Two provably secure k-out-of-n oblivious transfer schemes

Oblivious transfer (OT) is a fundamental cryptographic tool. In a k-out-of-n oblivious transfer (OT) model, one party Alice (the sender) sends n bits to another party Bob (the receiver), Bob can get only k bits from n bits. However, Alice cannot know which k bits Bob received. In this paper, we propose two efficient k-out-of-n oblivious transfer schemes, which are proved security without using random oracle. At the same time, security of the two schemes is based on DDH assumption. As efficiency of computation and communication, the cost of communication and computation of the receiver is independent of number n of messages; a prominent advantage is that the sender only computes one exponentiation in the second oblivious transfer scheme. To the best of my knowledge, it is least computation in the oblivious transfer available.