This scheme uses only boring cryptography (Diffie-Helman ftw) and boring tables. The gist explores the problem space too. I don't think the problem needs mix-networks, homomorphic or zero-knowledge intersection schemes.
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How does this change if the *where* does turn out to be important? If epidemiologists are trying to identify hot spots and map them?
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Once a contact can be identified, I suspect a lot of people would then give up their location history to the epidemiologist. That's different than having a very convenient searchable trove. It does make it more work for them to identify hotspots though.
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Have you heard about CEN and DP3T ? If not this might make for an interesting read :https://www.zfnd.org/blog/private-contact-tracing-protocols-compared/ …
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Yes :) There's an issue open where two of us made the same suggesting of using full-mesh DH in that context too.https://github.com/DP-3T/documents/issues/87 …
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Great write-up! Is there a reason to upload the shared value? If the users keep it on-device, and only upload the shares when they are tested positive. Other users can download/match their shares locally. Similar to haveibeenpwned, which also only stores compromised passwords.
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That way even the fact that A and B were ever together is secret. And more importantly A would never learn that it was B that infected them.
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