Editing Zero-knowledge proof (section)

==== Zero-knowledge ====
Peggy's answers do not reveal the original Hamiltonian cycle in {{mvar|G}}. In each round, Victor will learn only {{mvar|H}}'s isomorphism to {{mvar|G}} or a Hamiltonian cycle in {{mvar|H}}. He would need both answers for a single {{mvar|H}} to discover the cycle in {{mvar|G}}, so the information remains unknown as long as Peggy can generate a distinct {{mvar|H}} every round. If Peggy does not know of a Hamiltonian cycle in {{mvar|G}}, but somehow knew in advance what Victor would ask to see each round, then she could cheat. For example, if Peggy knew ahead of time that Victor would ask to see the Hamiltonian cycle in {{mvar|H}}, then she could generate a Hamiltonian cycle for an unrelated graph. Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph {{mvar|H}} (in which she also does not know a Hamiltonian cycle). Victor could simulate the protocol by himself (without Peggy) because he knows what he will ask to see. Therefore, Victor gains no information about the Hamiltonian cycle in {{mvar|G}} from the information revealed in each round.