Abstract. In this paper, we introduce the first protocols for multiparty, privacy-preserving, fair reconciliation of ordered sets. Our contributions are twofold. First, we 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, we propose new constructions for fair, multi-party, privacy-preserving reconciliation of ordered sets based on multiset operations. We prove that all our protocols are privacy-preserving in the semi-honest model. We furthermore provide a detailed performance analysis of our new protocols and show that the constructions based on multisets generally outperform the round-based approach.

Privacy-preserving reconciliation protocols on ordered sets are protocols that solve a particular subproblem of secure multiparty computation. Here, each party holds a private input set of equal size in which the elements are ordered according to the party's preferences. The goal of a reconciliation protocol on these ordered sets is then to find all common elements in the parties' input sets that maximize the joint preferences of the parties. In this paper, we present two main contributions that improve on the current state of the art. First, we propose two new protocols for privacypreserving reconciliation and prove their correctness and security properties. We implement and evaluate our protocols as well as two previously published multi-party reconciliation protocols. Our implementation is the first practical solution to reconciliation problems in the multi-party setting. Our comparison shows that our new protocols outperform the original protocols. The basic optimization idea is to reduce the highest degree polynomial in the protocol design. Second, we generalize privacy-preserving reconciliation protocols, i. e., relaxing the input constraint from totally ordered input sets of equal size to pre-ordered input sets of arbitrary size.

Abstract-Fair and privacy-preserving reconciliation protocols on ordered sets have been introduced recently. Despite the fact that these protocols promise to have a great impact in a variety of applications, so far their practical use has been explored to a limited extent only. This paper addresses this gap. As main contributions, this paper identifies e-voting, auctions, event scheduling, and policy reconciliation as four far-reaching areas of application and shows how fair and privacy-preserving reconciliation protocols can be used effectively in these contexts.

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