Orienting supersingular isogeny graphs

Leonardo Colò (1) , David Kohel (1)

1 I2M - Institut de Mathématiques de Marseille

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

Domaines: Théorie des nombres [math.NT]; Théorie de l'information et codage [math.IT]

Leonardo Colò, David Kohel. Orienting supersingular isogeny graphs. Journal of Mathematical Cryptology, 2020, 14 (1), pp.414-437. ⟨10.1515/jmc-2019-0034⟩. ⟨hal-03089563⟩