# Is the following protocol perfect zero knowledge or computational zero knowledge?

So I have this protocol for the hamiltonian cycle:

repeat t times:

1. Peggy chooses a random permutation $\pi$ on $V$, and computes $G_1=\pi(G)$
2. For each of the $\frac{|V|(|V|-1)}{2}$ possible edges of $G_1$ Peggy computes a different commitment and sends the commitnet to Victor. ($\forall v_1,v_2\in \pi(V)$ if $(v_1,v_2)\in \pi(E)$ then the commitment is on 1, and 0 otherwise)
3. Victor chooses a random $i\in {1,2}$ and sends it to Peggy
4. If $i=1$ the Peggy sends $\pi$ to Victor and reveals all the commitments on $G_1$. Otherwise, Peggy revelas the commitments on $|V|$ edges which form a hamiltonian cycle on $G$.
Note that no commitment scheme can be both perfectly binding and hiding. In addition, the class of perfect zero knowledge proofs (unconditional soundness) is contained in $AM \cap co-AM$ and so is very unlikely to contain an $NP$-complete problem.