On the Security of OSIDH

The Oriented Supersingular Isogeny Diffie–Hellman is a post-quantum key exchange scheme recently introduced by Colò and Kohel. It based on the group action of an ideal class quadratic imaginary order subset supersingular elliptic curves, in this sense it can be viewed as generalization popular isogeny CSIDH. From algorithmic standpoint, however, OSIDH quite different from In sense, uses groups which are more structured than CSIDH, creating potential weakness that was already recognized To circumvent weakness, they proposed ingenious way to realize exchanging partial information how acts neighborhood public conjectured additional would not impact security. work we revisit security presenting new attack, building upon previous Onuki. Our attack has exponential complexity, but practically breaks Kohel’s parameters unlike Onuki’s attack. We also discuss countermeasures our analyze their OSIDH, both efficiency functionality point view.