  We study the index coding problem in the presence of an eavesdropper, where
the aim is to communicate without allowing the eavesdropper to learn any single
message aside from the messages it may already know as side information. We
establish an outer bound on the underlying secure capacity region of the index
coding problem, which includes polymatroidal and security constraints, as well
as the set of additional decoding constraints for legitimate receivers. We then
propose a secure variant of the composite coding scheme, which yields an inner
bound on the secure capacity region of the index coding problem. For the
achievability of secure composite coding, a secret key with vanishingly small
rate may be needed to ensure that each legitimate receiver who wants the same
message as the eavesdropper, knows at least two more messages than the
eavesdropper. For all securely feasible index coding problems with four or
fewer messages, our numerical results establish the secure index coding
capacity region.
