While Vehicular Ad-hoc Networks (VANETs) can potentially improve driver safety and traffic mangement efficiency (e.g. through timely sharing of traffic status among vehicles), security and privacy are two ongoing issues that need to be addressed. Hence, security solutions such as conditional privacy-preserving authentication (CPPA) protocols have been proposed. However, CPPA protocols are generally far from being ready for deployment in VANETs, for example due key/certificate management limitations in PKI-based protocols or intractable private key updating in ID-based protocols. Although serveral blockchain-based CPPA (BCPPA) protocols have been proposed to mitigiate these challenges, there still exist some intractabilities such as revoking private key, or frequent interactions, or requiring an idea hardware. Thus, in this paper, we are motivated to propose a novel BCPPA protocol without these existing issues. Specifically, we present a PKI-based solution (using a typical digital signature protocol, such as ECDSA) based on Ethereum (a public blockchain), which is designed to facilitate secure communication in VANETs. In other words, we combine the blockchain technology and a key derivation algorithm to realize an effective certificate management. This reduces the need for participating vehicles to store a large number of private keys. To reduce the verification time cost, our BCPPA suppotrs replacing ECDSA with modified ECDSA for batch verification or directly adopting other PKI-based signatures with batch verification. In addition to introducing the concrete design, we also present the security requirements that our BCPPA protocol can satisfy. We then implement BCPPA in the Ethereum test network (i.e. Rinkeby ) and provide simulations using VanetMobiSim and NS-2 to show its feasibility (i.e. milliseconds).