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
pairs 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 computing of the exchanges. However, the proposed
approaches to date either only compute an approximative solution to the KEP or
they suffer from a huge decrease in performance. In this paper, we suggest a
novel privacy-preserving protocol that computes an exact solution to the KEP
and significantly outperforms the other existing exact approaches. Our novel
protocol is based on Integer Programming which is the most efficient method for
solving the KEP in the non privacy-preserving case. We achieve an improved
performance compared to the privacy-preserving approaches known to date by
extending the output of the ideal functionality to include the termination
decisions of the underlying algorithm. We implement our protocol in the SMPC
benchmarking framework MP-SPDZ and compare its performance to the existing
protocols for solving the KEP. In this extended version of our paper, we also
evaluate whether and if so how much information can be inferred from the
extended output of the ideal functionality.Comment: This is the updated and extended version of the work published in
19th Annual International Conference on Privacy, Security and Trust
(PST2022), August 22-24, 2022, Fredericton, Canada / Virtual Conference,
https://doi.org/10.1109/PST55820.2022.985196