Hybrid classes of balanced Boolean functions with good cryptographic properties

Khan, Mansoor Ahmed
Özbudak, Ferruh
Cryptographically strong Boolean functions play an imperative role in the design of almost every modern symmetric cipher. In this context, the cryptographic properties of Boolean functions, such as non-linearity, algebraic degree, correlation immunity and propagation criteria, are critically considered in the process of designing these ciphers. More recently, with the emergence of algebraic and fast algebraic attacks, algebraic immunity has also been included as an integral property to be considered. As a result, several constructions of Boolean functions with high non-linearity, maximal algebraic degree and optimal algebraic immunity have been devised since then. This paper focuses on some of these constructions and presents two hybrid classes of Boolean functions. The functions constructed within these classes possess maximal algebraic degree for balanced functions, optimal algebraic immunity, high non-linearity and good resistance to algebraic and fast algebraic attacks. A hybrid class of 1-resilient functions has also been proposed that also possesses high algebraic degree, optimal algebraic immunity, high non-linearity and good resistance to algebraic and fast algebraic attacks. (c) 2014 Elsevier Inc. All rights reserved.


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In this paper we present a Walsh spectrum based method derived from the genetic hill climbing algorithm to improve the non-linearity of functions belonging to Carlet-Feng infinite class of Boolean functions, without degrading other cryptographic properties they possess. We implement our modified algorithms to verify the results and also present a comparison of the resultant cryptographic properties with the original functions.
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Bent and semi-bent functions play an important role in cryptography and coding theory. They are widely studied as parts of building blocks in symmetric key cryptosystems because they provide resistance to fast correlation attacks and linear cryptanalysis due to their high nonlinearity. Besides, they can possess other desirable cryptographic properties such as low autocorrelation, propagation criteria, resiliency and high algebraic degree. Therefore, parallel to the advances in cryptanalysis techniques, the ...
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Sulak, Fatih; Doğanaksoy, Ali; Department of Cryptography (2006)
In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.
Citation Formats
M. A. Khan and F. Özbudak, “Hybrid classes of balanced Boolean functions with good cryptographic properties,” INFORMATION SCIENCES, pp. 319–328, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34731.