Computing isogenies between elliptic curves over $GF(p^n)$ using Couveignes's algorithm
Lercier, Reynald ; Morain, François
HAL, hal-01102025 / Harvested from HAL
Text on HAL
The heart of the improvements of Elkies to Schoof's algorithm for computing the cardinality of elliptic curves over a finite field is the ability to compute isogenies between curves. Elkies' approach is well suited for the case where the characteristic of the field is large. Couveignes showed how to compute isogenies in small characteristic. The aim of this paper is to describe the first successful implementation of Couveignes's algorithm. In particular, we describe the use of fast algorithms for performing incremental operations on series. We also insist on the particular case of the characteristic 2.
Publié le : 2000-01-04
Classification:  Primary 11G20; Secondary 11T71, 94A60, 11Y16,  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 
@article{hal-01102025,
     author = {Lercier, Reynald and Morain, Fran\c cois},
     title = {Computing isogenies between elliptic curves over $GF(p^n)$ using Couveignes's algorithm},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01102025}
}

Lercier, Reynald; Morain, François. Computing isogenies between elliptic curves over $GF(p^n)$ using Couveignes's algorithm. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01102025/