There are cryptographic ways to compute a set intersection between two sets A and B held by two different parties without A and B revealing the membership of el

There are cryptographic ways to compute a set intersection between two sets A and B held by two different parties without A and B revealing the membership of elements of the set. If set A is the set of users shown ads for Merchant M, and set B is the set of customers at merchant M who purchased something, then this intersection can tell you what percentage of the ads were shown to people who made a purchase without revealing who made the purchase to A or revealing who was shown an ad to B. There’s probably a way to do it with differential privacy as well but it might be less efficient.