The Capacity of Oblivious Transfer with Replicated Databases and Binary Erasure Multiple Access Channel
Tianyou Pei, Wei Kang, Nan Liu · 2023
Both the oblivious transfer (OT) problem and the symmetric private information retrieval (SPIR) problem studies the scenario where a client retrieves information privately and securely from databases, i.e., the privacy of the client is protected from the databases, and the undesired information is protected from the client. The OT problem studies the case of one database plus additional noisy resources between the database and the client. The SPIR problem studies the case of multiple replicated and non-colluding databases. In this paper, we combine the two models and propose a new problem of oblivious transfer (OT) with two replicated databases and a binary erasure multiple access channel connecting the databases and the client. We first provide an upper bound on the OT capacity. We then propose a protocol which achieves the upper bound. Therefore, we obtain the capacity of OT for this model. In our achievability and converse proofs, we utilized the techniques from both traditional OT and PIR. Compared to schemes that utilizes only techniques from OT, we see a 100% increase in the achieved OT rate.