Open AccessMathematicsComputer Science

Leonardo Colò, David Kohel

2020.1.1Journal of Mathematical Cryptology

DOI: 10.1515/jmc-2019-0034

tlooto Summary

A category of 𝓞-oriented supersingular elliptic curves is introduced and properties of the associated oriented and nonoriented ℓ-isogeny supersingULAR isogeny graphs are derived.

Abstract

Abstract We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-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.

Citation format

COLÒ, Leonardo; KOHEL, David. Orienting supersingular isogeny graphs [preprint]. arXiv, 2020. arXiv:2012.10803.