By using pseudo‐identity‐based signature, a conditional privacy‐preserving authentication scheme was proposed in this paper, called EECB, to solve the anonymous authentication issue in vehicular ad hoc networks. In this scheme, pseudo‐identities and the corresponding private keys are generated by the private key generator alone, which is credible and independent. So only Adding private key generators can satisfy the increasing pseudo‐identities demand. In other words, it has achieved the extensible of the scheme. However, the malicious vehicle can only be traced by trust authority. Furthermore, the protocol supports batch verification and the operation of a signature verification only needs two bilinear pairings and some point multiplication. The security of the signature scheme in EECB can be proved to be equivalent to the standard computational Diffie–Hellman problem in the random oracle. The experiment and the analysis indicated that, compared with the existing well‐known schemes, EECB has higher authentication efficiency and less communication cost. Copyright © 2017 John Wiley & Sons, Ltd.