Computing Logarithms in GF (2n)

  • I. F. Blake
  • R. C. Mullin
  • S. A. Vanstone
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 196)


Consider the finite field having q elements and denote it by GF(q). Let α be a generator for the nonzero elements of GF(q). Hence, for any element b≠0 there exists an integer x, 0≤xq−2, such that bx. We call x the discrete logarithm of b to the base α and we denote it by x=log α b and more simply by log b when the base is fixed for the discussion. The discrete logarithm problem is stated as follows:

Find a computationally feasible algorithm to compute log α b for any bGF(q), b≠0.


Authentication Scheme Discrete Logarithm Irreducible Polynomial Random Integer Discrete Logarithm Problem 
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 1985

Authors and Affiliations

  • I. F. Blake
    • 1
  • R. C. Mullin
    • 2
  • S. A. Vanstone
    • 2
  1. 1.Department of Electrical EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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