A Secure Median Implementation for the Federated Secure Computing Architecture

In Secure Multiparty Computation (MPC or SMPC), functions are evaluated in encrypted peer-to-peer networks without revealing the private inputs of the participating parties. The median is a non-trivial computation in MPC and is particularly relevant in fields like medicine and economics. Here, we provide an MPC implementation of the median for the Federated Secure Computing (FSC) framework. It is tested on synthetic datasets with varying sizes (N=102 to N=107) and number of participants (M=2 to M=10) across different network environments and hardware configurations. Using minimal networking and computational resources on a commercial hyperscaler, we evaluated real-world performance with breast cancer (N=569) and heart disease (N=920) datasets. Our results showed effective scaling up to N=106 entries with runtime between 1 and 4 s, but runtime exceeded 15 s for 107 entries. The runtime increased linearly with the number of parties, remaining below one minute for up to M=10 parties. Tests with real-world medical data highlight significant network overhead, with runtime increasing from 16 to 17 s locally to over 800 s across hyperscaler regions, emphasizing the need to minimize latency for practical deployment.