Murphy, S. and Paterson, Maura B. (2009) Geometric ideas for cryptographic equation solving in even characteristic. In: Parker, M.G. (ed.) Cryptography and Coding. Lecture Notes in Computer Science 5921. Berlin, Germany: Springer, pp. 202-221. ISBN 9783642108679.
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Abstract
The GeometricXL algorithm is a geometrically invariant version of the XL algorithm that uses polynomials of a much smaller degree than either a standard Groebner basis algorithm or an XL algorithm for certain multivariate equation systems. However, the GeometricXL algorithm as originally described is not well-suited to fields of even characteristic. This paper discusses adaptations of the GeometricXL algorithm to even characteristic, in which the solution to a multivariate system is found by finding a matrix of low rank in the linear span of a collection of matrices. These adaptations of the GeometricXL algorithm, termed the EGHAM process, also use polynomials of a much smaller degree than a Groebner basis or an XL algorithm for certain equation systems. Furthermore, the paper gives a criterion which generally makes a Groebner basis or standard XL algorithm more efficient in many cryptographic situations.
Metadata
| Item Type: | Book Section |
|---|---|
| Additional Information: | 12th IMA International Conference, Cryptography and Coding 2009, Cirencester, UK, December 15-17, 2009. Proceedings |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Maura Paterson |
| Date Deposited: | 11 Jan 2013 15:51 |
| Last Modified: | 29 Jul 2025 03:51 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/5352 |
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