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Another thing from that same section that worried me was their discussion of inference attacks on first and last names. Their results assume names will be queried based on a particular distribution instead of an arbitrary (maybe even adversarially-chosen) one. This is a very, very weak model of security that categorically eliminates realistic attacks.

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The thing is that anybody who is able to initiate queries has access to that data. No need to do inference attacks over there :-) So, an adversary cannot query data based on particular distribution b/c it cannot initiate meaningful queries.

If an active server-side adversary can trick the client into doing certain queries is another question though.

You're not understanding my problem. You modeled security against a certain attack by picking one particular distribution of queries and saying "we resist this attack this much with this query distribution". An attacker doesn't need to choose the query distribution for your result to not apply, it just needs to be any other possible distribution than the one you chose.

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