Hybrid classes of balanced Boolean functions with good cryptographic properties

Date

2014-07-20

Author

Khan, Mansoor Ahmed
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

199
views

0
downloads

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.

Subject Keywords

Boolean function, Symmetric cipher, Non-linearity, Algebraic degree, Algebraic immunity, Optimal algebraic immunity

URI

https://hdl.handle.net/11511/34731

Journal

INFORMATION SCIENCES

DOI

https://doi.org/10.1016/j.ins.2014.02.157

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Improvement in non-linearity of carlet-feng infinite class of boolean functions Khan, Mansoor Ahmed; Özbudak, Ferruh (2012-12-01) 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.
Construction of cryptographically strong boolean functions well suited for symmetric cryptosystems Ahmed Khan, Mansoor; Özbudak, Ferruh; Department of Cryptography (2013) Boolean functions are amongst the vital ingredients of any symmetric cryptosystem in order to implement principles of confusion and di usion. These are utilized as non-linear filtering functions or combiner functions in LFSR-based stream ciphers and as s-box component functions or non-linear encryption functions in Fiestel structure based block ciphers. Consequently, the cryptographic properties of Boolean functions are amongst the main contributors to the strength of these ciphers against cryptanalysis. Th...
On constructions and enumeration of bent and semi-bent functions Koçak, Neşe; Doğanaksoy, Ali; Saygı, Zülfükar; Department of Cryptography (2015) 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 ...
Generalized rotation symmetric and dihedral symmetric boolean functions - 9 variable boolean functions with nonlinearity 242 Kavut, Selcuk; Yucel, Melek Diker (2007-12-20) Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral Symmetric Boolean Functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, ...
Equivariant vector fields on three dimensional representation spheres Gürağaç, Hami Sercan; Önder, Mustafa Turgut; Department of Mathematics (2011) Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary so...

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.