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Erschienen in:
2008 | OriginalPaper | Buchkapitel
An Equivalence Between Zero Knowledge and Commitments
verfasst von : Shien Jin Ong, Salil Vadhan
Erschienen in: Theory of Cryptography
Verlag: Springer Berlin Heidelberg
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We show that a language in NP has a zero-knowledge protocol if and only if the language has an “instance-dependent” commitment scheme. An instance-dependent commitment schemes for a given language is a commitment scheme that can depend on an instance of the language, and where the hiding and binding properties are required to hold only on the yes and no instances of the language, respectively.
The novel direction is the
only if
direction. Thus, we confirm the widely held belief that commitments are not only sufficient for zero knowledge protocols, but
necessary
as well. Previous results of this type either held only for restricted types of protocols or languages, or used nonstandard relaxations of (instance-dependent) commitment schemes.