Laconic Oblivious Transfer and Its Applications

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 D (of length M) via a short message. Subsequently, a single short message by a sender allows the receiver to learn mD[L], where the messages m0,m1 and the location L ∈ [M ] are dynamically chosen by the sender. All prior constructions of OT required the receiver’s outgoing message to grow with D. Our key contribution is an instantiation of this primitive based on the Decisional DiffieHellman (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. ∗Research supported by a postdoc fellowship of the German Academic Exchange Service (DAAD). †Research supported in part from 2017 AFOSR YIP Award, DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, NSF CRII Award 1464397, and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). The views expressed are those of the author and do not reflect the official policy or position of the funding agencies. ‡Work done while at University of California, Berkeley. §Part of the work done while visiting University of California, Berkeley. Research supported in part the National Science Foundation under Grant No. 1617676, IBM under Agreement 4915013672, and the Packard Foundation under Grant 2015-63124.