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Constructing Isogenies Between Elliptic Curves Over Finite Fields
 LMS J. Comput. Math
, 1999
"... Let E 1 and E 2 be ordinary elliptic curves over a finite field Fp such that #E1 (Fp ) = #E2 (Fp ). Tate's isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp . The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny. ..."
Abstract

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Let E 1 and E 2 be ordinary elliptic curves over a finite field Fp such that #E1 (Fp ) = #E2 (Fp ). Tate's isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp . The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny.