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Original Articles

Finding the Eigenvalue in Elkies' Algorithm

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Pages 275-285 | Published online: 04 Apr 2012
 

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 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.

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