Secure multiparty linear programming using fixed-point arithmetic

Collaborative optimization problems can often be modeled as a linear program whose objective function and constraints combine data from several parties. However, important applications of this model (e.g., supply chain planning) involve private data that the parties cannot reveal to each other. Traditional linear programming methods cannot be used in this case. The problem can be solved using cryptographic protocols that compute with private data and preserve data privacy. We present a practical solution using multiparty computation based on secret sharing. The linear programming protocols use a variant of the simplex algorithm and secure computation with fixed-point rational numbers, optimized for this type of application. We present the main protocols as well as performance measurements for an implementation of our solution.