Bent and generalized bent Boolean functions
Authors
Stănică, Pantelimon
Martinsen, Thor
Gangopadhyay, Sugata
Singh, Brajesh Kumar
Subjects
Advisors
Date of Issue
2012-02
Date
2012-02
Publisher
Language
Abstract
In this paper, we investigate the properties of generalized bent functions defined
on Zn2
with values in Zq, where q ≥ 2 is any positive integer. We characterize the class of
generalized bent functions symmetric with respect to two variables, provide analogues of
Maiorana–McFarland type bent functions and Dillon’s functions in the generalized set up. A
class of bent functions called generalized spreads is introduced and we show that it contains
all Dillon type generalized bent functions and Maiorana–McFarland type generalized bent
functions. Thus, unification of two different types of generalized bent functions is achieved.
The crosscorrelation spectrum of generalized Dillon type bent functions is also characterized.
We further characterize generalized bent Boolean functions defined on Zn2 with values in Z4 and Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.
Type
Article
Description
Mathematics Subject Classification (2000) 94A60 · 94C10 · 06E30
The article of record as published may be found at http://dx.doi.org/10.1007/s10623-012-9622-5;
The article of record as published may be found at http://dx.doi.org/10.1007/s10623-012-9622-5;
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funding
Format
Citation
Des. Codes Cryptogr. Received: 6 July 2011 / Revised: 4 November 2011 / Accepted: 24 January 2012
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.