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Security analysis of word problem-based cryptosystems

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Abstract

We investigate two schemes based on the word problem on groups. From a complexity-theoretic point of view, we show that the problems underlying those schemes are equivalent. We then present a reaction attack on one of the schemes, thus easily transposed to the other. The attack, besides its efficiency, permits to recover an equivalent secret key.

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References

  1. Abisha P.J., Thomas D.G., Subramanian K.G.: Public key cryptosystems based on free partially commutative monoids and groups. In: Proceedings of INDOCRYPT 2003, LNCS, vol. 2904, pp. 218–227. Springer, Berlin, Heidelberg (2003).

  2. Book R.V.: Confluent and other types of thue systems. J. ACM29, 171–182 (1982)

    Article MATH MathSciNet  Google Scholar 

  3. Book R.V., Otto F.: String-Rewriting Systems. Texts and Monographs in Computer Science. Springer-Verlag, New York (1993).

  4. González-Vasco M.I., Steinwandt R.: Pitfalls in public key systems based on free partially commutative monoids and groups. Appl. Math. Lett.19(10), 1037–1041 (2006)

    Article MATH MathSciNet  Google Scholar 

  5. González-Vasco M.I., Steinwandt R.: A reaction attack on a public key cryptosystem based on the word problem. Appl. Algebra Eng. Commun. Comput.14(5), 335–340 (2004)

    Article MATH  Google Scholar 

  6. Levy-dit-Vehel F., Perret L.: On the Wagner–Magyarik cryptosystem. Revised Selected Papers of WCC 2005 Conference, LNCS, vol. 3969, pp. 316–329. Springer, Berlin (2006).

  7. Novikov P.S.: On the algorithmic unsolvability of the word problem in group theory. Trudy Mat. Inst. Steklov44, 1–143 (1955)

    Google Scholar 

  8. Wagner N.R., Magyarik M.R.: A public key cryptosystem based on the word problem. In: Proceedings of CRYPTO’84, LNCS, vol. 96, pp. 19–36. Springer-Verlag, Berlin.

  9. Wrathall C.: The word problem for free partially commutative groups. J. Symb. Comput.6, 99–104 (1988)

    Article MATH MathSciNet  Google Scholar 

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Authors and Affiliations

  1. ENSTA, 32 Boulevard Victor, 75739, Paris Cedex 15, France

    Françoise Levy-dit-Vehel

  2. LIP6/INRIA/SALSA, University Paris 6, Site Passy-Kennedy 104 avenue du Président Kennedy, 75016, Paris, France

    Ludovic Perret

Authors
  1. Françoise Levy-dit-Vehel

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  2. Ludovic Perret

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Correspondence toFrançoise Levy-dit-Vehel.

Additional information

Communicated by P. Wild.

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Levy-dit-Vehel, F., Perret, L. Security analysis of word problem-based cryptosystems.Des. Codes Cryptogr.54, 29–41 (2010). https://doi.org/10.1007/s10623-009-9307-x

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