Device-to-Device (D2D) communication is mainly launched by the transmission requirements between devices for specific applications such as Proximity Services in Long-Term Evolution Advanced (LTE-A) networks, and each application will form a group of devices for the network-covered and network-absent D2D communications. Although there are many privacy concerns in D2D communication, they have not been well-addressed in current communication standards. This work introduces network-covered and network-absent authenticated key exchange protocols for D2D communications to guarantee accountable group anonymity, end-to-end security to network operators, as well as traceability and revocability for accounting and management requirements. We formally prove the security of those protocols, and also develop an analytic model to evaluate the quality of authentication protocols by authentication success rate in D2D communications. Besides, we implement the proposed protocols on android mobile devices to evaluate the computation costs of the protocols. We also evaluate the authentication success rate by the proposed analytic model and prove the correctness of the analytic model via simulation. Those evaluations show that the proposed protocols are feasible to the performance requirements of D2D communications.