On interactive proofs with a laconic prover (extended abstract)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2076 LNCS, Issue , 2001, Pages 334-345

  Goldreich, Oded ^a   Vadhan, Salil ^b   Wigderson, Avi ^c  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b HARVARD UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Arthur Merlin games; Gme theory; Iteractive proofs; Satistical zero knowledge; Smpling proto cols

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS; AUTOMATA THEORY; GAME THEORY; SAMPLING;

ARTHUR-MERLIN GAMES; GME THEORY; ITERACTIVE PROOFS; SMPLING PROTO-COLS; ZERO KNOWLEDGE; INTERACTIVE PROOFS; NP-COMPLETE LANGUAGE; PROOF SYSTEM; SAMPLING PROTOCOL; STATISTICAL ZERO KNOWLEDGE; UPPER BOUND;

AUTOMATA THEORY; COMPUTATIONAL LINGUISTICS;

EID: 84879513926     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48224-5_28     Document Type: Conference Paper

References (28)

1. William Aiello and Johan Hastad. Statistical zero-knowledge languages can be recognized in two rounds. Journal of Computer and System Sciences, 42(3):327-345, June 1991.
2. V. Arvind and J. K̈obler. On resource-bounded measure and pseudoran-domness. In Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science, pages 235-249. LNCS 1346, Springer-Verlag, 1997.
3. Ĺaszĺo Babai. Trading group theory for randomness. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, pages 421-429, Providence, Rhode Island, 6-8 May 1985.
4. Ĺaszĺo Babai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36:254-276, 1988.
5. Mihir Bellare, Oded Goldreich, and Madhu Sudan. Free bits, PCPs, and nonapproximability-towards tight results. SIAM Journal on Computing, 27(3):804-915 (electronic), 1998.
6. Ravi B. Boppana, Johan Hastad, and Stathis Zachos. Does co-NP have short interactive proofs Information Processing Letters, 25:127-132, 1987.
7. Gilles Brassard, David Chaum, and Claude Cŕepeau. Minimum disclosure proofs of knowledge. Journal of Computer and System Sciences, 37(2):156-189, October 1988.
8. Lance Fortnow. The complexity of perfect zero-knowledge. In Silvio Micali, editor, Advances in Computing Research, volume 5, pages 327-343. JAC Press, Inc. , 1989.
9. Oded Goldreich. Modern Cryptography, Probabilistic Proofs, and Pseu-dorandomness. Number 17 in Algorithms and Combinatorics. Springer-Verlag, 1999.
10. Oded Goldreich and Shafi Goldwasser. On the limits of nonapproximability of lattice problems. Journal of Computer and System Sciences, 60(3):540-563, 2000.
11. Oded Goldreich and Johan Hastad. On the complexity of interactive proofs with bounded communication. Information Processing Letters, 67(4):205-214, 1998.
12. Oded Goldreich and Eyal Kushilevitz. A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm. Journal of Cryptology, 6:97-116, 1993.
13. Oded Goldreich, Silvio Micali, and Avi Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. Journal of the ACM, 38(1):691-729, 1991.
14. Oded Goldreich, Rafail Ostrovsky, and Erez Petrank. Computational complexity and knowledge complexity. SIAM Journal on Computing, 27(4):1116-1141, August 1998.
15. Oded Goldreich and Erez Petrank. Quantifying knowledge complexity. Computational Complexity, 8(1):50-98, 1999.
16. Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof systems. SIAM Journal on Computing, 18(1):186-208, February 1989.
17. Shafi Goldwasser and Michael Sipser. Private coins versus public coins in interactive proof systems. In Silvio Micali, editor, Advances in Computing Research, volume 5, pages 73-90. JAC Press, Inc. , 1989.
18. Joe Kilian. A note on efficient zero-knowledge proofs and arguments (extended abstract). In Proceedings of the Twenty-Fourth Annual ACM Symposium on the Theory of Computing, pages 723-732, Victoria, British Columbia, Canada, 4-6 May 1992.
19. Adam R. Klivans and Dieter van Melkebeek. Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. In Proceedings of the Thirty-first Annual ACM Symposium on Theory of Computing, pages 659-667, Atlanta, 1-4 May 1999.
20. Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan. Algebraic methods for interactive proof systems. Journal of the ACM, 39(4):859-868, October 1992.
21. Peter Bro Miltersen and N. V. Vinodchandran. Derandomizing Arthur-Merlin games using hitting sets. In 40th Annual Symposium on Foundations of Computer Science, New York, NY, 17-19 October 1999. IEEE.
22. Tatsuaki Okamoto. On relationships between statistical zero-knowledge proofs. Journal of Computer and System Sciences, 60(1):47-108, February 2000.
23. Erez Petrank and Ǵabor Tardos. On the knowledge complexity of NP. In 37th Annual Symposium on Foundations of Computer Science, pages 494-503, Burlington, Vermont, 14-16 October 1996. IEEE.
24. Amit Sahai and Salil P. Vadhan. A complete promise problem for statistical zero-knowledge. In 38th Annual Symposium on Foundations of Computer Science, pages 448-457, Miami Beach, Florida, 20-22 October 1997. IEEE.
25. Adi Shamir. IP = PSPACE. Journal of the ACM, 39(4):869-877, October 1992.
26. Michael Sipser. Introduction to the Theory of Computation. PWS Publishing, 1997.
27. Alan Tucker. Applied combinatorics. John Wiley & Sons Inc. , New York, third edition, 1995.
28. Salil Vadhan. Probabilistic proof systems I: Interactive and zero-knowledge proofs. Lecture Notes from the IAS/PCMI Graduate Summer School on Computational Complexity, August 2000. Available from http://eecs. harvard. edu/̃salil/.