# Computing Logarithms in GF (2^{n})

Conference paper

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## Abstract

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≤*x*≤*q*−2, such that *b*=α^{x}. 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 *b*∈*GF*(*q*), *b*≠0.

## Keywords

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