English

Orienting supersingular isogeny graphs

Number Theory 2020-12-22 v1

Abstract

We introduce a category of O\mathcal{O}-orientedsupersingularellipticcurves and derive properties of the associated oriented and nonoriented \ell-isogeny supersingular isogeny graphs. As an application we introduce an oriented super-singular isogeny Diffie-Hellman protocol (OSIDH), analogous to the supersingular isogeny Diffie-Hellman (SIDH) protocol and generalizing the commutative supersingular isogeny Diffie-Hellman (CSIDH) protocol.

Keywords

Cite

@article{arxiv.2012.10803,
  title  = {Orienting supersingular isogeny graphs},
  author = {Leonardo Colò and David Kohel},
  journal= {arXiv preprint arXiv:2012.10803},
  year   = {2020}
}
R2 v1 2026-06-23T21:06:11.163Z