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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. ..."
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Cited by 30 (3 self)
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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.
ECC: Do We Need to Count?
, 1999
"... A prohibitive barrier faced by elliptic curve users is the difficulty of computing the curves' cardinalities. Despite recent theoretical breakthroughs, point counting still remains very cumbersome and intensively time consuming. ..."
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Cited by 1 (0 self)
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A prohibitive barrier faced by elliptic curve users is the difficulty of computing the curves' cardinalities. Despite recent theoretical breakthroughs, point counting still remains very cumbersome and intensively time consuming.