## 3 Main Scheme
### Algorithm III. Meaningful Shares Scheme  
We try to give the shares produced by Algorithm II with meaning in this subsection. To specify the ratio of a share that is required to be covered, we create the parameter \(\gamma\)\((0\leq\gamma\leq 1)\) in this case. When \(d=0\) (with probability 1-\(\gamma\)), Algorithm III directly copies the output pixels of Algorithm II as the final output share. When \(d=1\) (with probability \(\gamma\)), Algorithm III first copies the camouflaged pixels into the final output shares, and then encrypts them to remove the disguised parts when decrypting. When \(\gamma=1\), it means that the whole share is camouflaged. When \(\gamma=0.5\), it means that the proportion of pixels that are camouflaged in a share is about 50% of all pixels, and the proportion of pixels that are not camouflaged is 50% of all pixels. When \(\gamma=0\), it means that the whole share has no disguise. The size of the \(\gamma\) also affects the quality of the restored image, and the flexible adjustment of \(\gamma\) makes it easier for users to make decisions. Therefore, as \(\gamma\) increases, more of the shares are camouflaged. We design four different methods for Algorithm III so that users can choose the method that best satisfies their needs depending on the condition. Algorithm 3 represents Method 1, called average encryption; the other three methods will use it as the basic idea of the extension. The flow chart for Method 1 Steps 1-4 is shown in Figure 4.  
Figure 4: The flow chart of Method 1 Steps 1–4. In the most important step (main different step with other methods), Step 4 when \(d\) = 1, we must encrypt the camouflage image \(D\) into the share \(M\). First, give the value of the camouflage image to the meaningful sharing image \(M_{0-n-1}((i+k\times w/p)\bmod w,j)=D_{0-n-1}((i+k\times w/p)\bmod w,j)\) for \(k\) = 0 to \(p\). Next, we must calculate whether the result of the Boolean XOR operation on the shares \(M_{0}\sim M_{n-1}\) is the same as the selected \(Z\)th secret image \(S_{Z}((i+k\times w/p)\bmod w,j)\). If it is different, proceed with the following calculation: let \(X\) is \(7n/27\), and we randomly select one \(M_{j}\) among \(n\) meaningful sharing images. If the selected image is among \(M_{0}\sim M_{X-1}\), let the new value of \(M_{f}((i+k\times w/p)\bmod w,j)\) to be \(M_{f}((i+k\times w/p)\bmod w,j)\). If the selected \(M_{f}\) is among \(M_{X}\sim M_{n-1}\), let the new value of \(M_{f}((i+(k+Z)\times w/p)\bmod w,j)\) be \(M_{f}((i+(k+Z)\times w/p)\bmod w,j)\). Executing \(p\) times generates the pixels in these positions. \(k\) has an initial value of 0 and is incremented by 1 each time it finishes. ```
Input:\(N\) secret images \(S_{0},\ S_{1},\ \ldots,\ S_{N-1}\), \(n\) meaningless shares \(C_{0},\ C_{1},\ \ldots,\ C_{n-1},\ n\) camouflage images \(D_{0},\ D_{1},\ \ldots,\ D_{n-1}\), all of them with size \(w\times h\), and a positive integer \(p\). Output:\(n\) meaningful shares \(M_{0},\ldots,\ M_{n-1}\) with size \(w\times h\). 1. Let \(X=\lceil n/2\rceil\), \(Y=\lceil n/2\rceil\), and randomly select a pixel \((i,j)\{0\leq i\leq w,\ 0\leq j\leq h\}\). 2. \(Z\) = random \((0,\ N-1)\). 3. Define a number \(d\) = random \((0,\ 1)\), which is 1 with probability \(\gamma\). 4. If \(d=0\)then For\(k=0\)to\(p\)do For\(r\) = 0 to\(n-1\)do \(M_{r}((i+k\times w/p)\ \%\ w,j)=C_{r}((i+k\times w/p)\ \%\ w,j)\) else For\(k=0\)to\(p\)do For\(r\) = 0 to\(n-1\)do \(M_{r}((i+k\times w/p)\ \%\ w,j)=D_{r}((i+k\times w/p)\ \%\ w,j)\). For\(k=0\)to\(p\)do If\((M_{0}((i+k\times w/p)\%\ w,\ j)\oplus\ldots\oplus M_{X-1}((i+k\times w/p)\% w,\ j)\oplus M_{X}((i+(k+Z)\times w/p)\% w,\ j)\oplus\ldots\oplus M_{n-1}((i+(k+Z) \times w/p)\% w,\ j)\
eq S_{z}((i+k\times w/p)\% w,\ j))\), then  Let \(f\) = random(0, \(n-1\)). If\((f<X)\)then \(M_{f}((i+k\times w/p)\ \%\ w,\ j)=\overline{M_{f}((i+k\times w/p)\ \%\ w,\ j)). else \(M_{f}((i+(k+Z)\times w/p)\ \%\ w,\ j))=\overline{M_{f}((i+(k+Z)\times w/p)\ \%\ w,\ j). 5.