Cryptology ePrint Archive: Report 2020/985

Orienting supersingular isogeny graphs

Leonardo ColÚ and 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.

Category / Keywords: cryptographic protocols / Supersingular isogeny graphs, isogeny-based cryptography

Date: received 15 Aug 2020

Contact author: Leonardo Colo at univ-amu fr, David Kohel@univ-amu fr

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Version: 20200818:083715 (All versions of this report)

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