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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2006: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science pp 105–116Cite as

On Obtaining Pseudorandomness from Error-Correcting Codes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4337))

Abstract

A number of recent results have constructed randomness extractors and pseudorandom generators (PRGs) directly from certain error-correcting codes. The underlying construction in these results amounts to picking a random index into the codeword and outputting m consecutive symbols (the codeword is obtained from the weak random source in the case of extractors, and from a hard function in the case of PRGs).

We study this construction applied to general cyclic error-correcting codes, with the goal of understanding what pseudorandom objects it can produce. We show that every cyclic code with sufficient distance yields extractors that fool all linear tests. Further, we show that every polynomial code with sufficient distance yields extractors that fool all low-degree prediction tests. These are the first results that apply to univariate (rather than multivariate) polynomial codes, hinting that Reed-Solomon codes may yield good randomness extractors.

Our proof technique gives rise to a systematic way of producing unconditional PRGs against restricted classes of tests. In particular, we obtain PRGs fooling all linear tests (which amounts to a construction of ε-biased spaces), and we obtain PRGs fooling all low-degree prediction tests.

This research was supported by NSF grant CCF-0346991 and by BSF grant 2004329.

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Authors and Affiliations

  1. Dept of Computer Science, California Institute of Technology, Pasadena, CA, 91125

    Shankar Kalyanaraman & Christopher Umans

Authors
  1. Shankar Kalyanaraman
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  2. Christopher Umans
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, P.O. Box, 110016, New Delhi, India

    S. Arun-Kumar

  2. Indian Institute of Technology, Delhi

    Naveen Garg

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© 2006 Springer-Verlag Berlin Heidelberg

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Kalyanaraman, S., Umans, C. (2006). On Obtaining Pseudorandomness from Error-Correcting Codes. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_12

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  • DOI: https://doi.org/10.1007/11944836_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49994-7

  • Online ISBN: 978-3-540-49995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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