Authentication is one the important parameters in designing security for vehicular ad hoc network (VANET). Authentication protocols based on public key infrastructure (PKI), elliptical curve digital signature algorithm (ECDSA) suffer from overhead problem at the road side unit (RSU) and extracting of certificates from the trusted authority. Traditional identity-based signature scheme is used to provide the privacy and authenticate the vehicle-to-vehicle communication and vehicle-to-road side unit of the VANET. ID-based signature scheme employs elliptic curve cryptosystem form authentication process and also provides batch message verification mechanism. ECC-based traditional scheme requires 160-bit key size to encrypt the message transferred between RSU and vehicle. It requires large memory space as well as consumes more energy and leads to high communication and computational overhead. In order to overcome the above-mentioned limitation, a new lightweight privacy-aware secure authentication scheme is proposed for VANET. The proposed authentication scheme employs the advantage of hyperelliptic curve cryptosystem to sign the message transferred between RSU and vehicle. Since HECC requires lesser 80-bit key size than the traditional signature scheme, it provides greater level of security with less communication and computational overhead. It also traces the real identity of the vehicle using pseudo-identities which eliminates the process of extracting the certificates from the trusted authority. Finally, compare the performance analysis of both traditional and proposed ID-based signature scheme using the different simulation parameters. © Springer Nature Singapore Pte Ltd. 2018.