Lecture 11 : Zero - Knowledge Proofs - III

We finished the last lecture by discussing a physical zero-knowledge protocol for Graph 3-Coloring problem. In this protocol, the prover first generates a permutation π(w) of the 3-coloring w for instance graph G, where π(·) is a random permutation. He then colors G using π(w) and then hides the colored vertices of the graph using inverted cups. When the verifier issues a challenge (i, j), the prover simply removes the inverted cups on the vertices i and j and reveals the colors assigned to them. This process is then repeated several times (where the prover uses a fresh random permutation each time) to achieve a small soundness error.