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

Xiangyong ZENG  Lei HU  

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: 
DOI: 10.1093/ietfec/e88-a.1.59
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Key Cryptography
Boolean function,  nonlinearity,  algebraic degree,  balancedness,  Walsh spectrum,  

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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.