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.

翻译：接触者追踪是控制COVID-19等传染病传播的有效工具。它通过中央可信机构对人们随时间推移的物理接近程度进行数字监测和记录，以便当一名用户报告感染时，能够识别出在过去相关时间段内与该人员有过密切接触的所有其他用户并发出警报。实现这一目标的一种方法是在服务器上记录所有用户随时间变化的位置信息（例如通过读取和报告智能手机的GPS坐标）。尽管这种方法简单，但隐私问题阻碍了其广泛应用。能够实现数据"隐藏"的技术将大大有助于缓解隐私顾虑，并推动大规模接触者追踪的实施。本文描述了一种通用的数据隐藏方法。所谓隐藏，是指我们不再披露数据值x，而是披露x的"编码"版本E(x)，其中E(x)易于计算，但从计算角度而言极难反推。我们提出了此类函数E的通用构造方法，并证明其能保证完美召回——即所有可能暴露于感染风险的个体都将收到警报，同时仅产生微不足道的虚警——即仅有可忽略不计的未实际暴露个体被错误告知其已暴露。