Efficient arguments without short PCPs

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2007, Pages 278-291

  Ishai, Yuval ^a   Kushilevitz, Eyal ^a   Ostrovsky, Rafail ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENCODING (SYMBOLS); LINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING; PROGRAM COMPILERS; THEOREM PROVING;

CRYPTOGRAPHIC TECHNIQUES; HOMOMORPHIC ENCRYPTION; LINEAR FUNCTIONS;

CRYPTOGRAPHY;

EID: 34748860506     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2007.10     Document Type: Conference Paper

References (33)

1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof Verification and the Hardness of Approximation Problems. J. ACM 45(3): 501-555, 1998. Preliminary version in FOCS '92.
2. S. Arora, and S. Safra. Probabilistic Checking of Proofs: A New Characterization of NP. J. ACM 45(1): 70-122, 1998. Preliminary version in FOCS '92.
3. L. Babai, L. Fortnow, L. A. Levin, and M. Szegedy. Checking Computations in Polylogarithmic Time. In STOC 1991, pages 21-31.
4. B. Barak. How to Go Beyond the Black-Box Simulation Barrier. In FOCS 2001, pages 106-115.
5. B. Barak and O. Goldreich. Universal Arguments and their Applications. In CCC 2002, pages 194-203.
6. E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. P. Vadhan. Robust PCPs of proximity, shorter PCPs and applications to coding. SIAM J Comput 36(4): 889-974, 2006. Earlier version in STOC 2004.
7. E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. P. Vadhan. Short PCPs Verifiable in Polylogarithmic Time. In CCC 2005, pages 120-134.
8. E. Ben-Sasson and M. Sudan. Simple PCPs with poly-log rate and query complexity. In STOC 2005, pages 266-275.
9. G. Brassard, D. Chaum, and C. Crépeau. Minimum Disclosure Proofs of Knowledge. J. Comput. Syst. Sci. 37(2): 156-189, 1988. Preliminary version in FOCS '86.
10. M. Blum, M. Luby, and R. Rubinfeld. Self-Testing/Correcting with Applications to Numerical Problems. J Comput. Syst. Sci. 47(3): 549-595, 1993. Preliminary version in STOC '90.
11. D. Boneh, E.J. Goh, and K. Nissim. Evaluating 2-DNF formulas on ciphertexts. In Proc. 2nd TCC, pages 325-341, 2005.
12. B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan. Private information retrieval. J of the ACM, 45:965-981, 1998.
13. I. Dinur. The PCP theorem by gap amplification. In STOC 2006, pages 241-250.
14. I. Dinur and O. Reingold. Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem. In FOCS 2004, pages 155-164.
15. T. ElGamal. A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory, v. IT-31, n. 4, 1985, pages 469-472.
16. U. Feige, S. Goldwasser, L. Lovasz, S. Safra, and M. Szegedy. Interactive Proofs and the Hardness of Approximating Cliques. J. ACM 43(2): 268-292, 1996. Preliminary version in FOCS '91.
17. O. Goldreich. Foundations of Cryptography: Basic Applications. Cambridge University Press, 2004.
18. O. Goldreich and J. Håstad. On the Complexity of Interactive Proofs with Bounded Communication. Inf. Process. Lett. 67(4): 205-214, 1998.
19. O. Goldreich, S. P. Vadhan, and A. Wigderson. On interactive proofs with a laconic prover. Computational Complexity 11(1-2): 1-53, 2002.
20. S. Goldwasser and S. Micali. Probabilistic encryption. JCSS, 28(2):270-299, 1984. Preliminary version in STOC '82.
21. S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM J. Comput., Vol. 18, No. 1, pp. 186-208, 1989.
22. Y. Ishai, E. Kushilevitz and R. Ostrovsky. Sufficient Conditions for Collision-Resistant Hashing. In Proc. 2nd TCC, pages 445-456, 2005.
23. J. Kilian. A Note on Efficient Zero-Knowledge Proofs and Arguments. In STOC1992, pages 723-732.
24. J. Kilian. Improved Efficient Arguments. In CRYPTO 1995, pages 311-324.
25. R. C. Merkle. A Certified Digital Signature. In CRYPTO 1989, pages 218-238.
26. S. Micali. Computationally Sound Proofs. SIAM Journal on Computing, 30(4):1253-1298, 2000.
27. S. Micali, M. Rabin and J. Kilián. Zero knowledge sets. In Proc. FOCS 2003, pages 80-91.
28. M. Naor and K. Nissim. Communication preserving protocols for secure function evaluation. In STOC 2001, pages 590-599.
29. R. Ostrovsky, C. Rackoff, and A. Smith. Efficient Consistency Proofs for Generalized Queries on a Committed Database. In Proc. ICALP 2004, pages 1041-1053.
30. P. Paillier. Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In EUROCRYPT 1999, pages 223-238.
31. A. Polishchuk, and D. A. Spielman. Nearly-linear size holographic proofs. In STOC1994, pages 194-203.
32. A. Ta-Shma. A Note on PCP vs. MIP. Inf. Process. Lett. 58(3): 135-140, 1996.
33. M. Zimand. Probabilistically Checkable Proofs the Easy Way. In IFIP TCS 2002, pages 337-351.