Long Term Evaluation Advanced (LTE-A) is the third generation partnership project for cellular network that allows subscribers to roam into networks (i.e., the Internet and wireless connections) using spacial purpose base-stations, such as wireless access points and home node B. In such LTE-A based networks, neither base-stations, nor the Internet and wireless connections are trusted because base-stations are operated by un-trusted subscribers. Attackers may exploit these vulnerabilities to violate the privacy of the LTE-A subscribers. On the other hand, the tradeoff between privacy and authentication is another challenge in such networks. Therefore, in this paper, we propose two anonymous authentication schemes based on one-time pseudonymes and Schnorr Zero Knowledge Protocols. Instead of the international mobile subscriber identity, these schemes enable the user equipment, base-stations and mobility management entity to mutually authenticate each others and update the location of the user equipment without evolving the home subscriber server. The security analysis demonstrate that the proposed schemes thwart security and privacy attacks, such as malicious, international mobile subscriber identity catching, and tracking attacks. Additionally, our proposed schemes preserve the location privacy of user equipment since no entity except the mobility management entity and Gate-Way Mobile Location Center can link between the pseudonymes and the international mobile subscriber identity. Also attackers have no knowledge about international mobile subscriber identity. Hence, the proposed schemes achieve backward/forward secrecy. Furthermore, the performance evaluation shows that the proposed handover schemes impose a small overhead on the mobile nodes and it has smaller computation and communication overheads than those in other schemes.