Treffer: A Maiorana-McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity > 2n-1 - 2n/2 + 2n/2-2

Title:
A Maiorana-McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity > 2n-1 - 2n/2 + 2n/2-2
Authors:
MAITRA, Subhamoy, PASALIC, Enes
Source:
Coding and cryptographyDiscrete applied mathematics. 154(2):357-369
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 31 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Ordre, treillis, structures algébriques ordonnées, Order, lattices, ordered algebraic structures, Borne supérieure, Upper bound, Cota superior, Combinatoire, Combinatorics, Combinatoria, Fonction autocorrélation, Autocorrelation function, Función autocorrelación, Fonction booléenne, Boolean function, Función booliana, Fonction n variables, N variable function, Función n variables, Non linéarité, Nonlinearity, No linealidad, Elasticité, Resiliency, Autocorrelation
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Applied Stutistics Unit, Indiun Statistical Institute, 203 B.T. Road, Kolkata 700 108, India
INRIA, projet CODES, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay, France
ISSN:
0166-218X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17520332
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17520332
Database:
PASCAL Archive

Weitere Informationen

In this paper, we present a construction method of m-resilient Boolean functions with very high nonlinearity for low values of m. The construction only considers functions in even number of variables n. So far the maximum nonlinearity attainable by resilient functions was 2n-1 - 2n/2 + 2n/2-2. Here, we show that given any m, one can construct n-variable, m-resilient functions with nonlinearity 2n-1 - 11·2n/2-4 for all n ≥ 8m + 6 which is strictly greater than 2n-1 - 2n/2 + 2n/2-2. We also demonstrate that in some specific cases one may get such nonlinearity even for some values of n, where n < 8m +6. Further, we show that for sufficiently large n, it is possible to get such functions with nonlinearity reaching almost 2n-1 - 2n/2 + 4 32n/2-2. This is the upper bound on nonlinearity when one uses our basic construction recursively. Lastly, we discuss the autocorrelation property of the functions and show that the maximum absolute value in the autocorrelation spectra is ≤ 2n-3.