A self-certified implicit certificate has desirable features which are suitable for use in constrained environments such as in vehicular communication networks. An implicit certificate is shorter in length than an explicit certificate. A self-certified implicit certificate scheme allows a user to generate its private key and the associated public key. It is also desirable in vehicular communication networks to protect the privacy of drivers and preserve their anonymity. In this paper, we propose a broadcast communication protocol to preserve the anonymity of drivers using a self-certified implicit certificate scheme. We revise our previously proposed broadcast communication protocol to solve its linkability problem. In our proposed scheme, recipients of a broadcast message in Vehicle-to-Vehicle (V2V) communication networks, for example, can authenticate and validate the integrity of the message without identifying the transmitter. In case of a dispute and malicious activities, the identity of the vehicle which broadcasted the disputed message can be revealed only by a trusted authority.