Decision-based attack poses a severe threat to real-world applications since it regards the target model as a black box and only accesses the hard prediction label. Great efforts have been made recently to decrease the number of queries; however, existing decision-based attacks still require thousands of queries in order to generate good quality adversarial examples. In this work, we find that a benign sample, the current and the next adversarial examples can naturally construct a triangle in a subspace for any iterative attacks. Based on the law of sines, we propose a novel Triangle Attack (TA) to optimize the perturbation by utilizing the geometric information that the longer side is always opposite the larger angle in any triangle. However, directly applying such information on the input image is ineffective because it cannot thoroughly explore the neighborhood of the input sample in the high dimensional space. To address this issue, TA optimizes the perturbation in the low frequency space for effective dimensionality reduction owing to the generality of such geometric property. Extensive evaluations on ImageNet dataset show that TA achieves a much higher attack success rate within 1,000 queries and needs a much less number of queries to achieve the same attack success rate under various perturbation budgets than existing decision-based attacks. With such high efficiency, we further validate the applicability of TA on real-world API, i.e., Tencent Cloud API.
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