skip to main content
10.1145/28395.28418acmconferencesArticle/Chapter ViewAbstractPublication PagesstocConference Proceedingsconference-collections
Article
Free Access

The complexity of perfect zero-knowledge

Published:01 January 1987Publication History

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.

References

  1. B.Babai, L., "Trading Group Theory for Randomness'', Proc. 17th STOC, 1985, pp. 421- 429. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. BH.Boppana, R. and J. Hastad, "Does co-NP Have Short Interactive Proofs?", IPL, to appear. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 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 ScholarGoogle Scholar
  4. CW.Carter, J.L. and M.N. Wegman, "Universal Classes of Hash Functions", JC$$18 2, 1979, pp.143-154.Google ScholarGoogle Scholar
  5. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  6. GMR.Goldwasser, S., S. Micali and C. Rackoff, "The Knowledge Complexity of Interactive Proof-Systems", Proc. 17th $TOC, 1985, pp. 291-304. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. GS.Goldwasser, S. and M. Sipser, "Private Coins versus Public Coins in Interactive Proof Systems'', Proc. 18ih STOC, 1986, pp. 59-68. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. S.Sipser, M., "A Complexity Theoretic Approach to Randomness", Proc. 15th STOC, 1983, pp. 330-335. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. The complexity of perfect zero-knowledge

                          Recommendations

                          Comments

                          Login options

                          Check if you have access through your login credentials or your institution to get full access on this article.

                          Sign in
                          • Published in

                            cover image ACM Conferences
                            STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing
                            January 1987
                            471 pages
                            ISBN:0897912217
                            DOI:10.1145/28395

                            Copyright © 1987 ACM

                            Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

                            Publisher

                            Association for Computing Machinery

                            New York, NY, United States

                            Publication History

                            • Published: 1 January 1987

                            Permissions

                            Request permissions about this article.

                            Request Permissions

                            Check for updates

                            Qualifiers

                            • Article

                            Acceptance Rates

                            STOC '87 Paper Acceptance Rate50of165submissions,30%Overall Acceptance Rate1,469of4,586submissions,32%

                            Upcoming Conference

                            STOC '24
                            56th Annual ACM Symposium on Theory of Computing (STOC 2024)
                            June 24 - 28, 2024
                            Vancouver , BC , Canada

                          PDF Format

                          View or Download as a PDF file.

                          PDF

                          eReader

                          View online with eReader.

                          eReader