# 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
Interaction with the blockchain was handled via the Web3.py library, and communication with IPFS used the ipfshttpclient library. The datasets used in this study include the North Carolina Voter Registration List (NCVR), the DBLP-Scholar dataset, and the DBLP-ACM dataset. All three datasets are publicly available and widely used in privacy-preserving record linkage research. The independent variables in the experiments include the size of the data source, the number of participating parties, and the perturbation ratio. We extracted 5 K, 10 K, 50 K, 100 K, and 500 K records from the datasets. The number of participating parties was set to 3, 5, 7, and 9, respectively. To more accurately reflect real-world data errors, we applied perturbation processing to the original datasets, generating datasets with different noise levels. Specifically, we created three perturbed versions, introducing spelling errors, semantic changes, and structural adjustments. The perturbation operations included character deletion, random replacement, word order adjustment, and character insertion. To maintain control over the perturbations, we defined three error levels: Mod-1, where each record has at most one error; Mod-2, where each record has at most two errors; and Mod-3, where each record has at most three errors. Through this design, the datasets better align with real-world scenarios, providing effective support for evaluating the robustness and matching capabilities of privacy-preserving record linkage methods under different noise environments. We adopt five key metrics to evaluate the overall scalability, linkage quality, and security of the proposed method: runtime, precision, recall, F-score, and reconstruction rate. Among them, precision measures the proportion of actual matching record pairs in the total number of candidate record pairs, reflecting the method's accuracy; recall represents the proportion of actual matching record pairs relative to all true matching record pairs, indicating the method's coverage capability. The F-score, as a comprehensive metric combining precision and recall, is calculated using the following formula:

\[\text{F}=2\ \frac{Recall\times Precision}{Recall+Precision} \tag{17}\]

The reconstruction rate is a metric used to assess an attacker's ability to recover original data. It measures the extent to which an attacker, by controlling a subset of computation nodes, successfully reconstructs the information in Bloom filters. Suppose there are M Bloom filter pairs, each decomposed into t shares, randomly distributed to t nodes among N nodes [37]. Randomly select c colluding nodes from the N nodes and check how many Bloom filters have all t shares controlled by the colluding nodes. Theoretically, considering the impact of permutations, the reconstruction rate (i.e., the probability that an attacker successfully obtains all t shares for a specific Bloom filter and guesses its correct permutation) is calculated as follows:

\[Reconstruction\ Rate=\frac{\binom{c}{t}}{\binom{N}{t}}\times\frac{1}{t!} \tag{18}\]

### Experimental Results and Analysis

#### 6.2.1 Scalability Assessment

In evaluating scalability, we primarily use runtime as the key metric to analyze the system's performance under different data sizes and computational node configurations. To ensure security, our method employs secret sharing techniques and smart contract management, which significantly reduce the method's efficiency. Therefore, we use multi-node distributed computing and attribute-based partitioning methods to accelerate this process.