Certified_Watermarks is the first to provide a watermark certificate against l_2-norm watermark removal attacks, by leveraging the randomized smoothing techniques for certified robustness to adversarial attacks. However, the randomized smoothing techniques suffer from hardness of certified robustness in high-dimensional space against l_p-norm attacks for large p (p>2). The certified watermark method based on the randomized smoothing is no exception, i.e., fails to provide meaningful certific…