  When an initial failure of nodes occurs in interdependent networks, a cascade
of failure between the networks occurs. Earlier studies focused on random
initial failures. Here we study the robustness of interdependent networks under
targeted attack on high or low degree nodes. We introduce a general technique
and show that the {\it targeted-attack} problem in interdependent networks can
be mapped to the {\it random-attack} problem in a transformed pair of
interdependent networks. We find that when the highly connected nodes are
protected and have lower probability to fail, in contrast to single scale free
(SF) networks where the percolation threshold $p_c=0$, coupled SF networks are
significantly more vulnerable with $p_c$ significantly larger than zero. The
result implies that interdependent networks are difficult to defend by
strategies such as protecting the high degree nodes that have been found useful
to significantly improve robustness of single networks.
