# Quantum Image Steganography Schemes for Data Hiding: A Survey
## 3 Quantum Image Steganography Schemes
### Quantum EMD Protocol  
The exploiting modification direction steganography protocol (EMD) is a classical scheme presented by [PERSON] et al. [18] which inspired future quantum renditions. The method operates by converting a hidden text, image, or any type of message into a series of digits with an odd base in the notational system, then all digits belonging to the \((2n+1)\)-ary from the system are moved by \(n\) pixels. In addition, these pixels can be added or subtracted by 1. To apply this method into quantum image representations, [PERSON] et al. [42] created a quantum version of the EMD steganography protocol (QIS-EMD). The image model used for this process was NEQR. The concept of EMD embedding suggests that \(n\) pixels will capture each Dt belonging to the \((2n+1)\) carrying system. Below, the listed steps (with \(N=2\)) represent the embedding and extraction processes done by the new algorithm:  
To store the data of gray value \(\mathrm{gn}\) (\(0\leq\mathrm{gn}\leq 255\)) of the digital gray image, it requires 8 qubits in NEQR per 1 pixel. For instance, a quantum carrier image \(\mid C\rangle\) having \(0\leq\mathrm{gn}\leq 255\) and size \(2^{n}\times 2^{n}\) is consequently indicated as:  
\[\mid C\rangle=\frac{1}{2^{n}}\sum_{i=0}^{2^{2n}-1}\mid c(i)\rangle\mid i\rangle =\ \frac{1}{2^{n}}\sum_{i=0}^{2^{2n}-1}\mid c_{\gamma}^{i}c_{6}^{i}\ldots c_{0}^{ i}\rangle\ \mid i\rangle \tag{14}\]  
On the sender's end, with each comprising of \(L\) qubits, the binary flow of hidden information is segmented into a vast number of parts. The decimal digit of each hidden fragment is equal to:  
\[L=\ [P\bullet\log_{2}5] \tag{15}\]  
where \(P\) is the digits included in the above-mentioned notational system. With EMD embedding, each Dt maps to a comparable carrier pixel-group. Once all are embedded, the quantum carrier image \(\mid C\rangle\) is converted to a quantum stego image \(\mid C^{\prime}\rangle\). This completes the embedding section. The extraction function is applied by the receiver on the stego pixel group to draw out an equivalent secret digit. To complete the extraction section, each drawn-out secret digit is converted into a secret piece, building up the full binary stream of hidden information. In 2021, [PERSON] et al. [17] further enhanced the QIS-EMD scheme by creating the improved quantum EMD protocol (QIS-IEMD), where two additional improvements were added to the previous scheme. The first is employing the expanding modification range method, which modifies the carrier pixel's values of numerous bit planes to achieve good imperceptibility and enlarge the capacity to its greatest extent. After the employment of this modern protocol, an addition or subtraction by 1 can be applied on the modified pixels, signifying the level of modification depending on the modification range. Moreover, \(L\)'s upper bound increases, ensuing a new value of \(L\) that equals:  
\[L=\ \left\lfloor\log_{2}\left(2 cn+1\right)\right\rfloor \tag{16}\]  
The second protocol added to the new variation is the dynamic sharing of subgroups, which aims to achieve better embedding efficiency and compress the redundancy by making neighboring pixel groups be shared dynamically together. As such, during the embedding procedure, after modifying one pixel possessed by the 1 st pixel group, the next pixel group will start the modification, sharing the rest of the pixels with the modified one in the first group. However, it must be noted that the modification of pixels shared between the allocated groups is prohibited. Finally, we provide a summary of all the recently presented quantum steganography schemes in Table 1. Moreover, we included a short description of each scheme's methodology, along with the latest advances and outcomes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Methodology** & **Recent Outcomes** & **Limitations** \\ \hline \multirow{6}{*}{LSBq [4; 6; 8]} & \multirow{6}{*}{Embeds the secret message’s qubits to the carrier image’s least significant qubits.}