Contact tracing is an effective tool in controlling the spread of infectious diseases such as COVID-19. It involves digital monitoring and recording of physical proximity between people over time with a central and trusted authority, so that when one user reports infection, it is possible to identify all other users who have been in close proximity to that person during a relevant time period in the past and alert them. One way to achieve this involves recording on the server the locations, e.g. by reading and reporting the GPS coordinates of a smartphone, of all users over time. Despite its simplicity, privacy concerns have prevented widespread adoption of this method. Technology that would enable the "hiding" of data could go a long way towards alleviating privacy concerns and enable contact tracing at a very large scale. In this article we describe a general method to hide data. By hiding, we mean that instead of disclosing a data value x, we would disclose an "encoded" version of x, namely E(x), where E(x) is easy to compute but very difficult, from a computational point of view, to invert. We propose a general construction of such a function E and show that it guarantees perfect recall, namely, all individuals who have potentially been exposed to infection are alerted, at the price of an infinitesimal number of false alarms, namely, only a negligible number of individuals who have not actually been exposed will be wrongly informed that they have.
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