Explicit isogenies in quadratic time in any characteristic

Cyril Hugounenq
Cyril Hugounenq
Jérôme Plût
Jérôme Plût

Lms Journal of Computation and Mathematics, pp. 267-282, 2016.

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Abstract:

Consider two ordinary elliptic curves $E,Eu0027$ defined over a finite field $F_q$, and suppose that there exists an isogeny $psi$ between $E$ and $Eu0027$. We propose an algorithm that determines $psi$ from the knowledge of $E$, $Eu0027$ and of its degree $r$, by using the structure of the $l$-torsion of the curves (where $l$~is...More

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