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Public-key distance bounding protocols are well suited to defeat relay attacks in proximity access control systems when the author assume no prior shared key. At AsiaCCS 2014, Gambs, Onete, and Robert designed such a protocol with privacy protection for the prover. That is, the protocol hides the identity of the prover to active adversaries and the prover remains anonymous. In this study the author contradicts the result on this protocol by proving that an active adversary can easily identify one prover out of two possible ones. At WISEC 2013, Hermans, Peeters, and Onete proposed another protocol which is proven to protect the privacy of the prover. In this study the author complete their results and show that the protocol does not protect it in a strong sense. That is, if the adversary can corrupt the provers, then privacy is not guaranteed any more.