On oriented supersingular elliptic curves

We revisit theoretical background on OSIDH, that is an isogeny-based key-exchange protocol proposed by Colo and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Colo and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters that the protocol works, and estimate the size of the parameters for a certain security level.

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