IIRC, this was announced as part of a program that uses double-blinded crypto that allows google to perform matching against this data in aggregate (Set intersection knowledge), but not individually identity of what a given user purchased, at the same time preventing the merchants from learning the identities of individuals either.
According to what they presented at a crypto conference, they went to great pains to avoid capturing personally identifiable transactions. The overall strategy is that Google Knows = Set A = (all ads shown for user X at Merchant Y) Merchant/Credit Card Proccessor Knows = Set B =
(all $$$ paid by User X at Merchant Y), and that it is possible to cryptographically compute sum($$$ of A intersect B) without either side learning Set(User X).
Now whether you believe in the security of the algorithm and whether there are side channel leaks or attacks is another issue.
According to what they presented at a crypto conference, they went to great pains to avoid capturing personally identifiable transactions. The overall strategy is that Google Knows = Set A = (all ads shown for user X at Merchant Y) Merchant/Credit Card Proccessor Knows = Set B = (all $$$ paid by User X at Merchant Y), and that it is possible to cryptographically compute sum($$$ of A intersect B) without either side learning Set(User X).
Now whether you believe in the security of the algorithm and whether there are side channel leaks or attacks is another issue.
Edit: http://bristolcrypto.blogspot.com/2017/01/rwc-2017-secure-mp...
About 10 minutes in https://www.youtube.com/watch?v=ee7oRsDnNNc