  The SARS-CoV-2 outbreak changed the everyday life of almost all the people over the world.Currently, we are facing with the problem of containing the spread of the virus both using the more effective forced lockdown, which has the drawback of slowing down the economy of the involved countries, and by identifying and isolating the positive individuals, which, instead, is an hard task in general due to the lack of information. For this specific disease, the identificato of the infected is particularly challenging since there exists cathegories, namely the asymptomatics, who are positive and potentially contagious, but do not show any of the symptoms of SARS-CoV-2. Until the developement and distribution of a vaccine is not yet ready, we need to design ways of selecting those individuals which are most likely infected, given the limited amount of tests which are available each day. In this paper, we make use of available data collected by the so called contact tracing apps to develop an algorithm, namely PPTO, that identifies those individuals that are most likely positive and, therefore, should be tested. While in the past these analysis have been conducted by centralized algorithms, requiring that all the app users data are gathered in a single database, our protocol is able to work on a device level, by exploiting the communication of anonymized information to other devices. 
A privacy-preserving tests optimization algorithm for epidemics   containment