Direct Zero Knowledge Proofs of Computational Power in Five Rounds

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


Zero-knowledge proofs of computational power have been proposed by Yung and others. In this paper, we propose an efficient (direct) and constant round (five round) construction of zero knowledge proofs of computational power. To formulate the classes that can be applied to these efficient protocols, we introduce a class of invulnerable problems, FewPR and FewPR U. We show that any invulnerable problem in FewPR and FewPR U has an efficient and constant round zero knowledge proof of computational power, assuming the existence of a one-way function. We discuss some applications of these zero-knowledge proofs of computational power.


  1. [AABFH]
    M. Abadi, E. Allender, A. Broder, F. Feigenbaum, and L. Hemachandra, “On Generating Solved Instances of Computational Problems,” the Proceedings of Crypto (1988)Google Scholar
  2. [BDLP]
    J. Brandt, I. Damgård, P. Landrock, T. Pedersen, “Zero-Knowledge Authentication Scheme with Secret Key Exchange,” (Preprint)Google Scholar
  3. [BMO]
    M. Bellare, S. Micali, and R. Ostrovsky, “Perfect Zero-Knowledge in Constant Rounds,” the Proceedings of STOC, pp.482–493 (1990)Google Scholar
  4. [FeS]
    U. Feige, A. Shamir, “Zero-Knowledge Proofs of Knowledge in Two Rounds,” the Proceedings of Crypto’89, pp.526–544 (1989)Google Scholar
  5. [FFS]
    U. Feige, A. Fiat and A. Shamir, “Zero Knowledge Proofs of Identity,” the Proceedings of STOC, pp.210–217 (1987)Google Scholar
  6. [FiS]
    A. Fiat and A. Shamir, “How to Prove Yourself,” the Proceedings of Crypto (1986)Google Scholar
  7. [GM]
    S. Goldwasser, S. Micali, “Probabilistic Encryption,” Journal of Computer and System Science, pp270–299 (1984)Google Scholar
  8. [GMR]
    S. Goldwasser, S. Micali, and C. Rackoff, “Knowledge Complexity of Interactive Proofs,” the Proceedings of STOC, pp291–304 (1985)Google Scholar
  9. [GMW]
    O. Goldreich, S. Micali, and A. Wigderson, “Proofs that Yield Nothing But their Validity and a Methodology of Cryptographic Protocol Design,” the Proceedings of FOCS, pp.174–187 (1986)Google Scholar
  10. [H]
    J. Håstad, “Pseudo-Random Generators under Uniform Assumptions,” the Proceedings of STOC, pp.395–404 (1990)Google Scholar
  11. [ILL]
    R. Impagliazzo, L. Levin, M. Luby “Pseudo-Random Number Generation from One-Way Functions,” the Proceedings of STOC, pp.12–24 (1989)Google Scholar
  12. [K]
    K. Kurosawa, “Dual Zero Knowledge Interactive Proof Systems,” Technical Report of the IEICE. Japan, ISEC88-33 (1988)Google Scholar
  13. [OkOh]
    T. Okamoto, and K. Ohta, “Zero Knowledge Proofs for Possession of Blackboxes,” SCIS’89 (in Japan) (1989)Google Scholar
  14. [N]
    M. Naor, “Bit Commitment Using Pseudo-Randomness,” the Proceedings of Crypto’89 (1989)Google Scholar
  15. [TW]
    M. Tompa and H. Woll, “Random Self-Reducibility and Zero Knowledge Interactive Proofs of Possession of Information,” the Proceedings of FOCS, pp.472–482 (1987)Google Scholar
  16. [Y]
    M. Yung, “Zero-Knowledge Profs of Computational Power,” the Proceedings of Eurocrypt’89, (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.NTT LaboratoriesNippon Telegraph and Telephone CorporationYokosuka-shi, Kanagawa-kenJapan
  2. 2.Centre for Mathematics and Computer ScienceAmsterdamNetherlands

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