ABSTRACT
A Perfect Zero-Knowledge interactive proof system convinces a verifier that a string is in a language without revealing any additional knowledge in an information-theoretic sense. We show that for any language that has a perfect zero-knowledge proof system, its complement has a short interactive protocol. This result implies that there are not any perfect zero-knowledge protocols for NP-complete languages unless the polynomial time hierarchy collapses. This paper demonstrates that knowledge complexity can be used to show that a language is easy to prove.
- B.Babai, L., "Trading Group Theory for Randomness'', Proc. 17th STOC, 1985, pp. 421- 429. Google ScholarDigital Library
- BH.Boppana, R. and J. Hastad, "Does co-NP Have Short Interactive Proofs?", IPL, to appear. Google ScholarDigital Library
- BC.Brassard, G. and C. Cr6peau, "Non- Transitive Transfer of Confidence' A Perfect Zero-Knowledge Interactive Protocol for SAT and Beyond", Pvoc. z97th FOCS, 1986, pp. 188-195.Google Scholar
- CW.Carter, J.L. and M.N. Wegman, "Universal Classes of Hash Functions", JC$$18 2, 1979, pp.143-154.Google Scholar
- GMW.Goldreich, O., S. Micali and A. Wigderson, "Proofs that Yield Nothing But their Validity and a Methodology of Cryptographic Protocol Design", Proc. 27th FOCS, 1986, pp. 174-187.Google ScholarDigital Library
- GMR.Goldwasser, S., S. Micali and C. Rackoff, "The Knowledge Complexity of Interactive Proof-Systems", Proc. 17th $TOC, 1985, pp. 291-304. Google ScholarDigital Library
- GS.Goldwasser, S. and M. Sipser, "Private Coins versus Public Coins in Interactive Proof Systems'', Proc. 18ih STOC, 1986, pp. 59-68. Google ScholarDigital Library
- S.Sipser, M., "A Complexity Theoretic Approach to Randomness", Proc. 15th STOC, 1983, pp. 330-335. Google ScholarDigital Library
Index Terms
- The complexity of perfect zero-knowledge
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