A Family of p-ary Binomial Bent Functions

Dabin ZHENG  Xiangyong ZENG  Lei HU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.9   pp.1868-1872
Publication Date: 2011/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1868
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
p-ary binomial Bent functions,  exponential sum,  Hamming weight,  

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For a prime p with p≡3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function fa,b(x)=Tr1n(axpm-1)+Tr12 is characterized, where n=2m, aF*pn, and bF*p2. The necessary and sufficient conditions of fa,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 fa,b(x) by the Hamming weight of a sequence.