Paper 2009/343
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications
Kenneth KoonHo Wong, Gregory V. Bard, and Robert H. Lewis
Abstract
We present a novel approach for solving systems of polynomial equations via graph partitioning. The concept of a variablesharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the system of equations is actually two separate systems that can be solved individually. This can provide a significant speedup in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting a small number of vertices on the graph, the variablesharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations are separated into smaller ones of similar sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimumweight 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 to the QUAD family of stream ciphers, algebraic cryptanalysis of the stream cipher Trivium and its variants, as well as some mathematical problems in game theory and computational algebraic geometry are presented. In each of these cases, the systems of polynomial equations involved are wellsuited to our graph partitioning method, and constructive results are discussed.
Metadata
 Available format(s)
 Publication info
 Published elsewhere. submitted to a journal.
 Keywords
 Balanced vertex partitionsgraph partitioningpolynomial systems of equationsQUADTriviumresultantsalgebraic cryptanalysis.
 Contact author(s)
 bard @ fordham edu
 History
 20090714: received
 Short URL
 https://ia.cr/2009/343
 License

CC BY
BibTeX
@misc{cryptoeprint:2009/343, author = {Kenneth KoonHo Wong and Gregory V. Bard and Robert H. Lewis}, title = {Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications}, howpublished = {Cryptology ePrint Archive, Paper 2009/343}, year = {2009}, note = {\url{https://eprint.iacr.org/2009/343}}, url = {https://eprint.iacr.org/2009/343} }