I was considering using Microsoft's SIDH implementation for post-quantum public-key encryption because of its relatively small key size. I realized however, thanks to Issue #4, that it might not be as ideal as I had hoped:
SIKE is IND-CCA2 secure, which means that it's ok to reuse the key pair generated [...] whereas SIDH is insecure with re-used keys [...]
So here we go:
Is SIDH actually insecure when keys are reused?
Is SIKE actually secure even when keys are reused?
If so, why? How can SIDH actually be broken? Can you demonstrate an attack?
What prevents an attacker from encrypting many messages with a SIDH public key and breaking it that way?
What's the difference between the two that makes it so one can securely use reused keypairs and one can't?