Kidney donations from living donors form an a ractive alternative to long waiting times on a list for a post-mortem donation. However, even if a living donor for a given patient is found, the donor's kidney might not meet the patient's medical requirements. If several patients are in this position, they may be able to exchange donors in a cyclic fashion. Current algorithmic approaches for determining such exchange cycles neglect the privacy requirements of donors and patients as they require their medical data to be centrally collected and evaluated. In this paper, we present the rst distributed privacy-preserving protocol for kidney exchange that ensures the correct computing of the exchange cycles while at the same time protecting the privacy of the patients' sensitive medical data. We prove correctness and security of the new protocol and evaluate its practical performance.

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The kidney exchange problem (KEP) is to find a constellation of exchanges that maximizes the number of transplants that can be carried out for a set of patients with kidney disease and their incompatible donors. Recently, this problem has been tackled from a privacy perspective in order to protect the sensitive medical data of patients and donors and to decrease the potential for manipulation of the computed exchanges. However, the proposed approaches either do not provide the same functionality as the conventional solutions to the KEP or they come along with a huge performance impact. In this paper, we provide a novel privacy-preserving protocol for the KEP which significantly outperforms the existing approaches by allowing a small information leakage. This leakage allows us to base our protocol on Integer Programming which is the most efficient method for solving the KEP in the non privacypreserving case. We implement our protocol in the SMPC benchmarking framework MP-SPDZ and compare its performance to the existing protocols for solving the KEP.