Geometric Stability Estimates For 3D-Object Encryption Through Permutations and Rotations

Abstract: 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