The haar analysis of nonlinearity cryptographic security criterion
One of the main security criteria that mostly influence the strength of a conventional cipher system is the Nonlinearity criterion. A classical cipher system is considered strong if it is characterized by high nonlinearity. That is, the underlying Boolean function employed within the system is req...
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The Institute of Electrical and Electronics Engineers, Inc.
2016
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| Online Access: | http://irep.iium.edu.my/55717/ http://irep.iium.edu.my/55717/ http://irep.iium.edu.my/55717/1/55717_The%20Haar%20Analysis%20of%20Nonlinearity.pdf http://irep.iium.edu.my/55717/7/55717-The%20haar%20analysis%20of%20nonlinearity%20cryptographic%20security%20criterion_SCOPUS.pdf |
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iium-557172017-03-30T08:26:56Z http://irep.iium.edu.my/55717/ The haar analysis of nonlinearity cryptographic security criterion Rafiq, Hashum M. Siddiqi, Mohammad Umar TK5101 Telecommunication. Including telegraphy, radio, radar, television One of the main security criteria that mostly influence the strength of a conventional cipher system is the Nonlinearity criterion. A classical cipher system is considered strong if it is characterized by high nonlinearity. That is, the underlying Boolean function employed within the system is required to be far from being linear. The measure of a Boolean function’s nonlinearity can be done with the help of the Walsh transform as a tool. This paper presents an analysis of the nonlinearity criterion from the Haar transform domain perspective. The paper proceeds by utilizing the connection between the Haar and the Walsh transforms. The work provides two main contributions in the form of the definition of nonlinearity given the Haar spectrum of an arbitrary Boolean function and a Haar-Walsh hybrid algorithm for measuring the nonlinearity given the Haar spectrum. The derived algorithm is then simulated along with the Walsh benchmark and the results are presented in a comparison study. The paper then follows up by presenting a discussion on the computational advantages of employing the Haar-Walsh hybrid method in terms of time and space complexities. It is shown that, the Haar-Walsh hybrid method performs better when the transformed function is characterized by high number of input variables (n > 11). The paper concludes with a summary of the presented work and suggestions for future work. The Institute of Electrical and Electronics Engineers, Inc. 2016 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/55717/1/55717_The%20Haar%20Analysis%20of%20Nonlinearity.pdf application/pdf en http://irep.iium.edu.my/55717/7/55717-The%20haar%20analysis%20of%20nonlinearity%20cryptographic%20security%20criterion_SCOPUS.pdf Rafiq, Hashum M. and Siddiqi, Mohammad Umar (2016) The haar analysis of nonlinearity cryptographic security criterion. In: 2016 International Conference on Computer & Communication Engineering ICCCE 2016, 25th-27th July 2016, Kuala Lumpur. http://ieeexplore.ieee.org/document/7808291/?reload=true |
| 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 The haar analysis of nonlinearity cryptographic security criterion |
| description |
One of the main security criteria that mostly
influence the strength of a conventional cipher system is the Nonlinearity criterion. A classical cipher system is
considered strong if it is characterized by high nonlinearity. That is, the underlying Boolean function employed within the system is required to be far from being linear. The measure of a Boolean function’s nonlinearity can be done with the help of the Walsh transform as a tool. This paper presents an analysis of the nonlinearity criterion from the Haar transform domain perspective. The paper proceeds by utilizing the connection between the Haar and the Walsh transforms. The work provides two main contributions in the form of the definition of nonlinearity given the Haar spectrum of an arbitrary Boolean function and a Haar-Walsh hybrid algorithm for measuring the nonlinearity given the Haar spectrum. The derived algorithm is then simulated along with the Walsh benchmark and the results are presented in a comparison study. The paper then follows up by presenting a discussion on the computational advantages of employing the Haar-Walsh hybrid method in terms of time and space complexities. It is shown that, the Haar-Walsh hybrid method performs better when the transformed function is characterized by high number of input variables (n > 11). The paper concludes with a summary of the presented work and suggestions for 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 |
The haar analysis of nonlinearity cryptographic security criterion |
| title_short |
The haar analysis of nonlinearity cryptographic security criterion |
| title_full |
The haar analysis of nonlinearity cryptographic security criterion |
| title_fullStr |
The haar analysis of nonlinearity cryptographic security criterion |
| title_full_unstemmed |
The haar analysis of nonlinearity cryptographic security criterion |
| title_sort |
haar analysis of nonlinearity cryptographic security criterion |
| publisher |
The Institute of Electrical and Electronics Engineers, Inc. |
| publishDate |
2016 |
| url |
http://irep.iium.edu.my/55717/ http://irep.iium.edu.my/55717/ http://irep.iium.edu.my/55717/1/55717_The%20Haar%20Analysis%20of%20Nonlinearity.pdf http://irep.iium.edu.my/55717/7/55717-The%20haar%20analysis%20of%20nonlinearity%20cryptographic%20security%20criterion_SCOPUS.pdf |
| first_indexed |
2023-09-18T21:18:41Z |
| last_indexed |
2023-09-18T21:18:41Z |
| _version_ |
1777411735010934784 |