  Deep neural networks (DNNs) are one of the most prominent technologies of our
time, as they achieve state-of-the-art performance in many machine learning
tasks, including but not limited to image classification, text mining, and
speech processing. However, recent research on DNNs has indicated
ever-increasing concern on the robustness to adversarial examples, especially
for security-critical tasks such as traffic sign identification for autonomous
driving. Studies have unveiled the vulnerability of a well-trained DNN by
demonstrating the ability of generating barely noticeable (to both human and
machines) adversarial images that lead to misclassification. Furthermore,
researchers have shown that these adversarial images are highly transferable by
simply training and attacking a substitute model built upon the target model,
known as a black-box attack to DNNs.
  Similar to the setting of training substitute models, in this paper we
propose an effective black-box attack that also only has access to the input
(images) and the output (confidence scores) of a targeted DNN. However,
different from leveraging attack transferability from substitute models, we
propose zeroth order optimization (ZOO) based attacks to directly estimate the
gradients of the targeted DNN for generating adversarial examples. We use
zeroth order stochastic coordinate descent along with dimension reduction,
hierarchical attack and importance sampling techniques to efficiently attack
black-box models. By exploiting zeroth order optimization, improved attacks to
the targeted DNN can be accomplished, sparing the need for training substitute
models and avoiding the loss in attack transferability. Experimental results on
MNIST, CIFAR10 and ImageNet show that the proposed ZOO attack is as effective
as the state-of-the-art white-box attack and significantly outperforms existing
black-box attacks via substitute models.
