## Cryptology ePrint Archive: Report 2017/491

Laconic Oblivious Transfer and its Applications

Chongwon Cho and Nico Döttling and Sanjam Garg and Divya Gupta and Peihan Miao and Antigoni Polychroniadou

Abstract: 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 $m_{D[L]}$, where the messages $m_0, m_1$ and the location $L \in [M]$ 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 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.

Category / Keywords: public-key cryptography / Oblivious Transfer, Laconic OT, Secure Computation, Homomorphic Encryption for RAM

Original Publication (with minor differences): IACR-CRYPTO-2017

Date: received 30 May 2017, last revised 13 Jul 2017

Contact author: peihan at berkeley edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2017/491

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