Deep Neural Networks have been widely used in many fields. However, studies have shown that DNNs are easily attacked by adversarial examples, which have tiny perturbations and greatly mislead the correct judgment of DNNs. Furthermore, even if malicious attackers cannot obtain all the underlying model parameters, they can use adversarial examples to attack various DNN-based task systems. Researchers have proposed various defense methods to protect DNNs, such as reducing the aggressiveness of adversarial examples by preprocessing or improving the robustness of the model by adding modules. However, some defense methods are only effective for small-scale examples or small perturbations but have limited defense effects for adversarial examples with large perturbations. This paper assigns different defense strategies to adversarial perturbations of different strengths by grading the perturbations on the input examples. Experimental results show that the proposed method effectively improves defense performance. In addition, the proposed method does not modify any task model, which can be used as a preprocessing module, which significantly reduces the deployment cost in practical applications.

Recent defenses published at venues like NIPS, ICML, ICLR and CVPR are mainly focused on mitigating white-box attacks. These defenses do not properly consider adaptive adversaries. In this paper, we expand the scope of these defenses to include adaptive black-box adversaries. Our evaluation is done on nine defenses including Barrage of Random Transforms, ComDefend, Ensemble Diversity, Feature Distillation, The Odds are Odd, Error Correcting Codes, Distribution Classifier Defense, K-Winner Take All and Buffer Zones. Our investigation is done using two black-box adversarial models and six widely studied adversarial attacks for CIFAR-10 and Fashion-MNIST datasets. Our analyses show most recent defenses provide only marginal improvements in security, as compared to undefended networks. Based on these results, we propose new standards for properly evaluating defenses to black-box adversaries. We provide this security framework to assist researchers in developing future black-box resistant models.