On the Security of Index Coding With Side Information

Security aspects of the index coding with side information (ICSI) problem are investigated. Building on the results of Bar-Yossef (2006), the properties of linear index codes are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown that the linear index code based on a matrixL, whose column space codeC(L) has lengthn, minimum distanced, and dual distanced⊥, is (d-1-t) -block secure (and hence also weakly secure) if the adversary knows in advancet≤d-2 messages, and is completely insecure if the adversary knows in advance more thann-d⊥messages. Strong security is examined under the conditions that the adversary: 1) possessestmessages in advance; 2) eavesdrops at most μ transmissions; 3) corrupts at most δ transmissions. We prove that for sufficiently largeq, an optimal linear index code which is strongly secure against such an adversary has length κq+μ+2δ . Here, κqis a generalization of the min-rank over Fqof the side information graph for the ICSI problem in its original formulation in the work of Bar-Yossef et al.