he increasing development and progress in wireless mobile communications has attracted an important amount of attention on the security, anonymity and privacy issues. To provide secure communications over un-trusted network, authenticated key agreement protocols are crucial primitive by establishing secure session keys. Achieving secure communications between communicating entities is an important issue for mobile environment. Anonymous authentication is a means of authorizing a user without revealing his/her identification. Mobile technologies such PDAs and mobile phone systems are increasingly being deployed in mobile computing. These mobile devices have raised public concern regarding violation of privacy, anonymity and information confidentiality. Considering these concerns, there is a growing need to discover and develop techniques and methods to overcome the threats described above. In this paper we propose several protocols which enhance the authentication, security and access control in mobile computing and yet preserves the security requirements of the system. Our proposed protocols are based on different cryptographic techniques including Elliptic Curve techniques, Map-to-Curve function, Weil/bilinear pairing techniques and elliptic curve based Identity Schemes. Our proposed protocols achieve many of desirable security requirements including man-in-the-middle attack, dictionary attack, perfect forward secrecy, etc. In addition, a comparative study in terms of computational and communication load over comparably many authenticated key agreement protocol (i.e., B-SPEKE, SRP, AMP, EC-SRP, etc) is given