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In light of the growing concerns regarding the unauthorized use of facial recognition systems and its implications on individual privacy, the exploration of adversarial perturbations as a potential countermeasure has gained traction. However, challenges arise in effectively deploying this approach against unauthorized facial recognition systems due to the effects of JPEG compression on image distribution across the internet, which ultimately diminishes the efficacy of adversarial perturbations. Existing JPEG compression-resistant techniques struggle to strike a balance between resistance, transferability, and attack potency. To address these limitations, we propose a novel solution referred to as \emph{low frequency adversarial perturbation} (LFAP). This method conditions the source model to leverage low-frequency characteristics through adversarial training. To further enhance the performance, we introduce an improved \emph{low-mid frequency adversarial perturbation} (LMFAP) that incorporates mid-frequency components for an additive benefit. Our study encompasses a range of settings to replicate genuine application scenarios, including cross backbones, supervisory heads, training datasets, and testing datasets. Moreover, we evaluated our approaches on a commercial black-box API, \texttt{Face++}. The empirical results validate the cutting-edge performance achieved by our proposed solutions.