Tiny families of functions with random properties: A quality-size trade-off for hashing (Preliminary version)

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129502, Issue , 1994, Pages 574-583

  Goldreich, Oded ^a   Wigderson, Avi ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; HASH FUNCTIONS; MAPPING; ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL LINGUISTICS; FUNCTION EVALUATION; MATHEMATICAL MODELS; RANDOM PROCESSES; THEOREM PROVING;

ERROR PARAMETERS; EXPLICIT CONSTRUCTIONS; EXTRACTION PROPERTIES; FIRST CONSTRUCTIONS; NEW CONSTRUCTIONS; PSEUDO-RANDOM PROPERTIES; RANDOM PROPERTIES; UNIVERSAL HASHING;

ECONOMIC AND SOCIAL EFFECTS; BOOLEAN FUNCTIONS;

EXTRACTION PROPERTY; HASH FUNCTIONS; MIXING PROPERTIES;

EID: 0028123964     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/195058.195410     Document Type: Conference Paper

References (37)

1. M. Ajtai, J. Komlos, E. Szemeredi, "Deterministic Simulation in LOGSPACE", Proc. 19th STOC, 1987, pp. 132-140.
2. N. Alon, "Eigenvalues, Geometric Expanders, Sorting in Rounds and Ramsey Theory", Combinatorica, 6 (1986), pp. 231-243.
3. N. Alon, O. Goldreich, J. Hastad, R. Peralta, "Simple Constructions of Almost ?-wise Independent Random Variables", Journal of Random structures and Algorithms, Vol. 3, No. 3, (1992), pp. 289-304.
4. N. Alon and V.D. Milman, "Eigenvalues, Expanders and Superconcentrators", 25th FOCS, 1984, pp. 320-322.
5. M. Bellare, O. Goldreich, and S. Goldwasser "Randomness in Interactive Proofs", 31st FOCS, 1990, pp. 318-326.
6. R. Canetti, G. Even and O. Goldreich, "Lower Bounds for Sampling Algorithms", submitted to IPL, 1993.
7. L. Carter and M. Wegman, "Universal Classes of Hash Functions", J. Computer and System Sciences, Vol. 18, pp. 143-154 (1979).
8. A. Cohen, A. Wigderson, " Dispersers, Deterministic Amplification and Weak random Sources", Proc. of the 30th FOCS, pp. 14-19, 1989.
9. B. Chor and O. Goldreich, "Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity", SIAM J. Comput., Vol. 17, No. 2, April 1988, pp. 230261.
10. B. Chor and O. Goldreich, "On the Power of Two-Point Based Sampling, " Jour, of Complexity, Vol 5, 1989, pp. 96-106.
11. A. Cohen and A. Wigderson, "Dispensers, Deterministic Amplification, and Weak Random Sources", 30th FOCS, 1989, pp. 14-19.
12. P. Erdos and J. Spencer, Probabilistic Methods in Combinatorics, Academic Press, 1974.
13. G. Even, "Construction of Small Probability Spaces for Deterministic Simulation", M.Sc. thesis, Computer Science Department, Tech- nion, Haifa, Israel, 1991. (In Hebrew, abstract in English).
14. G. Even, O. Goldreich, M. Luby, N. Nisan, and B. Velickovic, "Approximations of General Independent Distributions", 24th STOC, pp. 1016, 1992.
15. O. Gaber and Z. Galil, "Explicit Constructions of Linear Size Superconcentrators", JCSS, 22 (1981), pp. 407-420.
16. O. Goldreich, H. Krawcyzk and M. Luby, "On the Existence of Pseudorandom Generators", 29th FOCS, pp. 12-24, 1988.
17. O. Goldreich and A. Wigderson, Technical Report CS94-03, Weizmann Institute, Israel, 1994.
18. S. Goldwasser and M. Sipser, "Private Coins versus Public Coins in Interactive Proof Systems", 18th STOC, pp. 59-68, 1986.
19. R. Impagliazzo and M. Luby, "One-Way Functions are Essential for Complexity Based Cryptography", 30th FOCS, pp. 230-235, 1989.
20. R. Impagliazzo and L.A. Levin, "No Better Ways to Generate Hard NP Instances than Picking Uniformly at Random ", 31st FOCS, pp. 812-821, 1990.
21. R. Impagliazzo, L.A. Levin, and M.G. Luby, "Pseudorandom Generators from any OneWay Functions", 21st STOC, pp. 12-24, 1989.
22. R. Impagliazzo and D. Zuckerman, "How to Recycle Random Bits", 30th FOCS, 1989, pp. 248-253.
23. R.M. Karp, N. Pippinger and M. Sipser, "A Time-Randomness Tradeoff", AMS Conference on Probabilistic Computational Complexity, Durham, New Hampshire (1985).
24. A. Lubotzky, R. Phillips, P. Sarnak, "Explicit Expanders and the Ramanujan Conjectures", Proc. 18th STOC, 1986, pp. 240-246.
25. G.A. Margulis, "Explicit Construction of Concentrators", Prob. Per. Infor. 9 (4) (1973), 7180. (English translation in Problems of Infor. Trans. (1975), 325-332.).
26. J. Naor and M. Naor, "Small-bias Probability Spaces: Efficient Constructions and Applications", 22nd STOC, 1990, pp. 213-223.
27. N. Nisan, "Pseudorandom Generators for Space Bounded Machines", 22nd STOC, pp. 204-212, 1990.
28. N. Nisan, "RL C SC", 24th STOC, pp. 619623, 1992.
29. N. Nisan and D. Zuckerman, "More Deterministic Simulation in LOGSPACE", 25th STOC, pp. 235-244, 1993.
30. M. Sipser, "A Complexity Theoretic Approach to Randomness", 15th STOC, 1983, pp. 330335.
31. M. Sipser, "Expanders Randomness or Time vs Space", Structure in Complexity Theory (proceedings), 1986.
32. L. Stockmeyer, "The Complexity of Approximate Counting", 15th STOC, 1983, pp. 118126.
33. M. Santha and U. Vazirani, "Generating Quasi-Random Sequences from Slightly Random Sources", JCSS, Vol. 33, No. 1, pp. 75-87, 1986.
34. A. Srinivasan and D. Zuckerman, "Computing with Very Weak Random Sources", manuscript, 1993.
35. L. Valiant and V.V. Vazirani, "NP is as Easy as Detecting Unique Solutions", Theoretical Computer Science, Vol. 47, 1986, pp. 85-93.
36. U. Vazirani and V. Vazirani, "Random Polynomial Time Equal to Semi-Random Polynomial Time", Proc. 26th FOCS, pp. 417-428, 1985.
37. D. Zuckerman, "Simulating BPP Using a General Weak Random Source, " 32nd FOCS, 1991, pp. 79-89.