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# A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields

Leonard M. Adleman and Jonathan Demarrais
Mathematics of Computation
Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer (Jul., 1993), pp. 1-15
DOI: 10.2307/2152932
Stable URL: http://www.jstor.org/stable/2152932
Page Count: 15
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## 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 $c \in \mathfrak{R}_{>0}$ such that for all sufficiently large prime powers pn, the algorithm computes discrete logarithms over GF(pn) within expected time: ec(log(pn) log log(pn))1/2.

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