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Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm

Pierrick Gaudry 1, 2, 3 François Morain 1, 3
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : The Schoof-Elkies-Atkin algorithm is the only known method for counting the number of points of an elliptic curve defined over a finite field of large characteristic. Several practical and asymptotical improvements for the phase called eigenvalue computation are proposed.
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Submitted on : Friday, January 13, 2006 - 9:41:10 AM
Last modification on : Thursday, March 5, 2020 - 6:26:01 PM
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Pierrick Gaudry, François Morain. Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm. ISSAC '06: Proceedings of the 2006 international symposium on symbolic and algebraic computation, Jul 2006, Genoa, Italy, pp.109 - 115, ⟨10.1145/1145768.1145791⟩. ⟨inria-00001009⟩

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