Multiple characters transforms and generalized Boolean functions
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Authors
Mesnager, Sihem
Riera, Constanza
Stănică, Pantelimon
Subjects
Generalized Boolean functions
characters
bent
plateaued
characters
bent
plateaued
Advisors
Date of Issue
2019
Date
2019
Publisher
Springer
Language
en_US
Abstract
In this paper we investigate generalized Boolean functions whose spectrum is flat with respect to a set of Walsh-Hadamard transforms defined using various complex primitive roots of 1. We also study some differential properties of the generalized Boolean functions in even dimension defined in terms of these different characters. We show that those functions have similar properties to the vectorial bent functions. We next clarify the case of gbent functions in odd dimension. As a by-product of our proofs, more generally, we also provide several results about plateaued functions. Furthermore, we find characterizations of plateaued functions with respect to different characters in terms of second derivatives and fourth moments.
Type
Preprint
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
15 p.
Citation
S. Mesnager, C. Riera, P. Stanica, Multiple characters transforms and generalized Boolean functions, Cryptography & Communication - CCDS 11:6 (2019), 1247-1260.
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.