Privacy Preserving Linear Programming

With the rapid increase in computing, storage and networking resources, data is not only collected and stored, but also analyzed. This creates a serious privacy problem which often inhibits the use of this data. In this chapter, we investigate and resolve the privacy issues in a fundamental optimization problem -- linear programming (LP) which is formulated by data collected from different parties. We first consider the case where the objective function and constraints of the linear programming problem are not partitioned between two parties where one party privately holds the objective function while the other party privately holds the constraints. Second, we present a privacy preserving technique for the case that objective function and constraints are arbitrarily partitioned between two parties where each party privately holds a share of objective function and constraints. Finally, we extend the technique for securely solving two-party arbitrarily partitioned linear programming problems to a multi-party scenario. In summary, we propose a set of efficient and secure transformation based techniques that create significant value-added benefits of being independent of the specific algorithms used for solving the linear programming problem.