# Quantum Image Steganography Schemes for Data Hiding: A Survey
## 3 Quantum Image Steganography Schemes
### Quantum Image Scrambling  
Image steganography discusses the concept of disguising data inside of an image to transfer to the recipient, such that only the recipient can distinguish the existence of the secret data [34]. Quantum image scrambling is a pre-processing method that is applied through an image-scrambling algorithm which accounts for the quantum representations of the hidden image's data in a secure manner that turns the quantum image into a disordered image before sending it to the receiver [35]. As a result, unauthorized attackers would just be met with a meaningless image had they succeeded in the attempt of extracting the data.  
The concept of quantum image scrambling was proposed in 2016 by [PERSON] et al. [3] who introduced their methodology using the image model FRQI by employing an Arnold and Fibonacci transition. Correspondingly, an alternative quantum image-scrambling method that utilizes an algorithm of the Hilbert scanning matrix called quantum Hilbert image scrambling was introduced to scramble a flexible representation of quantum images.  
Figure 3: Mach–Zehnder interferometer ([13]).  
In 2022, this concept was incorporated into recent research conducted by [PERSON] et al. [14], where they utilized the disordered version of the covert image and an applied graph wavelet transformation on both the disordered covert image and the cover image while subsequently alpha blending both image signals during the embedding. Alpha blending \(\alpha\) is the method of conjoining two images to produce a new one. Their research indicates that their image steganography method uses images as carrier media and hidden media. It also comprises two main frameworks, which are the implanting framework and the withdrawal framework of the covert image.  
Using quantum scrambling, the implanting framework in the proposed scheme scrambles the hidden image. The quantum Hilbert image-scrambling protocol produces exceptional scrambled media by using layered as well as recursive circuits, establishing confidentiality and robustness. After that, a graph wavelet analysis is applied to both the scrambled image along with the carrier image. Lastly, the proposed scheme applies the alpha blending function on the produced graph wavelets of the scrambled confidential image with the cover image to achieve the stego image.  
\[\left(Ab\right)_{G}=\left(Ci\right)_{G}+\left.\alpha\left(SSi\right)_{G}\right. \tag{13}\]  
The \(\left(Ab\right)_{G}\) refers to the stego image produced after the blending procedure. Meanwhile, \(\left(Ci\right)_{G}\) denotes the cover image and \(\left(SSi\right)_{G}\) represents the scrambled covert image. In the mentioned formula, the \(\alpha\) indicates the embedding strength aspect for ruling the robustness of the produced image and its imperceptibility. A stego image is then obtained after the graph wavelet-synthesis process is applied to the image generated by the merging operation shown in Formula (13).  
For the withdrawal framework stage, a graph wavelet-synthesis analysis is first operated on both the hidden and cover image. Afterward, the scheme attains the scrambled image \(\left(SSi\right)_{G}\) by applying the alpha blending procedure to the produced images. Consequently, the procedure performs a graph wavelet-based synthesis operation on the steganographic image followed by the inversed Hilbert image scrambling protocol, attaining the hidden image.