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An efficient parallel repetition theorem for Arthur-Merlin games

Published:11 June 2007Publication History

ABSTRACT

We show a parallel-repetition theorem for constant-round Arthur-Merlin Games, using an efficient reduction. As a consequence, we show that parallel repetition reduces the soundness-error at an optimal rate (up to a negligible factor) in constant-round public-coin argument systems, and constant-round public-coinproofs of knowledge. The former of these results resolves an open questionposed by Bellare, Impagliazzo and Naor (FOCS '97).

References

  1. {1} L. Babai and S. Moran. Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes. JCSS, Vol. 36, pages 254-276, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. {2} M. Bellare, R. Impagliazzo and M. Naor. Does Parallel Repetition Lower the Error in Computationally Sound Protocols? In 38th FOCS, pages 374-383, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. {3} M. Bellare and O. Goldreich. On Defining Proofs of Knowledge. In CRYPTO '92, pages 390-420, 1993. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. {4} M. Blum. How to prove a Theorem So No One Else Can Claim It. Proc. of the International Congress of Mathematicians, Berkeley, California, USA, pages 1444-1451, 1986.Google ScholarGoogle Scholar
  5. {5} G. Brassard, D. Chaum and C. Crépeau. Minimum Disclosure Proofs of Knowledge. JCSS, Vol. 37, No. 2, pages 156-189, 1988. Preliminary version by Brassard and Crépeau in 27th FOCS, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. {6} R. Canetti and S. Halevi and M. Steiner. Hardness Amplification of Weakly Verifiable Puzzles. In 2nd TCC, Springer LNCS 3876, pages 17-33, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. {7} O. Goldreich and R. Impagliazzo and L. A. Levin and R. Venkatesan and D. Zuckerman. Security Preserving Amplification of Hardness. In 31th FOCS, pages 318-326, 1990.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. {8} M. Ben-or and S. Goldwasser and J. Kilian and A. Wigderson. Multi Prover Interactive Proofs: How to Remove Intractability. In 20th STOC, pages 113-131, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. {9} U. Feige and A. Fiat and A. Shamir. Zero-Knowledge Proofs of Identity. In J. Cryptology, 1(2), pages 77-94, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. {10} U. Feige and J. Kilian. Two prover protocols: low error at affordable rates. In 26th STOC, pages 172-183, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. {11} L. Fortnow and J. Rompel and M. Sipser. On the power of multi-prover interactive protocols. In Theor. Comput. Sci., 134(2), pages 545-557, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. {12} U. Feige and A. Shamir. Zero Knowledge Proofs of Knowledge in Two Rounds. In Crypto89, Springer LNCS 435, pages. 526-544, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. {13} O. Goldreich. Foundations of Cryptography - Basic Tools. Cambridge University Press, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. {14} O. Goldreich and H. Krawczyk. On the composition of Zero-Knowledge Proof Systems. SIAM Journal on Computing, Vol. 25(1), pages 169-192, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. {15} S. Goldwasser and S. Micali. Probabilistic Encryption. JCSS, Vol. 28, No 2, pages 270-299, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  16. {16} S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof-systems. In STOC 85, pages 291-304, 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. {17} S. Goldwasser, S. Micali and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM Jour. on Computing, Vol. 18(1), pp. 186-208, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. {18} S. Goldwasser, S. Micali and R.L. Rivest. A Digital Signature Scheme Secure Against Adaptive Chosen Message Attacks. SIAM Jour. on Computing, Vol. 17, No. 2, pp. 281-308, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. {19} S. Goldwasser, S. Micali and A. Wigderson. Proofs that Yield Nothing But Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems. JACM, Vol. 38(1), pp. 691-729, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. {20} K. Pietrzak and D. Wikström. Parallel Repetition of Computationally Sound Protocols Revisited. To appear in TCC 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. {21} R. Richardson and J. Kilian. On the Concurrent Composition of Zero-Knowledge Proofs. Eurocrypt 99, Springer LNCS 1592, pages 415-431, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. {22} R. Raz. A parallel repetition theorem. In 27th STOC, pages 447-456, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. {23} M. Tompa, H. Woll. Random Self-Reducibility and Zero Knowledge Interactive Proofs of Possession of Information. In 28th FOCS, pages 472-482, 1987.Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. {24} A. Yao. Theory and Applications of Trapdoor Functions. In 23th FOCS, pages 80-91, 1982.Google ScholarGoogle ScholarCross RefCross Ref

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      cover image ACM Conferences
      STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
      June 2007
      734 pages
      ISBN:9781595936318
      DOI:10.1145/1250790

      Copyright © 2007 ACM

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      • Published: 11 June 2007

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