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Revision #1 to TR06-139 | 9th April 2007 00:00

Zero Knowledge and Soundness are Symmetric

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Revision #1
Authors: Shien Jin Ong, Salil Vadhan
Accepted on: 9th April 2007 00:00
Downloads: 1903
Keywords: 


Abstract:

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 intersect 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.


Paper:

TR06-139 | 14th November 2006 00:00

Zero Knowledge and Soundness are Symmetric





TR06-139
Authors: Shien Jin Ong, Salil Vadhan
Publication: 15th November 2006 16:01
Downloads: 1900
Keywords: 


Abstract:

We give a complexity-theoretic characterization of the class of problems in NP having zero-knowledge argument systems that is symmetric in its treatment of the zero knowledge and the soundness conditions. From this, we deduce that the class of problems in NP intersect 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.



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