Highly Nonlinear Vector Boolean Functions

Takashi SATOH  Kaoru KUROSAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.5   pp.807-814
Publication Date: 1999/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Boolean function,  bent function,  balancedness,  nonlinearity,  

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In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF(2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlinearity achieved by any previous construction method for (n,m)-functions. Finally, our basic method is developed to construct an (n,m)-bent function and discuss its maximum algebraic degree.