This weird hashing scheme comes from safe browsing (which blacklists sites that install malware etc.). I guess (without specific knowledge of it) it was just reused for this ads thing because they had all the code handy for it, both the browser-side code and serving code.

For safe browsing, as I recall the data format was designed with Mozilla -- that tech predated the existence of Chrome. There's some history about it here: https://wiki.mozilla.org/Security/Safe_Browsing and https://wiki.mozilla.org/Phishing_Protection:_Design_Documen...

I recall the weird hashing scheme was carefully designed to balance some concerns. For example when it phones home, it phones home with a hash of the current URL so that it doesn't reveal the current URL to the server (unless the URL is already in the server-side blacklist). I also think it was intentional that the client didn't get a list of all known-malware URLs. I can't find any design docs for it at the moment better than https://developers.google.com/safe-browsing/v4/ . It may well be the case that the hashing scheme doesn't make sense at all in this context.