RAND was asked to evaluate whether the Programming Computation on Encrypted Data program—which expands the knowledge base of the global cryptographic community—is likely to provide more benefits to the United States than it does to its global rivals.

Space debris, the man-made orbital junk that represents a collision risk to operational satellites, 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'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's orbital information.

Satellite anomalies are mission-degrading events that negatively affect on-orbit operational spacecraft. All satellites experience anomalies of some kind during their operational lifetime. They range in severity from temporary errors in noncritical subsystems to loss-of-contact and complete mission failure. There is a range of causes for these anomalies, and investigations by the satellite operator or manufacturer to determine the cause of a specific anomaly are sometimes conducted at significant expense. Maintaining an anomaly database is one way to build an empirical understanding of what situations are more or less likely to result in satellite anomalies, and help determine causal relationships. These databases can inform future design and orbital regimes, and can help determine measures to prolong the useful life of an on-orbit spacecraft experiencing problems. However, there is no centralized, up-to-date, detailed, and broadly available database of anomalies covering many different satellites. This report describes the nature and causes of satellite anomalies, and the potential benefits of a shared and centralized satellite anomaly database. Findings indicate that a shared satellite anomaly database would bring significant benefits to the commercial community, and the main obstacles are reluctance to share detailed information with the broader community, as well as a lack of dedicated resources available to any trusted third party to build and manage such a database. Trusted third parties and cryptographic methods such as secure multiparty computing or differential privacy are not complete solutions, but show potential to be further tailored to help resolve the issue of securely sharing anomaly data.

An integer N is called congruent if it corresponds to the area of a right triangle with three rational sides. The problem of classifying congruent numbers has an extensive history, and is as yet unresolved. The most promising approach to this problem utilizes elliptic curves. In this thesis we explicitly lay out the correspondence between the congruence of a number n and the rank of the elliptic curve Y2̂ = X3̂ - N2. By performing two-descents on this curve and isogenous curves for N=P a prime, we are able to obtain a simple and unified proof of the majority of the known results concerning the congruence of primes. Finally, by calculating the equations for homogeneous spaces associated to the curve when P = 1 mod 8, we position the problem for future analysis.