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2001 Finding the Eigenvalue in Elkies' Algorithm
Markus Maurer, Volker Müller
Experiment. Math. 10(2): 275-286 (2001).

Abstract

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 form 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.

Citation

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Markus Maurer. Volker Müller. "Finding the Eigenvalue in Elkies' Algorithm." Experiment. Math. 10 (2) 275 - 286, 2001.

Information

Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 1065.11044
MathSciNet: MR1837676

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 2 • 2001
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