A separator theorem for graphs of bounded genus
Journal of Algorithms
The NP-completeness column: An ongoing guide
Journal of Algorithms
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
LINK: a system for graph computation
Software—Practice & Experience - Special issue on discrete algorithm engineering
HPCN Europe 1996 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
A proper model for the partitioning of electrical circuits
DAC '72 Proceedings of the 9th Design Automation Workshop
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Algorithms for solving linear and polynomial systems of equations over finite fields, with applications to cryptanalysis
Slid Pairs in Salsa20 and Trivium
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Cube Attacks on Tweakable Black Box Polynomials
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Speeding up Collision Search for Byte-Oriented Hash Functions
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
Algebraic Cryptanalysis
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Multilevel heuristic algorithm for graph partitioning
EvoWorkshops'03 Proceedings of the 2003 international conference on Applications of evolutionary computing
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Simulatable VRFs with applications to multi-theorem NIZK
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Two trivial attacks on TRIVIUM
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Attacking Bivium using SAT solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Algebraic attacks on clock-controlled cascade ciphers
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Algebraic attacks on combiners with memory and several outputs
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
QUAD: a practical stream cipher with provable security
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Algebraic attacks on clock-controlled stream ciphers
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Solving Trivium-based Boolean Equations Using the Method of Syllogisms
Fundamenta Informaticae - Cryptology in Progress: 10th Central European Conference on Cryptology, Będlewo Poland, 2010
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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 achieve 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.