Analysis of autocorrelation function of Boolean functions in Haar domain

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.

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Abstract

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.

Item Type:	Conference or Workshop Item (Plenary Papers)
Additional Information:	5072/55718
Uncontrolled Keywords:	Spectral Coefficients, Cryptographic Boolean Functions, Bent Functions, Haar/Walsh Transform, Autocorrelation Function, Rademacher Functions, Walsh Orderings, Power Spectrum
Subjects:	T Technology > TK Electrical engineering. Electronics Nuclear engineering > TK5101 Telecommunication. Including telegraphy, radio, radar, television
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Electrical and Computer Engineering
Depositing User:	Prof. Dr. Mohammad Umar Siddiqi
Date Deposited:	06 Mar 2017 17:00
Last Modified:	21 Apr 2017 16:37
URI:	http://irep.iium.edu.my/id/eprint/55718

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