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. 
Lawrence Ong, Badri N. Vellambi, Phee Lep Yeoh, J\"org Kliewer,   Jinhong Yuan
cs.IT math.IT