Fingerprinting is an emerging technology to protect multimedia data from piracy, where each distributed copy is labelled with unique identification information. To protect the rights of both the merchant and the customer, the fingerprinting is designed to be asymmetric, where the merchant can trace the traitor by means of the embedded fingerprint and the customer is immune to being framed due to the asymmetric property. This paper proposes an asymmetric fingerprinting scheme that is efficient from the bandwidth usage point of view, where a one-out-of-two oblivious transfer protocol is used to achieve the asymmetric property. In our scheme, symmetric encryption instead of public-key encryption, is performed on the multimedia data, which can reduce the complexity and communication cost. In addition, multicast that is an efficient transport technology for one-to-many communication is exploited, which can reduce the bandwidth usage significantly.