The illegal copying and redistribution of digitally-stored information is a crucial problem to distributors who electronically sell digital data. Fingerprinting provides a means which a copyright owner can trace illegal redistributors of electronic information. Various fingerprinting schemes have appeared as techniques for copyright protection from symmetric fingerprinting by Boneh and Shaw [3], asymmetric fingerprinting by Pfitzmann and Schunter [14], and anonymous fingerprinting by Pfitzmann and Waidner [15]. In most of previous schemes, the computational capability of clients has been assumed to roughly be equal to each other and even to their servers. In particular, the key size of known algorithms for fingerprinting schemes keeps back from their practical implementation. In this paper, we propose a scheme for anonymous fingerprinting based on the bilinear Diffie-Hellman problem and prove its security. Our scheme exhibits all computations are performed more efficiently than previous schemes and the key size is quite reasonable for practical use.