Cryptanalysis of Stickel’s Key Exchange Scheme

  • Vladimir Shpilrain
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


We offer cryptanalysis of a key exchange scheme due to Stickel [11], which was inspired by the well-known Diffie-Hellman protocol. We show that Stickel’s choice of platform (the group of invertible matrices over a finite field) makes the scheme vulnerable to linear algebra attacks with very high success rate in recovering the shared secret key (100% in our experiments). We also show that obtaining the shared secret key in Stickel’s scheme is not harder for the adversary than solving the decomposition search problem in the platform (semi)group.


Free Variable Braid Group Invertible Matrice Echelon Form Platform Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Garber, D., Kaplan, S., Teicher, M., Tsaban, B., Vishne, U.: Probabilistic solutions of equations in the braid group. Advances in Applied Mathematics 35, 323–334 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Ko, K.H., Lee, S.J., Cheon, J.H., Han, J.W., Kang, J., Park, C.: New public-key cryptosystem using braid groups. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 166–183. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Menezes, A.J.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)Google Scholar
  4. 4.
    Myasnikov, A.G., Shpilrain, V., Ushakov, A.: A practical attack on some braid group based cryptographic protocols. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 86–96. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Ruinskiy, D., Shamir, A., Tsaban, B.: Cryptanalysis of group-based key agreement protocols using subgroup distance functions. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 61–75. Springer, Heidelberg (2007)Google Scholar
  6. 6.
    Shpilrain, V.: Hashing with polynomials. In: Rhee, M.S., Lee, B. (eds.) ICISC 2006. LNCS, vol. 4296, pp. 22–28. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Shpilrain, V., Ushakov, A.: Thompson’s group and public key cryptography. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 151–164. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Shpilrain, V., Ushakov, A.: A new key exchange protocol based on the decomposition problem. Contemp. Math., Amer. Math. Soc. 418, 161–167 (2006)Google Scholar
  9. 9.
    Sidelnikov, V.M., Cherepnev, M.A., Yashcenko, V.Y.: Systems of open distribution of keys on the basis of noncommutative semigroups. Ross. Acad. Nauk Dokl. 332, (1993); English translation: Russian Acad. Sci. Dokl. Math. 48, 384–386 (1994) Google Scholar
  10. 10.
    Sramka, M.: On the Security of Stickel’s Key Exchange Scheme (preprint)Google Scholar
  11. 11.
    Stickel, E.: A New Method for Exchanging Secret Keys. In: Proc. of the Third International Conference on Information Technology and Applications (ICITA 2005), vol. 2, pp. 426–430 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vladimir Shpilrain
    • 1
  1. 1.Department of MathematicsThe City College of New YorkNew York

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