Bootstrapped Oblivious Transfer and Secure Two-Party Function Computation

TL;DR

This paper introduces a new information-theoretic framework for secure two-party computation, extending oblivious transfer protocols to improve efficiency and privacy trade-offs, and establishes capacity bounds for these protocols.

Contribution

It proposes the notion of SFC capacity, extends string OT to sample-wise OT, and develops efficient protocols with privacy-rate trade-offs, along with capacity bounds for binary erasure channels.

Findings

Efficient, perfectly private OT protocol using binary erasure channels.

Bootstrap string OT protocol with disjoint privacy and increased rate.

Lower bounds on SFC capacity for binary erasure channels.

Abstract

We propose an information theoretic framework for the secure two-party function computation (SFC) problem and introduce the notion of SFC capacity. We study and extend string oblivious transfer (OT) to sample-wise OT. We propose an efficient, perfectly private OT protocol utilizing the binary erasure channel or source. We also propose the bootstrap string OT protocol which provides disjoint (weakened) privacy while achieving a multiplicative increase in rate, thus trading off security for rate. Finally, leveraging our OT protocol, we construct a protocol for SFC and establish a general lower bound on SFC capacity of the binary erasure channel and source.