  Many proximity-based tracing (PCT) protocols have been proposed and deployed
to combat the spreading of COVID-19. In this paper, we take a systematic
approach to analyze PCT protocols. We identify a list of desired properties of
a contact tracing design from the four aspects of Privacy, Utility, Resiliency,
and Efficiency (PURE). We also identify two main design choices for PCT
protocols: what information patients report to the server, and which party
performs the matching. These two choices determine most of the PURE properties
and enable us to conduct a comprehensive analysis and comparison of the
existing protocols.
