Zero Knowledge and Soundness Are Symmetric

We give a complexity-theoretic characterization of the class of problems in NP having 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 ∩ coNP having zero-knowledge arguments is closed under complement. Furthermore, we show that a problem in NP has a statistical zero-knowledge argument system if and only if its complement has a computational zero-knowledge proof system. 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 NP having zero-knowledge arguments, such as equivalences between honest-verifier and malicious-verifier zero knowledge, private coins and public coins, inefficient provers and...

• Type: Conference
• Year: 2007
• Where: EUROCRYPT
• Authors: Shien Jin Ong, Salil P. Vadhan
• Keywords: Cryptography, EUROCRYPT 2007, Zero-knowledge Argument, Zero-knowledge Argument Systems, Zero-knowledge Proof Systems