Distributed Oblivious Transfer with Adaptive Queries

We study Distributed Oblivious Transfer (DOT) scheme in the adaptive version, which means the receiver should ask threshold number of servers to retrieve each secret, and the receiver could adaptively determine which secret would be retrieved and which servers to query. This protocol has both advantages of DOT and adaptive OT, thus inherently has good broad uses. Our first attempt to build such scheme follows the present DOT scheme and considers the semi-honest parties. The second protocol strengthens the security of the first one. It prevents potential malicious behaviors of servers, therefore it is a verifiable distributed oblivious transfer scheme with adaptive queries.