Deterministic extractors for bit-fixing sources and exposure-resilient cryptography

SIAM Journal on Computing

Volumn 36, Issue 5, 2006, Pages 1231-1247

  Kamp, Jesse ^a   Zuckerman, David ^a  

^a University of Texas at Austin   (United States)

Author keywords

Bit fixing sources; Cryptography; Deterministic; Exposure resilient; Extractors; Random walks; Randomness; Resilient function

Indexed keywords

CONSTANT FRACTION; RANDOM BITS; RESILIENT CRYPTOGRAPHY; RESILIENT FUNCTION;

ADAPTIVE SYSTEMS; ALGORITHMS; CONSTRUCTION; CRYPTOGRAPHY;

BITS;

EID: 35448977790     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539705446846     Document Type: Article

References (34)

1. M. AJTAI, J. KOMLÓS, AND E. SZEMERÉ DI, Deterministic simulation in Logspace, in the 19th ACM Symposium on Theory of Computing, New York, NY, 1987, pp. 132-140.
2. M. AJTAI AND N. LINIAL, The influence of large coalitions, Combinatorica, 13 (1993), pp. 129-145.
3. M. BEN-OR AND N. LINIAL, Collective coin flipping, in Randomness and Computation, S. Micali, ed., Academic Press, New York, 1990, pp. 91-115.
4. J BIERBRAUER AND H. SCHELLWAT, Almost independent and weakly biased arrays: Efficient constructions and cryptologie applications, in Advances in Cryptology - CRYPTO 2000, Lecture Notes in Comput. Sci. 1880, Springer-Verlag, Berlin, 2000, pp. 531-543.
5. M. BLAZE, High-bandwidth encryption with low-bandwidth smartcards, in Fast Software Encryption, Third International Workshop, Cambridge, UK, Lecture Notes in Comput. Sci 1039, Springer-Verlag, Berlin, 1996, pp. 33-40.
6. B. BOLLOBÁS AND I. LEADER, Exact edge-isoperimetric inequalities, European J. Combin., 11 (1990), pp. 335-340.
7. B. BOLLOBAS AND A. J. RADCLIFFE, Isoperimetric inequalities for faces of the cube and the grid, European J. Combin., 11 (1990), pp. 323-333.
8. J. BOURGAIN, On the Construction of Affine Extractors, Geom. Funct. Anal., to appear.
9. V. BOYKO, On the security properties of the oaep as an all-or-nothing transform, in Advances in Cryptology-CRYPTO 1999, M. Wiener, ed., Lecture Notes in Comput. Sci. 1666, Springer-Verlag, Berlin, 1999, pp. 503-518.
10. R. CANETTI, Y. DODIS, S. HALEVI, E. KUSHILEVITZ, AND A. SAHAI, Exposure-resilient functions and all-or-nothing transforms, in Advanees in Cryptology - EUROCRYPT 2000, B. Preneel, ed., Lecture Notes in Comput. Sci. 1807, Springer-Verlag, Berlin, 2000, pp. 453-469.
11. B. CHOR, J. FRIEDMAN, O. GOLDREICH, J. HÅSTAD, S. RUDICH, AND R. SMOLENSKY, The bit extraction problem or t-resilient functions, in 26th Annual Symposium on Foundations of Computer Science, Portland, OR, 1985, pp. 396-407.
12. A. COHEN AND A. WIGDERSON, Dispersera, deterministic amplification, and weak random sources, in 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, 1989, pp. 14-19.
13. P. DIACONIS, Group Representations in Probability and Statistics, Lecture Notes-Monograph Series 11, Institute of Mathematical Statistics, Hay ward, CA, 1988.
14. Y. DODIS, Exposure-Resilient Cryptography, Ph.D. thesis, MIT, Cambridge, MA, 2000.
15. Y. DODIS, A. SAHAI, AND A. SMITH, On perfect and adaptive security in exposure-resilient cryptography, in Advances in Cryptology - EUROCRYPT 2001, Birgit Pfitzmann, ed., Lecture Notes in Computer Sci. 2045, Springer-Verlag, 2001, pp. 301-324.
16. J. FRIEDMAN, On the bit extraction problem, in 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, PA, 1992, pp. 314-319.
17. O. GABBER AND Z. GALIL, Explicit construction of linear sized superconcentrators, J. Comput. System Sci., 22 (1981), pp. 407-420.
18. A. GABIZON, R. RAZ, AND R. SHALTIEL, Deterministic extractors for bit-fixing sources by obtaining an independent seed, in 45th Annual Symposium on Foundations of Computer Science, Rome, Italy, 2004, pp. 394-403.
19. R. IMPAGLIAZZO AND D. ZUCKERMAN, How to recycle random bits, in the 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, 1989, pp. 248-253.
20. M. JAKOBSSON, J. P. STERN, AND M. YUNG, Scramble all, encrypt small, Lecture Notes in Comput. Sci. 1636 (1999), pp. 95-111.
21. J. KAHN, G. KALAI, AND N. LINIAL, The influence of variables on Boolean functions, in the 29th Annual Symposium on Foundations of Computer Science, White Plains, NY, 1988, pp. 68-80.
22. J. KAMP, A. RAO, S. VADHAN, AND D. ZUCKERMAN, Deterministic extractors for small space sources, in the 38th ACM Symposium on Theory of Computing, Seattle, WA, 2006, pp. 691-700.
23. K. KUROSAWA, T. JOHANSSON, AND D. R. STINSON, Almost k-wise independent sample spaces and their cryptologie applications, J. Cryptology, 14 (2001), pp. 231-253.
24. L. LOVÁSZ, Random walks on graphs: A survey, in Combinatorics, Paul Erdös is Eighty, Vol. 2, D. Miklós, V. T. Sós, and T. Szonyi, eds., János Bolyai Math. Soc., Budapest, 1996, pp. 353-398.
25. A. LUBOTZKY, Discrete Groups, Expanding Graphs and Invariant Measures, Birkhäuser-Verlag, Basel, Switzerland, 1994.
26. A. LUBOTZKY, R. PHILIPS, AND P. SARNAK, Ramanujan graphs, Combinatorica, 8 (1988), pp. 261-277.
27. S. MATYAS, M. PEYRAVIAN, AND A. ROGINSKY, Encryption of long blocks using a short-block encryption procedure. http://grouper.ieee.org/groups/1363/P1363a/LongBlock.html.
28. N. NISAN AND D. ZUCKERMAN, Randomness is linear in space, J. Comput. System Sci., 52 (1996), pp. 43-52.
29. O. REINGOLD, S. VADHAN, AND A. WIGDERSON, Entropy waves, the zig-zag product, and new constant-degree expanders and extractors, Ann. of Math. (2), 155 (2002), pp. 155-187.
30. R. L. RIVEST, All-or-nothing encryption and the package transform, Lecture Notes in Comput. Sei., 1267 (1997), pp. 210-218.
31. A. RUSSELL AND D. ZUCKERMAN, Perfect-information leader election in log* n + 0(1) rounds, J. Comput. System Sci., 63 (2001), pp. 612-626.
32. M. SANTHA AND U. V. VAZIRANI, Generating quasi-random sequences from semi-random sources, J. Comput. System Sci., 33 (1986), pp. 75-87.
33. R. SHALTIEL, Recent developments in explicit constructions of extractors, Bull. Eu. Assoc. Theor. Comput. Sci., (2002), pp. 67-95.
34. L. TREVISAN AND S. P. VADHAN, Extracting randomness from samplable distributions, in the 41st Annual Symposium on Foundations of Computer Science, Redondo Beach, CA, IEEE Comput. Soc. Press, Los Alamitos, CA, 2000, pp. 32-42.