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...
| Main Authors: | , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English English |
| Published: |
The Institute of Electrical and Electronics Engineers, Inc.
2016
|
| Subjects: | |
| 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 |
| Summary: | 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. |
|---|