  We study the security of communication between a single transmitter and
multiple receivers in a broadcast channel in the presence of an eavesdropper.
We consider several special classes of channels. As the first model, we
consider the degraded multi-receiver wiretap channel where the legitimate
receivers exhibit a degradedness order while the eavesdropper is more noisy
with respect to all legitimate receivers. We establish the secrecy capacity
region of this channel model. Secondly, we consider the parallel multi-receiver
wiretap channel with a less noisiness order in each sub-channel, where this
order is not necessarily the same for all sub-channels. We establish the common
message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we
study a special class of degraded parallel multi-receiver wiretap channels and
provide a stronger result. In particular, we study the case with two
sub-channels two users and one eavesdropper, where there is a degradedness
order in each sub-channel such that in the first (resp. second) sub-channel the
second (resp. first) receiver is degraded with respect to the first (resp.
second) receiver, while the eavesdropper is degraded with respect to both
legitimate receivers in both sub-channels. We determine the secrecy capacity
region of this channel. Finally, we focus on a variant of this previous channel
model where the transmitter can use only one of the sub-channels at any time.
We characterize the secrecy capacity region of this channel as well.
