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We propose a simple and efficient Bayesian Optimization~(BO) based approach for developing black-box adversarial attacks. Issues with BO's performance in high dimensions are avoided by searching for adversarial examples in a structured low-dimensional subspace. We demonstrate the efficacy of our proposed attack method by evaluating both $\\ell_\\infty$ and $\\ell_2$ norm constrained untargeted and targeted hard label black-box attacks on three standard datasets - MNIST, CIFAR-10 and ImageNet. 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