Experimental Mathematics

Finding the Eigenvalue in Elkies' Algorithm

Markus Maurer and Volker Müller

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.

Article information

Source
Experiment. Math., Volume 10, Issue 2 (2001), 275-286.

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
https://projecteuclid.org/euclid.em/999188637

Mathematical Reviews number (MathSciNet)
MR1837676

Zentralblatt MATH identifier
1065.11044

Keywords
elliptic curve Elkies' algorithm point counting

Citation

Maurer, Markus; Müller, Volker. Finding the Eigenvalue in Elkies' Algorithm. Experiment. Math. 10 (2001), no. 2, 275--286. https://projecteuclid.org/euclid.em/999188637


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