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Cryptanalysis of the Public Key Cryptosystem Based on the Word Problem on the Grigorchuk Groups

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Cryptography and Coding (Cryptography and Coding 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2898))

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Abstract

We demonstrate that the public key cryptosystem based on the word problem on the Grigorchuk groups, as proposed by M. Garzon and Y. Zalcstein, is insecure. We do this by exploiting information contained in the public key in order to construct a key which behaves like the private key and allows successful decryption of ciphertexts. Before presenting our attack, we briefly describe the Grigorchuk groups and the proposed cryptosystem.

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References

  1. Garzon, M., Zalcstein, Y.: The Complexity of Grigorchuk Groups with Application to Cryptography. Theoretical Computer Science 88, 83–98 (1991)

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  2. Grigorchuk, R.I.: Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means. Math. USSR Izvestiya 25(2), 259–300 (1985)

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  3. Grigorchuk, R.I., Nekrashevich, V.V., Sushchanskii, V.I.: Automata, Dynamical Systems and Groups. In: Proc. of the Steklov Institute of Mathematics, vol. 231 (2000)

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  4. Hofheinz, D., Steinwandt, R.: Cryptanalysis of a Public Key Cryptosystem Based on Grigorchuk Groups (unpublished)

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  5. Wagner, N., Magyarik, M.: A Public Key Cryprosystem Based on the Word Problem. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 19–36. Springer, Heidelberg (1985)

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Authors and Affiliations

  1. Department of Mathematics, UMIST, P.O. Box 88, Sackville Street, Manchester, M60 1QD, UK

    George Petrides

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  1. George Petrides
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Editor information

Editors and Affiliations

  1. Information Security Group, Royal Holloway, University of London, TW20 0EX, Egham, Surrey, U.K.

    Kenneth G. Paterson

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© 2003 Springer-Verlag Berlin Heidelberg

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Petrides, G. (2003). Cryptanalysis of the Public Key Cryptosystem Based on the Word Problem on the Grigorchuk Groups. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_19

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  • DOI: https://doi.org/10.1007/978-3-540-40974-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20663-7

  • Online ISBN: 978-3-540-40974-8

  • eBook Packages: Springer Book Archive

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