IEICE Trans - On the Balanced Elementary Symmetric Boolean Functions

On the Balanced Elementary Symmetric Boolean Functions

Longjiang QU  Qingping DAI  Chao LI

Publication
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
Keyword:
algebraic degree,  Boolean functions,  elementary symmetric,  balanced,

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Summary:
In this paper, we give some results towards the conjecture that σ_2^t+1l-1,2^t 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=2^m+2^t-1 where m,t (m>t) are two non-negative integers, which verified the conjecture for a large infinite class of integer n.