Key agreement over a 3-receiver broadcast channel

In this paper, we consider the problem of secret key agreement in state-dependent 3-receiver broadcast channels. In the proposed model, there are two legitimate receivers, an eavesdropper and a transmitter where the channel state information is non-causally available at the transmitter. We consider two setups. In the first setup, the transmitter tries to agree on a common key with the legitimate receivers while keeping concealed from the eavesdropper. Simultaneously, the transmitter agrees on a private key with each of the legitimate receiver that needs to be kept secret from the other legitimate receiver and the eavesdropper. For this setup, we derive inner and outer bounds on the secert key capacity region. In the second setup, we assume that a backward public channel is available betwen the receivers and the transmitter. Each legitimate receiver wishes to share a private key with the transmitter. For this setup, an outer bound on the secret key-private capacity is found when the channel state information is non-causally available at the transmitter and is shown to coincide with an inner bounf for some special cases. Furthermore, the capacity region of the secret key in the state-dependent wiretap channel can be deduced from our inner and outer bound.