No. The simple relay thing only works if you can trust that they aren't comparing notes. But if I could trust them not to do so, I would already trust them when

No. The simple relay thing only works if you can trust that they aren't comparing notes. But if I could trust them not to do so, I would already trust them when they say that they do not log your identity. ZKPs allow you to be the relay between Chase and Pornhub, and you know exactly which data is shared between the two. Chase would obviously have no idea whether you used the certificate for Pornhub or anything else; and Pornhub will know that their request was validated by _a_ trusted ID provider, but not necessarily which particular one out of a group (issuer-hidden ZKPs).