Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-99-01043-1
MathSciNet review: 1622281
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11T71, 94A60

Retrieve articles in all journals with MSC (1991): 11T71, 94A60


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

DOI: https://doi.org/10.1090/S0025-5718-99-01043-1
Received by editor(s): August 8, 1997
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society