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.