Secure index coding: existence and construction

We investigate the construction of weakly-secure index codes for a sender to send messages to multiple receivers with side information in the presence of an eavesdropper. We derive a sufficient and necessary condition for the existence of index codes that are secure against an eavesdropper with access to any subset of messages of cardinality t, for any fixed t. In contrast to the benefits of using random keys in secure network coding, we prove that random keys do not promote security in three classes of index-coding instances.