On constructing parallel pseudorandom generators from one-way functions

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2005, Pages 183-197

  Viola, Emanuele ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Black box; Constant depth circuit; Hardness amplification; Noise sensitivity; One way function; Pseudorandom generator construction; Restriction

Indexed keywords

BLACK-BOX; CONSTANT-DEPTH CIRCUIT; HARDNESS AMPLIFICATION; NOISE SENSITIVITY; ONE-WAY FUNCTIONS; PSEUDORANDOM GENERATOR CONSTRUCTION; RESTRICTION;

FUNCTIONS; NETWORKS (CIRCUITS); PH EFFECTS; POLYNOMIALS; QUERY LANGUAGES;

RANDOM NUMBER GENERATION;

EID: 27644449284     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2005.16     Document Type: Conference Paper

References (48)

1. Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing, Seattle, Washington, 15-17 May 1989.
2. 1-formulae on finite structures. Ann. Pure Appl. Logic, 24(1):1-48, 1983.
3. M. Ajtai and M. Ben-Or. A theorem on probabilistic constant depth computation. In ACM, editor, Proceedings of the sixteenth annual ACM Symposium on Theory of Computing, Washington, DC, April 30-May 2, 1984, pages 471-474, 1984. ACM order no. 508840.
4. 0. In 45th Annual Symposium on Foundations of Computer Science, Rome, ITALY, 17-19 Oct. 2004. IEEE.
5. L. Babai, L. Fortnow, and C. Lund. Nondeterministic exponential time has two-prover interactive protocols. Comput. Complexity, 1(1):3-40, 1991.
6. D. Beaver and J. Feigenbaum. Hiding instances in multioracle queries. In 7th Annual Symposium on Theoretical Aspects of Computer Science, volume 415 of Lecture Notes in Computer Science, pages 37-48, Rouen, France, 22-24 Feb. 1990. Springer.
7. M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. on Computing, 13(4):850-864, Nov. 1984.
8. A. Bogdanov and L. Trevisan. On worst-case to average-case reductions for NP problems. In 44th Annual Symposium on Foundations of Computer Science, Cambridge, Massachusetts, 11-14 Oct. 2003. IEEE.
9. R. B. Boppana. The average sensitivity of bounded-depth circuits. Inform. Process. Lett., 63(5):257-261, 1997.
10. R. B. Boppana and J. C. Lagarias. One-way functions and circuit complexity. Inform, and Comput., 74(3):226-240, 1987.
11. J.-Y. Cai, A. Pavan, and D. Sivakumar. On the hardness of the permanent. In 16th International Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Trier, Germany, March 4-6 1999. Springer-Verlag. To appear.
12. J.-Y. Cai, D. Sivakumar, and M. Strauss. Constant depth circuits and the lutz hypothesis. In 38th Annual Symposium on Foundations of Computer Science [27], pages 595-604.
13. J. L. Carter and M. N. Wegman. Universal classes of hash functions. J. Comput. System Sci., 18(2):143-154, 1979.
14. U. Feige and C. Lund. On the hardness of computing the permanent of random matrices. Computational Complexity, 6(2):101-132, 1996.
15. J. Feigenbaum and L. Fortnow. Random-self-reducibility of complete sets. SIAM J. on Computing, 22(5):994-1005, Oct. 1993.
16. M. L. Furst, J. B. Saxe, and M. Sipser. Parity, circuits, and the polynomial-time hierarchy. Mathematical Systems Theory, 17(1):13-27, April 1984.
17. R. Gennaro and L. Trevisan. Lower bounds on the efficiency of generic cryptographic constructions. In 41st Annual Symposium on Foundations of Computer Science (Redondo Beach, CA, 2000), pages 305-313. IEEE Comput. Soc. Press, Los Alamitos, CA, 2000.
18. M. Goldmann, M. Näslund, and A. Russell. Complexity bounds on general hard-core predicates. J. Cryptology, 14(3):177-195, 2001.
19. O. Goldreich. Foundations of Cryptography. Volume 1 - Basic Techniques. Cambridge University Press, Cambridge, 2001.
20. O. Goldreich, S. Goldwasser, and S. Micali. How to construct random functions. J. ACM, 33(4):792-807, Oct. 1986.
21. O. Goldreich, H. Krawczyk, and M. Luby. On the existence of pseudorandom generators. SIAM J. Comput., 22(6): 1163-1175, 1993.
22. O. Goldreich and L. A. Levin. A hard-core predicate for all one-way functions. In ACM [1], pages 25-32.
23. O. Goldreich, N. Nisan, and A. Wigderson. On Yao's XOR lemma. Technical Report TR95-050, Electronic Colloquium on Computational Complexity, March 1995. http://www.eccc.uni-trier.de/eccc.
24. J. Histad. Computational limitations of small-depth circuits. MIT Press, 1987.
25. J. Håstad, R. Impagliazzo, L. A. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM J. Comput., 28(4):1364-1396 (electronic), 1999.
26. A. Healy, S. Vadhan, and E. Viola, Using nondeterminism to amplify hardness. In Proceedings of the Thirty-Six Annual ACM Symposium on the Theory of Computing, pages 192-201, Chicago, IL, 13-15 June 2004.
27. Invited to SIAM Journal of Computing, STOC Special Issue.
28. IEEE. 38th Annual Symposium on Foundations of Computer Science, Miami Beach, Florida, 20-22 Oct. 1997.
29. R. Impagliazzo and M. Naor. Efficient cryptographic schemes provably as secure as subset sum. Journal of Cryptology: the journal of the International Association for Cryptologic Research, 9(4):199-216, Fall 1996.
30. R. Impagliazzo and S. Rudich. Limits on the provable consequences of one-way permutations. In ACM [1], pages 44-61.
31. M. Kharitonov, A. V. Goldberg, and M. Yung. Lower bounds for pseudorandom number generators. In 30th Annual Symposium on Foundations of Computer Science, pages 242-247, Research Triangle Park, North Carolina, 30 Oct.-1 Nov. 1989. IEEE.
32. L. A. Levin. One way functions and pseudorandom generators. Combinatorica, 7(4):357-363, 1987.
33. N. Linial, Y. Mansour, and N. Nisan. Constant depth circuits, Fourier transform, and learnability. J. Assoc. Comput. Mach., 40(3):607-620, 1993.
34. R. Lipton. New directions in testing. In Proceedings of DI-MACS Workshop on Distributed Computing and Cryptography, 1989.
35. Y. Mansour, N. Nisan, and P. Tiwari. The computational complexity of universal hashing. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing (May 14-16 1990: Baltimore, MD, USA), pages 235-243, New York, NY 10036, USA, 1990. ACM Press.
36. M. Naor. Bit commitment using pseudorandomness. Journal of Cryptology: the journal of the International Association for Cryptologic Research, 4(2):151-158, 1991.
37. M. Naor and O. Reingold. Number-theoretic constructions of efficient pseudo-random functions. In 38th Annual Symposium on Foundations of Computer Science [27], pages 458-467.
38. N. Nisan. Pseudorandom bits for constant depth circuits. Combinatorica, 11(1):63-70, 1991.
39. N. Nisan and A. Wigderson. Hardness vs randomness. J. Computer & Systems Sciences, 49(2):149-167, Oct. 1994.
40. N. Nisan and D. Zuckerman. Randomness is linear in space. J. Comput. Syst. Sci., 52(1):43-52, Feb. 19%.
41. J. H. Reif and J. D. Tygar. Efficient parallel pseudo-random number generation. In H. C. Williams, editor, Advances in Cryptology - CRYPTO '85, volume 218 of Lecture Notes in Computer Science, pages 433-446. Springer-Verlag, 1986, 18-22 Aug. 1985.
42. O. Reingold, L. Trevisan, and S. Vadhan. Notions of reducibility between cryptographic primitives. In Proceedings of the 1st Theory of Cryptography Conference (Feb 19-21, 2004: Cambridge, MA. USA). Springer-Verlag, 2004.
43. M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. J. Comput. System Sci., 62(2):236-266, 2001.
44. Special issue on the Fourteenth Annual IEEE Conference on Computational Complexity (Atlanta, GA, 1999).
45. L. Trevisan and S. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th Annual IEEE Conference on Computational Complexity, pages 129-138, Montréal, CA, May 2002. IEEE.
46. E. Viola. The complexity of constructing pseudorandom generators from hard functions. Comput. Complexity, 13(3-4):147-188, 2004.
47. A. C. Yao. Theory and applications of trapdoor functions (extended abstract). In 23rd Annual Symposium on Foundations of Computer Science, pages 80-91, Chicago, Illinois, 3-5 Nov. 1982. IEEE.
48. X. Yu and M. Yung. Space lower-bounds for pseudorandom-generators. In Ninth Annual Structure in Complexity Theory Conference, pages 186-197. IEEE Computer Soc., Los Alamitos, CA, 1994.