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Unconditional pseudorandom generators for low degree polynomials

Published:17 May 2008Publication History

ABSTRACT

We give an explicit construction of pseudorandom generators against low degree polynomials over finite fields. We show that the sum of 2d small-biased generators with error ε2O(d) is a pseudorandom generator against degree d polynomials with error ε. This gives a generator with seed length 2O(d) log(n/ε). Our construction follows the recent breakthrough result of Bogadnov and Viola. Their work shows that the sum of d small-biased generators is a pseudo-random generator against degree d polynomials, assuming the Inverse Gowers Conjecture. However, this conjecture is only proven for d=2,3. The main advantage of our work is that it does not rely on any unproven conjectures.

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    • Published in

      cover image ACM Conferences
      STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing
      May 2008
      712 pages
      ISBN:9781605580470
      DOI:10.1145/1374376

      Copyright © 2008 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 17 May 2008

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      STOC '08 Paper Acceptance Rate80of325submissions,25%Overall Acceptance Rate1,469of4,586submissions,32%

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