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

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    María Isabel González Vasco

  2. Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Systemsicherheit, Prof. Dr. Th. Beth, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Rainer Steinwandt

Authors
  1. María Isabel González Vasco
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  2. Rainer Steinwandt
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Correspondence to Rainer Steinwandt.

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Keywords: Finitely presented groups, Word problem, Public key encryption, Cryptanalysis.

Work partially supported by the projects BFM2001-3239-C03-01, GE-EXP01-08

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Vasco, M., Steinwandt, R. A Reaction Attack on a Public Key Cryptosystem Based on the Word Problem. AAECC 14, 335–340 (2004). https://doi.org/10.1007/s00200-003-0135-3

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  • DOI: https://doi.org/10.1007/s00200-003-0135-3

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