  The problem of secure broadcasting with independent secret keys is studied.
The particular scenario is analyzed in which a common message has to be
broadcast to two legitimate receivers, while keeping an external eavesdropper
ignorant of it. The transmitter shares independent secret keys of sufficiently
high rates with both legitimate receivers, which can be used in different ways:
they can be used as one-time pads to encrypt the common message, as fictitious
messages for wiretap coding, or as a hybrid of these. In this paper, capacity
results are established when the broadcast channels involving the three
receivers are degraded. If both legitimate channels are degraded versions of
the eavesdropper's channel, it is shown that the one-time pad approach is
optimal for several cases, yielding corresponding capacity expressions.
Alternatively, the wiretap coding approach is shown to be optimal if the
eavesdropper's channel is degraded with respect to both legitimate channels,
establishing capacity in this case as well. If the eavesdropper's channel is
neither the strongest nor the weakest, an intricate scheme that carefully
combines both concepts of one-time pad and wiretap coding with fictitious
messages turns out to be capacity-achieving. Finally we also obtain some
results for the general non-degraded broadcast channel.
