Analysis of autocorrelation function of Boolean functions in Haar domain

Design of strong symmetric cipher systems requires that the underlying cryptographic Boolean function meet specific security requirements. Some of the required security criteria can be measured with the help of the autocorrelation function as a tool, while other criteria can be measured using the W...

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Main Authors:	Rafiq, Hashum M., Siddiqi, Mohammad Umar
Format:	Conference or Workshop Item
Language:	English English
Published:	The Institute of Electrical and Electronics Engineers, Inc. 2016
Subjects:	TK5101 Telecommunication. Including telegraphy, radio, radar, television
Online Access:	http://irep.iium.edu.my/55718/ http://irep.iium.edu.my/55718/ http://irep.iium.edu.my/55718/1/55718_Analysis%20of%20Autocorrelation%20Function.pdf http://irep.iium.edu.my/55718/7/55718_Analysis%20of%20autocorrelation%20function_Scopus.pdf

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recordtype	eprints
spelling	iium-557182017-04-21T08:37:23Z http://irep.iium.edu.my/55718/ Analysis of autocorrelation function of Boolean functions in Haar domain Rafiq, Hashum M. Siddiqi, Mohammad Umar TK5101 Telecommunication. Including telegraphy, radio, radar, television Design of strong symmetric cipher systems requires that the underlying cryptographic Boolean function meet specific security requirements. Some of the required security criteria can be measured with the help of the autocorrelation function as a tool, while other criteria can be measured using the Walsh transform as a tool. The connection between the Walsh transform and the autocorrelation function is given by the well known Wiener- Khintchine theorem. In this paper, we present an analysis of the Autocorrelation function from the Haar spectral domain. We start by presenting a brief review on Boolean functions and the Autocorrelation function. Then we exploit the analogy between the Haar and Walsh in deriving the Haar general representation of the Autocorrelation function. The derivations are carried out in two ways namely; in terms of individual spectral coefficients, and based on zones within the spectrum. The main contribution of the paper is the establishment of the link between the Haar transform and the Wiener-Khintchine theorem. This is done by deducing the connection between the Haar transform, the autocorrelation, and the Walsh power spectrum for an arbitrary Boolean function. In the process we show that, the same characteristics of the Wiener-Khintchine theorem holds locally within the Haar spectral zones, instead of globally as with the Walsh domain. The Haar general representations of autocorrelation function are given for arbitrary Boolean functions in general and Bent Boolean functions in particular. Finally, we present a conclusion of the work with a summary of findings and future work. The Institute of Electrical and Electronics Engineers, Inc. 2016-07 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/55718/1/55718_Analysis%20of%20Autocorrelation%20Function.pdf application/pdf en http://irep.iium.edu.my/55718/7/55718_Analysis%20of%20autocorrelation%20function_Scopus.pdf Rafiq, Hashum M. and Siddiqi, Mohammad Umar (2016) Analysis of autocorrelation function of Boolean functions in Haar domain. In: 2016 International Conference on Computer & Communication Engineering ICCCE 2016, 25th-27th July 2016, Kuala Lumpur. http://ieeexplore.ieee.org/document/7808292/
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	TK5101 Telecommunication. Including telegraphy, radio, radar, television
spellingShingle	TK5101 Telecommunication. Including telegraphy, radio, radar, television Rafiq, Hashum M. Siddiqi, Mohammad Umar Analysis of autocorrelation function of Boolean functions in Haar domain
description	Design of strong symmetric cipher systems requires that the underlying cryptographic Boolean function meet specific security requirements. Some of the required security criteria can be measured with the help of the autocorrelation function as a tool, while other criteria can be measured using the Walsh transform as a tool. The connection between the Walsh transform and the autocorrelation function is given by the well known Wiener- Khintchine theorem. In this paper, we present an analysis of the Autocorrelation function from the Haar spectral domain. We start by presenting a brief review on Boolean functions and the Autocorrelation function. Then we exploit the analogy between the Haar and Walsh in deriving the Haar general representation of the Autocorrelation function. The derivations are carried out in two ways namely; in terms of individual spectral coefficients, and based on zones within the spectrum. The main contribution of the paper is the establishment of the link between the Haar transform and the Wiener-Khintchine theorem. This is done by deducing the connection between the Haar transform, the autocorrelation, and the Walsh power spectrum for an arbitrary Boolean function. In the process we show that, the same characteristics of the Wiener-Khintchine theorem holds locally within the Haar spectral zones, instead of globally as with the Walsh domain. The Haar general representations of autocorrelation function are given for arbitrary Boolean functions in general and Bent Boolean functions in particular. Finally, we present a conclusion of the work with a summary of findings and future work.
format	Conference or Workshop Item
author	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_facet	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_sort	Rafiq, Hashum M.
title	Analysis of autocorrelation function of Boolean functions in Haar domain
title_short	Analysis of autocorrelation function of Boolean functions in Haar domain
title_full	Analysis of autocorrelation function of Boolean functions in Haar domain
title_fullStr	Analysis of autocorrelation function of Boolean functions in Haar domain
title_full_unstemmed	Analysis of autocorrelation function of Boolean functions in Haar domain
title_sort	analysis of autocorrelation function of boolean functions in haar domain
publisher	The Institute of Electrical and Electronics Engineers, Inc.
publishDate	2016
url	http://irep.iium.edu.my/55718/ http://irep.iium.edu.my/55718/ http://irep.iium.edu.my/55718/1/55718_Analysis%20of%20Autocorrelation%20Function.pdf http://irep.iium.edu.my/55718/7/55718_Analysis%20of%20autocorrelation%20function_Scopus.pdf
first_indexed	2023-09-18T21:18:41Z
last_indexed	2023-09-18T21:18:41Z
_version_	1777411735160881152

Analysis of autocorrelation function of Boolean functions in Haar domain

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