VANET (Vehicular Ad hoc NETwork) is a subgroup of MANET (Mobile Ad hoc NETwork) where the nodes refer to vehicles. Vehicular ad hoc network first divides the precinct into several domains, in which Road Side Units (RSUs) are responsible for distributing group private keys and managing vehicles in a localized manner. Then, use a Hash Message Authentication Code (HMAC) to avoid time consuming CRL checking and to ensure the integrity of messages before batch group authentication. Cooperative message authentication scheme is used to reduce the authentication burden. The scheme is more efficient in terms of authentication speed, when keeping conditional privacy in VANETs.