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Two Constructions of Semi-Bent Functions with Perfect Three-Level Additive Autocorrelation
Deng TANG Shaojing FU Yang YANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2018/12/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section LETTER (Special Section on Signal Design and Its Applications in Communications)
Category: Cryptography and Information Security
semi-bent function, nonlinearity, algebraic degree, autocorrelation,
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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.