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In this paper, the authors introduce the first protocols for multi-party, privacy-preserving, fair reconciliation of ordered sets. The contributions are twofold. First, they show that it is possible to extend the round-based construction for fair, two-party privacy-preserving reconciliation of ordered sets to multiple parties using a multi-party privacy-preserving set intersection protocol. Second, they propose new constructions for fair, multi-party, privacy-preserving reconciliation of ordered sets based on multi-set operations. They prove that all the protocols are privacy-preserving in the semi-honest model. They furthermore provide a detailed performance analysis of the new protocols and show that the constructions based on multi-sets generally outperform the round-based approach.
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