# Is there an interactive proof system for factoring with the perfect zero knowledge property?

Given the decision version of the factoring problem, is there an interactive proof system with the perfect zero knowledge property? I know there is for just the zero knowledge property, but is there without the assumption of one way functions?

perfect zero knowledge property: Let P and V be randomized algorithms of an interactive proof system for the decision problem L. This proof system has the perfect zero knowledge property if for every polynomial time randomized algorithm V' that can replace V, there is a randomized algorithm A with polynomially bounded worst case expected runtime that for each $x\in L$ produces what is communicated between P and V' with the same probabilities.

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