Cryptanalysis of Stickel's key exchange scheme

Authors:
Vladimir Shpilrain
Affiliations:
Department of Mathematics, The City College of New York, New York, NY
Venue:
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Year:
2008

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Abstract

We offer cryptanalysis of a key exchange scheme due to Stickel [11], which was inspired by the well-known Diffie-Hellman protocol. We show that Stickel's choice of platform (the group of invertible matrices over a finite field) makes the scheme vulnerable to linear algebra attacks with very high success rate in recovering the shared secret key (100% in our experiments). We also show that obtaining the shared secret key in Stickel's scheme is not harder for the adversary than solving the decomposition search problem in the platform (semi)group.