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.

中文翻译：

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基于新型多参数余弦数变换的3D医学图像加密。

本文提出了一种多参数余弦数变换。使用三维余弦数变换（3D-CNT）的基向量构成在有限域中评估的立方晶格图的Laplacian可能的本征基数这一事实，即可获得这种变换。提出的变换被识别为三维可控余弦数变换（3D-SCNT），并通过使用有限域旋转算子旋转3D-CNT基矢量来定义。我们介绍一种基于3D-SCNT的3D医学图像加密方案，该方案使用旋转角度作为秘密参数。通过计算机实验，我们已经验证了该方案可以抵抗主要的密码攻击。