Orienting supersingular isogeny graphs

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.

Keywords

• supersingular elliptic curves
• isogeny graphs
• 11g05
• 11g07
• 11g15
• 11t71
• 14h10
• 14h52
• 14k02
• 14k22