Computing isogenies between supersingular elliptic curves over F_p [article]

Christina Delfs, Steven D. Galbraith
2013 arXiv   pre-print
Let p>3 be a prime and let E, E' be supersingular elliptic curves over F_p. We want to construct an isogeny phi: E --> E'. The currently fastest algorithm for finding isogenies between supersingular elliptic curves solves this problem by performing a "meet-in-the-middle" breadth-first search in the full supersingular 2-isogeny graph over F_p^2. In this paper we consider the structure of the isogeny graph of supersingular elliptic curves over F_p. We give an algorithm to construct isogenies
more » ... en such supersingular elliptic curves that works faster than the usual algorithm. We then discuss how this results can be used to obtain an improved algorithm for the general supersingular isogeny problem.
arXiv:1310.7789v1 fatcat:pvbpmuwzrvgoncxbqfzaje72nm