Oblivious transfer (OT) protocol is a fundamental cryptographical tool and widely used as a building block of secure computation. In this work, we propose two efficient t-out-of-n oblivious transfer schemes with the designated receiver. A common advantage of the two schemes is efficient. The total computation cost of the sender and the receiver is n+2t+1 modular exponentiations in first scheme that is three-round, and the total one of the sender and receiver is n+3t modular exponentiations in second scheme that is two-round. Another advantage of both schemes is designable.
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