Several Classes of Even-Variable Balanced Boolean Functions with Optimal Algebraic Immunity

Chik-How TAN  Siong-Thye GOH  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.1   pp.165-171
Publication Date: 2011/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.165
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Mathematics
Keyword: 
cryptography,  boolean function,  optimal algebraic immunity,  nonlinearity,  

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Summary: 
In this paper, we constructed six infinite classes of balanced Boolean functions. These six classes of Boolean functions achieved optimal algebraic degree, optimal algebraic immunity and high nonlinearity. Furthermore, we gave the proof of the lower bound of the nonlinearities of these balanced Boolean functions and proved the better lower bound of nonlinearity for Carlet-Feng's Boolean function.