We propose a new anonymous fingerprinting scheme using Okamoto-Uchiyama cryptosystem [1]. In the previous schemes [2]-[4] the enciphering rate is so small that it seems very difficult to implement for any applications. In order to improve the rate, we have applied the Okamoto-Uchiyama cryptosystem for our fingerprinting protocol. As the results, a buyer can commit a fingerprint to a merchant being embedded in a digital content anonymously and efficiently, and then the amount of encrypted data is controlled in a reasonable size. The security can also be protected for both of a buyer and a merchant in our scheme.