Algorithms for computing isogenies between elliptic curves

Abstract : 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.
Type de document :
Communication dans un congrès
D.A. Buell; J.T. Teitelbaum. Computational Perspectives on Number Theory, 1995, Chicago, United States. American Mathematical Society; Internationnal Press, Proceedings of a Conference in Honor of A. O. L. Atkin, 7, pp.77-96, 1998, AMS/IP Studies in Advanced Mathematics. 〈http://www.ams.org/bookstore?fn=20&arg1=amsipseries&item=AMSIP-7〉
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https://hal.archives-ouvertes.fr/hal-01102041
Contributeur : Reynald Lercier <>
Soumis le : lundi 12 janvier 2015 - 00:50:56
Dernière modification le : jeudi 9 février 2017 - 15:14:50

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  • HAL Id : hal-01102041, version 1

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Reynald Lercier, François Morain. Algorithms for computing isogenies between elliptic curves. D.A. Buell; J.T. Teitelbaum. Computational Perspectives on Number Theory, 1995, Chicago, United States. American Mathematical Society; Internationnal Press, Proceedings of a Conference in Honor of A. O. L. Atkin, 7, pp.77-96, 1998, AMS/IP Studies in Advanced Mathematics. 〈http://www.ams.org/bookstore?fn=20&arg1=amsipseries&item=AMSIP-7〉. 〈hal-01102041〉

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