But it isn't zero-knowledge. If it was zero-knowledge, you would be able to know what you had the same gift/crush, but it would be impossible to prove to someone else.

Mere hashing doesn't do that. For the crush example (This site), your crush could show everyone the link and their name. For that matter, someone could enter the names of everyone you knew in turn, until you were outed.

Non interactive zero knowledge allows one proof to be checked by many verifiers. I think folks would still consider that to be a zero knowledge proof no?

That said, yeah this hashing example is not zero knowledge because, among other things, the hash is not hiding.

It's been a while since I read about zero-knowledge proofs, so I wasn't aware of the non-interactive kind. But I read up on them, and as I understand, you have to pre-commit to a finite set of participants in the protocol who can verify that you have the proof.

Which makes sense: If the evidence (that you have a mathematical proof) could be convincingly shared with absolutely everyone, it wouldn't be zero-knowledge any longer. The whole point of zero-knowledge proof is that the evidence is only useful for the recipient(s).

An actual zero-knowledge way to do that would be the Socialist Millionaires' Protocol.

It is n-bit knowledge which is a more complete and valuable concept.

My favorite analogy is someone has a Wheres Waldo photo. They can prove to you they know where Waldo is by getting a piece of paper (the size of the photo) with a cut out around Waldo. When they hold it up and show you Waldo through the cutout you have zero knowledge about his location.

If the mask paper is the same size as the waldo photo, one can trivially tell where waldo is by just looking at the location of the cutout

I think for this to work, the piece of paper with the cutout must be much larger than the full waldo photo. The actual cutout would always be in the center of this mask paper. Then the waldo photo can be moved around behind this mask.

But then you cannot prove anymore that you know where Waldo is, no?

Previously, the proof relied on the alignment between the picture and mask being constant, but this is no longer the case. Now wherever Waldo actually is, every mask fits since you can just freely move around the picture.

To align the cutout with Waldo, you need to know where he is. Since the entire picture would be hidden behind the mask, the other person won't know where in the picture that location is, but by aligning the mask cutout you can prove _your_ knowledge about Waldo's location.

The point of the proof is to demonstrate that the prover knows where Waldo is, not to convey Waldo's location to proof recipient.

Good catch

As the sibling comment says, neither gp comment nor this post are zero-knowledge.

But in addition to the definition given in sibling comment, here's another necessary condition of a zero-knowledge proof: it must be possible to forge transcripts (i.e., one party writing both sides of the interaction) of a zk proof even without possessing the secret.