  In this work, we study the secure index coding problem where there are
security constraints on both legitimate receivers and eavesdroppers. We develop
two performance bounds (i.e., converse results) on the symmetric secure
capacity. The first one is an extended version of the basic acyclic chain bound
(Liu and Sadeghi, 2019) that takes security constraints into account. The
second converse result is a novel information-theoretic lower bound on the
symmetric secure capacity, which is interesting as all the existing converse
results in the literature for secure index coding give upper bounds on the
capacity.
