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 {\it dependency-first} to {\it 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. We show that while `dependency-first' strategy increases the short-term impact of the initial attack, in the long-term the cascade slows down compared with the case of random attacks, and vise-versa for `dependency-last'. 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.
This highlights the importance of understanding the dynamics of avalanches that may occur due to different scenarios of failures in order to design resilient critical infrastructures.