Leonardo Colò, David Kohel
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.