Two-Message Statistically Sender-Private OT from LWE

We construct a two-message oblivious transfer (OT) protocol without setup that guarantees statistical privacy for the sender even against malicious receivers. Receiver privacy is game based and relies on the hardness of learning with errors (LWE). This flavor of OT has been a central building block for minimizing the round complexity of witness indistinguishable and zero knowledge proof systems, non-malleable commitment schemes and multi-party computation protocols, as well as for achieving circuit privacy for homomorphic encryption in the malicious setting. Prior to this work, all candidates in the literature from standard assumptions relied on number theoretic assumptions and were thus insecure in the post-quantum setting. This work provides the first (presumed) post-quantum secure candidate and thus allows to instantiate the aforementioned applications in a post-quantum secure manner. Technically, we rely on the transference principle: Either a lattice or its dual must have short vectors. Short vectors, in turn, can be translated to information loss in encryption. Thus encrypting one message with respect to the lattice and one with respect to its dual guarantees that at least one of them will be statistically hidden.