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Plateaued rotation symmetric boolean functions on odd number of variables

Maximov, Alexander LU ; Hell, Martin LU and Maitra, Subhamoy (2005) First Workshop on Boolean Functions : Cryptography and Applications In [Host publication title missing]
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
[Host publication title missing]
editor
Michon, Jean-Francis; Valarcher, Pierre; Yunés, Jean-Baptiste; ; and
publisher
PURH
conference name
First Workshop on Boolean Functions : Cryptography and Applications
ISBN
2-87775-403-0
language
English
LU publication?
yes
id
34afb061-b107-41b8-92ff-3a09675fc535 (old id 1266838)
date added to LUP
2008-11-12 12:44:15
date last changed
2016-04-16 08:33:15
@inproceedings{34afb061-b107-41b8-92ff-3a09675fc535,
  abstract     = {The class of Rotation Symmetric Boolean Functions (RSBFs) has <br/><br>
received serious<br/><br>
attention in searching functions of cryptographic significance.<br/><br>
These functions are invariant under circular translation of indices.<br/><br>
In this paper we study such functions on odd number of variables and<br/><br>
interesting combinatorial properties related to Walsh spectra of such functions<br/><br>
are revealed. In particular we concentrate on plateaued functions (functions<br/><br>
with three valued Walsh spectra) in this class and derive necessary<br/><br>
conditions for existence of balanced rotation symmetric plateaued functions.<br/><br>
As application of our result we theoretically show the non existence<br/><br>
of 9-variable, 3-resilient RSBF with nonlinearity 240 that has been posed<br/><br>
as an open question in FSE 2004. Further we show how one can make efficient<br/><br>
search in the space of RSBFs based on our theoretical results and as example<br/><br>
we complete the search for unbalanced 9-variable, 3rd order correlation<br/><br>
immune plateaued RSBFs with nonlinearity 240.},
  author       = {Maximov, Alexander and Hell, Martin and Maitra, Subhamoy},
  booktitle    = {[Host publication title missing]},
  editor       = {Michon, Jean-Francis and Valarcher, Pierre and Yunés, Jean-Baptiste},
  isbn         = {2-87775-403-0},
  language     = {eng},
  publisher    = {PURH},
  title        = {Plateaued rotation symmetric boolean functions on odd number of variables},
  year         = {2005},
}