Many proximity-based tracing (PCT) protocols have been proposed and deployed to combat the spreading of COVID-19. In this article, 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.