Deterministic extractors for independent-symbol sources

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

Volumn 4051 LNCS, Issue , 2006, Pages 84-95

  Lee, Chia Jung ^a   Lu, Chi Jen ^b   Tsai, Shi Chun ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

^b INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; CODES (SYMBOLS); COMPUTER PROGRAMMING; ERROR ANALYSIS;

EXTRACTORS; INDEPENDENT-SYMBOL SOURCES; RANDOMNESS;

RANDOM PROCESSES;

EID: 33746379296     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11786986_9     Document Type: Conference Paper

References (34)

1. N. Alon, O. Goldreich, J. Håstad, and R. Peralta. Simple constructions of almost k-wise independent random variables. FOCS'90, pp. 544-553.
2. N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4), pp. 567-583, 1986.
3. B. Barak, R. Impagliazzo, and A. Wigderson, Extracting randomness using few independent sources. FOCS'04, pp- 384-393.
4. B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson. Simulating Independence: New constructions of condensers, Ramsey graphs, dispersers, and extractors. STOC'05, pp. 1-10.
5. J. Bourgain. More on the sum-product phenomenon in prime fields and its applications. International Journal of Number Theory, 1(1), pp. 1-32, 2005.
6. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2), pp. 230-261, 1988.
7. B. Chor, O. Goldreich, J. Håstad, J. Friedman, S. Rudich, and Roman Smolensky. The bit extraction problem of t-resilient functions. FOCS'85, pp. 396-407.
8. Y. Dodis, A. Elbaz, R. Oliveira, and R. Raz. Improved randomness extraction from two independent sources. RANDOM'04, pp. 334-344.
9. A. Gabizon, R. Raz, and R. Shaltiel. Deterministic extractors for bit-fixing sources by obtaining an Independent seed, FOCS'04, pp. 394-403.
10. R. Irnpagliazzo, R. Shaltiel, and A. Wigdorson. Extractors and pseudo-random generators with optimal seed length, STOC'00, pp. 1-10.
11. S. Jukna, Extrernal Combinatorics. Springer-Verlag, 2001.
12. J. Kamp, A. Rao, S. Vahan, and D. Zuckerman, Deterministic extractors For small-space sources, STOC'06, to appear.
13. J. Kamp and D. Zuckerman. Deterministic extractors for bit-fixing sources and exposure-resiliont cryptography. FOCS'03, pp. 92-101.
14. R. König and U. Maurer. Generalized strong extractors and deterministic privacy amplification, In Proc. Cryptography and Coding, pp. 322-339, 2005.
15. C.-J. Lee, C.-J. Lu, S.-C. Tsai, and W.-G. Tzeng. Extracting randomness from multiple independent sources. IEEE Transactions on Information Theory, 51(6), pp. 2224-2227, 2005.
16. C.-J. Lu. Encryptiori against storage-bounded adversaries from on-line strong extractors. J. Cryptology, 17(1), pp. 27-42, 2004.
17. C.-J. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: Optimal up to constant factors. STOC'03, pp. 602-611.
18. J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications. SIAM J. Comput., 22(4), pp. 838-856, 1993.
19. N. Nisan and A. Ta-Shma. Extracting randomness: A survey and new constructions. J. Comput. Syst. Sci., 58(1), pp. 148-173, 1999.
20. N. Nisan and D. Zuckerman, Randomness is linear in space. J. Comput. Syst. Sci., 52(1), pp. 43-52, 1996.
21. R. Raz. Extractors with weak random seeds. STOC'05, pp. 11-20.
22. R. Raz, O. Reingold, and S. Vadhan, Extracting all the randomness and reducing the error in Trevisan's extractors. STOC'99, pp. 149-158.
23. J. Radhakrishnan and A. Ta-Shma. Bounds for dispersers, extractors, and depth-two superconcentrators. SIAM J. Discrete Math., 13(1), pp. 2-24, 2000.
24. O. Reingold, R. Shaltiel, and A. Wigderson. Extracting randomness via repeated condensing. FOCS'00, pp. 12-14.
25. R. Shaltiel. Recent developments in explicit constructions of extractors. Bulletin of the European Association for Theoretical Computer Science, 77, pp. 67-95, 2002.
26. R. Shaltiel and C. Umans. Simple extractors for all min-entroples and a new pseudo-random generator. FOCS'01, pp. 648-657.
27. A. Ta-Shma, C. Umans, and David Zuckerman. Loss-less condensers, unbalanced expanders, and extractors. STOC'01, pp. 143-152.
28. A. Ta-Shma and D. Zuckerman, Extractor codes. STOC'01, pp. 193-199.
29. L. Trevisan. Extractors and pseudorandom generators. JACM, 48(4), pp. 860-879, 2001.
30. S. Vadhan. Constructing locally computable extractors and cryptosystems in the bounded-storage model. J. Cryptology, 17(1), pp. 43-77, 2004.
31. A. Wigderson and D. Zuckerman. Expanders that beat the eigenvalue bound: Explicit construction and applications. Combinatorica, 19(1), pp. 125-138, 1999.
32. D. Zuckerman. General weak random sources. FOCS'90, pp. 534-543.
33. D. Zuckerman. Simulating BPP using a general weak random sourcs. Algorithmica, 16(4/5), pp. 307-391, 1996.
34. D. Zuckerman, Randomness-optimal oblivious sampling. Random Structures and Algorithms, 11, pp. 345-367, 1997.