## Cryptology ePrint Archive: Report 2009/563

A Family of $p$-ary Binomial Bent Functions

Dabin Zheng and Xiangyong Zeng and Lei Hu

Abstract: For a prime $p$ with $p\equiv 3\,({\rm mod}\, 4)$ and an odd number $m$, the Bentness of the $p$-ary binomial function $f_{a,b}(x)={\rm Tr}_{1}^n(ax^{p^m-1})+{\rm Tr}_{1}^2(bx^{\frac{p^n-1}{4}})$ is characterized, where $n=2m$, $a\in \bF_{p^n}^*$, and $b\in \bF_{p^2}^*$. The necessary and sufficient conditions of $f_{a,b}(x)$ being Bent are established respectively by an exponential sum and two sequences related to $a$ and $b$. For the special case of $p=3$, we further characterize the Bentness of the ternary function $f_{a,b}(x)$ by the Hamming weight of a sequence.

Category / Keywords: foundations /

Date: received 17 Nov 2009

Contact author: dbzheng at gucas ac cn

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