Journal article
Construction of bent functions via Niho power functions
Ruhr-University Bochum, Postfach 102148, 44780 Bochum, Germany1
INRIA-Projet CODES, BP 105, 78153 Le Chesnay Cedex, France2
Equipe Arithmtique Codage et Cryptographie, Universite de Limoges, France3
A Boolean function with an even number n=2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. Boolean functions of the form f(x)=tr(α1xd1+α2xd2), α1,α2,x∈F2n, are considered, where the exponents di (i=1,2) are of Niho type, i.e. the restriction of xdi on F2k is linear.
We prove for several pairs of (d1,d2) that f is a bent function, when α1 and α2 fulfill certain conditions. To derive these results we develop a new method to prove that certain rational mappings on F2n are bijective.
Language: | English |
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Year: | 2004 |
Pages: | 779-798 |
ISSN: | 10960899 and 00973165 |
Types: | Journal article |
DOI: | 10.1016/j.jcta.2005.07.009 |