Constructing Isogenies between Elliptic Curves Over Finite Fields

Steven D. Galbraith
1999 LMS Journal of Computation and Mathematics  
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). The
more » ... all). The significance of these results to elliptic curve cryptography is discussed.
doi:10.1112/s1461157000000097 fatcat:oz7viwelubhqtlta7cijadeniu