O is a random oracle then it is infeasible to find an input x such that the input-output pair (x,O(x)) has some desired property. In this paper, we observe relationships between zero-knowledge protocols and CIFEs. Specifically, we show that, in the non-uniform model, the existence of CIFEs implies that 3-round auxiliary-input zero-knowledge (AIZK) AM interactive proofs exist only for BPP languages. In the uniform model, we show that 3-round AIZK AM interactive proofs with perfect completeness exist only for easy-to-approximate languages. These conditional triviality results extend to constant-round AIZK AM interactive proofs assuming the existence of multi-input CIFEs, where "multi-input" means that the correlation intractability is satisfied with respect to multiple input-output pairs. Also, as a corollary, we show that any construction of uniform multi-input CIFEs from uniform one-way functions proves unconditionally that constant-round AIZK AM interactive proofs with perfect completeness only for easy-to-approximate languages." />


Zero-Knowledge and Correlation Intractability

Satoshi HADA  Toshiaki TANAKA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2894-2905
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2894
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
Keyword: 
one-way functions,  correlation intractability,  zero-knowledge,  interactive proofs,  round complexity,  random oracle,  

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Summary: 
The notion of correlation intractable function ensembles (CIFEs) was introduced in an attempt to capture the "unpredictability" property of random oracles [12]: If O is a random oracle then it is infeasible to find an input x such that the input-output pair (x,O(x)) has some desired property. In this paper, we observe relationships between zero-knowledge protocols and CIFEs. Specifically, we show that, in the non-uniform model, the existence of CIFEs implies that 3-round auxiliary-input zero-knowledge (AIZK) AM interactive proofs exist only for BPP languages. In the uniform model, we show that 3-round AIZK AM interactive proofs with perfect completeness exist only for easy-to-approximate languages. These conditional triviality results extend to constant-round AIZK AM interactive proofs assuming the existence of multi-input CIFEs, where "multi-input" means that the correlation intractability is satisfied with respect to multiple input-output pairs. Also, as a corollary, we show that any construction of uniform multi-input CIFEs from uniform one-way functions proves unconditionally that constant-round AIZK AM interactive proofs with perfect completeness only for easy-to-approximate languages.