Encryption of 3D medical images based on a novel multiparameter cosine number transform

In this paper, a multiparameter cosine number transform is proposed. Such a transform is obtained using the fact that the basis vectors of the three-dimensional cosine number transform (3D-CNT) constitute a possible eigenbasis for the Laplacian of the cubical lattice graph evaluated in a finite field. The proposed transform is identified as three-dimensional steerable cosine number transform (3D-SCNT) and is defined by rotating the 3D-CNT basis vectors, using a finite field rotation operator. We introduce a 3D medical image encryption scheme based on the 3D-SCNT, which uses the rotation angles as secret parameters. By means of computer experiments, we have verified that the scheme is resistant against the main cryptographic attacks.