Constructing Boolean Functions by Modifying Maiorana-McFarland's Superclass Functions

Xiangyong ZENG  Lei HU 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E88-A  No.1  pp.59-66
Publication Date: 2005/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Key Cryptography
Keyword: 
Boolean function,  nonlinearity,  algebraic degree,  balancedness,  Walsh spectrum, 

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Summary: 
In this study, we construct balanced Boolean functions with a high nonlinearity and an optimum algebraic degree for both odd and even dimensions. Our approach is based on modifying functions from the Maiorana-McFarland's superclass, which has been introduced by Carlet. A drawback of Maiorana-McFarland's function is that their restrictions obtained by fixing some variables in their input are affine. Affine functions are cryptographically weak functions, so there is a risk that this property will be exploited in attacks. Due to the contribution of Carlet, our constructions do not have the potential weakness that is shared by the Maiorana-McFarland construction or its modifications.