On Boolean Functions Which Are Bent and Negabent

Bent functions f : Fm 2 → F2 achieve largest distance to all linear functions. Equivalently, their spectrum with respect to the Hadamard-Walsh transform is flat (i.e. all spectral values have the same absolute value). That is equivalent to saying that the function f has optimum periodic autocorrelation properties. Negaperiodic correlation properties of f are related to another unitary transform called the nega-Hadamard transform. A function is called negabent if the spectrum under the nega-Hadamard transform is flat. In this paper, we consider functions f which are simultaneously bent and negabent, i.e. which have optimum periodic and negaperiodic properties. Several constructions and classifications are presented. Keywords. bent function, Boolean function, unitary transform, Hadamard-Walsh transform, correlation.

• Type: Conference
• Year: 2007
• Where: SSC
• Authors: Matthew G. Parker, Alexander Pott
• Keywords: Cryptography, Hadamard-Walsh Transform, Nega-Hadamard Transform, SSC 2007, Unitary Transform