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AbstractLetE1andE2be ordinary elliptic curves over a finite fieldFpsuch that #E1(Fp) = #E2(Fp). Tate's isogeny theorem states that there is an isogeny fromE1toE2which is defined overFp. The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny.The algorithm proposed in this paper has exponential complexity in the worst case. Nevertheless, it is efficient in certain situations (that is, when the class number of the endomorphism ring is small). Thedoi:10.1112/s1461157000000097 fatcat:oz7viwelubhqtlta7cijadeniu