Network Oblivious Transfer via Noisy Channels: Limits and Capacities

TL;DR

This paper explores the fundamental limits and capacities of oblivious transfer over noisy channels, extending classical results to multi-party settings with honest or malicious participants, and introduces protocols and rate characterizations.

Contribution

It provides new information-theoretic bounds and protocols for oblivious transfer over noisy channels, including multi-party scenarios with honest or malicious parties.

Findings

Characterized oblivious transfer capacity over noisy channels.

Developed a protocol reducing multi-party channels to correlation models.

Established achievable rate regions for malicious receiver scenarios.

Abstract

In this paper, we study the information-theoretic limits of oblivious transfer via noisy channels. We also investigate oblivious transfer over a noisy multiple-access channel with two non-colluding senders and a single receiver. The channel is modeled through correlations among the parties, who may be honest-but-curious or, in the case of the receiver, potentially malicious. We first revisit the information-theoretic limits of two-party oblivious transfer and then extend these results to the multiple-access setting. For honest-but-curious participants, we introduce a multiparty protocol that reduces a general multiple access channel to a suitable correlation model. In scenarios with a malicious receiver, we characterize an achievable oblivious transfer rate region.