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**2013/493**

**Title:**

A new class of semi-bent quadratic Boolean functions

**Authors:**
Chunming Tang, Yanfeng Qi

**Abstract:**

In this paper, we present a new class of semi-bent quadratic Boolean functions of the form f(x)=\sum_{i=1}^{\lfloor\frac{m-1}{2}\rfloor}Tr^n_1(c_ix^{1+4^{i}}) ~(c_i\in \mathbb{F}_4,n=2m). We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when m is odd. For the case: m=p^r, where p is an odd prime with some conditions, we enumerate the semi-bent functions. Further, we give a simple characterization of semi-bentness for these functions with linear properties of c_i. In particular, for a special case of p, any quadratic Boolean function f(x)=\sum_{i=1}^{\frac{p-1}{2}}Tr^{2p}_1(c_ix^{1+4^{i}}) over \mathbb{F}_{2^{2p}} is a semi-bent function.

**ePrint:**
https://eprint.iacr.org/2013/493

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