Strong Secrecy in Pairwise Key Agreement over a Generalized Multiple Access Channel

TL;DR

This paper investigates pairwise secret key agreement over a generalized MAC without public communication, proposing schemes based on secrecy codes and induced sources, with capacity bounds and examples showing potential rate improvements.

Contribution

It introduces novel key agreement schemes for generalized MACs, providing capacity bounds and exact characterizations for specific cases, advancing secure communication methods.

Findings

Inner and outer bounds on secret-key capacity are established.

Exploiting the generalized MAC can significantly increase key rates.

Exact capacity characterization is achieved for a special case.

Abstract

This paper considers the problem of pairwise key agreement without public communication between three users connected through a generalized multiple access channel (MAC). While two users control the channel inputs, all three users observe noisy outputs from the channel and each pair of users wishes to agree on a secret key hidden from the remaining user. We first develop a "pre-generated" key-agreement scheme based on secrecy codes for the generalized MAC, in which the channel is only used to distribute pre-generated secret keys. We then extend this scheme to include an additional layer of rate-limited secret-key generation by treating the observed channel outputs as induced sources. We characterize inner and outer bounds on the strong secret-key capacity region for both schemes. For a special case of the "pre-generated" scheme, we obtain an exact characterization. We also illustrate with some binary examples that exploiting the generalized nature of the generalized MAC may lead to significantly larger key-agreement rates.