# Secret Image Sharing Revisited: Forbidden Type, Support Type, and Their Two Approaches
## 4 Discussion: Other Details of the Design
### Sharing that Requires All Departments
(**b–c**) Any 2 of the 4 shadows can be used together to recover (**a**) without errors. Here, (**b**) is obtained by doctors \(\{D_{1},\)\(D_{3}\}\); whereas (**c**) is by doctors \(\{D_{2},\)\(D_{4}\}\). However, if the two shadows are from the forbidden combination \(\{D_{1},\)\(D_{2}\}\), then the recovery is (**d**), i.e., without the medical history of the patient. \(2295=(4\times 255)+(5\times 255)\) where 255 is the largest possible gray value, and 5 is the largest element of the matrix \(A\) whose \(Row_{i}=(I,i+1)\) for \(I=1,\ldots,4\). Hence, each integer needs \(\lceil(\log 2,296)/(\log 2)\rceil=12\) bits, or equivalently, 12/8 bytes. Hence each doctor holds \(512\times 256\times(12/8+1)=512\times 256\times(5/2)\) bytes as his shadow data. Therefore, each shadow size is \((512\times 1024)/(512\times 256\times 2.5)=1.6\) times smaller than the size of the image of Figure 4a. For military, the image in Figure 4a can be replaced by a military image such as Figure 5, and then shared likewise so that certain combination of participants are forbidden to view the dynamics data shown in the right half of Figure 5.  
The above are the practical applications of the sharing with forbidden combinations. Below we discuss the practical applications of the sharing with cross-department support. In some events, quite often there are several departments involved in the same events simultaneously. For example, after a terrorist attack in a city, many departments of the government will repeatedly check the same encrypted items such as the photos of the suspects, the weapons being used, or the protection program of the eyewitness. In this case, the national security department, the provincial police department, and the city police department form the three departments \(\{DEP_{H},DEP_{M},DEP_{L}\}\) mentioned in Section 3. Let each participant (security agent or policeman) belong to one of the three departments. Without loss of generality, assume the parameter pair (\(t\) = threshold, n = number of people in this department) for the three departments are, respectively, (\(t_{H}\) = 3, \(n_{H}\) = 4) for \(DEP_{H}\), (\(t_{M}\) = 5, \(n_{M}\) = 6) for \(DEP_{M}\), and (\(t_{L}\) = 7, \(n_{L}\) = 7) for \(DEP_{L}\). For the 4 officers in department \(DEP_{H}\), any 3 of them can recover Figure 6. For the 6 officers in department \(DEP_{M}\), any 5 of them can recover Figure 6. For the 7 officers in department \(DEP_{L}\), all 7 of them must gather together in order to recover Figure 6. However, due to illness, road accident, or business trips abroad, not every officer of the same department comes to the office every day. It is thus quite possible that on some working days, the department has insufficient personnel to unveil the secret. For the government to still function, our cross-department support system can help us to unveil Figure 6 through the cooperation of multiple departments. Using the design in Section 3.1, we did the experiments and found that the image in Figure 6 could be really unveiled as described in Table 2, either within-department or cross-department. Figure 5: The application example when Figure 4a is replaced by a military image. Figure 6: An image for crime investigation. The other application example is for the mobile-phone/automobile/airplane/ship factories or any company using blueprint to build machine or product (see Figure 7). We can treat the blueprint as a secret image. Then the blueprint is shared among the engineers of the production department. It is also shared among the managers of the administration departments, or among the co-owners of the company. Hence, the cross-department support system is also helpful for the same reasons mentioned in the last paragraph.