Length-based attacks in polycyclic groups

TL;DR

This paper demonstrates that polycyclic groups with high Hirsch length are resistant to length-based attacks in cryptographic protocols, suggesting they are secure platforms for conjugacy search-based cryptosystems.

Contribution

It shows that polycyclic groups with high Hirsch length resist length-based attacks, offering a new secure platform for conjugacy search problem-based cryptography.

Findings

Polycyclic groups with high Hirsch length resist length-based attacks.

Polycyclic groups can secure conjugacy search-based cryptosystems.

Potential application to non-commutative cryptographic protocols.

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.