Theoretical Study of Random Noise Defense against Query-Based Black-Box Attacks

The query-based black-box attacks, which don't require any knowledge about the attacked models and datasets, have raised serious threats to machine learning models in many real applications. In this work, we study a simple but promising defense technique, dubbed Random Noise Defense (RND) against query-based black-box attacks, which adds proper Gaussian noise to each query. It is lightweight and can be directly combined with any off-the-shelf models and other defense strategies. However, the theoretical guarantee of random noise defense is missing, and the actual effectiveness of this defense is not yet fully understood. In this work, we present solid theoretical analyses to demonstrate that the defense effect of RND against the query-based black-box attack and the corresponding adaptive attack heavily depends on the magnitude ratio between the random noise added by the defender (i.e., RND) and the random noise added by the attacker for gradient estimation. Extensive experiments on CIFAR-10 and ImageNet verify our theoretical studies. Based on RND, we also propose a stronger defense method that combines RND with Gaussian augmentation training (RND-GT) and achieves better defense performance.