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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.

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