Extracting randomness using few independent sources

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2004, Pages 384-393

  Barak, Boaz ^a   Impagliazzo, Russell ^b   Wigderson, Avi ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DETERMINISTIC EXTRACTORS; MIN-ENTROPY; RAMSEY NUMBER; RANDOM BITS;

ALGORITHMS; BIT ERROR RATE; DISTRIBUTED COMPUTER SYSTEMS; ENTROPY; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

RANDOM PROCESSES;

EID: 17744376438     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. [AKS02] M. Agrawal, N. Kayal, and N. Saxena. PRIMES is in P. Report, Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Kanpur-208016, India, Aug. 2002.
2. +04] B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson. Simulating Independence: New Constructions of Condensers, Ramsey Graphs, Disersers, and Extractors, 2004. In Preparations.
3. [BST03] B. Barak, R. Shaltiel, and E. Tromer. True Random Number Generators Secure in a Changing Environment. In Workshop on Cryptographic Hardware and Embedded Systems (CUES), pages 166-180, 2003. LNCS no. 2779.
4. [Blu84] M. Blum. Independent Unbiased Coin Rips From a Correlated Biased Source: A Finite State Markov Chain. In Proc. 25th FOCS, pages 425-433. IEEE, 1984.
5. [BKT03] J. Bourgain, N. Katz, and T. Tao. A sum-product estimate in finite fields, and applications. Arxiv technical report, http://arxiv.org/abs/ math.CO/0301343, 2003. To appear in GAFA.
6. [CG85] B. Chor and O. Goldreich. Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity. In Proc. 26th FOCS, pages 429-442. IEEE, 1985.
7. +85] B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, and R. Smolensky. The Bit Extraction Problem of t-Resilient Functions (Preliminary Version). In Proc. 26th FOCS, pages 396-407. IEEE, 1985.
8. [CW89] A. Cohen and A. Wigderson. Dispensers, Deterministic Amplification, and Weak Random Sources. In Proc. 30th FOCS, pages 14-19. IEEE, 1989.
9. [CV86] R. Cole and U. Vishkin. Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms. In Proc. 18th STOC, pages 206-219. ACM, 1986.
10. [DO03] Y. Dodis and R. Oliveira. On Extracting Private Randomness over a Public Channel. In Proc. of RANDOM. LNCS, 2003.
11. [DS02] Y. Dodis and J. Spencer. On the (non)Universality of the One-Time Pad. In Proc. 43rd FOCS, pages 376-388. IEEE, 2002.
12. [Elb03] A. Elbaz. Improved Constructions for Extracting Quasi-Random Bits from Sources of Weak Randomness. Master's thesis, Weizmann Institute of Science, 2003.
13. [FN93] A. Fiat and M. Naor. Implicit O(1) probe search. SIAM J. Comput., 22(1):1-10, Feb. 1993.
14. [Gow98] W. T. Gowers. A new proof of Szemerédi's theorem for arithmetic progressions of length four. Geom. Fund. Anal., 8(3):529-551, 1998.
15. [GRS80] R. L. Graham, B. L. Rothschild, and J. L. Spencer. Ramsey Theory. John Wiley & Sons, 1980.
16. [HILL89] 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, 1999. Preliminary versions appeared in STOC' 89 and STOC' 90.
17. [KZ03] Kamp and Zuckerman. Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography. In Proc. 44rd FOCS. IEEE, 2003.
18. [Kon03] S. Konyagin. A sum-product estimate in fields of prime order. Arxiv technical report, http://arxiv.org/abs/math.NT/0304217, 2003.
19. [LRVW03] C.-J. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: optimal up to constant factors. In Proc. 35th STOC, pages 602-611. ACM, 2003.
20. [MP90] J. L. McInnes and B. Pinkas. On the Impossibility of Private Key Cryptography with Weakly Random Keys. In Crypto '90, pages 421-436, 1990. LNCS No. 537.
21. [MU02] Mossel and Umans. On the Complexity of Approximating the VC Dimension. J. Comput. Syst. Sci., 65, 2002.
22. [Nat96] M. B. Nathanson. Additive number theory. Inverse Problems and the Geometry of Sumsets, volume 165 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1996.
23. [Per92] Y. Peres. Iterating von Neumann's procedure for extracting random bits. Ann. Statist., 20(1):590-597, 1992.
24. [PR04] P. Pudlak and V. Rodl. Pseudorandom sets and explicit constructions of Ramsey graphs, 2004. Submitted for publication.
25. [Ruz96] I. Z. Ruzsa. Sums of finite sets. In Number theory (New York, 1991-1995), pages 281-293. Springer, New York, 1996.
26. [SRW03] M. Saks, O. Reingold, and A. Wigderson. Personal Communication, 2003.
27. [SV84] M. Santha and U. V. Vazirani. Generating Quasi-Random Sequences from Slightly-Random Sources. In Proc. 25th FOCS, pages 434-440. IEEE, 1984.
28. [Sha02] R. Shaltiel. Recent developments in extractors. Bulletin of the European Association for Theoretical Computer Science, 2002.
29. [TV00] L. Trevisan and S. Vadhan. Extracting randomness from samplable distributions. In Proc. 41st FOCS, pages 32-42. IEEE, 2000.
30. [Vaz85] U. Vazirani. Strong Communication Complexity or Generating Quasi-Random Sequences from Two Communicating Semi-Random Sources. Combinatorica, 7, 1987. Preliminary version in STOC' 85.
31. [Vaz87] U. V. Vazirani. Efficiency Considerations in Using Semirandom Sources. In Proc. 19th STOC, pages 160-168.ACM, 25-27 May 1987.
32. [vN51] J. von Neumann. Various Techniques Used in Connection with Random Digits. Applied Math Series, 12:36-38, 1951.
33. [Zuc90] D. Zuckerman. General Weak Random Sources. In Proc. 31st FOCS, pages 534-543. IEEE, 1990.
34. [Zuc91] D. Zuckerman. Simulating BPP Using a General Weak Random Source. Algorithmica, 16(4/5):367-391, Oct./Nov. 1996. Preliminary version in FOGS' 91.