  In this paper, we consider a scenario where a source node wishes to broadcast
two confidential messages to two receivers, while a wire-tapper also receives
the transmitted signal. This model is motivated by wireless communications,
where individual secure messages are broadcast over open media and can be
received by any illegitimate receiver. The secrecy level is measured by the
equivocation rate at the eavesdropper. We first study the general
(non-degraded) broadcast channel with an eavesdropper. We present an inner
bound on the secrecy capacity region for this model. This inner bound is based
on a combination of random binning, and the Gelfand-Pinsker binning. We further
study the situation in which the channels are degraded. For the degraded
broadcast channel with an eavesdropper, we present the secrecy capacity region.
Our achievable coding scheme is based on Covers superposition scheme and random
binning. We refer to this scheme as the Secret Superposition Scheme. Our
converse proof is based on a combination of the converse proof of the
conventional degraded broadcast channel and Csiszar Lemma. We then assume that
the channels are Additive White Gaussian Noise (AWGN) and show that the Secret
Superposition Scheme with Gaussian codebook is optimal. The converse proof is
based on Costas entropy power inequality. Finally, we use a broadcast strategy
for the slowly fading wire-tap channel when only the eavesdroppers channel is
fixed and known at the transmitter. We derive the optimum power allocation for
the coding layers, which maximizes the total average rate.
