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arXiv · 2012.10803

Orienting supersingular isogeny graphs

Leonardo Colò·David Kohel
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Abstract

We introduce a category of $\mathcal{O}$-orientedsupersingularellipticcurves and derive properties of the associated oriented and nonoriented $\ell$-isogeny supersingular isogeny graphs. As an application we introduce an oriented super-singular isogeny Diffie-Hellman protocol (OSIDH), analogous to the supersingular isogeny Diffie-Hellman (SIDH) protocol and generalizing the commutative supersingular isogeny Diffie-Hellman (CSIDH) protocol.

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Leonardo Colò, David Kohel. 2020-12-19. Orienting supersingular isogeny graphs. https://doi.org/10.1515/jmc-2019-0034

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