# Encryption of 3D or Higher-Dimensional Images: A Review
## 4 Literature Review  
Table 1 provides an overview of the works considered in the review and the answers found to the research questions. [PERSON] et al. [33] proposed a light field image encryption scheme based on the steerable cosine number transform (SCNT), whose rotation angles are used as a secret key. It is one of the pioneering works with regard to the application of encryption in all four dimensions of the image, taking into account spatial and angular characteristics at the same time. The method is robust against entropy and differential attacks, and is highly sensitive to changes in the secret key. [PERSON] and [PERSON] [34] suggest a hybrid amalgamation of advanced encryption methods with S-box- and chaotic Henon map-based encryption, which is efficient in processing multidimensional 3D images of a voluminous nature. With these two methods, it is possible to increase the security of medical images against a series of attacks, such as algebraic attacks and differential attacks. The paper focuses on calculating the time spent on each step of the encryption scheme and the time efficiency of this hybrid method. [PERSON] et al. [35] developed an encryption scheme for color light field images based on DNA sequences and chaotic systems. The method employs a 2D angular domain to represent a multi-view image and, in sequence, obtain a sub-view image in the spatial domain. A DNA sequence and the chaotic system are used to encrypt the sub-view image. Their encryption algorithm contains multiple secret keys, generated in the chaotic system, which achieves a fundamental change each time, making it difficult for the attacker to obtain information. Furthermore, the Arnold transform is applied to perform the final encryption. The results are presented in terms of the statistical analysis, resistance to differential attack analysis, and key space analysis, in which the key space size equal to \(2^{315}\) stands out, being sufficient to prevent brute force attacks. Medical images are fundamental in the diagnosis of a wide variety of diseases and their respective treatments. [PERSON] et al. [5] presented a novel multiparameter cosine number transform (3D-SCNT). This transform is defined by rotating the 3D-CNT basis vector using a finite field rotation operator, whose rotation angles are used as a secret key in the 3D medical image encryption scheme. The results and discussion show that the method is resistant to the main plaintext and cryptographic attacks. An encryption scheme must have a sufficiently large key space to make brute force attack unfeasible. The key space in the method by [PERSON] et al. [5] is \(2^{1344}\), enough to make brute force attacks nonviable. In the paper on encryption in medical images by [PERSON] and [PERSON] [34], the analysis of the key space is not carried out. [PERSON] and [PERSON] [36] proposed a new random sequence generator based on a cat map and hybrid chaos system. In addition to 3D images, the authors reported that the method can also be applied to color and multiple images. The researchers emphasized that in the data flow between the transmitter and the receiver, it is possible that some part of the data may be lost or noise may affect it. Given this fact, noise and data loss attacks were analyzed. In order to evaluate the performance and security of the scheme, the keyspace, sensitivity, and complexity were also analyzed. It is noteworthy that the method was evaluated considering only two-dimensional images. [PERSON] et al. [37] proposed a new encryption scheme for light fields based on the spatial-angular characteristic. The spatial domain characteristic of the image is considered using the discrete fractional Fourier transform (DFrFT). Afterwards, the difference in viewing angles extracted from multiple angles is used to compose an image of the epipolar plane (EPI) in the frequency domain. This representation is used as a form of representation capable of sending the angular and spatial characteristics of the LF.