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With the swift progression of three-dimensional (3D) modeling and multimedia technology, the unauthorized duplication and manipulation of 3D point cloud data has become more prevalent. Existing watermarking algorithms designed for 3D point cloud data lack robustness against rotation, cropping, and random point addition attacks. To address the aforementioned issues, we propose a robust watermarking algorithm based on the Mahalanobis distance (MD) and feature point extraction, including zero-watermarking algorithm based on MD and watermarking algorithm based on the Intrinsic Shape signatures (ISS) feature points. Firstly, calculate the MD of point cloud data and use it to construct feature matrix. A zero-watermark image is constructed through the XOR operation of the feature matrix and the copyright information matrix. Secondly, ISS feature points can be extracted from point cloud data, which using the X and Y coordinates of the feature points as indexes. The color information of the feature points is used as host data to embed the watermark. The scale invariance of MD and the stability of ISS feature points augment the robustness of the algorithm. Experimental results demonstrate that the scheme we propose exhibits strong robustness against geometric attacks, simplification attacks, cropping attacks, reordering, and noise attacks while ensuring point cloud data coordinates are lossless. [ABSTRACT FROM AUTHOR]