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**2017/197**

**Title:**

A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group

**Authors:**
Wenying Zhang, Zhaohui Xing, 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.

**ePrint:**
https://eprint.iacr.org/2017/197

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