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A Subexponential Algorithm for Discrete Logarithms over All Finite Fields

  • Leonard M. Adleman
  • Jonathan DeMarrais
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 773)

Abstract

There are numerous subexponential algorithms for computing discrete logarithms over certain classes of finite fields. However, there appears to be no published subexponential algorithm for computing discrete logarithms over all finite fields. We present such an algorithm and a heuristic argument that there exists a c ∈ ℜ>0 such that for all sufficiently large prime powers p n, the algorithm computes discrete logarithms over GF(p n) within expected time:
$$ e^{c(\log (p^n )\log {\mathbf{ }}\log (p^n ))^{1/2} } $$

Keywords

Prime Ideal Finite Field Discrete Logarithm Discrete Logarithm Problem Cyclotomic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Leonard M. Adleman
    • 1
  • Jonathan DeMarrais
    • 1
  1. 1.Department of Computer ScienceUniversity of Southern CaliforniaLos Angeles

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