Algorithms for computing
isogenies between elliptic curves.
In D.A. Buell and J.T. Teitelbaum, editors,
Computational Perspectives on Number Theory: Proceedings of a Conference in
Honor of A. O. L. Atkin, volume 7 of AMS/IP Studies in Advanced
Mathematics, pages 77-96, Providence, 1998. American Mathematical Society
& Internationnal Press.
Held in 1995 at the University of Illinois at Chicago..
The efficient implementation of Schoof's algorithm for
computing the cardinality of elliptic curves over finite
fields requires the computation of isogenies between
elliptic curves. We make a survey of algorithms used for
accomplishing this task. When the characteristic of the
field is large, P-Weierstrass's functions can be used. When
the characteristic of the field is small, we now have three
algorithms at our disposal, two due to Couveignes and one to
the first author. We treat the same example using these
three algorithms and make some comparisons between them.
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