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Multiplicative character sums of Fermat quotients and pseudorandom sequences

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Abstract

We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients modulo p: bounds on the well-distribution measure, the correlation measure of order ℓ, and the linear complexity.

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Authors and Affiliations

  1. University of Cantabria, Avd. de los Castros s/n, Santander, Spain

    Domingo Gomez

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, A-4040, Linz, Austria

    Arne Winterhof

Authors
  1. Domingo Gomez
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  2. Arne Winterhof
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Correspondence to Domingo Gomez.

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Gomez, D., Winterhof, A. Multiplicative character sums of Fermat quotients and pseudorandom sequences. Period Math Hung 64, 161–168 (2012). https://doi.org/10.1007/s10998-012-3747-1

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  • DOI: https://doi.org/10.1007/s10998-012-3747-1

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