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Using number fields to compute logarithms in finite fields

Authors:	Oliver Schirokauer

Institution:	Department of Mathematics, Oberlin College, Oberlin, OH 44074

Abstract:	We describe an adaptation of the number field sieve to the problem of computing logarithms in a finite field. We conjecture that the running time of the algorithm, when restricted to finite fields of an arbitrary but fixed degree, is $L_{q}1/3; (64/9)^{1/3}+o(1)],$ where is the cardinality of the field, $L_{q}s;c]={\exp }(c(\log q)^{s}(\log \log q)^{1-s}),$ and the is for $q\to \infty$ . The number field sieve factoring algorithm is conjectured to factor a number the size of in the same amount of time.

Keywords:	Finite field discrete logarithm number field sieve

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