[Resource Topic] 2009/563: A Family of $p$-ary Binomial Bent Functions

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A Family of p-ary Binomial Bent Functions

Authors: Dabin Zheng, Xiangyong Zeng, Lei Hu


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.

ePrint: https://eprint.iacr.org/2009/563

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