Covid notions: Towards formal definitions - and documented understanding - of privacy goals and claimed protection in proximity-tracing services.

The recent SARS-CoV-2 pandemic gave rise to management approaches using mobile apps for contact tracing. The corresponding apps track individuals and their interactions, to facilitate alerting users of potential infections well before they become infectious themselves. Naïve implementation obviously jeopardizes the privacy of health conditions, location, activities, and social interaction of its users. A number of protocol designs for colocation tracking have already been developed, most of which claim to function in a privacy preserving manner. However, despite claims such as "GDPR compliance", "anonymity", "pseudonymity" or other forms of "privacy", the authors of these designs usually neglect to precisely define what they (aim to) protect. We make a first step towards formally defining the privacy notions of proximity tracing services, especially with regards to the health, (co-)location, and social interaction of their users. We also give a high-level intuition of which protection the most prominent proposals likely can and cannot achieve. This initial overview indicates that all proposals include some centralized services, and none protects identity and (co-)locations of infected users perfectly from both other users and the service provider.