A fair blind signature scheme allows the trustee to revoke blindness so that it provides authenticity and anonymity to honest users while preventing malicious users from abusing the anonymity to conduct blackmail etc. Although plausible constructions that offer efficient tricks for anonymity revocation have been published, security, especially one-more unforgeability and revocability against adaptive and parallel attacks, has not been studied well. We point out a concrete vulnerability of some of the previous schemes and present an efficient fair blind signature scheme with a security proof against most general attacks. Our scheme offers tight revocation where each signature and issuing session can be linked by the trustee.