Things You May Not Know About Adversarial Example: A Black-box Adversarial Image Attack
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Numerous methods for crafting adversarial examples were proposed recently with high attack success rate. Most of the existing works normalize images into a continuous vector, domain firstly, and then craft adversarial examples in the continuous vector space. However, "adversarial" examples may become benign after de-normalizing them back into discrete integer domain, known as the discretization problem. The discretization problem was mentioned in some work, but was despised and have received relatively little attention. In this work, we conduct the first comprehensive study of this discretization problem. We theoretically analyzed 34 representative methods and empirically studied 20 representative open source tools for crafting discretization images. Our findings reveal that almost all of existing works suffer from the discretization problem and the problem is far more serious than we thought. This suggests that the discretization problem should be taken into account when crafting adversarial examples. As a first step towards addressing the discretization problem, we propose a black-box attack method to encode the adversarial example searching problem as a derivative-free optimization problem. Our method is able to craft "real" adversarial images by derivative-free search on the discrete integer domain. Experimental results show that our method achieves significantly higher attack success rates on the discrete integer domain than most of the other tools, no matter white-box or black-box. Moreover, our method is able to handle any model that is not differentiable and we successfully break the winner of NIPS 17 competition on defense with a 95% success rate.
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