A Reaction Attack on a Public Key Cryptosystem Based on the Word Problem

Authors:
María Isabel González Vasco;Rainer Steinwandt
Affiliations:
Universidad de Oviedo, Departamento de Matemáticas, Spain;Arbeitsgruppe Systemsicherheit, Institut für Algorithmen und Kognitive Systeme, Germany
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2004

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Abstract

Wagner and Magyarik outlined a conceptual public key cryptosystem based on the hardness of the word problem for finitely presented groups. At the same time, they gave a specific example of such a system. We prove that in the present form their approach is vulnerable to so-called reaction attacks. In particular, for the proposed instance it is possible to retrieve the private key just by watching the performance of a legitimate recipient.