Finding the Eigenvalue in Elkies' Algorithm

One essential part of Elkies' algorithm for computing the group order of an elliptic curve defined over a finite field is the determination of the eigenvalue of the Frobenius endomorphism. Here we compare from a practical point of view several strategies for this search: the use of rational fun...

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Bibliographic Details
Published inExperimental mathematics Vol. 10; no. 2; pp. 275 - 285
Main Authors Maurer, Markus, Müiler, Volker
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2001
A K Peters, Ltd
Subjects
Elkies' algorithm
elliptic curve
point counting
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ISSN1058-6458
1944-950X
1944-950X
DOI10.1080/10586458.2001.10504448

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Summary:One essential part of Elkies' algorithm for computing the group order of an elliptic curve defined over a finite field is the determination of the eigenvalue of the Frobenius endomorphism. Here we compare from a practical point of view several strategies for this search: the use of rational functions, the use of division polynomials, the babystep-giantstep method, and a new modification of this method that avoids the need for two fast exponentiations.
ISSN:1058-6458
1944-950X
1944-950X
DOI:10.1080/10586458.2001.10504448