On the Construction of Boolean Functions with Optimal Algebraic Immunity Based on Factorization of Numbers of Variables

Huajin CHEN  Wenfeng Qi  Chuangui MA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.1   pp.15-24
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.15
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Key Cryptography
Boolean function,  algebraic attack,  algebraic immunity,  balancedness,  nonlinearity,  

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In this paper, we put forward a new method to construct n-variable Boolean functions with optimal algebraic immunity based on the factorization of n. Computer investigations for small values of n indicate that a class of Boolean functions constructed by the new method has a very good nonlinearity and also a good behavior against fast algebraic attacks.