Abstract
Contact tracing is among the most important interventions to mitigate the spread of any pandemic, usually in the form of manual contact tracing. Smartphone-facilitated digital contact tracing may help to increase tracing capabilities and extend the coverage to those contacts one does not know in person. Most implemented protocols use local Bluetooth Low Energy (BLE) communication to detect contagion-relevant proximity, together with cryptographic protections, as necessary to improve the privacy of the users of such a system. However, current decentralized protocols, including DP3T [T+20], do not sufficiently protect infected users from having their status revealed to their contacts, which raises fear of stigmatization.
We alleviate this by proposing a new and practical solution with stronger privacy guarantees against active adversaries. It is based on the upload-what-you-observed paradigm, includes a separation of duties on the server side, and a mechanism to ensure that users cannot deduce which encounter caused a warning with high time resolution. Finally, we present a simulation-based security notion of digital contact tracing in the real–ideal setting, and prove the security of our protocol in this framework.
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Notes
- 1.
See https://coronadetective.eu for a service that detects the contacts that caused a warning for DP3T-based approaches.
- 2.
This captures a relaxed notion of “proximity”, as high-gain antennas could be used to register a contact, although not physically being in proximity.
- 3.
Internally, the author(s) humorously prefer to read the name of \(\mathcal {F}_{\text {mat}}\) as “the matrix”.
- 4.
We give a simple example of how this might be done. Note however, our protocol uses a different method, see Sect. 3.2. For this example, let \(\mathsf {H}\) be a hash function, such that \(\mathsf {H}(k \Vert x)\) is a pseudorandom function (PRF) with key \(k \in \{0,1\}^n\) evaluated on input x. For every time period t, the device generates a random key
, and computes \(\mathsf {sid}_t := \mathsf {H}(k_t \Vert 0)\) and \(\mathsf {pid}_t := \mathsf {H}(k_t \Vert 1)\), stores them, and anonymously uploads \(k_t\) to the central server, who recomputes \(\mathsf {sid}_t, \mathsf {pid}_t\) in the same way. Both parties store \((\mathsf {sid}_t, \mathsf {pid}_t)\). - 5.
To make sure servers do not collude, they should be run by different organizations whose independence is guaranteed by law, e.g. supervisory agencies on privacy (ideally multiple different ones per nation-state) and non-governmental organisations that are widely trusted by the general public.
- 6.
One might use remotely verifiable electronic ID cards instead.
- 7.
If a user A has been in contact with an infected user B, and if B takes up to three weeks to show symptoms and have a positive test result, the data retention on the matching server is sufficient to deliver a warning to A.
- 8.
In practice, parties can make their uploads a few days ahead of time without incurring additional risk.
- 9.
While it would be perfectly possible for an environment to use as a contact graph a fresh, and independently sampled random graph on \(\mathcal {P}\) for each short-term epoch, the costs of implementing this in real time for 15 min epochs would be quite challenging.
, and computes References
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Acknowledgements
We would like to express our gratitude to Michael Klooß and Jeremias Mechler for helpful comments. This work was supported by funding from the topic Engineering Secure Systems of the Helmholtz Association (HGF) and by KASTEL Security Research Labs. We thank Serge Vaudenay for his comments.
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Beskorovajnov, W., Dörre, F., Hartung, G., Koch, A., Müller-Quade, J., Strufe, T. (2021). ConTra Corona: Contact Tracing against the Coronavirus by Bridging the Centralized–Decentralized Divide for Stronger Privacy. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13091. Springer, Cham. https://doi.org/10.1007/978-3-030-92075-3_23
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