Laconic Oblivious Transfer and its Applications - Cho, Chongwon; Doettling, Nico; Garg, Sanjam; Gupta, Divya; Miao, Peihan; Polychroniadou, Antigoni (CRYPTO, 2017)
In this work, we introduce a novel technique for secure computation over large inputs. Specifically, we provide a new oblivious transfer (OT) protocol with a laconic receiver. Laconic OT allows a receiver to commit to a large input (of length ) via a short message. Subsequently, a single short message by a sender allows the receiver to learn m_[D[L]], where the messages and the location are dynamically chosen by the sender. All prior constructions of OT required the receiver's outgoing message to grow with . Our key contribution is an instantiation of this primitive based on the Decisional Diffie-Hellman (DDH) assumption in the common reference string (CRS) model. The technical core of this construction is a novel use of somewhere statistically binding (SSB) hashing in conjunction with hash proof systems. Next, we show applications of laconic OT to non-interactive secure computation on large inputs and multi-hop homomorphic encryption for RAM programs.