  Security aspects of the Index Coding with Side Information (ICSI) problem are
investigated. Building on the results of Bar-Yossef et al. (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 matrix $L$, whose column space code $C(L)$ has length $n$,
minimum distance $d$ and dual distance $d^\perp$, is $(d-1-t)$-block secure
(and hence also weakly secure) if the adversary knows in advance $t \leq d-2$
messages, and is completely insecure if the adversary knows in advance more
than $n - d$ messages. Strong security is examined under the conditions that
the adversary: (i) possesses $t$ messages in advance; (ii) eavesdrops at most
$\mu$ transmissions; (iii) corrupts at most $\delta$ transmissions. We prove
that for sufficiently large $q$, an optimal linear index code which is strongly
secure against such an adversary has length $\kappa_q+\mu+2\delta$. Here
$\kappa_q$ is a generalization of the min-rank over $F_q$ of the side
information graph for the ICSI problem in its original formulation in the work
of Bar- Yossef et al.
