Secure Capacity Region for Erasure Broadcast Channels with Feedback
  We formulate and study a cryptographic problem relevant to wireless: a sender, Alice, wants to transmit private messages to two receivers, Bob and Calvin, using unreliable wireless broadcast transmissions and short public feedback from Bob and Calvin. We ask, at what rates can we broadcast the private messages if we also provide (information-theoretic) unconditional security guarantees that Bob and Calvin do not learn each-other's message? We characterize the largest transmission rates to the two receivers, for any protocol that provides unconditional security guarantees. We design a protocol that operates at any rate-pair within the above region, uses very simple interactions and operations, and is robust to misbehaving users. 
L\'aszl\'o Czap and Vinod M. Prabhakaran and Suhas Diggavi and   Christina Fragouli
cs.IT math.IT