This paper proposes an anonymous fingerprinting scheme based on the additively homomorphic public key cryptosystems. The proposed fingerprinting scheme enables the merchant to identify the illegal distributors without the help of a trusted third party when he/she finds an illegally redistributed fingerprinted copy. Furthermore, it allows two-party trials, i.e. there is no need for the accused (and possibly innocent) buyer to take part in the dispute resolution protocol and reveal his/her secrets. In addition, the problem of how to construct the anonymous public key and private key pairs is also addressed in the scheme. The security analysis shows that the proposed scheme is secure for both seller and buyer, and has the properties of anonymity and unlinkability for the buyer.