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On the discrete logarithm in the divisor class group of curves
Authors:Hans-Georg Rü  ck.
Affiliation:Institut für Experimentelle Mathematik, Universität GH Essen, Ellernstr.~29, D-45326 Essen, Germany
Abstract:Let $X$ be a curve which is defined over a finite field $k$ of characteristic $p$. We show that one can evaluate the discrete logarithm in $Pic_0(X)_{p^n}$ by $O(n^2 log p)$ operations in $k$. This generalizes a result of Semaev for elliptic curves to curves of arbitrary genus.

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