This stuff is mindbending, but the paper itself is pretty impressive. Microsoft actually got this working:
We present a full-fledged, high-speed implementation of (unauthenticated)
ephemeral SIDH that currently provides 128 bits of quantum security and 192 bits of classical security.
This implementation uses 48-byte private keys to produce 751-byte ephemeral Diffie-Hellman
public keys, and is currently written almost entirely in C with only a limited set of functions
written in assembly. To our knowledge, our library presents the first SIDH software that
runs in constant-time, i.e., that is designed to resist timing and cache timing attacks.
We present a full-fledged, high-speed implementation of (unauthenticated) ephemeral SIDH that currently provides 128 bits of quantum security and 192 bits of classical security. This implementation uses 48-byte private keys to produce 751-byte ephemeral Diffie-Hellman public keys, and is currently written almost entirely in C with only a limited set of functions written in assembly. To our knowledge, our library presents the first SIDH software that runs in constant-time, i.e., that is designed to resist timing and cache timing attacks.