Constructions of Semi-Bent Functions by Modifying the Supports of Quadratic Boolean Functions

Feng HU  Sihong SU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.5   pp.749-756
Publication Date: 2020/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1131
Type of Manuscript: PAPER
Category: Cryptography and Information Security
Keyword: 
Boolean function,  bent function,  semi-bent function,  algebraic normal form,  

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Summary: 
Semi-bent functions have almost maximal nonlinearity. In this paper, two classes of semi-bent functions are constructed by modifying the supports of two quadratic Boolean functions $f_1(x_1,x_2,cdots,x_n)=igopluslimits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+1geq3$ and $f_2(x_1,x_2,cdots,x_n)=igopluslimits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+2geq4$. Meanwhile, the algebraic normal forms of the newly constructed semi-bent functions are determined.