Secret message capacity of erasure broadcast channels with feedback

We characterize the secret message capacity of a wiretapped erasure channel where causal channel state informa- tion of the honest nodes is publicly available. In doing so, we establish an intimate connection between message secrecy and secret key generation for the same channel setup. We propose a linear coding scheme that has polynomial encoding/decoding complexity, and prove a converse that shows the optimality of our scheme. Our work also demonstrates the value of causal public feedback, which has previously been shown for the secret key generation problem.