## 3 Main Results
### (\(n\), \(n\)) XOR-Based VCS with Color Secret and Covers  
Similarly, in Algorithm 6, for the red, blue, and green channels, we calculate the value \(P_{x}^{R}(i,\,j)\), \(P_{x}^{G}(i,\,j)\), \(P_{x}^{B}(i,\,j)\) for each pixel of each cover, and choose the minimum \(P_{\min}^{R}\), \(P_{\min}^{G}\), \(P_{\min}^{B}\), \(P_{\min}^{B}\) from all \(x\) in \(\{1,\,2,\,\ldots,\,n\}\) separately. In each channel, if more than two values are identical and are also the minimum value, we randomly choose a share with an equal probability to change the pixel. Then, for each channel \(A\) (\(A=R\), \(G\) or \(B\)), the \(min\)-th share pixel is set to the value produced by XORing \(S^{A}(i,\,j)\) with the other \(n-1\) pixels. Other \(n-1\) shares \(R_{x}^{R}(i,\,j)\), \(R_{x}^{G}(i,\,j)\), \(R_{x}^{B}(i,\,j)\) are set to be \(C_{x}^{R}(i,\,j)\), \(C_{x}^{G}(i,\,j)\), \(C_{x}^{B}(i,\,j)\), respectively. The schematic and the flow chart of Algorithm 6 are shown in Figures 6 and 7, respectively.  
Figure 4: The basic schematic of (\(n\), \(n\)) XOR-based VCS with grayscale secret and covers.  
Figure 5: The flow chart of Algorithm 5.  
```
Input: A secret grayscale image \(S\) and \(n\) cover grayscale image \(C_{1}\),..., \(C_{n}\), all of them with \(H\times W\) pixels. Output:\(n\) gray meaningful shares \(R_{1}\),..., \(R_{n}\), each of which is \(H\times W\) in size.
1. Choose one position \((i,j)\) from \(H\times W\).
2. For each chosen \(C_{1}(i,j)\),..., \(C_{n}(i,j)\), calculate the value \(P_{x}(i,j)=|\,C_{x}(i,j)-(C_{1}(i,j)\oplus\ldots\oplus C_{x-1}(i,j)\oplus C_{ x+1}(i,j)\oplus\ldots\oplus C_{n}(i,j)\oplus(j,j))\,|\,.\)
3. Choose \(min\) from \(\{1,\,2,\,\ldots,\,n\}\) such that \(P_{min}(i,j)=\min\{P_{1}(i,j),\,P_{2}(i,j),\,\ldots,\,P_{n}(i,j)\}\).
4.\(R_{min}(i,j)\) is set to \(R_{min}(i,j)=C_{1}(i,j)\oplus\ldots\oplus C_{min-1}(i,j)\oplus C_{min+1}(i,j) \oplus\ldots\oplus C_{n}(i,j)\oplus C(i,j)\).
```  
**Algorithm 5**\((n,n)\) XOR-based VC scheme with grayscale meaningful shares.  
```
Input: A secret color image \(S\) and \(n\) cover color image \(C_{1}\),..., \(C_{n}\), all of them with \(H\times W\) pixels. Output:\(n\) color meaningful shares \(R_{1}\),..., \(R_{n}\), each of which is \(H\times W\) in size.
1. Choose one position \((i,j)\) from \(H\times W\).
2. For each channel \(A\in\{R,\,G,\,B\}\) do Step 3-5.
3. For each \(x\in\{1,\,2,\,\ldots,\,n\}\), calculate the value \(P_{x}^{A}(i,j)=|\,C_{x}^{A}(i,j)-(C_{1}^{A}(i,j)\oplus\ldots\oplus C_{x-1}^{A }(i,j)\oplus C_{x+1}^{A}(i,j)\oplus\ldots\oplus C_{n}^{A}(i,j)\oplus S^{A}(i, j))\,|\,.\)
4. Choose \(min\) from \(\{1,\,2,\,\ldots,\,n\}\) such that \(P_{min}^{A}=\min\{P_{1}^{A}(i,j),\,P_{2}^{A}(i,j),\,\ldots,\,P_{n}^{A}(i,j)\}\).
5.\(R_{min}^{A}(i,j)\) is set to be \(R_{min}^{A}(i,j)=C_{1}^{A}(i,j)\oplus\ldots\oplus C_{min-1}^{A}(i,j)\oplus C _{min+1}^{A}(i,j)\oplus\ldots\oplus C_{n}^{A}(i,j)\oplus S^{A}(i,j)\). Finally, other \(n-1\) share pixels are set to be \(C^{A}(i,j)\), such that \(R_{1}^{A}(i,j)=C_{1}^{A}(i,j),\,\ldots,\,R_{min-1}^{A}(i,j)=C_{min-1}^{A}(i,j)\), \(R_{min+1}^{A}(i,j),\,R_{min+1}^{A}(i,j)=C_{min+1}^{A}(i,j)\).
6. Repeat Steps 1-5 until all secret pixels have been processed, and output \(n\) shares \(R_{1}\),..., \(R_{n}\), each of which has the same image size as the secret image.
```  
**Algorithm 6**\((n,n)\) XOR-based VC scheme with color meaningful shares  
Figure 6: The basic schematic of Algorithm 6.  
Figure 7: The flow chart of Algorithm 6.