# Advancement of the DRPE Encryption Algorithm for Phase CGHs by Random Pixel Shuffling
## 1 Introduction  
Considering that the visual sense has the highest bandwidth among all human senses, an image is one of the most natural ways to receive large amounts of information. For this reason, science and technology have always shown a particular interest in understanding and modeling all aspects related to image formation, modification, storage, and transmission. Optics is the discipline that embodies this knowledge, accumulated over centuries, and provides a model for the propagation of information and energy through electromagnetic waves (in the visible spectrum) [1]. However, it is in recent decades that photonic and optical techniques have emerged as powerful tools for processing the information contained in an image, especially as previously developed models have been implemented into computer-executable algorithms. Among all these technologies, Computer-Generated Holograms (CGHs) have proven to be a viable option for massive information storage, typically associated with 2D images or 3D scenes. This process requires a significant amount of computational resources, which,in some cases, exceed the capabilities of current computers if synthesis is to be performed within acceptable time frames. The creation, manipulation, storage, and encryption of images (initially in black and white and later in color) have been the subject of interest and study since the beginning of all civilizations. However, it is nowadays, with the evolution of technologies linked to the digital era, that the need to protect and securely transmit this type of information has become more evident. Image encryption is a dynamic discipline that currently allows for multiple approaches [2,3]. Similarly, the information contained in the CGH must also be securely stored and transmitted. A CGH needs more information for its synthesis. From an optical point of view, it is necessary to know the contribution of the amplitudes and phases of the elements of the scene for each element (pixel) of the CGH, which means that characteristics typical of traditional images (e.g., correlations between nearby pixels or information redundancy) usually do not occur. Consequently, specialized encryption techniques have been developed in parallel to safeguard the integrity of CGHs and prevent unauthorized access [4,5]. We must keep in mind that a CGH can store images, but it can also store more complex data structures, for example, 3D scenes. The differential characteristic of working with 3D virtual scenes defined by triangle meshes is that they allow for modeling the aspects of shape and appearance, offering the possibility of obtaining different views of the scene. However, to retrieve this information (stored in a file format to be determined), it is necessary to know parameters such as the geometry of the scene, its location with respect to the observer, the resolution used, and the illumination used. In this paper, we focus on the use of CGH as a solvent option that allows for saving this information in an image-like format (i.e., saving the phase pattern in a png file for later presentation to display devices such as SLMs). This approach allows for easily integrating encryption and decryption processes well known in the field of digital imaging. In this context, our work consists of the following steps and contributions:  
* From a complex virtual scene, designed by means of computer graphics (CGs), we generate a CGH in which relevant scene information such as luminosity, depth, and occlusion is stored. * To encrypt this information, we present an evolution of the DRPE algorithm by incorporating random pixel shuffling. This significantly increases the robustness of the encryption against brute force attacks. * Two keys are defined: one for the pixel shuffling process and one for the random mask phase modification process. * The proposal allows these keys to be generated from a single key or to be independent in order to improve the level of encryption security. * The decrypted scene is obtained by simulation or in the laboratory.