Secure Coordination with a Two-Sided Helper

We investigate the problem of secure source coding with a two-sided helper in a game-theoretic framework. Alice (A) and Helen (H) view iid correlated information sequences $X^n$ and $Y^n$ respectively. Alice communicates to Bob (B) at rate $R$, while H broadcasts a message to both A and B at rate $R_H$. Additionally, A and B share secret key $K$ at rate $R_0$ that is independent of $(X^n,Y^n)$. An active adversary, Eve (E) sees all communication links while having access to a (possibly degraded) version of the past information. We characterize the rate-payoff region for this problem. We also solve the problem when the link from A to B is private. Our work recovers previous results of Schieler-Cuff and Kittichokechai et al.