Despite the success of Test-time adaptation (TTA), recent work has shown that adding relatively small adversarial perturbations to a limited number of samples leads to significant performance degradation. Therefore, it is crucial to rigorously evaluate existing TTA algorithms against relevant threats and implement appropriate security countermeasures. Importantly, existing threat models assume test-time samples will be labeled, which is impractical in real-world scenarios. To address this gap, we propose a new attack algorithm that does not rely onaccess to labeled test samples, thus providing a concrete way to assess the security vulnerabilities of TTA algorithms. Our attack design is grounded in theoretical foundations and can generate strong attacks against different state of the art TTA methods. In addition, we show that existing defense mechanisms are almost ineffective, which emphasizes the need for further research on TTA security. Through extensive experiments on CIFAR10-C, CIFAR100-C, and ImageNet-C, we demonstrate that our proposed approach closely matches the performance of state-of-the-art attack benchmarks, even without access to labeled samples. In certain cases, our approach generates stronger attacks, e.g., more than 4% higher error rate on CIFAR10-C.