|
Isomorphisms between Artin-Schreier towers
Author(s):
Jean-Marc
Couveignes.
Journal:
Math. Comp.
69
(2000),
1625-1631.
MSC (1991):
Primary 11Y40;
Secondary 12E20
Posted:
April 13, 2000
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
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  over a fixed field  can be computed, composed, and inverted in time essentially linear in  . The method relies on an approximation process.
References:
-
- 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
 -isogenies with the  -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:
10.1090/S0025-5718-00-01193-5
PII:
S 0025-5718(00)01193-5
Received by editor(s):
February 5, 1997
Received by editor(s) in revised form:
July 24, 1998
Posted:
April 13, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org