On (Im)possibility of Network Oblivious Transfer via Noisy Channels and Non-Signaling Correlations

2026-02-03

AI Summary

This work investigates the fundamental feasibility of implementing network oblivious transfer (OT) in a three-party setting with honest-but-curious participants, leveraging noisy multiple-access or broadcast channels together with arbitrary non-signaling correlations among the parties. By unifying shared resources as non-signaling boxes and integrating tools from non-signaling theory, information-theoretic security, and communication complexity, the study establishes—for the first time within a unified framework—that perfect OT is impossible in this model. Moreover, even under asymptotic repeated use of the resources, some leakage of the sender’s non-target message remains unavoidable. Notably, while receiver privacy faces no inherent limitation, the receiver’s ability to distinguish between non-target messages improves with resource reuse, thereby inevitably compromising sender privacy.

Technology Category

• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• oblivious transfer
• noisy channels
• non-signaling correlations
• information leakage
• network communication

Innovation

• network oblivious transfer
• noisy channels
• non-signaling correlations
• information leakage
• impossibility result