Pairwise Key Agreement over a Generalized Multiple Access Channel: Capacity Bounds and Game-Theoretic Analysis

A pairwise key agreement between three users is considered in which each pair of the users wishes to agree on a secret key hidden from the remaining user. The three users communicate through a noisy channel where two users transmit the channel inputs and all the three users receive noisy outputs from the channel. In this setup, inner and outer bounds of the secret key capacity region are derived as well as a special case where the two bounds match. Furthermore, an achievable secret key rate region is derived for AWGN channels. In this Gaussian setup, we investigate the interaction between the two transmitting users from a game-theoretic perspective and we analyze the Nash equilibrium of the non-cooperative game considering two strategies for the transmitting users: power control and cooperative jamming. Finally we illustrate our results through numerical simulations.