## 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{3}{*}{1} & \(R_{0}\) & 0.75828 & 0.80167 & 1.00000 & 1.00000 \\ \cline{2-6}  & \(R_{1}\) & 0.75806 & 0.80166 & 0.51906 & 1.00000 \\ \hline \multirow{3}{*}{0.7} & \(R_{0}\) & 0.82518 & 0.85985 & 0.99821 & 0.99846 \\ \cline{2-6}  & \(R_{1}\) & 0.82533 & 0.85961 & 0.66205 & 0.99829 \\ \hline \multirow{3}{*}{0.5} & \(R_{0}\) & 0.87733 & 0.89863 & 0.99709 & 0.99723 \\ \cline{2-6}  & \(R_{1}\) & 0.87721 & 0.89842 & 0.75523 & 0.99726 \\ \hline \multirow{3}{*}{0.3} & \(R_{0}\) & 0.92243 & 0.93629 & 0.99585 & 0.99591 \\ \cline{2-6}  & \(R_{1}\) & 0.92264 & 0.93640 & 0.84933 & 0.99598 \\ \hline \multirow{3}{*}{0} & \(R_{0}\) & 0.99438 & 0.99441 & 0.99445 & 0.99449 \\ \cline{2-6}  & \(R_{1}\) & 0.99450 & 0.99442 & 0.99443 & 0.99456 \\ \hline \hline \end{tabular} \({}^{*}R_{0}\) and \(R_{1}\) represent the first and the second restored image, respectively.

\end{table} 
Table 4: The Sensitivity analysis of the proposed schemes. \[E(K)=\frac{1}{w\times h}\sum_{i=1}^{w\times h}K_{i} \tag{8}\]

\[S_{I}=\sqrt{\frac{1}{w\times h}\sum_{i=1}^{w\times h}\left(I_{i}\!\!-\!E(I) \right)^{2}} \tag{9}\]

\[S_{K}=\sqrt{\frac{1}{w\times h}\sum_{i=1}^{w\times h}\left(K_{i}\!\!-\!E(K) \right)^{2}} \tag{10}\]

\[S_{IK}=\frac{1}{w\times h}\sum_{i=1}^{w\times h}\left(I_{i}\!\!-\!E(I)\right) \times\left(K_{i}\!\!-\!E(K)\right) \tag{11}\]

We perform SSIM analysis for each of our proposed methods with \(p=45\), \(N=2\), and \(n=5\) in different \(\gamma\), then present the results together. A total of 7! (= 5040) experimental results were averaged and given in Table 5.

Observing Tables 4 and 5, we can find that in Methods 1, 2 and 4, as \(\gamma\) decreases, the sensitivity and SSIM value of the restored images becomes better and are almost identical. In turns of sensitivity, Method 4 gives the best result; Method 2 is slightly better than Method 1. In Method 3, as \(\gamma\) decreases, the sensitivity of the first restored image becomes slightly worse, but the second restored image becomes better, while the first recovered image has a sensitivity close to 1 and is always better than the second recovered image. In conclusion, the average sensitivity result of the restored image for Method 4 is the best. Method 1 has the best average SSIM results for the restored images. Method 3 has the best SSIM for the single restored image. ### Security Analysis

In the proposed scheme, we need to stack all shares to fully recover the original secret image; otherwise, the secret image cannot be leaked. For each pixel, it is only encrypted for two consecutive secret images, or is used as a camouflage image. When the pixel is used as a camouflage image, if we stack only \(k\) (\(k<n\)) shares, it just like we XOR \(k\) random values by our Algorithm III, so the original secret image cannot be reconstructed. It also produces unpredictable images because it is impossible to determine whether the stacked pixels are black or white. Therefore, it is impossible to correctly recover any secret image without collecting all \(N\) shares when \(\gamma\
eq 0\). On the other hand, if we collect all of the first \(n/2\) shares (or the last \(n/2\) shares) and stack them using the XOR operation, \(G_{1}\) (or \(G_{2}\)) will be recovered if \(\gamma=0\). Note that, from the constructing of Algorithm 1, we seem to be