Prioritization and exchange chains in privacy-preserving kidney exchange

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.