IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)
Yu ZHOULin WANGWeiqiong WANGXiaoni DU
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2015 Volume E98.A Issue 6 Pages 1313-1319

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Abstract

The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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