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Noninteractive mercurial commitments from oneway functions  ECRYPT (PROVILAB
, 2005
"... At Eurocrypt 2005 Chase et al. introduced the notion of mercurial commitment schemes. The main application of mercurial commitments is that, used together with collision resistant hash functions, they suffice to construct zeroknowledge sets (ZKS), introduced by Micali et al. at FOCS 2003. In partic ..."
Abstract

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At Eurocrypt 2005 Chase et al. introduced the notion of mercurial commitment schemes. The main application of mercurial commitments is that, used together with collision resistant hash functions, they suffice to construct zeroknowledge sets (ZKS), introduced by Micali et al. at FOCS 2003. In particular, Chase et al. show how to construct noninteractive mercurial commitments in the so called shared random string model under the assumption that noninteractive zeroknowledge proofs exist. Their result implies that one can construct noninteractive zeroknowledge sets, in the shared random string model, from the assumptions that collision resistant hash functions and noninteractive zeroknowledge proofs exist. The same result was independently achieved by Ostrovsky et al. at ICALP 2004. These two results can be seen as initial solutions to the problem, left open by Micali et al., of reducing the computational assumptions required to construct noninteractive zeroknowledge sets in the shared random string model. However, the problem of determining the exact complexity of noninteractive mercurial commitments and zeroknowledge sets in the shared random string model, is still open. In this paper we solve this problem by showing how to construct noninteractive mercurial commitments in the shared random string model, under the sole assumption that oneway functions exist. This, combined with the results of Chase et al., allows us to prove that (in the shared random string model) noninteractive zeroknowledge sets are actually equivalent to collisionresistant hash functions.