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Skeleton-based action recognition has attracted increasing attention due to its strong adaptability to dynamic circumstances and potential for broad applications such as autonomous and anonymous surveillance. With the help of deep learning techniques, it has also witnessed substantial progress and currently achieved around 90\% accuracy in benign environment. On the other hand, research on the vulnerability of skeleton-based action recognition under different adversarial settings remains scant, which may raise security concerns about deploying such techniques into real-world systems. However, filling this research gap is challenging due to the unique physical constraints of skeletons and human actions. In this paper, we attempt to conduct a thorough study towards understanding the adversarial vulnerability of skeleton-based action recognition. We first formulate generation of adversarial skeleton actions as a constrained optimization problem by representing or approximating the physiological and physical constraints with mathematical formulations. Since the primal optimization problem with equality constraints is intractable, we propose to solve it by optimizing its unconstrained dual problem using ADMM. We then specify an efficient plug-in defense, inspired by recent theories and empirical observations, against the adversarial skeleton actions. Extensive evaluations demonstrate the effectiveness of the attack and defense method under different settings.