Constructing and Counting Boolean Functions on Even Variables with Maximum Algebraic Immunity

Yuan LI
Haibin KAN

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.3    pp.640-643
Publication Date: 2010/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.640
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Boolean functions,  algebraic attack,  algebraic immunity,  construction,  lower bound,  

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A method to construct Boolean functions with maximum algebraic immunity have been proposed in . Based on that method, we propose a different method to construct Boolean functions on even variables with maximum algebraic immunity in this letter. By counting on our construction, a lower bound of the number of such Boolean functions is derived, which is the best among all the existing lower bounds.