We compute precise estimates for dimensions of 3D-encryption techniques of 3D-point clouds which use permutations and rigid body motion, in which geometric stability is to be guaranteed. Few attempts are made in this direction. An attempt is established using the notions of dimensional and spatial stability by Jolfaei et al. (2015), who also proposed a 3D object encryption algorithm, claiming that it preserves dimensional and spatial stability. However, as we mathematically prove neither the algorithm, nor the associated estimates are correct. We introduce more rigorous definitions of the geometric stability of such 3D data encryption algorithms, followed by dimensionality measures

翻译：我们计算了使用置换和刚体运动的三维点云加密技术维度的精确估计，其中需保证几何稳定性。目前该方向鲜有尝试。Jolfaei等人（2015）曾尝试利用维数稳定性和空间稳定性的概念，提出一种三维物体加密算法，声称该算法能保持维数稳定性和空间稳定性。然而，我们通过数学证明，该算法及其相关估计均不正确。我们为此类三维数据加密算法的几何稳定性引入了更严格的定义，随后给出了维度度量方法。