It took me a minute to fully get this, so I'm adding this so it's a bit more obv...

thaumasiotes · 2024-06-22T10:28:20 1719052100

Unfortunately that completely defeats the idea of the proof.

Here's an alternative procedure:

1. Get a very large sheet of paper, and cut a Waldo-shaped hole in it.

2. Get some more paper, and paint a picture of Waldo on it.

3. Paste your image of Waldo on the back of the paper you prepared in step 1.

4. Place this composite over a Where's Waldo book.

5. You've found Waldo!

If you can't tell where the book is, there is no evidence that the image of Waldo is part of the book.

pxx · 2024-06-22T14:57:27 1719068247

if you can tell where the book is, it's not zero-knowledge anymore...

see my other comments -- the idea is that in each round you should be able to verify the construction (there's a Waldo-sized hole and the correct book and page when the pieces are separated) or the proposed solution (Waldo through the hole) but never the offset of the book and hole (because then you can deduce where Waldo is).

a cheating prover (utilizing your strategy, or just Waldo from a different book or whatever) would try to guess which one you will want but only has probability 1/2 of succeeding. through iteration the verifier can be exponentially increasingly confident that the prover knows where Waldo is.