English

Length-based attacks in polycyclic groups

Group Theory 2014-11-25 v2 Cryptography and Security

Abstract

After the Anshel-Anshel-Goldfeld (AAG) key-exchange protocol was introduced in 1999, it was implemented and studied with braid groups and with the Thompson group as its underlying platforms. The length-based attack, introduced by Hughes and Tannenbaum, has been used to extensively study AAG with the braid group as the underlying platform. Meanwhile, a new platform, using polycyclic groups, was proposed by Eick and Kahrobaei. In this paper, we show that with a high enough Hirsch length, the polycyclic group as an underlying platform for AAG is resistant to the length-based attack. In particular, polycyclic groups could provide a secure platform for any cryptosystem based on conjugacy search problem such as non-commutative Diffie-Hellman, ElGamal and Cramer-Shoup key exchange protocols.

Cite

@article{arxiv.1305.0548,
  title  = {Length-based attacks in polycyclic groups},
  author = {David Garber and Delaram Kahrobaei and Ha T. Lam},
  journal= {arXiv preprint arXiv:1305.0548},
  year   = {2014}
}

Comments

J. Math. Crypt. 2014

R2 v1 2026-06-22T00:10:28.570Z