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Zero Knowledge and Soundness Are Symmetric

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 4515)


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 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.


  • Commitment Scheme
  • Argument System
  • Knowledge Argument
  • Promise Problem
  • Zero Knowledge

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A preliminary version of this paper appeared in theElectronic Colloquium on Computational Complexity [OV]. Both the authors were supported by NSF grant CNS-0430336 and ONR grant N00014-04-1-0478.


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Ong, S.J., Vadhan, S. (2007). Zero Knowledge and Soundness Are Symmetric. In: Naor, M. (eds) Advances in Cryptology - EUROCRYPT 2007. EUROCRYPT 2007. Lecture Notes in Computer Science, vol 4515. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-540-72539-8

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