Improved algebraic cryptanalysis of QUAD, Bivium and trivium via graph partitioning on equation systems
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Description
We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.
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ID Code: | 34332 | ||
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Item Type: | Chapter in Book, Report or Conference volume (Conference contribution) | ||
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Measurements or Duration: | 18 pages | ||
DOI: | 10.1007/978-3-642-14081-5_2 | ||
ISBN: | 978-3-642-14080-8 | ||
Pure ID: | 32144401 | ||
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Institutes > Information Security Institute Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
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Copyright Owner: | Copyright 2010 Springer | ||
Copyright Statement: | This is the author-version of the work. Conference proceedings published, by Springer Verlag, will be available via Lecture Notes in Computer Science http://www.springer.de/comp/lncs/ | ||
Deposited On: | 06 Sep 2010 01:31 | ||
Last Modified: | 14 May 2024 11:46 |
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