# Encryption of 3D or Higher-Dimensional Images: A Review
## 5 Contributions and Discussion  
Among the selected works, it is noted that encryption is carried out predominantly in the spatial domain. Articles that use the frequency domain make use of transforms, predominantly the Fourier Transform [33; 38; 40] and fractional Fourier Transform [37; 39; 48]. Figure 12 shows the grouping of articles that apply encryption in the frequency domain and the respective transforms used. The literature lacks works in which encryption is performed completely on the image, since the authors choose to perform the encryption partially on three-dimensional or higher-dimensional images, as shown in Figure 13; that is, the encryption is performed separately. It was only in 2023 that articles reported the application of full encryption in the image and in all dimensions [33; 34]. Regarding the encryption of LF images, there may be a disadvantage in the encryption process that does not explore the entire structure of the image. It is important to highlight that, among the works cited, only [33; 37] explore both the spatial and angular characteristics of the LF image and that only [33] simultaneously considers the spatial and angular characteristics of the LF image, that is, the entire 4D structure. The approach of considering the dimensional structure of the image as a whole contributes to reducing the correlation between neighboring pixels, which consequently increases the robustness of the proposed scheme against statistical attacks. In the medical 3D image encryption scenario, the concern is also the same as encryption in LF images. In [5], the authors report that there is a scarcity of papers on 3D medical image encryption that perform encryption on the 3D structure of the image. For the authors, encryption performed on each slice of the three-dimensional image can favor correlation attacks. [PERSON] et al. [33] performed encryption on the RGB layers of the LF image. On the other hand, [PERSON] et al. [37] proposed encryption methods only on LF images in grayscale, leaving the application of the method to the RGB layers of the light field image as a future direction. Figure 12: Distribution of transforms used in selected articles. Figure 13: Representation when encryption occurs completely or partially in the image. [PERSON] and [PERSON] [36] presented a new random sequence generator based on a cat map and hybrid chaos system, leaving as a gap the evaluation of the scheme on 3D images, such as key space size, statistical analysis, and entropy, among others. A future direction would be to apply this proposed algorithm to multiple images captured through a light field system. Permutation is a technique for reorganizing the elements of a finite set with the aim of breaking the correlation between neighboring elements. The positions of the elements are permuted using some scrambling technique, such as matrix transformation, swapping rows and columns. In an image, for example, each pixel is highly correlated with its neighbors. A good permutation method reduces this correlation to close to zero, which can make the image visually unreadable. This technique is widely used in one of the stages of the encryption process, since it guarantees diffusion and confusion to the system [49]. It is verified that, among all the studies evaluated, a percentage of 56.25% uses chaotic sequences, according to Table 1.  
Artificial intelligence is one area of techniques used for optimizing various tasks today. Linked to this fact, the memristive neural network (MNN) is a type of artificial neural network (ANN), based on the \"memristor bionic synapse\", which replaces traditional resistors with memristors in the circuit realization process [50]. These models have been applied to neuromorphic computing systems and chaotic circuits; however, they have not received much attention when it comes to encryption techniques [51]. [PERSON] et al. [51] presented a new neuron model with chaotic characteristics, coupling a memristor to the proposed neuron. With this, a new memristive neuron model was subsequently obtained.