# A Secure Median Implementation for the Federated Secure Computing Architecture
## 3 Materials and Methods
### Implementation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Duration [s]**} \\ \cline{2-5}  & **Parties** & **Localhost** & **AWS-Localhost** & **AWS-Regions** \\ \hline breast-cancer & 2 & 3.55 & 4.12 & 261.09 \\ heart-disease & 4 & 15.64 & 16.91 & 804.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of durations for different datasets and configurations. of several parties, provides empty input to the computation. Generally, this issue cannot be entirely prevented, as empty or extreme values might be valid inputs. For use cases where such inputs are not expected, parties should impose additional constraints on input data, such as a minimum number of input elements or a specified input range. They should also verify the validity of inputs in the initial stage of the protocol and check their plausibility between stages. Apart from these measures, our implementation does not introduce any additional communication between the parties compared to the original protocol. Consequently, parties do not gain any extra information from each other, and the security analysis of the original algorithm remains valid. While the datasets remain hidden, in general, revealing the exact \(k\)th-ranked value, e.g., the median, reveals one data point and thus the exact value of one individual, which could be used to compromise data of targeted individuals [25]. One solution to additionally protect the output of the computation is to use additional differential privacy techniques, either adding noise to the output or randomly selecting a value from a probabilistic distribution of possible values [9; 26; 27]. Despite concerns about increased computational overhead, [PERSON] and [PERSON] [26] argue that this overhead is minimal, while [PERSON] and [PERSON] [9] demonstrate the remarkable efficiency of a specific protocol. ### Limitations

This study has several limitations that should be noted. Our benchmarking was conducted in a semi-honest setting, meaning our implementation does not address scenarios involving malicious actors. While [PERSON] et al. [10] describe additional measures for handling malicious settings and commercial solutions like Sharemind MPC [4] as a backend to FSC offer protections against such threats, these models were outside the scope of our baseline implementation. Additionally, our performance evaluation used synthetic datasets to explore various sizes and participant counts. Although this approach provides insights into computational scaling, it may not fully capture the complexities and variability of real-world data. To address this, we incorporated two medical datasets, which, while limited to the healthcare domain, offer insights into the computational scaling of real-world data irrespective of the domain. The medical context, though, is a particularly interesting application domain due to the sensitivity of patient information, highlighting the need for privacy-preserving techniques in practical applications. Additionally, we chose not to minimize network latencies in our experiments to demonstrate a range of possible computation times with real datasets. We also conducted experiments using hyperscalers in various regions to cover the spectrum of network latency. In practice, parties could replicate their data privately within the same region, allowing secure peer-to-peer computations to be performed in a low-latency environment, thus achieving computation times closer to the lower end observed in our experiments in local deployment. ## 6 Conclusions

The application of methods of MPC offers solutions to various challenges of collective research. In our study, we bridge the gap between theoretical advancements in MPC and their practical deployment in medical research, offering the implementation and real-world benchmarking of a theoretical protocol tailored for rank-based statistics within the framework of FSC. By analyzing real-world datasets, we provide a concrete use case demonstrating the applicability of our approach in cloud environments.