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Adversarial examples are known as carefully perturbed images fooling imageclassifiers. We propose a geometric framework to generate adversarial examplesin one of the most challenging black-box settings where the adversary can onlygenerate a small number of queries, each of them returning the top-$1$ label ofthe classifier. Our framework is based on the observation that the decisionboundary of deep networks usually has a small mean curvature in the vicinity ofdata samples. We propose an effective iterative algorithm to generatequery-efficient black-box perturbations with small $\ell_p$ norms for $p \ge1$, which is confirmed via experimental evaluations on state-of-the-art naturalimage classifiers. Moreover, for $p=2$, we theoretically show that ouralgorithm actually converges to the minimal $\ell_2$-perturbation when thecurvature of the decision boundary is bounded. We also obtain the optimaldistribution of the queries over the iterations of the algorithm. Finally,experimental results confirm that our principled black-box attack algorithmperforms better than state-of-the-art algorithms as it generates smallerperturbations with a reduced number of queries.

GeoDA: a geometric framework for black-box adversarial attacks