We revisit theoretical background on OSIDH (Oriented Supersingular Isogeny Diffie-Hellman protocol), which is an isogeny-based key-exchange protocol proposed by Colò and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Colò and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters for the protocol to work, and estimate the size of the parameters for a certain security level.

中文翻译：

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定向超奇异椭圆曲线

我们回顾了OSIDH（定向的超奇异基因异构Diffie-Hellman协议）的理论背景，这是Colò和Kohel在NutMiC 2019上提出的基于异构的密钥交换协议。我们给出了OSIDH基本定理的证明。该定理由Colò和Kohel提出，没有证明。此外，我们考虑了OSIDH的参数，在参数上给出了足以使协议起作用的条件，并为特定的安全级别估计了参数的大小。