Abstract. An oblivious signature with n keys (or messages) is a signature that the recipient can choose one of n keys (or messages) to get signed while the signer cannot find out on which key (or message) the recipient has got the signature. This kind of signature is firstly introduced by L. Chen in 1994. However, the previous reference does not crisply formalize the notion. Furthermore, the proposed constructions are less efficient in both communication and computation. In this paper, we first give formal definitions on the model of oblivious signatures. Then, based on the Schnorr signature, we propose our efficient oblivious signature scheme. A comparison result is also provided in this paper which shows that our scheme is more efficient than Chen's schemes and those using a combination of a signature scheme and an oblivious transfer protocol. Key words: 1-out-of-n signature, oblivious signature, oblivious transfer, Schnorr signature.