IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Signal Design and Its Applications in Communications
Two Constructions of Semi-Bent Functions with Perfect Three-Level Additive Autocorrelation
Deng TANGShaojing FUYang YANG
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2018 Volume E101.A Issue 12 Pages 2402-2404

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Abstract

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.

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© 2018 The Institute of Electronics, Information and Communication Engineers
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