Skip to content

A subexponential algorithm for evaluating large degree isogenies

13Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.
Get full text
This PDF is freely available from an open access repository. It may not have been peer-reviewed.

Abstract

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring, the previous best known algorithm has a worst case running time which is exponential in the length of the input. In this paper we show this problem can be solved in subexponential time under reasonable heuristics. Our approach is based on factoring the ideal corresponding to the kernel of the isogeny, modulo principal ideals, into a product of smaller prime ideals for which the isogenies can be computed directly. Combined with previous work of Bostan et al., our algorithm yields equations for large degree isogenies in quasi-optimal time given only the starting curve and the kernel. © 2010 Springer-Verlag Berlin Heidelberg.

Cite

CITATION STYLE

APA

Jao, D., & Soukharev, V. (2010). A subexponential algorithm for evaluating large degree isogenies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 219–233). https://doi.org/10.1007/978-3-642-14518-6_19

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