Confidentiality-preserving proof theories for distributed proof systems

A distributed proof system is an effective way for deriving useful information by combining data from knowledge bases managed by multiple different principals across different administrative domains. As such, many researchers have proposed using these types of systems as a foundation for distributed authorization and trust management in decentralized systems. However, to account for the potentially sensitive nature of the underlying information, it is important that such proof systems be able to protect the confidentiality of the logical facts and statements.\ud \ud In this paper, we explore the design space of sound and safe confidentiality-preserving distributed proof systems. Specifically, we develop a framework to analyze the theoretical best-case proving power of these types of systems by analyzing confidentiality-preserving proof theories for Datalog-like languages within the context of a trusted third party evaluation model. We then develop a notion of safety based on the concept of non-deducibility and analyze the safety of several confidentiality-enforcing proof theories from the literature. The results in this paper show that the types of discretionary access control enforced by most systems on a principal-to-principal basis are indeed safe, but lack proving power when compared to other systems. Specifically, we show that a version of the Minami-Kotz (MK) proof system can prove more facts than the simple DAC system while retaining the safety property of the simple system. We further show that a seemingly-useful modification of the MK to support commutative encryption breaks the safety of the system without violating soundness