Due to the burden at a trusted center, a decentralized fingerprinting system has been proposed by delegating authority to an authorized server so that the center does not participate in the tracing protocol. As a fingerprinting code is used to retain a collusion resistance, the calculation of correlation score for each user is required to identify illegal users from a pirated copy. Considering the secrecy of code parameters, the computation must be executed by a seller in an encrypted domain to realize the decentralized tracing protocol. It requires much computational costs as well as the communication costs between the center and a seller because encrypted database (DB) is necessary for the computation. In this paper, we propose a method to reduce such costs by using the EIGamal cryptosystem over elliptic curve instead of the Paillier cryptosystem used in the conventional scheme. Our experimental results indicate that the time consumption becomes almost 100 times shorter and the size of encrypted DB reduced by a factor of 7/32 under 112-bit security level. The encrypted DB is further compressed by introducing an index table.