Orienting supersingular isogeny graphs

Leonardo Colò; David Kohel

Paper 2020/985 Original: eprint.iacr.org/2020/985 ↗

Orienting supersingular isogeny graphs

Leonardo Colò

David Kohel

Abstract

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

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
History: 2020-08-18: last updated; 2020-08-18: published
Short URL: https://ia.cr/2020/985
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2020/985,
      author = {Leonardo Colò and David Kohel},
      title = {Orienting supersingular isogeny graphs},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/985},
      year = {2020},
      url = {https://eprint.iacr.org/2020/985}
}