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I'm not sure if they're planning on collecting every homepage domain here, or just asking something like "Is your homepage domain in the list of top 1000 domain

I'm not sure if they're planning on collecting every homepage domain here, or just asking something like "Is your homepage domain in the list of top 1000 domains?". In the former case, just having the domain listed could leak information. In the latter case, I can't see any issues.

Ajedi32 9y ago
It's more like: "Is your homepage google.com? Flip a coin, if it's heads tell me the truth, otherwise flip another coin and answer yes if it's heads or no if it's tails." (A bit simplified, but that's the general idea behind differential privacy.)