  Modern large network systems normally work in cooperation and incorporate
dependencies between their components for purposes of efficiency and
regulation. Such dependencies may become a major risk since they can cause
small scale failures to propagate throughout the system. Thus, the dependent
nodes could be a natural target for malicious attacks that aim to exploit these
vulnerabilities. Here, we consider for the first time a new type of targeted
attacks that are based on the dependency between the networks. We study
strategies of attacks that range from dependency-first to dependency-last,
where a fraction $1-p$ of the nodes with dependency links, or nodes without
dependency links, respectively, are initially attacked. We systematically
analyze, both analytically and numerically, the percolation transition of
partially interdependent Erd\H{o}s-R\'{e}nyi (ER) networks, where a fraction
$q$ of the nodes in each network are dependent upon nodes the other network. We
find that for a broad range of dependency strength $q$, `dependency-first'
strategy, which intuitively is expected to increase the system's vulnerability,
actually leads to a more stable system, in terms of lower critical percolation
threshold $p_c$, compared with random attacks of the same size. In contrast,
the `dependency-last' strategy leads to a more vulnerable system, i.e., higher
$p_c$, compared with a random attack. By exploring the dynamics of the
cascading failures initiated by dependency-based attacks, we explain this
counter-intuitive effect. Our results demonstrate that the most vulnerable
components in a system of interdependent networks are not necessarily the ones
that lead to the maximal immediate impact but those which initiate a cascade of
failures with maximal accumulated damage.
