Privacy-preserving cooperative scientific computations

The growth of the Internet has triggered tremendous opportunities for cooperative computation, in which multiple parties need to jointly conduct computation tasks based on the private inputs they each supply. These computations could occur between mutually untrusted parties, or even between competitors. For example, two competing financial organizations might jointly invest in a project that must satisfy both organizations' private and valuable constraints. Today, to conduct such a computation, one must usually know the inputs from all the participants; however if nobody can be trusted enough to know all the inputs, privacy will become a primary concern. Linear systems of equations problem and linear least-square problem problems are two important scientific computations that involve linear equations. Solutions to these problems are widely used in many areas such as banking, manufacturing, and telecommunications. However, the existing solutions do not extend to the privacy-preserving cooperative computation situation, in which the linear equations are shared by multiple parties, who do not want to disclose their data to the other parties. In this paper, we formally define these specific privacy-preserving cooperative computation problems, and present protocols to solve them.