## 7 Unbalanced PSI-CA Protocol Based on Dual-Cloud Assistance
### Experimental Analysis
#### 7.5.2 Protocol Running Time  
After introducing all three protocols, this section primarily discusses the running times of the protocols. The running time of a protocol is an important benchmark for evaluation in this paper because it directly reflects the protocol's efficiency in practical operations. The factors affecting the running time of the protocol include computational time and communication time. As shown in Table 5, experiments were conducted to record the running times of the protocols under various data volume combinations. Table 5 also places the running times of the unbalanced PSI -CA protocol based on Cuckoo filter, unbalanced PSI-CA protocol based on single-cloud assistance, and unbalanced PSI-CA protocol based on dual-cloud assistance side by side for comparative analysis. Here, Protocol I refers to the unbalanced PSI-CA protocol based on Cuckoo filter, Protocol II refers to the unbalanced PSI-CA protocol based on single-cloud assistance, and Protocol III refers to the unbalanced PSI-CA protocol based on dual-cloud assistance. It is noteworthy that the preprocessing stages of all three protocols can be completed offline, meaning they do not directly contribute to online operation delays. Therefore, the recorded running times in this paper refer to the total time of all processes, excluding preprocessing. Specifically, in Protocol I this primarily refers to the total duration of the intersection process; in Protocols II and III, it refers to the total duration of both the outsourcing and intersection processes. Through experimental analysis, the paper draws the following conclusions: At smaller data volumes, the performance differences between the three protocols are not significant. However, as the data volume increases, the differences in running times between the protocols become apparent. Generally, the unbalanced PSI-CA protocol based on Cuckoo filter tends to have the longest running time, while the unbalanced PSI-CA protocol based on single-cloud assistance has the shortest running time, and the performance of the unbalanced PSI-CA protocol based on dual-cloud assistance is in the middle. This phenomenon can be explained by the complexity of data handling and the differences in communication overhead among the protocols. The unbalanced PSI-CA protocol based on Cuckoo filter, due to its direct and unoptimized calculations, is less efficient when handling large volumes of data. Nevertheless, at very small data volumes, where the proportion of communication time is relatively high, the impact of data transmission costs on total running time becomes significant. In such cases, the unbalanced PSI-CA protocol based on Cuckoo filter does not necessarily appear inefficient because other protocols might be even less efficient in data transmission. Especially in environments with poor network conditions or limited data transfer rates, the lower communication demands of the unbalanced PSI-CA protocol based on Cuckoo filter might, in some cases, lead to better performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Data Volume**} & \multicolumn{1}{c}{**Protocol I**} & \multicolumn{1}{c}{**Protocol II**} & \multicolumn{1}{c}{**Protocol III**} \\  & **Running Time (s)** & **Running Time (s)** & **Running Time (s)** \\ \hline \(2^{10}|2^{15}\) & 0.1539 & 0.1543 & 0.1612 \\ \(2^{10}|2^{17}\) & 0.1569 & 0.1573 & 0.1742 \\ \(2^{10}|2^{20}\) & 0.1616 & 0.1611 & 0.1736 \\ \(2^  
Moreover, the running times of the unbalanced PSI-CA protocol based on single-cloud assistance and the unbalanced PSI-CA protocol based on dual-cloud assistance are significantly reduced through distributed computing and the use of cloud resources, especially when dealing with large-scale datasets. In summary, choosing the appropriate protocol requires a comprehensive consideration of factors such as data volume, computational resources, and network environment.