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On the Wagner–Magyarik Cryptosystem

  • Françoise Levy-dit-Vehel
  • Ludovic Perret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

We investigate a monoid variant of the scheme based on the word problem on groups proposed by Wagner and Magyarik at Crypto’84, that has the advantage of being immune to reaction attacks so far. We study the security of this variant. Our main result is a complexity-theoretic one: we show that the problem underlying this cryptosystem, say WM, is NP-hard. We also present an algorithm for solving WM. Its complexity permits to shed light on the size of the parameters to choose to reach a given level of security.

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References

  1. 1.
    Abisha, P.J., Thomas, D.G., Subramanian, K.G.: Public Key Cryptosystems Based on Free Partially Commutative Monoids and Groups. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 218–227. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Book, R.V.: Confluent and Other Types of Thue Systems. Journal of the ACM 29, 171–182 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Book, R.V., Liu, H.N.: Rewriting Systems and Word Problems in a Free Partially Commutative Monoid. Inform. Proc. Letters 26, 29–32 (1987/88)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cori, R., Perrin, D.: Automates et commutations partielles. R.A.I.R.O. Informatique théorique 19, 21–32 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    González-Vasco, M.I., Steinwandt, R.: A Reaction Attack on a Public Key Cryptosystem Based on the Word Problem. AAECC 14(5), 335–340 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Knuth, D.E., Bendix, P.B.: Simple Word Problems in Universal Algebras. Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, New York (1970)zbMATHGoogle Scholar
  7. 7.
    Levy-dit-Vehel, F., Perret, L.: Attacks on Public Key Cryptosystems Based on Free Partially Commutative Monoids and Groups. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 275–289. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    McNaughton, R.: Contributions of Ronald V. Book to the Theory of String Rewriting Systems. Rensselaer Polytechnic Institute T.R. n0 96 − 19 (1996)Google Scholar
  9. 9.
    Turing, A.M.: The Word Problem in Semi-groups with Cancellation. Annals of Math 52, 491–505 (1950)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Wagner, N.R., Magyarik, M.R.: A Public Key Cryptosystem Based on the Word Problem. In: Peterson, J.L. (ed.) Computer Programs for Spelling Correction. LNCS, vol. 96, pp. 19–36. Springer, Heidelberg (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Françoise Levy-dit-Vehel
    • 1
  • Ludovic Perret
    • 1
  1. 1.ENSTAParisFrance

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