Plateaued rotation symmetric boolean functions on odd number of variables
(2005) First Workshop on Boolean Functions : Cryptography and Applications- 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:
https://lup.lub.lu.se/record/1266838
- author
- Maximov, Alexander LU ; Hell, Martin LU and Maitra, Subhamoy
- organization
- publishing date
- 2005
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- [Host publication title missing]
- editor
- Michon, Jean-Francis ; Valarcher, Pierre and Yunés, Jean-Baptiste
- publisher
- PURH
- conference name
- First Workshop on Boolean Functions : Cryptography and Applications
- conference location
- Rouen, France
- conference dates
- 2005-03-07 - 2005-03-08
- ISBN
- 2-87775-403-0
- language
- English
- LU publication?
- yes
- id
- 34afb061-b107-41b8-92ff-3a09675fc535 (old id 1266838)
- date added to LUP
- 2016-04-04 10:55:42
- date last changed
- 2018-11-21 21:01:36
@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}},
url = {{https://lup.lub.lu.se/search/files/5654325/1266839.pdf}},
year = {{2005}},
}