# 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
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**N**} & \multirow{2}{*}{**c**} & **Theoretical** & **Experimental** \\  & & **Reconstruction Rate** & **Reconstruction Rate** \\ \hline
50 & 10 & \(2.683\times 10^{-17}\) & 0 \\ \hline
50 & 20 & \(4.956\times 10^{-12}\) & 0 \\ \hline
50 & 40 & \(2.274\times 10^{-8}\) & 0.0000002 \\ \hline
100 & 20 & \(2.941\times 10^{-15}\) & 0 \\ \hline
100 & 40 & \(1.349\times 10^{-11}\) & 0 \\ \hline
100 & 80 & \(2.621\times 10^{-8}\) & 0.0000001 \\ \hline
200 & 40 & \(1.04\times 10^{-14}\) & 0 \\ \hline
200 & 80 & \(2.021\times 10^{-11}\) & 0 \\ \hline
200 & 160 & \(2.601\times 10^{-8}\) & 0.0000001 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of theoretical and experimental reconstruction rates under different collusion scenarios. The experimental reconstruction rates in high collusion scenarios (e.g., 2 \(\times\) 10\({}^{-7}\) for N = 50, c = 40) are observed to be higher than the recalculated theoretical rates (e.g., 2.274 \(\times\) 10\({}^{-8}\) for N = 50, c = 40). This difference might be attributed to factors in the experimental setup or inherent randomness. However, both theoretical (recalculated) and experimental rates are extremely low, and the general trends (effect of N and c) align. The results show that even with 80% node collusion, the t = 10 configuration results in experimentally observed reconstruction rates around 1-2 \(\times\) 10\({}^{-7}\). This is an extremely low rate. To put this into perspective, a reconstruction rate of 1-2\(\times\)10\({}^{-7}\) signifies approximately one to two successful reconstructions per ten million attempts, making the orders of magnitude rarer than one successful reconstruction per thousand. The dual protection of secret sharing and permutation confirms SBB-PPRL's strong privacy protection under high collusion scenarios. ## 7 Conclusions

We propose a privacy-preserving record linkage method based on secret sharing and blockchain (SSB-PPRL), designed for secure and efficient record linkage across multiple data sources. By leveraging secret sharing, blockchain coordination, and IPFS storage, the method enhances privacy, scalability, and fault tolerance. Experimental results demonstrate that it maintains high linkage quality and scalability while ensuring data privacy. Nevertheless, there is room for improvement in computational efficiency, protocol optimization, and resilience against extreme attack scenarios. Future research will focus on advancing the following key directions: Firstly, efforts will continue to optimize system performance and efficiency, including refining blockchain-IPFS interactions and enhancing node scheduling and core computation strategies managed by smart contracts. Secondly, work will aim to enhance overall system security and robustness, with a focus on researching stronger Byzantine fault-tolerant mechanisms for critical coordination and verification stages (potentially involving new smart contract designs), advanced collusion-resistant techniques, dynamic trust models, and comprehensive defenses and emergency response protocols against various DoS attacks, to effectively address extreme situations of large-scale computation and validation node failures or malicious behavior [38]. Furthermore, attention will be given to ensuring linkage quality under non-ideal conditions, particularly by investigating more fault-tolerant secret sharing aggregation algorithms and computation result consistency verification techniques to stabilize and control false positive/negative rates that may arise from partial node failures or data inconsistencies.