Privacy and Accessing a database keyed by domain name

Both Mozilla and Google have lists of domain names or URLs that are bad. How do they preserve privacy but still be able to access information about those domains or URLs?

I ask because a bargain extension developer said it was too intrusive to provide a notification or badge counter as it would need to lookup every site.

I and another user want this feature but I agree that a lookup of every site would be intrusive.

How has it been solved in the past?

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The idea is to load the page and then do the lookup, or do the lookup before loading the page? In the latter case, I think you would want the extension to use a built-in list to avoid delaying page load.

Firefox downloads new lists from time to time. For risky EXEs, the phishing/malware code may do a live lookup.

Updates? I think this maybe called “differential privacy” - https://en.wikipedia.org/wiki/Differential_privacy