  In recent years, deep neural networks demonstrated state-of-the-art
performance in a large variety of tasks and therefore have been adopted in many
applications. On the other hand, the latest studies revealed that neural
networks are vulnerable to adversarial examples obtained by carefully adding
small perturbation to legitimate samples. Based upon the observation, many
attack methods were proposed. Among them, the optimization-based CW attack is
the most powerful as the produced adversarial samples present much less
distortion compared to other methods. The better attacking effect, however,
comes at the cost of running more iterations and thus longer computation time
to reach desirable results. In this work, we propose to leverage the
information of gradients as a guidance during the search of adversaries. More
specifically, directly incorporating the gradients into the perturbation can be
regarded as a constraint added to the optimization process. We intuitively and
empirically prove the rationality of our method in reducing the search space.
Our experiments show that compared to the original CW attack, the proposed
method requires fewer iterations towards adversarial samples, obtaining a
higher success rate and resulting in smaller $\ell_2$ distortion.
