Open Access

Georg Neugebauer, Lucas Brutschy, Ulrike Meyer, Susanne Wetzel

• 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 privacy-preserving 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.