The kidney exchange problem (KEP) seeks to find possible exchanges among pairs of patients and their incompatible kidney donors while meeting specific optimization criteria such as maximizing the overall number of possible transplants. Recently, several privacy-preserving protocols for solving the KEP have been proposed. However, the protocols known to date lack scalability in practice since the KEP is an NP-complete problem. We address this issue by proposing a novel privacy-preserving protocol which computes an approximate solution for the KEP that scales well for the large numbers of patient-donor pairs encountered in practice. As opposed to prior work on privacy-preserving kidney exchange, our protocol is generic w.r.t. the security model that can be employed. Compared to the most efficient privacy-preserving protocols for kidney exchange existing to date, our protocol is entirely data oblivious and it exhibits a far superior run time performance. As a second contribution, we use a real-world data set to simulate the application of our protocol as part of a kidney exchange platform, where patient-donor pairs register and de-register over time, and thereby determine its approximation quality in a real-world setting.

Traditionally, kidney exchange allows patients with an incompatible living kidney donor to exchange their donors in form of exchange cycles. Today, additional transplants are achieved through so-called exchange chains. These are initiated by an altruistic donor, who donates a kidney without requiring anything in return. In practice, kidney exchange is typically facilitated through central platforms, which compute potential exchange cycles and chains for a large number of patients and donors. To overcome the severe security issues of this centralized approach, several secure multi-party computation (SMPC) protocols for kidney exchange have been proposed recently. However, the privacy-preserving protocols proposed to date either do not scale for a sufficient number of patients and donors or do not support exchange chains. In this paper, we present the first SMPC protocol that both supports exchange chains and yields efficient run times for a large number of patients and donors. We have implemented our protocol in the framework MP-SPDZ and evaluated its run time performance. Besides, we present evaluation results based on real-world data for the use of our protocol in a dynamic setting, where patient-donor pairs and altruistic donors arrive and depart over time.

The Kidney Exchange Problem (KEP) aims at finding an optimal set of exchanges among pairs of patients and their medically incompatible living kidney donors as well as altruistic donors who are not associated with any particular patient but want to donate a kidney to any person in need. Existing platforms that offer the finding of such exchanges for patient-donor pairs and altruistic donors are organized in a centralized fashion and operated by a single platform operator. This makes them susceptible to manipulation and corruption. Recent research has targeted these security issues by proposing decentralized Secure Multi-Party Computation (SMPC) protocols for solving the KEP. However, these protocols fail to meet two important requirements for kidney exchange in practice. First, they do not allow for altruistic donors. While such donors are not legally allowed in all countries, they have been shown to have a positive effect on the number of transplants that can be found. Second, the existing SMPC protocols do not support prioritization, which is used in existing platforms to give priority to certain exchanges or patient-donor pairs, e.g., to patients who are hard to match due to their medical characteristics. In this paper, we introduce a generic gate for implementing prioritization in kidney exchange. We extend two existing SMPC protocols for solving the KEP such that they allow for altruistic donors and prioritization and present one novel SMPC protocol for solving the KEP with altruistic donors and prioritization based on dynamic programming. We prove the security of all protocols and analyze their complexity. We implement all protocols and evaluate their performance for the setting where altruistic donors are legally allowed and for the setting where they are not. Thereby, we determine the performance impact of the inclusion of altruistic donors and obtain those approaches that perform best for each setting.

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.

The kidney exchange problem (KEP) seeks to determine a constellation of exchanges that maximizes the number of possible transplants between a set of patients and their incompatible donors. Recently, Secure Multi-Party Computation (SMPC) techniques were used to devise privacy-preserving protocols that allow the solving of the KEP in a distributed fashion. However, these protocols lack sufficient performance in practice. In the non-privacy-preserving case, the most efficient algorithms solving the KEP are based on integer programming. It is in this context, that we propose a privacy-preserving protocol based on these integer programming techniques that efficiently solves the KEP in a privacy-preserving fashion. We prove the security of this protocol and analyze its complexity. Furthermore, we provide a comprehensive performance evaluation of an implementation of the protocol in the SMPC benchmarking framework MP-SPDZ.

Secure Multi-Party Computation (SMPC) allows a set of parties to securely compute a functionality in a distributed fashion without the need for any trusted external party. Usually, it is assumed that the parties know each other and have already established authenticated channels among each other. However, in practice the parties sometimes must stay anonymous. In this paper, we conceptualize a framework that enables the repeated execution of an SMPC protocol for a given functionality such that the parties can keep their participation in the protocol executions private and at the same time be sure that only authorized parties may take part in a protocol execution. We identify the security properties that an implementation of our framework must meet and introduce a first implementation of the framework that achieves these properties.