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

P. Mihailescu; F. Morain; É Schost

doi:10.1145/1277548.1277587

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

P. Mihailescu
, F. Morain
, É Schost

Georg-August-Universität Göttingen
University of Western Ontario

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 nding the eigenvalue.

Original language	English
Title of host publication	ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation
Publisher	Association for Computing Machinery
Pages	285-292
Number of pages	8
ISBN (Print)	1595937439, 9781595937438
DOIs	https://doi.org/10.1145/1277548.1277587
Publication status	Published - 1 Jan 2007
Event	ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation - London, ON, Canada Duration: 29 Jul 2007 → 1 Aug 2007

Publication series

Name	Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference	ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation
Country/Territory	Canada
City	London, ON
Period	29/07/07 → 1/08/07

Keywords

Elliptic curves
Finite fields
SEA algorithm

Access to Document

10.1145/1277548.1277587

Cite this

Mihailescu, P., Morain, F., & Schost, É. (2007). Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. In ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation (pp. 285-292). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). Association for Computing Machinery. https://doi.org/10.1145/1277548.1277587

Mihailescu, P. ; Morain, F. ; Schost, É. / Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2007. pp. 285-292 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).

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title = "Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts",

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 nding the eigenvalue.",

keywords = "Elliptic curves, Finite fields, SEA algorithm",

author = "P. Mihailescu and F. Morain and {\'E} Schost",

year = "2007",

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doi = "10.1145/1277548.1277587",

language = "English",

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booktitle = "ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation",

note = "ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation ; Conference date: 29-07-2007 Through 01-08-2007",

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Mihailescu, P, Morain, F & Schost, É 2007, Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. in ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, Association for Computing Machinery, pp. 285-292, ISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation, London, ON, Canada, 29/07/07. https://doi.org/10.1145/1277548.1277587

Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. / Mihailescu, P.; Morain, F.; Schost, É.
ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2007. p. 285-292 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Mihailescu P, Morain F, Schost É. Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts. In ISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery. 2007. p. 285-292. (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). doi: 10.1145/1277548.1277587

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

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