That still lets Alice find out.

I don't see a clear way of mapping the concept of a zero knowledge proof to the crush problem.

But the best I can come up with is:

1) No one learns that Alice (claims to) have a crush on Bob

2) Unless Bob also claims to have a crush on Alice, in which case.

3) Only Bob learns that Alice has a crush on him.

4) If Bob learns that Alice has a crush on him, Alice learns that Bob has a crush on her.

5) All the above guarantees are symmetric if you swap Bob and Alice.

Seems to me such a system must make it expensive to claim to have a crush on someone. Otherwise Bob can just claim to have a crush on everyone and will find out who crushes on him.

For heaven’s sake just call her!

That lets Bob confess semi-deniably to Alice (if Alice is willing to share her private key, she can still show Bob's confession to Carroll and prove that it's authentic). But it still doesn't do any matching; Alice will know about Bob's feelings whether she returns then or not.

Yup, everyone publishes their public keys. No one’s private keys gets published (fake crush created).

I’m not sure if zero-knowledge proofs exist for love outside of action - repeated acts of commitment over time (to reduces the confidence that someone doesn’t love you).