A Verifiable Multiparty Computation Solver for the Linear Assignment Problem: And Applications to Air Traffic Management

Abstract

The assignment problem is an essential problem in many application fields and frequently used to optimize resource usage. The problem is well understood and various efficient algorithms exist to solve the problem. However, it was unclear what practical performance could be achieved for privacy-preserving implementations based on multiparty computation (MPC) by leveraging more efficient solution strategies than MPC-based generic simplex solvers for linear programs. We solve this question by implementing and comparing different optimized MPC algorithms to solve the assignment problem for reasonable problem sizes. Our empirical approach revealed various insights to MPC-based optimization and we measured a significant (50x) speed-up compared to the known simplex-based approach. Furthermore, we also study the overhead introduced by making the results publicly verifiable by means of non-interactive zero-knowledge proofs. By leveraging modern proof systems we also achieve significant speed-up for proof and verification times compared to the previously proposed approaches as well as compact proof sizes. Our research was motivated by a real-world use case, based on detailed discussions with representative stakeholders from the aviation industry.