Broadcasting Private Messages Securely

Consider a source, Alice, broadcasting private messages to multiple receivers through a broadcast erasure channel; users send back to Alice public feedback that she causally uses to decide the coding strategy for her following transmissions. Recently, the multiple unicast capacity region for this problem has been exactly characterized for a number of special cases; namely the 2-user, 3-user, symmetric K-user, and one-sidedly fair K-user [1], [2]. In this paper, we show that for all the cases where such characterizations exist, we can also optimally characterize the "secure" communication rates, where the message that Alice transmits to each user is information theoretically secure from the other users, even if these collude. We show that a simple, two-phase strategy, where appropriate amounts of secret keys are first generated and then consumed, matches a new outer bound we derive.