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Nowadays, neural-network-based image- and video-quality metrics perform better than traditional methods. However, they also became more vulnerable to adversarial attacks that increase metrics' scores without improving visual quality. The existing benchmarks of quality metrics compare their performance in terms of correlation with subjective quality and calculation time. Nonetheless, the adversarial robustness of image-quality metrics is also an area worth researching. This paper analyses modern metrics' robustness to different adversarial attacks. We adapted adversarial attacks from computer vision tasks and compared attacks' efficiency against 15 no-reference image- and video-quality metrics. Some metrics showed high resistance to adversarial attacks, which makes their usage in benchmarks safer than vulnerable metrics. The benchmark accepts submissions of new metrics for researchers who want to make their metrics more robust to attacks or to find such metrics for their needs. The latest results can be found online: https://videoprocessing.ai/benchmarks/metrics-robustness.html.