Year: 2013
Type: preprint
Abstract: 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 between 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.
Source: arXiv (Cornell University)
Authors: Delfs, Christina, Galbraith, Steven D.
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953201355