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Existing score-based adversarial attacks mainly focus on crafting top-1 adversarial examples against classifiers with single-label classification. Their attack success rate and query efficiency are often less than satisfactory, particularly under small perturbation requirements; moreover, the vulnerability of classifiers with multilabel learning is yet to be studied. In this paper, we propose a comprehensive surrogate free score-based attack, named geometric score-based black-box attack (GSBAK), to craft adversarial examples in an aggressive top-K setting for both untargeted and targeted attacks, where the goal is to change the top-K predictions of the target classifier. We introduce novel gradient-based methods to find a good initial boundary point to attack. Our iterative method employs novel gradient estimation techniques, particularly effective in top-K setting, on the decision boundary to effectively exploit the geometry of the decision boundary. Additionally, GSBAK can be used to attack against classifiers with top-K multi-label learning. Extensive experimental results on ImageNet and PASCAL VOC datasets validate the effectiveness of GSBAK in crafting top-K adversarial examples. 

Decision-based black-box attacks often necessitate a large number of queries to craft an adversarial example. Moreover, decision-based attacks based on querying boundary points in the estimated normal vector direction often suffer from inefficiency and convergence issues. In this paper, we propose a novel query-efficient \b curvature-aware \b geometric decision-based \b black-box \b attack (CGBA) that conducts boundary search along a semicircular path on a restricted 2D plane to ensure finding a boundary point successfully irrespective of the boundary curvature. While the proposed CGBA attack can work effectively for an arbitrary decision boundary, it is particularly efficient in exploiting the low curvature to craft high-quality adversarial examples, which is widely seen and experimentally verified in commonly used classifiers under non-targeted attacks. In contrast, the decision boundaries often exhibit higher curvature under targeted attacks. Thus, we develop a new query-efficient variant, CGBA-H, that is adapted for the targeted attack. In addition, we further design an algorithm to obtain a better initial boundary point at the expense of some extra queries, which considerably enhances the performance of the targeted attack. Extensive experiments are conducted to evaluate the performance of our proposed methods against some well-known classifiers on the ImageNet and CIFAR10 datasets, demonstrating the superiority of CGBA and CGBA-H over state-of-the-art non-targeted and targeted attacks, respectively.