Oblivious Transfer with Adaptive Queries

We provide protocols for the following two-party problem: One party, the sender, has N values and the other party, the receiver, would like to learn k of them, deciding which ones in an adaptive manner (i.e. the ith value may depend on the first i− 1 values). The sender does not want the receiver to obtain more than k values. This is a variant of the well known Oblivious Transfer (OT) problem and has applications in protecting privacy in various settings. We present efficient protocols for the problem that require an O(N) computation in the preprocessing stage and fixed computation (independent of k) for each new value the receiver obtains. The on-line computation involves roughly log N invocations of a 1-out-2 OT protocol. The protocols are based on a new primitive, sum consistent synthesizers.