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Mathematics of Computation

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On the discrete logarithm
in the divisor class group of curves

Author: Hans-Georg Rück
Journal: Math. Comp. 68 (1999), 805-806
MSC (1991): Primary 11T71; Secondary 94A60
MathSciNet review: 1622281
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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.

References [Enhancements On Off] (What's this?)

  • 1. G. Frey and H.-G. Rück, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Math. Comp. 62 (1994), 865-874. MR 94h:11056
  • 2. I. A. Semaev, Evaluation of discrete logarithms in a group of $p$-torsion points of an elliptic curve in characteristic $p$, Math. Comp. 67 (1998), 353-356. MR 98c:94017
  • 3. J. P. Serre, Sur la topologie des variétés algébriques en caractéristique p, Sympos. Internat. Topologia Algebraica, Mexico City 1956, 24-53. MR 20:4559

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Hans-Georg Rück
Affiliation: Institut für Experimentelle Mathematik, Universität GH Essen, Ellernstr. 29, D-45326 Essen, Germany

Received by editor(s): August 8, 1997
Article copyright: © Copyright 1999 American Mathematical Society

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