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

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.

💡 Research Summary

This paper investigates the fundamental limits of implementing oblivious transfer (OT) in a network setting where multiple parties communicate over noisy multiple‑access (MAC) and broadcast (BC) channels while sharing an arbitrary tripartite non‑signaling (NS) correlation. The authors model the shared resource as a general three‑party NS‑box, which captures both classical channel noise and any additional correlations that could arise from quantum or super‑quantum mechanisms. By formalizing OT over a discrete‑memoryless MAC with two senders (Alice‑1, Alice‑2) and one receiver (Bob), they define correctness (the receiver recovers the selected message), security for the senders (Bob learns nothing about the unchosen messages), and security for the receiver (the senders learn nothing about the receiver’s choice). Analogous definitions are given for the broadcast scenario with one sender and multiple receivers.

The main contributions are two impossibility results. First, perfect OT—zero error and zero information leakage—is shown to be impossible even when the parties have access to any tripartite NS‑box. The proof combines information‑theoretic arguments with the non‑signaling constraints, demonstrating that if Bob can perfectly recover his chosen message, then some mutual information must inevitably leak to the senders, contradicting the non‑signaling property. Second, the authors prove an asymptotic leakage amplification theorem: while a single use of a non‑trivial NS‑box may allow arbitrarily small leakage, repeated independent uses cause the leakage to grow exponentially, eventually making the “negligible” leakage assumption untenable. This result highlights that the mere presence of noise and non‑signaling correlations does not suffice to hide the unchosen messages in the long run.

A notable nuance is that the receiver’s privacy (the senders’ ignorance of the receiver’s choice) does not suffer from a universal impossibility bound. The paper shows that protocols can be designed such that the senders remain completely oblivious to the receiver’s selection, even when the NS‑box is shared among all three parties. This asymmetry stems from the directional nature of the non‑signaling constraints: while the receiver’s output may depend on the senders’ inputs, the senders’ outputs are independent of the receiver’s input.

The work also distinguishes between bipartite and tripartite NS‑boxes. For point‑to‑point discrete memoryless channels (DMCs) assisted by a bipartite NS‑box that includes both communicating parties, OT remains impossible. Conversely, a non‑trivial tripartite NS‑box can enlarge the capacity region of a MAC (as shown in prior work), but this enlargement does not translate into a positive OT capacity region. The authors formalize “non‑trivial” NS‑boxes as those satisfying (I(I_1,I_2;J|Y) > 0); such boxes create dependence of the receiver’s output on the joint inputs of the senders, yet this dependence is insufficient to achieve perfect OT.

In the broadcast setting, a single sender holds multiple message pairs while each receiver privately selects one. The same non‑signaling framework applies, and the impossibility of perfect OT carries over. Nevertheless, the privacy of each receiver’s choice with respect to the sender and the other receivers can still be maintained.

Overall, the paper provides a unified, information‑theoretic treatment of OT in multi‑user noisy networks augmented by general non‑signaling resources. It demonstrates that neither channel noise nor arbitrary NS correlations can overcome the fundamental barrier to perfect OT, and that repeated use of such resources inevitably amplifies any residual leakage. The results have direct implications for the design of future 6G and quantum‑enhanced communication systems, where shared noisy media and exotic correlations are expected to play a role. The authors suggest that future work should explore alternative resource models, multi‑party cryptographic primitives beyond OT, and experimental realizations of non‑signaling boxes to better understand the practical limits of network‑level information‑theoretic security.