Space debris{u2014}the man-made orbital junk that represents a collision risk to operational satellites{u2014}is a growing threat that will increasingly affect future space-related mission designs and operations. Since 2007, the number of orbiting debris objects has increased by over 40 percent as a result of the 2007 Chinese antisatellite weapon test and the Iridium/Cosmos collision in 2009. With this sudden increase in debris, there is a renewed interest in reducing future debris populations using political and technical means. The 2010 U.S. Space Policy makes several policy recommendations for addressing the space congestion problem. One of the policy{u2019}s key suggestions instructs U.S. government agencies to promote the sharing of satellite positional data, as this can be used to predict (and avoid) potential collisions. This type of information is referred to as space situational awareness (SSA) data, and, traditionally, it has been treated as proprietary or sensitive by the organizations that keep track of it because it could be used to reveal potential satellite vulnerabilities. This document examines the feasibility of using modern cryptographic tools to improve SSA. Specifically, this document examines the applicability and feasibility of using cryptographically secure multiparty computation (MPC) protocols to securely compute the collision probability between two satellites. These calculations are known as conjunction analyses. MPC protocols currently exist in the cryptographic literature and would provide satellite operators with a means of computing conjunction analyses while maintaining the privacy of each operator{u2019}s orbital information.