Constructing locally computable extractors and cryptosystems in the bounded-storage model

Journal of Cryptology

Volumn 17, Issue 1, 2004, Pages 43-77

  Vadhan, Salil P ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Averaging samplers; Bounded storage model; Everlasting security; Expander graphs; Extractors; Space bounded adversaries; Unconditional security

Indexed keywords

AVERAGING SAMPLERS; BOUNDED STORAGE MODELS; EVERLASTING SECURITY; EXPANDER GRAPHS; EXTRACTORS; SPACE BOUNDED ADVERSARIES; UNCONDITIONAL SECURITY;

CODES (SYMBOLS); DATA PRIVACY; ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS; GRAPH THEORY; MATHEMATICAL MODELS; SECURITY OF DATA; THEOREM PROVING;

CRYPTOGRAPHY;

EID: 4344628859     PISSN: 09332790     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00145-003-0237-x     Document Type: Article

References (44)

1. [ADR] Yonatan Aumann, Yan Zong Ding, and Michael O. Rabin. Everlasting security in the bounded storage model. IEEE Transactions on Information Theory, 48(6):1668-1680, June 2002.
2. [AR] Yonatan Aumann and Michael O. Rabin. Information theoretically secure communication in the limited storage space model. In Advances in Cryptology - CRYPTO '99, 15-19 August 1999, pages 65-79. Volume 1666 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1999.
3. [ASE] Noga Alon, Joel H. Spencer, and Paul Erdös. The Probabilistic Method. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York, 1992.
4. [BBR] Charles H. Bennett, Gilles Brassard, and Jean-Marc Robert. Privacy amplification by public discussion. SIAM Journal on Computing, 17(2):210-229, 1988. Special issue on cryptography.
5. [BGG] Mihir Beliare, Oded Goldreich, and Shafi Goldwasser. Randomness in interactive proofs. Computational Complexity, 3(4):319-354, 1993.
6. [BR] Mihir Bellare and John Rompel. Randomness-efficient oblivious sampling. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, 20-22 November 1994, pages 276-287.
7. [BRST] Ziv Bar-Yossef, Omer Reingold, Ronen Shaltiel, and Luca Trevisan. Streaming computation of combinatorial objects. In Proceedings of the Seventeenth Annual IEEE Conference on Computational Complexity, Montreal, 21-24 May 2002, pages 165-174. IEEE Computer Society Press, Los Alamitos, CA, 2002.
8. [BY] Mihir Bellare and Bennet Yee. Forward-security in private-key cryptography. In M. Joye, editor, Topics in Cryptology - CT-RSA 03, pages 1-18. Volume 2612 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2003.
9. [CEG] Ran Canetti, Guy Even, and Oded Goldreich. Lower bounds for sampling algorithms for estimating the average. Information Processing Letters, 53(1):17-25, January 1995.
10. [CG1] Benny Chor and Oded Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM Journal on Computing, 17(2):230-261, April 1988.
11. [CG2] Benny Chor and Oded Goldreich. On the power of two-point based sampling. Journal of Complexity, 5(1):96-106, 1989.
12. [CM] Christian Cachin and Ueli Maurer. Unconditional security against memory-bounded adversaries. In Burton S. Kaliski Jr., editor, Advances in Cryptotogy - CRYPTO '97, pages 292-306. Volume 1294 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1997.
13. [DM] Stefan Dziembowski and Ueli Maurer. Optimal randomizer efficiency in the bounded-storage model. Journal of Cryptology, this issue, pp. 5-26.
14. [DR] Yan Zong Ding and Michael O. Rabin. Hyper-encryption and everlasting security (extended abstract). In STACS 2002 - 19th Annual Symposium on Theoretical Aspects of Computer Science, 14-16 March 2002, pages 1-26. Volume 2285 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2002.
15. [DS] Devdatt Dubhashi and Sandeep Sen. Concentration of measure for randomized algorithms: techniques and analysis. In S. Rajasekaran et al., editor, Handbook of Randomized Computing, Volume I, chapter 3, pages 35-100. Kluwer, Dordrecht, 2001.
16. [G1] David Gillman. A Chernoff bound for random walks on expander graphs. SIAM Journal on Computing, 27(4): 1203-1220 (electronic), 1998.
17. [G2] Oded Goldreich. A Sample of Samplers: A Computational Perspective on Sampling. Technical Report TR97-020, Electronic Colloquium on Computational Complexity, May 1997.
18. [GG] Ofer Gabber and Zvi Galil. Explicit constructions of linear-sized superconcentrators. Journal of Computer and System Sciences, 22(3):407-420, June 1981.
19. [GW] Oded Goldreich and Avi Wigderson. Tiny families of functions with random properties: a quality-size trade-off for hashing. Random Structures & Algorithms, 11(4):315-343, 1997.
20. [HILL] Johan Håstad, Russell Impagliazzo, Leonid A. Levin, and Michael Luby. A pseudorandom generator from any one-way function. SIAM Journal on Computing, 28(4): 1364-1396 (electronic), 1999.
21. [L] Chi-Jen Lu. Encryption against storage-bounded adversaries from on-line strong extractors. Journal of Cryptology, this issue, pp. 27-42.
22. [LRVW] Chi-Jen Lu, Omer Reingold, Salil Vadhan, and Avi Wigderson. Extractors: Optimal up to constant factors. In Proceedings of the 35th ACM Symposium on Theory of Computing, San Diego, CA, June 2003, pages 602-611.
23. [M1] G. A. Margulis. Explicit constructions of expanders. Problemy Peredči Informacii, 9(4):71-80, 1973.
24. [M2] Ueli Maurer. Conditionally-perfect secrecy and a provably-secure randomized cipher. Journal of Cryptology, 5(1):53-66, 1992.
25. [M3] Ueli M. Maurer. Secret key agreement by public discussion from common information. IEEE Transactions on Information Theory, 39(3):733-742, 1993.
26. [N] Noam Nisan. Pseudorandom generators for space-bounded computation. Combinatorica, 12(4):449-461, 1992.
27. [NT] Noam Nisan and Amnon Ta-Shma. Extracting randomness: a survey and new constructions. Journal of Computer and System Sciences, 58(1):148-173, 1999.
28. [NZ] Noam Nisan and David Zuckerman. Randomness is linear in space. Journal of Computer and System Sciences, 52(1):43-52, February 1996.
29. [R] Michael O. Rabin. Personal communication, December 2001.
30. [RT] Jaikumar Radhakrishnan and Amnon Ta-Shma. Bounds for dispersers, extractors, and depth-two superconcentrators. SIAM Journal on Discrete Mathematics, 13(1):2-24 (electronic), 2000.
31. [RRV] Ran Raz, Omer Reingold, and Salil Vadhan. Extracting all the randomness and reducing the error in Trevisan's extractors. Journal of Computer and System Sciences, 65(1):97-128, 2002.
32. [RSW] Omer Reingold, Ronen Shaltiel, and Avi Wigderson. Extracting randomness via repeated condensing. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science, Redondo Beach, CA, 12-14 November 2000, pages 22-31.
33. [RVW] Omer Reingold, Salil Vadhan, and Avi Wigderson. Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pages 3-13, 2000.
34. [S1] Ronen Shaltiel. Recent developments in explicit constructions of extractors. Bulletin of the European Association for Theoretical Computer Science, 77:67-95, June 2002.
35. [S2] Claude E. Shannon. Communication theory of secrecy systems. Bell System Technical Journal, 28:656-715, 1949.
36. [SSZ] Michael Saks, Aravind Srinivasan, and Shiyu Zhou. Explicit OR-dispersers with polylogarithmic degree. Journal of the ACM, 45(1): 123-154, January 1998.
37. [SU] Ronen Shaltiel and Christopher Umans. Simple extractors for all min-entropies and a new pseudorandom generator. In Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, 14-17 October 2001, pages 648-657.
38. [T1] Amnon Ta-Shma. Almost optimal dispersers. Combinatorica, 22(1):123-145, 2002.
39. [T2] Luca Trevisan. Extractors and pseudorandom generators. Journal of the ACM, 48(4): 860-879, July 2001.
40. [TZS] Amnon Ta-Shma, David Zuckerman, and Shmuel Safra. Extractors from Reed-Muller codes. In Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, 14-17 October 2001, pages 638-647.
41. [V1] Salil P. Vadhan. On constructing locally computable extractors and cryptosystems in the bounded storage model. Cryptology ePrint Archive, Report 2002/162, 2002. http://eprint.iacr.org/.
42. [V2] Salil P. Vadhan. On constructing locally computable extractors and cryptosystems in the bounded storage model. In Dan Boneh, editor, Advances in Cryptology - CRYPTO '03, 17-21 August 2003, pages 61-77. Volume 2729 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2003.
43. [Z1] David Zuckerman. Simulating BPP using a general weak random source. Algorithmica, 16(4/5):367-391, October/November 1996.
44. [Z2] David Zuckerman. Randomness-optimal oblivious sampling. Random Structures & Algorithms, 11(4):345-367, 1997.