International Workshop on Public Key Cryptography

PKC 2006: Public Key Cryptography - PKC 2006 pp 302-314

Random Subgroups of Braid Groups: An Approach to Cryptanalysis of a Braid Group Based Cryptographic Protocol

  • Alexei Myasnikov
  • Vladimir Shpilrain
  • Alexander Ushakov
Conference paper

DOI: 10.1007/11745853_20

Volume 3958 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Myasnikov A., Shpilrain V., Ushakov A. (2006) Random Subgroups of Braid Groups: An Approach to Cryptanalysis of a Braid Group Based Cryptographic Protocol. In: Yung M., Dodis Y., Kiayias A., Malkin T. (eds) Public Key Cryptography - PKC 2006. PKC 2006. Lecture Notes in Computer Science, vol 3958. Springer, Berlin, Heidelberg

Abstract

Motivated by cryptographic applications, we study subgroups of braid groups Bn generated by a small number of random elements of relatively small lengths compared to n. Our experiments show that “most” of these subgroups are equal to the whole Bn, and “almost all” of these subgroups are generated by positive braid words. We discuss the impact of these experimental results on the security of the Anshel-Anshel-Goldfeld key exchange protocol [2] with originally suggested parameters as well as with recently updated ones.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexei Myasnikov
    • 1
  • Vladimir Shpilrain
    • 2
  • Alexander Ushakov
    • 3
  1. 1.Department of MathematicsMcGill UniversityQuebec
  2. 2.Department of MathematicsThe City College of New YorkNew York
  3. 3.Department of MathematicsStevens Institute of TechnologyHoboken