On the Balanced Elementary Symmetric Boolean Functions

Longjiang QU  Qingping DAI  Chao LI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.2   pp.663-665
Publication Date: 2013/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.663
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
algebraic degree,  Boolean functions,  elementary symmetric,  balanced,  

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In this paper, we give some results towards the conjecture that σ2t+1l-1,2t are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. At first, a unified and simple proof of some earlier results is shown. Then a property of balanced elementary symmetric Boolean functions is presented. With this property, we prove that the conjecture is true for n=2m+2t-1 where m,t (m>t) are two non-negative integers, which verified the conjecture for a large infinite class of integer n.