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This paper proposes a reversible data hiding method to authenticate 3D meshes by modulating the distances from the mesh faces to the mesh centroid to embed a fragile watermark. It keeps the modulation information in the watermarked mesh so that the reversibility of the embedding process is achieved. Since the embedded watermark is sensitive to geometrical and topological processing, unauthorized modifications on the watermarked mesh can be therefore detected by retrieving and comparing the embedded watermark with the original one. Furthermore, as long as the watermarked mesh is intact, the original mesh can be recovered using some priori knowledge.