  In this paper, we consider a scenario where a source node wishes to broadcast
two confidential messages for two respective 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 equivocation rate at the eavesdropper. We first study the general
(non-degraded) broadcast channel with confidential messages. We present an
inner bound on the secrecy capacity region for this model. The inner bound
coding scheme is based on a combination of random binning and the
Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the
broadcast channel without confidentiality constraint. We further study the
situation where the channels are degraded. For the degraded broadcast channel
with confidential messages, we present the secrecy capacity region. Our
achievable coding scheme is based on Cover's superposition scheme and random
binning. We refer to this scheme as Secret Superposition Scheme. In this
scheme, we show that randomization in the first layer increases the secrecy
rate of the second layer. This capacity region matches the capacity region of
the degraded broadcast channel without security constraint. It also matches the
secrecy capacity for the conventional wire-tap channel. Our converse proof is
based on a combination of the converse proof of the conventional degraded
broadcast channel and Csiszar lemma. Finally, we assume that the channels are
Additive White Gaussian Noise (AWGN) and show that secret superposition scheme
with Gaussian codebook is optimal. The converse proof is based on the
generalized entropy power inequality.
