Reliable deniable communication: Hiding messages in noise

Alice may wish to reliably send a message to Bob over a binary symmetric channel (BSC) while ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie observes a “significantly noisier” transmission than Bob does, he should be unable to estimate even whether Alice is transmitting or not. Even when Alice's (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over n channel uses Alice can transmit a message of length O(√n) bits to Bob, deniably from Willie. We also prove information-theoretically order-optimality of our results.