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The Algebraic Eraser (AE) is a cryptographic primitive that can be used toobscure information in certain algebraic cryptosystems. The Colored Burau KeyAgreement Protocol (CBKAP), which is built on the AE, was introduced by I.Anshel, M. Anshel, D. Goldfeld, and S. Lemieux in 2006 as a protocol suitablefor use on platforms with constrained computational resources, such as RFID andwireless sensors. In 2009 A. Myasnikov and A. Ushnakov proposed an attack onCBKAP that attempts to defeat the generalized simultaneous conjugacy searchproblem, which is the public-key computational problem underlying CBKAP. Inthis paper we investigate the effectiveness of this attack. Our findings arethat success of the attack only comes from applying it to short keys, and thatwith appropriate keys the attack fails in 100% of cases and does not pose athreat against CBKAP. Moreover, the attack makes assumptions about CBKAP thatdo not hold in practical implementations, and thus does not represent a threatto the use of CBKAP in applications.

On the cryptanalysis of the generalized simultaneous conjugacy search problem and the security of the Algebraic Eraser