On Boolean functions which are bent and negabent

Authors:
Matthew G. Parker;Alexander Pott
Affiliations:
The Selmer Center, Department of Informatics, University of Bergen, Bergen, Norway;Institute for Algebra and Geometry, Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany
Venue:
SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Year:
2007

Citing 5
Cited 6

Designs and their codes

Designs and their codes
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar

Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Quaternary constant-amplitude codes for multicode CDMA

IEEE Transactions on Information Theory
One and two-variable interlace polynomials: a spectral interpretation

WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Generalized Bent Criteria for Boolean Functions (I)

IEEE Transactions on Information Theory

Negabent Functions in the Maiorana---McFarland Class

SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On quadratic approximations in block ciphers

Problems of Information Transmission
On the Symmetric Negabent Boolean Functions

INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Nega-hadamard transform, bent and Negabent functions

SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Characterizing negabent boolean functions over finite fields

SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
The selfnegadual properties of generalised quadratic Boolean functions

Designs, Codes and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bent functions f : F2m → 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.