Derandomized constructions of k-wise (almost) independent permutations

Eyal Kaplan, Moni Naor, Omer Reingold

Research output: Contribution to journalConference articlepeer-review

28 Scopus citations

Abstract

Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces "pseudorandom walks" on undirected graphs with a consistent labelling. One such generator is implied by Reingold's log-space algorithm for undirected connectivity [21, 22]. We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is O(kn + log 1/δ).

Original languageEnglish
Pages (from-to)354-365
Number of pages12
JournalLecture Notes in Computer Science
Volume3624
DOIs
StatePublished - 2005
Externally publishedYes
Event8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 - Berkeley, CA, United States
Duration: 22 Aug 200524 Aug 2005

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