On (Im)possibility of Network Oblivious Transfer via Noisy Channels and Non-Signaling Correlations
Hadi Aghaee, Christian Deppe, Holger Boche
TL;DR
This paper analyzes network oblivious transfer under the lens of tripartite non-signaling correlations, modeling NS resources as a shared box interacting with DM-MAC and DM-BC channels. It establishes strong impossibility results: perfect OT is unattainable and asymptotic leakage cannot be avoided when NS assistance is present, due to inherent non-signaling constraints conflicting with OT's causal structure. The results also reveal that Bob’s security is not universally guaranteed, highlighting protocol-dependent trade-offs and a causal collapse induced by NS correlations. By contrasting NS-assisted networks with nonlocal primitives like PR-boxes, the work clarifies why NS resources do not universally enhance OT capacity in networked channels, while leaving open questions for bipartite NS correlations as potential avenues for future exploration.
Abstract
This work investigates the fundamental limits of implementing network oblivious transfer via noisy multiple access channels and broadcast channels between honest-but-curious parties when the parties have access to general tripartite non-signaling correlations. By modeling the shared resource as an arbitrary tripartite non-signaling box, we obtain a unified perspective on both the channel behavior and the resulting correlations. Our main result demonstrates that perfect oblivious transfer is impossible. In the asymptotic regime, we further show that even negligible leakage cannot be achieved, as repeated use of the resource amplifies the receiver(s)'s ability to distinguish messages that were not intended for him/them. In contrast, the receiver(s)'s own privacy is not subject to a universal impossibility limitation.