Universally Composable Adaptive Oblivious Transfer

In an oblivious transfer (OT) protocol, a Sender with messages M1, . . . ,MN and a Receiver with indices σ1, . . . , σk ∈ [1, N ] interact in such a way that at the end the Receiver obtains Mσ1 , . . . ,Mσk without learning anything about the other messages and the Sender does not learn anything about σ1, . . . , σk. In an adaptive protocol, the Receiver may obtain Mσi−1 before deciding on σi. Efficient adaptive OT protocols are interesting both as a building block for secure multiparty computation and for enabling oblivious searches on medical and patent databases. Historically, adaptive OT protocols were analyzed with respect to a “half-simulation” definition which Naor and Pinkas showed to be flawed. In 2007, Camenisch, Neven, and shelat, and subsequent other works, demonstrated efficient adaptive protocols in the full-simulation model. These protocols, however, all use standard rewinding techniques in their proofs of security and thus are not universally composable. Recently, Peikert, Vaikuntanathan and Waters presented universally composable (UC) non-adaptive OT protocols (for the 1-out-of-2 variant). However, it is not clear how to preserve UC security while extending these protocols to the adaptive k-outof-N setting. Further, any such attempt would seem to require O(N) computation per transfer for a database of size N . In this work, we present an efficient and UC-secure adaptive k-out-of-N OT protocol, where after an initial commitment to the database, the cost of each transfer is constant. Our construction is secure under bilinear assumptions in the standard model.