Reliable, deniable and hidable communication

Alice wishes to potentially communicate covertly with Bob over a Binary Symmetric Channel while Willie the wiretapper listens in over a channel that is noisier than Bob´s. We show that Alice can send her messages reliably to Bob while ensuring that even whether or not she is actively communicating is (a) deniable to Willie, and (b) optionally, her message is also hidable from Willie. We consider two different variants of the problem depending on the Alice´s “default” behavior, i.e., her transmission statistics when she has no covert message to send: 1) When Alice has no covert message, she stays “silent”, i.e., her transmission is 0; 2) When has no covert message, she transmits “innocently”, i.e., her transmission is drawn uniformly from an innocent random codebook; We prove that the best rate at which Alice can communicate both deniably and hid ably in model 1 is O(1/√n). On the other hand, in model 2, Alice can communicate at a constant rate.