General weak random sources

  • Authors:
  • D. Zuckerman

  • Affiliations:
  • Div. of Comput. Sci., California Univ., Berkeley, CA, USA

  • Venue:
  • SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
  • Year:
  • 1990

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Abstract

The following model for a weak random source is considered. The source is asked only once for R bits, and the source outputs an R-bit string such that no string has probability more than 2/sup - delta R/ of being output. for some fixed delta 0. A pseudorandom generator that runs in time n/sup O(log n)/ and simulates RP using as a seed a string from such a source is exhibited. Under the generalized Paley graph conjecture, a generator that runs in polynomial time and simulates RP is given, as well as a different generator that produces almost perfectly random bits at a rate arbitrarily close to optimal using as seeds strings from a constant number of independent weak random sources.