In 2004, C. Park proposed an authentication protocol to provide user anonymity and untraceability in wireless mobile communication systems. The real user identities are hidden and randomized by means of error-correcting codes. In this work, it is shown that Park's protocol does not provide anonymity and untraceability. More precisely, the users real identities can be obtained easily by an eavesdropper. Furthermore, the protocol is not secure since the session key established in the authentication phase can also be obtained, breaking the confidentiality of the radio link.