Zero knowledge with efficient provers

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn 2006, Issue , 2006, Pages 287-295

  Nguyen, Minh Huyen ^a   Vadhan, Salil ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Computational complexity; Cryptography; Language dependent commitment schemes; Zero knowledge

Indexed keywords

CHARACTERIZATION; COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; FUNCTIONS; STATISTICAL METHODS; THEOREM PROVING;

LANGUAGE-DEPENDENT COMMITMENT SCHEMES; PROBABILISTIC POLYNOMIALS; ZERO-KNOWLEDGE;

PROBLEM SOLVING;

EID: 33748119637     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132559     Document Type: Conference Paper

References (34)

1. W. Aiello and J. Hastad. Statistical zero-knowledge languages can be recognized in two rounds. J. Comput. Syst. Sci., 42(3):327-345, June 1991.
2. L. Babai and S. Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. J. Comput. Syst. Sci., 36:254-276, 1988.
3. B. Barak. How to go beyond the black-box simulation barrier. Proc. of the 42nd FOCS, 2001.
4. M. Bellare and S. Goldwasser. The complexity of decision versus search. SIAM Journal on Computing, 23(1):97-119, Feb. 1994.
5. M. Bellare, S. Micali, and R. Ostrovsky. Perfect zero-knowledge in constant rounds. In Proceedings of the Twenty Second Annual ACM Symposium on Theory of Computing, pages 482-493, 1990.
6. M. Bellare and E. Petrank. Making zero-knowledge provers efficient. In Proceedings of the Twenty-Fourth Annual ACM Symposium on the Theory of Computing, pages 711-722, 1992.
7. M. Ben-Or, O. Goldreich, S. Goldwasser, J. Håstad, J. Kilian, S. Micali, and P. Rogaway. Everything provable is provable in zero-knowledge, CRYPTO '88.
8. M. Blum. How to prove a theorem so no one else can claim it. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pages 1444-1451, Providence, RI, 1987.
9. T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley & Sons, Inc., 2nd edition, 1991.
10. Y. Ding, D. Harnik, A. Rosen, and R. Shaltiel. Constant-round oblivious transfer in the bounded storage model. In Proceedings of the First Theory of Cryptography Conference, pages 446-472, 2004.
11. S. Even, A. L. Selman, and Y. Yacobi. The complexity of promise problems with applications to public-key cryptography. Information and Control, 61(2):159-173, May 1984.
12. L. Fortnow. The complexity of perfect zero-knowledge. In S. Micali, editor, Advances in Computing Research, volume 5, pages 327-343. JAC Press, Inc., 1989.
13. O. Goldreich. Foundations of Cryptography: Basic Tools. Cambridge University Press, 2001.
14. O. Goldreich, S. Micali, and A. Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM, 38(1):691-729, 1991.
15. O. Goldreich, A. Sahai, and S. Vadhan. Honest verifier statistical zero-knowledge equals general statistical zero-knowledge. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 399-408, Dallas, 23-26 May 1998.
16. O. Goldreich, A. Sahai, and S. Vadhan. Can statistical zero-knowledge be made non-interactive?, or On the relationship of SZK and NISZK. In Advances in Cryptology - CRYPTO '99.
17. O. Goldreich and S. Vadhan. Comparing entropies in statistical zero-knowledge with applications to the structure of SZK. In Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity, pages 54-73, 1999.
18. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18(1):186-208, February 1989.
19. S. Goldwasser and M. Sipser. Private coins versus public coins in interactive proof systems. In S. Micali, editor, Advances in Computing Research, volume 5, pages 73-90. JAC Press, Inc., 1989.
20. J. Håstad, R. Impagliazzo, L. A. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM Journal on Computing, 28(4):1364-1396 (electronic), 1999.
21. R. Impagliazzo and M. Yung. Direct minimum-knowledge computations. In Advances in Cryptology - CRYPTO '87, pages 40-51.
22. T. Itoh, Y. Ohta, and H. Shizuya. A language-dependent cryptographic primitive. Journal of Cryptology, 10(1):37-49, 1997.
23. A. R. Klivans and D. 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, 1999.
24. D. Micciancio and S. Vadhan. Statistical zero-knowledge proofs with efficient provers: lattice problems and more. In D. Boneh, editor, Advances in Cryptology - CRYPTO '03, pages 282-298.
25. P. B. Miltersen and N. V. Vinodchandran. Derandomizing arthur-merlin games using hitting sets. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS '99), pages 71-80, 1999.
26. M. Naor. Bit commitment using pseudorandomness. Journal of Cryptology, 4(2):151-158, 1991.
27. M. Naor, R. Ostrovsky, R. Venkatesan, and M. Yung. Perfect zero-knowledge arguments for np using any one-way permutation. Journal of Cryptology, 11(2):87-108, 1998.
28. T. Okamoto. On relationships between statistical zero-knowledge proofs. Journal of Computer and System Sciences, 60(1):47-108, February 2000.
29. R. Ostrovsky. One-way functions, hard on average problems, and statistical zero-knowledge proofs. In Proceedings of the Sixth Annual Structure in Complexity Theory Conference, pages 133-138, 1991.
30. R. Ostrovsky and A. Wigderson. One-way functions are essential for non-trivial zero-knowledge. In Proceedings of the Second Israel Symposium on Theory of Computing and Systems, 1993.
31. A. Sahai and S. Vadhan. A complete problem for statistical zero knowledge. Journal of the ACM, 50(2):196-249, March 2003.
32. S. P. Vadhan. A Study of Statistical Zero-Knowledge Proofs. PhD thesis, Massachusetts Institute of Technology, August 1999.
33. S. P. Vadhan. On transformations of interactive proofs that preserve the prover's complexity. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pages 200-207, Portland, OR, May 2000.
34. S. P. Vadhan. An unconditional study of computational zero knowledge. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS '04), pages 176-185.