Multi-terminal Secrecy in a Linear Non-coherent Packetized Networks

We consider a group of m+1 trusted nodes that aim to create a shared secret key K over a network in the presence of a passive eavesdropper, Eve. We assume a linear non-coherent network coding broadcast channel (over a finite field F_q) from one of the honest nodes (i.e., Alice) to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is also overheard by Eve. For this setup, we propose upper and lower bounds for the secret key generation capacity assuming that the field size q is very large. For the case of two trusted terminals (m = 1) our upper and lower bounds match and we have complete characterization for the secrecy capacity in the large field size regime.

💡 Research Summary

The paper investigates the problem of generating a common secret key among a group of m + 1 trusted terminals that communicate over a linear non‑coherent network‑coding broadcast channel in the presence of a passive eavesdropper, Eve. The model assumes that a single honest node (Alice) broadcasts packets to the remaining m trusted nodes and to Eve using random linear transformations over a finite field F_q. The transformation matrix changes independently from one transmission to the next and is unknown to all receivers, which is the essence of the “non‑coherent” assumption. In addition to the broadcast channel, all parties have access to a cost‑free public discussion channel that is fully observable by Eve. The goal is to determine the secret‑key generation capacity, i.e., the maximum rate at which the trusted nodes can agree on a key K while guaranteeing that Eve’s mutual information I(K; Z, Φ) with the key (where Z denotes her observations from the broadcast and Φ her view of the public discussion) is asymptotically negligible.

The authors first derive an information‑theoretic converse (upper bound). By applying Fano’s inequality, the data‑processing inequality, and the secrecy constraint, they show that any achievable key rate must satisfy

 C_s ≤