Secure Linear Programming Using Privacy-Preserving Simplex

The SecureSCM project (www.securescm.org) aims to develop cryptographic solutions to the problem of data sharing in Supply Chain Optimization (SCO). The SCO problem has a precise mathematical structure. It is an instance of the general Linear Programming (LP) problem. However, standard techniques for LP problems are not suitable for this purpose because they require participants to reveal private data needed as input to the algorithm. The risk of revealing this information far exceeds the benefits gained. Therefore, the aim of the project is to develop efficient techniques for securely solving LP problems. In this paper we give a summary of work done in the cryptographic aspects of the project. We describe the state-of-the art building blocks for secure linear programming along with an analysis of their complexity.