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Most of previous research on survivable networks has been focused on protecting the unicast traffic against random failures. In this paper we propose a new approach, called RA (resistant-to-attack), to provide protection of anycast and unicast communications against attacks on irregular (e.g. scale-free) networks. We use the single backup path approach to provide protection against a single node failure. For anycast traffic, we assume the utilization of different working and backup replica servers. We provide a new metrics of link costs used in working path computations (resulting in omitting nodes of high degree by the working paths), and locating the replica servers at low degree nodes (i.e. of low probability of breaking due to attacks). The ILP model to find the optimal paths for anycast and unicast flows has been formulated and followed by an efficient heuristic algorithm. The results show that our method remarkably reduces (up to 7.47 times) the total number of connections broken due to attacks, compared to the common case of utilizing the metrics of distance to find both working and backup paths.