On the discrete logarithm in the divisor class group of curves
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- by Hans-Georg Rück PDF
- Math. Comp. 68 (1999), 805-806 Request permission
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
- Gerhard Frey and Hans-Georg Rück, A remark concerning $m$-divisibility and the discrete logarithm in the divisor class group of curves, Math. Comp. 62 (1994), no. 206, 865–874. MR 1218343, DOI 10.1090/S0025-5718-1994-1218343-6
- 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), no. 221, 353–356. MR 1432133, DOI 10.1090/S0025-5718-98-00887-4
- Jean-Pierre Serre, Sur la topologie des variétés algébriques en caractéristique $p$, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 24–53 (French). MR 0098097
Additional Information
- Hans-Georg Rück
- Affiliation: Institut für Experimentelle Mathematik, Universität GH Essen, Ellernstr. 29, D-45326 Essen, Germany
- Email: rueck@exp-math.uni-essen.de
- Received by editor(s): August 8, 1997
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 805-806
- MSC (1991): Primary 11T71; Secondary 94A60
- DOI: https://doi.org/10.1090/S0025-5718-99-01043-1
- MathSciNet review: 1622281