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Oblivious transfer plays a fundamental role in the area of secure distributed computation. In particular, this primitive is used to search items in decentralized databases. Using a variant of smooth projective hash previously presented by Zeng , we construct a practical framework for t-out-of- n oblivious transfer in the plain model without any set-up assumption. It can be implemented under a variety of standard intractability assumptions, including the decisional Diffie-Hellman assumption, the decisional N -th residuosity assumption, the decisional quadratic residuosity assumption, and the learning with error problem. It is computationally secure in the presence of covert adversaries and only requires four rounds of communication. Compared to existing practical protocols with fully-simulatable security against covert adversaries or malicious adversaries, our framework is generally more efficient.