Zero Knowledge and Soundness Are Symmetric

We give a complexity-theoretic characterization of the class of problems in NPhaving zero-knowledge argument systems. This characterization is symmetric in its treatment of the zero knowledge and the soundness conditions, and thus we deduce that the class of problems in NP驴 coNPhaving zero-knowledge arguments is closed under complement. Furthermore, we show that a problem in NPhas a statisticalzero-knowledge argument system if and only if its complement has a computational zero-knowledge proofsystem. What is novel about these results is that they are unconditional, i.e., do not rely on unproven complexity assumptions such as the existence of one-way functions.Our characterization of zero-knowledge arguments also enables us to prove a variety of other unconditional results about the class of problems in NPhaving zero-knowledge arguments, such as equivalences between honest-verifier and malicious-verifier zero knowledge, private coins and public coins, inefficient provers and efficient provers, and non-black-box simulation and black-box simulation. Previously, such results were only known unconditionally for zero-knowledge proof systems, or under the assumption that one-way functions exist for zero-knowledge argument systems.