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Abstract: We present three explicit constructions of hash functions, which exhibit a trade-o# between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudo-random property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. (Update)
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BibTeX entry: (Update)
O. Goldreich and A. Wigderson, "Tiny Families of Functions with Random Properties: A Quality-Size Trade-off for Hashing", 26th STOC, 1994. http://citeseer.ist.psu.edu/goldreich03tiny.html More
@inproceedings{ goldreich94tiny,
author = "Oded Goldreich and Avi Wigderson",
title = "Tiny Families of Functions with Random Properties: A Quality-Size Trade-off for Hashing (Preliminary Version)",
booktitle = "{ACM} Symposium on Theory of Computing",
pages = "574-583",
year = "1994",
url = "citeseer.ist.psu.edu/goldreich03tiny.html" }
Citations (may not include all citations):957 The Probabilistic Method (context) - Alon, Spencer - 1992 ACM DBLP
358 Universal Classes of Hash Functions (context) - Carter, Wegman - 1979 DBLP
163 NP is as Easy as Detecting Unique Solutions (context) - Valiant, Vazirani - 1986
128 A Complexity Theoretic Approach to Randomness (context) - Sipser - 1983
128 Simple Constructions of Almost k-wise Independent Random Var.. - Alon, Goldreich et al. - 1992 DBLP
122 How to Recycle Random Bits - Impagliazzo, Zuckerman - 1989 DBLP
120 Unbiased Bits from Sources of Weak Randomness and Probabilis.. - Chor, Goldreich - 1988
98 Private Coins versus Public Coins in Interactive Proof Syste.. (context) - Goldwasser, Sipser - 1989 ACM DBLP
88 Deterministic Simulation in LogSpace (context) - Ajtai, Komlos et al. - 1987 ACM DBLP
84 Simulating BPP Using a General Weak Random Source - Zuckerman - 1996 ACM DBLP
79 One-Way Functions are Essential for Complexity Based Cryptog.. (context) - Impagliazzo, Luby - 1989
75 Randomness is Linear in Space - Nisan, Zuckerman - 1993
70 the Power of Two--Point Based Sampling - Chor, Goldreich - 1989
68 Pseudorandom Generators for Space Bounded Computation (context) - Nisan - 1992
61 Expanders that Beat the Eigenvalue Bound, Explicit Construct.. - Wigderson, Zuckerman - 1993
60 Computing with Very Weak Random Sources - Srinivasan, Zuckerman - 1994
58 Construction of Asymptotically Good, Low-Rate Error-Correcti.. (context) - Alon, Bruck et al. - 1992
57 Probabilistic Methods in Combinatorics - Erdos, Spencer - 1974
54 Explicit Construction of Concentrators (context) - Margulis
45 Randomness in Interactive Proofs - Bellare, Goldreich et al. - 1993 ACM DBLP
40 Approximations of General Independent Distributions - Even, Goldreich et al. - 1992 ACM DBLP
40 Explicit Expanders and the Ramanujan Conjectures (context) - Lubotzky, Phillips et al. - 1986 ACM DBLP
37 No Better Ways to Generate Hard NP Instances than Picking Un.. (context) - Impagliazzo, Levin - 1990 DBLP
35 the Existence of Pseudorandom Generators (context) - Goldreich, Krawcyzk et al. - 1993
34 Small-bias Probability Spaces: E#cient Constructions and App.. (context) - Naor, Naor - 1993
30 Isoperimetric Inequalities for Graphs and Superconcentrators (context) - Alon, Milman - 1985
30 Pseudorandom Generators from any One-Way Functions (context) - Impagliazzo, Levin et al. - 1989
24 The Complexity of Approximate Counting (context) - Stockmeyer - 1983 ACM
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19 Explicit Constructions of Linear Size Superconcentrators (context) - Gaber, Galil - 1981 DBLP
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9 Expanders, Randomness or Time vs Space (context) - Sipser - 1986
8 Eigenvalues, Geometric Expanders, Sorting in Rounds and Rams.. (context) - Alon - 1986
7 Randomness-Optimal Sampling, Extractors, and Constructive Le.. (context) - Zuckerman - 1996
5 Journal of Computational Complexity (context) - Nisan, SC - 1994
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