Adversarial robustness of neural networks is an increasingly important area of research, combining studies on computer vision models, large language models (LLMs), and others. With the release of JPEG AI - the first standard for end-to-end neural image compression (NIC) methods - the question of its robustness has become critically significant. JPEG AI is among the first international, real-world applications of neural-network-based models to be embedded in consumer devices. However, research on NIC robustness has been limited to open-source codecs and a narrow range of attacks. This paper proposes a new methodology for measuring NIC robustness to adversarial attacks. We present the first large-scale evaluation of JPEG AI's robustness, comparing it with other NIC models. Our evaluation results and code are publicly available online (link is hidden for a blind review).