Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Isomorphisms between Artin-Schreier towers


Author: Jean-Marc Couveignes
Journal: Math. Comp. 69 (2000), 1625-1631
MSC (1991): Primary 11Y40; Secondary 12E20
DOI: https://doi.org/10.1090/S0025-5718-00-01193-5
Published electronically: April 13, 2000
MathSciNet review: 1680863
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We give a method for efficiently computing isomorphisms between towers of Artin-Schreier extensions over a finite field. We find that isomorphisms between towers of degree $p^n$ over a fixed field $\mathbb{F}_q$ can be computed, composed, and inverted in time essentially linear in $p^n$. The method relies on an approximation process.


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

  • 1. David G. Cantor, On arithmetical algorithms over finite fields, Journal of Combinatorics, series A 50 (1989), 285-300. MR 90f:11100
  • 2. Jean-Marc Couveignes, Computing $l$-isogenies with the $p$-torsion, Algorithmic Number Theory, A.N.T.S. II (H. Cohen, ed.), vol. 1122, Springer, 1996, pp. 59-65. MR 98j:11046
  • 3. Noam D. Elkies, Elliptic and modular curves over finite fields and related computational issues, Computational perspectives on number theory, in honor of A.O.L Atkin, AMS/IP Studies in Advanced Mathematics, vol. 7, AMS/IP, 1998, pp. 21-76. MR 99a:11078
  • 4. Reynald Lercier and François Morain, Counting the number of points on elliptic curves over finite fields: strategies and performances, Advances in Cryptology, EUROCRYPT 95 (L.C. Guillou and J.-J. Quisquater, eds.), Lecture Notes in Computer Science, vol. 921, Springer, 1995, pp. 79-94.
  • 5. -, Algorithms for computing isogenies between elliptic curves, Computational perspectives on number theory, in honor of A.O.L. Atkin, AMS/IP Studies in Advanced Mathematics, vol. 7, AMS/IP, 1998, pp. 77-94. MR 96h:11060
  • 6. René Schoof, Counting points on elliptic curves over finite fields, Journal de Théorie des Nombres de Bordeaux 7 (1995), no. 1. MR 97i:11070
  • 7. Jean-Pierre Serre, Groupes algébriques et corps de classes, Hermann, 1959. MR 21:1973
  • 8. John Tate, Endomorphisms of abelian varieties over finite fields, Inventiones Math. 2 (1966), 134-144. MR 34:5829

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 11Y40, 12E20

Retrieve articles in all journals with MSC (1991): 11Y40, 12E20


Additional Information

Jean-Marc Couveignes
Affiliation: Groupe de Recherche en Mathématiques et Informatique du Mirail, Université de Toulouse II, Le Mirail, France
Email: couveign@math.u-bordeaux.fr

DOI: https://doi.org/10.1090/S0025-5718-00-01193-5
Received by editor(s): February 5, 1997
Received by editor(s) in revised form: July 24, 1998
Published electronically: April 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society