Currently several projects aim at designing and implementing protocols for privacy preserving automated contact tracing to help fight the current pandemic. Those proposal are quite similar, and in their most basic form basically propose an app for mobile phones which broadcasts frequently changing pseudorandom identifiers via (low energy) Bluetooth, and at the same time, the app stores IDs broadcast by phones in its proximity. Only if a user is tested positive, they upload either the beacons they did broadcast (which is the case in decentralized proposals as DP-3T, east and west coast PACT or Covid watch) or received (as in Popp-PT or ROBERT) during the last two weeks or so. Vaudenay [eprint 2020/399] observes that this basic scheme (he considers the DP-3T proposal) succumbs to relay and even replay attacks, and proposes more complex interactive schemes which prevent those attacks without giving up too many privacy aspects. Unfortunately interaction is problematic for this application for efficiency and security reasons. The countermeasures that have been suggested so far are either not practical or give up on key privacy aspects. We propose a simple non-interactive variant of the basic protocol that 1. (security) Provably prevents replay and (if location data is available) relay attacks. 2. (privacy) The data of all parties (even jointly) reveals no information on the location or time where encounters happened. 3. (efficiency) The broadcasted message can fit into 128 bits and uses only basic crypto (commitments and secret key authentication). Towards this end we introduce the concept of "delayed authentication", which basically is a message authentication code where verification can be done in two steps, where the first doesn't require the key, and the second doesn't require the message.
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