To this day, there are still some countries where the exchange of kidneys
between multiple incompatible patient-donor pairs is restricted by law.
Typically, legal regulations in this context are put in place to prohibit
coercion and manipulation in order to prevent a market for organ trade. Yet, in
countries where kidney exchange is practiced, existing platforms to facilitate
such exchanges generally lack sufficient privacy mechanisms. In this paper, we
propose a privacy-preserving protocol for kidney exchange that not only
addresses the privacy problem of existing platforms but also is geared to lead
the way in overcoming legal issues in those countries where kidney exchange is
still not practiced. In our approach, we use the concept of secret sharing to
distribute the medical data of patients and donors among a set of computing
peers in a privacy-preserving fashion. These computing peers then execute our
new Secure Multi-Party Computation (SMPC) protocol among each other to
determine an optimal set of kidney exchanges. As part of our new protocol, we
devise a privacy-preserving solution to the maximum matching problem on general
graphs. We have implemented the protocol in the SMPC benchmarking framework
MP-SPDZ and provide a comprehensive performance evaluation. Furthermore, we
analyze the practicality of our protocol when used in a dynamic setting (where
patients and donors arrive and depart over time) based on a data set from the
United Network for Organ Sharing.

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