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.

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.