Vehicular networks are organized with high-mobility vehicles, which are a challenge to key agreement and secured communication among vehicles; hence, efficient cryptography schemes for lightweight ciphers are essential. Many security schemes for vehicular networks particularly take the secure propagation of traffic-related information into account. Group communication is desirable in vehicular networks, while groups of friends drive the vehicles to travel together. In this study, it is applied an asymmetric key mechanism and a group-based Elliptic Curve cryptograph to authenticate data propagation as also to individually secure group communication. The data propagation includes a flooding delay mechanism, where each vehicle participant in the propagation calculates an individual delay for propagation. As groups of vehicles move on the roadway toward same destinations, two alternative schemes of group key agreement in vehicle-to-vehicle and vehicle-to-infrastructure modes are proposed to secure group communication among the vehicles. Security analysis results present that the proposed schemes can effectively prevent malicious vehicle from participating in vehicular communications. Evaluation results show that the propagation delay mechanism can effectively reduce broadcast collision, and the delay results of the group key agreement schemes are acceptable.