Continuous authentication is mainly associated with the use of biometrics to guarantee that a resource is being accessed by the same user throughout the usage period. Wireless devices can also serve as a supporting technology for continuous authentication or even as a complete alternative to biometrics when accessing proximity-based services. In modern societies, the number of mobile users has dramatically risen in recent years. In this paper, an efficient authentication scheme for distributed mobile cloud computing services is proposed. The proposed scheme provides security and convenience for mobile users to access multiple mobile cloud computing services from multiple service providers using only a single private key. The proposed scheme is based on bilinear pairing cryptosystem and dynamic nonce generation. the scheme supports mutual authentication, key exchange, user anonymity, and user untraceability. The system use smart card generator (SCG) service and cloud computing service providers. The trusted SCG serves as the secure key distributor for distributed cloud service providers and mobile clients.