## 3 Main Scheme
### Algorithm III. Meaningful Shares Scheme
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\gamma\) & **Image \({}^{*}\)** & **Method 1** & **Method 2** & **Method 3** & **Method 4** \\ \hline \multirow{2}{*}{1} & \(R_{0}\) & 0.51361 & 0.00633 & 1.00000 & 0.00000 \\ \cline{2-6}  & \(R_{1}\) & 0.51371 & 0.00623 & 0.02929 & 0.00000 \\ \hline \multirow{2}{*}{0.7} & \(R_{0}\) & 0.65416 & 0.29760 & 0.99657 & 0.22111 \\ \cline{2-6}  & \(R_{1}\) & 0.65418 & 0.29742 & 0.30329 & 0.21992 \\ \hline \multirow{2}{*}{0.5} & \(R_{0}\) & 0.75793 & 0.49789 & 0.99442 & 0.45613 \\ \cline{2-6}  & \(R_{1}\) & 0.75782 & 0.49791 & 0.50376 & 0.45631 \\ \hline \multirow{2}{*}{0.3} & \(R_{0}\) & 0.84490 & 0.69740 & 0.84933 & 0.68785 \\ \cline{2-6}  & \(R_{1}\) & 0.84469 & 0.69795 & 0.69750 & 0.68774 \\ \hline \multirow{2}{*}{0} & \(R_{0}\) & 0.98884 & 0.98885 & 0.98889 & 0.98889 \\ \cline{2-6}  & \(R_{1}\) & 0.98902 & 0.98892 & 0.98887 & 0.98897 \\ \hline \hline \end{tabular} \({}^{*}R_{0}\) and \(R_{1}\) represent the first and the second restored image, respectively.

\end{table} 
Table 5: The SSIM analysis of our schemes. sacrificing some security in the pursuit of optimizing the contrast of the restored image. From Algorithm 1, it can be found that if we XOR the output \(G_{1}\) or \(G_{2}\) with a version of itself shifted over by \(w/p\) pixels, then we get an image where most of the pixels depend only on the secret images: \(G_{1}(i,j)\oplus G_{1}(i+w/p,j)=S_{A}(i+w/p,j)\oplus S_{A+1}(i,j)\) and \(G_{2}(i+Aw/p,j)\oplus G_{2}(i+(A+)w/p,j)=S_{A}(i,j)\oplus S_{A+1}(i,j)\). The latter one implies \(G_{2}(i,j)\oplus G_{2}(i+w/p,j)=S_{A}(i-Aw/p,j)\oplus S_{A+1}(i-Aw/p,j)\). However, since \(A\) is randomly selected from 0 to \(N\)-1, it is impossible to tell which pixel is encrypted by which two consecutive secret pixels. This means that the stacked image will be a complex image where all the secret images and their shifted images are interleaved together; there are \(2N\) possibilities, so it is still impossible to identify any single secret image. Even taking into account the edge case where all but one of the secret images (\(A\)) are completely 0, this still does not fully reveal the remaining secret image--there are still two possibilities: \(G_{1}(i,j)\oplus G_{1}(i+w/p,j)=S_{A}(i+w/p,j)\) or \(S_{A}(i,j)\) and \(G_{2}(i,j)\oplus G_{2}(i+w/p,j)=S_{A}(i-Aw/p,j)\) or \(S_{A}(i-(A-1)w/p,j)\). That means it will appear as a mixed image of the secret image \(A\) and itself shift by \(w/p\) pixels. However, this is still an unwelcome result. A good choice when there are very few secret images is to use Method 1 and set \(\gamma=1\). In this case, an influence of the Algorithm 1 will disappear, and the problems that may be caused can be solved at the same time. The original secrets can still be restored, but the contrast of the restored image cannot be as high as when using Algorithm 1 (\(\gamma<1\)) (see Table 2). Fortunately, Algorithms II and III (Algorithms 3, 4, 5 or 6) can generate interference and increase the uncertainty of shares and make leaks less likely, provided that \(\gamma\) cannot be equal to 0. Since the proposed scheme uses Algorithms I, II and III (Algorithms 3, 4, 5 or 6) completely sequentially, the user cannot obtain \(G_{1}\) or \(G_{2}\) directly. Under such observation, the value of \(p\) cannot be set too small, the value of \(\gamma\) cannot be too close to 0, and avoid setting all but one secret image to white (in the same position). In addition, KK2 and KK3 can be selected for \(f_{XRG}\) and \(f_{XORG}\) instead of KK1 for Algorithm I. This will avoid the above problem, but the performance of the new algorithm will not be as good as it currently is. ## 5 Concluding Remarks

This paper studies the \((n,n)\) XOR-based multi-secret sharing schemes with meaningful sharing. There are four different methods held in Algorithm III. The shares and restored images produced by these four methods are different. It can be said that we have designed four different VCSs.