Since message forgery or alteration in VANET may cause severe consequences, authentication of critical messages must be provided. However, using normal digital signature may infringe privacy of drivers. Therefore, VANET requires authentication systems that provide conditional anonymity. In this paper, we propose a new authentication system for VANET. In our proposed system, each vehicle can update its pseudonym using re-encryption technique and digitally sign messages using representation problem on the pseudonym. By limiting the usage period, revocation of individual pseudonym is not required. Moreover, we also provide a way to revoke the vehicle itself. Secureness of our system partially rely on the usage of tamper-resistance hardware.