Cryptology ePrint Archive: Report 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.

Category / Keywords: secret-key cryptography /

Date: received 27 Feb 2017

Contact author: wzhang at esat kuleuven be

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

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