Existing authentication protocols to secure vehicular ad hoc networks (VANETs) raise challenges such as certificate distribution and revocation, avoidance of computation and communication bottlenecks, and reduction of the strong reliance on tamper-proof devices. This paper efficiently copes with these challenges with a decentralized group-authentication protocol in the sense that the group is maintained by each roadside unit (RSU) rather than by a centralized authority, as in most existing protocols that are employing group signatures. In our proposal, we employ each RSU to maintain and manage an on-the-fly group within its communication range. Vehicles entering the group can anonymously broadcast vehicle-to-vehicle (V2V) messages, which can be instantly verified by the vehicles in the same group (and neighboring groups). Later, if the message is found to be false, a third party can be invoked to disclose the identity of the message originator. Our protocol efficiently exploits the specific features of vehicular mobility, physical road limitations, and properly distributed RSUs. Our design leads to a robust VANET since, if some RSUs occasionally collapse, only the vehicles that are driving in those collapsed areas will be affected. Due to the numerous RSUs sharing the load to maintain the system, performance does not significantly degrade when more vehicles join the VANET; hence, the system is scalable.