# Privacy Protection Based on Special Identifiers of Intersection Base Computing Technology
## 4 Discussion
### Experimental Evaluation  
We have implemented the above protocols separately to compare their specific performance. Both protocols were implemented using the Python language, and the testing platform was equipped with a Core (TM) i7-8750H [EMAIL_ADDRESS] GHz 2.21 GHz Model processor (Intel Corporation, Santa Clara, CA, USA) and 16 GB 1867 MHz DDR3 memory. This test was completed in a LAN network environment with low network latency. For the following two protocols, we implemented them using the Python language. Our implementation is divided into two stages: one is the online communication stage and the other is the offline operation stage. For the above two protocols, we have uniformly ignored the process of generating and interacting with the sender's key, and the length of our key is set to 3072 bits, which can fully ensure our information security. In the offline stage [23], the offline stage mainly deals with polynomial roots and the corresponding encryption and decryption operations. Our protocol mainly handles operations such as encryption, decryption, and scalar multiplication encryption during the offline phase. In the online stage, Ref. [23] mainly obtains encrypted polynomials through the interaction process between both parties and can obtain intersections. However, our protocol mainly matches by specific identifiers, finds approximately identical terms, and sends them to the other party. The specific performance is shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Protocol** & **Time Complexity** & **Space Complexity** & **Rounds** \\ \hline The text’s & \(O(n)\sim O(mn)\) & \(O(n)\sim O(mn)\) & 2 \\ Reference [23]’s & \(O(n^{2})\) & \(O(n^{2})\) & 6 \\ protocol & & & \\ \hline \end{tabular}
\end{table}
Table 2: Performance analysis.  
After analyzing the above table, we found that the effect of our protocol in the offline stage is far superior to that of [23]. In order to see the specific changes in the two protocols more directly, we specially drew Figure 4, in which we used the red line to represent the offline calculation stage of our protocol, and the blue line to describe the offline calculation stage [23]. In this experiment, the number of elements in \(X\) set is kept constant at 50, and the number of elements in \(Y\) set is 1 to 10 times that of \(X\), so the \(X\)-axis represents the ratio of the number of elements in the \(X\) and \(Y\) sets, and the \(Y\)-axis represents the corresponding running time. It is obvious from Figure 4 that our protocol efficiency is relatively efficient.  
Our protocol has been tested and it was found that when our protocol is faced with an imbalance of two elements, the effect of offline computing is far better than the equilibrium situation. Moreover, after some modifications to our protocol, we can quickly find the intersection elements. We only need to add a new guide to [PERSON]'s element in the pre-processing stage, and we can change to a new encryption, which can only be seen by ourselves, and send the element to [PERSON]. When [PERSON] calculates the element, it is only necessary to form a list with the guide to participate in the operation, and send it to [PERSON]. Then, [PERSON] calculates the 0 element, and can find the corresponding set intersection element through the corresponding guide of the 0 element.