Length based attack and braid groups: Cryptanalysis of Anshel-Anshel- Goldfeld key exchange protocol

Abstract

The length based attack on Anshel-Anshel-Goldfeld commutator key-exchange protocol [1] was initially proposed by Hughes and Tannenbaum in [9]. Several attempts have been made to implement the attack [6], but none of them had produced results convincing enough to believe that attack works. In this paper we show that accurately designed length based attack can successfully break a random instance of the simultaneous conjugacy search problem for certain parameter values and argue that the public/private information chosen uniformly random leads to weak keys. © International Association for Cryptologic Research 2007.