Reynald Lercier

R. Lercier and F. Morain. 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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