Deterministic extractors for bit-fixing sources by obtaining an independent seed

Ariel Gabizon, Ran Raz, Ronen Shaltiel

Research output: Contribution to journalConference articlepeer-review

26 Scopus citations

Abstract

An (n, k)-bit-fixing source is a distribution X over {0,1} n such that there is a subset of k variables in X 1,..., X n which are uniformly distributed and independent of each other, and the remaining n - k variables are fixed. A deterministic bit-fixing source extractor is a function E: {0, 1} n → {0, l} m which on an arbitrary (n, k)-bit-fixing source outputs m bits that are statistically-close to uniform. Recently, Kamp and Zuckerman [13] gave a construction of deterministic bit-fixing source extractor that extracts Ω(k 2/n) bits, and requires k > √n. In this paper we give constructions of deterministic bit-fixing source extractors that extract (1 - o(1))k bits whenever k > (log n) c for some universal constant c > 0. Thus, our constructions extract almost all the randomness from bit-fixing sources and work even when k is small. For k ≫ √n the extracted bits have statistical distance 2 -nΩ(1) from uniform, and for k ≤ √n the extracted bits have statistical distance k -Ω(1) from uniform. Our technique gives a general method to transform deterministic bit-fixing source extractors that extract few bits into extractors which extract almost all the bits.

Original languageEnglish (US)
Pages (from-to)394-403
Number of pages10
JournalProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
StatePublished - Dec 1 2004
Externally publishedYes
EventProceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004 - Rome, Italy
Duration: Oct 17 2004Oct 19 2004

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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