In the third generation mobile telecommunication systems such as UMTS, one of the important problems for value-added services is to check the recoverability of costs used by a mobile user. Previous authentication and payment schemes for value-added services by a mobile user across multiple service domains, rely on the concept of the on-line TTP, which serves as the users certification authority. In the third generation systems with many service providers, a wide range of services, and a diverse user population, authentication mechanisms with the on-line TTP provide a far from ideal solution. In this paper we present an efficient public-key protocol for mutual authentication and key exchange designed for value-added services in the third generation mobile telecommunications systems. The proposed ticket based authentication and payment protocol provides an efficient way for VASP to check the recoverability of costs without communication with the on-line TTP Furthermore, the proposed ticket based protocol can provide anonymous service usage for a mobile user.