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An analysis of the RC4 family of stream ciphers against algebraic attacks

Wong, Kenneth Koon-Ho, Carter, Gary, & Dawson, Ed (2010) An analysis of the RC4 family of stream ciphers against algebraic attacks. In Boyd, Colin & Susilo, Willy (Eds.) Conferences in Research and Practice in Information Technology CRPIT, Australian Computer Society, Brisbane, Australia, pp. 67-74.

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Abstract

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.

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ID Code: 34330
Item Type: Conference Paper
Additional Information: An open access copy of this article can also be accessed from the publisher's webpage - see Official URL above.
Keywords: algebraic attacks, stream ciphers, RC4, polynomial equations, boolean functions
ISBN: 978-1-920682-86-6
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Numerical Computation (080205)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > DATA FORMAT (080400) > Data Encryption (080402)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Institutes > Information Security Institute
Copyright Owner: Copyright 2010 Australian Computer Society, Inc.
Copyright Statement: This paper appeared at the Australasian Information Security Conference (AISC2010), Brisbane, Australia. Conferences in Research and Practice in Information Technology (CRPIT), Vol. 103, Colin Boyd and Willy Susilo, Ed. Reproduction for academic, not-for profit purposes permitted provided this text is included.
Deposited On: 03 Sep 2010 14:16
Last Modified: 01 Mar 2012 00:18

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