## 7 Unbalanced PSI-CA Protocol Based on Dual-Cloud Assistance
### Experimental Analysis  
#### 7.5.1 Data Computation Volume  
When evaluating the performance of these protocols, the computational load borne by the small health app developer is undoubtedly a critical factor. Since all three protocols have been introduced, this section specifically focuses on the computational volume of the small health app developer to accurately gauge and compare the efficiency of the three distinct protocols in operation. Specifically, this section will conduct a detailed analysis and comparison of the main computational tasks that the small health app developer must execute across these protocols to fully assess each protocol's demand on the small health app developer's computational resources. This analysis will primarily focus on the types of operations involved, aiming to clarify which protocol demonstrates relative advantages in reducing the small health app developer's computational burden, thus providing a solid basis for selecting the most appropriate protocol. Below is an analysis of the main types of operations involved in each protocol, focusing primarily on the outsourcing and intersection processes, as the preprocessing can be completed offline. 1. **Unbalanced PSI-CA protocol based on Cuckoo filter:** Two rounds of modular exponentiation operations and filter retrieval. 2. **Unbalanced PSI-CA protocol based on single-cloud assistance**: A single round of multiplication operations. 3. **Unbalanced PSI-CA protocol based on dual-cloud assistance**: Two rounds of multiplication operations. An analysis of the single-instance time consumption for these four operations offers a practical insight into the computational volume differences:  
1. **Modular Exponentiation Operation**: Representing computation-intensive operations, modular exponentiation becomes particularly time-consuming. On a standard hardware setup, the time required for a single modular exponentiation operation depends primarily on the size of the numbers involved and the efficiency of the algorithm. 2. **Multiplication Operation**: Compared to modular exponentiation, multiplication operations execute much faster on modern computing systems, even when involving large numbers. Therefore, whether it is a single round of multiplication in the single-cloud protocol or two rounds in the dual-cloud protocol, the processing times are relatively short. 3. **Cuckoo Filter Retrieval**: Although relatively quick, the retrieval operation for a Cuckoo filter involves memory access, which may make it slightly slower than simple arithmetic operations. The exact time required for this operation depends on the size of the filter and the efficiency of the implementation. After a detailed analysis and comparison, this section has conducted a thorough exploration of the key computational tasks executed by the small health app developer across the three different protocols. These tasks include modular exponentiation, multiplication operations, and Cuckoo filter retrieval By assessing these types of computations and their specific time consumptions, the following conclusions can be drawn:  
1. **Unbalanced PSI-CA Protocol Based On Cuckoo Filter**: Primarily relies on two rounds of modular exponentiation, which are computation-intensive, especially when dealing with large numbers, making it the most time-consuming of all the operations reviewed. Additionally, the filter retrieval operation is also involved. 2. **Unbalanced PSI-CA Protocol Based On Single-Cloud Assistance**: By executing a single round of multiplication, it significantly alleviates the computational burden on the small health app developer. Multiplication operations, even for large numbers, can be done quickly. 3. **Unbalanced PSI-CA Protocol Based On Dual-Cloud Assistance**: Includes two rounds of multiplication operations, also aiming to distribute the computational pressure on the small health app developer. Although it involves two rounds of multiplication, due to the inherent efficiency of the operation, the total processing time remains within an acceptable range.