Correlation immunity and resiliency of boolean functions from haar domain perspective

The strength of any conventional cipher system relies on the underlying cryptographic Boolean functions employed in the system. The design of such systems requires that the employed Boolean functions meet specific security criteria. Two of such criteria are the correlation immunity and resiliency of...

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Main Authors:	Rafiq, Hashum M., Siddiqi, Mohammad Umar
Format:	Article
Language:	English
Published:	Asian Research Publishing Network (ARPN) 2015
Subjects:	TK5101 Telecommunication. Including telegraphy, radio, radar, television
Online Access:	http://irep.iium.edu.my/48971/ http://irep.iium.edu.my/48971/ http://irep.iium.edu.my/48971/1/jeas_1215_3156_%281%29.pdf

id	iium-48971
recordtype	eprints
spelling	iium-489712016-07-18T03:45:23Z http://irep.iium.edu.my/48971/ Correlation immunity and resiliency of boolean functions from haar domain perspective Rafiq, Hashum M. Siddiqi, Mohammad Umar TK5101 Telecommunication. Including telegraphy, radio, radar, television The strength of any conventional cipher system relies on the underlying cryptographic Boolean functions employed in the system. The design of such systems requires that the employed Boolean functions meet specific security criteria. Two of such criteria are the correlation immunity and resiliency of a given Boolean function. To determine whether such criteria are met, a designer needs the help of spectral transform tool and in this case the Walsh spectral transform. Most of the cryptographic criteria have been generalized in terms of the Walsh transform. In this paper, we present an alternative view of such criteria from the Haar spectral transform point of view. The Haar along with the Walsh are the two methods considered suitable for representing Boolean functions. The paper exploits the analogy between the two transforms to derive the Haar general representation of the correlation-immunity and the resiliency security criteria. The paper presents the Haar-based conditions on which a given Boolean function should meet to be considered correlationimmune of order k (CI(k)) or resilient of order k (R(k)). In addition, the paper presents a Haar-based algorithm for testing correlation-immunity of an arbitrary Boolean function including experimental results related to the algorithm. The results in this presentation are based on a simulation study of the Haar-based algorithm in comparison to its Walsh-counterpart. The results portray the computational advantage of the Haar method over the Walsh approach for the correlation-immunity measure. The paper includes as well, a discussion on the worst-case scenario with advantages and flexibility of the Haar method in conjunction with the lower order Walsh transform. A summary of the work is then presented in the conclusion of the paper. Asian Research Publishing Network (ARPN) 2015-12 Article PeerReviewed application/pdf en http://irep.iium.edu.my/48971/1/jeas_1215_3156_%281%29.pdf Rafiq, Hashum M. and Siddiqi, Mohammad Umar (2015) Correlation immunity and resiliency of boolean functions from haar domain perspective. ARPN Journal of Engineering and Applied Sciences, 10 (22). pp. 17232-17238. ISSN 1819-6608 http://www.arpnjournals.com/jeas/volume_22_2015.htm
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	TK5101 Telecommunication. Including telegraphy, radio, radar, television
spellingShingle	TK5101 Telecommunication. Including telegraphy, radio, radar, television Rafiq, Hashum M. Siddiqi, Mohammad Umar Correlation immunity and resiliency of boolean functions from haar domain perspective
description	The strength of any conventional cipher system relies on the underlying cryptographic Boolean functions employed in the system. The design of such systems requires that the employed Boolean functions meet specific security criteria. Two of such criteria are the correlation immunity and resiliency of a given Boolean function. To determine whether such criteria are met, a designer needs the help of spectral transform tool and in this case the Walsh spectral transform. Most of the cryptographic criteria have been generalized in terms of the Walsh transform. In this paper, we present an alternative view of such criteria from the Haar spectral transform point of view. The Haar along with the Walsh are the two methods considered suitable for representing Boolean functions. The paper exploits the analogy between the two transforms to derive the Haar general representation of the correlation-immunity and the resiliency security criteria. The paper presents the Haar-based conditions on which a given Boolean function should meet to be considered correlationimmune of order k (CI(k)) or resilient of order k (R(k)). In addition, the paper presents a Haar-based algorithm for testing correlation-immunity of an arbitrary Boolean function including experimental results related to the algorithm. The results in this presentation are based on a simulation study of the Haar-based algorithm in comparison to its Walsh-counterpart. The results portray the computational advantage of the Haar method over the Walsh approach for the correlation-immunity measure. The paper includes as well, a discussion on the worst-case scenario with advantages and flexibility of the Haar method in conjunction with the lower order Walsh transform. A summary of the work is then presented in the conclusion of the paper.
format	Article
author	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_facet	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_sort	Rafiq, Hashum M.
title	Correlation immunity and resiliency of boolean functions from haar domain perspective
title_short	Correlation immunity and resiliency of boolean functions from haar domain perspective
title_full	Correlation immunity and resiliency of boolean functions from haar domain perspective
title_fullStr	Correlation immunity and resiliency of boolean functions from haar domain perspective
title_full_unstemmed	Correlation immunity and resiliency of boolean functions from haar domain perspective
title_sort	correlation immunity and resiliency of boolean functions from haar domain perspective
publisher	Asian Research Publishing Network (ARPN)
publishDate	2015
url	http://irep.iium.edu.my/48971/ http://irep.iium.edu.my/48971/ http://irep.iium.edu.my/48971/1/jeas_1215_3156_%281%29.pdf
first_indexed	2018-09-07T06:54:55Z
last_indexed	2018-09-07T06:54:55Z
_version_	1610930764556271616

Correlation immunity and resiliency of boolean functions from haar domain perspective

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