Plateaued rotation symmetric boolean functions on odd number of variables
Author
Editor
- Jean-Francis Michon
- Pierre Valarcher
- Jean-Baptiste Yunés
Summary, in English
The class of Rotation Symmetric Boolean Functions (RSBFs) has
received serious
attention in searching functions of cryptographic significance.
These functions are invariant under circular translation of indices.
In this paper we study such functions on odd number of variables and
interesting combinatorial properties related to Walsh spectra of such functions
are revealed. In particular we concentrate on plateaued functions (functions
with three valued Walsh spectra) in this class and derive necessary
conditions for existence of balanced rotation symmetric plateaued functions.
As application of our result we theoretically show the non existence
of 9-variable, 3-resilient RSBF with nonlinearity 240 that has been posed
as an open question in FSE 2004. Further we show how one can make efficient
search in the space of RSBFs based on our theoretical results and as example
we complete the search for unbalanced 9-variable, 3rd order correlation
immune plateaued RSBFs with nonlinearity 240.
received serious
attention in searching functions of cryptographic significance.
These functions are invariant under circular translation of indices.
In this paper we study such functions on odd number of variables and
interesting combinatorial properties related to Walsh spectra of such functions
are revealed. In particular we concentrate on plateaued functions (functions
with three valued Walsh spectra) in this class and derive necessary
conditions for existence of balanced rotation symmetric plateaued functions.
As application of our result we theoretically show the non existence
of 9-variable, 3-resilient RSBF with nonlinearity 240 that has been posed
as an open question in FSE 2004. Further we show how one can make efficient
search in the space of RSBFs based on our theoretical results and as example
we complete the search for unbalanced 9-variable, 3rd order correlation
immune plateaued RSBFs with nonlinearity 240.
Publishing year
2005
Language
English
Publication/Series
[Host publication title missing]
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Document type
Conference paper
Publisher
PURH
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Conference name
First Workshop on Boolean Functions : Cryptography and Applications
Conference date
2005-03-07 - 2005-03-08
Conference place
Rouen, France
Status
Published
ISBN/ISSN/Other
- ISBN: 2-87775-403-0