Cryptanalysis of a non-commutative key exchange protocol

TL;DR

This paper presents a polynomial-time attack on certain non-commutative key exchange protocols, demonstrating their vulnerabilities and reducing the security of a patented system to factoring.

Contribution

It introduces a new efficient attack method on non-commutative key exchange protocols and links the security of a patented system to the factoring problem.

Findings

The attack breaks variants of the protocols in polynomial time.

Breaking the patented cryptosystem reduces to factoring.

The attack is demonstrated with efficiency examples.

Abstract

In the papers by Alvarez et al. and Pathak and Sanghi a non-commutative based public key exchange is described. A similiar version of it has also been patented (US7184551). In this paper we present a polynomial time attack that breaks the variants of the protocol presented in the two papers. Moreover we show that breaking the patented cryptosystem US7184551 can be easily reduced to factoring. We also give some examples to show how efficiently the attack works.