## 7 Unbalanced PSI-CA Protocol Based on Dual-Cloud Assistance
### Extensions
#### 7.7.2 Data Updates  
To further enhance the practicality of the scheme, this paper also designs a data update mode compatible with the scheme, making the overall scheme more practical and reliable. * **Data Updates on the Large Medical Institution's Side:** As shown in Figure 5, the update details of the large medical institution are as follows: \[Z=\left\{Z_{1},Z_{2}\...,Z_{n_{3}}\right\}\] \[\forall k,1\leq k\leq n_{3}\] \[Z^{\prime}_{k}=E_{pkC}(a)^{\alpha*H(Z_{k})}\] \[\exists U=\left\{u_{1},u_{2}\...\ u_{n_{3}}|u_{k}=(update_{k},Z^{ \prime}_{k})\right\}\] \[\forall k,1\leq k\leq  
5. \(z_{k}^{\prime}\) represents the data \(z_{k}\) after encryption processing. 6. \(\text{update}_{k}\) represents the operation index, used to determine whether the update operation is an insertion or deletion. 7. \(U\) represents the set of data sent by the large medical institution to the cloud-assisted server \(H_{2}\); \(u_{k}\) represents the \(k\)-th element of \(U\). **Update process:**  
1. The large medical institution has a set of elements \(Z\) it wants to insert or delete. These elements are blinded before being sent to cloud server \(H_{2}\). Specifically, \(z_{k}^{\prime}=E_{pk_{c}}(a)^{\ast H(z_{k})}\). 2. In addition to sending the blinded elements, the large medical institution also sends an identifier variable \(\text{update}_{k}\) to inform the small health app developer whether the operation is an insertion or a deletion. 3. During an insertion operation, \(H_{2}\) first checks whether the current filter's load factor \(\omega\) exceeds 0.95. 4. If the load factor \(\omega\) is greater than 0.95, then \(H_{2}\) must request the large medical institution to generate a new filter using all elements to maintain high spatial and lookup efficiency of the filter. 5. If the load factor \(\omega\) is less than or equal to 0.95, then \(H_{2}\) can directly insert the element into the current filter \(CF\). 6. In a deletion operation, \(H_{2}\) removes the specified element from the filter \(CF\), a process that does not require generating a new filter. * **Data Updates on the Small Health App Developer's Side:** As shown in Figure 6, the update details of the small health app developer are as follows:  
**Definition of main participants and related symbols:**  
1. Small health app developer: Represents the small health app developer who wants to perform data updates. 2. Cloud server \(H_{1}\) represents the cloud-assisted server \(H_{1}\) that assists the small health app developer in completing update operations. 3. Cloud server \(H_{2}\) represents the cloud-assisted server \(H_{2}\) that assists the small health app developer in completing update operations. 4. \(Z\) represents the set of data to be updated; \(z_{k}\) represents the \(k\)-th element of \(Z\). 5. \(z_{k}^{\prime}\) represents the data after being processed by the hash function \(H\). 6. \(k\) represents the data index, used to determine the type of update, either insertion or deletion, and to retrieve the updated data based on the index. Figure 6: Data updates on the small health app developer’s side. When adding data, date\({}_{k}\) represents the data processed through the dual-cloud scheme and sent to the two cloud-assisted servers. When deleting, date\({}_{k}\) is null. * 8. \(V\) represents the set of data sent by the small health app developer to the cloud-assisted server \(H_{1}\); \(v_{k}\) represents the \(k\)-th element of \(V\). * 9. \(V^{\prime}\) represents the set of data sent by the small health app developer to the cloud-assisted server \(H_{2}\); \(v^{\prime}_{k}\) represents the \(k\)-th element of \(V^{\prime}\). **Update process:**  
1. The small health app developer has a set of elements \(Z\) it wants to insert or delete. In both cases, the small health app developer blinds each element and sends them to \(H_{1}\) and \(H_{2}\), respectively. 2. The small health app developer sends a data index \(K\) to inform the cloud servers about the type of update, whether it is an insertion or a deletion.