Skip to content

Pairing the volcano

N/ACitations
Citations of this article
3Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Isogeny volcanoes are graphs whose vertices are elliptic curves and whose edges are l-isogenies. Algorithms allowing to travel on these graphs were developed by Kohel in his thesis (1996) and later on, by Fouquet and Morain (2001). However, up to now, no method was known, to predict, before taking a step on the volcano, the direction of this step. Hence, in Kohel's and Fouquet-Morain algorithms, we take many steps before choosing the right direction. In particular, ascending or horizontal isogenies are usually found using a trial-and-error approach. In this paper, we propose an alternative method that efficiently finds all points P of order l such that the subgroup generated by P is the kernel of an horizontal or an ascending isogeny. In many cases, our method is faster than previous methods. © 2010 Springer-Verlag Berlin Heidelberg.

Cite

CITATION STYLE

APA

Ionica, S., & Joux, A. (2010). Pairing the volcano. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 201–218). https://doi.org/10.1007/978-3-642-14518-6_18

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free