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Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts

Preda Mihailescu 1 François Morain 2, 3 Eric Schost 4
1 Mathematisches Institut
2 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
4 ORCCA and Computer Science Department
Abstract : The Schoof-Elkies-Atkin algorithm is the best known method for counting the number of points of an elliptic curve defined over a finite field of large characteristic. We use abelian properties of division polynomials to design a fast theoretical and practical algorithm for computing the eigenvalue search.
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https://hal.inria.fr/inria-00130142
Contributor : François Morain <>
Submitted on : Friday, February 9, 2007 - 2:27:51 PM
Last modification on : Monday, December 14, 2020 - 3:46:13 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 2:44:07 AM

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Preda Mihailescu, François Morain, Eric Schost. Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. 2007. ⟨inria-00130142⟩

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