Finding the Eigenvalue in Elkies' Algorithm
Maurer, Markus ; Müller, Volker
Experiment. Math., Tome 10 (2001) no. 3, p. 275-286 / Harvested from Project Euclid
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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.
Publié le : 2001-05-14
Classification:  elliptic curve,  Elkies' algorithm,  point counting 
@article{999188637,
     author = {Maurer, Markus and M\"uller, Volker},
     title = {Finding the Eigenvalue in Elkies' Algorithm},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 275-286},
     language = {en},
     url = {http://dml.mathdoc.fr/item/999188637}
}

Maurer, Markus; Müller, Volker. Finding the Eigenvalue in Elkies' Algorithm. Experiment. Math., Tome 10 (2001) no. 3, pp.  275-286. http://gdmltest.u-ga.fr/item/999188637/