

**Date: **received 27 Feb 2017

**Contact author: **wzhang at esat kuleuven be

**Available format(s): **PDF | BibTeX Citation

**Version: **20170228:194525 (All versions of this report)

**Short URL: **ia.cr/2017/197

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