# A Privacy-Preserving Record Linkage Method Based on Secret Sharing and Blockchain
## 4 Methods
### Output and Audit Module
#### 4.4.4 Record Keeping and Provenance
When the number of participating parties is 3, the perturbation ratio is 30%, the number of secret shares is 5, and the number of masks is 5 sets, the runtime of the proposed method (in the approximate matching phase and the audit verification phase) varies with increasing data source size, as shown in Figure 5.

As the dataset size increases, the specific runtime for different numbers of nodes is shown in Table 1.

When the data size is 50 k, the perturbation ratio is 30%, the number of secret shares is 5, and the number of masks is 5 sets, the running time of the proposed method (for the approximate matching phase and the audit verification phase) varies with the increase in the number of participants, as shown Figure 6.

As the number of participants increases, the specific runtime for different numbers of nodes is shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset Size** & **Node Count = 64** & **Node Count = 128** & **Node Count = 256** \\ \hline
5 K & 5.73 & 3.02 & \(1.57\) \\ \hline
10 K & 22.92 & 12.13 & 6.28 \\ \hline
50 K & 572.92 & 300.00 & 154.25 \\ \hline
100 K & 2291.67 & 1201.00 & 617.34 \\ \hline
500 K & 57,291.67 & 30,120.00 & 15,480.50 \\ \hline \end{tabular}
\end{table} 
Table 1: The runtime performance for varying node counts with growing dataset size. Figure 5: The runtime of the proposed method varies with increasing data source size. #### 6.2.2 Method Performance Evaluation

To comprehensively evaluate the linkage quality of the proposed method, we assessed the SSB-PPRL method in terms of precision, recall, and F-score. The evaluation examined how these three metrics vary with an increasing number of participants, given a fixed data size, across datasets with three different levels of perturbation. Under datasets with 20,000 records perturbed to varying degrees (Mod-1 to Mod-3), the precision of all methods decreases as the number of participants and data error rates increase, with the most significant decline observed under high error rates (Mod-3). Benefiting from its neural network matching mechanism, the Yao method achieves the highest prediction precision and robust performance. The Vatsalan method, relying on precise privacy-preserving computation, is primarily constrained by the performance of its Bloom filter and Dice similarity function. Our proposed method, based on accurate secret sharing computation, incurs no additional precision loss and demonstrates precision comparable to the Vatsalan method. Notably, under complex conditions with a high number of participants and elevated error rates, our method outperforms Han, exhibiting a clear advantage in precision. This avoids the potential negative impact of the binary tree structure on matching accuracy observed in the Han method. The precision variation with the number of participants in the three perturbed datasets is shown in Figure 7.

The specific precision values for the three perturbed datasets as the number of participants varies are shown in Table 3.

As the number of participants and perturbation levels increase, the recall rates of all methods show a downward trend. Notably, the decline in recall from Mod-1 to Mod-2 is particularly significant. The Yao method stands out, maintaining the highest recall across all test conditions. Additionally, the Vatsalan method and our proposed SSB-PPRL method also sustain relatively high recall rates, outperforming the Han method, which aligns with their core privacy-preserving mechanisms that theoretically introduce no additional False \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Participants** & **Node Count = 64** & **Node Count = 128** & **Node Count = 256** \\ \hline
3 & 572.92 & 300 & 154.25 \\ \hline
5 & 2291.67 & 1201 & 617.34 \\ \hline
7 & 5156.25 & 2700 & 1388 \\ \hline
9 & 9166.67 & 4815 & 2475.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The runtime performance for varying node counts with increasing participant numbers. Figure 6: The runtime performance for varying node counts with increasing participant numbers. Negatives.