Network Oblivious Transfer via Noisy Channels: Limits and Capacities
Hadi Aghaee, Bahareh Akhbari, Christian Deppe
TL;DR
This work studies the information-theoretic limits of oblivious transfer (OT), extending OT analysis to two non-colluding senders communicating with a single receiver over noisy multiple-access channels. It develops reductions to symmetric basic correlations (SBC/SU-SBC), proposes protocol constructions achieving OT correctness and security under honest-but-curious behavior, and derives capacity regions and bounds for malicious receivers in DM-MAC settings. The results include information-theoretic formulations of OT, upper and lower bounds for OT capacity over point-to-point and MAC channels, and illustrative examples on BAC/BE-MAC channels. The findings advance understanding of how channel noise enables OT in network settings and point to future work on collusion and broader MAC models in secure multiparty computation.
Abstract
In this paper, we aim to study the information-theoretical limits of oblivious transfer. This work also investigates the problem of oblivious transfer over a noisy multiple access channel involving two non-colluding senders and a single receiver. The channel model is characterized by correlations among the parties, with the parties assumed to be either honest-but-curious or, in the receiver's case, potentially malicious. At first, we study the information-theoretical limits of oblivious transfer between two parties and extend it to the multiple access channel model. We propose a multiparty protocol for honest-but-curious parties where the general multiple access channel is reduced to a certain correlation. In scenarios where the receiver is malicious, the protocol achieves an achievable rate region.