Recently group-oriented applications over unsecure open networks such as Internet or wireless networks have become very popular.Thus, group communication security over unsecure open networks has become a vital concern. Group key establishment (GKE) protocols are used to satisfy the confidentiality requirement of a newly started communication session by the generation or sharing of an ephemeral common key between the group members. In this study, we analyze the computation and communication efficiency of GKE protocols. Besides confidentiality, the security characteristics of identification and integrity control are also required for all steps of the protocol implementations. Thus, the main contribution of this work is to provide the computation and communication efficiency analysis of the same GKE protocols along with the identification of the group entities and integrity control of messages during the protocol steps. The specific implementation and analysis of GKE protocols are performed by group key agreement (GKA) with pairing based cryptography and group key distribution (GKD) with verifiable secret sharing, respectively. Finally, a comparison of GKA and GKD protocols on the basis of their strong points and cost characteristics are also provided to inform potential users.