Two Constructions of Semi-Bent Functions with Perfect Three-Level Additive Autocorrelation

Deng TANG  Shaojing FU  Yang YANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2402-2404
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2402
Type of Manuscript: Special Section LETTER (Special Section on Signal Design and Its Applications in Communications)
Category: Cryptography and Information Security
Keyword: 
semi-bent function,  nonlinearity,  algebraic degree,  autocorrelation,  

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Summary: 
Semi-bent functions have very high nonlinearity and hence they have many applications in symmetric-key cryptography, binary sequence design for communications, and combinatorics. In this paper, we focus on studying the additive autocorrelation of semi-bent functions. We provide a lower bound on the maximum additive autocorrelation absolute value of semi-bent functions with three-level additive autocorrelation. Semi-bent functions with three-level additive autocorrelation achieving this bound with equality are said to have perfect three-level additive autocorrelation. We present two classes of balanced semi-bent functions with optimal algebraic degree and perfect three-level additive autocorrelation.