C -differential bent functions and perfect nonlinearity
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Authors
Stănică, Pantelimon
Gangopadhyay, Sugata
Geary, Aaron
Riera, Constanza
Tkachenko, Anton
Subjects
Boolean and p-ary function Autocorrelation
c-differential bent
Differential uniformity
Perfect and almost perfect c-nonlinearity
c-differential bent
Differential uniformity
Perfect and almost perfect c-nonlinearity
Advisors
Date of Issue
2022
Date
Publisher
Elsevier
Language
Abstract
Drawing inspiration from Nyberg’s paper (Nyberg, 1991) on perfect nonlinearity and the c-differential notion we defined in Ellingsen et al. (2020), in this paper we introduce the concept of c-differential bent functions in two different ways (thus extending Kumar et al. (1985) classical definition). We further extend the notion of perfect c-nonlinear introduced in Ellingsen et al. (2020), also in two different ways, and show that, in both cases, the concepts of c-differential bent and perfect c-nonlinear are equivalent (under some natural restriction of the parameters). Some constructions of functions with these properties are also provided; one such construction provides a large class of PcN functions with respect to all c in some subfield of the field under consideration. We also show that both our classes of 0-differential bents are supersets of permutation polynomials, and that Maiorana–McFarland bent functions are not differential bent (of the first kind).
Type
Article
Description
17 USC 105 interim-entered record; under review.
The article of record as published may be found at https://doi.org/10.1016/j.dam.2021.10.010
The article of record as published may be found at https://doi.org/10.1016/j.dam.2021.10.010
Series/Report No
Department
Applied Mathematics (MA)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funding
Pantelimon Stănică acknowledges the sabbatical support from Naval Postgraduate School from September 2020 to July 2021.
Format
12 p.
Citation
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.