Edges: A-B, B-C, C-D, D-E, E-F, F-G, G-H, H-A, A-E.

0 completed openings in this view. Only the most recent 20 are retained. Switching prover or restarting an exercise clears history.

Eight vertices, nine public edges and two fixed supplied colorings. The graph is colorable; the cheating example supplies an invalid coloring, not a graph with no valid coloring. A global color permutation preserves all equality/difference checks. Real commitments must hide and bind, and opening checks must match the original commitments; grey boxes only illustrate these constraints.

New rounds independently sample one of six color permutations. A repeated visible color pair can occur by chance. A round number is an identifier, not the permutation or a secrecy measurement. Opening many edges of one committed coloring would leak that coloring, so each commitment can be opened once. Randomness does not make the page itself a secure protocol: the source contains the example colorings, both roles execute together and no cryptographic commitments or formal simulator run here.

Under ideal hiding commitments, an honest edge’s six ordered distinct color pairs are equally likely after a uniform permutation. They can be simulated without its original coloring; that is the intuition for zero knowledge. A complete cryptographic proof, arbitrary adversarial strategies and modern proof systems are outside this illustration.

Yuval Ishai’s graph-coloring protocol explanation · Yale cryptography notes: commitments and graph coloring