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Cryptanalysing variants of Stickel’s key agreement scheme. (English) Zbl 1211.94033
Summary: Stickel’s key agreement scheme was successfully cryptanalysed by V. Shpilrain [in: Computer science — theory and applications. Third international computer science symposium in Russia, CSR 2008 Moscow, Russia, June 7–12, 2008. Proceedings. Lect. Notes Comput. Sci. 5010, 283–288 (2008; Zbl 1142.94360)] when GL($$n, q)$$ is used as a platform. Shpilrain suggested the algebra of all (not necessarily invertible) $$n \times n$$ matrices defined over some finite ring $$R$$ would make a more secure platform. He also suggested a more general method of generating keys, involving polynomials of matrices over $$R$$. When $$R = \mathbb F_q$$, we show that these variants of Stickel’s scheme are susceptible to a linear algebra attack. We discuss other natural candidates for $$R$$, and conclude that until a suitable ring is proposed, the variant schemes may be considered insecure.

##### MSC:
 94A60 Cryptography
##### Keywords:
cryptanalysis; group-based cryptography
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##### References:
 [1] DOI: 10.1006/jsco.1996.0125 · Zbl 0898.68039
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