  Providing security guarantees for wireless communication is critically
important for today's applications. While previous work in this area has
concentrated on radio frequency (RF) channels, providing security guarantees
for RF channels is inherently difficult because they are prone to rapid
variations due small scale fading. Wireless optical communication, on the other
hand, is inherently more secure than RF communication due to the intrinsic
aspects of the signal propagation in the optical and near-optical frequency
range. In this paper, secure communication over wireless optical links is
examined by studying the secrecy capacity of a direct detection system. For the
degraded Poisson wiretap channel, a closed-form expression of the secrecy
capacity is given. A complete characterization of the general rate-equivocation
region is also presented. For achievability, an optimal code is explicitly
constructed by using the structured code designed by Wyner for the Poisson
channel. The converse is proved in two different ways: the first method relies
only on simple properties of the conditional expectation and basic information
theoretical inequalities, whereas the second method hinges on the recent link
established between minimum mean square estimation and mutual information in
Poisson channels.
